Wolf Weiss

The shock tube study in extended thermodynamics

In this paper we investigate the shock tube experiment with extended thermodynamics. Extended thermodynamics (ET) provides dissipative field equations for monatomic gases which are symmetrically hyperbolic. The theory relies on the extension of the set of variables in order to describe extreme nonequilibrium processes. As an example for such a process we focus on the start-up phase of the shock tube experiment. We show numerically that ET succeeds to describe this short time behavior. For small times more and more variables are needed for a physically valid description. In the limit of very small times the solution of ET for the start-up phase converges to the solution of the free-flight-equation. Additionally it turns out that the system of Navier–Stokes and Fourier fails to describe the start-up phase of a shock tube even qualitatively.

Light scattering and extended thermodynamics

The interaction of light and matter leads to the scattering of light and the scattered light carries information about the thermodynamic properties of the matter. The light scattered on dilute gases carries far more information about the gas than is comprised within the Navier-Stokes-Fourier theory of gases. It takes extended thermodynamics of many moments to satisfactorily describe the characteristic features of such light quantitatively.

The balance of entropy on earth

Entropy is absorbed and emitted in the. atmosphere and in the litho- and hydrosphere of the earth by absorption and emission of radiation. The value of the total production rate of entropy may be decomposed into the production rates ofradiative entropy andof material entropy. Although the latter amounts to only 3,4 % of the total, the material entropy production rate is the one that is relevant to meteorology, life science and ecology. Civilization accounts for less than 1 % of the material entropy production.

Comments on ‘‘Existence of kinetic theory solutions to the shock structure problem’’ [Phys. Fluids 7, 911 (1964)]

H. Holway presented a proof, based on the Boltzmann equation, in which he shows that for the moment method there exists a critical Mach number beyond which no continuous shock solution is possible. In this paper, the results of Holway’s proof are reinterpreted. From this reinterpretation, it follows that no upper bound for a critical Mach number exists.

The Riemann-Problem in Extended Thermodynamics

In this paper we will approach the shock tube problem, or mathematically speaking the Riemann problem with extended thermodynamics. Extended thermodynamics (ET) provides dissipative field equations which are symmetric hyperbolic [1]. Thus, the solution to the shock-tube-problem may be obtained using the well known analytic and numerical methods for hyperbolic systems.

The State of Deformation in Earthlike Self-Gravitating Objects

This book presents an in-depth continuum mechanics analysis of the deformation due to self-gravitation in terrestrial objects, such as the inner planets, rocky moons and asteroids. Following a brief history of the problem, modern continuum mechanics tools are presented in order to derive the underlying field equations, both for solid and fluid material models. Various numerical solution techniques are discussed, such as Runge-Kutta integration, series expansion, finite differences, and (adaptive) FE analysis. Analytical solutions for selected special cases, which are worked out in detail, are also included. All of these methods are then applied to the problem, quantitative results are compared, and the pros and cons of the analytical solutions and of all the numerical methods are discussed. The book culminates in a multi-layer model for planet Earth according to the PREM Model (Preliminary Earth Model) and in a viscoelastic analysis of the deformation problem, all from the viewpoint of rational continuum theory and numerical analysis

Miscellaneous Applications and Outlook

This chapter is devoted toward attempts for more realistic modeling. First, we will investigate the impact of a multilayered shell structure on the deformation behavior of a self-gravitating planet. Second, we will start modeling time-dependent deformation in terms of a deformation-wise linear viscoelastic model of the Kelvin–Voigt type, which allows for a closed-form solution. As a new result it will turn out that in the early days of planet formation a Love radius does not exist and that it takes time for its development.

Nonlinear Strain Theory

Modern nonlinear continuum theories are based on the concepts of reference and current configurations. In many “nonlinear applications,” for example, for describing metal forming processes the stress-free, undeformed configuration, i.e., an undeformed sheet of metal with known material properties is the natural starting point for an analysis.

Linear Strain Theory

Linear Hookean elasticity formulated in terms of linear strain measures is the simplest way of modeling deformation in self-gravitating terrestrial bodies.

The Symmetric Hyperbolic Equations of Extended Thermodynamics

Extended thermodynamics employs quasilinear first order field equations of symmetric hyperbolic type. The number of variables used in the theory is dictated by the initial and boundary values. If the Fourier components of these data contain high frequencies and wavelengths, we must choose a theory whose dispersion relation (of sound) and scattering spectrum (of light) is well described up to and including such frequencies and wave lengths.