Landau damping in the multiscale Vlasov theory

Vlasov kinetic theory is extended by adopting an extra one particle distribution function as an additional state variable characterizing the micro-turbulence internal structure. The extended Vlasov equation keeps the reversibility, the Hamiltonian structure, and the entropy conservation of the original Vlasov equation. In the setting of the extended Vlasov theory we then argue that the Fokker-Planck type damping in the velocity dependence of the extra distribution function induces the Landau damping. The same type of extension is made also in the setting of fluid mechanics

Shopping Area KIKA in Ostrava - Traffic Solution

Import 07/02/2010Řešená lokalita se nachází v katastrálním území Ostrava -Zábřeh nad Odrou, jižně od Shopping parku Avion, přes pozemní komunikaci Rudná I/11. Práce se zabývá návrhem pozemních komunikací obsluhujících obchodní domy Strip Mall, Kika, ČSPH a jejich technologické zařízení. Jedná se jak o obsluhu ze strany zásobování, tak i o zákazníky a jejich parkování v dané oblasti. Součástí řešení je i napojení areálu na veřejnou síť pozemních komunikací přes nově navrženou okružní křižovatku s pěti rameny na místo stykové křižovatky na vrcholu příjezdové rampySolving location is situated in cadastral territory Ostrava – Zábřeh nad Odrou, south of Shopping park Avion, across the road Rudná I/11. Thesis deals with design communications over land used for department stores Stip Mall, Kika, ČSPH and their building equipment. Way will be used both for supply and for customers. Part of solve this location is parking for supply and customers too. Next component of solve is connecting shopping zone with public network communications over land across new projecting rotary intersection with five intersection legs in place of currently node on top of access ramp.Prezenční227 - Katedra dopravního stavitelstvívýborn

Ehrenfest regularization of Hamiltonian systems

Imagine a freely rotating rigid body. The body has three principal axes of rotation. It follows from mathematical analysis of the evolution equations that pure rotations around the major and minor axes are stable while rotation around the middle axis is unstable. However, only rotation around the major axis (with highest moment of inertia) is stable in physical reality (as demonstrated by the unexpected change of rotation of the Explorer 1 probe). We propose a general method of Ehrenfest regularization of Hamiltonian equations by which the reversible Hamiltonian equations are equipped with irreversible terms constructed from the Hamiltonian dynamics itself. The method is demonstrated on harmonic oscillator, rigid body motion (solving the problem of stable minor axis rotation), ideal fluid mechanics and kinetic theory. In particular, the regularization can be seen as a birth of irreversibility and dissipation. In addition, we discuss and propose discretizations of the Ehrenfest regularized evolution equations such that key model characteristics (behavior of energy and entropy) are valid in the numerical scheme as well

Extra mass flux in fluid mechanics

The conditions of existence of extra mass flux in single component dissipative non-relativistic fluids are clarified. By considering Galilean invariance we show that if total mass flux is equal to total momentum density, then mass, momentum, angular momentum and booster (center-of-mass) are conserved. However, these conservation laws may be fulfilled also by other means. We show an example of weakly non-local hydrodynamics where the conservation laws are satisfied as well although the total mass flux is different from momentum density

Hamiltonian Coupling of Electromagnetic Field and Matter

Reversible part of evolution equations of physical systems is often generated by a Poisson bracket. We discuss geometric means of construction of Poisson brackets and their mutual coupling (direct, semidirect and matched-pair products) as well as projections of Poisson brackets to less detailed Poisson brackets. This way the Hamiltonian coupling between transport of mixtures and electrodynamics is elucidated

Continuum Mechanics and Thermodynamics in the Hamilton and the Godunov-type Formulations

Continuum mechanics with dislocations, with the Cattaneo type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov type system of the first order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov type formulation brings the mathematical rigor (the well-posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization)

Particle-based approach to the Eulerian distortion field and its dynamics

The Eulerian distortion field is an essential ingredient for the continuum modeling of finite elastic and inelastic deformations of materials; however, its relation to finer levels of description has not yet been established. This paper provides a definition of the Eulerian distortion field in terms of the arrangement of the constituent microscopic particles, which is beneficial for fundamental studies as well as for the analysis of computer simulations, e.g., molecular dynamics simulations. Using coarse graining and nonequilibrium thermodynamics, the dynamics of the Eulerian distortion field is examined in detail and related to the underlying dynamics of the particles. First, the usual kinematics of the distortion and the known expression for the Cauchy stress tensor are recovered. And second, it is found that the Mandel stress and the plastic deformation-rate tensor in the natural configuration constitute the relevant force–flux pair for the relaxation of the distortion. Finally, the procedure is illustrated on two examples, namely on an amorphous solid and on a crystalline solid with one slip system.</p

Globally time-reversible fluid simulations with smoothed particle hydrodynamics

This paper describes an energy-preserving and globally time-reversible code for weakly compressible smoothed particle hydrodynamics (SPH). We do not add any additional dynamics to the Monaghan's original SPH scheme at the level of ordinary differential equation, but we show how to discretize the equations by using a corrected expression for density and by invoking a symplectic integrator. Moreover, to achieve the global-in-time reversibility, we have to correct the initial state, implement a conservative fluid-wall interaction, and use the fixed-point arithmetic. Although the numerical scheme is reversible globally in time (solvable backwards in time while recovering the initial conditions), we observe thermalization of the particle velocities and growth of the Boltzmann entropy. In other words, when we do not see all the possible details, as in the Boltzmann entropy, which depends only on the one-particle distribution function, we observe the emergence of the second law of thermodynamics (irreversible behavior) from purely reversible dynamics.Comment: Submitted to a journa