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A kinematic approach to the geometric phase for mixed quantal states in nonunitary evolution is proposed. This phase is manifestly gauge invariant and can be experimentally tested in interferometry. It leads to well-known results when the…
Micro/Nano-positioning stages are of great importance in a wide range of manufacturing machines and instruments. In recent years, the drastically growing demand for higher throughput and reduced power consumption in various IC manufacturing…
We develop expressions for the nonlinear wave damping and frequency correction of a field of random, spatially homogeneous, acoustic waves. The implications for the nature of the equilibrium spectral energy distribution are discussed
The elastic behavior of materials is of critical importance for the design, fabrication, and testing of industrial and structural components. The ease with which the wave angle of incidence can be varied makes ultrasonic techniques well…
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…
The paper gives a description of wave propagation in discrete-periodic one-dimensional media with block structure. For one-dimensional problems mathematical models are proposed that describe block structures in the form of a mass chain or…
We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multi-core waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an…
Dispersion studies demonstrate that waveguide layout can be used to enhance the bandwidth performance of multimode polymer waveguides for use in board-level optical interconnects, providing >40 GHzxm without the need for any launch…
Adaptive quantum design identifies the best broken-symmetry configurations of atoms and molecules that enable a desired target function response. In this work, numerical optimization is used to design atomic clusters with specified…
Nonreciprocity in space-time modulated photonic crystals has been investigated in the context of nonreciprocal propagation and polarization. Here, we investigate a reconfigurable nonreciprocal wave growth in space-time modulated crystals.…
In nonlinear dynamical systems with highly nonorthogonal linear eigenvectors, linear non-modal analysis is more useful than normal mode analysis in predicting turbulent properties. However, the non-trivial time evolution of non-modal…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
Topological defects, such as disclination lines in nematic liquid crystals, are fundamental to many physical systems and applications. In this work, we study the behavior of nematic disclinations in thin parallel-plate geometries with…
A nonlinear model of the scalar field with a coupling between the field and its gradient is developed. It is shown, that such model is suitable for the description of phase transition accompanied by formation of spatial inhomogeneous…
By designing tailor-made resonance modes with structured atoms, metamaterials allow us to obtain constitutive parameters outside their limited range from natural or composite materials. Nonetheless, tuning the constitutive parameters relies…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…
We introduce a trainable coded modulation scheme that enables joint optimization of the bit-wise mutual information (BMI) through probabilistic shaping, geometric shaping, bit labeling, and demapping for a specific channel model and for a…
Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A…
A geometric numerical method for simulating suspensions of spherical and non-spherical particles with Stokes drag is proposed. The method combines divergence-free matrix-valued radial basis function interpolation of the fluid velocity field…