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Sensory integration in the hydrodynamic world of rainbow trout.

Water movements, of both abiotic and biotic origin, provide a wealth of information for fishes. They detect these water movements by arrays of hydrodynamic sensors located on the surface of the body as superficial neuromasts and embedded in subdermal lateral line canals. Recently, the anatomical dichotomy between superficial and canal neuromasts has been matched by demonstrations of a corresponding functional dichotomy. Superficial neuromasts are sensitive to water flows over the surface of the fish and are the sub-modality that participates in orientation to water currents, a behaviour known as rheotaxis. The canal neuromasts are sensitive to water vibration and it is this sub-modality that determines the localization of artificial prey. Recently, however, it has been shown that the complex behaviour of natural prey capture in the dark requires input from both lateral line sensory submodalities and here we show that the ability of trout to hold station behind a stationary object in fast flowing water also requires integration of information from both sub-modalities.

Animals↗

Hydrodynamic modelling of aquatic suction performance and intra-oral pressures: limitations for comparative studies.

The magnitude of sub-ambient pressure inside the bucco-pharyngeal cavity of aquatic animals is generally considered a valuable metric of suction feeding performance. However, these pressures do not provide a direct indication of the effect of the suction act on the movement of the prey item. Especially when comparing suction performance of animals with differences in the shape of the expanding bucco-pharyngeal cavity, the link between speed of expansion, water velocity, force exerted on the prey and intra-oral pressure remains obscure. By using mathematical models of the heads of catfishes, a morphologically diverse group of aquatic suction feeders, these relationships were tested. The kinematics of these models were fine-tuned to transport a given prey towards the mouth in the same way. Next, the calculated pressures inside these models were compared. The results show that no simple relationship exists between the amount of generated sub-ambient pressure and the force exerted on the prey during suction feeding, unless animals of the same species are compared. Therefore, for evaluating suction performance in aquatic animals in future studies, the focus should be on the flow velocities in front of the mouth, for which a direct relationship exists with the hydrodynamic force exerted on prey.

Animals↗

Towards the simplest hydrodynamic lattice-gas model.

It has been known since 1986 that it is possible to construct simple lattice-gas cellular automata whose hydrodynamics are governed by the Navier-Stokes equations in two dimensions. The simplest such model heretofore known has six bits of state per site on a triangular lattice. In this work, we demonstrate that it is possible to construct a model with only five bits of state per site on a Kagome lattice. Moreover, the model has a simple, deterministic set of collision rules and is easily implemented on a computer. In this work, we derive the equilibrium distribution function for this lattice-gas automaton and carry out the Chapman-Enskog analysis to determine the form of the Navier-Stokes equations.

Computer Simulation↗

Hydrodynamics of granular gases of viscoelastic particles.

Our study examines the long-time behaviour of a force-free granular gas of viscoelastic particles, for which the coefficient of restitution depends on the impact velocity, as it follows from the solution of the impact problem for viscoelastic spheres. Starting from the Boltzmann equation, we derived the hydrodynamic equations and obtained microscopic expressions for the transport coefficients in terms of the elastic and dissipative parameters of the particle material. We performed the stability analysis of the linearized set of equations and found that any inhomogeneities and vortices vanish after a long time and the system approaches the flow-free stage of homogeneous density. This behaviour is in contrast to that of a gas consisting of particles which interact via a (non-realistic) constant coefficient of restitution, for which inhomogeneities (clusters) and vortex patterns have been proven to arise and to continuously develop.

Colloids↗

Generalized hydrodynamics of reaction-diffusion systems and dissipative structures.

Generalized hydrodynamics (GH) are derived and used to describe a reaction-diffusion system. The derived GH equations are hyperbolic and are shown to be more general and more suitable than the conventional parabolic reaction-diffusion equations, especially in small geometries. These equations are applied to the study of dissipative structures in glycolysis and are solved numerically using the finite-element method. The solution exhibits a multitude of wave and Turing patterns. The time evolution of the calortropy production for the obtained pattern seems to correlate with the increasing complexity of the system.

Journal Article↗

Discrete-element modelling and smoothed particle hydrodynamics: potential in the environmental sciences.

Particle-based simulation methods, such as the discrete-element method and smoothed particle hydrodynamics, have specific advantages in modelling complex three-dimensional (3D) environmental fluid and particulate flows. The theory of both these methods and their relative advantages compared with traditional methods will be discussed. Examples of 3D flows on realistic topography illustrate the environmental application of these methods. These include the flooding of a river valley as a result of a dam collapse, coastal inundation by a tsunami, volcanic lava flow and landslides. Issues related to validation and quality data availability are also discussed.

Algorithms↗

An automated hydrodynamic process for controlled, unbiased DNA shearing.

An automated, inexpensive, easy-to-use, and reproducible technique for controlled, random DNA fragmentation has been developed. The technique is based on point-sink hydrodynamics that result when a DNA sample is forced through a small hole by a syringe pump. Commercially available components are used to reduce the cost and complexity of the instrument. The design is optimized to reduce the volume of sample required and to speed processing time. Shearing of the samples can be completely automated by computer control. Ninety percent of sheared DNA fragments fall within a twofold size distribution that is highly reproducible. Three parameters are critical: the flow geometry, the flow rate, and a minimum number of iterations. Shearing is reproducible over a wide range of temperatures, DNA concentrations, and initial DNA size. The cloning efficiency of the sheared DNA is very good even without end repair, the distribution of assembled sequences is random, and there is no sequence bias at the ends of sheared fragments that have been cloned. The instrument, called the Point-sink Shearer (PtS), has already been exported successfully to many other laboratories.

Automation↗

Hydrodynamics of resonance oscillations of columns of inelastic particles.

We study oscillations of a one-dimensional (1D) column of N slightly inelastic particles, produced by a piston vibrating at one end of a closed tube. It is found that for large enough vibrational amplitudes of the piston, the column oscillates periodically with the period equal to the vibrational period. The oscillation patterns are governed by the shock waves propagating across the column. The averaged kinetic energy per particle is shown to be proportional to the square of the vibrational frequency, omega. This energy also strongly depends on the vibrational amplitude. The maximal value of this kinetic energy achievable by these external vibrations is found to be of order omega(2)L(2), where L is the total volume (length) of the tube free of particles. The above results on the column resonance oscillations are also predicted by a 3D hydrodynamic model of an inelastic granular gas.

Journal Article↗

Bosonization, vicinal surfaces, and hydrodynamic fluctuation theory.

Through a Euclidean path integral we establish that the density fluctuations of a Fermi fluid in one dimension are related to vicinal surfaces and to the stochastic dynamics of particles interacting through long range forces with inverse distance decay. In the surface picture one easily obtains the Haldane relation, and identifies the scaling exponents governing the low energy, Luttinger liquid behavior. For the stochastic particle model we develop a hydrodynamic fluctuation theory, through which in some cases the large distance Gaussian fluctuations are proved nonperturbatively.

Journal Article↗

Hydrodynamic simulation of subpicosecond laser interaction with solid-density matter

The interaction of ultrashort subpicosecond laser pulses with initially cold and solid matter is investigated in a wide intensity range (10(11) to 10(17) W/cm(2)) by means of the hydrodynamic code MULTI-FS, which is an extension of the long pulse version of MULTI [R. Ramis, R. Schmalz, and J. Meyer-ter-Vehn, Comput. Phys. Commun. 49, 475 (1988)]. Essential modifications for the treatment of ultrashort pulses are the solution of Maxwell's equations in a steep gradient plasma, consideration of the nonequilibrium between electrons and ions, and a model for the electrical and thermal conductivity covering the wide range from the solid state to the high temperature plasma. The simulations are compared with several absorption measurements performed with aluminum targets at normal and oblique incidence. Good agreement is obtained by an appropriate choice of the electron-ion energy exchange time (characterized by 10 to 20 ps in cold solid Al). In addition we discuss the intensity scaling of the temperature, of the pressure, and of the density, where the laser energy is deposited in the expanding plasma, as well as the propagation of the heat wave and the shock wave into the solid. For laser pulse durations >/=150 fs considered in this paper the amount of isochorically heated matter at solid density is determined by the depth of the electron heat wave in the whole intensity range.

Journal Article↗

Hydrodynamic theory of density relaxation in near-critical fluids

This paper gives a complete hydrodynamic theory of density relaxation after a temperature step at the boundary of a cell filled with a nearly supercritical pure fluid in microgravity conditions. It uses the matched asymptotic expansion technique to solve the one-dimensional Navier-Stokes equations written for a viscous, low-heat-diffusing, near-critical van der Waals gas. The continuous description obtained for density relaxation in space and time confirms that it is governed by two fundamental mechanisms, the piston effect and heat diffusion. It gives a space-resolved description of density inside the cell during the divergently long heat diffusion time, which is shown to be the ultimate one to achieve complete thermodynamic equilibrium. On that very long time scale, the still measurable density inhomogeneities are shown to follow the diffusion of the vanishingly small temperature perturbations left by the piston effect. Temperature, which relaxes first to nonmeasurable values, and density, which relaxes on a much longer time scale, may thus appear to be uncoupled. The relaxation of density on the diffusion time scale is shown to be driven by a bulk expansion-compression process slowly moving at the heat diffusion speed, which is generated by heat diffusion coupled with the large compressibility of the near-critical fluid. The process is shown to be the signature of the thermoacoustic events that occur during the very short piston effect time period. The generalization of the theory to real critical behavior opens the present results to future experimental investigation.

Journal Article↗

Disjoining potential and spreading of thin liquid layers in the diffuse-interface model coupled to hydrodynamics

The hydrodynamic phase field model is applied to the problem of film spreading on a solid surface. The disjoining potential, responsible for modification of the fluid properties near a three-phase contact line, is computed from the solvability conditions of the density field equation with appropriate boundary conditions imposed on the solid support. The equations describing the motion of a spreading film are derived in the lubrication approximation (in the limit of small contact angles). In the case of quasiequilibrium spreading, it is shown that the correct sharp-interface limit is obtained, and sample solutions are obtained by numerical integration. It is further shown that evaporation or condensation may strongly affect the dynamics near the contact line, and that it is necessary to account for kinetic retardation of the interphase transport to build up a consistent theory.

Journal Article↗

Hydrodynamic theory for granular gases

A granular gas subjected to a permanent injection of energy is described by means of hydrodynamic equations derived from a moment expansion method. The method uses as reference function not a Maxwellian distribution f(M) but a distribution f(0)=Phif(M), such that Phi adds a fourth cumulant kappa to the velocity distribution. The formalism is applied to a stationary conductive case showing that the theory fits extraordinarily well the results coming from our Newtonian molecular dynamic simulations once we determine kappa as a function of the inelasticity of the particle-particle collisions. The shape of kappa is independent of the size N of the system.

Journal Article↗

Two-dimensional hydrodynamic lattice-gas simulations of binary immiscible and ternary amphiphilic fluid flow through porous media

The behavior of two-dimensional binary and ternary amphiphilic fluids under flow conditions is investigated using a hydrodynamic lattice-gas model. After the validation of the model in simple cases (Poiseuille flow, Darcy's law for single component fluids), attention is focused on the properties of binary immiscible fluids in porous media. An extension of Darcy's law which explicitly admits a viscous coupling between the fluids is verified, and evidence of capillary effects is described. The influence of a third component, namely, surfactant, is studied in the same context. Invasion simulations have also been performed. The effect of the applied force on the invasion process is reported. As the forcing level increases, the invasion process becomes faster and the residual oil saturation decreases. The introduction of surfactant in the invading phase during imbibition produces new phenomena, including emulsification and micellization. At very low fluid forcing levels, this leads to the production of a low-resistance gel, which then slows down the progress of the invading fluid. At long times (beyond the water percolation threshold), the concentration of remaining oil within the porous medium is lowered by the action of surfactant, thus enhancing oil recovery. On the other hand, the introduction of surfactant in the invading phase during drainage simulations slows down the invasion process-the invading fluid takes a more tortuous path to invade the porous medium-and reduces the oil recovery (the residual oil saturation increases).

Journal Article↗

Instability of symmetric couette flow in a granular gas: hydrodynamic field profiles and transport

We investigated the inelastic hard-disk gas sheared by two parallel bumpy walls (Couette flow). In our molecular dynamic simulations we found a sensitivity to the asymmetries of the initial particle positions and velocities and an asymmetric stationary state, where the deviation from (anti)symmetric hydrodynamic fields is stronger as the normal restitution coefficient decreases. For better understanding of this sensitivity we carried out a linear stability analysis of the former kinetic theoretical solution [J. T. Jenkins and M. W. Richman, J. Fluid. Mech. 171, 53 (1986)] and found it to be unstable. The effect of this asymmetry on the self-diffusion coefficient is also discussed.

Journal Article↗

Nonlinear hydrodynamical approach to granular materials.

We propose a nonlinear hydrodynamical model of granular materials. We show how this model describes the formation of a sandpile from a homogeneous distribution of material under gravity, and then discuss a simulation of a rotating sandpile which shows, in qualitative agreement with experiment, a static and dynamic angle of repose.

Journal Article↗

Finite time singularities in a class of hydrodynamic models.

Models of inviscid incompressible fluid are considered, with the kinetic energy (i.e., the Lagrangian functional) taking the form L approximately integral k(alpha)/vk/2dk in 3D Fourier representation, where alpha is a constant, 0<alpha<1. Unlike the case alpha=0 (the usual Eulerian hydrodynamics), a finite value of alpha results in a finite energy for a singular, frozen-in vortex filament. This property allows us to study the dynamics of such filaments without the necessity of a regularization procedure for short length scales. The linear analysis of small symmetrical deviations from a stationary solution is performed for a pair of antiparallel vortex filaments and an analog of the Crow instability is found at small wave numbers. A local approximate Hamiltonian is obtained for the nonlinear long-scale dynamics of this system. Self-similar solutions of the corresponding equations are found analytically. They describe the formation of a finite time singularity, with all length scales decreasing like (t*-t)(1/(2-alpha)), where t* is the singularity time.

Journal Article↗

Hydrodynamic approach to the interaction of a relativistic ultrashort laser pulse with an underdense plasma.

The interaction of an ultrashort, high peak power laser pulse with an underdense plasma is investigated within a physical model based on the three-dimensional cold hydrodynamic approach, which allows one to study the dynamics of the laser pulse and of the generated wakefields self-consistently, in the fully relativistic, strongly nonlinear regime. Our model is developed with the aim of describing very short laser pulses (with l(0)<lambdap and l(0)<<l perpendicular, where l(0),l perpendicular, lambdap are the pulse length, its transverse scale, and the plasma wavelength, respectively) down to single cycle radiation wave packets, which have become available with the recent progress in laser technology. The space-time structure and the evolution of large quasistatic electric and magnetic fields are studied, together with the pulse dynamics, by the direct numerical integration of the relativistic fluid and field equations, within the extended paraxial approximation.

Journal Article↗