Related papers: The Optimal Shape of a Javelin
In this article we formulate frictionless atom cooling in harmonic traps as a time-optimal control problem, permitting imaginary values of the trap frequency for trasient time intervals during which the trap becomes an expulsive parabolic…
Shaping the reachable set of a dynamical system is a fundamental challenge in control design, with direct implications for both performance and safety. This paper considers the problem of selecting the optimal input matrix for a linear…
We study a well known machine learning model -the perceptron- as a simple model of jamming of hard objects. We exhibit two regimes: 1) a convex optimisation regime where jamming is hypostatic and non-critical. 2) a non convex optimisation…
We study the minimum-time damping of a physical pendulum by means of a bounded control. In the similar problem for a linear oscillator each optimal trajectory possesses a finite number of control switchings from the maximal to the minimal…
Using a recently introduced mapping between a scalar elastic network tethered at its boundaries and a diffusion problem with permanent traps, we study various vibrational properties of progressively tethered disordered fractals. Different…
Extremal Optimization, a recently introduced meta-heuristic for hard optimization problems, is analyzed on a simple model of jamming. The model is motivated first by the problem of finding lowest energy configurations for a disordered spin…
This paper discusses the utility of using simple stiffness and vibrations models, based on the Jacobian matrix of a manipulator and only the rigidity of the actuators, whenever its geometry is optimised. In many works, these simplified…
We investigate experimentally the distribution of configurations of a ring with an elementary topological constraint, a ``figure-8'' twist. Using vibrated granular chains, which permit controlled preparation and direct observation of such a…
This study presents a topology optimization scheme for realizing a bound state in the continuum along an open acoustic waveguide comprising a periodic array of elastic materials. First, we formulate the periodic problem as a system of…
Many eukaryotic cells use the active waving motion of flexible flagella to self-propel in viscous fluids. However, the criteria governing the selection of particular flagellar waveforms among all possible shapes has proved elusive so far.…
In this article a topology optimization method is developed, which is aware of material uncertainties. The uncertainties are handled in a worst-case sense, i.e. the worst possible material distribution over a given uncertainty set is taken…
In this work we deal with the optimal design and optimal control of structures undergoing large rotations. In other words, we show how to find the corresponding initial configuration and the corresponding set of multiple load parameters in…
An elastic rod, straight in its undeformed state, has a mass attached at one end and a variable length, due to a constraint at the other end by a frictionless sliding sleeve. The constraint is arranged with the sliding direction parallel to…
A ring crystal of ions trapped in a linear multipole trap is studied as a basis for an optical frequency standard. The equilibrium conditions and cooling possibilities are discussed through an analytical model and molecular dynamics…
This article treats two problems dealing with control of linear systems in the presence of a jammer that can sporadically turn off the control signal. The first problem treats the standard reachability problem, and the second treats the…
Computing the Jacobian of the solution of an optimization problem is a central problem in machine learning, with applications in hyperparameter optimization, meta-learning, optimization as a layer, and dataset distillation, to name a few.…
We consider the problem of optimally insulating a given domain $\Omega$ of ${\mathbb{R}}^d$; this amounts to solve a nonlinear variational problem, where the optimal thickness of the insulator is obtained as the boundary trace of the…
In free-space optical communications and other applications, it is desirable to design optical beams that have reduced or even minimal scintillation. However, the optimization problem for minimizing scintillation is challenging, and few…
This study numerically investigates the influence of the taper on the flow-induced vibrations of an elastically mounted circular cylinder under Vortex-induced vibrations. The dynamic response of three different taper ratios defined as 12…
In this article, we study the free vibration and the mechanical buckling of plates using a three dimensional consistent approach based on the scaled boundary finite element method. The in-plane dimensions of the plate are modeled by…