Related papers: A variational mode solver for optical waveguides b…
We develop and demonstrate two numerical methods for solving the class of open cavity problems which involve a curved, cylindrically symmetric conducting mirror facing a planar dielectric stack. Such dome-shaped cavities are useful due to…
We develop a new approach to robust adaptive beamforming in the presence of signal steering vector errors. Since the signal steering vector is known imprecisely, its presumed (prior) value is used to find a more accurate estimate of the…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
In this work, we consider an extension to parabolic problems of the variational multiscale method with spectral approximation of the sub-scales. We first discretize in time using a finite difference scheme and second, apply the…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
We present a numerical approach to efficiently calculate spin-wave dispersions and spatial mode profiles in magnetic waveguides of arbitrarily shaped cross section with any non-collinear equilibrium magnetization which is translationally…
A method to probe the guiding characteristics of waveguides formed in real-time is proposed and evaluated. It is based on the analysis of the time dependent light distribution observed at the exit face of the waveguide while progressively…
We present applications of variational-wavelet approach to nonlinear (rational) rms envelope equations. We have the solution as a multiresolution (multiscales) expansion in the base of compactly supported wavelet basis. We give extension of…
Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the…
A widespread, intuitive and computationally inexpensive method to analyze light guidance through waveguide bends is by introducing an equivalent straight waveguide with refractive index profile modified to account for actual waveguide bend.…
We present a variational wavefunction which explains the behaviour of the supersolid state formed by hard-core bosons on the triangular lattice. The wavefunction is a linear superposition of {\em only and all} configurations minimising the…
In this paper, modulating functions-based method is proposed for estimating space-time dependent unknowns in one-dimensional partial differential equations. The proposed method simplified the problem into a system of algebraic equations…
Automatically determining the number of intrinsic mode functions (IMFs) and their center frequencies in Variational Mode Decomposition (VMD) remains an open mathematical challenge. Existing methods rely on heuristic settings,…
We use singular value decomposition techniques to generalize the wavelet transform modulus maxima method to the multifractal analysis of vector-valued random fields. The method is calibrated on synthetic multifractal 2D vector measures and…
Dynamic optical sensors, as those based on the reflectivity of isotropic dielectrical interfaces, can be useful for measuring small changes in the refractive index of fluid media. Exact and approximated explicit formulas for their…
In this paper, we develop an accurate and efficient framework for computing subwavelength guided modes in high-contrast periodic media with line defects, based on a tight-binding approximation. The physical problem is formulated as an…
Guided wave modes in a symmetric slab waveguide formed by an isotropic dielectric layer with cubic nonlinear response placed in the hyperbolic surrounding medium are investigated theoretically. Optical axis of the hyperbolic medium is…
Considered here is an efficient technique to compute approximate profiles of solitary wave solutions of fractional Korteweg-de Vries equations. The numerical method is based on a fixed-point iterative algorithm along with extrapolation…
We report on the fabrication and characterization of composite multimode waveguide structures that consist of a stack of single-mode waveguides fabricated by ultrafast laser inscription. We explore 2 types of composite structures; those…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…