arXiv subjects

Harry L. Swinney

Publications and source records attributed to Harry L. Swinney.

At least 37 records · Page 2Linked to original sources

arXiv2007

Geometry-induced asymmetric diffusion

Past work has shown that ions can pass through a membrane more readily in one direction than the other. We demonstrate here in a model and an experiment that for a mixture of small and large particles such asymmetric diffusion can arise solely from an asymmetry in the geometry of the pores of the membrane. Our deterministic simulation considers a two-dimensional gas of elastic disks of two sizes diffusing through a membrane, and our laboratory experiment examines the diffusion of glass beads of two sizes through a metal membrane. In both experiment and simulation, the membrane is permeable only to the smaller particles, and the asymmetric pores lead to an asymmetry in the diffusion rates of these particles. The presence of even a small percentage of large particles can clog a membrane, preventing passage of the small particles in one direction while permitting free flow of the small particles in the other direction. The purely geometric kinetic constraints may play a role in common biological contexts such as membrane ion channels.

cond-mat.soft↗

arXiv2006

An invariant distribution in static granular media

We have discovered an invariant distribution for local packing configurations in static granular media. This distribution holds in experiments for packing fractions covering most of the range from random loose packed to random close packed, for beads packed both in air and in water. Assuming only that there exist elementary cells in which the system volume is subdivided, we derive from statistical mechanics a distribution that is in accord with the observations. This universal distribution function for granular media is analogous to the Maxwell-Boltzmann distribution for molecular gasses.

cond-mat.dis-nn↗

arXiv2006

Phase transition in a static granular system

We find that a column of glass beads exhibits a well-defined transition between two phases that differ in their resistance to shear. Pulses of fluidization are used to prepare static states with well-defined particle volume fractions $ϕ$ in the range 0.57-0.63. The resistance to shear is determined by slowly inserting a rod into the column of beads. The transition occurs at $ϕ=0.60$ for a range of speeds of the rod.

cond-mat.soft↗

arXiv2006

Role of friction in pattern formation in oscillated granular layers

Particles in granular flows are often modeled as frictionless (smooth) inelastic spheres; however, there exist no frictionless grains, just as there are no elastic grains. Our molecular dynamics simulations reveal that friction is essential for realistic modeling of vertically oscillated granular layers: simulations of frictionless particles yield patterns with an onset at a container acceleration about 30% smaller than that observed in experiments and simulations with friction. More importantly, even though square and hexagonal patterns form for a wide range of the oscillation parameters in experiments and in our simulations of frictional inelastic particles, only stripe patterns form in the simulations without friction, even if the inelasticity is increased to obtain as much dissipation as in frictional particles. We also consider the effect of particle friction on the shock wave that forms each time the granular layer strikes the container. While a shock wave still forms for frictionless particles, the height and time dependence of the hydrodynamic fields differ for the cases with and without friction.

cond-mat.soft↗

arXiv2006

Fjords in viscous fingering: Selection of width and opening angle

Our experiments on viscous fingering of air into oil contained between closely spaced plates reveal two selection rules for the fjords of oil that separate fingers of air. (Fjords are the building blocks of solutions of the zero-surface-tension Laplacian growth equation.) Experiments in rectangular and circular geometries yield fjords with base widths 1/2 lambda_c, where lambda_c is the most unstable wavelength from a linear stability analysis. Further, fjords open at an angle of 8.0 degrees plus or minus 1.0 degree. These selection rules hold for a wide range of pumping rates and fjord lengths, widths, and directions.

nlin.PS↗

arXiv2006

Signatures of glass formation in a fluidized bed of hard spheres

We demonstrate that a fluidized bed of hard spheres during defluidization displays properties associated with formation of a glass. The final state is rate dependent, and as this state is approached, the bed exhibits heterogeneity with increasing time and length scales. The formation of a glass results in the loss of fluidization and an arrest of macroscopic particle motion. Microscopic motion persists in this state, but the bed can be jammed by application of a small increase in flow rate. Thus a fluidized bed can serve as a test system for studies of glass formation and jamming.

cond-mat.stat-mech↗

arXiv2006

Statistical mechanics of two-dimensional turbulence

The statistical mechanical description of two-dimensional inviscid fluid turbulence is reconsidered. Using this description, we make predictions about turbulent flow in a rapidly rotating laboratory annulus. Measurements on the continuously forced, weakly dissipative flow reveal coherent vortices in a mean zonal flow. Statistical mechanics has two crucial requirements for equilibrium: statistical independence of macro-cells (subsystems) and additivity of invariants of macro-cells. We use additivity to select the appropriate Casimir invariants from the infinite set available in vortex dynamics, and we do this in such a way that the exchange of micro-cells within a macro-cell does not alter an invariant of a macro-cell. A novel feature of the present study is our choice of macro-cells, which are continuous phase space curves based on mean values of the streamfunction. Quantities such as energy and enstrophy can be defined on each curve, and these lead to a local canonical distribution that is also defined on each curve. Our approach leads to the prediction that on a mean streamfunction curve there should be a linear relation between the ensemble-averaged potential vorticity and the time-averaged streamfunction, and our laboratory data are in good accord with this prediction. Further, the approach predicts that although the probability distribution function for potential vorticity in the entire system is non-Gaussian, the distribution function of micro-cells should be Gaussian on the macro-cells, i.e., for curves defined by mean values of the streamfunction. This prediction is also supported by the data. While the statistical mechanics approach used was motivated by and applied to experiments on turbulence in a rotating annulus, the approach is quite general and is applicable to a large class of Hamiltonian systems.

cond-mat.soft↗

arXiv2005

The Universality Class of Diffusion Limited Aggregation and Viscous Fingering

We investigate whether fractal viscous fingering and diffusion limited aggregates are in the same scaling universality class. We bring together the largest available viscous fingering patterns and a novel technique for obtaining the conformal map from the unit circle to an arbitrary singly connected domain in two dimensions. These two Laplacian fractals appear different to the eye; in addition, viscous fingering is grown in parallel and the aggregates by a serial algorithm. Nevertheless, the data strongly indicate that these two fractal growth patterns are in the same universality class.

cond-mat.dis-nn↗

arXiv2005

From time series to superstatistics

Complex nonequilibrium systems are often effectively described by a `statistics of a statistics', in short, a `superstatistics'. We describe how to proceed from a given experimental time series to a superstatistical description. We argue that many experimental data fall into three different universality classes: chi^2-superstatistics (Tsallis statistics), inverse chi^2-superstatistics, and log-normal superstatistics. We discuss how to extract the two relevant well separated superstatistical time scales tau and T, the probability density of the superstatistical parameter beta, and the correlation function for beta from the experimental data. We illustrate our approach by applying it to velocity time series measured in turbulent Taylor-Couette flow, which is well described by log-normal superstatistics and exhibits clear time scale separation.

cond-mat.stat-mech↗

arXiv2005

Stationary state volume fluctuations in a granular medium

A statistical description of static granular material requires ergodic sampling of the phase space spanned by the different configurations of the particles. We periodically fluidize a column of glass beads and find that the sequence of volume fractions phi of post-fluidized states is history independent and Gaussian distributed about a stationary state. The standard deviation of phi exhibits, as a function of phi, a minimum corresponding to a maximum in the number of statistically independent regions. Measurements of the fluctuations enable us to determine the compactivity X, a temperature-like state variable introduced in the statistical theory of Edwards and Oakeshott [Physica A {\bf 157}, 1080 (1989)].

cond-mat.stat-mech↗

arXiv2005

Extraction of coherent structures in a rotating turbulent flow experiment

The discrete wavelet packet transform (DWPT) and discrete wavelet transform (DWT) are used to extract and study the dynamics of coherent structures in a turbulent rotating fluid. Three-dimensional (3D) turbulence is generated by strong pumping through tubes at the bottom of a rotating tank (48.4 cm high, 39.4 cm diameter). This flow evolves toward two-dimensional (2D) turbulence with increasing height in the tank. Particle Image Velocimetry (PIV) measurements on the quasi-2D flow reveal many long-lived coherent vortices with a wide range of sizes. The vorticity fields exhibit vortex birth, merger, scattering, and destruction. We separate the flow into a low-entropy ``coherent'' and a high-entropy ``incoherent'' component by thresholding the coefficients of the DWPT and DWT of the vorticity fields. Similar thresholdings using the Fourier transform and JPEG compression together with the Okubo-Weiss criterion are also tested for comparison. We find that the DWPT and DWT yield similar results and are much more efficient at representing the total flow than a Fourier-based method. Only about 3% of the large-amplitude coefficients of the DWPT and DWT are necessary to represent the coherent component and preserve the vorticity probability density function, transport properties, and spatial and temporal correlations. The remaining small amplitude coefficients represent the incoherent component, which has near Gaussian vorticity PDF, contains no coherent structures, rapidly loses correlation in time, and does not contribute significantly to the transport properties of the flow. This suggests that one can describe and simulate such turbulent flow using a relatively small number of wavelet or wavelet packet modes.

physics.flu-dyn↗

arXiv2005

Velocity difference statistics in turbulence

We unify two approaches that have been taken to explain the non-Gaussian probability distribution functions (PDFs) obtained in measurements of longitudinal velocity differences in turbulence, and we apply our approach to Couette-Taylor turbulence data. The first approach we consider was developed by Castaing and coworkers, who obtained the non-Gaussian velocity difference PDF from a superposition of Gaussian distributions for subsystems that have a particular energy dissipation rate at a fixed length scale [Castaing et al., {\it Physica D} {\bf 46}, 177 (1990)]. Another approach was proposed by Beck and Cohen, who showed that the observed PDFs can be obtained from a superposition of Gaussian velocity difference PDFs in subsystems conditioned on the value of an intensive variable (inverse ``effective temperature'') in each subsystem [Beck and Cohen, {\it Physica A} {\bf 322}, 267 (2003)]. The intensive variable was defined for subsystems assuming local thermodynamic equilibrium, but no method was proposed for determining the size of a subsystem. We show that the Castaing and Beck-Cohen methods are related, and we present a way to determine subsystem size in the Beck-Cohen method. The application of our approach to Couette-Taylor turbulence (Reynolds number $540~000$) yields a log-normal distribution of the intensive parameter, and the resultant velocity difference PDF agrees well the observed non-Gaussian velocity difference PDFs.

cond-mat.soft↗

arXiv2004

Mach cone in a shallow granular layer

We study the V-shaped wake (Mach cone) formed by a cylindrical rod moving through a thin, vertically vibrated granular layer. The wake, analogous to a shock (hydraulic jump) in shallow water, appears for rod velocities v_R greater than a critical velocity c. We measure the half-angle, theta, of the wake as a function of v_R and layer depth, h. The angle satisfies the Mach relation, sin(theta)=c/v_R, where c=sqrt(gh), even for h as small as one particle diameter.

cond-mat.soft↗

arXiv2004

Crucial role of sidewalls in velocity distributions in quasi-2D granular gases

Our experiments and three-dimensional molecular dynamics simulations of particles confined to a vertical monolayer by closely spaced frictional walls (sidewalls) yield velocity distributions with non-Gaussian tails and a peak near zero velocity. Simulations with frictionless sidewalls are not peaked. Thus interactions between particles and their container are an important determinant of the shape of the distribution and should be considered when evaluating experiments on a tightly constrained monolayer of particles.

cond-mat.stat-mech↗

arXiv2004

Pattern formation and shocks in granular gases

Granular media such as sand and sugar are ubiquitous in nature and industry but are less well understood than fluids or solids. We consider the behavior of rapid granular flows where the transfer of momenta by collisions dominates. The physics is quite different for the opposite limit of static or slowly moving grains (e.g., sand piles). To gain understanding of granular flows we consider two problems that have been investigated with experiments, particle simulations and hydrodynamic theory: vertically oscillating granular layers and flow past an obstacle. Oscillating granular layers spontaneously form spatial patterns when the container acceleration amplitude exceeds a critical value, about 2.5 times the gravitational acceleration. Simulations with hard spheres that conserve linear momentum and dissipate energy in collisions are in qualitative accord with some but not all aspects of the observed patterns. It is necessary to include friction and angular momentum conservation in the simulations to achieve quantitative accord with observations. [Abridged]

cond-mat.soft↗

arXiv2004

Dynamics of drag and force distributions for projectile impact in a granular medium

Our experiments and molecular dynamics simulations on a projectile penetrating a two-dimensional granular medium reveal that the mean deceleration of the projectile is constant and proportional to the impact velocity. Thus, the time taken for a projectile to decelerate to a stop is independent of its impact velocity. The simulations show that the probability distribution function of forces on grains is time-independent during a projectile's penetration of the medium. At all times the force distribution function decreases exponentially for large forces.

physics.flu-dyn↗

arXiv2004

Cracks in rubber under tension exceed the shear wave speed

The shear wave speed is an upper limit for the speed of cracks loaded in tension in linear elastic solids. We have discovered that in a non-linear material, cracks in tension (Mode I) exceed this sound speed, and travel in an intersonic range between shear and longitudinal wave speeds. The experiments are conducted in highly stretched sheets of rubber; intersonic cracks can be produced simply by popping a balloon.

cond-mat.mtrl-sci↗

arXiv2004

Resonance tongues and patterns in periodically forced reaction-diffusion systems

Various resonant and near-resonant patterns form in a light-sensitive Belousov-Zhabotinsky (BZ) reaction in response to a spatially-homogeneous time-periodic perturbation with light. The regions (tongues) in the forcing frequency and forcing amplitude parameter plane where resonant patterns form are identified through analysis of the temporal response of the patterns. Resonant and near-resonant responses are distinguished. The unforced BZ reaction shows both spatially-uniform oscillations and rotating spiral waves, while the forced system shows patterns such as standing-wave labyrinths and rotating spiral waves. The patterns depend on the amplitude and frequency of the perturbation, and also on whether the system responds to the forcing near the uniform oscillation frequency or the spiral wave frequency. Numerical simulations of a forced FitzHugh-Nagumo reaction-diffusion model show both resonant and near-resonant patterns similar to the BZ chemical system.

nlin.PS↗