Traveling Fronts in a Reactive Boussinesq System: Bounds and Stability

This paper considers a simplified model of active combustion in a fluid flow, with the reaction influencing the flow. The model consists of a reaction-diffusion-advection equation coupled with an incompressible Navier-Stokes system under the Boussinesq approximation in an infinite vertical strip. We prove that for certain ignition nonlinearities, including all that are C², and for any domain width, planar traveling front solutions are nonlinearly and exponentially stable within certain weighted H² spaces, provided that the Rayleigh number ρ is small enough. The same result holds for bistable nonlinearities in unweighted H² spaces. We also obtain uniform bounds on the Nusselt number, the bulk burning rate, and the average maximum vertical velocity for chemistries that include bistable and ignition nonlinearities.     

On Transient Time Reduction of a 2.4 GHz Relativistic Traveling Wave Oscillator with a Hollow Slow Wave System

The decrease in the transient time in a relativistic microwave traveling wave oscillator, in which the interaction is carried out between the relativistic electron beam and the fundamental harmonic of the forward-traveling electromagnetic wave slowed down to the speed of light in the hollow slow wave system system, has been numerically and experimentally demonstrated. It is shown that in this mode a high beam-to-wave coupling impedance up to ≈10 Ω is achieved, which ensures reduction of the transient time. In the experiment, a microwave peak power of 210 ± 30 MW at a frequency of 2.45 GHz in a guiding magnetic field of 0.16 T was obtained. The efficiency of the oscillator to convert the power of the electron beam into microwave power was 17 ± 3%. At the beam current pulse duration of about 50 ns the microwave pulse duration was about 20 ns and the transient time was about 22 ns.

     

Analytic Representation of Traveling Wave Solution and Dispersive Relation in Tyson's Model

The researches on traveling wave solution and dispersive relation in Tyson's model were only confined to numerical simulation and theoretically formal expression in the past, because of lack of the analytic representation of speed of the traveling wave. In this paper we give its analytic expression by Painlevé analysis, and so we can obtain the explicit representation of traveling wave solution and dispersive relation.     

质量密度相关模型研究CFL奇异夸克物质性质

在质量--密度相关模型下研究了CFL奇异夸克物质, 并将结果与传统的袋模型结果进行比较. 两个模型均表明, 在合理的参数范围内, CFL相比正常核物质更稳定. 然而, 低密度时声速的行为完全相反, 这使得CFL夸克星的最大质量在质量-密度相关模型下比袋模型大.     

密度相关袋常数的夸克介子耦合模型关于核物质和有限核的研究

由满足手征对称的Nambu-Jona-Lasinio(NJL)模型出发, 计算得到袋常数的密度相关性, 并将其与夸克介子耦合(QMC)模型相结合, 研究核物质和有限核的性质. 结果表明, 该模型能够成功地描述核物质的性质, 但得到的有限核结合能过大, 其中重整势起了非常关键的作用.     

Peaked Traveling Wave Solutions to a Generalized Novikov Equation with Cubic and Quadratic Nonlinearities

The Camassa-Holm equation, Degasperis-Procesi equation and Novikov equation are the three typical integrable evolution equations admitting peaked solitons. In this paper, a generalized Novikov equation with cubic and quadratic nonlinearities is studied, which is regarded as a generalization of these three well-known studied equations. It is shown that this equation admits single peaked traveling wave solutions, periodic peaked traveling wave solutions, and multi-peaked traveling wave solutions.     

On the Diffusion in a Lattice Gas Model: Group-Theoretic Approach

Motivated by some recent results concerning the model of a noninteracting one-dimensional lattice gas with an order preservation of particles where multiple occupancy of the sites is not excluded, we give new symmetries and new reductions of the corresponding continuum nonlinear partial differential equation. Closed-form analytic solutions are found.     

Bifurcations and Dynamics of Traveling Wave Solutions to a Fujimoto-Watanabe Equation

In this paper, we study the bifurcations and dynamics of traveling wave solutions to a Fujimoto-Watanabe equation by using the method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions of the parametric space. Then we show the sufficient conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, compactions and kink-like and antikink-like wave solutions. Moreover, the expressions of solitary wave solutions and periodic wave solutions are implicitly given,while the expressions of kink-like and antikink-like wave solutions are explicitly shown. The dynamics of these new traveling wave solutions will greatly enrich the previews results and further help us understand the physical structures and analyze the propagation of the nonlinear wave.     

W-Band Second-Harmonic Gyrotron Traveling Wave Amplifier with Distributed-Loss and Severed Structures

The second harmonic TE₀₂ gyrotron traveling wave amplifier (gyro-TWT) is a high-power, broadband, millimeter-wave amplifier with a low applied magnetic field. Mode-selective interaction circuits were applied to suppressing spurious oscillations. However, the mode-selective interaction circuit may perturb the operating mode in the gyro-TWT. A multi-stage gyro-TWT design with distributed-loss and severed structures is proposed to stabilize the amplification. This study presents a nonlinear analysis of typical oscillations, including absolute instability, gyrotron backward oscillation (gyro-BWO) and reflective oscillation. The lossy and severed sections of the multi-stage gyro-TWT seem to increase effectively the start-oscillation currents of the absolute instability, gyro-BWO, and reflection oscillation. The multi-stage gyro-TWT is predicted to yield a peak output power of 215 kW at 89.9 GHz with an efficiency of 14.3 %, a saturated gain of 60 dB and a bandwidth of 1.7 GHz for a 100 kV, 15 A electron beam with an axial velocity spread _z/ _z = 5%.     

Anomalous Diffusion in a Model with a Variable Percolation Radius

Anomalous diffusion models for random 1-D cluster and comb structures of length L = 100 with finite fingers and different boundary conditions are considered. The effect of electric field on anomalous diffusion is discussed. The cases with different percolation radii are compared. The comb-structure model with periodic boundary conditions is shown to be useful in studying various types of anomalous diffusion. A new diffusion type, where the average rate is higher than the typical rate, is predicted. Physical causes for this diffusion are revealed.     

On a Competitive Model of Laplacian Growth

We introduce a competitive model of Laplacian growth in both stochastic and deterministic versions. This defines two different aggregation laws with probabilities λ and 1−λ. The parameter λ varying from 0 to 1 is used to weight a ratio between the inner and outer harmonic measures that leads to a competition between the Eden-like process and the DLA solved with site-sticking conditions. We perform numerical and qualitative analysis of the competitive growth.     

Diffusion of Wave Packets in a Markov Random Potential

We consider the evolution of a tight binding wave packet propagating in a time dependent potential. If the potential evolves according to a stationary Markov process, we show that the square amplitude of the wave packet converges, after diffusive rescaling, to a solution of a heat equation.     

Chaotic Behavior in the Raman Interaction of a Trapped Ultracold Ion with Two Traveling Wave Lasers

By means of the Bloch-Maxwell equation,the Raman interaction of a trapcd ultracold ion with two traveling wave lasers is treated semiclassically.As the model works without limitation of the Lamb-Dicke limit and the weak excitation regime,we study chaotic behavior of the system in the wide range of the parameters,It is shown that the chaotic behavior is more and more pronounced with the increase of the Lamb-Dicke Parameter and Rabi frequency,and can e exhitited experimentally by using quantum jump technique.     

Non-Classical Traveling Solutions in a Nonlinear Klein Gordon Model

A model with interparticle inharmonic interaction under the Φ⁴ external potential is studied. Making use of the special relation of relevant parameters, in the continuous limit, it was possible to obtain various non-classical soliton solutions, specifically, compact and peak-like solutions. The solutions undergo a jump on their first derivatives at some points of the space-time manifold. These analytic solutions were obtained by considering strong restrictions on their velocities and on the jump conditions. The energy concentrated in these solutions shows in several cases a discrete spectrum.     

Dynamics of a Wave Packet of Whispering-Gallery-Mode Type in an Optical Waveguide in the Presence of a Traveling Refractive-Index Wave

It is demonstrated that strong ultrafast modulation of a tunneling wave packet of the whispering-gallery-mode type can be implemented in a cylindrical optical waveguide exhibiting spatiotemporal inhomogeneity induced by a travelling refractive-index wave. The corresponding optical waveguides can be used for efficient generation of picosecond and subpicosecond laser pulses.     

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, d≥1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.     

A Note on a Model System with Sudden Directional Diffusion

We study qualitative properties of solutions to a monodimensional problem

Optimizing the Longitudinal Dynamics of a Non-Relativistic Charged Particle Bunch in the Field of a Traveling Wave

Physics of Particles and Nuclei Letters - Using the Lagrangian equation for the envelopes of the longitudinal motion of a non-relativistic charged particle bunch in the field of a traveling wave,...     

Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model

We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements H _xy , indexed by \({x,y \in \Lambda \subset \mathbb{Z}^d}\), are independent, uniformly distributed random variables if \({\lvert{x-y}\rvert}\) is less than the band width W, and zero otherwise. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales \({t\ll W^{d/3}}\). We also show that the localization length of the eigenvectors of H is larger than a factor W ^d/6 times the band width. All results are uniform in the size \({\lvert{\Lambda}\rvert}\) of the matrix.     

Formation of the Shock Pressure Regime in the Form of a Traveling Wave in Nematic Twisted Cells

Physics of the Solid State - The paper presents a numerical study, within a nonlinear generalization of the classical Ericksen–Leslie theory, of a new nonlinear mechanism for the formation of...