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[en] The authors employ singular perturbation methods to examine the generalized Langevin equation which describes the dynamics of a Brownian particle in an arbitrary potential force field, acted on by a fluctuating force describing collisions between the Brownian particle and lighter particles comprising a thermal bath. In contrast to models in which the collisions occur instantaneously, and the dynamics are modeled by a Langevin stochastic equation, they consider the situation in which the collisions do not occur instantaneously, so that the process is no longer a Markov process and the generalized Langevin equation must be employed. They compute expressions for the mean exit time of the Brownian particle from the potential well in which it is confined

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[en] The MVC (mean vorticity and covariance) turbulence closure is derived for three-dimensional turbulent flows. The derivation utilizes Lagrangian time expansion techniques applied to the unclosed terms of the mean vorticity and covariance equations. The closed mean vorticity equation is applied to the numerical solution of fully developed three-dimensional channel flow. Anisotropies in the wall region are modelled by pairs of counterrotating streamwise vortices. The numerical results are in close agreement with experimental data. Analysis of the contributions of the terms in the mean vorticity equation gives insight into the dynamics of the turbulent boundary. 41 references, 7 figures

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[en] A new approach is described to the connection of wave amplitudes across the turning points and singular points of second-order, linear, analytic, ordinary differential equations which can describe the modulation of physical waves or oscillators. The general class of singular points thereby defined (refer to section 15) contains many irregular ones of greater complexity than have been accessible before; however, genuine coalescence of singular points is not considered here. The asymptotic connection formulae are shown to result directly from the branch structure of the singular point (refer to section 15), indeed, to a first approximation, they reflect merely the gross, local branch structure. The proof (refer to section 15) relates the local structure of the solutions at the singular point to the asymptotic wave structure by a limit process justified by bounds on the degree of irregularity of solution structure. 8 references

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[en] The authors consider a two-step model reaction from combustion theory which includes an intermediate species, or radical. The resulting equations do not exhibit the ''cold boundary difficulty.'' For the corresponding equations for a traveling flame front they prove existence of a solution to the appropriate boundary value problem. Use is made of a five-parameter shooting argument

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[en] Steady, planar propagation of a condensed phase reaction front is unstable to disturbances corresponding to pulsating and spinning waves for sufficiently large values of a parameter related to the activation energy. This paper considers the nonlinear evolution equations for the amplitudes of the pulsating and spinning waves in a neighborhood of a double eigenvalue of the problem linearized about the steady, planar solution. In particular, near a degenerate Hopf bifurcation point, closed branches of solutions which represent new quasi-periodic modes of combustion are described

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[en] An effective approach to the solution of a large class of mixed boundary value problems (those reducible to an n-series problem) is developed. The method is based on the deduction of the equivalent Riemann-Hilbert problem and its solution. This generalized n-series approach leads to analytical descriptions of the coupling of electromagnetic waves through apertures in canonical structures into open or enclosed regions. In particular, it is applied to the canonical problem of plane wave coupling to an infinite circular cylinder with multiple infinite axial slots. Numerical results for currents induced by an H-polarized plane wave on a circular cylinder with a single slit are given. 9 references, 3 figures

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[en] In this paper the authors examine the mathematical structure of a model for three-phase, incompressible flow in a porous medium. They show that, in the absence of diffusive forces, the system of conservation laws describing the flow is not necessarily hyperbolic. They present an example in which there is an elliptic region in saturation space for reasonable relative permeability data. A linearized analysis shows that in nonhyperbolic regions solutions grow exponentially. However, the nonhyperbolic region, if present, will be of limited extent which inherently limits the exponential growth. To examine these nonlinear effects they resort to fine grid numerical experiments with a suitably dissipative numerical method. These experiments indicate that the solutions of Riemann problems remain well behaved in spite of the presence of a linearly unstable elliptic region in saturation space. In particular, when initial states are outside the elliptic region the Riemann problem solution appears to stay outside the region. Furthermore, stable shocks are formed connecting states inside the nonhyperbolic regions with states outside

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[en] A model equation containing a memory integral is posed. The extent of the memory, the relaxation time lambda, controls the bifurcation behavior as the control parameter R is increased. Small (large) lambda gives steady (periodic) bifurcation. There is a double eigenvalue at lambda = lambda

_{1}, separating purely steady (lambda < lambda_{1}) from combined steady/T-periodic (lambda > lambda_{1}) states with T → infinity as lambda → lambda^{+}_{1}. Analysis leads to the co-existence of stable steady/periodic states and as R is increased, the periodic states give way to the steady states. Numerical solutions show that this behavior persists away from lambda = lambda_{1}Primary Subject

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[en] The authors consider nonadiabatic premixed flame propagation in a long cylindrical channel. A steadily propagating planar flame exists for heat losses below a critical value. It is stable provided that the Lewis number and the volumetric heat loss coefficient are sufficiently small. At critical values of these parameters, bifurcated states, corresponding to time-periodic pulsating cellular flames, emanate from the steadily propagating solution. The authors analyze the problem in a neighborhood of a multiple primary bifurcation point. By varying the radius of the channel, they split the multiple bifurcation point and show that various types of stable periodic and quasi-periodic pulsating flames can arise as secondary, tertiary, and quaternary bifurcations. Their analysis describes several types of spinning and pulsating flame propagation which have been experimentally observed in nonadiabatic flames, and also describes additional quasi-periodic modes of burning which have yet to be documented experimentally

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[en] The problem of transport of a passive solute in a porous medium by convection and dispersion is analysed by the method of homogenization. Assuming that the geometry is periodic, the expressions for the macroscopic dispersion coefficients are derived. A few possible scalings are compared and we find that the most interesting one provides a local balance between drift and diffusion

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