Related papers: The Optimal Shape of a Javelin
Common criteria used for measuring performance of vibrating systems have one thing in common: they do not depend on initial conditions of the system. In some cases it is assumed that the system has zero initial conditions, or some kind of…
When an optical beam propagates through a turbulent medium such as the atmosphere or ocean, the beam will become distorted. It is then natural to seek the best or optimal beam that is distorted least, under some metric such as intensity or…
We investigate an alternative solution method to the joint signal-beamformer optimization problem considered by Setlur and Rangaswamy[1]. First, we directly demonstrate that the problem, which minimizes the received noise, interference, and…
We transform the two-dimensional Dirac-Weyl equation, which governs the charge carriers in graphene, into a non-linear first-order differential equation for scattering phase shift, using the so-called variable phase method. This allows us…
We formulate the quadratic eigenvalue problem underlying the mathematical model of a linear vibrational system as an eigenvalue problem of a diagonal-plus-low-rank matrix $A$. The eigenvector matrix of $A$ has a Cauchy-like structure.…
Superconducting amplifiers are key components of modern quantum information circuits. To minimize information loss and reduce oscillations a tapered impedance transformer of new design is needed at the input/output for compliance with other…
The optimal wavelet basis is used to develop quantitative, experimentally applicable criteria for self-organization. The choice of the optimal wavelet is based on the model of self-organization in the wavelet tree. The framework of the…
Super-oscillating beams can be used to create light spots whose size is below the diffraction limit with a side ring of high intensity adjacent to them. Optical traps made of the super-oscillating part of such beams exhibit superior…
In this paper we study an optimal control problem that is affine in two-dimensional bounded control. The problem is related to the stabilization of an inverted spherical pendulum in the vicinity of the upper unstable equilibrium. We find…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
We use the parabolic wave equation to study the propagation of x-rays in tapered waveguides by numercial simulation and optimization. The goal of the study is to elucidate how beam concentration can be best achieved in x-ray optical…
A system consisting of a doubly clamped beam with an attached body (slider) free to move along the beam has been studied recently by multiple research groups. Under harmonic base excitation, the system has the capacity to passively adapt…
A classical two-stranded rope can be made by twisting two identical strands together under strain. Despite being conceptually simple, the contact-equations for helically twisted identical strands have only been solved within the last 20…
A novel optimization concept for an oscillator with two degrees of freedom is proposed. By using specially defined motion ratios, we control the action of springs and dampers to each degree of freedom of the oscillator. If the potential…
We study linear transient dynamics in a thin Keplerian disc employing a method based on variational formulation of optimisation problem. It is shown that in a shearing sheet approximation due to a prominent excitation of density waves by…
How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a…
In this paper, we study several important geometric optimization problems arising in machine learning. First, we revisit the Minimum Enclosing Ball (MEB) problem in Euclidean space $\mathbb{R}^d$. The problem has been extensively studied…
In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…
We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the…
This study experimentally optimizes the mixing of a turbulent jet at $Re=10000$ with the surrounding air by targeted shear layer actuation. The forcing is composed of superposed harmonic signals of different azimuthal wavenumber $m$…