Related papers: Heat and Gravitation. II. Stability
In this work we extend our previously developed formalism of Newtonian multi-fluid hydrodynamics to allow for coupling between the fluids and the electromagnetic and gravitational field. This is achieved within the convective variational…
In [12], the authors studied a particular class of equilibrium solutions of the Helfrich energy which satisfy a second order condition called the reduced membrane equation. In this paper we develop and apply a second variation formula for…
A variational formulation for nonequilibrium thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include…
We determine the onset point of secular instability for the nonaxisymmetric bar mode in rigidly rotating equilibrium configurations in the Post-Newtonian approximation, in order to apply it to neutron stars. The treatment is based on a…
Gravitational stability of a disc consisting of the gaseous and the stellar components are studied in the linear regime when the gaseous component is turbulent. A phenomenological approach is adopted to describe the turbulence, in which not…
We construct steady states of the Euler-Poisson system with a barotropic equation of state as minimizers of a suitably defined energy functional. Their minimizing property implies the non-linear stability of such states against general,…
The field theoretical description of thermo-hydrodynamics is given. It is based on the duality between the physical space--time and the "material space-time" which we construct here. The material space appearing in a natural way in the…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by a novel variational method, where the velocity profile is assumed to be monotonic and analytic. Unstable eigenvalues of the Rayleigh…
We derive the set of inequalities that is necessary and sufficient for nonlinear causality and linear stability of first-order relativistic hydrodynamics with either a $U(1)_V$ conserved current or a $U(1)_A$ current with a chiral anomaly…
The variational principle for the special and general relativistic hydrodynamics are discussed in view of its application to obtain approximate solutions to these problems. We show that effective Lagrangians can be obtained for suitable…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
One goal of this paper is to discuss the classical definition of granular temperature as an extension of its thermodynamic equivalent and a useful concept which provides an important characterization of fluidized granular matter. Following…
The purpose of this work is to analyze the mathematical model governing motion of $n$-component, heat conducting reactive mixture of compressible gases. We prove sequential stability of weak variational entropy solutions when the state…
Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…
The variational argument is presented to establish the attainability of homogeneity of degree one in the number of particles for any functional $F[n, f]$ that depends on both the state variable $f$ and the particle count $n$. Euler's…
We consider a three-dimensional domain occupied by a homogeneous, incompressible, non-Newtonian, heat-conducting fluid with prescribed nonuniform temperature on the boundary and no-slip boundary conditions for the velocity. No external body…
We establish stability criterion for a two-class retrial system with Poisson inputs, general class-dependent service times and class-dependent constant retrial rates. We also characterise an interesting phenomenon of partial stability when…
Using the wave equation as an example, it is shown how to extend the hydrodynamic Lagrangian-picture method of constructing field evolution using a continuum of trajectories to second-order theories. The wave equation is represented through…
A simultaneous variational principle is introduced that offers a novel avenue to the description of the equilibrium configurations, and at the same time of the elementary excitations, or undulations, of fluid lipid membranes, described by a…