Related papers: Nambu-Poisson dynamics with some applications
Quantum effects play a significant role in nanometric plasmonic devices, such as small metal clusters and metallic nanoshells. For structures containing a large number of electrons, ab-initio methods such as the time-dependent density…
Nonequilibrium thermodynamics has shown its applicability in a wide variety of different situations pertaining to fields such as physics, chemistry, biology, and engineering. As successful as it is, however, its current formulation…
We propose a generalization of equations of quantum mechanics in the hydrodynamic form by introducing the terms taking into account the diffusion velocity at zero and finite temperatures and the density energy of diffusion pressure of the…
In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.
The equation of state of the linear sigma model in the mean field approximation is used as input in a relativistic hydrodynamical numerical routine. Longitudinal and transverse energy distributions are calculated and compared with those…
Integration of nonlinear partial differential equations with the help of the non-commutative integration over octonions is studied. An apparatus permitting to take into account symmetry properties of PDOs is developed. For this purpose…
The aim of this paper is to show two applications of metric currents to complex analysis. After recalling the basic definitions, we give a detailed proof of the comparison theorem between metric currents and classical ones on a manifold. In…
In this proceeding, we will briefly review our recent progress on implementing deep learning to relativistic hydrodynamics. We will demonstrate that a successfully designed and trained deep neural network, called {\tt stacked U-net}, can…
A recent area of interest in thermal applications has been nanofluids, with extensive research conducted in the field, and numerous publications expounding on new results coming to the fore. The properties of such fluids depend on their…
We simulate the space-time dynamics of high-energy collisions based on a microscopic kinetic description in the conformal relaxation time approximation, in order to determine the range of applicability of an effective description in…
Microscopic understanding of liquid properties is essential for advancing a wide range of applications from energy applications such as nuclear reactors and batteries to biomedical applications including drug delivery and microfluidics.…
On the basis of Liouville theorem the generalization of the Nambu mechanics is considered. For three-dimensional phase space the concept of vector hamiltonian and vector lagrangian is entered.
The induction equation of kinematic magnetohydrodynamics is mathematically equivalent to a system of integral equations for the magnetic field in the bulk of the fluid and for the electric potential at its boundary. We summarize the recent…
We investigate the three dimensional compressible Navier-Stokes and the continuity equations in Cartesian coordinates for Newtonian fluids. The polytropic equation of sate is used as closing condition. The key idea is the three-dimensional…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
We present a reduction-consistent and thermodynamically consistent formulation and an associated numerical algorithm for simulating the dynamics of an isothermal mixture consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids…
We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.
During the past decade a number of attempts to formulate a continuum description of complex states of matter have been proposed to circumvent more cumbersome many-body and simulation methods. Typically these have been quantum systems (e.g.,…
In this paper we consider the problem of obtaining a general port-Hamiltonian formulation of Newtonian fluids. We propose the port-Hamiltonian models to describe the energy flux of rotational three-dimensional isentropic and non-isentropic…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…