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Haptic upper limb exoskeletons are robots that assist human operators during task execution while having the ability to render virtual or remote environments. Therefore, the stability of such robots in physical human-robot-environment…
Friction is an unavoidable phenomenon that exists in all mechanical systems incorporating parts with relative motion. It is well-known that friction is a serious impediment for precise servo control, hence the interest to devise a procedure…
In a general setting of a Hamiltonian system with two degrees of freedom and assuming some properties for the undergoing potential, we study the dynamics close and tending to a singularity of the system which in models of $N$-body problems…
Theoretically, solutions of the damped harmonic oscillator asymptotically approach equilibrium, i.e., the zero energy state, without ever reaching it exactly, and the critically damped solution approaches equilibrium faster than the…
Non-conservative loads of the follower type are usually believed to be the source of dynamic instabilities such as flutter and divergence. It is shown that these instabilities (including Hopf bifurcation, flutter, divergence, and…
We investigate finite number effects in collisions between two states of an initially well known number of identical bosons with contact interactions, oscillating in the presence of harmonic confinement in one dimension. We investigate two…
Autonomous coverage of a specified area by robots operating in close proximity with each other has many potential applications such as real-time monitoring of rapidly changing environments, and search and rescue; however, coordination and…
Existing smart composite piezoelectric beam models in the literature mostly ignore the electro-magnetic interactions and adopt the linear elasticity theory. However, these interactions substantially change the controllability and…
The dynamics of a one-degree of freedom oscillator with arbitrary polynomial non-linearity subjected to an external periodic excitation is studied. The sequences (cascades) of harmonic and subharmonic stationary solutions to the equation of…
The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…
We consider the numerical approximations for a phase field model consisting of incompressible Navier--Stokes equations with a generalized Navier boundary condition, and the Cahn-Hilliard equation with a dynamic moving contact line boundary…
In this paper we present numerical simulations of a macroscopic vision-based model [1] derived from microscopic situation rules described in [2]. This model describes an approach to collision avoidance between pedestrians by taking…
Using an adiabatic approximation method, which searches for Tomlinson model-like instabilities for a simple but still realistic model for two crystalline surfaces in the extremely light contact limit, with mobile molecules present at the…
Under certain conditions we prove the existence of a steady-state transport regime for interacting mesoscopic systems coupled to reservoirs (leads). The partitioning and partition-free scenarios are treated on an equal footing. Our…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
This paper applies the theory of rate-independent systems to model the locomotion of bio-mimetic soft crawlers. We prove the well-posedness of the approach and illustrate how the various strategies adopted by crawlers to achieve locomotion,…
We study the asymptotic stability of periodic solutions for sweeping processes defined by a polyhedron with translationally moving faces. Previous results are improved by obtaining a stronger $W^{1,2}$ convergence. Then we present an…
Interacting bosons or fermions give rise to some of the most fascinating phases of matter, including high-temperature superconductivity, the fractional quantum Hall effect, quantum spin liquids and Mott insulators. While these systems are…
Plasmas whose Coulomb-collision rates are very small may relax on shorter time scales to non-Maxwellian quasi-equilibria, which, nevertheless, have a universal form, with dependence on initial conditions retained only via an infinite set of…
Model Hamiltonians with long-range interaction yield energies that are corrected taking into account the universal behavior of the electron-electron interaction at short range. Although the intention of the paper is to explore the…