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The motion of a rolling ball actuated by internal point masses that move inside the ball's frame of reference is considered. The equations of motion are derived by applying Euler-Poincar\'e's symmetry reduction method in concert with…
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…
We present a reversible and symplectic algorithm called ROLL, for integrating the equations of motion in molecular dynamics simulations of simple fluids on a hypersphere $\mathcal{S}^d$ of arbitrary dimension $d$. It is derived in the…
Broader access to high-quality movement analysis could greatly benefit movement science and rehabilitation, such as allowing more detailed characterization of movement impairments and responses to interventions, or even enabling early…
We prove PSPACE-completeness of Push-1: given a rectangular grid of 1 x 1 cells, each possibly occupied by a movable block, can a robot move from one specified location to another, given the ability to push up to one block at a time? In…
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
Particle in Cell (PIC) simulations have become a vital tool for the investigation of kinetic processes in plasma physics. Many of the systems investigated with PIC simulations contain particles with relativistic velocities. The correct…
We propose a method for planning motion for robots with actuation uncertainty that incorporates contact with the environment and the compliance of the robot to reliably perform manipulation tasks. Our approach consists of two stages: (1)…
Dynamic properties of molecular motors whose motion is powered by interactions with specific lattice bonds are studied theoretically with the help of discrete-state stochastic "burnt-bridge" models. Molecular motors are depicted as random…
Motivated by recent experiments on objects moved vertically through a bed a glass beads, a simple model to study granular drag is proposed. The model consists of dimers on a slanted two-dimensional lattice through which objects are dragged…
Anytime a robot manipulator is controlled via visual feedback, the transformation between the robot and camera frame must be known. However, in the case where cameras can only capture a portion of the robot manipulator in order to better…
Our ability to numerically model and understand the complex flow behavior of solid-bearing suspensions has increased significantly over the last couple of years, partly due to direct numerical simulations that compute flow around individual…
In this paper we consider ill-posed inverse problems, both linear and nonlinear, by a heavy ball method in which a strongly convex regularization function is incorporated to detect the feature of the sought solution. We develop ideas on how…
We introduce a new isometric strain model for the study of the dynamics of cloth garments in a moderate stress environment, such as robotic manipulation in the neighborhood of humans. This model treats textiles as surfaces which are…
In recent years, model collapse has become a critical issue in language model training, making it essential to understand the underlying mechanisms driving this phenomenon. In this paper, we investigate recursive parametric model training…
Accurate dynamic models for racket-ball bounces are essential for reliable control in robotic table tennis. Existing models typically assume simple linear models and are restricted to inverted rubbers, limiting their ability to generalize…
We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with recent experiments of \emph{Escherichia coli}, the polymer dynamics are…
We show that non-entangled polymers display an elastic-like behaviour at a macroscopic scale (probed at some 0.100 mm thickness) up to at least hundred degrees above the glass transition temperature. This observation, found under…
In recent years, advanced model-based and data-driven control methods are unlocking the potential of complex robotics systems, and we can expect this trend to continue at an exponential rate in the near future. However, ensuring safety with…
We consider a model of an extensible semiflexible filament moving in two dimensions on a motility assay of motor proteins represented explicitly as active harmonic linkers. Their heads bind stochastically to polymer segments within a…