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multicomponent Smoluchowski equation</title> <meta name="description" content="Search results for: multicomponent Smoluchowski equation"> <meta name="keywords" content="multicomponent Smoluchowski equation"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science 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method="get" action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="multicomponent Smoluchowski equation"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 2029</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: multicomponent Smoluchowski equation</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2029</span> Fast and Accurate Finite-Difference Method Solving Multicomponent Smoluchowski Coagulation Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alexander%20P.%20Smirnov">Alexander P. Smirnov</a>, <a href="https://publications.waset.org/abstracts/search?q=Sergey%20A.%20Matveev"> Sergey A. Matveev</a>, <a href="https://publications.waset.org/abstracts/search?q=Dmitry%20A.%20Zheltkov"> Dmitry A. Zheltkov</a>, <a href="https://publications.waset.org/abstracts/search?q=Eugene%20E.%20Tyrtyshnikov"> Eugene E. Tyrtyshnikov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We propose a new computational technique for multidimensional (multicomponent) Smoluchowski coagulation equation. Using low-rank approximations in Tensor Train format of both the solution and the coagulation kernel, we accelerate the classical finite-difference Runge-Kutta scheme keeping its level of accuracy. The complexity of the taken finite-difference scheme is reduced from O(N^2d) to O(d^2 N log N ), where N is the number of grid nodes and d is a dimensionality of the problem. The efficiency and the accuracy of the new method are demonstrated on concrete problem with known analytical solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=tensor%20train%20decomposition" title="tensor train decomposition">tensor train decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=multicomponent%20Smoluchowski%20equation" title=" multicomponent Smoluchowski equation"> multicomponent Smoluchowski equation</a>, <a href="https://publications.waset.org/abstracts/search?q=runge-kutta%20scheme" title=" runge-kutta scheme"> runge-kutta scheme</a>, <a href="https://publications.waset.org/abstracts/search?q=convolution" title=" convolution"> convolution</a> </p> <a href="https://publications.waset.org/abstracts/40417/fast-and-accurate-finite-difference-method-solving-multicomponent-smoluchowski-coagulation-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40417.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">432</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2028</span> A Geometrical Method for the Smoluchowski Equation on the Sphere</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Adriano%20Valdes-Gomez">Adriano Valdes-Gomez</a>, <a href="https://publications.waset.org/abstracts/search?q=Francisco%20Javier%20Sevilla"> Francisco Javier Sevilla</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We devise a numerical algorithm to simulate the diffusion of a Brownian particle restricted to the surface of a three-dimensional sphere when the particle is under the effects of an external potential that is coupled linearly. It is obtained using elementary geometry, yet, it converges, in the weak sense, to the solutions to the Smoluchowski equation. Rotations on the sphere, which are the analogs of linear displacements in euclidean spaces, are calculated using algebraic operations and then by a proper scaling, which makes the algorithm efficient and quite simple, especially to what may be the short-time propagator approach. Our findings prove that the global effects of curvature are taken into account in both dynamic and stationary processes, and it is not restricted to work in configuration space, neither restricted to the overdamped limit. We have generalized it successfully to simulate the Kramers or the Ornstein-Uhlenbeck process, where it is necessary to work directly in phase space, and it may be adapted to other two dimensional surfaces with non-constant curvature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=diffusion%20on%20the%20sphere" title="diffusion on the sphere">diffusion on the sphere</a>, <a href="https://publications.waset.org/abstracts/search?q=Fokker-Planck%20equation%20on%20the%20sphere" title=" Fokker-Planck equation on the sphere"> Fokker-Planck equation on the sphere</a>, <a href="https://publications.waset.org/abstracts/search?q=non%20equilibrium%20processes%20on%20the%20sphere" title=" non equilibrium processes on the sphere"> non equilibrium processes on the sphere</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20methods%20for%20diffusion%20on%20the%20sphere" title=" numerical methods for diffusion on the sphere"> numerical methods for diffusion on the sphere</a> </p> <a href="https://publications.waset.org/abstracts/126691/a-geometrical-method-for-the-smoluchowski-equation-on-the-sphere" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/126691.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">182</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2027</span> Modeling Aggregation of Insoluble Phase in Reactors</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Brener">A. Brener</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Ismailov"> B. Ismailov</a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20Berdalieva"> G. Berdalieva</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the paper we submit the modification of kinetic Smoluchowski equation for binary aggregation applying to systems with chemical reactions of first and second orders in which the main product is insoluble. The goal of this work is to create theoretical foundation and engineering procedures for calculating the chemical apparatuses in the conditions of joint course of chemical reactions and processes of aggregation of insoluble dispersed phases which are formed in working zones of the reactor. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=binary%20aggregation" title="binary aggregation">binary aggregation</a>, <a href="https://publications.waset.org/abstracts/search?q=clusters" title=" clusters"> clusters</a>, <a href="https://publications.waset.org/abstracts/search?q=chemical%20reactions" title=" chemical reactions"> chemical reactions</a>, <a href="https://publications.waset.org/abstracts/search?q=insoluble%20phases" title=" insoluble phases"> insoluble phases</a> </p> <a href="https://publications.waset.org/abstracts/4173/modeling-aggregation-of-insoluble-phase-in-reactors" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4173.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">307</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2026</span> On the Mathematical Modelling of Aggregative Stability of Disperse Systems </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arnold%20M.%20Brener">Arnold M. Brener</a>, <a href="https://publications.waset.org/abstracts/search?q=Lesbek%20Tashimov"> Lesbek Tashimov</a>, <a href="https://publications.waset.org/abstracts/search?q=Ablakim%20S.%20Muratov"> Ablakim S. Muratov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper deals with the special model for coagulation kernels which represents new control parameters in the Smoluchowski equation for binary aggregation. On the base of the model the new approach to evaluating aggregative stability of disperse systems has been submitted. With the help of this approach the simple estimates for aggregative stability of various types of hydrophilic nano-suspensions have been obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=aggregative%20stability" title="aggregative stability">aggregative stability</a>, <a href="https://publications.waset.org/abstracts/search?q=coagulation%20kernels" title=" coagulation kernels"> coagulation kernels</a>, <a href="https://publications.waset.org/abstracts/search?q=disperse%20systems" title=" disperse systems"> disperse systems</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematical%20model" title=" mathematical model"> mathematical model</a> </p> <a href="https://publications.waset.org/abstracts/10336/on-the-mathematical-modelling-of-aggregative-stability-of-disperse-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10336.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">309</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2025</span> Modeling of Electrokinetic Mixing in Lab on Chip Microfluidic Devices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Virendra%20J.%20Majarikar">Virendra J. Majarikar</a>, <a href="https://publications.waset.org/abstracts/search?q=Harikrishnan%20N.%20Unni"> Harikrishnan N. Unni</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper sets to demonstrate a modeling of electrokinetic mixing employing electroosmotic stationary and time-dependent microchannel using alternate zeta patches on the lower surface of the micromixer in a lab on chip microfluidic device. Electroosmotic flow is amplified using different 2D and 3D model designs with alternate and geometric zeta potential values such as 25, 50, and 100 mV, respectively, to achieve high concentration mixing in the electrokinetically-driven microfluidic system. The enhancement of electrokinetic mixing is studied using Finite Element Modeling, and simulation workflow is accomplished with defined integral steps. It can be observed that the presence of alternate zeta patches can help inducing microvortex flows inside the channel, which in turn can improve mixing efficiency. Fluid flow and concentration fields are simulated by solving Navier-Stokes equation (implying Helmholtz-Smoluchowski slip velocity boundary condition) and Convection-Diffusion equation. The effect of the magnitude of zeta potential, the number of alternate zeta patches, etc. are analysed thoroughly. 2D simulation reveals that there is a cumulative increase in concentration mixing, whereas 3D simulation differs slightly with low zeta potential as that of the 2D model within the T-shaped micromixer for concentration 1 mol/m<sup>3</sup> and 0 mol/m<sup>3</sup>, respectively. Moreover, 2D model results were compared with those of 3D to indicate the importance of the 3D model in a microfluidic design process. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=COMSOL%20Multiphysics%C2%AE" title="COMSOL Multiphysics®">COMSOL Multiphysics®</a>, <a href="https://publications.waset.org/abstracts/search?q=electrokinetic" title=" electrokinetic"> electrokinetic</a>, <a href="https://publications.waset.org/abstracts/search?q=electroosmotic" title=" electroosmotic"> electroosmotic</a>, <a href="https://publications.waset.org/abstracts/search?q=microfluidics" title=" microfluidics"> microfluidics</a>, <a href="https://publications.waset.org/abstracts/search?q=zeta%20potential" title=" zeta potential"> zeta potential</a> </p> <a href="https://publications.waset.org/abstracts/65595/modeling-of-electrokinetic-mixing-in-lab-on-chip-microfluidic-devices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/65595.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">242</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2024</span> Measurements and Predictions of Hydrates of CO₂-rich Gas Mixture in Equilibrium with Multicomponent Salt Solutions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdullahi%20Jibril">Abdullahi Jibril</a>, <a href="https://publications.waset.org/abstracts/search?q=Rod%20Burgass"> Rod Burgass</a>, <a href="https://publications.waset.org/abstracts/search?q=Antonin%20Chapoy"> Antonin Chapoy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Carbon dioxide (CO₂) is widely used in reservoirs to enhance oil and gas production, mixing with natural gas and other impurities in the process. However, hydrate formation frequently hinders the efficiency of CO₂-based enhanced oil recovery, causing pipeline blockages and pressure build-ups. Current hydrate prediction methods are primarily designed for gas mixtures with low CO₂ content and struggle to accurately predict hydrate formation in CO₂-rich streams in equilibrium with salt solutions. Given that oil and gas reservoirs are saline, experimental data for CO₂-rich streams in equilibrium with salt solutions are essential to improve these predictive models. This study investigates the inhibition of hydrate formation in a CO₂-rich gas mixture (CO₂, CH₄, N₂, H₂ at 84.73/15/0.19/0.08 mol.%) using multicomponent salt solutions at concentrations of 2.4 wt.%, 13.65 wt.%, and 27.3 wt.%. The setup, test fluids, methodology, and results for hydrates formed in equilibrium with varying salt solution concentrations are presented. Measurements were conducted using an isochoric pressure-search method at pressures up to 45 MPa. Experimental data were compared with predictions from a thermodynamic model based on the Cubic-Plus-Association equation of state (EoS), while hydrate-forming conditions were modeled using the van der Waals and Platteeuw solid solution theory. Water activity was evaluated based on hydrate suppression temperature to assess consistency in the inhibited systems. Results indicate that hydrate stability is significantly influenced by inhibitor concentration, offering valuable guidelines for the design and operation of pipeline systems involved in offshore gas transport of CO₂-rich streams. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CO%E2%82%82-rich%20streams" title="CO₂-rich streams">CO₂-rich streams</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrates" title=" hydrates"> hydrates</a>, <a href="https://publications.waset.org/abstracts/search?q=monoethylene%20glycol" title=" monoethylene glycol"> monoethylene glycol</a>, <a href="https://publications.waset.org/abstracts/search?q=phase%20equilibria" title=" phase equilibria"> phase equilibria</a> </p> <a href="https://publications.waset.org/abstracts/193488/measurements-and-predictions-of-hydrates-of-co2-rich-gas-mixture-in-equilibrium-with-multicomponent-salt-solutions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/193488.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">17</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2023</span> Fokas-Lenells Equation Conserved Quantities and Landau-Lifshitz System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Riki%20Dutta">Riki Dutta</a>, <a href="https://publications.waset.org/abstracts/search?q=Sagardeep%20Talukdar"> Sagardeep Talukdar</a>, <a href="https://publications.waset.org/abstracts/search?q=Gautam%20Kumar%20Saharia"> Gautam Kumar Saharia</a>, <a href="https://publications.waset.org/abstracts/search?q=Sudipta%20Nandy"> Sudipta Nandy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fokas-Lenells equation (FLE) is one of the integrable nonlinear equations use to describe the propagation of ultrashort optical pulses in an optical medium. A 2x2 Lax pair has been introduced for the FLE and from that solving the Riccati equation yields infinitely many conserved quantities. Thereafter for a new field function (S) of the Landau-Lifshitz (LL) system, a gauge equivalence of the FLE with the generalised LL equation has been derived. We hope our findings are useful for the application purpose of FLE in optics and other branches of physics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conserved%20quantities" title="conserved quantities">conserved quantities</a>, <a href="https://publications.waset.org/abstracts/search?q=fokas-lenells%20equation" title=" fokas-lenells equation"> fokas-lenells equation</a>, <a href="https://publications.waset.org/abstracts/search?q=landau-lifshitz%20equation" title=" landau-lifshitz equation"> landau-lifshitz equation</a>, <a href="https://publications.waset.org/abstracts/search?q=lax%20pair" title=" lax pair"> lax pair</a> </p> <a href="https://publications.waset.org/abstracts/165239/fokas-lenells-equation-conserved-quantities-and-landau-lifshitz-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165239.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">110</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2022</span> Asymptotic Expansion of the Korteweg-de Vries-Burgers Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jian-Jun%20Shu">Jian-Jun Shu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20expansion" title="asymptotic expansion">asymptotic expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equation" title=" differential equation"> differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Korteweg-de%20Vries-Burgers%20%28KdVB%29%20equation" title=" Korteweg-de Vries-Burgers (KdVB) equation"> Korteweg-de Vries-Burgers (KdVB) equation</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton" title=" soliton"> soliton</a> </p> <a href="https://publications.waset.org/abstracts/78883/asymptotic-expansion-of-the-korteweg-de-vries-burgers-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/78883.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">249</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2021</span> Mechanical and Tribological Performances of (Nb: H-D: a-C) Thin Films for Biomedical Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sara%20Khamseh">Sara Khamseh</a>, <a href="https://publications.waset.org/abstracts/search?q=Kambiz%20Javanruee"> Kambiz Javanruee</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamid%20Khorsand"> Hamid Khorsand</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Plenty of metallic materials are used for biomedical applications like hip joints and screws. Besides, it is reported that metal platforms such as stainless steel show significant deterioration because of wear and friction. The surface of metal substrates has been coated with a variety of multicomponent coatings to prevail these problems. The carbon-based multicomponent coatings such as metal-added amorphous carbon and diamond coatings are crucially important because of their remarkable tribological performance and chemical stability. In the current study, H-D contained Nb: (a-C) multicomponent coatings (H-D: hexagonal diamond, a-C: amorphous carbon) coated on A 304 steel substrates using an unbalanced magnetron (UBM) sputtering system. The effects of Nb and H-D content and ID/IG ratio on microstructure, mechanical and tribological characteristics of (Nb: H-D: a-C) composite coatings were investigated. The results of Raman spectroscopy represented that a-C phase with a Graphite-like structure (GLC with high value of sp2 carbon bonding) is formed, and its domain size increased with increasing Nb content of the coatings. Moreover, the Nb played a catalyst for the formation of the H-D phase. The nanoindentation hardness value of the coatings ranged between ~17 to ~35 GPa and (Nb: H-D: a-C) composite coatings with more H-D content represented higher hardness and plasticity index. It seems that the existence of extra-hard H-D particles straightly increased hardness. The tribological performance of the coatings was evaluated using the pin-on-disc method under the wet environment of SBF (Simulated Body Fluid). The COF value of the (Nb: H-D: a-C) coatings decreased with an increasing ID/IG ratio. The lower coefficient of friction is a result of the lamelliform array of graphitic domains. Also, the wear rate of the coatings decreased with increasing H-D content of the coatings. Based on the literature, a-C coatings with high hardness and H3/E2 ratio represent lower wear rates and better tribological performance. According to the nanoindentation analysis, hardness and H3/E2 ratio of (Nb: H-D: a-C) multicomponent coatings increased with increasing H-D content, which in turn decreased the wear rate of the coatings. The mechanical and tribological potency of (Nb: H-D: a-C) composite coatings on A 304 steel substrates paved the way for the development of innovative advanced coatings to ameliorate the performance of A 304 steel for biomedical applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=COF" title="COF">COF</a>, <a href="https://publications.waset.org/abstracts/search?q=mechanical%20properties" title=" mechanical properties"> mechanical properties</a>, <a href="https://publications.waset.org/abstracts/search?q=%28Nb%3A%20H-D%3A%20a-C%29%20coatings" title=" (Nb: H-D: a-C) coatings"> (Nb: H-D: a-C) coatings</a>, <a href="https://publications.waset.org/abstracts/search?q=wear%20rate" title=" wear rate"> wear rate</a> </p> <a href="https://publications.waset.org/abstracts/163287/mechanical-and-tribological-performances-of-nb-h-d-a-c-thin-films-for-biomedical-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/163287.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">103</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2020</span> The Preparation of 2H-Indazolo [2, 1-b] Phthalazinetriones by One-Pot 4,4ʹ-Bipyridinium Dichloride Ordered Mesoporous Silica</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aigin%20Bashti">Aigin Bashti</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Preparation of multicomponent reactions (MCRs) via a simple one-pot strategy is considered a novel procedure which has attracted a lot of interest from organic and medicinal chemists. Due to the great importance of phthalazide triones, it was decided to introduce a novel and cost-effective green procedure for the preparation of these derivatives. In this methodology, an efficient 4,4ʹ-Bipyridinium Dichloride Ordered Mesoporous Silica functionalized catalyst (BP-SBA-15) was utilized. The catalyst was characterized by X-ray diffraction analysis (XRD), field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), thermo-gravimetric analysis (TGA), and Fourier-transform infrared spectroscopy (FT-IR) analysis. In conclusion, it should be mentioned that this methodology has some advantages, including short reaction time, high yield of the products, recyclable catalyst, green procedure, and facile work-up procedure. The catalyst was successfully utilized for the one-pot preparation of various phthalazinetrione derivatives. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dimedone" title="dimedone">dimedone</a>, <a href="https://publications.waset.org/abstracts/search?q=green%20procedure" title=" green procedure"> green procedure</a>, <a href="https://publications.waset.org/abstracts/search?q=multicomponent%20reactions" title=" multicomponent reactions"> multicomponent reactions</a>, <a href="https://publications.waset.org/abstracts/search?q=phthalhydrazide" title=" phthalhydrazide"> phthalhydrazide</a> </p> <a href="https://publications.waset.org/abstracts/154586/the-preparation-of-2h-indazolo-2-1-b-phthalazinetriones-by-one-pot-44-bipyridinium-dichloride-ordered-mesoporous-silica" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/154586.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">99</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2019</span> An Analytical Method for Solving General Riccati Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20Pala">Y. Pala</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20O.%20Ertas"> M. O. Ertas</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Riccati%20equation" title="Riccati equation">Riccati equation</a>, <a href="https://publications.waset.org/abstracts/search?q=analytical%20solution" title=" analytical solution"> analytical solution</a>, <a href="https://publications.waset.org/abstracts/search?q=proper%20solution" title=" proper solution"> proper solution</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear" title=" nonlinear"> nonlinear</a> </p> <a href="https://publications.waset.org/abstracts/64988/an-analytical-method-for-solving-general-riccati-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/64988.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">354</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2018</span> Operator Splitting Scheme for the Inverse Nagumo Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sharon-Yasotha%20Veerayah-Mcgregor">Sharon-Yasotha Veerayah-Mcgregor</a>, <a href="https://publications.waset.org/abstracts/search?q=Valipuram%20Manoranjan"> Valipuram Manoranjan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=inverse%2Fbackward%20equation" title="inverse/backward equation">inverse/backward equation</a>, <a href="https://publications.waset.org/abstracts/search?q=operator-splitting" title=" operator-splitting"> operator-splitting</a>, <a href="https://publications.waset.org/abstracts/search?q=Nagumo%20equation" title=" Nagumo equation"> Nagumo equation</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-posed" title=" ill-posed"> ill-posed</a>, <a href="https://publications.waset.org/abstracts/search?q=finite-difference" title=" finite-difference"> finite-difference</a> </p> <a href="https://publications.waset.org/abstracts/182287/operator-splitting-scheme-for-the-inverse-nagumo-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/182287.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">98</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2017</span> Closed Form Exact Solution for Second Order Linear Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Saeed%20Otarod">Saeed Otarod</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=explicit" title="explicit">explicit</a>, <a href="https://publications.waset.org/abstracts/search?q=linear" title=" linear"> linear</a>, <a href="https://publications.waset.org/abstracts/search?q=differential" title=" differential"> differential</a>, <a href="https://publications.waset.org/abstracts/search?q=closed%20form" title=" closed form"> closed form</a> </p> <a href="https://publications.waset.org/abstracts/185365/closed-form-exact-solution-for-second-order-linear-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/185365.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">63</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2016</span> Image Transform Based on Integral Equation-Wavelet Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuan%20Yan%20Tang">Yuan Yan Tang</a>, <a href="https://publications.waset.org/abstracts/search?q=Lina%20Yang"> Lina Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Hong%20Li"> Hong Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonic%20model" title="harmonic model">harmonic model</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation%20%28PDE%29" title=" partial differential equation (PDE)"> partial differential equation (PDE)</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20equation" title=" integral equation"> integral equation</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20representation" title=" integral representation"> integral representation</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20measure%20formula" title=" boundary measure formula"> boundary measure formula</a>, <a href="https://publications.waset.org/abstracts/search?q=wavelet%20collocation" title=" wavelet collocation"> wavelet collocation</a> </p> <a href="https://publications.waset.org/abstracts/3920/image-transform-based-on-integral-equation-wavelet-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3920.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">558</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2015</span> Second Order Solitary Solutions to the Hodgkin-Huxley Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tadas%20Telksnys">Tadas Telksnys</a>, <a href="https://publications.waset.org/abstracts/search?q=Zenonas%20Navickas"> Zenonas Navickas</a>, <a href="https://publications.waset.org/abstracts/search?q=Minvydas%20Ragulskis"> Minvydas Ragulskis</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hodgkin-Huxley%20equation" title="Hodgkin-Huxley equation">Hodgkin-Huxley equation</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary%20solution" title=" solitary solution"> solitary solution</a>, <a href="https://publications.waset.org/abstracts/search?q=existence%20condition" title=" existence condition"> existence condition</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20method" title=" operator method"> operator method</a> </p> <a href="https://publications.waset.org/abstracts/37370/second-order-solitary-solutions-to-the-hodgkin-huxley-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37370.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">381</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2014</span> Study of Cahn-Hilliard Equation to Simulate Phase Separation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nara%20Guimar%C3%A3es">Nara Guimarães</a>, <a href="https://publications.waset.org/abstracts/search?q=Marcelo%20Aquino%20Martorano"> Marcelo Aquino Martorano</a>, <a href="https://publications.waset.org/abstracts/search?q=Douglas%20Gouv%C3%AAa"> Douglas Gouvêa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Cahn-Hilliard%20equation" title="Cahn-Hilliard equation">Cahn-Hilliard equation</a>, <a href="https://publications.waset.org/abstracts/search?q=miscibility%20gap" title=" miscibility gap"> miscibility gap</a>, <a href="https://publications.waset.org/abstracts/search?q=phase%20separation" title=" phase separation"> phase separation</a>, <a href="https://publications.waset.org/abstracts/search?q=dimensional%20domains" title=" dimensional domains"> dimensional domains</a> </p> <a href="https://publications.waset.org/abstracts/17579/study-of-cahn-hilliard-equation-to-simulate-phase-separation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17579.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">517</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2013</span> Study and Solving Partial Differential Equation of Danel Equation in the Vibration Shells </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hesamoddin%20Abdollahpour">Hesamoddin Abdollahpour</a>, <a href="https://publications.waset.org/abstracts/search?q=Roghayeh%20Abdollahpour"> Roghayeh Abdollahpour</a>, <a href="https://publications.waset.org/abstracts/search?q=Elham%20Rahgozar"> Elham Rahgozar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=large%20amplitude" title="large amplitude">large amplitude</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20vibrations" title=" free vibrations"> free vibrations</a>, <a href="https://publications.waset.org/abstracts/search?q=analytical%20solution" title=" analytical solution"> analytical solution</a>, <a href="https://publications.waset.org/abstracts/search?q=Danell%20Equation" title=" Danell Equation"> Danell Equation</a>, <a href="https://publications.waset.org/abstracts/search?q=diagram%20of%20phase%20plane" title=" diagram of phase plane "> diagram of phase plane </a> </p> <a href="https://publications.waset.org/abstracts/66849/study-and-solving-partial-differential-equation-of-danel-equation-in-the-vibration-shells" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/66849.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">320</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2012</span> Modification of Rk Equation of State for Liquid and Vapor of Ammonia by Genetic Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Mousavian">S. Mousavian</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Mousavian"> F. Mousavian</a>, <a href="https://publications.waset.org/abstracts/search?q=V.%20Nikkhah%20Rashidabad"> V. Nikkhah Rashidabad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Cubic equations of state like Redlich–Kwong (RK) EOS have been proved to be very reliable tools in the prediction of phase behavior. Despite their good performance in compositional calculations, they usually suffer from weaknesses in the predictions of saturated liquid density. In this research, RK equation was modified. The result of this study shows that modified equation has good agreement with experimental data. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=equation%20of%20state" title="equation of state">equation of state</a>, <a href="https://publications.waset.org/abstracts/search?q=modification" title=" modification"> modification</a>, <a href="https://publications.waset.org/abstracts/search?q=ammonia" title=" ammonia"> ammonia</a>, <a href="https://publications.waset.org/abstracts/search?q=genetic%20algorithm" title=" genetic algorithm"> genetic algorithm</a> </p> <a href="https://publications.waset.org/abstracts/2790/modification-of-rk-equation-of-state-for-liquid-and-vapor-of-ammonia-by-genetic-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2790.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">382</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2011</span> Preparation of Superparamagnetic Functionalized Magnetite Nanoparticles for Magnetically Separable Catalysis </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Priya%20Arora">Priya Arora</a>, <a href="https://publications.waset.org/abstracts/search?q=Jaspreet%20K.%20Rajput"> Jaspreet K. Rajput</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Superparamagnetism has accelerated the research and use of more economical and ecological magnetically separable catalysts due to their more efficient isolation by response to an applied magnetic field. Magnetite nanomaterials coated by SiO2 shell have received a great deal of focus in the last decades as it provides high stability and also easy further surface functionalization depending upon the application. In this protocol, Fe3O4 magnetic nanoparticles have been synthesized by co-precipitation combined with sonication method. Further, Fe3O4 superparamagnetic nanoparticles have been functionalized by various moieties to serve as efficient catalysts for multicomponent reactions. The functionalized nanoparticles were characterized by techniques like Fourier transform infrared spectroscopy (FT-IR), transmission electron microscopy (TEM), scanning electron microscopy (SEM), vibrating sample magnetometer (VSM), thermogravimetric analysis (TGA), Brunauer-Emmett-Teller (BET) surface area analysis. The as prepared nanocatalysts can be reused for several times without any significant loss in its activity. The utilization of magnetic nanoparticles as catalysts for this reaction is one approach i.e. green, inexpensive, facile and widely applicable. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=functionalized" title="functionalized">functionalized</a>, <a href="https://publications.waset.org/abstracts/search?q=magnetite" title=" magnetite"> magnetite</a>, <a href="https://publications.waset.org/abstracts/search?q=multicomponent%20reactions" title=" multicomponent reactions"> multicomponent reactions</a>, <a href="https://publications.waset.org/abstracts/search?q=superparamagnetic" title=" superparamagnetic"> superparamagnetic</a> </p> <a href="https://publications.waset.org/abstracts/55353/preparation-of-superparamagnetic-functionalized-magnetite-nanoparticles-for-magnetically-separable-catalysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55353.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">340</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2010</span> Exact Solutions of a Nonlinear Schrodinger Equation with Kerr Law Nonlinearity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muna%20Alghabshi">Muna Alghabshi</a>, <a href="https://publications.waset.org/abstracts/search?q=Edmana%20Krishnan"> Edmana Krishnan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jacobi%20elliptic%20function" title="Jacobi elliptic function">Jacobi elliptic function</a>, <a href="https://publications.waset.org/abstracts/search?q=mapping%20methods" title=" mapping methods"> mapping methods</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Schrodinger%20Equation" title=" nonlinear Schrodinger Equation"> nonlinear Schrodinger Equation</a>, <a href="https://publications.waset.org/abstracts/search?q=tanh%20method" title=" tanh method"> tanh method</a> </p> <a href="https://publications.waset.org/abstracts/55053/exact-solutions-of-a-nonlinear-schrodinger-equation-with-kerr-law-nonlinearity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55053.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">315</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2009</span> Divergence Regularization Method for Solving Ill-Posed Cauchy Problem for the Helmholtz Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Benedict%20Barnes">Benedict Barnes</a>, <a href="https://publications.waset.org/abstracts/search?q=Anthony%20Y.%20Aidoo"> Anthony Y. Aidoo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=divergence%20regularization%20method" title="divergence regularization method">divergence regularization method</a>, <a href="https://publications.waset.org/abstracts/search?q=Helmholtz%20equation" title=" Helmholtz equation"> Helmholtz equation</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-posed%20inhomogeneous%20Cauchy%20boundary%20conditions" title=" ill-posed inhomogeneous Cauchy boundary conditions"> ill-posed inhomogeneous Cauchy boundary conditions</a> </p> <a href="https://publications.waset.org/abstracts/137727/divergence-regularization-method-for-solving-ill-posed-cauchy-problem-for-the-helmholtz-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/137727.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">189</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2008</span> Solution of the Nonrelativistic Radial Wave Equation of Hydrogen Atom Using the Green's Function Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=F.%20U.%20Rahman">F. U. Rahman</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Q.%20Zhang"> R. Q. Zhang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Green%E2%80%99s%20function" title="Green’s function">Green’s function</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrogen%20atom" title=" hydrogen atom"> hydrogen atom</a>, <a href="https://publications.waset.org/abstracts/search?q=Lippmann%20Schwinger%20equation" title=" Lippmann Schwinger equation"> Lippmann Schwinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=radial%20wave" title=" radial wave"> radial wave</a> </p> <a href="https://publications.waset.org/abstracts/42682/solution-of-the-nonrelativistic-radial-wave-equation-of-hydrogen-atom-using-the-greens-function-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42682.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">394</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2007</span> A Study of Non Linear Partial Differential Equation with Random Initial Condition</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ayaz%20Ahmad">Ayaz Ahmad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=drift%20term" title="drift term">drift term</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20time%20blow%20up" title=" finite time blow up"> finite time blow up</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20problem" title=" inverse problem"> inverse problem</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton%20solution" title=" soliton solution"> soliton solution</a> </p> <a href="https://publications.waset.org/abstracts/77445/a-study-of-non-linear-partial-differential-equation-with-random-initial-condition" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77445.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">215</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2006</span> The Physics of Turbulence Generation in a Fluid: Numerical Investigation Using a 1D Damped-MNLS Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Praveen%20Kumar">Praveen Kumar</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Uma"> R. Uma</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20P.%20Sharma"> R. P. Sharma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study investigates the generation of turbulence in a deep-fluid environment using a damped 1D-modified nonlinear Schrödinger equation model. The well-known damped modified nonlinear Schrödinger equation (d-MNLS) is solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation employs a finite difference method for temporal evolution and a pseudo-spectral approach to characterize spatial patterns. The results reveal a recurring periodic pattern in both space and time when the nonlinear Schrödinger equation is considered. Additionally, the study shows that the modified nonlinear Schrödinger equation disrupts the localization of structure and the recurrence of the Fermi-Pasta-Ulam (FPU) phenomenon. The energy spectrum exhibits a power-law behavior, closely following Kolmogorov's spectra steeper than k⁻⁵/³ in the inertial sub-range. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=water%20waves" title="water waves">water waves</a>, <a href="https://publications.waset.org/abstracts/search?q=modulation%20instability" title=" modulation instability"> modulation instability</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrodynamics" title=" hydrodynamics"> hydrodynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Schr%C3%B6dinger%27s%20equation" title=" nonlinear Schrödinger's equation"> nonlinear Schrödinger's equation</a> </p> <a href="https://publications.waset.org/abstracts/179074/the-physics-of-turbulence-generation-in-a-fluid-numerical-investigation-using-a-1d-damped-mnls-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/179074.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">73</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2005</span> Exact Soliton Solutions of the Integrable (2+1)-Dimensional Fokas-Lenells Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Meruyert%20Zhassybayeva">Meruyert Zhassybayeva</a>, <a href="https://publications.waset.org/abstracts/search?q=Kuralay%20Yesmukhanova"> Kuralay Yesmukhanova</a>, <a href="https://publications.waset.org/abstracts/search?q=Ratbay%20Myrzakulov"> Ratbay Myrzakulov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fokas-Lenells%20equation" title="Fokas-Lenells equation">Fokas-Lenells equation</a>, <a href="https://publications.waset.org/abstracts/search?q=integrability" title=" integrability"> integrability</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton" title=" soliton"> soliton</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20Hirota%20bilinear%20method" title=" the Hirota bilinear method"> the Hirota bilinear method</a> </p> <a href="https://publications.waset.org/abstracts/99044/exact-soliton-solutions-of-the-integrable-21-dimensional-fokas-lenells-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99044.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">224</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2004</span> Chern-Simons Equation in Financial Theory and Time-Series Analysis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ognjen%20Vukovic">Ognjen Vukovic</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Brownian%20motion" title="Brownian motion">Brownian motion</a>, <a href="https://publications.waset.org/abstracts/search?q=Chern-Simons%20theory" title=" Chern-Simons theory"> Chern-Simons theory</a>, <a href="https://publications.waset.org/abstracts/search?q=financial%20time%20series" title=" financial time series"> financial time series</a>, <a href="https://publications.waset.org/abstracts/search?q=econophysics" title=" econophysics"> econophysics</a> </p> <a href="https://publications.waset.org/abstracts/30127/chern-simons-equation-in-financial-theory-and-time-series-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30127.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">473</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2003</span> Fixed Point Iteration of a Damped and Unforced Duffing's Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Paschal%20A.%20Ochang">Paschal A. Ochang</a>, <a href="https://publications.waset.org/abstracts/search?q=Emmanuel%20C.%20Oji"> Emmanuel C. Oji</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=damping" title="damping">damping</a>, <a href="https://publications.waset.org/abstracts/search?q=Duffing%27s%20equation" title=" Duffing's equation"> Duffing's equation</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20point%20analysis" title=" fixed point analysis"> fixed point analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=second%20order%20differential" title=" second order differential"> second order differential</a>, <a href="https://publications.waset.org/abstracts/search?q=stability%20analysis" title=" stability analysis"> stability analysis</a> </p> <a href="https://publications.waset.org/abstracts/72553/fixed-point-iteration-of-a-damped-and-unforced-duffings-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/72553.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">292</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2002</span> Predicting and Obtaining New Solvates of Curcumin, Demethoxycurcumin and Bisdemethoxycurcumin Based on the Ccdc Statistical Tools and Hansen Solubility Parameters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=J.%20Ticona%20Chambi">J. Ticona Chambi</a>, <a href="https://publications.waset.org/abstracts/search?q=E.%20A.%20De%20Almeida"> E. A. De Almeida</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20A.%20Andrade%20Raymundo%20Gaiotto"> C. A. Andrade Raymundo Gaiotto</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20M.%20Do%20Esp%C3%ADrito%20Santo"> A. M. Do Espírito Santo</a>, <a href="https://publications.waset.org/abstracts/search?q=L.%20Infantes"> L. Infantes</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20L.%20Cuffini"> S. L. Cuffini</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The solubility of active pharmaceutical ingredients (APIs) is challenging for the pharmaceutical industry. The new multicomponent crystalline forms as cocrystal and solvates present an opportunity to improve the solubility of APIs. Commonly, the procedure to obtain multicomponent crystalline forms of a drug starts by screening the drug molecule with the different coformers/solvents. However, it is necessary to develop methods to obtain multicomponent forms in an efficient way and with the least possible environmental impact. The Hansen Solubility Parameters (HSPs) is considered a tool to obtain theoretical knowledge of the solubility of the target compound in the chosen solvent. H-Bond Propensity (HBP), Molecular Complementarity (MC), Coordination Values (CV) are tools used for statistical prediction of cocrystals developed by the Cambridge Crystallographic Data Center (CCDC). The HSPs and the CCDC tools are based on inter- and intra-molecular interactions. The curcumin (Cur), target molecule, is commonly used as an anti‐inflammatory. The demethoxycurcumin (Demcur) and bisdemethoxycurcumin (Bisdcur) are natural analogues of Cur from turmeric. Those target molecules have differences in their solubilities. In this way, the work aimed to analyze and compare different tools for multicomponent forms prediction (solvates) of Cur, Demcur and Biscur. The HSP values were calculated for Cur, Demcur, and Biscur using the chemical group contribution methods and the statistical optimization from experimental data. The HSPmol software was used. From the HSPs of the target molecules and fifty solvents (listed in the HSP books), the relative energy difference (RED) was determined. The probability of the target molecules would be interacting with the solvent molecule was determined using the CCDC tools. A dataset of fifty molecules of different organic solvents was ranked for each prediction method and by a consensus ranking of different combinations: HSP, CV, HBP and MC values. Based on the prediction, 15 solvents were selected as Dimethyl Sulfoxide (DMSO), Tetrahydrofuran (THF), Acetonitrile (ACN), 1,4-Dioxane (DOX) and others. In a starting analysis, the slow evaporation technique from 50°C at room temperature and 4°C was used to obtain solvates. The single crystals were collected by using a Bruker D8 Venture diffractometer, detector Photon100. The data processing and crystal structure determination were performed using APEX3 and Olex2-1.5 software. According to the results, the HSPs (theoretical and optimized) and the Hansen solubility sphere for Cur, Demcur and Biscur were obtained. With respect to prediction analyses, a way to evaluate the predicting method was through the ranking and the consensus ranking position of solvates already reported in the literature. It was observed that the combination of HSP-CV obtained the best results when compared to the other methods. Furthermore, as a result of solvent selected, six new solvates, Cur-DOX, Cur-DMSO, Bicur-DOX, Bircur-THF, Demcur-DOX, Demcur-ACN and a new Biscur hydrate, were obtained. Crystal structures were determined for Cur-DOX, Biscur-DOX, Demcur-DOX and Bicur-Water. Moreover, the unit-cell parameter information for Cur-DMSO, Biscur-THF and Demcur-ACN were obtained. The preliminary results showed that the prediction method is showing a promising strategy to evaluate the possibility of forming multicomponent. It is currently working on obtaining multicomponent single crystals. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=curcumin" title="curcumin">curcumin</a>, <a href="https://publications.waset.org/abstracts/search?q=HSPs" title=" HSPs"> HSPs</a>, <a href="https://publications.waset.org/abstracts/search?q=prediction" title=" prediction"> prediction</a>, <a href="https://publications.waset.org/abstracts/search?q=solvates" title=" solvates"> solvates</a>, <a href="https://publications.waset.org/abstracts/search?q=solubility" title=" solubility"> solubility</a> </p> <a href="https://publications.waset.org/abstracts/169651/predicting-and-obtaining-new-solvates-of-curcumin-demethoxycurcumin-and-bisdemethoxycurcumin-based-on-the-ccdc-statistical-tools-and-hansen-solubility-parameters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/169651.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">63</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2001</span> Modeling Aerosol Formation in an Electrically Heated Tobacco Product</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Markus%20Nordlund">Markus Nordlund</a>, <a href="https://publications.waset.org/abstracts/search?q=Arkadiusz%20K.%20Kuczaj"> Arkadiusz K. Kuczaj</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Philip Morris International (PMI) is developing a range of novel tobacco products with the potential to reduce individual risk and population harm in comparison to smoking cigarettes. One of these products is the Tobacco Heating System 2.2 (THS 2.2), (named as the Electrically Heated Tobacco System (EHTS) in this paper), already commercialized in a number of countries (e.g., Japan, Italy, Switzerland, Russia, Portugal and Romania). During use, the patented EHTS heats a specifically designed tobacco product (Electrically Heated Tobacco Product (EHTP)) when inserted into a Holder (heating device). The EHTP contains tobacco material in the form of a porous plug that undergoes a controlled heating process to release chemical compounds into vapors, from which an aerosol is formed during cooling. The aim of this work was to investigate the aerosol formation characteristics for realistic operating conditions of the EHTS as well as for relevant gas mixture compositions measured in the EHTP aerosol consisting mostly of water, glycerol and nicotine, but also other compounds at much lower concentrations. The nucleation process taking place in the EHTP during use when operated in the Holder has therefore been modeled numerically using an extended Classical Nucleation Theory (CNT) for multicomponent gas mixtures. Results from the performed simulations demonstrate that aerosol droplets are formed only in the presence of an aerosol former being mainly glycerol. Minor compounds in the gas mixture were not able to reach a supersaturated state alone and therefore could not generate aerosol droplets from the multicomponent gas mixture at the operating conditions simulated. For the analytically characterized aerosol composition and estimated operating conditions of the EHTS and EHTP, glycerol was shown to be the main aerosol former triggering the nucleation process in the EHTP. This implies that according to the CNT, an aerosol former, such as glycerol needs to be present in the gas mixture for an aerosol to form under the tested operating conditions. To assess if these conclusions are sensitive to the initial amount of the minor compounds and to include and represent the total mass of the aerosol collected during the analytical aerosol characterization, simulations were carried out with initial masses of the minor compounds increased by as much as a factor of 500. Despite this extreme condition, no aerosol droplets were generated when glycerol, nicotine and water were treated as inert species and therefore not actively contributing to the nucleation process. This implies that according to the CNT, an aerosol cannot be generated without the help of an aerosol former, from the multicomponent gas mixtures at the compositions and operating conditions estimated for the EHTP, even if all minor compounds are released or generated in a single puff. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=aerosol" title="aerosol">aerosol</a>, <a href="https://publications.waset.org/abstracts/search?q=classical%20nucleation%20theory%20%28CNT%29" title=" classical nucleation theory (CNT)"> classical nucleation theory (CNT)</a>, <a href="https://publications.waset.org/abstracts/search?q=electrically%20heated%20tobacco%20product%20%28EHTP%29" title=" electrically heated tobacco product (EHTP)"> electrically heated tobacco product (EHTP)</a>, <a href="https://publications.waset.org/abstracts/search?q=electrically%20heated%20tobacco%20system%20%28EHTS%29" title=" electrically heated tobacco system (EHTS)"> electrically heated tobacco system (EHTS)</a>, <a href="https://publications.waset.org/abstracts/search?q=modeling" title=" modeling"> modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=multicomponent" title=" multicomponent"> multicomponent</a>, <a href="https://publications.waset.org/abstracts/search?q=nucleation" title=" nucleation"> nucleation</a> </p> <a href="https://publications.waset.org/abstracts/47104/modeling-aerosol-formation-in-an-electrically-heated-tobacco-product" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47104.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">277</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2000</span> A Novel Method for Solving Nonlinear Whitham–Broer–Kaup Equation System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ayda%20Nikkar">Ayda Nikkar</a>, <a href="https://publications.waset.org/abstracts/search?q=Roghayye%20Ahmadiasl"> Roghayye Ahmadiasl</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=homotopy%20perturbation%20method" title="homotopy perturbation method">homotopy perturbation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Whitham%E2%80%93Broer%E2%80%93Kaup%20%28WBK%29%20equation" title=" Whitham–Broer–Kaup (WBK) equation"> Whitham–Broer–Kaup (WBK) equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Modified%20Boussinesq" title=" Modified Boussinesq"> Modified Boussinesq</a>, <a href="https://publications.waset.org/abstracts/search?q=Approximate%20Long%20Wave" title=" Approximate Long Wave"> Approximate Long Wave</a> </p> <a href="https://publications.waset.org/abstracts/35317/a-novel-method-for-solving-nonlinear-whitham-broer-kaup-equation-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35317.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">311</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multicomponent%20Smoluchowski%20equation&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multicomponent%20Smoluchowski%20equation&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multicomponent%20Smoluchowski%20equation&page=4">4</a></li> <li class="page-item"><a class="page-link" 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