Planar Media Research Articles

Kelvin's chirality of optical beams

Geometrical chirality is a property of objects that describes three-dimensional mirror-symmetry violation and therefore it requires a non-vanishing spatial extent. In contrary, optical chirality describes only the local handedness of electromagnetic fields and neglects the spatial geometrical structure of optical beams. In this manuscript, we put forward the physical significance of geometrical chirality of spatial structure of optical beams, which we term "Kelvin's chirality". Further, we report on an experiment revealing the coupling of Kelvin's chirality to optical chirality upon transmission of a focused beam through a planar medium. Our work emphasizes the importance of Kelvin's chirality in all light-matter interaction experiments involving structured light beams with spatially inhomogeneous phase and polarization distributions.

Radar methods for determining the thickness of dielectric layers

This paper describes two methods, the amplitude method and the method based on geometric optics. The methods were applied to practical data obtained by georadar tests. As a result, the refractive index and thickness of the investigated planar layered medium were calculated. When using the amplitude method, the refractive index of the investigated medium is 1.3, the thickness is 0.11 m. When using the method based on geometric optics, the refractive index of the investigated medium is 1.43, the thickness is 0.102 m. After comparing the results of these methods, it was found that the error of the amplitude method is higher than that of the geometrical optics method.

О решениях типа «кольцо» уравнений нейронного поля

The article is devoted to investigation of integro-differential equation with the Hammerstein integral operator of the following form: ∂_t u(t,x)=-τu(t,x,x_f )+∫_(R^2)▒〖ω(x-y)f(u(t,y) )dy, t≥0, x∈R^2 〗. The equation describes the dynamics of electrical potentials u(t,x) in a planar neural medium and has the name of neural field equation.We study ring solutions that are represented by stationary radially symmetric solutions corresponding to the active state of the neural medium in between two concentric circles and the rest state elsewhere in the neural field. We suggest conditions of existence of ring solutions as well as a method of their numerical approximation. The approach used relies on the replacement of the probabilistic neuronal activation function f that has sigmoidal shape by a Heaviside-type function. The theory is accompanied by an example illustrating the procedure of investigation of ring solutions of a neural field equation containing a typically used in the neuroscience community neuronal connectivity function that allows taking into account both excitatory and inhibitory interneuronal interactions. Similar to the case of bump solutions (i. e. stationary solutions of neural field equations, which correspond to the activated area in the neural field represented by the interior of some circle) at a high values of the neuronal activation threshold there coexist a broad ring and a narrow ring solutions that merge together at the critical value of the activation threshold, above which there are no ring solutions.

Fundamental limits to attractive and repulsive Casimir-Polder forces

We derive upper and lower bounds on the Casimir--Polder force between an anisotropic dipolar body and a macroscopic body separated by vacuum via algebraic properties of Maxwell's equations. These bounds require only a coarse characterization of the system---the material composition of the macroscopic object, the polarizability of the dipole, and any convenient partition between the two objects---to encompass all structuring possibilities. We find that the attractive Casimir--Polder force between a polarizable dipole and a uniform planar semi-infinite bulk medium always comes within 10% of the lower bound, implying that nanostructuring is of limited use for increasing attraction. In contrast, the possibility of repulsion is observed even for isotropic dipoles, and is routinely found to be several orders of magnitude larger than any known design, including recently predicted geometries involving conductors with sharp edges. Our results have ramifications for the design of surfaces to trap, suspend, or adsorb ultracold gases.

Сравнение математических моделей плоской и эллипсоидной сред с учетом влияния физиологических параметров тканей головы на амплитуду зрительных вызванных потенциалов

Сравнение математических моделей плоской и эллипсоидной сред с учетом влияния физиологических параметров тканей головы на амплитуду зрительных вызванных потенциалов

Crystalline evolutions with rapidly oscillating forcing terms

We consider the evolution by crystalline curvature of a planar set in a stratified medium, modeled by a periodic forcing term. We characterize the limit evolution law as the period of the oscillations tends to zero. Even if the model is very simple, the limit evolution problem is quite rich, and we discuss some properties such as uniqueness, comparison principle and pinning/depinning phenomena.

Fundamental Limits to Radiative Heat Transfer: The Limited Role of Nanostructuring in the Near-Field.

In a previous Letter, we derived fundamental limits to radiative heat transfer applicable in near- through far-field regimes, based on the choice of material susceptibilities and bounding surfaces enclosing arbitrarily shaped objects; the limits exploit algebraic properties of Maxwell's equations and fundamental principles such as electromagnetic reciprocity and passivity. In this Letter, we apply these bounds to two different geometric configurations of interest, namely dipolar particles or extended structures of infinite area in the near field of one another. We find that while near-field radiative heat transfer between dipolar particles can saturate purely geometric "Landauer" limits, bounds on extended structures cannot, instead growing very slowly with respect to a material response figure of merit (an "inverse resistivity" for metals) due to the deleterious effects of multiple scattering between bodies. While nanostructuring can produce infrared resonances, it is generally unable to further enhance the resonant energy transfer spectrum beyond what is practically achieved by planar media at the surface polariton condition.

Numerical Simulation and Analysis of Multicomponent Induction Logging Response in Anisotropic Formation

In this article, the response characteristics of multicomponent induction logging (MCIL) tool in anisotropic formation are analyzed. To solve the 1-D MCIL problems, we use a planar layered anisotropic medium (PLAM) Green's function (PLAMGF) method which is derived from the layered-medium Green's function (LMGF) and combined with MCIL excitation source and anisotropic formation environment, and then use it to investigate the equivalence of the MCIL tool responses in two models, i.e. the microscopic thin interbed formation and macroscopic anisotropic formation, and also analyze the effects of shoulder bed and formation dip on MCIL tools. In addition, in order to solve the complex 3-D problems, such as the effects of borehole, tool eccentricity and invasion on the tool response, we use the finite element method (FEM) based on a proposed new meshing scheme to simulate and analyze. This new meshing scheme includes two aspects: the use of cylindrical hexahedron element and the flexible meshing strategy combined with domain decomposition. Finally, some key detection performances of coaxial coils and coplanar coils of MCIL tool are studied. Numerical experiments are conducted to prove the effectiveness of our proposed method and provide the detailed results of the aforementioned aspects.

Sedimentary record of historical extreme storm surges on the Gulf of Gdańsk coast, Baltic Sea

The Baltic Sea is commonly viewed as a region with a low frequency of coastal hazards such as tsunamis or extreme storm surges. However, historical sources indicate that in the past, several catastrophic storm surges resulted in coastal floods and related casualties. Their sedimentological records and reconstructions of paleostorminess were so far studied mainly in the westernmost (Denmark) and easternmost (Estonia) parts of the Baltic Sea. The present study focus on southern Baltic coast (Gulf of Gdańsk), where storm surge sedimentary deposits left within coastal peatlands were investigated, and related to historical record in order to compare recent risk estimations and predictions of storm surge levels to geological data. To achieve this aim, the collected sediment cores were subjected to sedimentological, grain size, and diatom analyses, supported with 137Cs, 210Pb, and 14C datings. Two types of sandy event deposits were identified, and interpreted to be storm deposits formed under an inundation regime and overwash regime, respectively. The deposits formed under the inundation regime were characterised by an erosional lower boundary, massive structure and presence of rip-up clasts of underlying sediments, whereas the sediments formed under the overwash regime were low-angle planar cross-stratified medium sands with intercalations of massive fine sand. The recognized sandy storm deposits were dated mainly to the Little Ice Age period (XVIth–XIXth centuries). They were most likely left during the historical storms of 1825, 1872, and 1914 CE. It extends the sedimentary record of known historical events as mainly storms from 1497 CE and 1872 CE were reported previously from Baltic Sea. Notably, none of the historical storm events during the past 100-year period have formed a distinguishable sedimentary record. These findings clearly show that risk models and storm return period predictions, which are based on instrumental measurements from the last century, should also include geological evidence. The strongest storm surges from the past century may not be adequate reference of a worst case scenario.

Solution of the neutron survival probability equation using k-eigenmode expansion

A low order expansion in k-eigenmodes of a supercritical medium is shown to yield accurate results for the time dependent neutron chain survival probability as well as its steady state limit, the divergence probability. Numerical results for a 1D nonhomogeneous planar medium, when compared against an established nonlinear eigenvalue solution method, show the eigenmode expansion approach to be remarkably efficient under both weakly and strongly supercritical conditions. Specifically, two to three modes typically suffice to capture the temporal variation of the survival probability and one mode adequately describes the divergence probability for a weakly supercritical medium. Moreover, the dependence of the survival probability on the initiating neutron spatial and angular coordinates stabilizes within a fraction of a neutron lifetime of the chain starting, although the magnitude continues to change with time. Accuracy and numerical performance of the eigenmode expansion method are quantitatively assessed by comparison with the established technique, which itself is first benchmarked using the method of manufactured solutions.

An Inverse Source Problem Connected with Thermoacoustic Imaging in Multi-layer Planar Medium

We derived analytical forward and inverse solution of thermoacoustic wave equation for nonhomogeneous medium. We modelled the nonhomogeneous medium as a multi-layer planar medium and defined initial conditions, continuity conditions on the layer boundaries and radiation conditions at infinity assuming the source distribution existing in all layers. These solutions of thermoacoustic wave equation are based on the method of Green’s functions for layered planar media. For qualitative testing and comparison of the point-spread functions associated with the homogeneous and layered solutions, we performed numerical simulations. Our simulation results showed that the conventional inverse solution based on homogeneous medium assumption, as expected, produced incorrect locations of point sources, whereas our inverse solution involving the multi-layer planar medium produced point sources at the correct source locations. Also, we examined whether the performance of our layered inverse solution is sensitive to medium parameters used as priority information in the measured data. Our inverse solutions based on multi-layer planar media are applicable for cross-sectional two-dimensional imaging of abdominal structure and the organs such as breast and skin.

New Exact Image Methods for Impedance Boundary Half-Space Green’s Function and Their Fast Multipole Expansion

Two foremost barriers to the development of fast and efficient simulation algorithms for electromagnetic problems in half-space and planar media are efficient Sommerfeld integral evaluation techniques and fast solvers. In this paper, we focus on challenging these two difficulties in the impedance boundary half-space, which is a proper model for common air-lossy media half-space. Based on the Laplace transformation, we first propose an alternative exact image representation for the Sommerfeld integral in half-space Green's function. In addition to its fast and absolute convergence property, this new exact image version does not contain any singularities and interprets the Sommerfeld integral as an integral over real image line. Furthermore, this representation allows a rigorous fast multipole expansion (FME), and thus it can be applied to the development of fast multipole solver with controllable precision. However, this exact image representation is not valid for the all Sommerfeld integrals in half-space Green's function. Therefore, a more generalized single mirror image representation, also exact and computationally efficient, is then presented. The strength of the mirror image is obtained through Weyl's method and steep descent path approach. Subsequently, an approximated FME scheme for this representation is proposed and studied via numerical examples. We find this approximated FME scheme has a higher accuracy than that of previous work. Numerical results show that the proposed work provides exact and efficient evaluations for Sommerfeld integrals in impedance boundary half-space Green's function and valuable insights into the development of fast multipole solver for half-space electromagnetic problems.

Spectral radiative entropy generation in a non-gray planar participating medium including H2O and CO2

Spectral radiative entropy generation through a non-gray absorbing and emitting planar medium is studied. Spectral radiative properties are calculated using the correlated-k (CK) non-gray model with updated parameters based on the HITEMP2010 high-resolution database. The angular and spatial discretization of the radiative transfer equation and radiative entropy generation equation are performed using the discrete ordinates method and the finite volume method, respectively. First, results obtained using the CK model, are compared with the results of the gray model. The calculations reveal that there is a significant difference between results obtained by the gray model and the non-gray model, and the gray assumption generates a remarkable error in the calculations of radiative entropy generation. Then, for comprehensive analysis, five cases have been considered including two homogeneous and isothermal cases, two non-homogeneous and non-isothermal cases filled with H2O or CO2 and one homogeneous and non-isothermal case with a mixture of H2O and CO2. Spectral, local and total radiative entropy generation are calculated for each case and the effect of temperature of the medium, the concentration of participating gas and wall emissivity on radiative entropy generation is attentively investigated. Results show that the radiative entropy generation in the system increases as three aforementioned parameters increase but the effect of gas temperature variations is more than others. Further, the sensitivity of radiative entropy generation due to wall radiation to wall emissivity is decreased when εw rises.

Surface-Volume-Surface EFIE for Electromagnetic Analysis of 3-D Composite Dielectric Objects in Multilayered Media

The surface-volume-surface electric field integral equation (SVS-EFIE) is generalized for the case of scattering problems on the composite nonmagnetic dielectric objects situated in planar nonmagnetic layered medium. The piece-wise homogeneous regions of the scatterer can be arbitrarily positioned with respect to the layers of stratification. The SVS-EFIE being a class of single-source integral equations is formed by restricting the surface single-source electric field representation in each distinct region of the scatterer through the volume-EFIE (V-EFIE) enforced on the boundary of that region for only the tangential component of the total field. As a result, the SVS-EFIE utilizes only the electric field dyadic Green's functions. This allows for its cast into the mixed-potential form using classical Michalski-Zheng's formulation and method of moments (MoM) discretization featuring easily computable integrals with singularities no stronger than 1/R, R being the distance from the source to the observation point in such integrals. The matrices of MoM discretization are represented inhierarchical form (as H-matrices) enabling solution of the scattering problems in multilayered media with O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> log N) CPUtimeand memory complexities, where α is a geometry-dependent constant ranging from 1 to 1.5 depending on the shape of the scatterer. While the MoM surface and volume meshes discretizing the regions of the scatterer are constructed to ensure that no mesh element crosses interfaces between the layers, the clusters of both the surface and volume elements in their respective recursive partitionings in the process of H-matrix construction are allowed to span multiple layers of the medium. Upon computation of the layered medium Green's function kernels with the discrete complex image method allowing clusters of elements to cross dielectric interfaces between the layers is shown to preserve compressibility of the corresponding H-matrix blocks.

Role of Localized States in Photoluminescence Dynamics of High Optical Gain CsPbBr3 Nanocrystals

AbstractTemperature‐dependent time‐resolved photoluminescence (TRPL) spectroscopy of high optical gain CsPbBr3 nanocrystals (NCs) films along with temperature‐dependent steady‐state absorption and photoluminescence (PL) spectra is studied. A red shift in the optical band edge and the corresponding PL peak is observed by lowering the temperature from room temperature, analogous to hybrid perovskite semiconductors. However, the faster PL decay of CsPbBr3 NCs film at a low temperature as compared to room temperature is in contrast with many other traditional colloidal quantum dots. The TRPL spectroscopy as a function of temperature suggests the presence of a red‐shifted (≈75 ± 15 meV) defect‐induced emission peak at longer times. Temperature‐dependent PL intensity study shows an Arrhenius type of character with two activation energies: ≈77 ± 18 and ≈12 ± 3 meV. A qualitative model is developed where interaction between the excitonic level and these observed localized states as a function of temperature can qualitatively explain the contrasting PL decay mechanism of CsPbBr3 NCs film. To ensure the quality of in‐house synthesized CsPbBr3 NCs with a mixture of oleylamine and octylamine ligands, the amplified spontaneous emission from CsPbBr3 NCs film as a planar waveguide medium is studied, which shows state‐of‐art optical gain coefficient of ≈51cm−1 and a loss coefficient of ≈15cm−1 at room temperature.

Study on Thermal Contact Resistance Estimation in Planar Medium

Thermal contact resistance(TCR) is one of the important parameters in heat transfer problems of engineering, and it is necessary to estimate the value of TCR effectively in many engineering fields. Considering the limitation of current estimation methods of TCR such as only focusing on one-dimensional thermal conduction, getting a single value of TCR merely, and the temperature measuring points only being placed in temperature gradient direction of mediums, boundary element method(BEM) and conjugate gradient method are combined to estimate the TCR in planar mediums. The value of TCR in relation to the position of contact interface line is estimated with this method, and the positions of temperature measuring points can be selected randomly because of the characteristic of BEM that there is no necessity to discrete the inner area and it is sufficient to discrete the boundary. The analysis of calculation examples base on heat transfer model of planar medium demonstrates that:this method can estimate the TCR effectively, but the ill-posedness is also existed in this method which is one of the inverse problems, and the calculation error of TCR is increased with the distance from temperature measuring points to contact interface, the estimation precision and stability can be improved after optimization with least square method.

The dynamics of miscible viscous fingering from onset to shutdown

We examine the full ‘life cycle’ of miscible viscous fingering from onset to shutdown with the aid of high-resolution numerical simulations. We study the injection of one fluid into a planar two-dimensional porous medium containing another, more viscous fluid. We find that the dynamics are distinguished by three regimes: an early-time linearly unstable regime, an intermediate-time nonlinear regime and a late-time single-finger exchange-flow regime. In the first regime, the flow can be linearly unstable to perturbations that grow exponentially. We identify, using linear stability theory and numerical simulations, a critical Péclet number below which the flow remains stable for all times. In the second regime, the flow is dominated by the nonlinear coalescence of fingers which form a mixing zone in which we observe that the convective mixing rate, characterized by a convective Nusselt number, exhibits power-law growth. In this second regime we derive a model for the transversely averaged concentration which shows good agreement with our numerical experiments and extends previous empirical models. Finally, we identify a new final exchange-flow regime in which a pair of counter-propagating diffusive fingers slow exponentially. We derive an analytic solution for this single-finger state which agrees well with numerical simulations. We demonstrate that the flow always evolves to this regime, irrespective of the viscosity ratio and Péclet number, in contrast to previous suggestions.

Characterization of interface reflection coefficients using a finite-difference injection technique.

In this paper, a numerical wave field injection technique for characterizing the reflection coefficient of a planar medium interface is proposed. By injecting recorded wave field quantities into a three-dimensional (3D) finite-difference calculation, two key objectives are addressed: first, the recorded wave field is separated into its incident and reflected constituents without the need of spatial Fourier transforms or a temporal separation of incident and reflected parts in the recorded data. Second, the separated constituents are independently extrapolated to the location of the reflecting interface to determine its reflecting properties. The methodology is experimentally validated on 3D laboratory data consisting of reflections from the water-air interface in a water tank and is shown to give accurate results for incidence angles of up to 60°.

On the possibility of applying the bers apparatus to modeling the processes of heat and mass transfer caused by electrons in a planar multilayer medium

Some possibilities of joint application of the Bers factorial-function apparatus and matrix method to the mathematical modeling of heat and mass transfer processes in a multilayer medium are considered. The possibility of using this method is shown by the example of the diffusion of minority charge carriers generated by a wide electron beam in multilayer semiconductor planar structures. The results of calculations by this method for homogeneous and three-layer semiconductor structures are presented.

Radiative entropy generation in a gray absorbing, emitting, and scattering planar medium at radiative equilibrium

Radiative entropy generation through a gray absorbing, emitting, and scattering planar medium at radiative equilibrium with diffuse-gray walls is investigated. The radiative transfer equation and radiative entropy generation equations are solved using discrete ordinates method. Components of the radiative entropy generation are considered for two different boundary conditions: two walls are at a prescribed temperature and mixed boundary conditions, which one wall is at a prescribed temperature and the other is at a prescribed heat flux. The effect of wall emissivities, optical thickness, single scattering albedo, and anisotropic-scattering factor on the entropy generation is attentively investigated. The results reveal that entropy generation in the system mainly arises from irreversible radiative transfer at wall with lower temperature. Total entropy generation rate for the system with prescribed temperature at walls remarkably increases as wall emissivity increases; conversely, for system with mixed boundary conditions, total entropy generation rate slightly decreases. Furthermore, as the optical thickness increases, total entropy generation rate remarkably decreases for the system with prescribed temperature at walls; nevertheless, for the system with mixed boundary conditions, total entropy generation rate increases. The variation of single scattering albedo does not considerably affect total entropy generation rate. This parametric analysis demonstrates that the optical thickness and wall emissivities have a significant effect on the entropy generation in the system at radiative equilibrium. Considering the parameters affecting radiative entropy generation significantly, provides an opportunity to optimally design or increase overall performance and efficiency by applying entropy minimization techniques for the systems at radiative equilibrium.