Related papers: A phase-field approach for detecting cavities via …
This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce…
Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem to a constrained optimization problem…
We consider an overdetermined problem of Serrin-type with respect to an operator in divergence form with piecewise constant coefficients. We give sufficient condition for unique solvability near radially symmetric configurations by means of…
This paper addresses the inverse problem of qualitatively recovering a clamped cavity in a thin elastic plate using far-field measurements. We present a strengthened analysis of the linear sampling method by carefully examining the range of…
We consider an inverse elastic scattering problem of simultaneously reconstructing a rigid obstacle and the excitation sources using near-field measurements. A two-phase numerical method is proposed to achieve the co-inversion of multiple…
In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling points in the domain subject to random noise. We employ a…
Intuition dictates that a very long, very thin cavity (e.g., a fiber optic cable) could perhaps be modeled as an approximately one dimensional system. In this paper we rigorously explore the validity of such intuition from the perspective…
The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible.…
Spatial sound field interpolation relies on suitable models to both conform to available measurements and predict the sound field in the domain of interest. A suitable model can be difficult to determine when the spatial domain of interest…
Phase-retrieval from coded diffraction patterns (CDP) is important to X-ray crystallography, diffraction tomography and astronomical imaging, yet remains a hard, non-convex inverse problem. We show that CDP recovery can be reformulated…
We focus on BPS solutions of the gauged O(3) Sigma model, due to Schroers, and use these ideas to study the geometry of the moduli space. The model has an asymmetry parameter $\tau$ breaking the symmetry of vortices and antivortices on the…
We develop a phase-field model of eutectic growth that uses three phase fields, admits strictly binary interfaces as stable solutions, and has a smooth free energy functional. We use this model to simulate oscillatory limit cycles in…
A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the…
This paper is concerned with the uniqueness of inverse acoustic scattering problem for cavities with the modulus of the near-fields. With the aid of the reference ball technique and the superpositions of two point sources as the incident…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
We present a inverse-design framework framework for systematically engineering three-dimensional microwave cavity resonators that support modes with nonzero electromagnetic helicity. In contrast to heuristic approaches to cavity design,…
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…
A phase-field formulation is introduced to simulate quantitatively microstructural pattern formation in alloys. The thin-interface limit of this formulation yields a much less stringent restriction on the choice of interface thickness than…
Phase retrieval seeks to recover a signal x from the amplitude |Ax| of linear measurements. We cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called…
In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…