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Ripples or corrugations are common phenomena observed in unpaved roads in less developed countries or regions. They cause several damages in vehicles leading to increased maintenance and product costs. In this paper, we present a…
We introduce a deductive statistical mechanics approach for granular materials which is formally built from few realistic physical assumptions. The main finding is an universal behavior for the distribution of the density fluctuations. Such…
Goodness-of-fit testing is often criticized for its lack of practical relevance: since ``all models are wrong'', the null hypothesis that the data conform to our model is ultimately always rejected as the sample size grows. Despite this,…
Recently, the robustness of deep learning models has received widespread attention, and various methods for improving model robustness have been proposed, including adversarial training, model architecture modification, design of loss…
Softer than soft, squishy granular matter is composed of grains capable of significantly changing their shape (typically larger than 10% of deformation) without tearing or breaking. Because of the difficulty to test these materials…
In recent years, new flexible functional materials have attracted increasing interest, but there is a lack of the designing mechanisms of flexibility design with superstructures. In traditional engineering mechanics, the maximum bending…
Robustness of deep learning models is a property that has recently gained increasing attention. We explore a notion of robustness for generative adversarial models that is pertinent to their internal interactive structure, and show that,…
We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve…
Context. Grains in circumstellar disks are believed to grow by mutual collisions and subsequent sticking due to surface forces. Results of many fields of research involving circumstellar disks, such as radiative transfer calculations, disk…
This article reviews the current status of theoretical modeling of electric dipole radiation from spinning dust grains. The fundamentally simple problem of dust grain rotation appeals to a rich set of concepts of classical and quantum…
We study the dynamics of non-aligning, non-interacting self-propelled particles confined to a box in two dimensions. In the strong confinement limit, when the persistence length of the active particles is much larger than the size of the…
A gravity-driven flow of grains through a narrow pipe in vacuum is studied by means of a one-dimensional model with two coefficients of restitution. Numerical simulations show clearly how density waves form when a strikingly simple…
Composite of two kinds of grains is modeled in two-dimension and the elasticity is calculated using molecular dynamics method implementing Gear predictor-corrector of fifth order. It has been observed that same composite concentration can…
The concept of robustness of regulatory networks has been closely related to the nature of the interactions among genes, and the capability of pattern maintenance or reproducibility. Defining this robustness property is a challenging task,…
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…
We provide a functional view of distributional robustness motivated by robust statistics and functional analysis. This results in two practical computational approaches for approximate distributionally robust nonlinear optimization based on…
Robustness checks are routine in empirical work, but there is no standard statistical procedure to formally measure what one can learn from them. I propose a "robustness radius" measure to quantify the amount by which the robustness checks…
We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians…
We show that grains streaming through a fluid are generically unstable if their velocity, projected along some direction, matches the phase velocity of a fluid wave (linear oscillation). This can occur whenever grains stream faster than any…
We present several numerical results on granular mixtures. In particular, we examine the efficiency of diffusion as a mixing mechanism in these systems. The collisions are inelastic and to compensate the energy loss, we thermalize the…