Scattering From Isotropic Connected Wire Medium Metamaterials: Three-, Two-, and One-Dimensional Cases

The dispersion relations of the surface polariton in a semi-infinite wire medium with spatial dispersion are analysed. In comparison with the traditional spatial dispersive medium there only exists one branch instead of multibranch for the dispersion curve. The possibility of the experimentally observing the surface polaritons by attenuated total reflection is simulated numerically.

This paper presents the modelling of wire medium using a finite-difference time-domain (FDTD) method. The flat subwavelength lenses formed by the wire medium (lattices of parallel metallic wires) have been modelled in FDTD through the effect medium approach. The auxiliary differential equation (ADE) method has been applied in FDTD model in order to take into account both the frequency dispersion effect and the spatial dispersion effect which was found recently. The developed formulas have been implemented in a two-dimensional (2-D) FDTD model and validated by comparing transmission coefficient calculated from analytical solutions. The simulation results demonstrate the subwavelength imaging capability of the wire medium lenses.

This article analyzes the collimation behavior of a wire medium devoted to magnetic resonance imaging. In the first part, the point-spread function of a doubly infinite wire medium is analyzed for the magnetic field with the help of the array scanning method. In the second part, we present two methods to evaluate the field transmission by the wire medium based on the measure of the magnetic field computed with the method of moments. Simulation results obtained with the MoM are shown. This behavior is validated in the third part with experimental results obtained with a magnetic resonance imaging instrument at the University Hospital of Liége with a straight-wires collimator. Both simulation and experimental results confirm the ability of the wire medium to transfer electromagnetic fields in magnetic resonance imaging operational conditions.

Guided waves in a wire medium slab are studied. The wire medium is considered as a continuous medium described in terms of uniaxial permittivity dyadic. Nonlocal model of the wire medium, taking into account spatial dispersion, is used in the analysis. Different cases of an arrangement of the wires are considered. Analytic expressions for the fields in unbounded media and numerical solutions for eigenmodes spectrum in wire medium slab are obtained. Comparison of the results given by old (local) and new model of wire medium is presented.

The use of a Fourier heating model in high intensity laser material processing is limited due to the assumptions made in the model. An electron-kinetic theory may offer an alternative solution to the problem. Consequently, in the present study an electron-kinetic theory approach is introduced to model the 3-dimensional laser heating process. The phase change and conduction effects are encountered when driving the governing equations. To simulate the moving heat source, a scanning velocity of the laser beam is considered, in this case, the laser beam scans the workpiece surface with a constant velocity. The governing heat transfer equation is in the form of integro-differential equation, which does not yield the analytical solution. Therefore, a numerical method employing an explicit scheme is introduced to discretize the governing equations. To validate the theoretical predictions, an experiment is conducted to measure the surface temperatures of the workpiece substrate during Nd YAG laser heating process. It is found that the rapid increase in temperature occurs in surface vicinity due to the successive electron-lattice site atom collisions. The depth of melting zone increases as the heating progresses and the temperature remains almost constant at the melting temperature of the substrate in the surface vicinity. In addition, the theoretical predictions agree well with the experimental findings.

3-dimensional modeling of laser repetitive pulse heating: a phase change and a moving heat source considerations

Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. In this paper we present a review of such techniques and show how recent advances have opened the way for future studies of neural fields in both one and two dimensions that can incorporate realistic forms of axo-dendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons.

This study addresses a magneto-viscoelasticity problem, considering the one-dimensional case. The system under investigation is given by the coupling a non-linear partial differential equation with a linear integro-differential equation. The system models a viscoelastic body whose mechanical behavior, described by the linear integro-differential equation, is also influenced by an external magnetic field. The model here investigated aims to consider the concomitance of three different effects: viscoelasticity, aging and magnetization. In particular, the viscoelastic behavior is represented via an integro-differential equation whose kernel characterizes the properties of the material. In a viscoelastic material subject to the effects of aging, all changes in the response to deformation are due not only to the intrinsic memory of the material but also to deterioration with the age of the material itself. Thus, the relaxation function is not assumed to depend on the two times, present and past, via their difference, but to depend on both the present and past times as two independent variables. The sensibility to an external magnetic field is modeled by a non-linear partial differential equation taking its origin in the Landau-Lifschitz magnetic model. This investigation is part of a long-term research project aiming to provide new insight in the study of materials with memory and, in particular, viscoelastic materials. Specifically, the classical model of viscoelastic body introduced by Boltzmann represents the fundamental base from which a variety of generalizations have been considered in the literature. In particular, the effects on the viscoelastic body due to interaction with an external magnetic field are studied. The new aspect under investigation is the combined presence of the external magnetic field with the effect of aging. Indeed, the coupling of viscoelasticity, which takes into account the deterioration of the material with time, with the presence of an external magnetic field, was never considered in previous research. An existence and uniqueness result is proved under suitable regularity assumptions.

Nonlocality of wire media — Local thickness-dependent permittivity model

Steady two-dimensional potential flow past a semi-infinite flat-bottomed body is considered. This stern flow is assumed to separate tangentially from the body. Gravity waves of finite amplitude occur on the free surface. An exact relation between the amplitude of these waves and the Fronde number F is derived. It shows that these waves can exist only for F greater than the value F* = 2·23. This is slightly less than the value Fc = 2·26 at which breaking occurs. For F slightly larger than F*, the steepness is a multi-valued function of F, indicating the existence of more than one solution for these values of F. In addition, a numerical scheme based on an integro-differential equation formulation is derived to solve the problem in the fully nonlinear case. The shape of the free surface profile is computed for different values of F. As a check on the numerical results, they are shown to satisfy the exact relation between steepness and the Froude number.

A simplified formulation of photon transport in leaf canopies with scatterers of finite dimensions

In this paper, we investigate a Sparre Andersen risk model perturbed by diffusion with phase-type inter-claim times. We mainly study the distribution of maximum surplus prior to ruin. A matrix form of integro-differential equation for this quantity is derived, and its solution can be expressed as a linear combination of particular solutions of the corresponding homogeneous integro-differential equations. By using the divided differences technique and nonnegative real part roots of Lundberg’s equation, the explicit Laplace transforms of particular solutions are obtained. Specially, we can deduce closed-form results as long as the individual claim size is rationally distributed. We also give a concise matrix expression for the expected discounted dividend payments under a barrier dividend strategy. Finally, we give some examples to present our main results.

Mathematical simulation of nonlinear oscillations of viscoelastic pipelines conveying fluid

Slabs formed by wire medium metamaterials are capable of transmitting evanescent waves over several wavelengths, and enable perfect imaging of field patterns with deeply subwavelength features over such long distances. To date, perfect imaging has been limited to narrow frequency windows defined by the Fabry–Perot (FP) resonance condition. Away from such resonances, backreflections within the slab result in the excitation of surface waves supported by the wire medium. This leads to image distortions, thus severely limiting the use of wire media for broadband subwavelength imaging. Here, we propose and demonstrate that this limitation can be overcome by using ultrashort electromagnetic pulses as the field source, allowing separation of the initial pulse from subsequent backreflections, which cannot be achieved using continuous-wave sources. Using a terahertz (THz) near-field microscope based on a time-domain approach, we demonstrate ultrabroadband transmission of distortion-free images over the entire frequency band of the source (0.1–1.75 THz). Such performance requires the slabs to be sufficiently long; the limits of this approach are also demonstrated by imaging a resonant mode with high Q-factor through a short slab. Our results pave the way for the implementation of wire media in broadband imaging applications based on short electromagnetic pulses, such as THz pulse imaging or optical imaging with ultrashort laser pulses.

A new method is developed to calculate characteristics of contaminant transport (including non-classical regimes) in statistically homogeneous sharply contrasting media. A transport integro-differential equation in the space-time representation is formulated on the basis of the model earlier proposed by one of the authors (L. M.). Analytical expressions for transport characteristics in limiting time intervals in the one-dimensional case are derived. An interpolation form is proposed for the integral kernel of the transport equation. On a basis of this expression, an algorithm is developed for numerical modelling the contaminant transport in statistically homogeneous sharply contrasting media. Trial numerical 1D calculations are performed based on this algorithm. Good agreement was found between the numerical simulation results and the asymptotic analytical expressions.