arXiv subjects

Douglas J. Durian

Publications and source records attributed to Douglas J. Durian.

At least 37 records · Page 2Linked to original sources

arXiv2022

Average Evolution and Size-Topology Relations for Coarsening 2d Dry Foams

Two-dimensional dry foams coarsen according to the von Neumann law as $dA/dt \propto (n-6)$ where $n$ is the number of sides of a bubble with area $A$. Such foams reach a self-similar scaling state where area and side-number distributions are stationary. Combining self-similarity with the von Neumann law, we derive time derivatives of moments of the bubble area distribution and a relation connecting area moments with averages of the side-number distribution that are weighted by powers of bubble area. To test these predictions, we collect and analyze high precision image data for a large number of bubbles squashed between parallel acrylic plates and allowed to coarsen into the self-similar scaling state. We find good agreement for moments ranging from two to twenty.

cond-mat.soft↗

arXiv2022

Demonstration of Decentralized, Physics-Driven Learning

In typical artificial neural networks, neurons adjust according to global calculations of a central processor, but in the brain neurons and synapses self-adjust based on local information. Contrastive learning algorithms have recently been proposed to train physical systems, such as fluidic, mechanical, or electrical networks, to perform machine learning tasks from local evolution rules. However, to date such systems have only been implemented in silico due to the engineering challenge of creating elements that autonomously evolve based on their own response to two sets of global boundary conditions. Here we introduce and implement a physics-driven contrastive learning scheme for a network of variable resistors, using circuitry to locally compare the response of two identical networks subjected to the two different sets of boundary conditions. Using this innovation, our system effectively trains itself, optimizing its resistance values without use of a central processor or external information storage. Once the system is trained for a specified allostery, regression, or classification task, the task is subsequently performed rapidly and automatically by the physical imperative to minimize power dissipation in response to the given voltage inputs. We demonstrate that, unlike typical computers, such learning systems are robust to extreme damage (and thus manufacturing defects) due to their decentralized learning. Our twin-network approach is therefore readily scalable to extremely large or nonlinear networks where its distributed nature will be an enormous advantage; a laboratory network of only 500 edges will already outpace its in silico counterpart.

cond-mat.dis-nn↗

arXiv2022

Structuro-elasto-plasticity (StEP) model for plasticity in disordered solids

Elastoplastic lattice models for the response of solids to deformation typically incorporate structure only implicitly via a local yield strain that is assigned to each site. However, the local yield strain can change in response to a nearby or even distant plastic event in the system. This interplay is key to understanding phenomena such as avalanches in which one plastic event can trigger another, leading to a cascade of events, but typically is neglected in elastoplastic models. To include the interplay one could calculate the local yield strain for a given particulate system and follow its evolution, but this is expensive and requires knowledge of particle interactions, which is often hard to extract from experiments. Instead, we introduce a structural quantity, "softness," obtained using machine learning to correlate with imminent plastic rearrangements. We show that softness also correlates with local yield strain. We incorporate softness to construct a "structuro-elasto-plasticity" model that reproduces particle simulation results quantitatively for several observable quantities, confirming that we capture the influence of the interplay of local structure, plasticity, and elasticity on material response.

cond-mat.soft↗

arXiv2021

Physical learning beyond the quasistatic limit

Physical networks, such as biological neural networks, can learn desired functions without a central processor, using local learning rules in space and time to learn in a fully distributed manner. Learning approaches such as equilibrium propagation, directed aging, and coupled learning similarly exploit local rules to accomplish learning in physical networks such as mechanical, flow, or electrical networks. In contrast to certain natural neural networks, however, such approaches have so far been restricted to the quasistatic limit, where they learn on time scales slow compared to their physical relaxation. This quasistatic constraint slows down learning, limiting the use of these methods as machine learning algorithms, and potentially restricting physical networks that could be used as learning platforms. Here we explore learning in an electrical resistor network that implements coupled learning, both in the lab and on the computer, at rates that range from slow to far above the quasistatic limit. We find that up to a critical threshold in the ratio of the learning rate to the physical rate of relaxation, learning speeds up without much change of behavior or error. Beyond the critical threshold, the error exhibits oscillatory dynamics but the networks still learn successfully.

cond-mat.dis-nn↗

arXiv2021

Spatters and Spills: Spreading Dynamics for Partially Wetting Droplets

We present a solvable model inspired by dimensional analysis for the time-dependent spreading of droplets that partially wet a substrate, where the spreading eventually stops and the contact angle reaches a nonzero equilibrium value. We separately consider small droplets driven by capillarity and large droplets driven by gravity. To explore both regimes, we first measure the equilibrium radius versus a comprehensive range of droplet volumes for four household fluids, and we compare the results with predictions based on minimizing the sum of gravitational and interfacial energies. The agreement is good, and gives a reliable measurement of an equilibrium contact angle that is consistent in both small and large droplet regimes. Next we use energy considerations to develop equations of motion for the time dependence of the spreading, in both regimes, where the driving forces are balanced against viscous drag in the bulk of the droplet and by friction at the moving contact line. Our approach leads to explicit prediction of the functional form of the spreading dynamics. It successfully describes prior data for a small capillary-driven droplet, and it fits well to new data we obtain for large gravity-driven droplets with a wide range of volumes.

physics.flu-dyn↗

arXiv2021

Probing the Gardner transition in an active quasi-thermal pressure-controlled granular system

To experimentally search for signals of the Gardner transition, an active quasi-thermal granular glass is constructed using a monolayer of air-fluidized star-shaped granular particles. The pressure of the system is controlled by adjusting the tension exerted on an enclosing boundary. Velocity distributions of the internal particles and the scaling of the pressure, density, effective-temperature, and relaxation time are examined, demonstrating that the system has important features of a thermal system. Using a pressure-based quenching protocol that brings the system into deeper glassy states, signals of the Gardner transition are detected via cage size and separation order parameters for both particle positions and orientations, offering experimental evidence of the Gardner transition for a system with in low spatial dimensions that is quasi-thermal.

cond-mat.soft↗

arXiv2021

Quantifying the Long-Range Structure of Foams and Other Cellular Patterns with Hyperuniformity Disorder Length Spectroscopy

We investigate the local- and long-range structure of four different space-filling cellular patterns: bubbles in a quasi-2d foam plus Voronoi constructions made around points that are uncorrelated (Poisson patterns), low discrepancy (Halton patterns), and displaced from a lattice by Gaussian noise (Einstein patterns). We study distributions of local quantities including cell areas and topological features; the former is the widest for bubbles in a foam making them locally the most disordered but the latter show no significant differences between the cellular patterns. Long-range structure is probed by the spectral density and also by converting the real-space spectrum of number density or volume fraction fluctuations for windows of diameter $D$ to the effective distance $h(D)$ from the window boundary where these fluctuations occur. This real-space hyperuniformity disorder length spectroscopy is performed on various point patterns which are determined by the centroids of the bubbles in the foam, by the points patterns around which the Voronoi cells are created and by the centroids of the Voronoi cells. These patterns are either unweighted or weighted by the area of the cells they occupy. The unweighted bubble centroids have $h(D)$ that collapses for the different ages of of the foam with random Poissonian fluctuations at long distances. All patterns of area-weighted points have constant $h(D)=h_e$ for large $D$; $h_e=0.084 \sqrt{\left< a\right>}$ for the bubble centroids is the smallest value, meaning they are most uniform. All the weighted centroids collapse to the same constant $h_e=0.084 \sqrt{\left< a\right>}$ as for the foams. A similar analysis is performed on the edges of the cells where the spectra of $h(D)$ for the foam edges show $h(D) \sim D^{1-ε}$ where $ε=0.3$

cond-mat.soft↗

arXiv2020

Experimentally Testing a Generalized Coarsening Model for Individual Bubbles in Quasi-Two-Dimensional Wet Foams

We present high-precision data for the time evolution of bubble area $A(t)$ and circularity shape parameter $C(t)$ for quasi-2d foams consisting of bubbles squashed between parallel plates. In order to fully compare with predictions by Roth et al. [Phys. Rev. E 87 2013] and Schimming et al. [Phys. Rev. E 96 2017], foam wetness is systematically varied by controlling the height of the sample above a liquid reservoir which in turn controls the radius $r$ of the inflation of the Plateau borders. For very dry foams, where the borders are very small, classic von Neumann behavior is observed where a bubble's growth rate depends only on its number $n$ of sides. For wet foams, the inflated borders impede gas exchange and cause deviations from von Neumann's law that are found to be in accord with the generalized coarsening equation. In particular, the overall growth rate varies linearly with the film height, which decrease as surface Plateau borders inflate. And, more interestingly, the deviation from $dA/dt\propto (n-6)$ von Neumann behavior grows in proportion to $nCr/\sqrt{A}$. This is highlighted definitively by data for six-sided bubbles, which are forbidden to grow or shrink except for the existence of this term. And it is tested quantitatively by variation of all four relevant quantities: $n$, $C$, $r$, and $A$

cond-mat.soft↗

arXiv2019

Machine Learning Characterization of Structural Defects in Amorphous Packings of Dimers and Ellipses

Structural defects within amorphous packings of symmetric particles can be characterized using a machine learning approach that incorporates structure functions of radial distances and angular arrangement. This yields a scalar field, \emph{softness}, that correlates with the probability that a particle is about to rearrange. However, when particle shapes are elongated, as in the case of dimers and ellipses, we find the standard structure functions produce imprecise softness measurements. Moreover, ellipses exhibit deformation profiles in stark contrast to circular particles. In order to account for effects of orientation and alignment, we introduce new structure functions to recover predictive performance of softness, as well as provide physical insight to local and extended dynamics. We study a model disordered solid, a bidisperse two-dimensional granular pillar, driven by uniaxial compression and composed entirely of monomers, dimers, or ellipses. We demonstrate how the computation of softness via support vector machine extends to dimers and ellipses with the introduction of new orientational structure functions. Then, we highlight the spatial extent of rearrangements and defects, as well as their cross-correlation, for each particle shape. Finally, we demonstrate how an additional machine learning algorithm, recursive feature elimination, provides an avenue to better understand how softness arises from particular structural aspects. We identify the most crucial structure functions in determining softness and discuss their physical implications.

cond-mat.soft↗

arXiv2018

Stagnant Zone Formation in a 2D Bed of Circular and Elongated Grains under Penetration

When a large blunt object penetrates into a granular material, the force response exhibits an initial nonlinear relationship with depth that is widely attributed to the formation of a shear jammed stagnant zone. We present an experimental study of a model 2D granular system that preserves common aspects of slow granular penetration, such as a linear force law for large depths, while also allowing for direct and precise measurement of a stagnant zone. We also probe structural anisotropies throughout the bed and examine their characteristics inside and outside the stagnant zone. Finally, we simultaneously consider effects of concave elongated particle shapes (dimers) and find that while most results are not affected, the relationship between local structure and strain suggests a distinct fragility in the stagnant zone.

cond-mat.soft↗

arXiv2018

Eliminating Stripe Artifacts in Light-Sheet Fluorescence Imaging

We report two techniques to mitigate stripe artifacts in light-sheet fluorescence imaging. The first uses an image processing algorithm called the multidirectional stripe remover (MDSR) method to filter stripes from an existing image. The second uses an elliptical holographic diffuser (EHD) with strong scattering anisotropy to prevent stripe formation during image acquisition. These techniques facilitate accurate interpretation of image data, especially in denser samples. They are also facile and cost-effective.

physics.ins-det↗

arXiv2017

Anisotropic Particles Strengthen Granular Pillars under Compression

We probe the effects of particle shape on the global and local behavior of a two-dimensional granular pillar, acting as a proxy for a disordered solid, under uniaxial compression. This geometry allows for direct measurement of global material response, as well as tracking of all individual particle trajectories. In general, drawing connections between local structure and local dynamics can be challenging in amorphous materials due to lower precision of atomic positions, so this study aims to elucidate such connections. We vary local interactions by using three different particle shapes: discrete circular grains (monomers), pairs of grains bonded together (dimers), and groups of three bonded in a triangle (trimers). We find that dimers substantially strengthen the pillar and the degree of this effect is determined by orientational order in the initial condition. In addition, while the three particle shapes form void regions at distinct rates, we find that anisotropies in the local amorphous structure remain robust through the definition of a metric that quantifies packing anisotropy. Finally, we highlight connections between local deformation rates and local structure.

cond-mat.soft↗

arXiv2017

Friction controls submerged granular flows

We investigate the coupling between interstitial medium and granular particles by studying the hopper flow of dry and submerged system experimentally and numerically. In accordance with earlier studies, we find, that the dry hopper empties at a constant rate. However, in the submerged system we observe the surging of the flow rate. We model both systems using the discrete element method, which we couple with computational fluid dynamics in the case of a submerged hopper. We are able to match the simulations and the experiments with good accuracy. To do that, we fit the particle-particle contact friction for each system separately, finding that submerging the hopper changes the particle-particle contact friction from $μ_{vacuum}=0.15$ to $μ_{sub}=0.13$, while all the other simulation parameters remain the same. Furthermore, our experiments find a particle size dependence to the flow rate, which is comprehended based on arguments on the terminal velocity and drag. These results jointly allow us to conclude that at the large particle limit, the interstitial medium does not matter, in contrast to small particles. The particle size limit, where this occurs depends on the viscosity of the interstitial fluid.

cond-mat.soft↗

arXiv2017

Effect of interstitial fluid on the fraction of flow microstates that precede clogging in granular hoppers

We report on the nature of flow events for the gravity-driven discharge of glass beads through a hole that is small enough that the hopper is susceptible to clogging. In particular, we measure the average and standard deviation of the distribution of discharged masses as a function of both hole and grain sizes. We do so in air, which is usual, but also with the system entirely submerged under water. This damps the grain dynamics and could be expected to dramatically affect the distribution of the flow events, which are described in prior work as avalanche-like. Though the flow is slower and the events last longer, we find that the average discharge mass is only slightly reduced for submerged grains. Furthermore, we find that the shape of the distribution remains exponential, implying that clogging is still a Poisson process even for immersed grains. Per Thomas and Durian [Phys. Rev. Lett. 114, 178001 (2015]), this allows interpretation of the average discharge mass in terms of the fraction of flow microstates that precede, i.e. that effectively cause, a stable clog to form. Since this fraction is barely altered by water, we conclude that the crucial microscopic variables are the grain positions; grain momenta play only a secondary role in destabilizing weak incipient arches. These insights should aid on-going efforts to understand the susceptibility of granular hoppers to clogging.

cond-mat.soft↗

arXiv2016

The sands of time run faster near the end

Submerged granular hoppers exhibit an unexpected surge in discharge rate as they empty [Wilson et al. 2015]. With a more sensitive apparatus, we find that this surge depends on hopper diameter and also happens in air --- though the effect is smaller and previously unnoticed. We also find that the surge may be turned off by fixing the rate of fluid flow through the granular packing. With no flow control, dye injected on top of the packing gets drawn into the grains, at a rate that increases as the hopper empties. Thus we conclude that the surge is caused by a self-generated pumping of fluid through the packing. We successfully model this effect via a driving pressure set by the dilation of grains as they exit. This highlights a surprising and unrecognized role that interstitial fluid plays in setting the discharge rate, and likely also in controlling clog formation, for granular hoppers whether in air or under water.

cond-mat.soft↗

arXiv2015

Divergence of Voronoi cell anisotropy vector: A threshold-free characterization of local structure in amorphous materials

Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to the centroid of the Voronoi cell in which the particle resides. These vectors tend to point in toward regions of high free volume and away from regions of low free volume, reminiscent of sinks and sources in a vector field. We compute the local divergence of these vectors, for which positive values correspond to overpacked regions and negative values identify underpacked regions within the material. Distributions of this divergence are nearly Gaussian with zero mean, allowing for structural characterization using only the moments of the distribution. We explore how the standard deviation and skewness vary with packing fraction for simulations of bidisperse systems and find a kink in these moments that coincides with the jamming transition.

cond-mat.soft↗

arXiv2015

Deformation-Driven Diffusion and Plastic Flow in Two-Dimensional Amorphous Granular Pillars

We report a combined experimental and simulation study of deformation-induced diffusion in compacted two-dimensional amorphous granular pillars, in which thermal fluctuations play negligible role. The pillars, consisting of bidisperse cylindrical acetal plastic particles standing upright on a substrate, are deformed uniaxially and quasistatically by a rigid bar moving at a constant speed. The plastic flow and particle rearrangements in the pillars are characterized by computing the best-fit affine transformation strain and non-affine displacement associated with each particle between two stages of deformation. The non-affine displacement exhibits exponential crossover from ballistic to diffusive behavior with respect to the cumulative deviatoric strain, indicating that in athermal granular packings, the cumulative deviatoric strain plays the role of time in thermal systems and drives effective particle diffusion. We further study the size-dependent deformation of the granular pillars by simulation, and find that different-sized pillars follow self-similar shape evolution during deformation. In addition, the yield stress of the pillars increases linearly with pillar size. Formation of transient shear lines in the pillars during deformation becomes more evident as pillar size increases. The width of these elementary shear bands is about twice the diameter of a particle, and does not vary with pillar size.

cond-mat.soft↗

arXiv2015

Penetration depth scaling for impact into wet granular packings

We present experimental measurements of penetration depths for the impact of spheres into wetted granular media. We observe that the penetration depth in the liquid saturated case scales with projectile density, size, and drop height in a fashion consistent with the scaling observed in the dry case, but that penetration depths into saturated packings tend to be smaller. This result suggests that, for the range of impact energies observed, the stopping force is set by static contact forces between grains within the bed, and that the presence of liquid serves, primarily, to enhance these contact forces. The enhancement to the stopping force has a complicated dependence on liquid fraction, accompanied by a change in the drop-height dependence, that must be the consequence of accompanying changes in the conformation of the liquid phase in the interstices.

cond-mat.soft↗