Reduced Thermodynamic Description of Phase Separation in a Quasi-One-Dimensional Granular Gas.

We describe simulations of a quasi-one-dimensional, vibrated granular gas which exhibits an apparent phase separation into a liquidlike phase and a gaslike phase. In thermal equilibrium, such a phase separation in one dimension is prohibited by entropic considerations. We propose that the granular gas minimizes a function of the conserved mechanical variables alone: the particle number and volume. Simulations in small cells can be used to extract the equation of state and predict the coexisting pressure and densities, as confirmation of the minimization principle. Fluctuations in the system manifest themselves as persistent density waves but they do not destroy the phase-separated state.

The minimization of mechanical work in vibrated granular matter.

Experiments and computer simulations are carried out to investigate phase separation in a granular gas under vibration. The densities of the dilute and the dense phase are found to follow a lever rule and obey an equation of state. Here we show that the Maxwell equal-areas construction predicts the coexisting pressure and binodal densities remarkably well, even though the system is far from thermal equilibrium. This construction can be linked to the minimization of mechanical work associated with density fluctuations without invoking any concept related to equilibrium-like free energies.

Propulsion of a Two-Sphere Swimmer.

We describe experiments and simulations demonstrating the propulsion of a neutrally buoyant swimmer that consists of a pair of spheres attached by a spring, immersed in a vibrating fluid. The vibration of the fluid induces relative motion of the spheres which, for sufficiently large amplitudes, can lead to motion of the center of mass of the two spheres. We find that the swimming speed obtained from both experiment and simulation agree and collapse onto a single curve if plotted as a function of the streaming Reynolds number, suggesting that the propulsion is related to streaming flows. There appears to be a critical onset value of the streaming Reynolds number for swimming to occur. We observe a change in the streaming flows as the Reynolds number increases, from that generated by two independent oscillating spheres to a collective flow pattern around the swimmer as a whole. The mechanism for swimming is traced to a strengthening of a jet of fluid in the wake of the swimmer.

Spontaneous orbiting of two spheres levitated in a vibrated liquid.

In the absence of gravity, particles can form a suspension in a liquid irrespective of the difference in density between the solid and the liquid. If such a suspension is subjected to vibration, there is relative motion between the particles and the fluid which can lead to self-organization and pattern formation. Here, we describe experiments carried out to investigate the behavior of two identical spheres suspended magnetically in a fluid, mimicking weightless conditions. Under vibration, the spheres mutually attract and, for sufficiently large vibration amplitudes, the spheres are observed to spontaneously orbit each other. The collapse of the experimental data onto a single curve indicates that the instability occurs at a critical value of the streaming Reynolds number. Simulations reproduce the observed behavior qualitatively and quantitatively, and are used to identify the features of the flow that are responsible for this instability.

Emergent surface tension in vibrated, noncohesive granular media.

We describe experiments and simulations carried out to investigate spinodal decomposition in a vibrated, dry granular system. The dynamics is found to be similar to that of systems evolving under curvature-driven diffusion, which suggests the presence of an effective surface tension. By studying quasi-2D droplets in the steady state, we find behavior consistent with Laplace's equation, demonstrating the existence of an actual surface tension. Detailed measurements of the pressure tensor in the interfacial region show that the surface tension results predominantly from an anisotropy in the kinetic energy part of the pressure tensor, in contrast to thermodynamic systems where it arises from either the attractive interaction between particles or entropic considerations.

Liquid-gas phase separation in confined vibrated dry granular matter.

A new phase transition is observed experimentally in a dry granular gas subject to vertical vibration between two horizontal plates. Molecular dynamics simulations of this system allow us to investigate the observed phase separation in detail. We find a high-density, low temperature liquid, coexisting with a low-density, high temperature gas moving coherently. The importance of the coherent motion for phase separation is investigated using frequency modulation.

Chain formation of spheres in oscillatory fluid flows.

A collection of spherical particles subjected to horizontal oscillatory fluid flow is known to form chains perpendicular to the direction of the oscillation. We have developed computer simulations to model such a system and have validated them against experiments carried out in a small fluid-filled cell. In both experiment and simulation we find that the particles go through the same stages of evolution from a dispersed initial configuration to an ordered chain structure. We then use our computer simulations to investigate in detail the interactions responsible for chain formation and the interaction between fully formed chains.

Interaction between intruders in vibrated granular beds.

Two neutrally buoyant intruder particles in a granular bed fluidized by vertical, sinusoidal vibration are known to interact with each other over a range of about five intruder diameters. Using molecular dynamics simulations, we investigate in detail the spatial and temporal nature of this interaction. We show that the force of attraction between intruders can be calculated from the local density and kinetic energy using a simple equation of state. Moreover, the interaction can be changed from attractive to repulsive by reducing the coefficient of restitution between the intruders and host particles, one of the key results of this work.

Intruder clustering in three-dimensional granular beds.

We present results of computer simulations for neutrally buoyant intruders in a vertically vibrated three-dimensional granular bed of smaller host particles. Under sinusoidal excitation, pairs of intruders interact over a distance of several intruder diameters; a group of intruders forms a cluster. The strength of the interaction grows as the number of intruders is increased. We show that the tendency to cluster may be manipulated through the use of nonsinusoidal excitation, which allows partial mixing. Finally, we investigate the effects of walls on the clustering of intruders.

Interaction of spheres in oscillatory fluid flows.

Rigid spherical particles in oscillating fluid flows form interesting structures as a result of fluid mediated interactions. Here we show that spheres under horizontal vibration align themselves at right angles to the oscillation and sit with a gap between them. The details of this behavior have been investigated through experiments and simulations. We have carried out experiments in which a pair of stainless steel spheres is shaken horizontally in a cell filled with glycerol-water fluid mixtures of three different viscosities, at various frequencies and amplitudes of oscillation. There is an equilibrium gap between the particles resulting from a long-range attraction and a short-range repulsion. The size of the gap was found to depend on the fluid viscosity and the vibratory parameters, and we have identified two distinct scaling regimes for the dependence of the gap on the system parameters. Using a Navier-Stokes solver the same system was simulated. The interaction force between the spheres was measured and the streaming flows induced by the motion were determined.

Are Brazil nuts attractive?

We present event-driven simulation results for single and multiple intruders in a vertically vibrated granular bed. Under our vibratory conditions, the mean vertical position of a single intruder is governed primarily by a buoyancylike effect. Multiple intruders also exhibit buoyancy governed behavior; however, multiple neutrally buoyant intruders cluster spontaneously and undergo horizontal segregation. These effects can be understood by considering the dynamics of two neutrally buoyant intruders. We have measured an attractive force between such intruders which has a range of five intruder diameters, and we provide a mechanistic explanation for the origins of this force.

Controlled E-field gradient coils.

Peripheral neural stimulation is a major problem in current gradient coil designs. Induced current problems in patients relate directly to gradient strength and modulation frequency. Current designs of gradient coil tend to limit ultra-high-speed imaging methods such as echo-planar imaging through the effect of induced currents which produce tingling sensations and involuntary muscle twitch. Neural stimulation could also trigger epileptic fits and/or cardiac fibrillation. For reduction of induced currents, an important aspect is the coil geometry. It is desirable to design the gradient coil in such a way as to prevent closed loop circulating currents within the body. Preliminary results using a four-sector gradient coil with rectangular geometry, operating in a low mutual coupling mode, indicate significant reduction in the E-field within the subject volume of the coil. Reduction in induced currents in the patient allows safer operation at higher magnetic field strengths together with faster scans currently prohibited through neural stimulation effects in standard coil geometries.

Electric fields induced in a spherical volume conductor by temporally varying magnetic field gradients.

A homogeneous spherical volume conductor is used as a model system for the purpose of calculating electric fields induced in the human head by externally applied time-varying magnetic fields. We present results for the case where magnetic field gradient coils, used in magnetic resonance imaging (MRI), form the magnetic field, and we use these data to put limits on the rates of gradient change with time needed to produce nerve stimulation. The electric field is calculated analytically for the case of ideal longitudinal and transverse linear field gradients. We also show results from computer calculations yielding the electric field maps in a sphere when the field gradients are generated by a real MRI gradient coil set. In addition, the effect of shifting the sphere within each gradient coil volume is investigated. Numerical analysis shows similar results when applied to a model human head.

Analytic calculations of the E-fields induced by time-varying magnetic fields generated by cylindrical gradient coils.

Analytic expressions which allow the direct calculation of the electric field generated inside an infinite conducting cylinder by varying the current through the wires of any cylindrical coil are presented. These expressions provide some general insight into the spatial characteristics of the electric field generated inside the body by switched gradients and can be used to evaluate the locations where nerve stimulation by rapid gradient switching is likely to occur. They may also be employed at the design stage to produce gradient coils which can provide higher gradient switching rates without causing nerve stimulation. Using these expressions the electric field patterns produced by transverse and longitudinal, whole-body gradient coils were calculated. Example data are presented along with the associated magnetic field patterns. The effect on the induced electric field pattern of varying the body size and the size of the region of gradient linearity was explored.

A general approach to selection of multiple cubic volume elements using the ISIS technique.

The ISIS method is used regularly for the selection of a single cubic volume of tissue for in vivo investigation by high-resolution NMR spectroscopy. This technique has been extended on a theoretical basis to include the simultaneous selection of a number of cubes, the signals from which can be either assessed individually or in certain circumstances coadded to produce improvement in signal-to-noise ratio. The modification requires additional selective RF pulses in the spatial encoding prepulse period, and spatially localized spectra are produced by addition and subtraction of NMR signals in a manner similar to the original ISIS technique.