Academia.edu no longer supports Internet Explorer.
To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser.
2013, Physical Review E
We report on the experimental observation of spatially modulated kinks in a shallow one-dimensional fluidized granular layer subjected to a periodic air flow. We show the appearance of these solutions as the layer undergoes a parametric instability. Due to the inherent fluctuations of the granular layer, the kink profile exhibits an effective wavelength, a precursor, which modulates spatially the homogeneous states and drastically modifies the kink dynamics. We characterize the average and fluctuating properties of this solution. Finally, we show that the temporal evolution of these kinks is dominated by a hopping dynamics, related directly to the underlying spatial structure.
Physical Review E, 2001
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 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 onefourth 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 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.
Physical Review Letters, 1995
Experiments on vertically oscillated granular layers in an evacuated container reveal a sequence of well-defined pattern bifurcations as the container acceleration is increased. Period doublings of the layer center of mass motion and a parametric wave instability interact to produce hexagons and more complicated patterns composed of distinct spatial domains of different relative phase separated by kinks (phase discontinuities). Above a critical acceleration, the layer becomes disordered in both space and time.
We study the onset of patterns in vertically oscillated layers of frictionless dissipative particles. Using both numerical solutions of continuum equations to Navier-Stokes order and molecular dynamics ͑MD͒ simulations, we find that standing waves form stripe patterns above a critical acceleration of the cell. Changing the frequency of oscillation of the cell changes the wavelength of the resulting pattern; MD and continuum simulations both yield wavelengths in accord with previous experimental results. The value of the critical acceleration for ordered standing waves is approximately 10% higher in molecular dynamics simulations than in the continuum simulations, and the amplitude of the waves differs significantly between the models. The delay in the onset of order in molecular dynamics simulations and the amplitude of noise below this onset are consistent with the presence of fluctuations which are absent in the continuum theory. The strength of the noise obtained by fit to Swift-Hohenberg theory is orders of magnitude larger than the thermal noise in fluid convection experiments, and is comparable to the noise found in experiments with oscillated granular layers and in recent fluid experiments on fluids near the critical point. Good agreement is found between the mean field value of onset from the Swift-Hohenberg fit and the onset in continuum simulations. Patterns are compared in cells oscillated at two different frequencies in MD; the layer with larger wavelength patterns has less noise than the layer with smaller wavelength patterns.
Physica A: Statistical Mechanics and its Applications, 2002
Our experiments on a vertically oscillated granular layer reveal that spatial patterns emerge in two stages following a change of parameter into the pattern-forming regime: an initial, domain-forming stage and a later stage in which domains coarsen to form ultimately an extended regular pattern. We characterize the evolution of the pattern using a "disorder function" (ÿ), where ÿ is a moment of the disorder operator (Gunaratne et al., Phys. Rev. E 57 (1998) 5146). The disorder in the initial stage is found to be consistent with a decay given by (ÿ) ∼ t −ÿ=2 , in accord with theory that predicts that behavior in this stage should be universal for pattern forming systems. The ÿnal stage is non-universal.
2000
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 $\bar\delta (\beta) \sim t^{-\sigma_{E}}$, with $\sigma_{E} = {1/2}\beta$; this decay is universal. Coarsening of domains occurs in the second stage, in which $\bar\delta (\beta) \sim t^{-\sigma_{L}}$, where $\sigma_{L}$ is a nonlinear function of $\beta$ whose form is system and model dependent. Our experiments on a vertically oscillated granular layer are in accord with theory, yielding $\sigma_{E}\approx 0.5\beta$, and $\sigma_{L}$ a nonlinear function of $\beta$.
Physical Review E, 2001
Cell-filling spiral patterns are observed in a vertically oscillated layer of granular material when the oscillation amplitude is suddenly increased from below the onset of pattern formation into the region where stripe patterns appear for quasistatic increases in amplitude. These spirals are transients and decay to stripe patterns with defects. A transient spiral defect chaos state is also observed. We describe the behavior of the spirals, and the way in which they form and decay. Our results are compared with those for similar spiral patterns in Rayleigh-Bénard convection in fluids.
Formation dynamics of transient spiral and target patterns are studied for vertically oscillated thin granular layer systems. When the dimensionless acceleration amplitude is changed from 2.5 of a flat pattern state to 3.0 of a steady stripe pattern state by linearly ramping the oscillation amplitude in time at a constant oscillation frequency, two different routes to the stripe pattern are observed depending on the ramping rate. For small ramping rate, spiral or target patterns are formed as an intermediate state before the stripe pattern. For large ramping rate, however, stripe patterns are formed without the transient spiral or target pattern. Futhermore, we study the short time dynamics of spiral and target patterns.
Journal of Physics: Condensed Matter, 2005
We describe a series of experiments and computer simulations on vibrated granular media in a geometry chosen to eliminate gravitationally induced settling. The system consists of a collection of identical spherical particles on a horizontal plate vibrating vertically, with or without a confining lid. Previously reported results are reviewed, including the observation of homogeneous, disordered liquid-like states, an instability to a 'collapse' of motionless spheres on a perfect hexagonal lattice, and a fluctuating, hexagonally ordered state. In the presence of a confining lid we see a variety of solid phases at high densities and relatively high vibration amplitudes, several of which are reported for the first time in this article. The phase behavior of the system is closely related to that observed in confined hard-sphere colloidal suspensions in equilibrium, but with modifications due to the effects of the forcing and dissipation. We also review measurements of velocity distributions, which range from Maxwellian to strongly non-Maxwellian depending on the experimental parameter values. We describe measurements of spatial velocity correlations that show a clear dependence on the mechanism of energy injection. We also report new measurements of the velocity autocorrelation function in the granular layer and show that increased inelasticity leads to enhanced particle selfdiffusion.
Physical Review Letters, 1998
Numerical simulations and laboratory experiments are conducted for thin layers of particles in a vertically oscillated container as a function of the frequency f, amplitude A, and depth H. The same standing wave patterns (stripes, squares, or hexagons oscillating at f͞2 or f͞4) and wavelengths are obtained in the simulations and experiments for a wide range of ͑ f, A͒ and two layer depths. Two model parameters are determined by fits at just two points ͑ f, A, H͒. Simulation results lead to heuristic arguments for the onset of patterns and the crossover from squares to stripes.
Physical Review Letters, 1994
The standing wave patterns formed on the surface of a vertically oscillated fluid enclosed by a container have long been a subject of fascination, and are known as Faraday waves. In circular containers, stable, radially symmetrical Faraday wave-patterns are resonant phenomena, and occur at the vibrational modes where whole numbers of waves fit exactly onto the surface of the fluid sample. These phenomena make excellent systems for the study of pattern formation and complex nonlinear dynamics. We provide a systematic exploration of variables that affect Faraday wave pattern formation on water in vertical-walled circular containers including amplitude, frequency, volume (or depth), temperature, and atmospheric pressure. In addition, we developed a novel method for the quantification of the time taken for patterns to reach full expression following the onset of excitation. The excitation frequency and diameter of the container were the variables that most strongly affected pattern morphology. Amplitude affected the degree to which Faraday wave patterns were expressed but did not affect pattern morphology. Volume (depth) and temperature did not affect overall pattern morphology but in some cases altered the time taken for patterns to form. We discuss our findings in light of René Thom's catastrophe theory, and the framework of attractors and basins of attraction. We suggest that Faraday wave phenomena represent a convenient and tractable analogue model system for the study of morphogenesis and vibrational modal phenomena in dynamical systems in general, examples of which abound in physical and biological systems.
Physical Review Letters, 2003
We study the behavior of two particles moving in a bistable potential, colliding inelastically with each other and driven by a stochastic heat bath. The system has the tendency to clusterize, placing the particles in the same well at low drivings, and to fill all of the available space at high temperatures. We show that the hopping over the potential barrier occurs following the Arrhenius rate, where the heat bath temperature is replaced by the granular temperature. Moreover, within the clusterized "phase" one encounters two different scenarios: for moderate inelasticity, the jumps from one well to the other involve one particle at a time, whereas for strong inelasticity the two particles hop simultaneously. PACS numbers: 02.50.Ey, 05.20.Dd, 81.05.Rm Granular gases [1], i.e. assemblies of inelastic particles losing a little kinetic energy at each collision, exhibit a variety of complex behaviors, such as clustering [2], spontaneous formation of vortices [3], lack of energy equipartition [4], non-Maxwellian velocity distributions [5]
Physical Review E, 2015
Experiments on a thin layer of cohesive wet granular matter under vertical vibrations reveal kink separated domains that collide with the container at different phases. Due to the strong cohesion arising from the formation of liquid bridges between adjacent particles, the domains move collectively upon vibrations. Depending on the periodicity of this collective motion, the kink fronts may propagate, couple with each other and form rotating spiral patterns in the case of period tripling, or stay as standing wave patterns in the case of period doubling. Moreover, both patterns may coexist with granular 'gas bubbles' -phase separation into a liquidlike and a gaslike state. Stability diagrams for the instabilities measured with various granular layer mass m and container height H are presented. The onsets for both types of patterns and their dependency on m and H can be quantitatively captured with a model considering the granular layer as a single particle colliding completely inelastically with the container.
Physical Review Letters, 2000
We have measured the spectrum of velocity fluctuations in a granular system confined to a vertical plane and driven into a homogeneous, steady state by strong vertical vibration. The distribution of horizontal velocities is not Maxwell-Boltzmann and is given by P͑y͒ Cexp͓2b͑jyj͞s͒ a ͔ where a 1.55 6 0.1 at all frequencies and amplitudes investigated, and also for varying boundary conditions. The deviation from Maxwell-Boltzmann statistics occurs in the absence of spatial clustering and does not result from an inhomogeneous average over regions of varying local density. Surprisingly, P͑y͒ has the same shape over a wide range of densities. PACS numbers: 81.05.Rm, 05.20.Dd, 05.20.Jj, 83.10.Pp A granular fluid is made up of macroscopic grains that have no significant thermal motions but can be driven into motion by external forces . In a molecular fluid, the average kinetic energy is determined by the temperature of the thermal bath that the fluid is in contact with; the fluctuations about this average are given by a Maxwell-Boltzmann (MB) distribution with a width determined by the temperature, independent of the exact nature of the bath. In a granular fluid, at steady state, the average kinetic energy of grains (or "granular temperature") is set by a balance of energy supplied by the driving forces and energy dissipated by inelastic collisions between grains [2]. The basis for kinetic-theory approaches to describing granular fluids is the assumption that far away from the source of energy, the fluctuations about the average energy have a well-defined distribution that is independent of the details of the driving force. In this Letter, we demonstrate experimentally that such a distribution does exist in a dilute, nearly elastic granular gas. The distribution is determined completely by a single parameter-the granular temperature-but is broader than a MB distribution.
arXiv (Cornell University), 2022
Fingering instabilities akin to the Rayleigh-Taylor (RT) instability in fluids have been observed in a binary granular system consisting of dense and small particles layered on top of lighter and larger particles, when the system is subjected to vertical vibration and fluidizing gas flow. Using observations from experiments and numerical modelling we explore whether the theory developed to describe the Rayleigh-Taylor (RT) instability in fluids is also applicable to binary granular systems. Our results confirm the applicability of the classic RT instability theory for binary granular systems demonstrating that several key features are observed in both types of systems, viz: (i) The characteristic wavenumber of the instability is constant with time, (ii) the amplitude of the characteristic wavenumber initially grows exponentially and (iii) the dispersion relation between the wavenumbers k of the interface instability and the growth rates n(k) of their amplitudes holds in both fluid-fluid and binary granular systems. Our results also demonstrate that inter-particle friction is essential for the RT instability to occur in granular media. For zero particle friction the interface instability bears a greater resembles to the Richtmyer-Meshkov instability. We further define a yield criterion Y for the interface by treating the granular medium as a viscoplastic material; only for Y > 15 fingering occurs. Interestingly, previous work has shown that instabilities in the Earth's lower mantle, another viscoplastic material, also occur for similar values of Y.
Physica A: Statistical Mechanics and its Applications, 2000
Laboratory experiments are conducted to examine granular wave patterns near onset as a function of the container oscillation frequency f and amplitude A, layer depth H , and grain diameter D. The primary transition from a at grain layer to standing waves occurs when the layer remains dilated after making contact with the container. With a at layer and increasing dimensionless peak container acceleration = 4 2 f 2 A=g (g is the acceleration due to gravity), the wave transition occurs for ≈ 2:6, but with decreasing the waves persist to = 2:2. For 2:2 ¡ ¡ 3:8, patterns are squares for f ¡ fss and stripes for f ¿ fss; H determines the square/stripe transition frequency fss=0:33 g=H . The dispersion relations for layers with varying H collapse onto the curve =H = 1:0 + 1:1(f H=g) −1:32±0:03 when the peak container velocity v = 2 Af exceeds a critical value, vgm ≈ 3 √ Dg. Local collision pressure measurements suggest that vgm is associated with a transition in the horizontal grain mobility: for v ¿ vgm, there is a hydrodynamic-like horizontal sloshing motion, while for v ¡ vgm, the grains are essentially immobile and the stripe pattern apparently arises from a bending of the granular layer. For f at vgm less than fss and v ¡ vgm, patterns are tenuous and disordered.
Physical Review E, 1999
We present a linear stability analysis of an oscillating granular layer, treating it as an isothermal incompressible fluid with zero surface tension, which undergoes periodic collisions with and separations from an oscillating plate. Because the viscosity of the granular layer is unknown, we use the experimental value of the critical acceleration for the transition from a flat to patterned layer as input for the theory, and use the analysis to calculate the granular viscosity and the wavelength of the most unstable mode. The wavelength compares favorably with the experimental pattern wavelength. Further, we find that the wavelengths are controlled by the viscosity of the granular layer. ͓S1063-651X͑99͒11112-7͔
Physica A: Statistical Mechanics and its Applications, 1998
Experiments on vertically vibrated granular layers in evacuated containers reveal a variety of patterns for acceleration amplitudes above a critical value ( ≈ 2.5 g). Stripes, squares, hexagons, spirals, triangles, and targets, as well as particle-like localized excitations ("oscillons") and fronts ("kinks") between regions with di erent vibrational phase are observed as the layer depth and the container oscillation frequency and amplitude are varied. A zig-zag instability, unstable hexagons, phase-disordered patterns, and "two-phase" squares are also observed. With a few noteworthy exceptions, the patterns are essentially independent of the lateral boundary conditions.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009
We have made measurements of force and velocity fluctuations in a variety of dense, gravity-driven granular flows under flow conditions close to the threshold of jamming. The measurements reveal a microscopic state that evolves rapidly from entirely collisional to largely frictional, as the system is taken close to jamming. On coarse-grained time scales, some descriptors of the dynamics—such as the probability distribution of force fluctuations, or the mean friction angle—do not reflect this profound change in the micromechanics of the flow. Other quantities, such as the frequency spectrum of force fluctuations, change significantly, developing low-frequency structure in the fluctuations as jamming is approached. We also show evidence of spatial structure, with force fluctuations being organized into local collision chains. These local structures propagate rapidly in the flow, with consequences far away from their origin, leading to long-range correlations in velocity fluctuations.
Physical Review E, 2007
In this work we derive an analytic expression for the Kolmogorov-Sinai entropy of dilute wet granular matter, valid for any spatial dimension. The grains are modelled as hard spheres and the influence of the wetting liquid is described according to the Capillary Model, in which dissipation is due to the hysteretic cohesion force of capillary bridges. The Kolmogorov-Sinai entropy is expanded in a series with respect to density. We find a rapid increase of the leading term when liquid is added. This demonstrates the sensitivity of the granular dynamics to humidity, and shows that the liquid significantly increases the chaoticity of the granular gas.
Physical Review Letters, 2011
Pattern formation of a thin layer of vertically agitated wet granular matter is investigated experimentally. Rotating spirals with three arms, which correspond to the kinks between regions with different colliding phases, are the dominating pattern. This preferred number of arms corresponds to period tripling of the agitated granular layer, unlike predominantly subharmonic Faraday crispations in dry granular matter. The chirality of the spatiotemporal pattern corresponds to the rotation direction of the spirals.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.