In this paper, the existence and uniqueness of time-periodic generalized solutions and time-periodic classical solutions to a class of parabolic type equation of higher order are proved by Galerkin method.
In this paper, the existence and uniqueness of time-periodic generalized solutions and time-periodic classical solutions to a class of parabolic type equation of higher order are proved by Galerkin method.
In this paper, we consider a model system with two identical time-delayed coupled layers. Synchronization and anti-phase synchronization are exhibited in the reactive system without diffusion term. New segmented spira...
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In this paper, we consider a model system with two identical time-delayed coupled layers. Synchronization and anti-phase synchronization are exhibited in the reactive system without diffusion term. New segmented spiral waves, which are constituted by many thin trips, are found in each layer of two identical time-delayed coupled layers, and are different from the segmented spiral waves in a water-in-oil aerosol sodium bis(2-ethylhexyl) sulfosuccinate (AOT) microemulsion (ME) (BZ-AOT system), which consists of many small segments. "Anti-phase spiral wave synchronization" can be realized between the first layer and the second one. For different excitable parameters, we also give the minimum values of the coupling strength to generate segmented spiral waves and the tip orbits of spiral waves in the whole bilayer.
The spatiotemporal evolution of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect is investigated by carrying out fully nonlinear two-dimensional numerical simulations initiated by a pulselike d...
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The spatiotemporal evolution of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect is investigated by carrying out fully nonlinear two-dimensional numerical simulations initiated by a pulselike disturbance. The traveling wave packets for positive as well as negative separation factors ψ are obtained numerically for ethanol-water-like mixtures (Prandtl number Pr=10, Lewis number Le=0.01) and selected combinations of Rayleigh and Reynolds numbers at ψ=0.01, 0.1 and ψ=−0.1. The characteristics of the wave fronts and the transitions observed between absolute and convective instabilities when changing the parameters are compared with the results previously obtained by linear spatiotemporal stability analysis. The simulations are in very good agreement with the stability results, which confirms the validity of both approaches. Finally, in order to characterize the possible interaction between the two wave packets of the so-called downstream and upstream modes for ψ<0, the spatiotemporal stability analysis is used to detect a boundary curve in the (Re, Ra) parameter region beyond which the two wave packets will never completely separate. Numerical simulations illustrate the different evolutions of the wave packets on both sides of this boundary.
Understanding the nature of dense particle packings is a subject of intense research in the physical, mathematical, and biological sciences. The preponderance of previous work has focused on spherical particles and ve...
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Understanding the nature of dense particle packings is a subject of intense research in the physical, mathematical, and biological sciences. The preponderance of previous work has focused on spherical particles and very little is known about dense polyhedral packings. We formulate the problem of generating dense packings of nonoverlapping, nontiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem, which we call the adaptive shrinking cell (ASC) scheme. This optimization problem is solved here (using a variety of multiparticle initial configurations) to find the dense packings of each of the Platonic solids in three-dimensional Euclidean space R3, except for the cube, which is the only Platonic solid that tiles space. We find the densest known packings of tetrahedra, icosahedra, dodecahedra, and octahedra with densities 0.823…, 0.836…, 0.904…, and 0.947…, respectively. It is noteworthy that the densest tetrahedral packing possesses no long-range order. Unlike the densest tetrahedral packing, which must not be a Bravais lattice packing, the densest packings of the other nontiling Platonic solids that we obtain are their previously known optimal (Bravais) lattice packings. We also derive a simple upper bound on the maximal density of packings of congruent nonspherical particles and apply it to Platonic solids, Archimedean solids, superballs, and ellipsoids. Provided that what we term the “asphericity” (ratio of the circumradius to inradius) is sufficiently small, the upper bounds are relatively tight and thus close to the corresponding densities of the optimal lattice packings of the centrally symmetric Platonic and Archimedean solids. Our simulation results, rigorous upper bounds, and other theoretical arguments lead us to the conjecture that the densest packings of Platonic and Archimedean solids with central symmetry are given by their corresponding densest lattice packings. This can be regarded to be
We present some explicit self-similar blow-up solutions and some other solutions of the incompressible threedimensional Navier Stokes equations. These solutions indicate that in C^∞ the solution of Navier-Stokes equa...
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We present some explicit self-similar blow-up solutions and some other solutions of the incompressible threedimensional Navier Stokes equations. These solutions indicate that in C^∞ the solution of Navier-Stokes equations does not always tend to a solution of Euler equations.
The aerodynamics of freely falling objects is one of the most interesting flow mechanics *** a recent study,Andersen,Pesavento,and Wang[*** Mech.,vol.541,pp.65-90(2005)]presented the quantitative comparison between th...
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The aerodynamics of freely falling objects is one of the most interesting flow mechanics *** a recent study,Andersen,Pesavento,and Wang[*** Mech.,vol.541,pp.65-90(2005)]presented the quantitative comparison between the experimental measurement and numerical *** rich dynamical behavior,such as fluttering and tumbling motion,was ***,obvious discrepancies between the experimental measurement and numerical simulations still *** the current study,a similar numerical computation will be conducted using a newly developed unified coordinate gas-kinetic method[***,vol.222,pp.155-175(2007)].In order to clarify some early conclusions,both elliptic and rectangular falling plates will be *** the experimental condition,the numerical solution shows that the averaged translational velocity for both rectangular and elliptical plates are almost identical during the tumbling ***,the plate rotation depends strongly on the shape of the *** this study,the details of fluid forces and torques on the plates and plates movement trajectories will be presented and compared with the experimental measurements.
Having studied the initial state energy loss versus nuclear shadowing for the Drell-Yan dimuon pairproduction in the color string model,the inhomogeneous shadowing effect is considered in this *** find thatthe inhomog...
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Having studied the initial state energy loss versus nuclear shadowing for the Drell-Yan dimuon pairproduction in the color string model,the inhomogeneous shadowing effect is considered in this *** find thatthe inhomogeneous shadowing effect does amend the rate of energy loss per unit path length,-dE/***,thetheoretical results for the Drell-Yan differential cross-section ratios are compared with the E772 and E866 *** isfound that the theoretical results are in good agreement with the experimental data.
In this paper,we study the initial-boundary value problem of one class of nonlinear Schr(o)dinger equations described in molecular ***,the existence of the global solution is obtained by means of interpolation inequal...
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In this paper,we study the initial-boundary value problem of one class of nonlinear Schr(o)dinger equations described in molecular ***,the existence of the global solution is obtained by means of interpolation inequality and a priori estimation.
The semiclassical limit in the transient quantum drift-diffusion equations with isentropic pressure in one space dimension is rigorously proved. The equations are supplemented with homogeneous Neumann boundary conditi...
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The semiclassical limit in the transient quantum drift-diffusion equations with isentropic pressure in one space dimension is rigorously proved. The equations are supplemented with homogeneous Neumann boundary conditions. It is shown that the semiclassical limit of this solution solves the classical drift-diffusion model. In the meanwhile, the global existence of weak solutions is proved.
Lattice Boltzmann (LB) modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow...
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Lattice Boltzmann (LB) modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 (2007) 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests: shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.
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