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We study the extended hydrodynamics proposed by Rosenau [Phys. Rev. A 40, 7193 (1989)] in the context of a regularization of the Chapman-Enskog expansion. We are able to prove that shock waves appear in finite time in Rosenau's extended Burgers equation, and we discuss the physical implications of this fact and its connection with a possible extension of hydrodynamics to the short-wavelength domain.
Small perturbations of the homogeneous cooling state for a low density granular gas are described by means of the linearized Boltzmann equation. The spectrum of the generator for this dynamics is shown to contain points corresponding to hydrodynamic excitations. The corresponding eigenvectors and eigenvalues are calculated to Navier-Stokes order and shown to agree with those obtained by the Chapman-Enskog method. The conditions for the hydrodynamic excitations to dominate all other excitations are discussed.
We present a thermodynamically consistent discrete fluid particle model for the simulation of a recently proposed set of hydrodynamic equations for a phase separating van der Waals fluid mixture [P. Español and C.A.P. Thieulot, J. Chem. Phys. 118, 9109 (2003)]. The discrete model is formulated by following a discretization procedure given by the smoothed particle hydrodynamics (SPH) method within the thermodynamically consistent general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework. Each fluid particle carries information on the mass, momentum, energy, and the mass fraction of the different components. The discrete model allows one to simulate nonisothermal dynamic evolution of phase separating fluids with surface tension effects while respecting the first and second laws of thermodynamics exactly.
The hydrodynamic description of probabilistic ballistic annihilation, for which no conservation laws hold, is an intricate problem with hard spherelike dynamics for which no exact solution exists. We consequently focus on simplified approaches, the Maxwell and very-hard-particle (VHP) models, which allows us to compute analytically upper and lower bounds for several quantities. The purpose is to test the possibility of describing such a far from equilibrium dynamics with simplified kinetic models. The motivation is also in turn to assess the relevance of some singular features appearing within the original model and the approximations invoked to study it. The scaling exponents are first obtained from the (simplified) Boltzmann equation, and are confronted against direct Monte Carlo simulations. Then, the Chapman-Enskog method is used to obtain constitutive relations and transport coefficients. The corresponding Navier-Stokes equations for the hydrodynamic fields are derived for both Maxwell and VHP models. We finally perform a linear stability analysis around the homogeneous solution, which illustrates the importance of dissipation in the possible development of spatial inhomogeneities.
A closed macroscopic equation for the motion of the two-dimensional adiabatic piston is derived from standard hydrodynamics. It predicts a damped oscillatory motion of the piston towards a final rest position, which depends on the initial state. In the limit of large piston mass, the solution of this equation is in quantitative agreement with the results obtained from both hard disk molecular dynamics and hydrodynamics. The explicit forms of the basic characteristics of the piston's dynamics, such as the period of oscillations and the relaxation time, are derived. The limitations of the theory's validity, in terms of the main system parameters, are established.
The hydrodynamic state of an impurity immersed in a low density granular gas is analyzed. Explicit expressions for the temperature and density fields of the impurity in terms of the hydrodynamic fields of the gas are derived. It is shown that the ratio between the temperatures of the two components, measuring the departure from the energy equipartition, only depends on the mechanical properties of the particles, being therefore constant in the bulk of the system. This ratio plays an important role in determining the density profile of the intruder and its position with respect to the gas, since it determines the sign of the pressure diffusion coefficient. The theoretical predictions are compared with molecular dynamics simulation results for the particular case of the steady state of an open vibrated granular system in the absence of macroscopic fluxes, and a satisfactory agreement is found.
We report results of investigations of a high-speed drainage of thin aqueous films squeezed between randomly nanorough surfaces. A significant decrease in the hydrodynamic resistance force as compared with that predicted by Taylor's equation is observed. However, this reduction in force does not represent the slippage. The measured force is exactly the same as that between equivalent smooth surfaces obeying no-slip boundary conditions, but located at the intermediate position between peaks and valleys of asperities. The shift in hydrodynamic thickness is shown to be independent of the separation and/or shear rate. Our results disagree with previous literature data reporting very large and shear-dependent boundary slip for similar systems.
We develop a new simulation method of colloidal suspensions, which we call a "fluid particle dynamics" (FPD) method. This FPD method, which treats a colloid as a fluid particle, removes the difficulties stemming from a solid-fluid boundary condition in the treatment of hydrodynamic interactions between the particles. The importance of interparticle hydrodynamic interactions in the aggregation process of colloidal particles is demonstrated as an example. This method can be applied to a wide range of problems in colloidal science.
Relative motion in a two-component, trapped atomic gas provides a sensitive probe of interactions. By studying the lowest frequency excitations of a two-spin-state gas confined in a magnetic trap, we have explored the transition from the collisionless to the hydrodynamic regime. As a function of collision rate, we observe frequency shifts as large as 6% as well as a dramatic, nonmonotonic dependence of the damping rate. The measurements agree qualitatively with expectations for behavior in the collisionless and hydrodynamic limits and are quantitatively compared to a classical kinetic model.
Molecular dynamics (MD) results for the dynamic structure of a He(0.77)Ne(0.23) gas mixture at two densities (15.8 and 36.1 nm(-3)) show a clear crossover from hydrodynamic modes to distinct excitations for the two species. The higher density dispension curve neatly shows high- and low-frequency branches setting on with a rather localized transition. The lower density results agree very well with existing neutron scattering data and, in particular, display hydrodynamic behavior up to k approximately 2 nm(-1), in contrast with the conclusions of previous simulation studies. A smooth transition to fast sound is shown to take place for 2<k/nm(-1)<5, where the present MD data fill the existing gap in the experimental results.
We describe direct measurements of the dynamics of two colloidal spheres before hydrodynamic interactions have had time to fully develop. We find that the dynamics of the two spheres are coupled at times significantly shorter than tau(nu), the time required for vorticity to diffuse between the two spheres. From the distance dependence of the measured coupling, we infer that hydrodynamic interactions develop in a sonic time scale.
In Newtonian and relativistic hydrodynamics the Riemann problem determines the evolution of a fluid which is initially characterized by two states having different rest-mass density, pressure, and velocity. When the fluid is allowed to relax, one of three possible wave patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a relativistic Riemann problem when velocities tangential to the initial discontinuity are present. A smooth transition from one wave pattern to another can be produced by varying the initial tangential velocities while maintaining the initial states unmodified. These special relativistic effects are produced by the Lorentz factors and do not have a Newtonian counterpart.
We consider the hydrodynamic modes for dense trapped ultracold gases, where the interparticle distance is comparable to the scattering length. We show that the experimental determination of the hydrodynamic mode frequencies allows one to obtain quite directly the equation of state of a dense gas. As an example, we investigate the case of two equal fermionic populations in different hyperfine states with attractive interaction.
The pair annihilation of smectic c-director defects with winding numbers +/-1 in a freestanding SmC film as a representative of the XY model is studied numerically, considering a full coupling of orientational degrees of freedom and hydrodynamics. A reduction of the annihilation time compared to the nonhydrodynamic treatment is observed. It is demonstrated that the +1 disclination moves considerably faster than the -1 one primarily due to hydrodynamic flow, weakly assisted also by elastic anisotropy. The stress tensor terms and material parameters relevant for this effect are identified.
We combine fluorescence correlation spectroscopy and sedimentation velocity measurements to probe the hydrodynamic behavior of tubulin dimers and nanoscopic tubulin rings. The rings are rigid, have circular geometry, and are monodisperse in size. We use the high-precision ratio of the sedimentation coefficients and that of the translational diffusion coefficients to validate theories for calculating the hydrodynamic properties of supramolecular structures.
Collective field theory for the Calogero model represents particles with fractional statistics in terms of hydrodynamic modes--density and velocity fields. We show that the quantum hydrodynamics of this model can be written as a single evolution equation on a real holomorphic Bose field--the quantum integrable Benjamin-Ono equation. It renders tools of integrable systems to studies of nonlinear dynamics of 1D quantum liquids.
The first hohlraum experiments on the National Ignition Facility (NIF) using the initial four laser beams tested radiation temperature limits imposed by plasma filling. For a variety of hohlraum sizes and pulse lengths, the measured x-ray flux shows signatures of filling that coincide with hard x-ray emission from plasma streaming out of the hohlraum. These observations agree with hydrodynamic simulations and with an analytical model that includes hydrodynamic and coronal radiative losses. The modeling predicts radiation temperature limits with full NIF (1.8 MJ), greater, and of longer duration than required for ignition hohlraums.
Hydrodynamic coupling between closely apposed lipid bilayer membranes can substantially slow the time scale of thermal fluctuations. These effects could dominate the kinetics of macromolecular interactions at membrane interfaces, and may exert important influences over the interactions between living cells. Here, we study a reconstituted membrane system consisting of two planar bilayers with average separation distances of 30-60 nm. This spacing range is comparable to that of natural intercellular junctions. Using real-time fluorescence interference contrast imaging, spatial and temporal characteristics of the thermal fluctuation spectra are monitored simultaneously. Strong hydrodynamic damping of the fluctuation time scale is observed whereas fluctuation spatial dimensions are unaltered by proximity to another surface. These observations provide experimental confirmation of recent theoretical models.