Continuum physics

Turcotte, D. L. Schubert, G. (1982). Geodynamics. Applications of Continuum Physics to Geological Problems. New York John Wiley. 

In shock-wave-chemistiy research, compacts of solid powders are usually used as samples. Because of porosity, the samples are inhomogeneous and not a continuous medium, so models based on continuum physics are not suitable for tlie numerical simulation of these problems. A discrete meso-dynamic mctliod (denoted as DM ) developed by Tang et al. in recent years is a better metliod for tliis purpose [20]. 

Calderon, A., 1980, On an inverse boundary value problem Seminar on numerical analysis and its application to continuum physics, Rio de Janeiro. 

Once the continuum hypothesis has been adopted, the usual macroscopic laws of classical continuum physics are invoked to provide a mathematical description of fluid motion and/or heat transfer in nonisothermal systems - namely, conservation of mass, conservation of linear and angular momentum (the basic principles of Newtonian mechanics), and conservation of energy (the first law of thermodynamics). Although the second law of thermodynamics does not contribute directly to the derivation of the governing equations, we shall see that it does provide constraints on the allowable forms for the so-called constitutive models that relate the velocity gradients in the fluid to the short-range forces that act across surfaces within the fluid. 

Once we adopt the continuum hypothesis and choose to describe fluid motions and heat transfer processes from a macroscopic point of view, we derive the governing equations by invoking the familiar conservation principles of classical continuum physics. These are conservation of mass and energy, plus Newton s second and third laws of classical mechanics. 

So far, we have seen that the basic macroscopic principles of continuum mechanics lead to a set of five scalar DEs sometimes called the field equations of continuum mechanics -namely, (2 5) or (2 20), (2 32), and (2-51) or (2 52). On the other hand, we have identified many more unknown variables, u, T, 9,p, and q, plus various fluid or material properties such as p, Cp (or Cv), (dp/d())p, [or (dp/d0)p], which generally require additional equations of state to be determined from p and 9 if the latter are adopted as the thermodynamic state variables. Let us focus just on the independent variables u, T,9, p, and q. Taking account of the symmetry of T, these comprise 14 unknown scalar variables for which we have so far obtained only the five independent field equations that were just listed. It is evident that we require additional equations relating the various unknown variables if we are to achieve a well-posed problem from a mathematical point of view. Where are these equations to come from Why is it that the fundamental macroscopic principles of continuum physics do not, in themselves, lead to a mathematical problem with a closed set of equations ... 

Proton transfer at the surface of a protein or biomembrane is a cardinal reaction in the biosphere, yet its mechanism is far from clarification. The reaction, in principle, should be considered as a quantum chemistry event, and the reaction space as a narrow layer, 3-5 water molecules deep. What is more, local forces are intensive and vary rapidly with the precise molecular features of the domain. For this reason, approximate models that are based on pure chemical models or on continuum physical approximations are somewhat short of being satisfactory models with quantitative prediction power. 

Torgersen T, Drenkard S, State M, Schlosser P, Shapiro AM (1995) Mantle helium in ground waters of eastern North America time and space constraints on sources. Geology 23 675-678 Trail TW, Kurz MD, Jenkins WJ (1991) Diffusion of cosmogenic He in olivine and quartz Implications for surface exposure dating. Earth Planet Sci Lett 103 241-256 Turcotte DL, Schubert G. (1982) Geodynamics Applications of continuum physics to geological problems. Wiley, New York... 

As indicated above, as we move closer and closer to the microscopic size regime, we become increasingly concerned at the validity of such an approach derived from the continuum physics of macroscopic metals. Conversely, any theoretical treatment originating from the quantum chemistry standpoint (the Atoms and Molecules , regime in Fig. 1) would inevitably become unreasonable as we move from the microscopic to the mesoscopic regimes. This, of course, is the fascination - and the challenge - of the science of divided metals ... 

Trurnit P (1968) Pressure solution phenomena in detrital rocks. Sed Geol 2 89-114 Turcotte DL, Schubert G (1982) Geodynamics application of continuum physics to geological problems. Vol. iWiley, New York, 376 p... 

A. C. Eringen, Continuum Physics, Vol. 4, Polar and Nonlocal Field Theories, Academic Press, New York, 1976. 

Eringen, A.C. Basic principles continuum physics. In Eringen, A.C. (ed.) Continuum Mechanics of Single-Substance Bodies, vol. II. Academic, New York (1975)... 

Gurtin, M.E. Configurational Forces as Basic Concepts of Continuum Physics. Springer, New York (2000)... 

When studying phenomena such as dynamic interaction of molecules or the nonequilibrium movements of atoms in nanoscales, in which the object under consideration is a set of particles (i.e., molecules and atoms), particle methods are a natural choice. The current trend in computational methods is to use particle methods both as discretization tools and physical models for continuum physics simulation. 

While at one time certain theoretical statements were regarded as laws of physics, nowadays many theories prefer to regard each theory as a mathematical model of some aspect of nature. But, any mathematical theory of physics must have idealized nature. Then, every theory is only approximate in respect to nature itself. Particularly, it stands for continuous distribution of matter which is the principal assumption of continuum physics. 

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