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A logical error in the usual derivation of the energy conservation law is analyzed, and a way to avoid the error is presented.
A complete classification of low-order conservation laws is obtained for time-dependent generalized Korteweg-de Vries equations. Through the Hamiltonian structure of these equations, a corresponding classification of Hamiltonian symmetries…
Fluid dynamics accompanies with the entropy production thus increases the local temperature, which plays an important role in charged systems such as the ion channel in biological environment and electrodiffusion in capacitors/batteries. In…
In the context of scalar field theories, both real and complex, we derive the cutting description at finite temperature (with zero/finite chemical potential) from the cutting rules at zero temperature through the action of a simple thermal…
The primary goal of this paper is to characterize solutions to coupled reaction-diffusion systems. Indeed, we use operators theory to show that under suitable assumptions, then the solutions to the reaction-diffusion equations exist. As…
A new form of governing equations is derived from Hamilton's principle of least action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space. This form yields conservation laws…
A theoretical approach to describing transport of an entire ensemble of clusters with different sizes as a single species in gas has been developed. The major assumption is an existence of local partial chemical equilibrium between the…
We derive the macroscopic Fourier's Law of heat conduction from the exact gain-loss time convolutionless quantum master equation under three assumptions for the interaction kernel. To second order in the interaction, we show that the first…
A method based on Monte Carlo techniques is presented for evaluating thermonuclear reaction rates. We begin by reviewing commonly applied procedures and point out that reaction rates that have been reported up to now in the literature have…
DJIA is tested whether it can be described as a mechanical system conserving total energy with K (=v*v/2) + U, where U is calculated as the negative of work done by force obtained in terms of the second derivative of price, assuming unit…
Certain transformations of isolated physical systems underlying various conservation laws in physics are noted. As regards each of these transformations, there is a theoretical action that is equivalent to a matched physical action on the…
We confront, quantitatively, the theoretical description of the reaction-diffusion of a second order reaction to experiment. The reaction at work is \ca/CaGreen, and the reactor is a T-shaped microchannel, 10 $\mu$m deep, 200 $\mu$m wide,…
This paper introduces a novel approach to approximate a broad range of reaction-convection-diffusion equations using conforming finite element methods while providing a discrete solution respecting the physical bounds given by the…
Conservation laws are among the most fundamental geometric properties of a partial differential equation (PDE), but few known finite difference methods preserve more than one conservation law. All conservation laws belong to the kernel of…
In the context of electromagnetism and nonlinear optical interactions damping is generally introduced as a phenomenological, viscous term that dissipates energy, proportional to the temporal derivative of the polarization. Here, we follow…
Within the framework of the post-Newtonian $2\frac12$ approximation theory, a kinetic theory for relativistic gases in the presence of gravitational fields is developed. The Boltzmann equation and the equilibrium Maxwell-J\"uttner…
The atomic movement induced on melting has to overcome a viscous drag resistance. It is suggested that the latent heat of fusion supplies the required energy for this physical process. The viscosity model introduced here allows computation…
We prove that the special Kirchhoff equation studied by Pokhozhaev admits a third-order conservation law. We further show that if the energy of the solution is sufficiently small, then the $L^2$-norms of the derivatives up to third order of…
The relativistic continuity equations for the extensive thermodynamic quantities are derived based on the divergence theorem in Minkowski space outlined by St\"uckelberg. This covariant approach leads to a relativistic formulation of the…
Unparticle $\U$ with scaling dimension $d_\U$ has peculiar thermal properties due to its unique phase space structure. We find that the equation of state parameter $\omega_\U$, the ratio of pressure to energy density, is given by $1/(2d_\U…