New family of simple solutions of relativistic perfect fluid hydrodynamics

A new class of accelerating, exact and explicit solutions of relativistic hydrodynamics is found—more than 50 years after the previous similar result, the Landau–Khalatnikov solution. Surprisingly, the new solutions have a simple form, that generalizes the renowned, but accelerationless, Hwa–Bjorken solution. These new solutions take into account the work done by the fluid elements on each other, and work not only in one temporal and one spatial dimensions, but also in arbitrary number of spatial dimensions. They are applied here for an advanced estimation of initial energy density and life-time of the reaction in ultra-relativistic heavy ion collisions. New formulas are also conjectured, that yield further important increase of the initial energy density estimate and the measured life-time of the reaction if the value of the speed of sound is in the realistic range.     

一维非定常流体力学数值模拟

非线性的流体偏微分方程中的激波间断解是物理中很有挑战的问题,其中的Riemann问题可采用解析的方法求出理论解,但采用近似解的方法进行流体动力学数值模拟也可以有效地追踪和捕捉激波.本文以一维激波管为例,对非定常流体基本方程组采用Roe通量差分裂格式,并进行数值模拟.通过与理论解对比,发现其符合度较好.     

Convective heat conduction and diffusion in one-dimensional hydrodynamics

The impurity concentration in localized structures is described on the basis of analytic solutions of model equations for convective diffusion in the one-dimensional hydrodynamic approximation without pressure. The simplicity of the derivation of the analytic results depends on the ratio of the kinetic coefficients of the liquid (the Prandtl numbers). For the same kinetic coefficients, any time-dependent problem can be reduced to problems for the conventional heat conduction equation. For integer Prandtl numbers the problem of time-dependent convective diffusion in the flow field of a uniformly moving shock wave likewise reduces to problems for the heat conduction equation. Relations are established between problems whose Prandtl numbers differ by an integer. Various representations of the Green’s functions for the equations of convective diffusion are analyzed. For integer Prandtl numbers they can be expressed in terms of error functions. The asymptotic character of the solutions depends strongly on the satisfaction of global conservation laws. For global conservation of the impurity mass, coalescence of shock waves corresponds to merging of impurity solitons, i.e., clustering. Zh. éksp. Teor. Fiz. 116, 1616–1629 (November 1999)     

Stochastic model of a one-dimensional fluid

A one-dimensional point process with correlations constructed via a geometrical rule is shown to behave like a fluid at equilibrium. The equation of state is calculated and the “inverse problem” of finding an interaction potential underlying the system is considered. The effective potential is found to be dependent on macroscopic parameters via a dependence on the density of the system.     

Fluctuating hydrodynamics of a fluid with internal rotation

The fluctuating hydrodynamics theory of a fluid possessing internal rotation is set up following the Landau-Lifshitz approach.     

Collective modes in a one-dimensional nonuniform fluid model

A one-dimensional fluid with short-range repulsive interaction and one period of cosinusoidal attraction in a periodic container is transformed to a two-mode format. The system has both high-temperature single-phase regions and lowtemperature two-phase regions with a very broad spatial interface that can be stabilized by a weak external field. The case of vanishing external field brings out properties of the mode amplitude dependence which one expects to extend to more complex systems.     

Breakdown of time-dependent mean-field theory for a one-dimensional condensate of impenetrable bosons

We show that the time-dependent nonlinear Schrodinger equation of mean-field theory has limited utility for a one-dimensional condensate of impenetrable bosons. Mean-field theory with its associated order parameter predicts interference between split condensates that are recombined, whereas an exact many-body treatment shows minimal interference.     

Dynamic scaling in a simple one-dimensional model of dislocation activity

We examine a simple one-dimensional (1D) model of dislocation activity, including a stress-activated source and mutually interacting dislocations. We demonstrate, through numerical and analytical steps, that the dislocations emitted from a 1D stress-activated source evolve towards a distribution which is self-similar in time, and we derive the power-law forms and distribution function. We show that the asymptotic distribution is a step function, and the dislocation front moves out linearly in time. The spacing between dislocations in the asymptotic distribution is uniform and increases logarithmically in time. The number of dislocations increases as t/ln(t), and the strain increases as t ²/ln(t).     

Bulk and boundary effects in a one-dimensional water-like fluid

Sites of a one-dimensional lattice may be either vacant or occupied by molecules with two orientational states, a ‘monomer’ state taking up one site and a ‘dimer’ state taking up two sites. There is a nearest-neighbour energy — ε for all molecules and an additional bonding energy — ω for adjacent dimers. Hence low temperatures and pressures favour an open structure with molecules predominantly in the dimer state. Bulk behaviour is investigated by both matrix and combinatorial methods and maxima in density isobars and minima in isothermal compressibility curves are found at certain parameter values. These are anomalous properties similar to those occurring in fluid water.

Boundary effects in a chain with end sites are calculated by matrix methods for several types of boundary condition. The effect on the open structure is measured by the change in the number of dimer-dimer bonds due to the presence of the boundary. For a ‘structure-breaking’ boundary, which forces the adjacent molecule into the monomer state, occupation probabilities near the boundary are compared with bulk values. It is concluded that boundary effects in the fluid are confined to the first few layers of molecules.     

Three fluid hydrodynamics of superfluid3He

TheA ₂-transition from theA ₁ to theA-phase is the only known transition that seperates a state with a broken relative symmetry from one in which both constituent symmetries are independently broken. Therefore a question of interest here is what the Goldstone mode of this transition is. Employing two different points of view, one for its rigor and the other because of its plausible physical picture, a three fluid hydrodynamics is derived and employed to show that, with a grain of salt, theA ₂-transition can be taken as marked by the onset of spin wave in a restricted geometry and by that of second sound generally. More quantitatively, the transition of the Goldstone modes takes place below theA ₂ transitional temperature when the Leggett frequency is approached and is caused by two competing effects, hybridization and dispersion. In a fourth sound geometry these effects should be experimentally well accessible.     

Onset of shear thickening in a simple fluid

We report on nonequilibrium molecular-dynamics simulations of the shear-thickening transition in a simple fluid under shear. We relate the shear-thickening transition to the onset of instabilities in the flow profile and to that of dramatic variations in normal stress differences. The dependence of the critical shear rate, which indicates the onset of shear thickening, on density and temperature is rationalized by introducing a ratio between two characteristic times, quantifying the short-time mobility of a particle and the deformation imposed by the applied shear rate, respectively. The shear-thickening transition is shown to occur at a constant value for this ratio for all state points studied. From a structural point of view, this transition is accompanied by the formation of clusters as recently observed in experiments on complex fluids.Received: 26 July 2004, Published online: 21 September 2004PACS: 83.60.Rs Shear rate-dependent structure (shear thinning and shear thickening) - 47.50. + d Non-Newtonian fluid flows - 83.10.Mj Molecular dynamics, Brownian dynamics     

The one-dimensional Lennard-Jones system: collective fluctuations and breakdown of hydrodynamics

The dynamical correlations of a model consisting of particles constrained on the line and interacting with a nearest-neighbour Lennard-Jones potential are computed by molecular-dynamics simulations. A drastic qualitative change of the spectral shape, from a phonon-like to a diffusive form, is observed upon reducing the particle density even ad moderate temperatures. The latter scenario is due to the spontaneous fragmentation of the crystal-like structure into an ensemble of “clusters" colliding among themselves. In both cases, the spectral linewidths do not follow the usual q² behaviour for small wavenumbers q, thus signalling a breakdown of linearized hydrodynamics. This anomaly is traced back by the presence of correlations due to the reduced dimensionality.