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2014-15 Catalog | Caltech Academic Catalog

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</div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/Hum/"> Humanities </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/IST/"> Information Science and Technology </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/L/"> Languages </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/Law/"> Law </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/MS/"> Materials Science </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/Ma/"> Mathematics </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/ME/"> Mechanical Engineering </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/MedE/"> Medical Engineering </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/Mu/"> Music </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/NB/"> Neurobiology </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/PA/"> Performance and Activities </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/Pl/"> Philosophy </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/PE/"> Physical Education </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/Ph/"> Physics </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/PS/"> Political Science </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/Psy/"> Psychology </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/SS/"> Social Science </a> </div> </li> <li class="sidebar-menu-block__level-2__item d-flex flex-column menu-item"> <div class="sidebar-menu-block__level-2__item__wrapper "> <a class="sidebar-menu-block__level-2__link" href="/archive/2014-15/department/Wr/"> Writing </a> </div> </li> </ul> </div> </nav> </div> </section> </aside> <div class="left-sidebar-block__content grid-item col-sm-8 pb-5 pb-sm-0 js-sidebar-content"> <div class="course-description2 course-description2--not-offered" id="ce-90-abc"> <div class="course-description2__label"> CE 90 abc </div> <h2 class="course-description2__title"> Structural Analysis and Design </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (3-0-6)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">first, second, third terms</span> </div> <div class="course-description2__prerequisites">Prerequisites: ME 35 abc.</div> <div class="course-description2__description course-description2__general-text"> Structural loads; influence lines for statically determinate beams and trusses; deflection of beams; moment area and conjugate beam theorems; approximate methods of analysis of indeterminate structures; slope deflection and moment distribution techniques. Generalized stiffness and flexibility analyses of indeterminate structures. Design of selected structures in timber, steel, and reinforced concrete providing an introduction to working stress, load and resistance factor, and ultimate strength approaches. In each of the second and third terms a design project will be undertaken involving consideration of initial conception, cost-benefit, and optimization aspects of a constructed facility. Not offered 2014-15. </div> </div> <div class="course-description2 " id="ce-100"> <div class="course-description2__label"> CE 100 </div> <h2 class="course-description2__title"> Special Topics in Civil Engineering </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">Units to be based upon work done</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">any term</span> </div> <div class="course-description2__description course-description2__general-text"> Special problems or courses arranged to meet the needs of first-year graduate students or qualified undergraduate students. Graded pass/fail. </div> </div> <div class="course-description2 " id="aeaphceme-101-abc"> <div class="course-description2__label"> Ae/APh/CE/ME 101 abc </div> <h2 class="course-description2__title"> Fluid Mechanics </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (3-0-6)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">first, second, third terms</span> </div> <div class="course-description2__prerequisites">Prerequisites: APh 17 or ME 11 abc, and ME 12 or equivalent, ACM 95/100 or equivalent (may be taken concurrently).</div> <div class="course-description2__description course-description2__general-text"> Fundamentals of fluid mechanics. Microscopic and macroscopic properties of liquids and gases; the continuum hypothesis; review of thermodynamics; general equations of motion; kinematics; stresses; constitutive relations; vorticity, circulation; Bernoulli's equation; potential flow; thin-airfoil theory; surface gravity waves; buoyancy-driven flows; rotating flows; viscous creeping flow; viscous boundary layers; introduction to stability and turbulence; quasi one-dimensional compressible flow; shock waves; unsteady compressible flow; and acoustics. </div> <div class="course-description2__instructors course-description2__general-text"> <span class="course-description2__instructors__label font-weight-bold">Instructor:</span> Shepherd </div> </div> <div class="course-description2 " id="aeamceme-102-abc"> <div class="course-description2__label"> Ae/AM/CE/ME 102 abc </div> <h2 class="course-description2__title"> Mechanics of Structures and Solids </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (3-0-6)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">first, second, third terms</span> </div> <div class="course-description2__prerequisites">Prerequisites: ME 35 abc or equivalent.</div> <div class="course-description2__description course-description2__general-text"> Static and dynamic stress analysis. Two- and three-dimensional theory of stressed elastic solids. Analysis of structural elements with applications in a variety of fields. Variational theorems and approximate solutions, finite elements. A variety of special topics will be discussed in the third term such as, but not limited to, elastic stability, wave propagation, and introductory fracture mechanics. </div> <div class="course-description2__instructors course-description2__general-text"> <span class="course-description2__instructors__label font-weight-bold">Instructors:</span> Ortiz, Pellegrino </div> </div> <div class="course-description2 " id="ceaeam-108-ab"> <div class="course-description2__label"> CE/Ae/AM 108 ab </div> <h2 class="course-description2__title"> Computational Mechanics </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (3-0-6)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">first, second terms</span> </div> <div class="course-description2__prerequisites">Prerequisites: Ae/AM/ME/CE 102abc or Ae/GE/ME 160ab, or instructor&#x27;s permission.</div> <div class="course-description2__description course-description2__general-text"> Numerical methods and techniques for solving initial boundary value problems in continuum mechanics (from heat conduction to statics and dynamics of solids and structures). Finite difference methods, direct methods, variational methods, finite elements in small strains and at finite deformation for applications in structural mechanics and solid mechanics. Solution of the partial differential equations of heat transfer, solid and structural mechanics, and fluid mechanics. Transient and nonlinear problems. Computational aspects and development and use of finite element code. </div> <div class="course-description2__instructors course-description2__general-text"> <span class="course-description2__instructors__label font-weight-bold">Instructor:</span> Kochmann </div> </div> <div class="course-description2 course-description2--not-offered" id="ceme-112-ab"> <div class="course-description2__label"> CE/ME 112 ab </div> <h2 class="course-description2__title"> Hydraulic Engineering </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (3-0-6)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">second, third terms</span> </div> <div class="course-description2__prerequisites">Prerequisites: ME 19 or equivalent; ACM 95/100 or equivalent (may be taken concurrently).</div> <div class="course-description2__description course-description2__general-text"> A survey of topics in hydraulic engineering: open channel and pipe flow, subcritical/critical flow and the hydraulic jump, hydraulic structures (weirs, inlet and outlet works, dams), hydraulic machinery, hydrology, river and flood modeling, solute transport, sediment mechanics, groundwater flow. Not offered 2014-2015. </div> </div> <div class="course-description2 " id="amceme-150-abc"> <div class="course-description2__label"> AM/CE/ME 150 abc </div> <h2 class="course-description2__title"> Graduate Engineering Seminar </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">1 unit</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">each term</span> </div> <div class="course-description2__description course-description2__general-text"> Students attend a graduate seminar each week of each term and submit a report about the attended seminars. At least four of the attended seminars each term should be from the Mechanical and Civil Engineering seminar series. Students not registered for the M.S. and Ph.D. degrees must receive the instructor's permission. Graded pass/fail. </div> <div class="course-description2__instructors course-description2__general-text"> <span class="course-description2__instructors__label font-weight-bold">Instructor:</span> Staff </div> </div> <div class="course-description2 " id="amce-151-ab"> <div class="course-description2__label"> AM/CE 151 ab </div> <h2 class="course-description2__title"> Dynamics and Vibration </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (3-0-6)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">first, second terms</span> </div> <div class="course-description2__description course-description2__general-text"> Equilibrium concepts, conservative and dissipative systems, Lagrange's equations, differential equations of motion for discrete single and multi degree-of-freedom systems, natural frequencies and mode shapes of these systems (Eigen value problem associated with the governing equations), phase plane analysis of vibrating systems, forms of damping and energy dissipated in damped systems, response to simple force pulses, harmonic and earthquake excitation, response spectrum concepts, vibration isolation, seismic instruments, dynamics of continuous systems, Hamilton's principle, axial vibration of rods and membranes, transverse vibration of strings, beams (Bernoulli-Euler and Timoshenko beam theory), and plates, traveling and standing wave solutions to motion of continuous systems, Rayleigh quotient and the Rayleigh-Ritz method to approximate natural frequencies and mode shapes of discrete and continuous systems, frequency domain solutions to dynamical systems, stability criteria for dynamical systems, and introduction to nonlinear systems and random vibration theory. </div> <div class="course-description2__instructors course-description2__general-text"> <span class="course-description2__instructors__label font-weight-bold">Instructors:</span> Heaton, Asimaki </div> </div> <div class="course-description2 course-description2--not-offered" id="ce-160-ab"> <div class="course-description2__label"> CE 160 ab </div> <h2 class="course-description2__title"> Structural and Earthquake Engineering </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (3-0-6)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">second, third terms</span> </div> <div class="course-description2__description course-description2__general-text"> Matrix structural analysis of the static and dynamic response of structural systems, Newmark time integration, Newton-Raphson iteration methodology for the response of nonlinear systems, stability of iteration schemes, static and dynamic numerical analysis of planar beam structures (topics include the development of stiffness, mass, and damping matrices, material and geometric nonlinearity effects, formulation of a nonlinear 2-D beam element, uniform and nonuniform earthquake loading, soil-structure interaction, 3-D beam element formulation, shear deformations, and panel zone deformations in steel frames, and large deformation analysis), seismic design and analysis of steel moment frame and braced frame systems, steel member behavior (topics include bending, buckling, torsion, warping, and lateral torsional buckling, and the effects of residual stresses), reinforced concrete member behavior (topics include bending, shear, torsion, and PMM interaction), and seismic design requirements for reinforced concrete structures. Not offered 2014-15. </div> </div> <div class="course-description2 course-description2--not-offered" id="mece-163"> <div class="course-description2__label"> ME/CE 163 </div> <h2 class="course-description2__title"> Mechanics and Rheology of Fluid-Infiltrated Porous Media </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (3-0-6)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">third term</span> </div> <div class="course-description2__prerequisites">Prerequisites: Continuum Mechanics - Ae/Ge/ME 160ab.</div> <div class="course-description2__description course-description2__general-text"> This course will focus on the physics of porous materials (e.g., geomaterials, biological tissue) and their intimate interaction with interstitial fluids (e.g., water, oil, blood). The course will be split into two parts: Part 1 will focus on the continuum mechanics (balance laws) of multi-phase solids, with particular attention to fluid diffusion-solid deformation coupling. Part 2 will introduce the concept of effective stresses and state of the art rheology available in modeling the constitutive response of representative porous materials. Emphasis will be placed on poro-elasticity and poro-plasticity. Not offered 2014-15. </div> </div> <div class="course-description2 course-description2--not-offered" id="aece-165-ab"> <div class="course-description2__label"> Ae/CE 165 ab </div> <h2 class="course-description2__title"> Mechanics of Composite Materials and Structures </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (2-2-5)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">second, third terms</span> </div> <div class="course-description2__prerequisites">Prerequisites: Ae/AM/CE/ME 102 a or ME 65.</div> <div class="course-description2__description course-description2__general-text"> Introduction and fabrication technology, elastic deformation of composites, stiffness bounds, on- and off-axis elastic constants for a lamina, elastic deformation of multidirectional laminates (lamination theory, ABD matrix), effective hygrothermal properties, mechanisms of yield and failure for a laminate, strength of a single ply, failure models, splitting and delamination. Experimental methods for characterization and testing of composite materials. Design criteria, application of design methods to select a suitable laminate using composite design software, hand layup of a simple laminate and measurement of its stiffness and thermoelastic coefficients. Not offered 2014-15. </div> </div> <div class="course-description2 course-description2--not-offered" id="ce-180"> <div class="course-description2__label"> CE 180 </div> <h2 class="course-description2__title"> Experimental Methods in Earthquake Engineering </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (1-5-3)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">first term</span> </div> <div class="course-description2__prerequisites">Prerequisites: AM/CE 151 abc or equivalent.</div> <div class="course-description2__description course-description2__general-text"> Laboratory work involving calibration and performance of basic transducers suitable for the measurement of strong earthquake ground motion, and of structural response to such motion. Study of principal methods of dynamic tests of structures, including generation of forces and measurement of structural response. Not offered 2014-15. </div> </div> <div class="course-description2 " id="ce-181-ab"> <div class="course-description2__label"> CE 181 ab </div> <h2 class="course-description2__title"> Engineering Seismology </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (3-0-6)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">second, third terms</span> </div> <div class="course-description2__description course-description2__general-text"> Characteristics of potentially destructive earthquakes from the engineering point of view. Theory of seismometers, seismic waves in a continuum, plane waves in layered media, surface waves, basin waves, site effects, dynamic deformation of buildings, seismic sources, earthquake size scaling, earthquake hazard calculations, rupture dynamics. </div> <div class="course-description2__instructors course-description2__general-text"> <span class="course-description2__instructors__label font-weight-bold">Instructor:</span> Heaton </div> </div> <div class="course-description2 " id="ce-200"> <div class="course-description2__label"> CE 200 </div> <h2 class="course-description2__title"> Advanced Work in Civil Engineering </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">6 or more units as arranged</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">any term</span> </div> <div class="course-description2__description course-description2__general-text"> Members of the staff will arrange special courses on advanced topics in civil engineering for properly qualified graduate students. The following numbers may be used to indicate a particular area of study. </div> </div> <div class="course-description2 course-description2--not-offered" id="aeamceme-214-abc"> <div class="course-description2__label"> Ae/AM/CE/ME 214 abc </div> <h2 class="course-description2__title"> Computational Solid Mechanics </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (3-0-6)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">first, second, third terms</span> </div> <div class="course-description2__prerequisites">Prerequisites: AM 125 abc or equivalent; ACM 100 abc or equivalent; CE/AM/Ae 108 abc or equivalent or instructor&#x27;s permission; Ae/AM/CE/ME 102 abc or equivalent; Ae/Ge/ME 160 ab desirable or taken concurrently.</div> <div class="course-description2__description course-description2__general-text"> Introduction to the use of numerical methods in the solution of solid mechanics and materials problems. First term: geometrical representation of solids. Automatic meshing. Approximation theory. Interpolation error estimation. Optimal and adaptive meshing. Second term: variational principles in linear elasticity. Finite element analysis. Error estimation. Convergence. Singularities. Adaptive strategies. Constrained problems. Mixed methods. Stability and convergence. Variational problems in nonlinear elasticity. Consistent linearization. The Newton-Rahpson method. Bifurcation analysis. Adaptive strategies in nonlinear elasticity. Constrained finite deformation problems. Contact and friction. Third term: time integration. Algorithm analysis. Accuracy, stability, and convergence. Operator splitting and product formulas. Coupled problems. Impact and friction. Subcycling. Space-time methods. Inelastic solids. Constitutive updates. Stability and convergence. Consistent linearization. Applications to finite deformation viscoplasticity, viscoelasticity, and Lagrangian modeling of fluid flows. Not offered 2014-15. </div> </div> <div class="course-description2 " id="aece-221"> <div class="course-description2__label"> Ae/CE 221 </div> <h2 class="course-description2__title"> Space Structures </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">9 units (3-0-6)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">first term</span> </div> <div class="course-description2__description course-description2__general-text"> This course examines the links between form, geometric shape, and structural performance. It deals with different ways of breaking up a continuum, and how this affects global structural properties; structural concepts and preliminary design methods that are used in tension structures and deployable structures. Geometric foundations, polyhedra and tessellations, surfaces; space frames, examples of space frames, stiffness and structural efficiency of frames with different repeating units; sandwich plates; cable and membrane structures, form-finding, wrinkle-free pneumatic domes, balloons, tension-stabilized struts, tensegrity domes; deployable and adaptive structures, coiled rods and their applications, flexible shells, membranes, structural mechanisms, actuators, concepts for adaptive trusses and manipulators. </div> <div class="course-description2__instructors course-description2__general-text"> <span class="course-description2__instructors__label font-weight-bold">Instructor:</span> Pellegrino </div> </div> <div class="course-description2 course-description2--not-offered" id="cegeme-222"> <div class="course-description2__label"> CE/Ge/ME 222 </div> <h2 class="course-description2__title"> Earthquake Source Processes, Debris Flows, and Soil Liquefaction: Physics-based Modeling of Failure in Granular Media </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">6 units (2-0-4)</span> &nbsp; |&nbsp; <span class="course-description2__units-and-terms__item">third term</span> </div> <div class="course-description2__description course-description2__general-text"> A seminar-style course focusing on granular dynamics and instabilities as they relate to geophysical hazards such as fault mechanics, debris flows, and liquefaction. The course will consist of student-led presentations of active research at Caltech and discussions of recent literature. No offered 2014-2015. </div> </div> <div class="course-description2 " id="ce-300"> <div class="course-description2__label"> CE 300 </div> <h2 class="course-description2__title"> Research in Civil Engineering </h2> <div class="course-description2__units-and-terms"> <span class="course-description2__units-and-terms__item">Hours and units by arrangement</span> <span class="course-description2__units-and-terms__item"></span> </div> <div class="course-description2__description course-description2__general-text"> Research in the field of civil engineering. By arrangements with members of the staff, properly qualified graduate students are directed in research. </div> </div> </div> </div> </div> </div> <div class="page-published-at"> Published Date: July 28, 2022 </div> </main> <footer class="footer-container"> <div class="footer d-flex flex-column flex-wrap flex-sm-row justify-content-sm-between"> <div class="footer__torch-box"></div> <img alt="Caltech Torch" class="footer__torch" src="/static/theme7/img/flame.png"> <div class="footer__left"> <img alt="Caltech Logo" class="footer__left__caltech-wordmark" src="/static/theme7/img/caltech-new-logo.png"> <div class="footer__left__caltech-title">California Institute of Technology</div> </div> <div class="footer__right"> <img class="footer__right__map-marker" src="/static/theme7/img/icon-footerpin.png" alt="map marker"> <div class="footer__right__contact-info-row">1200 East California Boulevard</div> <div class="footer__right__contact-info-row">Pasadena, California 91125</div> </div> <nav class="footer__menu w-100 d-flex flex-wrap justify-content-center" aria-label="Footer"> <a class="footer__menu__link" href="https://www.caltech.edu/privacy-notice">Privacy Notice</a> <span class="footer__menu__link">Site content Copyright @ 2025</span> <a class="footer__menu__link footer__menu__link--login" href="/admin/login/">Log In</a> </nav> </div> </footer> <script src="https://cdn.jsdelivr.net/npm/anchor-js@5.0.0/anchor.min.js" integrity="sha256-aQmOEF2ZD4NM/xt4hthzREIo/2PFkOX/g01WjxEV7Ys=" crossorigin="anonymous"></script> <script> anchors.options = { visible: 'touch', titleText: 'Right-click here and choose "Copy Link" to get a link to this part of the page.', } anchors.add(); </script> </body> </html>

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