Autowaves in a near-threshold medium

Approximate and numerical methods are used to study the behavior of autowaves for parameters close to the propagation threshold. Under these conditions, the variations in wave velocity and amplitude are slow. A quasi-steady-state equation is derived for the velocity. This equation describes the relaxation to a steady state (uniform motion) in the above-threshold region and the initial damping stage that determines the time scale of this process in the below-threshold region. As the threshold is approached, the time scales indefinitely increase in the above-and below-threshold regions of parameters. Small random inhomogeneities of the active medium and other “ noise” sources produce intense velocity pulsations. These pulsations are comparable in scale to the mean velocity (as in the case of strong turbulence) and resemble the critical fluctuations in order parameter near the point of a continuous phase transition in their statistical properties. The pulsation spectrum exhibits a sharp peak at zero frequency. In contrast to flicker noise, this peak disappears as one recedes from the threshold. The solutions to the quasi-steady-state equation and the results of numerical simulations agree as long as the fluctuations are small— as in the theory of continuous transitions, beyond the fluctuation region.     

First-order Fréedericksz transition and front propagation in a liquid crystal light valve with feedback

Fréedericksz transition can become subcritical in the presence of a feedback mechanism that leads to the dependence of the local electric field onto the liquid crystal re-orientation angle. We have characterized experimentally the first-order Fréedericksz transition in a Liquid Crystal Light Valve with optical feedback. The bistability region is determined, together with the Fréedericksz transition point and the Maxwell point. We show the propagation of fronts connecting the different metastable states and we estimate the front velocity. Theoretically, we derive an amplitude equation, valid close to the Fréedericksz transition point, which accounts for the subcritical character of the bifurcation.Received: 21 October 2003, Published online: 6 January 2004PACS: 05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 64.60.-i General studies of phase transitions     

Wigner Rotations and Precession of Polarization

An easy and direct derivation of Thomas precession is obtained from infinitesimal Wigner rotations arising in unitary representations of the Poincaré group. For spin > 1/2, multipole parameters are studied from this point of view. The canonical 3-component definition of polarization arising naturally in this context is compared with formalisms which start form a pseudo 4-vector and an antisymmetric tensor respectively. The full Thomas equations, including Larmor precession, is derived using time derivatives of finite Wigner rotations. Exact solutions, with arbitrary initial conditions, are presented for constant magnetic fields and for orthogonal constant electric and magnetic fields. For a class of plane wave external fields exact solutions are obtained for the Dirac equation generalized by the inclusion of anomalous magnetic moment (Pauli) and electric dipole moment terms. Using the front form of dynamics, well-adapted to this context and coinciding with proper time dynamics, expectation values are calculated. The polarization pseudo 4-vector thus obtained is shown to satisfy the BMT equation, which is equivalent to the Thomas equation. This shows that the validity of the classical precession equations is not necessarily restricted to slowly varying external fields. These solutions can also be of interest in the study of spin 1/2 particles in laser fields and in the study of electric dipole moments.     

Nonlinear equation for curved nonstationary flames and flame stability

A time-dependent nonlinear equation for a nonstationary curved flame front of an arbitrary expansion coefficient is derived under the assumptions of a small but finite flame thickness and weak nonlinearity. On the basis of the derived equation, stability of two-dimensional curved stationary flames propagating in tubes with ideally adiabatic and slip walls is studied. The stability analysis shows that curved stationary flames become unstable for sufficiently wide tubes. The obtained stability limits are in a good agreement with the results of numerical simulations of flame dynamics and with semiqualitative stability analysis of curved stationary flames. Possible outcomes of the obtained instability at the nonlinear stage are discussed. The instability may result in extra wrinkles at a flame front close to the stability limits and in self-turbulization of the flame far from the limits. The self-turbulization can also be interpreted as a fractal structure. The fractal dimension of a flame front and velocity of a self-turbulized flame are evaluated.     

Confined diffusion

Summary An equation for the unidimensional confined diffusion is proposed. The equation coincides with the well-known homogeneous equation except the presence of a source term. This term which has the form of a dipole distribution is located on a moving front which sharply separates two distinct regions. In the first region (from the boundary up to the front) the confined solution coincides with a suitable solution of the homogeneous equation; in the second region (besides the front) it vanishes. The source term, moreover, switches off the diffusing flux at the front. The sharp confinement allows to relax the original boundary conditions of the homogeneous equation. Precisely, to the function depending on the time at the boundary, another arbitrary function depending on the space at the initial time is added. This new function (provided not vanishing) allows to obtain in general an acceptable evolution of the front and does not prevent the validity of the conservation law: flux at the boundary is equal to the time variation of the diffusing quantity contained between the boundary and the front. By a suitable choice of this new function, so that it results to be connected to the other boundary condition (that depending on time) it is possible to arrive at an evolution of the front such as: , where λ,K, corresponding, respectively, to a dimensionless parameter and diffusivity, depend on the medium. Under such simplifying assumption, it is possible to obtain an analytical expression for the confined solution. This solution, evaluated in a point of the space, arrives asymptotically at the same value reached by the solution of the homogeneous equation.     

Drying processes in the presence of temperature gradients--pore-scale modelling

The influence of temperature gradients on the drying of water-saturated porous networks has been studied. We have focussed on the influence of the temperature on the drying process via the equilibrium vapor density rhoe, because this is the most sensitive parameter with respect to variations of the temperature T. We have used a 2D model which accounts for both capillary and buoyancy forces. Invasion events by air or water are handled by standard rules of invasion percolation in a gradient (IPG). Vapor fluxes are calculated by solving a discretized version of the Laplace equation. In the model the temperature T varies linearly from the open side T0 to the closed side TL. The temperature gradients strongly influence the cluster evolution during the process, because they facilitate vapor transport through wet regions. When T0TL, the front movement is enhanced and the air ingress in the wet region behind the front is inhibited. The behavior of 3D systems differs from that of 2D systems, because the point where air percolates the system and the point where the water network breaks up in isolated clusters do not coincide. Before the latter fragmentation point the temperature will mainly influence the drying rates. After this point also the water distribution becomes sensitive to the temperature profile.     

On the influence of stochastic pulsations of a bubble on its translational motion

This communication is devoted to theoretical analysis of the dynamics of a solitary cavitation bubble pulsating in a compressible viscous liquid under the action of a nonuniform acoustic field. The system of two nonlinear ordinary second-order differential equations is integrated numerically. In the range of acoustic field parameters corresponding to the principal resonance region, the bubble performs large-scale spatial oscillations. It is shown that in a very small range of initial radii, the bubble stops its oscillatory motion due to stochastic pulsations and is expelled into the region of the acoustic-pressure block. Therefore, stochastic pulsations of the bubble radically change the form of the solution to the system of the above-mentioned equations.     

Features of the Magnetic Resonance of an Alkali Metal upon Biharmonic Pumping

The dynamics of spin projections of the electron shell of an alkali metal on the coordinate axis is considered in the electron paramagnetic resonance scheme with continuous pumping by biharmonic circularly polarized laser radiation. The working region is a cell with alkali vapor metal vapors and a buffer gas at a high concentration at temperature 60°C. It was found that the use of biharmonic pumping causes not only the expected electron-spin precession, but also pulsations of the electron-spin projection on the axis along which the magnetic field is directed. The frequency of these pulsations depends on the nuclear angular momentum of alkali metal atoms. In the case of the transverse electron magnetic resonance, this effect is absent.     

A mathematical model of hotspot condensed phase ignition in the presence of a competitive endothermic reaction

We consider the propagation of a combustion front resulting from the gasless combustion of a condensed state fuel. The propagation of the front, essentially a premixed laminar flame, is supported by an exothermic reaction subject to possible heat loss through a competitive endothermic reaction. The dynamics of the endothermic process inducing the heat loss strongly depend on the temperature and the local fuel concentration. Through an analysis based on high activation energy, the steady-state values of the final burnt temperature as well as the burning velocity are obtained, and the control parameters are identified. Using a linear perturbation method, we assess the stability of the propagating front and obtain a condition for oscillatory behaviour. The critical parameter values for the transition from steady to oscillatory burning speeds are identified. The results represent a generalization of those obtained by Matkowsky and Sivashinsky to include the effects of heat loss induced by a competitive endothermic reaction.     

Period-doubling behavior in frontal polymerization of multifunctional acrylates

Front dynamics in the frontal polymerization of two multifunctional acrylate monomers, 1,6-hexanediol diacrylate (HDDA) and trimethylolpropane ethoxylate triacrylate (TMPTA), with Lupersol 231 [1,1-di(t-butylperoxy)-3,3,5-trimethylcyclohexane] as the initiator, are studied. In most frontal polymerization systems, the dynamics are associated with a planar front propagating through the sample. However, in some cases, front behavior can be altered: the front becomes nonplanar characterized by complex patterns like spin modes and pulsations. To determine how these periodic and aperiodic modes arise, reactant solutions consisting of HDDA diluted with diethyl phthalate (DEP) and TMPTA diluted with dimethyl sulfoxide (DMSO) were used in the study. In the study we reveal frontal behavior characteristic of period-doubling behavior, a doubling of spin heads that degenerate into an apparently chaotic mode. Also, a pulsating symmetric mode has been observed. These observations have a striking similarity to observations made in studies of self-propagating high-temperature synthesis (SHS) in which the addition of an inert diluent afforded a rich variety of dynamical behavior. The degree of cross-linking has also been found to be a bifurcation parameter. The energy of activation of multifunctional acrylate polymerization is a strong function of the degree of polymerization. By adding a monoacrylate (benzyl acrylate: BzAc), such that the front temperature was invariant, we observed a period-doubling bifurcation sequence through changes in the energy of activation, which has not been previously reported. (c) 1999 American Institute of Physics.     

On the dynamics of a curved deflagration front

An equation describing evolution of a curved deflagration front of finite thickness is obtained for the case of an arbitrary equation of state of the “fuel”, an arbitrary type of energy release and an arbitrary type of thermal conduction. The equation is complemented by conservation laws for the mass flux and the momentum flux through the deflagration front of finite thickness. As an illustration of the method, the growth rates and the cutoff wavelengths for the linear stage of the flame instability are calculated for the case of a flame in an ideal gaseous fuel and for the case of a thermonuclear deflagration propagating in a strongly degenerate matter of white dwarfs. Zh. éksp. Teor. Fiz. 111, 514–527 (February 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Quantum turbulence in a propagating superfluid vortex front

We present experimental, numerical, and theoretical studies of a vortex front propagating into a region of vortex-free flow of rotating superfluid 3He-B. We show that the nature of the front changes from laminar through quasiclassical turbulent to quantum turbulent with decreasing temperature. Our experiment provides the first direct measurement of the dissipation rate in turbulent vortex dynamics of 3He-B and demonstrates that the dissipation becomes mutual-friction independent with decreasing temperature, and it is strongly suppressed when the Kelvin-wave cascade on vortex lines is predicted to be involved in the turbulent energy transfer to smaller length scales.     

Study of irradiation conditions and thermodynamics of optical glass in the problem of modification of materials by femtosecond laser pulses

The local heating of glass by a focused femtosecond laser pulse and cooling of an irradiated region are numerically modeled. The structural modifications that change the optical properties of glass are assumed to occur within a bulk region whose temperature after irradiation exceeds the glass transition temperature. The shape of the modified region obtained from the calculations coincides with that known from experimental data available. The size of this region is determined by the spatiotemporal dynamics of the laser beam under multiphoton absorption conditions. The heating of glass is maximal in front of a thin lens used for the beam focusing.     

Tidal dynamics of relativistic flows near black holes

We point out novel consequences of general relativity involving tidal dynamics of ultrarelativistic relative motion. Specifically, we use the generalized Jacobi equation and its extension to study the force‐free dynamics of relativistic flows near a massive rotating source. We show that along the rotation axis of the gravitational source, relativistic tidal effects strongly decelerate an initially ultrarelativistic flow with respect to the ambient medium, contrary to Newtonian expectations. Moreover, an initially ultrarelativistic flow perpendicular to the axis of rotation is strongly accelerated by the relativistic tidal forces. The astrophysical implications of these results for jets and ultrahigh energy cosmic rays are briefly mentioned.     

Front propagation in chaotic and noisy reaction-diffusion systems: a discrete-time map approach

We study the front propagation in reaction-diffusion systems whose reaction dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We have examined the influence of chaos and noise on the front propagation speed and on the wandering of the front around its average position. Assuming that the reaction term acts periodically in an impulsive way, the dynamical evolution of the system can be written as the convolution between a spatial propagator and a discrete-time map acting locally. This approach allows us to perform accurate numerical analysis. They reveal that in the pulled regime the front speed is basically determined by the shape of the map around the unstable fixed point, while its chaotic or noisy features play a marginal role. In contrast, in the pushed regime the presence of chaos or noise is more relevant. In particular the front speed decreases when the degree of chaoticity is increased, but it is not straightforward to derive a direct connection between the chaotic properties (e.g. the Lyapunov exponent) and the behaviour of the front. As for the fluctuations of the front position, we observe for the noisy maps that the associated mean square displacement grows in time as t ^1/2 in the pushed case and as t ^1/4 in the pulled one, in agreement with recent findings obtained for continuous models with multiplicative noise. Moreover we show that the same quantity saturates when a chaotic deterministic dynamics is considered for both pushed and pulled regimes. Received 17 July 2001     

Localized patterns and hole solutions in one-dimensional extended systems

The existence, stability properties, dynamical evolution and bifurcation diagram of localized patterns and hole solutions in one-dimensional extended systems are studied from the point of view of front interactions. An adequate envelope equation is derived from a prototype model that exhibits these particle-like solutions. This equation allows us to obtain an analytical expression for the front interaction, which is in good agreement with numerical simulations.     

Covariant Relativistic Statistical Mechanics of Many Particles

In this paper the quantum covariant relativistic dynamics of many bodies is reconsidered. It is emphasized that this is an event dynamics. The events are quantum statistically correlated by the global parameter τ. The derivation of an event Boltzmann equation emphasizes this. It is shown that this Boltzmann equation may be viewed as exact in a dilute event limit ignoring three event correlations. A quantum entropy principle is obtained for the marginal Wigner distribution function. By means of event linking (concatenations) particle properties such as the equation of state may be obtained. We further reconsider the generalized quantum equilibrium ensemble theory and the free event case of the Fermi-Dirac and Bose-Einstein distributions, and some consequences. The ultra-relativistic limit differs from the non-covariant theory and is a test of this point of view.     

Fluid-structure interaction via boundary operator method

This paper is an examination of a simple fluid-structure interaction problem in which a technique for solving time dependent boundary condition problems, the Boundary Operator Method (BOM), is used to gain further insight into fluid-structure response characteristics. The fluid-structure system consists of a compressible liquid having an acoustic pump at one boundary and a spring mass at the other boundary. The response of the spring mass as a result of the acoustic pulsations of the pump is the quantity of interest. This simple model closely represents a PWR core support barrel when excited by pressure waves due to circulating pump pulsations. The general solution of the pressure via the BOM is obtained as a function of the unknown spring mass response. This pressure is evaluated spatially at the spring mass end and the resulting equation of motion for the spring mass is found to be an integral-differential equation. Formulating the solution of the integral differential equation for a harmonic pump pulsation one obtains a normalized displacement of the spring mass as a function of three parameters. These parameters consist of a fluid to structure mass ratio, forcing frequency to uncoupled liquid natural frequency, and a ratio of forcing frequency to uncoupled structural frequency. A study is performed to determine the influence of the three parameters on the structural response.     

Flux front penetration in disordered superconductors

We investigate flux front penetration in a disordered type-II superconductor by molecular dynamics simulations of interacting vortices and find scaling laws for the front position and the density profile. The scaling can be understood by performing a coarse graining of the system and writing a disordered nonlinear diffusion equation. Integrating numerically the equation, we observe a crossover from flat to fractal front penetration as the system parameters are varied. The value of the fractal dimension indicates that the invasion process is described by gradient percolation.