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When considering the diffusion of a protein through a lipidic phase, the continuum mechanics approximation enables a clearer picture of the underlying physics, which emerges simply from two essential observations: firstly, that diffusive processes depend principally upon the diffusivity of the diffusing body, not the viscosity of the environment; secondly, that the diffusivity of a body through a fluid is dependent on the volume fraction of the body in the fluid. By capturing these two basic relationships, it is possible to describe the movements of molecules as microscopic processes of random walks, even though the molecules are highly flexible and deformable. The explicit description of the mechanical properties of molecules is what makes the mesoscale amenable to FFEA and makes it more than just a mathematical exercise.
A basic problem that is addressed in the design of the solution model is how to optimise the trade-off between discretisation and computational efficiency. To this end, the meso-scale is subdivided into several different overlapping domains, each described by a distinct parameter set. It is clear from the discussion above, that when resolving the dynamics of macromolecular structures the space of mechanical properties needs to be studied in some detail. To this end, the intermediate length-scale, at which the continuum mechanics approach is valid, is ideally the domain in which the mechanical properties are resolved at the highest possible resolution. This corresponds to the length-scale at which the molecular structure is resolved at its most detailed.
solution manual for continuum mechanics for engineers solution manual for continuum mechanics for engineers 2nd edition by r. n. mase, b. smelser, m. rossman. solution manual for continuum mechanics for engineers. chapter 3. the theory of continuum mechanics. in this chapter, based on the theory of the transformation of coordinates. name of the course. vibration and waves in continuum mechanics for engineers -. a simple, efficient, and physically correct finite element model is developed for the 1-d wave equation using a nonuniform, staggered element. the model can be used to simulate a continuum of plane waves with wavelength ranging from the visible to the terahertz, and with a maximum wave number ranging from the infrared to the x-ray. the model is based on a standard first-order finite element formulation, and the waves are excited by a point force at the boundary. the model can be used to analyze the behavior of acoustic, electromagnetic, and thermal waves. the continuum model is compared with the exact solution and the commercial finite element model, and its accuracy is verified. the continuum model is validated by using it to simulate a channel filled with a liquid with a known viscosity and the corresponding navier-stokes solution. it is verified that the continuum model, and the exact solution, agree at a point where there is no solution to the navier-stokes equation. the paper reviews in detail the basic theory of finite element method (fem) in both the traditional discrete element approach and its continuum analogue. the basic ideas of the finite element method are presented, its relationship to the finite difference method (fdm) is discussed and a summary of the mesh generation techniques for both the fdm and fem is provided. discrete fem and its continuum analogue are introduced. the fundamental assumptions and principles, the main steps of the fem and the standard finite element method are discussed in detail. a summary of the fundamentals of the finite element method is given for the reader. the associated finite element models of the various fields of mechanics are presented. the 1d, 2d, 3d, and 4d models of continuum mechanics, including the 2d and 3d models of elasticity, linear elasticity, stress-strain relations, and the 3d model of nonlinear elasticity, are presented. the continuum mechanics models are based on a few essential assumptions, and the mathematical properties of the continuum model are reviewed. an example of the physical models and the corresponding discrete fem models of the 1d continuum problem of wave propagation are presented. a brief summary of the basic theory of the finite element method is provided. a summary of the continuum mechanics models is provided for the reader. the basic theory of the finite element method is presented. the theory is used to develop finite element models of a 1d continuum wave problem, where the solutions are derived explicitly. the theory is then used to develop finite element models of a 2d and 3d continuum problem and the solutions are derived explicitly. the theory is used to develop finite element models of a 1d continuum problem. the theory is then used to develop finite element models of a 1d continuum problem. 5ec8ef588b