arXiv subjects

Deniz Ertas

Publications and source records attributed to Deniz Ertas.

At least 19 recordsLinked to original sources

arXiv2006

Velocity Correlations in Dense Gravity Driven Granular Chute Flow

We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We show that the correlation structure within planes parallel to the surface persists in the bulk. The two-point velocity correlation function exhibits exponential decay for small to intermediate values of the separation between spheres. The correlation lengths identified by exponential fits to the data show nontrivial dependence on the averaging time $\dt$ used to determine grain velocities. We discuss the correlation length dependence on averaging time, incline angle, pile height, depth of the layer, system size and grain stiffness, and relate the results to other length scales associated with the rheology of the system. We find that correlation lengths are typically quite small, of the order of a particle diameter, and increase approximately logarithmically with a minimum pile height for which flow is possible, $\hstop$, contrary to the theoretical expectation of a proportional relationship between the two length scales.

cond-mat.soft↗

arXiv2005

Coherent Structures in Dense Granular Flows

We present a theoretical derivation of a rheology for dense granular flow, based on the process of inelastic collapse of neighboring particles. This collapse creates regions of correlated motion, which control the viscous behavior of the flow on a large scale. The result is a rheology that obeys the scaling form observed experimentally by Pouliquen and by the "G.D.R. Midi" group author. We identify the nature of the constraints imposed by inelastic collapse on the grain-scale motions in the flow; finally, we show using an energy cascade argument that the inelastic collapse need not proceed to the final endpoint in order for the correlations we have identified to build up.

cond-mat.soft↗

arXiv2003

Reaction-limited sintering in nearly saturated environments

We study the shape and growth rate of necks between sintered spheres with dissolution-precipitation dynamics in the reaction-limited regime. We determine the critical shape that separates those initial neck shapes that can sinter from those that necessarily dissolve, as well as the asymptotic evolving shape of sinters far from the critical shape. We compare our results with past results for the asymptotic neck shape in closely related but more complicated models of surface dynamics; in particular we confirm a scaling conjecture, originally due to Kuczinsky. Finally, we consider the relevance of this problem to the diagenesis of sedimentary rocks and other applications.

cond-mat.mtrl-sci↗

arXiv2002

Ripening of Porous Media

We address the surface tension-driven dynamics of porous media in nearly saturated pore-space solutions. We linearize this dynamics in the reaction-limited regime near its fixed points -- surfaces of constant mean curvature (CMC surfaces). We prove that the only stable interface for this dynamics is the plane, and estimate the time scale for a CMC surface to become unstable. We also discuss the differences between open and closed system dynamics, pointing out the unlikelihood that CMC surfaces are ever realized in these systems on any time scale.

cond-mat.stat-mech↗

arXiv2002

Granular gravitational collapse and chute flow

Inelastic grains in a flow under gravitation tend to collapse into states in which the relative normal velocities of two neighboring grains is zero. If the time scale for this gravitational collapse is shorter than inverse strain rates in the flow, we propose that this collapse will lead to the formation of ``granular eddies", large scale condensed structures of particles moving coherently with one another. The scale of these eddies is determined by the gradient of the strain rate. Applying these concepts to chute flow of granular media, (gravitationally driven flow down inclined planes) we predict the existence of a bulk flow region whose rheology is determined only by flow density. This theory yields the experimental ``Pouliquen flow rule", correlating different chute flows; it also correctly accounts for the different flow regimes observed.

cond-mat.soft↗

arXiv2001

Stability of Monomer-Dimer Piles

We measure how strong, localized contact adhesion between grains affects the maximum static critical angle, theta_c, of a dry sand pile. By mixing dimer grains, each consisting of two spheres that have been rigidly bonded together, with simple spherical monomer grains, we create sandpiles that contain strong localized adhesion between a given particle and at most one of its neighbors. We find that tan(theta_c) increases from 0.45 to 1.1 and the grain packing fraction, Phi, decreases from 0.58 to 0.52 as we increase the relative number fraction of dimer particles in the pile, nu_d, from 0 to 1. We attribute the increase in tan(theta_c(nu_d)) to the enhanced stability of dimers on the surface, which reduces the density of monomers that need to be accomodated in the most stable surface traps. A full characterization and geometrical stability analysis of surface traps provides a good quantitative agreement between experiment and theory over a wide range of nu_d, without any fitting parameters.

cond-mat.soft↗

arXiv2001

Geometry of Frictionless and Frictional Sphere Packings

We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although frictionless packings of hard-spheres are always isostatic (with six contacts) regardless of construction history and restitution coefficient, frictional packings achieve a multitude of hyperstatic packings that depend on system parameters and construction history. Instead of immediately dropping to four, the coordination number reduces smoothly from $z=6$ as the friction coefficient $μ$ between two particles is increased.

cond-mat.soft↗

arXiv2000

Gravity-driven Dense Granular Flows

We report and analyze the results of numerical studies of dense granular flows in two and three dimensions, using both linear damped springs and Hertzian force laws between particles. Chute flow generically produces a constant density profile that satisfies scaling relations suggestive of a Bagnold grain inertia regime. The type of force law has little impact on the behavior of the system. Bulk and surface flows differ in their failure criteria and flow rheology, as evidenced by the change in principal stress directions near the surface. Surface-only flows are not observed in this geometry.

cond-mat.soft↗

arXiv1999

A Ball in a Groove

We study the static equilibrium of an elastic sphere held in a rigid groove by gravity and frictional contacts, as determined by contact mechanics. As a function of the opening angle of the groove and the tilt of the groove with respect to the vertical, we identify two regimes of static equilibrium for the ball. In the first of these, at large opening angle or low tilt, the ball rolls at both contacts as it is loaded. This is an analog of the "elastic" regime in the mechanics of granular media. At smaller opening angles or larger tilts, the ball rolls at one contact and slides at the other as it is loaded, analogously with the "plastic" regime in the mechanics of granular media. In the elastic regime, the stress indeterminacy is resolved by the underlying kinetics of the ball response to loading.

cond-mat↗

arXiv1998

Impurity mediated nucleation in hexadecane-in-water emulsions

We report detailed nucleation studies on the liquid-to-solid transition of hexadecane using nearly monodisperse hexadecane-in-water emulsions. A careful consideration of the kinetics of isothermal and nonisothermal freezing show deviations from predictions of classical nucleation theory, if one assumes that the emulsion droplet population is homogeneous. Similar deviations have been observed previously. As an explanation, we propose a novel argument based on the dynamic generation of droplet heterogeneity mediated by mobile impurities. This proposal is in excellent agreement with existing data.

cond-mat.soft↗

arXiv1998

Finite Temperature Depinning of a Flux Line from a Nonuniform Columnar Defect

A flux line in a Type-II superconductor with a single nonuniform columnar defect is studied by a perturbative diagrammatic expansion around an annealed approximation. The system undergoes a finite temperature depinning transition for the (rather unphysical) on-the-average repulsive columnar defect, provided that the fluctuations along the axis are sufficiently large to cause some portions of the column to become attractive. The perturbative expansion is convergent throughout the weak pinning regime and becomes exact as the depinning transition is approached, providing an exact determination of the depinning temperature and the divergence of the localization length.

cond-mat.supr-con↗

arXiv1998

Gutenberg Richter and Characteristic Earthquake Behavior in Simple Mean-Field Models of Heterogeneous Faults

The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the mean field version of a model for a segmented fault system in a three-dimensional elastic solid. The studies focus on the interplay between the roles of disorder, dynamical effects, and driving mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of dynamical weakening (or ``overshoot'') effects (epsilon) and the normal distance (L) of the driving forces from the fault. In general, small epsilon and small L are found to produce Gutenberg-Richter type power law statistics with an exponential cutoff, while large epsilon and large L lead to a distribution of small events combined with characteristic system-size events. In a certain parameter regime the behavior is bistable, with transitions back and forth from one phase to the other on time scales determined by the fault size and other model parameters. The implications for realistic earthquake statistics are discussed.

cond-mat.dis-nn↗

arXiv1997

Lateral Separation of Macromolecules and Polyelectrolytes in Microlithographic Arrays

A new approach to separation of a variety of microscopic and mesoscopic objects in dilute solution is presented. The approach takes advantage of unique properties of a specially designed separation device (sieve), which can be readily built using already developed microlithographic techniques. Due to the broken reflection symmetry in its design, the direction of motion of an object in the sieve varies as a function of its self-diffusion constant, causing separation transverse to its direction of motion. This gives the device some significant and unique advantages over existing fractionation methods based on centrifugation and electrophoresis.

cond-mat.soft↗

arXiv1996

Statistics of Largest Loops in a Random Walk

We report further findings on the size distribution of the largest neutral segments in a sequence of N randomly charged monomers [D. Ertas and Y. Kantor, Phys. Rev. E53, 846 (1996); cond-mat/9507005]. Upon mapping to one--dimensional random walks (RWs), this corresponds to finding the probability distribution for the size L of the largest segment that returns to its starting position in an N--step RW. We primarily focus on the large N, \ell = L/N << 1 limit, which exhibits an essential singularity. We establish analytical upper and lower bounds on the probability distribution, and numerically probe the distribution down to \ell \approx 0.04 (corresponding to probabilities as low as 10^{-15}) using a recursive Monte Carlo algorithm. We also investigate the possibility of singularities at \ell=1/k for integer k.

cond-mat↗

arXiv1996

Irreversibility, Mechanical Entanglement and Thermal Melting in Superconducting Vortex Crystals with Point Impurities

We discuss the onset of irreversibility and entanglement of vortex lines in high Tc superconductors due to point disorder and thermal fluctuations using a simplified cage model. A combination of Flory arguments, known results from directed polymers in random media, and a Lindemann criterion are used to estimate the field and temperature dependence of irreversibility, mechanical entanglement and thermal melting. The qualitative features of this dependence, including its nonmonotonicity when disorder is sufficiently strong, are in good agreement with recent experiments.

cond-mat↗

arXiv1995

Anisotropic Scaling in Threshold Critical Dynamics of Driven Directed Lines

The dynamical critical behavior of a single directed line driven in a random medium near the depinning threshold is studied both analytically (by renormalization group) and numerically, in the context of a Flux Line in a Type-II superconductor with a bulk current $\vec J$. In the absence of transverse fluctuations, the system reduces to recently studied models of interface depinning. In most cases, the presence of transverse fluctuations are found not to influence the critical exponents that describe longitudinal correlations. For a manifold with $d=4-ε$ internal dimensions, longitudinal fluctuations in an isotropic medium are described by a roughness exponent $ζ_\parallel=ε/3$ to all orders in $ε$, and a dynamical exponent $z_\parallel=2-2ε/9+O(ε^2)$. Transverse fluctuations have a distinct and smaller roughness exponent $ζ_\perp=ζ_\parallel-d/2$ for an isotropic medium. Furthermore, their relaxation is much slower, characterized by a dynamical exponent $z_\perp=z_\parallel+1/ν$, where $ν=1/(2-ζ_\parallel)$ is the correlation length exponent. The predicted exponents agree well with numerical results for a flux line in three dimensions. As in the case of interface depinning models, anisotropy leads to additional universality classes. A nonzero Hall angle, which has no analogue in the interface models, also affects the critical behavior.

cond-mat↗

arXiv1995

Randomly Charged Polymers, Random Walks, and Their Extremal Properties

Motivated by an investigation of ground state properties of randomly charged polymers, we discuss the size distribution of the largest Q-segments (segments with total charge Q) in such N-mers. Upon mapping the charge sequence to one--dimensional random walks (RWs), this corresponds to finding the probability for the largest segment with total displacement Q in an N-step RW to have length L. Using analytical, exact enumeration, and Monte Carlo methods, we reveal the complex structure of the probability distribution in the large N limit. In particular, the size of the longest neutral segment has a distribution with a square-root singularity at l=L/N=1, an essential singularity at l=0, and a discontinuous derivative at l=1/2. The behavior near l=1 is related to a another interesting RW problem which we call the "staircase problem". We also discuss the generalized problem for d-dimensional RWs.

cond-mat↗

arXiv1994

Extremal Segments in Random Sequences

We investigate the probability for the largest segment in with total displacement $Q$ in an $N$-step random walk to have length $L$. Using analytical, exact enumeration, and Monte Carlo methods, we reveal the complex structure of the probability distribution in the large $N$ limit. In particular, the size of the longest loop has a distribution with a square-root singularity at $\ell\equiv L/N=1$, an essential singularity at $\ell=0$, and a discontinuous derivative at $\ell=1/2$.

cond-mat↗