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A model for approximately stretched-exponential relaxation with continuously varying stretching exponentsNov 22 2016Jan 31 2017Relaxation in glasses is often approximated by a stretched-exponential form: $f(t) = A \exp [-(t/\tau)^{\beta}]$. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Cort\'e et al. [Nature Phys. 4, 420 (2008)] ... More

Generic transient memory formation in disordered systems with noiseJan 15 2011Jun 04 2011Out-of-equilibrium disordered systems may form memories of external driving in a remarkable fashion. The system "remembers" multiple values from a series of training inputs yet "forgets" nearly all of them at long times despite the inputs being continually ... More

Multiple transient memories in sheared suspensions: robustness, structure, and routes to plasticityJul 04 2013Sep 26 2013Multiple transient memories, originally discovered in charge-density-wave conductors, are a remarkable and initially counterintuitive example of how a system can store information about its driving. In this class of memories, a system can learn multiple ... More

A nonlinear, geometric Hall effect without magnetic fieldFeb 09 2019The classical Hall effect, the traditional means of determining charge-carrier sign and density in a conductor, requires a magnetic field to produce transverse voltages across a current-carrying wire. We show that along curved paths -- $\mathrm{\textit{without}}$ ... More

Multiple transient memories in experiments on sheared non-Brownian suspensionsApr 16 2014Jul 11 2014A system with multiple transient memories can remember a set of inputs but subsequently forgets almost all of them, even as they are continually applied. If noise is added, the system can store all memories indefinitely. The phenomenon has recently been ... More

Viscous to Inertial Crossover in Liquid Drop CoalescenceDec 06 2010Mar 15 2011Using an electrical method and high-speed imaging we probe drop coalescence down to 10 ns after the drops touch. By varying the liquid viscosity over two decades, we conclude that at sufficiently low approach velocity where deformation is not present, ... More

Toward the zero surface tension limit: The granular fingering instabilityDec 12 2007The finger-like branching pattern that occurs when a less viscous fluid displaces a more viscous one confined between two parallel plates has been widely studied as a classical example of a mathematically-tractable hydrodynamic instability since the time ... More

Vibration and Nonlinear Resonance in the Break-up of an Underwater BubbleJul 24 2013We use high-speed X-ray phase-contrast imaging, weakly nonlinear analysis and boundary integral simulations to characterize the final stage of underwater bubble break-up. The X-ray imaging study shows that an initial azimuthal perturbation to the shape ... More

Tunable failure: control of rupture through rigidityJan 17 2015Jul 13 2016We investigate how material rigidity acts as a key control parameter for the failure of solids under stress. In both experiments and simulations, we demonstrate that material failure can be continuously tuned by varying the underlying rigidity of the ... More

The inexorable resistance of inertia determines the initial regime of drop coalescenceApr 18 2012Drop coalescence is central to diverse processes involving dispersions of drops in industrial, engineering and scientific realms. During coalescence, two drops first touch and then merge as the liquid neck connecting them grows from initially microscopic ... More

Auxetic metamaterials from disordered networksOct 02 2017Recent theoretical work suggests that systematic pruning of disordered networks consisting of nodes connected by springs can lead to materials that exhibit a host of unusual mechanical properties. In particular, global properties such as the Poisson's ... More

Perspectives on opportunities in experimental soft-matter scienceOct 31 2016Soft materials consist of basic units that are significantly larger than an atom but much smaller than the overall dimensions of the sample. The label "soft condensed matter" emphasizes that the large basic building blocks of these materials produce low ... More

Controlling the direction and amount of a splash with textured surfaceFeb 13 2007Aug 17 2010Because splashing is such a violent process, one might naively expect that neither the direction of droplet emission nor the amount of ejected material can be controlled with any precision. Even though it is observed countless times in the course of a ... More

Scaling at the selective withdrawal transitionJan 16 2002In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above an unperturbed two-fluid interface. At low withdrawal rates, Q, the interface forms a steady state hump and only the upper fluid is withdrawn. ... More

An island of stability in a sea of fingers: emergent large-scale features of the viscous flow instabilityOct 28 2014Jan 29 2015The displacement of a more viscous fluid by a less viscous one in a quasi-two dimensional geometry leads to the formation of complex fingering patterns. This fingering has been characterized by a most unstable wavelength, $\lambda_c$, which depends on ... More

Fingering versus stability in the limit of zero interfacial tensionOct 28 2014The invasion of one fluid into another of higher viscosity in a quasi-two dimensional geometry typically produces complex fingering patterns. Because interfacial tension suppresses short-wavelength fluctuations, its elimination by using pairs of miscible ... More

On the stability and growth of single myelin figuresSep 28 2005Dec 18 2005Myelin figures are long thin cylindrical structures that typically grow as a dense tangle when water is added to the concentrated lamellar phase of certain surfactants. We show that, starting from a well-ordered initial state, single myelin figures can ... More

Echoes from Anharmonic Normal Modes in Model GlassesJan 20 2016Mar 20 2016Glasses display a wide array of nonlinear acoustic phenomena at temperatures $T\lesssim 1$ K. This behavior has traditionally been explained by an ensemble of weakly-coupled, two-level tunneling states, a theory that is also used to describe the thermodynamic ... More

Glassy dynamics in thermally-activated list sortingApr 01 2010Sorting the integers 1 through $N$ into an ordered list is a simple task that can be done rapidly. However, using an algorithm based on the thermally-activated pairwise exchanges of neighboring list elements, we find sorting can display many features ... More

Ultrafast Interference Imaging of Air in Splashing DynamicsAug 04 2011A drop impacting a solid surface with sufficient velocity will emit many small droplets creating a splash. However, splashing is completely suppressed if the surrounding gas pressure is lowered. The mechanism by which the gas affects splashing remains ... More

Splashing of liquids: interplay of surface roughness with surrounding gasAug 07 2006Dec 17 2007We investigate the interplay between substrate roughness and surrounding gas pressure in controlling the dynamics of splashing when a liquid drop hits a dry solid surface. We associate two distinct forms of splashing with each of these control parameters: ... More

Spout States in the Selective Withdrawal SystemAug 07 2006Aug 07 2006In selective withdrawal, fluid is withdrawn through a nozzle suspended above the flat interface separating two immiscible, density-separated fluids of viscosities $\nu_{upper}$ and $\nu_{lower} = \lambda \nu_{upper}$. At low withdrawal rates, the interface ... More

Approximately stretched-exponential relaxation in sheared non-Brownian suspensionsNov 22 2016Relaxation in glasses is often approximated by a stretched-exponential form: $f(t) = A \exp [-(t/\tau)^{\beta}]$. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Cort\'e et al. [Nature Phys. 4, 420 (2008)] ... More

Coalescence in low-viscosity liquidsSep 10 2007The expected universal dynamics associated with the initial stage of droplet coalescence are difficult to study visually due to the rapid motion of the liquid and the awkward viewing geometry. Here we employ an electrical method to study the coalescence ... More

Neutral meson properties in hot and magnetized quark matter: a new magnetic field independent regularization scheme applied to NJL-type modelDec 03 2018A magnetic field independent regularization scheme (zMFIR) based on the Hurwitz-Riemann zeta function is introduced. The new technique is applied to the regularization of the mean-field thermodynamic potential and mass gap equation within the SU(2) Nambu-Jona-Lasinio ... More

Comparison of splashing in high and low viscosity liquidsFeb 26 2014We explore the evolution of a splash when a liquid drop impacts a smooth, dry surface. There are two splashing regimes that occur when the liquid viscosity is varied, as is evidenced by its dependence on ambient gas pressure. A high-viscosity drop splashes ... More

Collision Dynamics of Particle Clusters in a Two-dimensional Granular GasOct 16 2013In a granular gas, inelastic collisions produce an instability in which the constituent particles cluster heterogeneously. These clusters then interact with each other, further decreasing their kinetic energy. We report experiments of the free collisions ... More

Comment on 'Repulsive Contact Interactions Make Jammed Particulate Systems Inherently Nonharmonic'Jun 06 2013Dec 31 2014In their Letter, Schreck, Bertrand, O'Hern and Shattuck [Phys. Rev. Lett. 107, 078301 (2011)] study nonlinearities in jammed particulate systems that arise when contacts are altered. They conclude that there is "no harmonic regime in the large system ... More

Directed aging, memory and Nature's greedMar 14 2019Disordered materials are often out of equilibrium and evolve very slowly. This allows a memory of the imposed strains or preparation conditions to be encoded in the material. Here we consider "directed aging", where the elastic properties of a material ... More

Normal Modes in Model Jammed Systems in Three DimensionsMar 18 2008Vibrational spectra and normal modes of mechanically stable particle packings in three dimensions are analyzed over a range of compressions, from near the jamming transition, where the packings lose their rigidity, to far above it. At high frequency, ... More

Energy Loss at Propagating Jamming Fronts in Granular Gas ClustersJun 12 2013Oct 15 2013We explore the initial moments of impact between two dense granular clusters in a two-dimensional geometry. The particles are composed of solid CO$_{2}$ and are levitated on a hot surface. Upon collision, the propagation of a dynamic "jamming front" produces ... More

Stress Transmission through Three-Dimensional Ordered Granular ArraysApr 24 2002We measure the local contact forces at both the top and bottom boundaries of three-dimensional face-centered-cubic and hexagonal-close-packed granular crystals in response to an external force applied to a small area at the top surface. Depending on the ... More

Patterns in Illinois Educational School DataJan 29 2015We examine Illinois educational data from standardized exams and analyze primary factors affecting the achievement of public school students. We focus on the simplest possible models: representation of data through visualizations and regressions on single ... More

Topology and ground state degeneracy of tetrahedral smectic vesiclesJul 16 2018Dec 17 2018Chemical design of block copolymers makes it possible to create polymer vesicles with tunable microscopic structure. Here we focus on a model of a vesicle made of smectic liquid-crystalline block copolymers at zero temperature. The vesicle assumes a faceted ... More

Anharmonicity and quasi-localization of the excess low-frequency vibrations in jammed solidsSep 21 2009We compare the harmonic and anharmonic properties of the vibrational modes in 3-dimensional jammed packings of frictionless spheres interacting via repulsive, finite range potentials. A crossover frequency is apparent in the density of states, the diffusivity ... More

Geometric origin of excess low-frequency vibrational modes in amorphous solidsSep 26 2004Sep 21 2005Glasses have a large excess of low-frequency vibrational modes in comparison with crystalline solids. We show that such a feature is a necessary consequence of the geometry generic to weakly connected solids. In particular, we analyze the density of states ... More

The Two Fluid Drop Snap-off Problem: Experiments and TheoryFeb 24 1999We address the dynamics of a drop with viscosity $\lambda \eta$ breaking up inside another fluid of viscosity $\eta$. For $\lambda=1$, a scaling theory predicts the time evolution of the drop shape near the point of snap-off which is in excellent agreement ... More

Thin Film Formation During Splashing of Viscous LiquidsMay 16 2010Aug 19 2010After impact onto a smooth dry surface, a drop of viscous liquid initially spreads in the form of a thick lamella. If the drop splashes, it first emits a thin fluid sheet that can ultimately break up into droplets causing the splash. Ambient gas is crucial ... More

Crumpling a Thin SheetNov 07 2001Crumpled sheets have a surprisingly large resistance to further compression. We have studied the crumpling of thin sheets of Mylar under different loading conditions. When placed under a fixed compressive force, the size of a crumpled material decreases ... More

Dynamics of viscous coalescing droplets in a saturated vapor phaseDec 21 2015The dynamics of two liquid droplets coalescing in their saturated vapor phase are investigated by Lattice Boltzmann numerical simulations. Attention is paid to the effect of the vapor phase on the formation and growth dynamics of the liquid bridge in ... More

Role of local response in manipulating the elastic properties of disordered solids by bond removalAug 23 2017We explore the range over which the elasticity of disordered spring networks can be manipulated by the removal of selected bonds. By taking into account the local response of a bond, we demonstrate that the effectiveness of pruning can be improved so ... More

Instabilities of jammed packings of frictionless spheres under compressionApr 04 2017We consider the contribution to the density of vibrational states and the distribution of energy barrier heights of incipient instabilities in a glass modeled by a jammed packing of spheres. On approaching an instability, the frequency of a normal mode ... More

Finite-Size Scaling at the Jamming TransitionApr 22 2012Jun 06 2012We present an analysis of finite-size effects in jammed packings of N soft, frictionless spheres at zero temperature. There is a 1/N correction to the discrete jump in the contact number at the transition so that jammed packings exist only above isostaticity. ... More

Structural signatures of the unjamming transition at zero temperatureJan 01 2006We study the pair correlation function $g(r)$ for zero-temperature, disordered, soft-sphere packings just above the onset of jamming. We find distinct signatures of the transition in both the first and split second peaks of this function. As the transition ... More

Force Distribution in a Granular MediumFeb 22 1999We report on systematic measurements of the distribution of normal forces exerted by granular material under uniaxial compression onto the interior surfaces of a confining vessel. Our experiments on three-dimensional, random packings of monodisperse glass ... More

Drop Splashing on a Dry Smooth SurfaceJan 28 2005The corona splash due to the impact of a liquid drop on a smooth dry substrate is investigated with high speed photography. A striking phenomenon is observed: splashing can be completely suppressed by decreasing the pressure of the surrounding gas. The ... More

Numerical Studies of the Compressible Ising Spin GlassSep 12 2005We study a two-dimensional compressible Ising spin glass at constant volume. The spin interactions are coupled to the distance between neighboring particles in the Edwards-Anderson model with +/- J interactions. We find that the energy of a given spin ... More

Two diverging length scales in the structure of jammed packingsOct 19 2017Jun 11 2018At densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first, $\xi_{Z}$, is associated with the two-point ... More

Linking microscopic and macroscopic response in disordered solidsJun 19 2017The modulus of a rigid network of harmonic springs depends on the sum of the energies in each of the bonds due to the applied distortion: compression in the case of the bulk modulus, $B$, or shear in the case of the shear modulus, $\mathcal{G}$. The distortion ... More

Period proliferation in periodic states in cyclically sheared jammed solidsMay 23 2017Athermal disordered systems can exhibit a remarkable response to an applied oscillatory shear: after a relatively few shearing cycles, the system falls into a configuration that had already been visited in a previous cycle. After this point the system ... More

Contact nonlinearities and linear response in jammed particulate packingsFeb 25 2014Dec 31 2014Packings of frictionless athermal particles that interact only when they overlap experience a jamming transition as a function of packing density. Such packings provide the foundation for the theory of jamming. This theory rests on the observation that, ... More

Tuning by pruning: exploiting disorder for global response and the principle of bond-level independenceFeb 10 2015Feb 13 2015We exploit the intrinsic difference between disordered and crystalline solids to create systems with unusual and exquisitely tuned mechanical properties. To demonstrate the power of this approach, we design materials that are either virtually incompressible ... More

Excess Vibrational Modes and the Boson Peak in Model GlassesNov 17 2006The excess low-frequency normal modes for two widely-used models of glasses were studied at zero temperature. The onset frequencies for the anomalous modes for both systems agree well with predictions of a variational argument, which is based on analyzing ... More

$π_0$ pole mass calculation in a strong magnetic field and lattice constraintsJun 18 2016Feb 21 2017The $\pi_0$ neutral meson pole mass is calculated in a strongly magnetized medium using the SU(2) Nambu-Jona-Lasinio model within the random phase approximation (RPA) at zero temperature and zero baryonic density. We employ a magnetic field dependent ... More

Level algebras through Buchsbaum* manifoldsJun 22 2010Stanley-Reisner rings of Buchsbaum* complexes are studied by means of their quotients modulo a linear system of parameters. The socle of these quotients is computed. Extending a recent result by Novik and Swartz for orientable homology manifolds without ... More

Observation and Characterization of the Vestige of the Jamming Transition in a Thermal 3D SystemJun 28 2012We study the dependence of the pair-correlation function, $g(r)$, and particle mobility on packing fraction in a dense three-dimensional packing of soft colloids made of poly N-isopropyl acrylamide (pNIPAM), a thermo-sensitive gel. We find that $g(r)$ ... More

Emergent SO(3) Symmetry of the Frictionless Shear Jamming TransitionSep 01 2016Mar 23 2017We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a ... More

Mapping the glassy dynamics of soft spheres onto hard-sphere behaviorJul 13 2011We show that the dynamics of soft-sphere systems with purely repulsive interactions can be described by introducing an effective hard-sphere diameter determined using the Andersen-Weeks-Chandler approximation. We find that this approximation, known to ... More

Drop splashing is independent of substrate wettingJul 29 2016A liquid drop impacting a dry solid surface with sufficient kinetic energy will splash, breaking apart into numerous secondary droplets. This phenomenon shows many similarities to forced wetting, including the entrainment of air at the contact line. Because ... More

Still water: dead zones and collimated ejecta from the impact of granular jetsApr 17 2013When a dense granular jet hits a target, it forms a large dead zone and ejects a highly collimated conical sheet with a well-defined opening angle. Using experiments, simulations, and continuum modeling, we find that this opening angle is insensitive ... More

Equivalence of glass transition and colloidal glass transition in the hard-sphere limitOct 05 2009We show that the slowing of the dynamics in simulations of several model glass-forming liquids is equivalent to the hard-sphere glass transition in the low-pressure limit. In this limit, we find universal behavior of the relaxation time by collapsing ... More

The Effect of Air on Granular Size Separation in a Vibrated Granular BedFeb 25 2005Apr 19 2005Using high-speed video and magnetic resonance imaging (MRI) we study the motion of a large sphere in a vertically vibrated bed of smaller grains. As previously reported we find a non-monotonic density dependence of the rise and sink time of the large ... More

The packing of granular polymer chainsNov 11 2009Rigid particles pack into structures, such as sand dunes on the beach, whose overall stability is determined by the average number of contacts between particles. However, when packing spatially extended objects with flexible shapes, additional concepts ... More

Collective behavior in a granular jet: Emergence of a liquid with zero surface-tensionJun 14 2007We perform the analog to the "water bell" experiment using non-cohesive granular material. When a jet of granular material, many particles wide, rebounds from a fixed cylindrical target, it deforms into a sharply-defined sheet or cone with a shape that ... More

Stress transmission through three-dimensional granular crystals with stacking faultsAug 27 2003We explore the effect of stacking fault defects on the transmission of forces in three-dimensional face-centered-cubic granular crystals. An external force is applied to a small area at the top surface of a crystalline packing of granular beads containing ... More

Memory formation in matterOct 19 2018Mar 21 2019Memory formation in matter is a theme of broad intellectual relevance; it sits at the interdisciplinary crossroads of physics, biology, chemistry, and computer science. Memory connotes the ability to encode, access, and erase signatures of past history ... More

Coalescence of bubbles and drops in an outer fluidJul 24 2014When two liquid drops touch, a microscopic connecting liquid bridge forms and rapidly grows as the two drops merge into one. Whereas coalescence has been thoroughly studied when drops coalesce in vacuum or air, many important situations involve coalescence ... More

Breakup of Air Bubbles in Water: Memory and Breakdown of Cylindrical SymmetryMay 26 2006Jul 31 2006Using high-speed video, we have studied air bubbles detaching from an underwater nozzle. As a bubble distorts, it forms a thin neck which develops a singular shape as it pinches off. As in other singularities, the minimum neck radius scales with the time ... More

Stability of jammed packings II: the transverse length scaleJan 29 2013Nov 22 2013As a function of packing fraction at zero temperature and applied stress, an amorphous packing of spheres exhibits a jamming transition where the system is sensitive to boundary conditions even in the thermodynamic limit. Upon further compression, the ... More

Heat transport in model jammed solidsAug 15 2009We calculate numerically the normal modes of vibrations in 3D jammed packings of soft spheres as a function of the packing fraction and obtain the energy diffusivity, a spectral measure of transport that controls sound propagation and thermal conductivity. ... More

Force distributions in 3D granular assemblies: Effects of packing order and inter-particle frictionSep 20 2000We present a systematic investigation of the distribution of normal forces at the boundaries of static packings of spheres. A new method for the efficient construction of large hexagonal-close-packed crystals is introduced and used to study the effect ... More

Emergent SO(3) Symmetry of the Frictionless Shear Jamming TransitionSep 01 2016We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a ... More

Effects of compression on the vibrational modes of marginally jammed solidsAug 18 2005Glasses have a large excess of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature is a necessary consequence of the weak connectivity of the solid, and that the frequency of modes in excess is very ... More

Creation of prompt and thin-sheet splashing by varying surface roughness or increasing air pressureMar 13 2012Jun 22 2012A liquid drop impacting a solid surface may splash by emitting a thin liquid sheet that subsequently breaks apart or by promptly ejecting droplets from the advancing liquid-solid contact line. Using high-speed imaging, we show that air pressure and surface ... More

Force distributions in three dimensional compressible granular packsJun 05 2002We present an experimental investigation of the probability distribution of normal contact forces, $P(F)$, at the bottom boundary of static three dimensional packings of compressible granular materials. We find that the degree of deformation of individual ... More

The limits of multifunctionality in tunable networksMay 01 2018Oct 05 2018Nature is rife with networks that are functionally optimized to propagate inputs in order to perform specific tasks. Whether via genetic evolution or dynamic adaptation, many networks create functionality by locally tuning interactions between nodes. ... More

Designing allostery-inspired response in mechanical networksJul 28 2016Recent advances in designing meta-materials have demonstrated that global mechanical properties of disordered spring networks can be tuned by selectively modifying only a small subset of bonds. Here, using a computationally-efficient approach, we extend ... More

Disordered surface vibrations in jammed sphere packingsDec 30 2014We study the vibrational properties near a free surface of disordered spring networks derived from jammed sphere packings. In bulk systems, without surfaces, it is well understood that such systems have a plateau in the density of vibrational modes extending ... More

The jamming scenario - an introduction and outlookJun 11 2010Jan 27 2011The jamming scenario of disordered media, formulated about 10 years ago, has in recent years been advanced by analyzing model systems of granular media. This has led to various new concepts that are increasingly being explored in in a variety of systems. ... More

Energy transport in jammed sphere packingsJun 19 2008Nov 17 2008We calculate the normal modes of vibration in jammed sphere packings to obtain the energy diffusivity, a spectral measure of transport. At the boson peak frequency, we find an Ioffe-Regel crossover from a diffusivity that drops rapidly with frequency ... More

Effective Temperatures of a Driven System Near JammingOct 13 2001Fluctuations in a model of a sheared, zero-temperature foam are studied numerically. Five different quantities that reduce to the true temperature in an equilibrium thermal system are calculated. All five have the same shear-rate dependence, and three ... More

Memory formation in matterOct 19 2018Memory formation in matter is a theme of broad intellectual relevance; it sits at the interdisciplinary crossroads of physics, biology, chemistry, and computer science. Memory connotes the ability to encode, access, and erase signatures of past history ... More

Impact dynamics of granular jets with non-circular cross-sectionsJul 25 2013Aug 23 2014Using high-speed photography, we investigate two distinct regimes of the impact dynamics of granular jets with non-circular cross-sections. In the steady-state regime, we observe the formation of thin granular sheets with anisotropic shapes and show that ... More

Asymptotics of Markov Kernels and the Tail ChainDec 24 2011An asymptotic model for extreme behavior of certain Markov chains is the "tail chain". Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics such as point process limits. We place this model in a ... More

Hidden Regular Variation: Detection and EstimationJan 27 2010Sep 03 2010Hidden regular variation defines a subfamily of distributions satisfying multivariate regular variation on $\mathbb{E} = [0, \infty]^d \backslash \{(0,0, ..., 0) \} $ and models another regular variation on the sub-cone $\mathbb{E}^{(2)} = \mathbb{E} ... More

Detecting a conditional extrme value modelFeb 17 2009In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value model assumes a ... More

Signatures of granular microstructure in dense shear flowsMar 27 2000Granular materials react to shear stresses differently than do ordinary fluids. Rather than deforming uniformly, materials such as dry sand or cohesionless powders develop shear bands: narrow zones containing large relative particle motion leaving adjacent ... More

Jamming in finite systems: stability, anisotropy, fluctuations and scalingJun 05 2014Dec 31 2014Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any ... More

Degree Growth Rates and Index Estimation in a Directed Preferential Attachment ModelAug 05 2018Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. In a directed preferential attachment model, despite the well-known marginal power-law degree distributions, not much ... More

Inelastic and elastic collision rates for triplet states of ultracold strontiumSep 05 2008May 03 2009We report measurement of the inelastic and elastic collision rates for ^{88}Sr atoms in the (5s5p)^3P_0 state in a crossed-beam optical dipole trap. This is the first measurement of ultracold collision properties of a ^3P_0 level in an alkaline-earth ... More

Minimal links and a result of GaetaApr 03 2008If $V$ is an equidimensional codimension $c$ subscheme of an $n$-dimensional projective space, and $V$ is linked to $V'$ by a complete intersection $X$, then we say that $V$ is {\em minimally linked} to $V'$ if $X$ is a codimension $c$ complete intersection ... More

The $β$-Mixing Rate of STIT TessellationsJun 11 2014We consider homogeneous STIT tessellations $Y$ in the $\ell$-dimensional Euclidean space $R^\ell$ and show that the (spatial) $\beta$-mixing rate converges to zero.

On the capacity functional of excursion sets of Gaussian random fields on $\R^2$Oct 28 2014When a random field $(X_t, \ t\in {\mathbb R}^2)$ is thresholded on a given level $u$, the excursion set is given by its indicator $~1_{[u, \infty)}(X_t)$. The purpose of this work is to study functionals (as established in stochastic geometry) of these ... More

Algorithms for strongly stable idealsOct 18 2011Dec 02 2011Strongly stable monomial ideals are important in algebraic geometry, commutative algebra, and combinatorics. Prompted, for example, by combinatorial approaches for studying Hilbert schemes and the existence of maximal total Betti numbers among saturated ... More

A tour of the Weak and Strong Lefschetz PropertiesSep 26 2011Sep 29 2011An artinian graded algebra, $A$, is said to have the Weak Lefschetz property (WLP) if multiplication by a general linear form has maximal rank in every degree. A vast quantity of work has been done studying and applying this property, touching on numerous ... More

Properties of cut ideals associated to ring graphsJun 03 2008Apr 28 2009A cut ideal of a graph records the relations among the cuts of the graph. These toric ideals have been introduced by Sturmfels and Sullivant who also posed the problem of relating their properties to the combinatorial structure of the graph. We study ... More

Segre's Regularity Bound for Fat Point SchemesNov 19 2016Motivated by questions in interpolation theory and on linear systems of rational varieties, one is interested in upper bounds for the Castelnuovo-Mumford regularity of arbitrary subschemes of fat points. An optimal upper bound, named after Segre, was ... More

Gorenstein algebras presented by quadricsJun 14 2011We establish restrictions on the Hilbert function of standard graded Gorenstein algebras with only quadratic relations. Furthermore, we pose some intriguing conjectures and provide evidence for them by proving them in some cases using a number of different ... More

The Lefschetz question for ideals generated by powers of linear forms in few variablesMar 21 2017Aug 07 2017The Lefschetz question asks if multiplication by a power of a general linear form, $L$, on a graded algebra has maximal rank (in every degree). We consider a quotient by an ideal that is generated by powers of linear forms. Then the Lefschetz question ... More

Equivariant Hilbert Series in non-Noetherian Polynomial RingsOct 09 2015Oct 19 2015We introduce and study equivariant Hilbert series of ideals in polynomial rings in countably many variables that are invariant under a suitable action of a symmetric group or the monoid $Inc(\mathbb{N})$ of strictly increasing functions. Our first main ... More