Thermal transport in a noncommutative hydrodynamics

Journal of Experimental and Theoretical Physics - We find the hydrodynamic equations of a system of particles constrained to be in the lowest Landau level. We interpret the hydrodynamic theory as a...     

Observation of shock waves in a strongly interacting Fermi gas

We study collisions between two strongly interacting atomic Fermi gas clouds. We observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as the clouds collide and subsequent evolution into a boxlike shape. We model the nonlinear dynamics of these collisions by using quasi-1D hydrodynamic equations. Our simulations of the time-dependent density profiles agree very well with the data and provide clear evidence of shock wave formation in this universal quantum hydrodynamic system.     

Polymer collapse in the presence of hydrodynamic interactions

We investigate numerically the dynamical behaviour of a polymer chain collapsing in a dilute solution. The rate of collapse is measured with and without the presence of hydrodynamic interactions. We find that hydrodynamic interactions both accelerate polymer collapse and alter the folding pathway.     

Relativistic hydrodynamic scaling from the dynamics of quantum field theory

Relativistic hydrodynamic scaling or boost invariance is a particularly important hydrodynamic regime, describing collective flows of relativistic many body systems and is used in the interpretation of experiments from high-energy cosmic rays to relativistic heavy-ion collisions. We show evidence for the emergence of hydrodynamic scaling from the dynamics of relativistic quantum field theory. We consider a scalar lambdaphi(4) model in 1+1 dimensions in the Hartree approximation and study the relativistic collisions of two kinks and the decay of a localized high-energy density region. We find that thermodynamic scalar isosurfaces show approximate boost invariance at high-energy densities.     

Giant amplification of interfacially driven transport by hydrodynamic slip: diffusio-osmosis and beyond

We demonstrate that "moderate" departures from the no-slip hydrodynamic boundary condition (hydrodynamic slip lengths in the nanometer range) can result in a very large enhancement--up to 2 orders of magnitude--of most interfacially driven transport phenomena. We study analytically and numerically the case of neutral solute diffusio-osmosis in a slab geometry to account for nontrivial couplings between interfacial structure and hydrodynamic slip. Possible outcomes are fast transport of particles in externally applied or self-generated gradient, and flow enhancement in nano- or microfluidic geometries.     

Longitudinal viscous hydrodynamic evolution for the shattered colour glass condensate

We investigate hydrodynamic evolution of the quark-gluon plasma for the colour glass condensate type initial conditions. We solve full second-order viscous hydrodynamic equations in the longitudinal direction to find that non-boost invariant expansion leads to visible deformation on the initial rapidity distribution. The results indicate that hydrodynamic evolution with entropy production from viscosity plays an important role in determining parameters for the initial distributions.     

Fluctuations of one dimensional Ginzburg-Landau models in nonequilibrium

We study the fluctuation of one dimensional Ginzburg-Landau models in nonequilibrium along the hydrodynamic (diffusion) limit. The hydrodynamic limit has been proved to be a nonlinear diffusion equation by Fritz, Guo-Papanicolaou-Varadhan, etc. We proved that if the potential is uniformly convex then the fluctuation process is governed by an Ornstein-Uhlenbeck process whose drift term is obtained by formally linearizing the hydrodynamic equation.Work partially supported by the National Science Foundation under grant no. DMS 8806731 and DMS 9101196     

The theoretical analysis of the lattice hydrodynamic models for traffic flow theory

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg-de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results.     

Hydrodynamic interactions in self similar structures, such as polymers

We study the hydrodynamic properties of polymers and more generally self-similar structures using a new recursion model. The hydrodynamic interaction between monomers is modeled by the standard Green's function of Stokes flow in which an ultrametric distance is substituted for the usual Euclidean distance. This leads to a model where the long-range hydrodynamic interactions and the long-range correlations of the polymer conformation can both be accounted for and yet allow for analytical solutions. We explore the asymptotic as well as the finite size corrections to the scaling behavior with this model. In order to compare the results of the present scheme with more conventional techniques a generalized version of the existing mean field results by Kirkwood and Riseman for the hydrodynamic drag is introduced. Received 26 August 1998 and Received in final form 7 December 1998     

Breakdown of hydrodynamics in a simple one-dimensional fluid

We investigate the behavior of a one-dimensional diatomic fluid under a shock wave excitation. We find that the properties of the resulting shock wave are in striking contrast with those predicted by hydrodynamic and kinetic approaches; e.g., the hydrodynamic profiles relax algebraically toward their equilibrium values. Deviations from local thermodynamic equilibrium are persistent, decaying as a power law of the distance to the shock layer. Nonequipartition is observed infinitely far from the shock wave, and the velocity-distribution moments exhibit multiscaling. These results question the validity of simple hydrodynamic theories to understand collective behavior in 1D fluids.     

Hydrodynamic Lyapunov Modes in Translation-Invariant Systems

We study the implications of translation invariance on the tangent dynamics of extended dynamical systems, within a random matrix approximation. In a model system, we show the existence of hydrodynamic modes in the slowly growing part of the Lyapunov spectrum, which are analogous to the hydrodynamic modes discovered numerically by Dellago, Posch, and Hoover. The hydrodynamic Lyapunov vectors lose the typical random structure and exhibit instead the structure of weakly perturbed coherent long-wavelength waves. We show further that the amplitude of the perturbations vanishes in the thermodynamic limit, and that the associated Lyapunov exponents are universal.     

Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids

In this paper, we study flexural vibrations of a cantilever beam with thin rectangular cross section submerged in a quiescent viscous fluid and undergoing oscillations whose amplitude is comparable with its width. The structure is modeled using Euler–Bernoulli beam theory and the distributed hydrodynamic loading is described by a single complex-valued hydrodynamic function which accounts for added mass and fluid damping experienced by the structure. We perform a parametric 2D computational fluid dynamics analysis of an oscillating rigid lamina, representative of a generic beam cross section, to understand the dependence of the hydrodynamic function on the governing flow parameters. We find that increasing the frequency and amplitude of the vibration elicits vortex shedding and convection phenomena which are, in turn, responsible for nonlinear hydrodynamic damping. We establish a manageable nonlinear correction to the classical hydrodynamic function developed for small amplitude vibration and we derive a computationally efficient reduced order modal model for the beam nonlinear oscillations. Numerical and theoretical results are validated by comparison with ad hoc designed experiments on tapered beams and multimodal vibrations and with data available in the literature. Findings from this work are expected to find applications in the design of slender structures of interest in marine applications, such as biomimetic propulsion systems and energy harvesting devices.     

Failure and success of hydrodynamic interaction models

In suspensions with charged particles, electrostatic forces and hydrodynamic interactions are both important to describe the system. We study different models of hydrodynamic interaction for monopolarly charged particles in a non-polar liquid. In this case, there is no screening of the Coulomb repulsion, so the repulsion between all pairs must be taken into account. The particles are expected to drift away from each other, however at a lower rate when hydrodynamic interaction between the particles is taken into account. Existing, frequently used models of hydrodynamic interactions tend to overestimate the slowing down of the charged particles, even to the extent that the particles effectively attract each other. This is demonstrated for some selected particle setups. We find that these anomalies even occur in dilute systems, if they contain sufficiently many particles. We explain why these anomalies can be avoided by an approach, in which the superposition of interactions is done in the friction tensor instead of the mobility tensor.     

Coherent structures in monolayers of swimming particles

We report various types of coherent structures in suspensions of spherical particles swimming in a monolayer. We solve the fluid dynamics precisely from far-field hydrodynamic interactions to lubrication between two near-contact surfaces. The simulation results clearly illustrate that coherent structures, such as aggregation, mesoscale spatiotemporal motion, and band formation, can be generated by purely hydrodynamic interactions.     

On the propagation of hydrodynamic interactions

We present explicit expressions in real space and time for the equilibrium correlation functions of the density and velocity fields in a compressible fluid. This allows to discuss the time scales involved in the propagation of hydrodynamic interactions and its relevance on the dynamics of suspended colloidal particles. We show that hydrodynamic interactions develop in a sonic time scale, not in a vorticity time scale.     

Effective screening of hydrodynamic interactions in charged colloidal suspensions

We investigate the hydrodynamic interaction in suspensions of charged colloidal silica spheres. The volume fraction as well as the range of the electrostatic repulsion between the spheres is varied. Using a combination of dynamic x-ray scattering, cross-correlated dynamic light scattering, and small angle x-ray scattering, the hydrodynamic function H(q) is determined experimentally. The effective hydrodynamic interactions are found to be screened, if the range of the direct interaction is relatively long and the static density correlations are strong. This observation of effective hydrodynamic screening is in marked contrast to hard-sphere-like systems.     

Hydrodynamic and viscoelastic effects in polymer diffusion

We develop a fluctuating hydrodynamics approach to study the impact of the hydrodynamic and viscoelastic interactions on the motion of the center of mass of a polymer as well as on the relaxation of Rouse modes, either in a Θ solvent or in a melt of identical unentangled chains. We show that this method allows us to describe the effect of hydrodynamic interactions beyond the Zimm (for a single chain in a Θ solvent) or the Rouse models (for an unentangled melt). In the latter case, we recover the same important effect of the viscoelastic hydrodynamic interactions on the center-of-mass diffusion, first described in Farago et?al (2011 Phys. Rev. Lett. 107 178301).     

Hydrodynamic flow patterns and synchronization of beating cilia

We calculate the hydrodynamic flow field generated far from a cilium which is attached to a surface and beats periodically. In the case of two beating cilia, hydrodynamic interactions can lead to synchronization of the cilia, which are nonlinear oscillators. We present a state diagram where synchronized states occur as a function of the distance of cilia and the relative orientation of their beat. Synchronized states occur with different relative phases. In addition, asynchronous solutions exist. Our work could be relevant for the synchronized motion of cilia generating hydrodynamic flows on the surface of cells.     

Nonlinear Dust Acoustic Waves in Strongly Coupled Dusty Plasmas with Positively Charged Dust Particles

The nonlinear propagation of dust acoustic waves is investigated in four-component plasmas consisting of positively charged dust grains, trapped ions, nonthermal electrons, and photoelectron due to ultraviolet irradiation.We use generalized viscoelastic hydrodynamic model for strongly coupled dust grain. In the weak nonlinearity limit, a modified Kadomstev–Petviashvili(KP) equation and a modified KP-Burger equation, which have a damping term coming from nonadiabatic charge variation, have been derived in the kinetic regime and hydrodynamic regime, respectively. With the increasing of UV photon flux, the hydrodynamic regime changes to kinetic regime. The approximate analytical line soliton and shock solutions are investigated in the kinetic regime and hydrodynamic regime, respectively.     

Hydrodynamic modes in dense trapped ultracold gases

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.