Related papers: Variational Principles for Stellar Structure
Thermodynamics is usually developed starting from entropy and the maximum entropy principle. We investigate here to what extent one can replace entropy with relative entropy which has several advantages, for example in the context of local…
A method for designing variational principles for the dynamics of a possibly dissipative and non-conservatively forced chain of particles is demonstrated. Some qualitative features of the formulation are discussed.
Dislocations are the main carriers of plastic deformation in crystalline materials. Physically based constitutive equations of crystal plasticity typically incorporate dislocation mechanisms, using a dislocation density based description of…
We present a unified variational treatment of evolving configurations in crystalline solids with microstructure. The crux of our treatment lies in the introduction of a vector configurational field. This field lies in the material, or…
Thermodynamic relations are derived from first principles of mechanics for non-equilibrium processes. Since the key role herein is played by the law of increase of entropy, the latter is analyzed at first. It is shown that its derivation…
A general formulation is presented to derive the equation of motion and to demonstrate thermodynamic consistency for several classes of phase field models at once. It applies to models with a conserved phase field, describing either uniform…
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…
The backbone of nonequilibrium thermodynamics is the stability structure, where entropy is related to a Lyapunov function of thermodynamic equilibrium. Stability is the background of natural selection: unstable systems are temporary, and…
Because of the mass density-dependence, an extra term should be added to the expression of pressure. However, it should not appear in that of energy according to both the general ensemble theory and basic thermodynamic principle. We give a…
Most numerical models of binary stars - in particular neutron stars in compact binaries - assume the companions to be either corotational or irrotational. Either one of these assumptions leads to a significant simplification in the…
In this article, we continue the program started in our previous article of exploring an important class of thermodynamic systems from a geometric point of view. In order to model the time evolution of systems verifying the two laws of…
The maximum entropy principle determines the values of thermodynamic variables in thermally isolated equilibrium systems. This paper extends the principle to a variational principle that applies to liquid-gas coexistence in heat conduction.…
Analysis of experimental kinetic dependences and results of the computer modeling of pairwise interactions in the heterogeneous system have shown that a character of its fractal property variation in the evolution process would be different…
The modeling of stellar spectra is pervasive in astronomy. Conventionally, the shapes of absorption lines are modeled by convolving thermal profiles (computed given some model stellar atmosphere and line list) with broadening kernels…
The Sun provides a critical benchmark for the general study of stellar structure and evolution. Also, knowledge about the internal properties of the Sun is important for the understanding of solar atmospheric phenomena, including the solar…
We show how the macroscopic state variables pressure, entropy and temperature of equilibrium thermodynamics can be consistently derived from the (quantum) chaotic spectral structure of one or two particles in two-dimensional domains. This…
The evolution of irregular galaxies is examined from two points of view: on the one hand, models of galactic chemical evolution have been computed and their predictions compared with the corresponding observational data on the element…
The conditions of thermodynamic equilibrium, local thermodynamic equilibrium, and statistical equilibrium are discussed in detail. The equations of statistical equilibrium and the supplementary equations are shown together with the…
This paper aims to study the configuration of two components caused by rotational and tidal distortions in the model of a binary system. The potentials of the two distorted components can be approximated to 2nd-degree harmonics.…
Stellar evolution codes play a major role in present-day astrophysics, yet they share common issues. In this work we seek to remedy some of those by the use of results from realistic and highly detailed 3D hydrodynamical simulations of…