Related papers: Variational principles and thermodynamics
Analyzing one example of LC circuit in [8], show its Lagrange problem only have other type critical points except for minimum type and maximum type under many circumstances. One novel variational principle is established instead of…
Noncommutativity of observables is a central feature of quantum physics. It plays a fundamental role in the formulation of the uncertainty principle for complementary variables and strongly affects the laws of thermodynamics for systems…
Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions…
Non-equilibrium thermodynamics with internal variables introduces a natural hierarchical arrangement of evolution equations. Three examples are shown: a hierarchy of linear constitutive equations in thermodynamic rhelogy with a single…
This article proposes an in-depth investigation into the emergence of thermoacoustic waves from a variational formalism rooted in non-equilibrium thermodynamics. Differing from traditional approaches based on linear simplifications, this…
Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…
In this second article of a series we propose to base criteria of stability on the hamiltonian functional that is provided by the variational principle, to replace the reliance that has often been placed on {\it ad hoc} definitions of the…
In view of the recent quest for well-behaved nonlinear extensions of the traditional Schroedinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the…
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
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.…
Logistic equations play a pivotal role in the study of any non linear evolution process exhibiting growth and saturation. The interest for the phenomenology, they rule, goes well beyond physical processes and cover many aspects of ecology,…
A dual variational principle is defined for the nonlinear system of PDE describing the dynamics of dislocations in elastic solids. The dual variational principle accounting for a specified set of initial and boundary conditions for a…
The evolution equations of quantum observables are derived from the classical Hamiltonian equations of motion with the only additional assumption that the phase space is non-commutative. The demonstration of the quantum evolution laws is…
We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…
Relativistic fluid dynamics finds application in astrophysics, cosmology and the physics of high-energy heavy-ion collisions. In this thesis, we present our work on the formulation of relativistic dissipative fluid dynamics within the…
In this article we address the question whether it is possible to learn the differential equations describing the physical properties of a dynamical system, subject to non-conservative forces, from observations of its realspace…
The relativistic fluid is a highly successful model used to describe the dynamics of many-particle, relativistic systems. It takes as input basic physics from microscopic scales and yields as output predictions of bulk, macroscopic motion.…
We reformulate the relativistic perfect fluid system on curved space-time. Using standard variables, the velocity field $u$,energy density $\rho$ and pressure $p$, the covariant Euler-Lagrange equation is obtained from variational…
Computing solutions to partial differential equations using the fast Fourier transform can lead to unwanted oscillatory behavior. Due to the periodic nature of the discrete Fourier transform, waves that leave the computational domain on one…
We present a formalism for Newtonian multi-fluid hydrodynamics derived from an unconstrained variational principle. This approach provides a natural way of obtaining the general equations of motion for a wide range of hydrodynamic systems…