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This paper is devoted to characterizing complex projective structures defined on Riemann surface orbifolds and giving rise to injective developing maps defined on the monodromy covering of the surface (orbifold) in question. The relevance…
We present a method for determining the 3D intensity distribution of directed laser radiation with micrometer resolution in restricted volumes. Our method is based on in-coupling and guiding properties of optical fibers, with the current…
In this paper, a surface geometric constraint approach is used in designing the orbits of a solar sail. We solve the solar sail equation of motion by obtaining a generalized Laplace-Runge-Lenz (LRL) vector with the assumption that the cone…
Designing component-based constraint solvers is a complex problem. Some components are required, some are optional and there are interdependencies between the components. Because of this, previous approaches to solver design and…
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…
This short tutorial presents several ideas for designing dual function radar communication (DFRC) systems aided by intelligent reflecting surfaces (IRS). These problems are highly nonlinear in the IRS parameter matrix, and further, the IRS…
A peculiar property of complex scattering potentials is the appearance of spectral singularities. These are energy eigenvalues for certain scattering states that similarly to resonance states have infinite reflection and transmission…
The aim of this paper is to review some of the models and solution techniques used in the simulation of high-power semiconductor lasers and to address open questions. We discuss some of the peculiarities in the description of the optical…
A few recent works suggest the possibility of controlling light propagation at the interface of periodic multilayers supporting Bloch surface waves (BSWs), but optical resonators based on BSWs are yet to demonstrate. Here we discuss the…
The far-field pattern of a simple one-dimensional laser array of emitters radiating into free space is considered. In the path of investigating the inverse problem for their near fields leading to a target beam form, surprisingly we found…
A relatively simple and accurate analytical model for studying the reflectivity of neutron multilayer monochromators and supermirrors is proposed. Design conditions that must be fulfilled in order to reach the maximum reflectivity are…
The spherical nature of the wavefronts exhibited in the near-field of antenna arrays enables advanced beamforming capabilities, such as beampointing and beamnulling. In this paper, we exploit these properties to design a near-field beam…
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…
In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or…
This paper investigates the solutions to the two-phase Serrin's problem, an overdetermined boundary value problem motivated by shape optimization. Specifically, we study the torsional rigidity of composite beams, where two distinct…
We study the surface modes of a homogeneous spherical gain medium and provide a comprehensive analytic treatment of a special class of these modes that support spectral singularities. Because the latter have a divergent quality factor, we…
In this paper, which is a sequel to math.DG/9902111, we analyze the limit of the p-form Laplacian under a collapse with bounded sectional curvature and bounded diameter to a singular limit space. As applications, we give results about upper…
Reconstructing detailed 3D scenes from single-view images remains a challenging task due to limitations in existing approaches, which primarily focus on geometric shape recovery, overlooking object appearances and fine shape details. To…
We study a class of degenerate parabolic equations with boundary point degeneracy in dimensions N>=2 and investigate the associated boundary observability problem by means of shape design. While one-dimensional degenerate models have been…
We present an extensive formulation of the inverse grating problem for exural waves, in which the energy of each diffracted mode is selected and the grating configuration is then obtained by solving a linear system of equations. The grating…