arXiv subjects

Daniel I. Goldman

Publications and source records attributed to Daniel I. Goldman.

86 records · Page 5Linked to original sources

arXiv2009

Ripples and Shear Bands in Plowed Granular Media

Monodisperse packings of dry, air-fluidized granular media typically exist between volume fractions from $Φ$= 0.585 to 0.64. We demonstrate that the dynamics of granular drag are sensitive to volume fraction $Φ$ and their exists a transition in the drag force and material deformation from smooth to oscillatory at a critical volume fraction $Φ_{c}=0.605$. By dragging a submerged steel plate (3.81 cm width, 6.98 cm depth) through $300 μm$ glass beads prepared at volume fractions between 0.585 to 0.635 we find that below $Φ_{c}$ the media deformation is smooth and non-localized while above $Φ_{c}$ media fails along distinct shear bands. At high $Φ$ the generation of these shear bands is periodic resulting in the ripples on the surface. Work funded by The Burroughs Wellcome Fund and the Army Research Lab MAST CTA

physics.flu-dyn↗

arXiv2009

Sensitive dependence of the motion of a legged robot on granular media

Legged locomotion on flowing ground ({\em e.g.} granular media) is unlike locomotion on hard ground because feet experience both solid- and fluid-like forces during surface penetration. Recent bio-inspired legged robots display speed relative to body size on hard ground comparable to high performing organisms like cockroaches but suffer significant performance loss on flowing materials like sand. In laboratory experiments we study the performance (speed) of a small (2.3 kg) six-legged robot, SandBot, as it runs on a bed of granular media (1 mm poppy seeds). For an alternating tripod gait on the granular bed, standard gait control parameters achieve speeds at best two orders of magnitude smaller than the 2 body lengths/s ($\approx 60$ cm/s) for motion on hard ground. However, empirical adjustment of these control parameters away from the hard ground settings, restores good performance, yielding top speeds of 30 cm/s. Robot speed depends sensitively on the packing fraction $ϕ$ and the limb frequency $ω$, and a dramatic transition from rotary walking to slow swimming occurs when $ϕ$ becomes small enough and/or $ω$ large enough. We propose a kinematic model of the rotary walking mode based on generic features of penetration and slip of a curved limb in granular media. The model captures the dependence of robot speed on limb frequency and the transition between walking and swimming modes but highlights the need for a deeper understanding of the physics of granular media.

physics.bio-ph↗

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↗

arXiv2005

Low density fragile states in cohesive powders

We discuss the difference between cohesive and non-cohesive granular media in the context of a recent report of "dry quicksand." Weak low density states with properties like dry quicksand are readily formed in common household powders. In contrast, such states cannot be formed in cohesionless granular media such as ordinary sand.

cond-mat.soft↗

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↗

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

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↗

arXiv2003

Persistent holes in a fluid

We observe stable holes in a vertically oscillated 0.5 cm deep aqueous suspension of cornstarch for accelerations a above 10g. Holes appear only if a finite perturbation is applied to the layer. Holes are circular and approximately 0.5 cm wide, and can persist for more than 10^5 cycles. Above a = 17g the rim of the hole becomes unstable producing finger-like protrusions or hole division. At higher acceleration, the hole delocalizes, growing to cover the entire surface with erratic undulations. We find similar behavior in an aqueous suspension of glass microspheres.

nlin.PS↗

arXiv2003

Kink-induced transport and segregation in oscillated granular layers

We use experiments and molecular dynamics simulations of vertically oscillated granular layers to study horizontal particle segregation induced by a kink (a boundary between domains oscillating out of phase). Counter-rotating convection rolls carry the larger particles in a bidisperse layer along the granular surface to a kink, where they become trapped. The convection originates from avalanches that occur inside the layer, along the interface between solidified and fluidized grains. The position of a kink can be controlled by modulation of the container frequency, making possible systematic harvesting of the larger particles.

cond-mat.soft↗

arXiv2003

Noise, coherent fluctuations, and the onset of order in an oscillated granular fluid

We study fluctuations in a vertically oscillated layer of grains below the critical acceleration for the onset of ordered standing waves. As onset is approached, transient disordered waves with a characteristic length scale emerge and increase in power and coherence. The scaling behavior and the shift in the onset of order agrees with the Swift-Hohenberg theory for convection in fluids. However, the noise in the granular system is four orders of magnitude larger than the thermal noise in a convecting fluid, making the effect of granular noise observable even 20% below the onset of long range order.

cond-mat↗

arXiv2003

Lattice Dynamics and Melting of a Nonequilibrium Pattern

We present a new description of nonequilibrium square patterns as a harmonically coupled crystal lattice. In a vertically oscillating granular layer, different transverse normal modes of the granular square-lattice pattern are observed for different driving frequencies ($f_d$) and accelerations. The amplitude of a mode can be further excited by either frequency modulation of $f_d$ or reduction of friction between the grains and the plate. When the mode amplitude becomes large, the lattice melts (disorders), in accord with the Lindemann criterion for melting in two-dimensions.

nlin.PS↗

arXiv2001

Phase Bubbles and Spatiotemporal Chaos in Granular Patterns

We use inelastic hard sphere molecular dynamics simulations and laboratory experiments to study patterns in vertically oscillated granular layers. The simulations and experiments reveal that {\em phase bubbles} spontaneously nucleate in the patterns when the container acceleration amplitude exceeds a critical value, about $7g$, where the pattern is approximately hexagonal, oscillating at one-fourth the driving frequency ($f/4$). A phase bubble is a localized region that oscillates with a phase opposite (differing by $π$) to that of the surrounding pattern; a localized phase shift is often called an ${\em arching}$ in studies of two-dimensional systems. The simulations show that the formation of phase bubbles is triggered by undulation at the bottom of the layer on a large length scale compared to the wavelength of the pattern. Once formed, a phase bubble shrinks as if it had a surface tension, and disappears in tens to hundreds of cycles. We find that there is an oscillatory momentum transfer across a kink, and this shrinking is caused by a net collisional momentum inward across the boundary enclosing the bubble. At increasing acceleration amplitudes, the patterns evolve into randomly moving labyrinthian kinks (spatiotemporal chaos). We observe in the simulations that $f/3$ and $f/6$ subharmonic patterns emerge as primary instabilities, but that they are unstable to the undulation of the layer. Our experiments confirm the existence of transient $f/3$ and $f/6$ patterns.

cond-mat.soft↗

arXiv2000

Characterization of the Emergence of Order in an Oscillated Granular Layer

The formation of textured patterns has been predicted to occur in two stages. The first is an early time, domain-forming stage with dynamics characterized by a disorder function $\barδ(β) \sim t^{-σ_{E}}$, with $σ_{E} = {1/2}β$; this decay is universal. Coarsening of domains occurs in the second stage, in which $\barδ(β) \sim t^{-σ_{L}}$, where $σ_{L}$ is a nonlinear function of $β$ whose form is system and model dependent. Our experiments on a vertically oscillated granular layer are in accord with theory, yielding $σ_{E}\approx 0.5β$, and $σ_{L}$ a nonlinear function of $β$.

nlin.PS↗