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We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
A topology optimization approach for designing large deformation contact-aided shape morphing compliant mechanisms is presented. Such mechanisms can be used in varying operating conditions. Design domains are described by regular hexagonal…
Precision motion stages are an essential part of a wide range of manufacturing equipment, and their motion performance are critical to the quality and throughput of the systems. The drastically increasing demand for higher manufacturing…
Dispersion relations govern wave behaviors, and tailoring them is a grand challenge in wave manipulation. We demonstrate inverse design of phononic dispersion using non-local interactions on one-dimensional spring-mass chains. For both…
We predict analytically and confirm with numerical simulations that inter-mode dispersion in nanowire waveguide arrays can be tailored through periodic waveguide bending, facilitating flexible spatio-temporal reshaping without break-up of…
We investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise. Adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of Besov scales,…
As an attempt to develop a reconfigurable surface architecture that can use liquid metal such as Galinstan to shape surface channels on demand, this paper considers a punctured surface where cavities are evenly distributed and can be filled…
We present two complementary models to study stationary nonlinear solutions in one-dimensional plasmonic slot waveguides made of a finite-thickness nonlinear dielectric core surrounded by metal regions. The considered nonlinearity is of…
We design and optimize a waveguide structure consisted of three segments of PT-symmetric coupler. It can amplify the difference mode with the attenuation of the sum mode, so performs an asymmetric optical amplifier. Also, the dependence of…
Transport properties of disordered electron system can be characterized by the conductance, Lyapunov exponent, or level spacing. Two additional parameters, $K_{11}$ and $\gamma $ were introduced recently which measure the non-homogeneity of…
Materials with nanoscale phase separation are considered. These materials are formed by a mixture of several phases, so that inside one phase there exist nanosize inclusions of other phases, with random shapes and random spatial locations.…
We describe a geometric method to quantify wave patterns observed in the nervous system, which are non-stationary and with a mixture of spiral, target, plane and irregular waves. The method analyzes fluctuations of the energy angular…
In this work we present the results of a study of the possibility of using a homogeneous basis and a new generalization of coupled modes theory to describe non-periodic structured waveguides. It was shown that for the studied…
Using finite difference time domain and band structure computer simulations, we show that it is possible to construct optical cavities and waveguide architectures in hyperuniform disordered photonic solids that are unattainable in photonic…
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of…
The construction of optimal non-uniform mappings for discrete input memoryless channels (DIMCs) is investigated. An efficient algorithm to find optimal mappings is proposed and the rate by which a target distribution is approached is…
In this contribution we investigate the application of phase-field fracture models on non-linear multiscale computational homogenization schemes. In particular, we introduce different phase-fields on a two-scale problem and develop a…
In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift…
Here we show how to design phase-shifting algorithms (PSAs) for nonuniform phase-shifted fringe patterns using their frequency transfer function (FTF). Assuming that the nonuniform/nonlinear (NL) phase-steps are known, we introduce the…
We outline here a simple yet efficient method for finding optimized configurations of the elements of radio-astronomical interferometers with fixed pad locations. The method can be successfully applied, as we demonstrate, to define new…