Two-dimensional Inhomogeneities Research Articles

On the Effect of Two-Dimensional Plasma Inhomogeneity in a Magnetic Island on the Parametric Excitation Threshold of Trapped Upper Hybrid Waves and the Level of Anomalous Absorption in ECRH Experiments

The effect of two-dimensional localization of an upper hybrid (UH) wave in a magnetic island is found. The influence of this effect on the threshold and saturation level of the absolute parametric decay instability of an extraordinary wave, which results in the excitation of two two-dimensional localized UH waves, is investigated.

Effect of Two-Dimensional Plasma Inhomogeneity in Magnetic Island on Threshold of Parametric Excitation of Trapped Upper Hybrid Waves and Level of Anomalous Absorption in ECRH Experiments

Effect of Two-Dimensional Plasma Inhomogeneity in Magnetic Island on Threshold of Parametric Excitation of Trapped Upper Hybrid Waves and Level of Anomalous Absorption in ECRH Experiments

Archeogeophysical application of non-traditional geoelectric arrays. A case study in a north-east Hungary site

With the continuous development of multielectrode geoelectrical tomography (ERT) as a geophysical technique, we became able to detect small size targets. In this paper, we present ERT interpretation results obtained at an archaeological site in Szendrő village in northeastern Hungary, where a 17th century fortress once stood. Several historical notes and a collapsed entrance recall the existence of tunnels under the fortress and a water well of uncertain depth. To detect these structures, geoelectrical multielectrode measurements were carried out using conventional and quasi-null arrays. The quasi-null array applies the arrangement of the current (A and B) and potential electrodes (M and N) in a special way, i.e., the electrodes A, M, B, N follow each other in line in special distances from each other. The horizontal sensitivity of the resistivity profiling method using these types of arrays has been proven to be better than that of the Wenner or other conventional arrays. The comparative study aims not just to investigate the archeological features, but to test the sensitivity of the non-traditional quasi-null arrays to these two-dimensional inhomogeneities. As a result, the optimal array can be chosen, and the identification and delineation of shallow structures can be made more reliably. In this paper, we present the very first archeogeophysical field measurements carried out by the gamma quasi null array (γqnull).

The Influence of Two-Dimensional Temperature Modulation on Floating Droplet Dynamics

We investigate the dynamics and instabilities of a droplet that floats on a liquid substrate. The substrate is cooled from below. In the framework of the slender droplet approximation and the precursor model, the problem is studied numerically. Oscillatory and stationary regimes of thermocapillary convection have been observed. The influence of a two-dimensional spatial inhomogeneity of temperature on the droplet dynamics is investigated. The two-dimensional spatial temperature inhomogeneity can suppress oscillations, changing the droplet’s shape. In a definite region of parameters, the two-dimensional spatial modulation can lead to the excitation of periodic oscillations. The influence of the Biot number on the shape of the droplets is studied.

Vysokochastotnaya vospriimchivost' ferromagnitnogo rezonansa v tonkikh plenkakh so sluchaynymi 1D- i 2D-neodnorodnostyami velichiny magnitnoy anizotropii

The effect of random one- (1D) and two-dimensional (2D) inhomogeneities of the magnetic anisotropy on the shape and width of ferromagnetic resonance line in a thin film has been studied in the standard and new self-consistent approximations. It has been shown that resonance peaks in the case of 2D inhomogeneities are much narrower than those for 1D ones. Peaks are asymmetric in both the 1D and 2D cases, but asymmetry is larger in the latter case. As the correlation wavenumber of inhomogeneities kc increases, the width of a resonance line decreases and its amplitude increases. The amplitude of the FMR peak for 2D inhomogeneities increases much faster than that for 1D inhomogeneities. At the critical dimensionless parameter kcd/π ~ 1, where d is the thickness of the film, the width of the resonance line has an inflection point and the asymmetry of this line and the shift of the ferromagnetic resonance peak are maximal. It has been shown that the new self-consistent approximation reproduces the shape of the resonance line much better than the standard self-consistent approximation.

On the application of principal component transport for compression ignition of lean fuel/air mixtures under engine relevant conditions

Principal component transport-based data-driven reduced-order models (PC-transport ROM) are being increasingly adopted as a combustion model of turbulent reactive flows to mitigate the computational cost associated with incorporating detailed chemical kinetics. Previous studies were mainly limited to replicating relatively-simple chemistry in canonical configurations. The objective of the present study, therefore, is to further explore the accuracy of PC-transport ROM on more complex combustion phenomenon where, for example, large hydrocarbon fuel chemistry spanning a broad range of thermochemical space governs sequential multi-stage compression ignition processes. The cumulative error of PC-transport for this problem, and for others that depend upon sequential highly nonlinear physics, has to be minimal as the combustion phasing and heat release rate in internal combustion engines depends upon accurate predictions of minor ignition species whose concentrations start from ashes and grow orders of magnitude over the course of low- and high-temperature autoignition. Specifically, the PC-transport ROM is applied to predict the compression ignition characteristics of lean n-heptane/air and primary reference fuel (PRF)/air mixtures in a two-dimensional (2-D) constant volume computational domain initialized with a two-dimensional isotropic turbulence spectrum and temperature inhomogeneities. PCA is used to define the low-dimensional manifold that represents the original thermochemical state vector, and artificial neural network (ANN) models are adopted to tabulate chemical kinetics, transport, and thermodynamic properties. A series of 2-D pseudo-turbulent simulations are performed at engine pressures by varying the initial mean and r.m.s. of temperature, turbulence intensity, and the composition of fuel/air mixture. The results show that the PC-transport ROM accurately reproduces the instantaneous and statistical ignition characteristics of the fuel/air mixture, aided by pre-processing techniques including species subsetting, data clustering, and data transformation. It is found that PCs are not properly scaled with a power transformer if reactants are included in the species subset, which leads to a decrease in the accuracy of the PC-transport ROM. A separation of the reactants from the species subset ensures that the temporal evolution of the PCs starts from zero and spans orders of magnitude with time, and as such, this approach is found to effectively redistribute both PCs and their source terms with a power transformer. The computational speed-up factor of the PC-transport ROM ranges between 5.1 and 15.0 for the cases with n-heptane/air mixture and PRF/air mixture, respectively. Moreover, a potential further speed-up is anticipated through a combination of reduction in grid resolution requirements and in the stiffness of the chemical system. As an example, many of the pre-processing methods for inhomogeneous compression ignition may also apply to other complex intermittent combustion phenomena.Novelty and significance statement• The PCA-based reduced-order model (PC-transport ROM) has been applied to the multi-stage compression ignition of large hydrocarbon fuels under HCCI-relevant conditions. The present work presents a systematic procedure to accurately capture the two-stage ignition behavior of lean n-heptane/air or PRF50/air mixture.• The present work demonstrates an advantage of the PC-transport ROM in terms of computational speed-up. The computational speed-up factor for the ROM is up to 15, and moreover, a potential additional speed-up is anticipated through the reduction in the spatial and temporal resolution required.• A series of 2-D PC-transport ROMs are conducted to demonstrate the robustness of the ROM. A limitation of the ROM against different operating conditions is also discussed.

Secondary flows induced by two-dimensional surface temperature heterogeneity in stably stratified channel flow

The structure and impact of thermally induced secondary motions in stably stratified channel flows with two-dimensional surface temperature inhomogeneities is studied using direct numerical simulation (DNS). Starting from a configuration with only spanwise varying surface temperature, where the streamwise direction is homogeneous (Bon & Meyers, J. Fluid Mech., 2022, pp. 1–38), we study cases where the periodic temperature strip length $l_x/h$ (with $h$ the half-channel height) assumes finite values. The patch width ( $l_y/h =\{{\rm \pi} /4, {\rm \pi}/8$ }) and length are varied at fixed stability and two different Reynolds numbers. Results indicate that for the investigated patch widths, the streamwise development of the secondary flows depends on the patch aspect ratio ( $a=l_x/l_y$ ), while they reach a fully developed state after approximately $25l_y$ . The strength of the secondary motions, and their impact on momentum and heat transfer through the dispersive fluxes, is strongly reduced as the length of the temperature strips decreases, and becomes negligible when $a\lesssim 1$ . We demonstrate that upward dispersive and turbulent heat transport in locally unstably stratified regions above the high-temperature patches lead to reduced overall downward heat transfer. Comparison to local Monin–Obukhov similarity theory (MOST) reveals that scaled velocity and temperature gradients in homogeneous stably stratified channel flow at $Re_\tau =550$ agree reasonably well with empirical correlations obtained from meteorological data. For thermally heterogeneous cases with strips of finite length, the similarity functions only collapse higher above the surface, where dispersive fluxes are negligible. Lastly, we show that mean profiles of all simulations collapse when using outer-layer scaling based on displacement thickness.

Shapes of floating droplets under non-uniform heating from below

Floating droplets (liquid lenses) are widely used in engineering applications. A typical way of droplet manipulation is the non-uniform heating. In the present work, the influence of two-dimensional spatial inhomogeneity of temperature on the dynamics and instabilities of a droplet floating on a heated liquid substrate is investigated. The problem is studied numerically in the framework of the slender droplet approximation and the precursor model. It is shown that spatial temperature inhomogeneity leads to the liquid redistribution in the substrate toward the region of lower temperature, which is accompanied by the change in the droplet shape. Heating from below can lead to the substrate layer's rupture due to its monotonic instability. Symmetric and asymmetric droplets under the action of spatial temperature inhomogeneity have been obtained.

High-Frequency Susceptibility of the Ferromagnetic Resonance in Thin Films with Random One- and Two-Dimensional Inhomogeneities in the Magnetic Anisotropy

High-Frequency Susceptibility of the Ferromagnetic Resonance in Thin Films with Random One- and Two-Dimensional Inhomogeneities in the Magnetic Anisotropy

A novel study on the MUSIC-type imaging of small electromagnetic inhomogeneities in the limited-aperture inverse scattering problem

We apply MUltiple SIgnal Classification (MUSIC) algorithm for the location reconstruction of a set of two-dimensional circle-like small inhomogeneities in the limited-aperture inverse scattering problem. Compared with the full- or limited-view inverse scattering problem, the collected multi-static response (MSR) matrix is no more symmetric (thus not Hermitian), and therefore, it is difficult to define the projection operator onto the noise subspace through the traditional approach. With the help of an asymptotic expansion formula in the presence of small inhomogeneities and the structure of the MSR-matrix singular vector associated with nonzero singular values, we define an alternative projection operator onto the noise subspace and the corresponding MUSIC imaging function. To demonstrate the feasibility of the designed MUSIC, we show that the imaging function can be expressed by an infinite series of integer-order Bessel functions of the first kind and the range of incident and observation directions. Furthermore, we identify that the main factors of the imaging function for the permittivity and permeability contrast cases are the Bessel function of order zero and one, respectively. This further implies that the imaging performance significantly depends on the range of incident and observation directions; peaks of large magnitudes appear at the location of inhomogeneities for permittivity contrast case, and for the permeability contrast case, peaks of large magnitudes appear at the location of inhomogeneities when the range of such directions is narrow, while two peaks of large magnitudes appear in the neighborhood of the location of inhomogeneities when the range is wide enough. The numerical simulation results via noise-corrupted synthetic data also show that the designed MUSIC algorithm can address both permittivity and permeability contrast cases.

Block copolymer self-assembly: Melt and solution by molecular density functional theory.

The self-assembly of block copolymer melts and solutions with two-dimensional density inhomogeneity is studied using modified inhomogeneous statistical associating fluid theory (iSAFT). A real-space combinatorial screening method under density functional theory formalism is proposed and used to map out the phase diagram of block copolymer melts including order-disorder transitions and order-order transitions. The predicted phase diagram agrees well with molecular dynamics simulation and self-consistent field theory. The compressibility effect on order-disorder transition temperature for block copolymer melts is modeled using iSAFT. The pressure induced temperature change by theory has a similar trend to experimental studies. Then, the lyotropic and thermotropic self-assembly phase behavior of block copolymer solutions is investigated. Detailed density distributions by iSAFT provide insight into the lyotropic properties of the block copolymer solutions at the molecular level. The effect of the block copolymer molecular architecture is studied by comparing block copolymers with different molecular packing parameters. Block copolymer solutions in the inverted hexagonal phase are predicted by theory for the block copolymer having a large molecular packing parameter. Finally, solvent selectivity is studied by modeling the block copolymers in a neutral good solvent. The enhanced local solvent concentration predicted by theory explains the reason for fewer ordered phases found in experiments.

On the Theory of Stimulated Brillouin Scattering in Plasma with Two-Dimensional Localization and Inhomogeneity of the Pump Wave

On the Theory of Stimulated Brillouin Scattering in Plasma with Two-Dimensional Localization and Inhomogeneity of the Pump Wave

One- and two-dimensional quantum lattice algorithms for Maxwell equations in inhomogeneous scalar dielectric media I: theory

ABSTRACT A quantum lattice algorithm (QLA) is developed for Maxwell equations in scalar dielectric media using the Riemann–Silberstein representation on a Cartesian grid. For x-dependent and y-dependent dielectric inhomogeneities, the corresponding QLA requires a minimum of 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the local collisional entanglement of these qubits. However, z-dependent inhomogeneities require a QLA with a minimum of 16 qubits/lattice site since the Pauli spin matrix is diagonal. For two-dimensional inhomogeneities, one can readily couple the 8–8 qubit schemes for x−y variations. z−x and y−z variations can be treated by either a 16–8 qubit scheme or a 16–16 qubit representation.

A circular inhomogeneity interacting with an open inhomogeneity designed to admit internal uniform hydrostatic stresses

We use analytic continuation and conformal mapping techniques to prove the existence of an internal uniform hydrostatic stress field inside a two-dimensional non-parabolic open inhomogeneity interacting with a nearby circular elastic inhomogeneity. The circular inhomogeneity and the surrounding matrix have distinct Poisson's ratios but identical shear moduli. The single complex constant appearing in the conformal mapping function is determined analytically. A simple condition is found that ensures that the internal stresses inside the non-parabolic inhomogeneity are uniform and hydrostatic. We also establish the existence of an internal uniform hydrostatic stress field inside a non-parabolic open inhomogeneity near an arbitrary number of circular elastic inhomogeneities. The circular inhomogeneities and the matrix have distinct Poisson's ratios but a common shear modulus. All of the complex constants in the conformal mapping function are uniquely determined by solving a set of non-linear equations via iterations.

Quantization of an electromagnetic field in two-dimensional photonic structures based on the scattering matrix formalism (S-quantization)

Based on the scattering matrix formalism, we have developed a method of quantization of an electromagnetic field in two-dimensional photonic nanostructures (S-quantization in the two-dimensional case). In this method, the fields at the boundaries of the quantization box are expanded into a Fourier series and are related with each other by the scattering matrix of the system, which is the product of matrices describing the propagation of plane waves in empty regions of the quantization box and the scattering matrix of the photonic structure (or an arbitrary inhomogeneity). The quantization condition (similarly to the onedimensional case) is formulated as follows: the eigenvalues of the scattering matrix are equal to unity, which corresponds to the fact that the set of waves that are incident on the structure (components of the expansion into the Fourier series) is equal to the set of waves that travel away from the structure (outgoing waves). The coefficients of the matrix of scattering through the inhomogeneous structure have been calculated using the following procedure: the structure is divided into parallel layers such that the permittivity in each layer varies only along the axis that is perpendicular to the layers. Using the Fourier transform, the Maxwell equations have been written in the form of a matrix that relates the Fourier components of the electric field at the boundaries of neighboring layers. The product of these matrices is the transfer matrix in the basis of the Fourier components of the electric field. Represented in a block form, it is composed by matrices that contain the reflection and transmission coefficients for the Fourier components of the field, which, in turn, constitute the scattering matrix. The developed method considerably simplifies the calculation scheme for the analysis of the behavior of the electromagnetic field in structures with a two-dimensional inhomogeneity. In addition, this method makes it possible to obviate difficulties that arise in the analysis of the Purcell effect because of the divergence of the integral describing the effective volume of the mode in open systems.

Features of the energy structure of acoustic fields in the ocean with two-dimensional random inhomogeneities

The paper is devoted to the analytic study and numerical simulation of mid-frequency acoustic signal propagation in a two-dimensional inhomogeneous random shallow-water medium. The study was carried out by the cross section method (local modes). We present original theoretical estimates for the behavior of the average acoustic field intensity and show that at different distances, the features of propagation loss behavior are determined by the intensity of fluctuations and their horizontal scale and depend on the initial regular parameters, such as the emission frequency and size of sound losses in the bottom. We establish analytically that for the considered waveguide and sound frequency parameters, mode coupling effect has a local character and weakly influences the statistics. We establish that the specific form of the spatial spectrum of sound velocity inhomogeneities for the statistical patterns of the field intensity is insignificant during observations in the range of shallow-water distances of practical interest.

Axisymmetric Thermo-elastic Deformation of the Cylinder with Two-dimensional Inhomogeneity of Material

The article discusses the use of a numerical method the calculation of finite cylinders into account the dependence of physical and mechanical properties of the material on temperature. If we have two-dimensional temperature field characteristics of the material depends on two coordinates. - r and z from which follows that the problem of thermoelasticity is also a two-dimensional. Using the numerical method allows to solve the problem for any state of the cylinder (plane stress or plane strain) and consider arbitrary boundary conditions at its ends.

Axisymmetric Thermo-elastic Deformation of the Cylinder with Two-dimensional Inhomogeneity of Material

The article discusses the use of a numerical method the calculation of finite cylinders into account the dependence of physical and mechanical properties of the material on temperature. If we have two-dimensional temperature field characteristics of the material depends on two coordinates. - and from which follows that the problem of thermoelasticity is also a two-dimensional. Using the numerical method allows to solve the problem for any state of the cylinder (plane stress or plane strain) and consider arbitrary boundary conditions at its ends.

Analysis of MUSIC-type imaging functionals for small two-dimensional electromagnetic inhomogeneities

In this study, the MUltiple SIgnal Classification (MUSIC) algorithm for imaging of small electromagnetic inhomogeneities in two-dimensional space is considered. We identify the structure of MUSIC-type imaging functionals, which are often adopted in inverse scattering problems, by establishing a relationship between the imaging functional and Bessel functions of integer order of the first kind. This relationship illuminates certain properties of MUSIC, as well as explaining some undiscovered phenomena. The results of some numerical simulations using noisy data are presented in order to support our investigation.

A study on the topological derivative-based imaging of thin electromagnetic inhomogeneities in limited-aperture problems

The topological derivative-based non-iterative imaging algorithm has demonstrated its applicability in limited-aperture inverse scattering problems. However, this has been confirmed through many experimental simulation results, and the reason behind this applicability has not been satisfactorily explained. In this paper, we identify the mathematical structure and certain properties of topological derivatives for the imaging of two-dimensional crack-like thin penetrable electromagnetic inhomogeneities that are completely embedded in a homogeneous material. To this end, we establish a relationship with an infinite series of Bessel functions of integer order of the first kind. Based on the derived structure, we discover a necessary condition for applying topological derivatives in limited-aperture inverse scattering problems, and thus confirm why topological derivatives can be applied. Furthermore, we analyze the structure of multi-frequency topological derivative, and identify why this improves the single-frequency topological derivative in limited-aperture inverse scattering problems. Various numerical simulations are conducted with noisy data, and the results support the derived structure and exhibit certain properties of single- and multi-frequency topological derivatives.