Reconstruction of thin electromagnetic inhomogeneity without diagonal elements of a multi-static response matrix

Generally, to apply the MUltiple SIgnal Classification (MUSIC) algorithm for the rapid imaging of small objects, complete elements of the multi-static response (MSR) matrix must be collected. However, in some real-world applications in microwave imaging, diagonal elements of the MSR matrix are unknown. Nevertheless, it is possible to obtain imaging results using a traditional approach but theoretical reason of the applicability has not been investigated yet. In this paper, we consider the application of MUSIC for a fast identification of small objects from collected MSR matrix in both transverse magnetic (TM) and transverse electric (TE) polarizations. In order to examine the applicability, fundamental limitation, and various properties of MUSIC, we establish mathematical structure of the three imaging functions and explore that the main factors of the imaging functions are Bessel function of order zero, one, and two. The established structures demonstrate why the existence and location of small objects can be retrieved via MUSIC without the diagonal elements of the MSR matrix. Results of numerical simulations with noise-corrupted synthetic data are also provided to support the identified structures.

Analysis of a multi-frequency electromagnetic imaging functional for thin, crack-like electromagnetic inclusions

Application of MUSIC algorithm for a fast identification of small perfectly conducting cracks in limited-aperture inverse scattering problem

We consider an inverse scattering problem in which small dielectric inhomogeneities in two-dimensional space are surrounded by randomly distributed scatterers. We approach this problem using a Multiple Signal Classification (MUSIC) algorithm. This is motivated by the fact that collected Multi-static Response (MSR) matrix data can be represented as an asymptotic expansion formula in the presence of such inhomogeneities. The results obtained by numerical simulations show that MUSIC performs satisfactorily, even under conditions where a significant number of random scatterers affect the data.

Transport equations for dilute gases with internal degrees of freedom

Generalized Phase-Space Representatives of Spin- J Operators in Terms of Bloch Coherent States

Analytical diagonal elements of regularized meshless method for regular domains of [formula omitted] Dirichlet Laplace problems

We develop a semiclassical theory of wave propagation based on invariant Lagrangian manifolds existing in conservative Hamiltonian systems with chaotic dynamics. They are stable and unstable manifolds of unstable periodic orbits, and their intersections consist of homoclinic and heteroclinic orbits. For arbitrarily long times, we find matrix elements of the evolution operator between wave functions constructed in the neighbourhood of short unstable periodic orbits, in terms of canonical invariants of homoclinic and heteroclinic orbits. We verify the accuracy of these expressions by computing millions of homoclinic orbits and thousands of heteroclinic ones in the hyperbola billiard. This second part in which we describe off-diagonal matrix elements serves as complement to a previous article (first part) where we have described diagonal matrix elements.

The paper deals with the problem of electromagnetic TE-polarized monochromatic light diffraction on three-dimensional thickening of the waveguide layer of regular three-layered open planar dielectric waveguide, which forms thin-film waveguide lens. The authors propose an approximate mathematical model in which open waveguide is placed inside the auxiliary closed waveguide, that leads to well-posed diffraction problem. It is shown, that properties of guided modes of the open waveguide are stable with respect to shifts of the closed waveguide boundaries. So, the proposed approach describes the propagation of polarized light in the open smoothly irregular waveguide adequately. The three-dimensional thickening of the waveguide layer forces us to deal with electromagnetic field in vector form due to depolarization effect. The diffraction problem, presented in the work, is solved in adiabatic approximation by the small parameter of irregularity of the waveguide layer. The numerical experiments show that decreasing of the small parameter tends the reflection coefficient matrix to zero-matrix, tends the transmittance coefficient matrix to identity matrix, and besides the non-diagonal matrix elements, corresponding to modes interaction, tend to zero by an order faster than diagonal matrix elements, which shows that depolarization effects in the given configuration can be neglected.

On the application of MUSIC algorithm for identifying short sound-hard arcs in limited-view inverse acoustic problem

Multi-frequency based location search algorithm of small electromagnetic inhomogeneities embedded in two-layered medium

The coexistence of prolate and oblate shapes in the light krypton isotopes was investigated by Coulomb excitation of radioactive 74Kr and 76Kr beams at sub-barrier energies from the SPIRAL facility at GANIL. States up to the 8+ in the ground-state band and several non-yrast states were populated in both cases via multi-step Coulomb excitation. A large set of both transitional and diagonal matrix elements was extracted from the measured differential Coulomb excitation cross sections. A complementary lifetime measurement using the recoil-distance Doppler shift method gave important constraints for the determination of the matrix elements. The signs of the quadrupole moments of the yrast and excited bands represent direct evidence for the coexistence of prolate and oblate shapes in both isotopes under study. The results are compared to recent configuration mixing calculations based on the generator coordinate method and Skyrme Hartree-Fock-Bogolyiubov mean-field states.

The magnetization of a system of many mesoscopic rings under nonequilibrium conditions is considered. The corresponding disorder-averaged current in a ring I(phi) is shown to be a sum of the "thermodynamic" and "kinetic" contributions both resulting from the electron-electron interaction. The thermodynamic part can be expressed through the diagonal matrix elements J(micro micro) of the current operator in the basis of exact many-body eigenstates and is a generalization of the equilibrium persistent current. The novel kinetic part is present only out of equilibrium and is governed by the off-diagonal matrix elements J(micro nu). It has drastically different temperature and magnetic field behavior.

In this paper formulas and recursion relations for the expectation values of the operators {1-exp[-a(r-${r}_{e}$${)]\mathrm{}}}^{n}$, (r-${r}_{e}$${)}^{n}$, exp[-a(r-${r}_{e}$${)]}^{n}$, and (r-${r}_{e}$){exp[-a(r-${r}_{e}$${)]\mathrm{}}}^{n}$ are derived for a rotating Morse oscillator. These equations can be used to calculate the diagonal (v=v', J=J') and off-diagonal (v\ensuremath{\ne}v', J\ensuremath{\ne}J') matrix elements. Asymptotic approximations for the diagonal elements of the (r-${r}_{e}$${)}^{n}$ operator, 〈vJ\ensuremath{\Vert}(r-${r}_{e}$)\ensuremath{\Vert}vJ〉 and 〈vJ\ensuremath{\Vert}(r-${r}_{e}$${)}^{2}$\ensuremath{\Vert}vJ〉, are also obtained.

Two numerical methods for formal integration of the Stokes transfer equations for line formation in a strong magnetic field were tested by computing Stokes profiles for a Zeeman triplet in a Milne-Eddington model atmosphere, and for the anomalously split Ca II K line in a realistic solar model. The first method is a Feautrier (1964) type method, in which the equations are written in second-order form and solved by finite-differences. The second method is a new solution called DELO, in which an integral equation for the Stokes vector is formulated in terms of the lambda operator (LO) associated with the diagonal elements (DE) of the absorption matrix. It is shown that the DELO method is faster and more accurate than the Feautrier method, and that both methods are more efficient than the Runge-Kutta integration method. 34 refs.