Unbounded Medium Research Articles

Propagation of an Ultrawideband Electromagnetic Pulse Along a Plasma-Filled Coaxial Line

The propagation of an ultrawideband (UWB) electromagnetic pulse along a coaxial line filled with a cold isotropic plasma is considered. The pulse shape evolution is studied both in the frequency domain through the Fourier transform analysis and in the time domain using either the high-frequency approximation or the finite-difference time-domain (FDTD) approach. The emphasis is placed on the behavior of the pulse shape for various values of the plasma density in the coaxial line. It is shown that transmission of a nanosecond TEM pulse in a plasma-filled coaxial line can serve for revealing the basic features of changes in the shape of such signals during their propagation in an unbounded plasma medium.

Automated hyperparameter optimization for simulating boundary conditions for acoustic and elastic wave propagation using deep learning

We have developed a deep learning framework to simulate the effect of boundary conditions for wave propagation in anisotropic media. To overcome the challenges associated with the stability of conventional implementation of boundary conditions for strongly anisotropic media, we develop an efficient algorithm using deep neural networks. We incorporate the hyperparameter optimization (HPO) workflow in the deep learning framework to automate the network training process. Hyperparameter selection is a crucial step in model building and has a direct impact on the performance of machine learning models. We implement three different HPO techniques, namely random search, Hyperband, and Bayesian optimization, for simulating boundary conditions and compare the strengths and drawbacks of these techniques. We train the network using a few shot locations and time slices enabling the network to learn how to remove boundary reflections and simulate wave propagation for unbounded media. The automated deep learning framework with HPO improves the performance of deep learning models by achieving the optimal minima and significantly improves the efficiency of the workflow. The benefit of this approach is its simple implementation and significant reduction of reflections at the boundaries, especially in the case of tilted transverse isotropic media. We validate our approach by comparing wave propagation at the boundaries using our algorithm with the output obtained using the unbounded media simulated by padding the model. Tests on different models with acoustic and elastic wave propagation verify the effectiveness of our approach.

Effect of boundaries on displacements and motion in two-dimensional fluid or elastic films and membranes.

Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, the resulting flows in an unbounded two-dimensional incompressible low-Reynolds-number fluid or displacements in a two-dimensional linearly elastic solid seem to diverge logarithmically with the distance from the force center, which has led to some debate. Recently, we have demonstrated that such divergences cancel when the total (net) force vanishes. Here, we illustrate that if a net force is present, the boundaries play a prominent role. Already a single no-slip boundary regulates the flow and displacement fields and leads to their decay to leading order inversely in distance from a force center and the boundary. In other words, it is the boundary that stabilizes the system in this situation, unlike the three-dimensional case, where an unbounded medium by itself is able to absorb a net force. We quantify the mobility and displaceability of an inclusion as a function of the distance from the boundary, as well as interactions between different inclusions. In the case of free-slip boundary conditions, a kinked boundary is necessary to achieve stabilization.

A Multitrace Surface Integral Equation Solver to Simulate Graphene-Based Devices

A multitrace surface integral equation (MT-SIE) solver is proposed to analyze electromagnetic field interactions on composite devices involving magnetized and nonmagnetized graphene sheets. The computation domain is decomposed into two subdomains: an exterior subdomain that represents the unbounded background medium where the device resides in an interior subdomain that represents the dielectric substrate. Resistive Robin transmission conditions (RRTCs) are formulated to describe the infinitesimally thin graphene sheet that partially covers the surface between the two subdomains. On the rest of this surface, traditional Robin transmission conditions (RTCs) are enforced. The electric and magnetic field equations are used as the governing equations in each subdomain. The governing equations of a subdomain are locally coupled to the governing equations of its neighbor using RRTCs and RTCs. The accuracy and the applicability of the proposed MT-SIE solver are demonstrated by various numerical examples.

Generalized thermoelastic MGT model for a functionally graded heterogeneous unbounded medium containing a spherical hole

Generalized thermoelastic MGT model for a functionally graded heterogeneous unbounded medium containing a spherical hole

Suppressing position approximation imaging artifacts in full waveform modeling and inversion of marine seismic data

Full-waveform inversion (FWI) is an advanced seismic imaging method for determining high resolution velocity models of different scales, such as in subseafloor geo-hazard monitoring and risk analysis. Among all two-way wave-equation based modeling methods, a mixed-grid finite-difference modeling (FDM) in frequency domain has the advantage of low numerical dispersion errors for mesh size up to 1/4 wave-length. However, irregular source and receiver positions situated away from the FDM nodes introduce position approximation error (PAE) as large as half mesh size. When a source or receiver is situated in strong heterogeneity or near a free surface, the PAE induces imaging artifacts in high frequencies. We propose an imaging artifact suppression method for multi-scale FDM and FWI in marine seismic survey. The delta function of the source or receiver position is approximated by a discrete Kaiser-windowed sinc function in unbounded medium. The free-surface effects to sources and receivers are compensated with the mirror source concept. The final coefficients for delta function approximation and wavefield interpolation are spatially confined tensor products. The results using ocean bottom cable and vertical cable survey layouts in synthetic models validate the accuracy and feasibility of this new FDM and FWI strategy. The FWI tests shows that this strategy has reduced small scale artifacts at high frequencies for survey layouts of good and poor illuminations. The extension of our method to 3-D visco-acoustic model or reverse time migration is straightforward.

Tapered photonic switching.

The advent of novel nonlinear materials has stirred unprecedented interest in exploring the use of temporal inhomogeneities to achieve novel forms of wave control, amidst the greater vision of engineering metamaterials across both space and time. When the properties of an unbounded medium are abruptly switched in time, propagating waves are efficiently converted to different frequencies, and partially coupled to their back-propagating phase-conjugate partners, through a process called time-reversal. However, in realistic materials the switching time is necessarily finite, playing a central role in the resulting temporal scattering features. By identifying and leveraging the crucial role of electromagnetic momentum conservation in time-reversal processes, here we develop a general analytical formalism to quantify time-reversal due to temporal inhomogeneities of arbitrary profile. We deploy our theory to develop a formalism, dual to spatial tapering, that enables the tailoring of a desired time-reversal spectral response, demonstrating its use for the realization of broadband frequency converters and filters.

An Alternative Experimental Method for Determination of Light Beam Attenuation Coefficient in Underwater Wireless Optical Communication

In wireless optical communication systems, the transmission of optical signals via the channel (air or water) is affected by absorption and scattering. These reduce the signal strength (attenuation) and transmission distance of the signals. In pure water, the blue-green region of the visible light gives low attenuation. Some models have been developed to characterize the underwater optical channel such as Beer Lambert’s law, Radiative Transfer equation and Monte Carlo model. In underwater optical communication, optical power meters are an invaluable tool in the determination of attenuation coefficients. However, optical power meters for underwater optical communication are very expensive. There is a need to be able to determine the attenuation in the underwater optical communication channel at a low cost, especially in the absence of underwater optical power meters. In this paper, we present an alternative low-cost experimental method of obtaining the approximate attenuation coefficient of the visible light beam in underwater optical wireless communication without the use of optical power meters. A wireless visible light communication system was set up experimentally for underwater measurements involving an oscilloscope as the only measuring device. The system uses sub-carrier frequency modulation; a white light-emitting diode array for the transmitter, and a solar panel at the receiver front end. A theoretical transmission model was developed from the experimental setup based on the line of sight method in an unbounded medium, Beer Lambert’s law, and the received sub-carrier signals; in order to provide an alternative method of determining approximately the attenuation coefficient of the underwater medium. Experiments were performed in air, clear water and in saline water. The attenuation in the air was used as a reference upon which attenuation in the clear water and the saline water was based. The saline water has a salt concentration of 6.7 g/100 mL by weight and a total dissolved solid of 86.2 ppt. The trend of the measured received sub-carrier signals showed deviation from the developed theoretical model, and the model was therefore adjusted to conform to the experimental results. From the adjusted model, the attenuation coefficient of 0.0007379 cm-1 and 0.02447 cm-1 were obtained for clear water and the saline water respectively. The method is simple, straightforward, easy to set up in a laboratory, low cost and can be applied to visible light of any wavelength.

Thermal plane waves in unbounded non-local medium exposed to a moving heat source with a non-singular kernel and higher order time derivatives

In this paper, the thermoelastic characteristics of a nonlocal unbounded viscoelastic medium due to an instantaneous heat source is investigated by considering a modified dual-phase-lag model with higher-order time derivatives. The fractional derivative and Eringen's non-local theory are also applied in the considered model. To extend the application of the classical Kelvin-Voigt model, a fractional derivative operator with non-single kernels based on the Atangana and Baleanu's concept is proposed. After applying the Laplace transform method, the governing systems of equations are expressed as vector-matrix differential form and solved by constructing an eigenvalue problem. Some comparative results are presented to analyze the effects of heat source velocity, nonlocal parameter, structural viscoelastic coefficients, phase lags, fractional and higher-order parameters on the behavior of physical fields.

System of cracks under the impact of plane elastic waves

The problem of determining the two-dimensional diffraction field and the stress state arising from the interaction of elastic waves with a system of arbitrarily located cracks is solved. Cracks are located in an unbounded elastic medium which is in a plane deformation state. The method of solution is based on the use of discontinuous solutions of the equations of motion of elastic media and the reduction of the original problem to a system of singular integro-differential equations. The obtained systems are solved numerically the mechanical quadrature method.

Magneto-Thermoelastic Response in an Unbounded Medium Containing a Spherical Hole via Multi-Time-Derivative Thermoelasticity Theories.

This article introduces magneto-thermoelastic exchanges in an unbounded medium with a spherical cavity. A refined multi-time-derivative dual-phase-lag thermoelasticity model is applied for this reason. The surface of the spherical hole is considered traction-free and under both constant heating and external magnetic field. A generalized magneto-thermoelastic coupled solution is developed utilizing Laplace’s transform. The field variables are shown graphically and examined to demonstrate the impacts of the magnetic field, phase-lags, and other parameters on the field quantities. The present theory is examined to assess its validity including comparison with the existing literature.

Dynamic response of large diameter, concrete‐lined vertical shafts under external and seismic excitation

AbstractThis article proposes a novel numerical model of the dynamic response of large diameter, concrete‐lined circular shafts, embedded in transversely isotropic soils. Excitation is given as time‐harmonic external loads applied to the base of the shaft, or vertically propagating, time‐harmonic pressure waves. The concrete lining is modeled with finite annular plate and cylindrical‐shell finite elements, while the contact tractions at the shaft–soil interface are modeled within a boundary elements framework. The response of the coupled system is obtained by imposing rigorous continuity and equilibrium conditions at the interface. The model yields accurate representation of the energy exchange between shaft and soil, as well as energy propagation through the soil as an unbounded medium. Original numerical results are presented on the response of the shaft and lining for selected geometric and constitutive parameters, frequencies and type of excitation, and anisotropic soil constitutions.

Stress changes caused by exsolution of magmatic fluids within an axisymmetric inclusion

SUMMARY In volcanic regions ascending magma is subject to depressurization and is generally accompanied by exsolution of volatiles. We assume a process in which these volatiles propagate upward across newly fractured and permeable rock layers, bringing a sharp increase of pore pressure and temperature within a thin disc-shaped region (inclusion). Thermo-poro-elastic (TPE) inclusion models provide a mechanism to explain seismicity and deformation induced by p and T changes in absence of new magma emplacement in volcanic contexts. They are also suitable to represent the mechanical effects due to fluid extraction and re-injection in geothermal fields. In the present work analytic solutions are provided for the displacement, strain and stress fields assuming a TPE unbounded medium. Significant deviatoric stress is generated by positive increments of pore pressure and temperature: the stress field is fully deviatoric outside the TPE inclusion, but a strong isotropic stress component is present within, leading to highly heterogeneous faulting mechanisms: if the disc plane is horizontal, thrust faulting mechanisms are favoured within the TPE disc over optimally oriented faults and normal mechanisms above. The model is easily generalized to a vertically thick disc with variable temperature and pore-pressure changes: then, an extensional environment can be obtained even within the TPE inclusion assuming upward decreasing of pore pressure and temperature changes. The supplied analytical solution may be used to model near-field TPE inclusion effects and to validate more complex numerical modelling.

Eigenvalues approach on thermo-elastic diffusions problem for an infinite material containing spherical holes

In this article, the thermoelastic diffusion interaction in an unbounded medium containing spherical holes in the context Green-Naghdi model of type III are studied. The inner surface of hole is taken to be tractions free and due to an exponent of the decayed heat flux. The Laplace transforms techniques are used. The eigenvalues approaches are adopted for the solutions of applications for infinite media with a spherical hole. The numerical results for the concentration, the displacement, the chemical potential, the temperature, and the stress are presented analytical and graphically.

Green's functions of the Boltzmann transport equation with the full scattering matrix for phonon nanoscale transport beyond the relaxation-time approximation

The phonon Boltzmann transport equation (BTE) has been widely utilized to study thermal transport in solids. While for a number of materials the exact solution to the BTE has been obtained for a uniform heat flow, problems arising in micro/nanoscale heat transport have been analyzed within the relaxation time approximation (RTA). Since the RTA breaks down at temperatures low compared to the Debye temperature, this approximation prevents the study of an important class of high Debye temperature materials such as diamond, graphite, graphene, and some other two-dimensional materials. We present a full scattering matrix formalism that goes beyond the RTA approximation and obtain a Green's function solution for the linearized BTE, which leads to an explicit expression for the phonon distribution and temperature field produced by an arbitrary spatiotemporal distribution of heat sources in an unbounded medium. The presented formalism is capable of describing a wide range of phenomena, from heat dissipation by nanoscale hot spots to the propagation of second sound waves. We provide numerical results for graphene for a spatially sinusoidal heating profile and discuss the importance of using the full scattering matrix compared to the RTA.

The effect of surfactant on the drag and wall correction factor of a drop in a bounded medium

Abstract In the present article, the analytical solution for creeping motion of a drop/bubble characterized by insoluble surfactant is examined at the instant it passes the center of a spherical container filled with Newtonian fluid at low Reynolds number. The presence of surfactant characterizes the interfacial region by an axisymmetric interfacial tension gradient and coefficient of surface dilatational viscosity. Under the assumption of the small capillary number, the deformation of spherical phase interface is not taken into account. The computations not only yield information on drag force and wall correction factor, but also on interfacial velocity and flow field for different values of surface tension gradient and surface dilatational viscosity. In the limiting cases, the analytical solutions describing the drag force and wall correction factor for a drop in a bounded medium reduces to expressions previously stated by other authors in literature. The results reveal the strong influence of the surface dilatational viscosity and surface tension gradient on the motion of drop/bubble. Increasing the surface tension gradient and surface dilatational viscosity, results in linear variation of drag force. When the surface tension gradient increases, the drag force for unbounded medium increases more as compared to the bounded medium hence wall correction factor decreases with increase in surface tension gradient whereas it increases with increase in surface dilatational viscosity.

On the Use of Absorbing Metasurfaces in Microwave Imaging

Microwave imaging (MWI) systems are usually enclosed within casings in order to contain the utilized coupling liquid or help mount the antenna system. On the other hand, inverse scattering algorithms often assume that the background medium of the imaging system extends to infinity (i.e., unbounded background medium assumption). Thus, they typically do not consider the reflections occurring at the system enclosure. For such algorithms to yield successful images, these reflections need to be minimized, e.g., via the use of a lossy coupling liquid. As an alternative to a lossy background medium which also reduces the desired signal level, this communication investigates the use of metallic-backed absorbing metasurfaces as the MWI system enclosure in order to 1) reduce these reflections and also 2) to shield the MWI system from external interference. Using simulated data, we then show that standard inverse scattering algorithms, employing the free-space assumption, can successfully process the data collected under the metasurface enclosure and yield acceptable permittivity images. The advantages and disadvantages of absorbing metasurface enclosure, along with the limitations of this study, will also be discussed. Finally, an absorbing metasurface is fabricated and its reflectivity is experimentally evaluated.

A time-domain approach for the simulation of three-dimensional seismic wave propagation using the scaled boundary finite element method

A direct time-domain approach to simulate seismic wave propagation in three-dimensional unbounded media is proposed based on the Scaled Boundary Finite Element Method (SBFEM). A domain of interest is commonly partitioned into a far field and a near field. The far field is modelled by the semi-analytical SBFEM satisfying rigorously the radiation conditions at infinity. Separate scaled boundary finite elements are employed to reach a balance between computational efficiency and accuracy. The near field is discretized into arbitrarily-shaped scaled boundary finite elements without the occurrence of hanging nodes. This advantage of the SBFEM in mesh generation is leveraged by incorporating the automatic octree-based meshing technique. By exploiting the geometrical similarity of both bounded and unbounded SBFE subdomains the computational cost is reduced. Inspired by the Domain Reduction Method (DRM), seismic waves are introduced to the system via a single layer of elements in the near field. This formulation of seismic input is mathematically convenient as it avoids the direct participation of the formulation of the far field. The proposed approach is attractive in a reliable simulation of the far field, flexible mesh generation of the near field and simple formulation of the seismic excitations. These merits are demonstrated through numerical simulations of seismic wave propagation in a free field and different examples featuring complex geometries in the near fields.

Temporal Parity-Time Symmetry for Extreme Energy Transformations.

Temporal interfaces introduced by abrupt switching of the constitutive parameters of unbounded media enable unusual wave phenomena. So far, their explorations have been mostly limited to lossless media. Yet, non-Hermitian phenomena leveraging material loss and gain, and their balanced combination in parity-time (PT)-symmetric systems, have been opening new vistas in photonics. Here, we unveil the role that temporal interfaces offer in non-Hermitian physics, introducing the dual of PT symmetry for temporal boundaries. Our findings reveal unexplored interference mechanisms enabling extreme energy manipulation, and open new scenarios for time-switched metamaterials, connecting them with the broad opportunities offered by non-Hermitian phenomena.

Achieving geometrical enhancement of fields in chiral nanoplasmonics using fractional calculus

In this paper, an analytical approach has been developed for electromagnetic field enhancement in fractal nanostructure under the quasi-static limit. A metallic fractal embedded in an unbounded, isotropic, and lossless chiral medium has been treated under this approach. In addition, the field enhancement is also noted by imposing surface plasmon resonance condition. To achieve the desired objective, Maxwell divergence equations are considered and written in an appropriate form by mean of fractional calculus.