Related papers: Energy based methods applied in mechanics by using…
In this paper, we introduce a statistical field theory that describes the macroscopic mechanical forces in inhomogeneous Coulomb fluids. Our approach employs the generalization of Noether's first theorem for the case of fluctuating order…
We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system…
We discuss the relation between canonical and metric energy-momentum tensors for field theories with actions that can depend on the higher derivatives of tensor fields in a flat spacetime. In order to obtain it we use a modification of the…
The energy--momentum tensor and the tensor continuity equation serve as the conservation laws of energy, linear momentum, and angular momentum for a continuous flow. Previously, we derived equations of motion for macroscopic electromagnetic…
Continuum electrodynamics is an axiomatic formal theory based on the macroscopic Maxwell equations and the constitutive relations. We apply the formal theory to a thermodynamically closed system consisting of an antireflection coated block…
A general method using multipliers for finding the conserved integrals for any system of partial differential equations (PDEs) is reviewed and further developed in several ways. Multipliers are expressions whose (summed) product with a PDE…
Since the seminal work of Emmy Noether it is well know that all conservations laws in physics, \textrm{e.g.}, conservation of energy or conservation of momentum, are directly related to the invariance of the action under a family of…
This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain a Noether's theorem for Lagrangian systems with external forces, among other results regarding…
We propose a thermodynamic formalism, within the particle-frame, for the energy-momentum tensor of irreversible anisotropic imperfect fluids subject to causality. Building on the Israel-Stewart extension of Eckart's theory, we further…
Applying the recently developed dynamical perturbation formalism on cosmological background to scalar-tensor theory, we provide a solid theoretical basis and a rigorous justification for phenomenological models of orbital dynamics that are…
Anisotropy of a space naturally leads to direction dependent electromagnetic tensors and electromagnetic potentials. Starting from this idea and using variational approaches and exterior derivative formalism, we extend some of the classical…
We present a general formalism which allows us to derive the evolution equations describing one-dimensional (1D) and isotropic 2D interfacelike systems, that is based on symmetries, conservation laws, multiple scale arguments, and exploits…
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…
We propose a new formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints (i.e. broken detailed balance at steady state) and furthermore driven by external time-dependent forces. A splitting of the second…
We present a generalization of the effective field theory (EFT) formalism for dark energy and modified gravity models to include operators with higher order spatial derivatives. This allows the extension of the EFT framework to a wider…
The relations between two construction methods (called multiplier and embedding methods) for conserved currents of general systems of ordinary or partial differential equations (DEs) are investigated. Recent studies indicate that the…
We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the the basic variables of electrodynamics and Maxwell's equations to general differentiable manifolds of any dimension, thus viewing…
The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by…
We explore the recently introduced modified Gauss-Bonnet gravity [1], $f(\mathcal{G},T)$ pragmatic with $\mathcal{G}$, the Gauss-Bonnet term, and ${T}$, the trace of the energy-momentum tensor. Noether symmetry approach has been used to…
The form of the coupling of the scalar field with gravity and the potential have been found by applying Noether theorem to two dimensional minisuperspaces in induced gravity model. It has been observed that though the forms thus obtained…