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Existing electromagnetic inverse design methods are often established in the spacial domain. This communication presents an inverse design method, which can design aperture field for the desired phaseless radiation pattern, from the…
The design of absorbing boundary conditions (ABC) in a numerical simulation is a challenging task. In the best cases, spurious reflections remain for some angles of incidence or at certain wave lengths. In the worst, ABC are not even…
We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo-…
Most technical polymers and many biopolymers contain very different molecular species (unlike chain length, molecular architecture and/or chemical composition) in contrast to pure low molecular weight compounds. This inconsistent…
Closed formulas are derived for the field in the focal region of a diffraction limited lens, such that the electric field component in a given direction at the focal point is larger than that of all other focused fields with the same power…
We present a spectral method for one-sided linear fractional integral equations on a closed interval that achieves exponentially fast convergence for a variety of equations, including ones with irrational order, multiple fractional orders,…
The reflectionless filter cell described in this article alleviates many system problems associated with excess out-of-band gain, impedance mismatches, and component interactions. The simplest filter cell exhibits a third-order Inverse…
Nowadays, fractional differential equations are a well established tool to model phenomena from the real world. Since the analytical solution is rarely available, there is a great effort in constructing efficient numerical methods for their…
We report the design and characterization of a high performance integrated arbitrary filter from 1450 nm to 1640 nm. The filter's target spectrum is chosen to suppress the night-sky OH emission lines, which is critical for ground-based…
Optimal extraction is a key step in processing the raw images of spectra as registered by two-dimensional detector arrays to a one-dimensional format. Previously reported algorithms reconstruct models for a mean one-dimensional spatial…
Fractal Interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse-grained Navier-Stokes equations. It is based on synthetically generating a scale-invariant…
We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from…
We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane. For the random energy model, we obtain the phase diagram in the…
A modified Green operator is proposed as an improvement of Fourier-based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media. Contrary to other methods, the number of iterations necessary…
Equilibrium measures are special invariant measures of chaotic dynamical systems and iterated function systems, commonly studied as salient examples of fractal measures. While useful analytic expressions are rare, computational exploration…
We present a new algorithm for finding isolated zeros of a system of real-valued functions in a bounded interval in $\mathbb{R}^n$. It uses the Chebyshev proxy method combined with a mixture of subdivision, reduction methods, and…
We develop a sparse spectral method for a class of fractional differential equations, posed on $\mathbb{R}$, in one dimension. These equations can include sqrt-Laplacian, Hilbert, derivative and identity terms. The numerical method utilizes…
In this paper, we consider controlling a class of single-input-single-output (SISO) commensurate fractional-order nonlinear systems with parametric uncertainty and external disturbance. Based on backstepping approach, an adaptive controller…
Classical approximation bases such as Chebyshev polynomials provide principled and interpretable representations, but their multivariate tensor-product constructions scale exponentially with dimension and impose axis-aligned structure that…
We derive an analytical expression for the effective indices of modes of circular step-index fibers valid near their cutoff wavelengths. The approximation, being a first-order Taylor series of a smooth function, is also valid for the real…