Related papers: Damping optimization of discrete mechanical system…
We describe a family of descent algorithms which generalizes common existing schemes used in applications such as neural network training and more broadly for optimization of smooth functions--potentially for global optimization, or as a…
We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretic extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally…
The real-time dynamics of local magnetic moments exchange coupled to a metallic system of conduction electrons is subject to dissipative friction even in the absence of spin-orbit coupling. Phenomenologically, this is usually described by a…
Equations of motion are developed for the oscillatory rotation of a disk suspended between twisted strings kept under tension by a hanging mass, to which additional forces may be applied. In the absence of forcing, damped harmonic…
We consider a finite region of a $d$-dimensional lattice, $d\in\mathbb{N}$, of weakly coupled harmonic oscillators. The coupling is provided by a nearest-neighbour potential (harmonic or not) of size $\varepsilon$. Each oscillator weakly…
We consider the optimization of the vector of grasping forces that support a known generalized force acting on the grasped object---a rigid body or a mechanism. Working in the framework of finite-dimensional normed vector spaces and their…
Optimal control is a central problem in quantum thermodynamics. When minimizing dissipated work and work fluctuations defined via the two-point measurement scheme in open quantum systems, existing approaches largely focus on the rapid- and…
Microscopic machines utilize free energy to create and maintain out-of-equilibrium organization in virtually all living things. Often this takes the form of converting the free energy stored in nonequilibrium chemical potential differences…
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…
An algorithm is presented for momentum gradient descent optimization based on the first-order differential equation of the Newtonian dynamics. The fictitious mass is introduced to the dynamics of momentum for regularizing the adaptive…
We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by…
We formulate the swarming optimization problem as a weakly coupled, dissipative dynamical system governed by a controlled energy dissipation rate and initial velocities that adhere to the nonequilibrium Onsager principle. In this framework,…
We propose a procedure - partly analytical and partly numerical - to find the frequency and the damping rate of the small-amplitude oscillations of a massless elastic capsule immersed in a two-dimensional viscous incompressible fluid. The…
In this paper, I aim to study free oscillations of a system of oscillators in more than one dimensions in the absence of damping. The basic approach lies in decoupling the motion in the individual perpendicular directions. Once the…
In this paper, the notion of contraction is used to solve the trajectory-tracking problem for a class of mechanical systems. Additionally, we propose a dynamic extension to remove velocity measurements from the controller while rejecting…
Spatially localized structures are key components of turbulence and other spatio-temporally chaotic systems. From a dynamical systems viewpoint, it is desirable to obtain corresponding exact solutions, though their existence is not…
In this study a new approach to the problem of transverse vibrations of an ideal string is presented. Unlike previous studies, assumptions such as constant tension, inextensibility, constant crosssectional area, small deformations and…
This paper proposes novel primal-dual dynamical systems for solving linear equality constrained convex optimization. First, we introduce a primal-dual dynamical system with implicit Hessian damping, which can neutralize the transversal…
We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function is taken to be log sub-additive, capturing decreasing impatience…
The response of an oscillating granular damper to an initial perturbation is studied using experiments performed in microgravity and granular dynamics mulations. High-speed video and image processing techniques are used to extract…