The Role of Model Dimensionality in Linear Inverse Scattering from Dielectric Objects

This paper deals with 3D and 2D linear inverse scattering approaches based on the Born approximation, and investigates how the model dimensionality influences the imaging performance. The analysis involves dielectric objects hosted in a homogenous and isotropic medium and a multimonostatic/multifrequency measurement configuration. A theoretical study of the spatial resolution is carried out by exploiting the singular value decomposition of 3D and 2D scattering operators. Reconstruction results obtained from synthetic data generated by using a 3D full-wave electromagnetic simulator are reported to support the conclusions drawn from the analysis of resolution limits. The presented analysis corroborates that 3D and 2D inversion approaches have almost identical imaging performance, unless data are severely corrupted by the noise.

Scattering Map for the Vlasov–Poisson System

We construct (modified) scattering operators for the Vlasov–Poisson system in three dimensions, mapping small asymptotic dynamics as $$t\rightarrow -\infty$$ t → - ∞ to asymptotic dynamics as $$t\rightarrow +\infty$$ t → + ∞ . The main novelty is the construction of modified wave operators, but we also obtain a new simple proof of modified scattering. Our analysis is guided by the Hamiltonian structure of the Vlasov–Poisson system. Via a pseudo-conformal inversion, we recast the question of asymptotic behavior in terms of local in time dynamics of a new equation with singular coefficients which is approximately integrated using a generating function.

The semiclassical limit on a star-graph with Kirchhoff conditions

We consider the dynamics of a quantum particle of mass m on a n-edges star-graph with Hamiltonian $$H_K=-(2m)^{-1}\hbar ^2 \Delta $$ H K = - ( 2 m ) - 1 ħ 2 Δ and Kirchhoff conditions in the vertex. We describe the semiclassical limit of the quantum evolution of an initial state supported on one of the edges and close to a Gaussian coherent state. We define the limiting classical dynamics through a Liouville operator on the graph, obtained by means of Kreĭn’s theory of singular perturbations of self-adjoint operators. For the same class of initial states, we study the semiclassical limit of the wave and scattering operators for the couple $$(H_K,H_{D}^{\oplus })$$ ( H K , H D ⊕ ) , where $$H_{D}^{\oplus }$$ H D ⊕ is the Hamiltonian with Dirichlet conditions in the vertex.

Dynamical C*-algebras and Kinetic Perturbations

The framework of dynamical C*-algebras for scalar fields in Minkowski space, based on local scattering operators, is extended to theories with locally perturbed kinetic terms. These terms encode information about the underlying spacetime metric, so the causality relations between the scattering operators have to be adjusted accordingly. It is shown that the extended algebra describes scalar quantum fields, propagating in locally deformed Minkowski spaces. Concrete representations of the abstract scattering operators, inducing this motion, are known to exist on Fock space. The proof that these representers also satisfy the generalized causality relations requires, however, novel arguments of a cohomological nature. They imply that Fock space representations of the extended dynamical C*-algebra exist, involving linear as well as kinetic and pointlike quadratic perturbations of the field.

Range-Dependent Seismo-Acoustic Propagation in the Marginal Ice Zone

Single-scattering operators are used to extend the seismo-acoustic parabolic equation to problems involving transitions between areas with and without ice cover, which are common in the marginal ice zone. Gradual transitions are handled with single-scattering operators for sloping fluid–solid interfaces. Sudden transitions, which may occur when the ice fractures and drifts, are handled with a single-scattering operator that conserves normal displacement and tangential stress across the vertical interfaces between the range-independent regions that are used to approximate a range-dependent environment. The approach is tested by making comparisons with a finite-element model for problems involving range-dependent features in the ice cover and in a sediment that supports shear waves.

Diffraction of the H-polarized plane wave by a finite layered graphene strip grating

The scattering of the H-polarized plane electromagnetic wave by a finite multilayer graphene strip grating is considered. The properties of the whole structure are obtained from the set of integral equations, which are written in the operator form. The scattering operators of a single layer are used and supposed to be known. Scattering and absorption characteristics as well as diffraction patterns are presented.