The Disturbance of Solitary Wave in the Diffusion Process of Ag Ultrafine Particles

With an example of Ag ultrafine particles, the "diffusion-trapping-reaction aggregation" model of ultrafine particles is proposed, and the spontaneous evolution of ultrafine particles is described. The evolution kinetic equation is established and the solitary wave solution of evolution kinetic equation is found and discussed in detail.     

Kinetic equation for a dense soliton gas

We propose a general method to derive kinetic equations for dense soliton gases in physical systems described by integrable nonlinear wave equations. The kinetic equation describes evolution of the spectral distribution function of solitons due to soliton-soliton collisions. Owing to complete integrability of the soliton equations, only pairwise soliton interactions contribute to the solution, and the evolution reduces to a transport of the eigenvalues of the associated spectral problem with the corresponding soliton velocities modified by the collisions. The proposed general procedure of the derivation of the kinetic equation is illustrated by the examples of the Korteweg-de Vries and nonlinear Schr?dinger (NLS) equations. As a simple physical example, we construct an explicit solution for the case of interaction of two cold NLS soliton gases.     

Kinetic theory for supernova explosions

Coupled kinetic equations for the time evolution of baryons and neutrinos are introduced in order to present a new solution approach for the problem of type II supernova core collapse and explosion. A test-particle method is introduced in order to cast these kinetic equations into numerically tractable form.     

A Two-Field Dilaton Model of Dark Energy

We investigate the cosmological evolution of a two-field model of dark energy, where one is a dilaton field with canonical kinetic energy and the other is a phantom field with a negative kinetic energy term. Phase-plane analysis shows that the ＂phantom＂-dominated scaling solution is the stable late-time attractor of this type of model. We find that during the evolution of the universe, the equation of state w changes from w 〉 -1 to w 〈 -1, which is consistent with recent observations.     

Pressure solution at the molecular scale

The topological evolution of the cleavage surface of a gypsum single crystal during its dissolution in a flowing undersaturated aqueous solution has been observed with an atomic force microscope. The matter transfer from solid to liquid proceeds through the migration of atomic steps. The step velocity has been measured and appears to depend on the force applied by the tip on the surface. Whereas the high force velocity enhancement is likely to stem from corrosive wear, the speed behavior at low force (<10 nN) differs drastically and can be interpreted as a consequence of the pressure solution of the crystal induced by the tip force. The step velocity evolution with the force obeys the known kinetic law of pressure solution. Hence these experiments enable us to evidence a first atomic mechanism at the origin of pressure solution.     

Cosmology with non-minimally coupled k-field

We consider a non-minimally coupled (with gravity) scalar field with non-canonical kinetic energy. The form of the kinetic term is of Dirac–Born–Infeld form. We study the early evolution of the universe when it is sourced only by the k-field, as well as late time evolution when both the matter and k-field are present. For the k-field, we have considered constant potential as well as potential inspired from boundary string field theory. We show that it is possible to have an inflationary solution in early time as well as late time accelerating phases. The solutions also exhibit attractor properties in a sense that they do not depend on the initial conditions for certain values of the parameters.     

The dynamics of the open bose gas

An exact kinetic equation governing the time evolution of a gas of Bosons interacting with a heat bath is derived by master equation techniques. Its solution is shown to exist globally and to converge to equilibrium; a Liapunov functional is constructed. The approach to equilibrium is exponentially fast at low density but shows critical slowing down in the two-phase region.     

A moving interface method for dynamic kinetic–fluid coupling

This paper is a continuation of earlier work [P. Degond, S. Jin, L. Mieussens, A smooth transition between kinetic and hydrodynamic equations, Journal of Computational Physics 209 (2005) 665–694] in which we presented an automatic domain decomposition method for the solution of gas dynamics problems which require a localized resolution of the kinetic scale. The basic idea is to couple the macroscopic hydrodynamics model and the microscopic kinetic model through a buffer zone in which both equations are solved. Discontinuities or sharp gradients of the solution are responsible for locally strong departures to local equilibrium which require the resolution of the kinetic model. The buffer zone is drawn around the kinetic region by introducing a cut-off function, which takes values between zero and one and which is identically zero in the fluid zone and one in the kinetic zone. In the present paper, we specifically consider the possibility of moving the kinetic region or creating new kinetic regions, by evolving the cut-off function with respect to time. We present algorithms which perform this task by taking into account indicators which characterize the non-equilibrium state of the gas. The method is shown to be highly flexible as it relies on the time evolution of the buffer cut-off function rather than on the geometric definition of a moving interface which requires remeshing, by contrast to many previous methods. Numerical examples are presented which validate the method and demonstrate its performances.     

A moving interface method for dynamic kinetic–fluid coupling

This paper is a continuation of earlier work [P. Degond, S. Jin, L. Mieussens, A smooth transition between kinetic and hydrodynamic equations, Journal of Computational Physics 209 (2005) 665–694] in which we presented an automatic domain decomposition method for the solution of gas dynamics problems which require a localized resolution of the kinetic scale. The basic idea is to couple the macroscopic hydrodynamics model and the microscopic kinetic model through a buffer zone in which both equations are solved. Discontinuities or sharp gradients of the solution are responsible for locally strong departures to local equilibrium which require the resolution of the kinetic model. The buffer zone is drawn around the kinetic region by introducing a cut-off function, which takes values between zero and one and which is identically zero in the fluid zone and one in the kinetic zone. In the present paper, we specifically consider the possibility of moving the kinetic region or creating new kinetic regions, by evolving the cut-off function with respect to time. We present algorithms which perform this task by taking into account indicators which characterize the non-equilibrium state of the gas. The method is shown to be highly flexible as it relies on the time evolution of the buffer cut-off function rather than on the geometric definition of a moving interface which requires remeshing, by contrast to many previous methods. Numerical examples are presented which validate the method and demonstrate its performances.     

Kinetic theory of dense fluids. II. The generalized Chapman-Enskog solution

In the second paper of this series we solve the kinetic equation proposed in the previous paper by a method following the spirit of Chapman and Enskog (generalized Chapman-Enskog method). The zeroth-order solution to the kinetic equation leads to the Euler equations in hydrodynamics for real fluids, and the first-order solution to the Navier-Stokes equations for real fluids. General formulas for transport coefficients such as viscosity and heat-conductivity coefficients are obtained for dense fluids, which are given in terms of time-correlation functions of fluxes conjugate to the thermodynamic forces. The results have the same formal structures as the time-correlation functions in linear response theory except for the collision operator appearing in place of the Liouville operator in the evolution operator for the system.     

Deceleration and monochromatization of atomic beams by laser radiation pressure

Deceleration and velocity distribution narrowing of an atomic beam irradiated by a counter-running resonant light wave is discussed. Velocity distribution evolution under the action of light pressure force and diffusion is found. The results of a numerical solution of the kinetic equation for the atomic velocity distribution function are presented. These results show the efficiency of using the light pressure to decelerate atomic beams and narrow their velocity distribution.     

Multi-pole dark energy

A scalar field with a pole in its kinetic term is often used to study cosmological inflation; it can also play the role of dark energy, which is called the pole dark energy model. We propose a generalized model where the scalar field may have two or even multiple poles in the kinetic term, and we call it the multi-pole dark energy. We find that the poles can place some restrictions on the values of the original scalar field with a non-canonical kinetic term. After the transformation to the canonical form, we get a flat potential for the transformed scalar field even if the original field has a steep one. The late-time evolution of the universe is obtained explicitly for the two pole model, while dynamical analysis is performed for the multiple pole model. We find that it does have a stable attractor solution, which corresponds to the universe dominated by the potential of the scalar field.     

H-theorem for a linear kinetic theory

A strongH-theorem is proved for the approximate linear kinetic theory of Bawzdziewicz and Cichocki, obtained by truncating a transformed hierarchy of evolution equations. For an ith truncation we define an entropy functional that is strictly increasing in time, unless the ith reduced distribution function depends on position coordinates only. It also follows that the only stationary solution of the linear kinetic theory is the equilibrium solution. In addition, we show that the usual symmetry properties of equilibrium time correlation functions are preserved by the approximate kinetic theory under consideration.On leave of absence from Institute of Physics, Szczecin University, Wielkopolska 15, Szczecin, Poland.     

Ostwald coagulation of acicular microparticles in solid disperse systems

The solution is given from the problem of the evolution of a system of polydisperse acicular particles distributed in a solid medium-a supersaturated solution. The general form is determined for the two-dimensional distribution function of microparticles from their characteristic surface radii and a number of other kinetic relations. A method is indicated for going over from the distribution function in the two-dimensional representation to the equations of motion- the laws of the growth and dissolution of characteristic parts of the surface of the microparticles. The application of the general formulas and expressions is illustrated with a specific example.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 26–28, July, 1987.     

Classical and quantum dynamics of a kicked relativistic particle in a box

We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation with delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters, the average kinetic energy can be quasi periodic, or fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing the trembling motion.     

Breakdown and fusion of vortex loops and dynamics of vortex tangle

The role of the processes of reconnection of vortex filaments in the structure and dynamics of vortex tangle in turbulent HeII has been studied. The evolution of a network of vortex loops has been investigated on the basis of the “kinetic” equation for the distribution function of the number of loops in the space of their lengths. The vortex tangle properties are discussed on the basis of the exact solution obtained for this equation.     

On the theory of transient nucleation at the intermediate stage of phase transitions

The evolution of a system of growing aggregates in a macroscopically homogeneous medium with account of both the reduction in metastability and the continuing initiation of new nuclei is studied. The corresponding integro-differential model describing the intermediate stage of phase transitions is solved analytically for arbitrary nucleation kinetics and growth rates of nuclei. An exact solution of the Fokker–Planck equation is found with allowance for the diffusivity along the axis of nucleus radii. In limiting cases of purely kinetic and mixed kinetic-diffusion rates of crystal growth for a special form of diffusivity, the obtained solutions transform to earlier known expressions.     

Studies on the Evolution of Silver Nanoparticles in Micelle by UV-Photoactivation

Ultraviolet (UV) photoirradiation of Ag(I) compounds in the presence of an aqueous Triton X-100 solution has been exploited for the first time to prepare reproducible yellow silver hydrosol. The evolution of nanosized silver particles has been examined critically under the influence of different anions/ligands. Hence, time dependent evolution of silver hydrosol from different silver compounds in micelle via photochemical reduction is observed. Anions/ligands of precursor salts have been found to show profound influence (due to electron scavenging property, solubility, stability etc.) on the evolution route and efficiency of photochemical reduction of Ag(I) to Ag(O) in micelle and thereby classification of silver compounds becomes possible. Kinetic results reveal that the formation of silver particles proceeds via autocatalytic growth mechanism. The observed variation in rate constant values for the evolution of nanoparticles from different silver compounds have been explained in terms of available thermodynamic and kinetic parameters. Nucleophile induced dissolution and reversible photogeneration of zerovalent silver particles have been investigated under ambient condition.