Effective dynamics for a spin-1/2 particle constrained to a curved layer with inhomogeneous thickness

We derive an effective Hamiltonian for a spin-1/2 particle confined within a curved thin layer with non-uniform thickness using the confining potential approach.Our analysis reveals the presence of a pseudo-magnetic field and effective spin–orbit interaction(SOI)arising from the curvature,as well as an effective scalar potential resulting from variations in thickness.Importantly,we demonstrate that the physical effect of additional SOI from thickness fluctuations vanishes in low-dimensional systems,thus guaranteeing the robustness of spin interference measurements to thickness imperfection.Furthermore,we establish the applicability of the effective Hamiltonian in both symmetric and asymmetric confinement scenarios,which is crucial for its utilization in one-side etching systems.

Review of Computational Approaches to Optimization Problems in Inhomogeneous Rods and Plates

In this paper,we review computational approaches to optimization problems of inhomogeneous rods and plates.We consider both the optimization of eigenvalues and the localization of eigenfunctions.These problems are motivated by physical problems including the determination of the extremum of the fundamental vibration frequency and the localization of the vibration displacement.We demonstrate how an iterative rearrangement approach and a gradient descent approach with projection can successfully solve these optimization problems under different boundary conditions with different densities given.

The multi-peak point phenomenon of broadband microwave reflection caused by inhomogeneous plasma

During spacecraft re-entry,the challenge of measuring plasma sheath parameters directly contributes to difficulties in addressing communication blackout.In this work,we have discovered a phenomenon of multiple peaks in reflection data caused by the inhomogeneous plasma.Simulation results show that the multi-peak points fade away as the characteristic frequency is approached,resembling a series of gradually decreasing peaks.The positions and quantities of these points are positively correlated with electron density,yet they show no relation to collision frequency.This phenomenon is of significant reference value for future studies on the spatial distribution of plasmas,particularly for using microwave reflection signals in diagnosing the plasma sheath.

Enhanced THz Radiation from Spatially Inhomogeneous Fields

Nonlinear terahertz(THz)radiation from gas media usually relies on the asymmetric laser-induced current produced by ultra-intense two-color laser fields with a specific phase delay.Here a new scheme is proposed and theoretically investigated,in which the radiation is generated by spatially inhomogeneous fields induced by relatively low-intensity monochromatic lasers and an array of single triangular metallic nanostructures.Our simulations are based on the classical photocurrent model and the time-dependent Schrodinger equations separately.It is found that the collective motion of the ionized electrons can be efficiently controlled by the inhomogeneous field,resulting in strong residual currents.The intensity of the THz radiation could be enhanced by about two orders of magnitude by increasing the spatial inhomogeneity of the field.

Local wavelength evolution and Landau damping of electrostatic plasma wave driven by an ultra-relativistic electron beam in dense inhomogeneous plasma

Evolution of an electrostatic plasma wave driven by a low-density ultra-relativistic electron beam in dense inhomogeneous plasma is considered. In particular, the wavelength variation as observed at fixed locations in the plasma is analyzed in terms of the wave characteristics. It is shown that for a negative density gradient, the observed local wavelength decreases monotonically with time, but for a positive density gradient, it first increases and then decreases with time, accompanied by reversal of the wave phase. However, in both cases the local wavelength eventually decreases with time since Landau damping becomes significant as the wavelength becomes of the order of the plasma Debye length. Results from particle-in-cell simulations agree well with theoretical analyses of the wavelength variation.

Separation of inhomogeneous blended seismic data

The frequencies of sources involved m conventional blended acquisition are the same. Each source transmits the full frequency band, and in general, significant effort is required to successfully produce and operate wideband sources. To solve this problem, inhomogeneous blended or decentralized blended acquisition is used, in which the dominant frequency and bandwidth of the source units in a blended array are not equal. When the inhomogeneous and conventional blending acquisitions adopt the same geometry and separation methods, the former has low signal-to-blending noise ratio. Therefore, we present a new separation method for such blended acquisition based on the synchrosqueezed wavelet transform. The proposed method offers better separation quality and decreases the computation time to approximately 1/3.

Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method

The dynamic inhomogeneous finite element method is studied for use in the transient analysis of one dimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.

Inhomogeneous Differential Realization, Boson-Fermion Realization of OSP(2,1) Superalgebra and Its Representations

Homogeneous and inhornogeneous differential realizations of the OSP(2,1)superalgebra on the spaces of homogeneous and inhomogeneous polynomials and the corresponding boson-fermioii realizations are studied.The new indecomposable and irreducible representations of the OSP(2,1)are given on subspaces and quotient spaces of the universal enveloping algebras of Heisenberg-Weyl superalgebra.All the finite dimensional irreducible representation of the OSP(2,1)superalgebra is naturally obtained as special cases.

A new method for computing the uniaxial modulus of articular cartilages using modified inhomogeneous triphasic model

It is well known that subtle changes in structure and tissue composition of articular cartilage can lead to its degeneration. The present paper puts forward a modified layered inhomogeneous triphasic model with four parameters based on the inhomogeneous triphasic model proposed by Narmoneva et al. Incorporating a piecewise fitting optimization criterion, the new model was used to obtain the uniaxial modulus Ha, and predict swelling pattern for the articular cartilage based on ultrasound-measured swelling strain data. The results show that the new method can be used to provide more accurate estimation on the uniaxial modulus than the inhomogeneous triphasic model with three parameters and the homogeneous mode, and predict effectively the swell- ing strains of highly nonuniform distribution of degenerated articular cartilages. This study can provide supplementary information for exploring mechanical and material properties of the cartilage, and thus be helpful for the diagnosis of osteoarthritis-related diseases.

Preparation, Properties and Mechanism of Inhomogeneous Calcium Alginate Ion Cross-linking Gel Microspheres

Inhomogeneous calcium alginate ion cross\|linking gel microspheres, a novel ion absorbent, were prepared by dropping a sodium alginate solution to a calcium chloride solution via an electronic droplet generator. Calcium alginate microspheres have uniform particle sizes, a smooth surface and a microporous structure. The electrode probe reveals the inhomogeneous distribution of calcium ions with the highest concentration on the surface, and the lowest concentration in the cores of the spheres. As a novel ion adsorbent, calcium alginate gel microspheres have a lower limiting adsorption mass concentration, a higher enrichment capacity and a higher adsorption capacity for Pb 2+ than usual ion exchange resins. The highest percentage of the adsorption is 99 79%. The limiting adsorption mass concentration is 0 0426 mg/L. The adsorption capacity for Pb 2+ is 644 mg/g. Calcium alginate gel microspheres have a much faster ion exchange velocity than D418 chelating resin and D113 polyacrylate resin. The moving boundary model was employed to interpret the ion exchange kinetics process, which indicates that the ion exchange process is controlled by intraparticle diffusion of adsorbable ions. So the formation of inhomogeneous gel microspheres reduces the diffusion distance of adsorbable ions within the spheres and enhances the ion exchange velocity. Alginate has a higher selectivity for Pb 2+ than for Ca 2+ and the selectivity coefficient K Pb Ca is 316. As an ion cross\|linking gel, calcium alginate inhomogeneous microspheres can effectively adsorb heavy metal Pb 2+ at a higher selectivity and a higher adsorption velocity. It is a novel and good ion adsorbent.

Effect of inhomogeneous broadening on threshold current of GaN-based green laser diodes

The inhomogeneous broadening parameter and the internal loss of green LDs are determined by experiments and theoretical fitting. It is found that the inhomogeneous broadening plays an important role on the threshold current density of green LDs. The green LD with large inhomogeneous broadening even cannot lase. Therefore, reducing inhomogeneous broadening is a key issue to improve the performance of green LDs.

NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF NONNEGATIVE SOLUTIONS OF INHOMOGENEOUS p-LAPLACE EQUATION

Let Ω be a smooth bounded domain in R^n. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous p-Laplace equation --△pu = ｜u｜^q-1 u ＋ λf（x） on Ω, and identify necessary and sufficient conditions on Ω and f（x） which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration.

FDTD Analysis of Reflection of Electromagnetic Wave From a Conductive Plane Covered with Inhomogeneous Time-Varying Plasma

A finite-difference time-domain (FDTD) algorithm is applied to study the electromagnetic reflection of conduction plane covered with inhomogeneous time-varying plasma, homogeneous plasma and inhomogeneous plasma. The collision frequency of plasma is a function of electron density and plasma temperature. The number density profile follows a parabolic function. A discussion on the effect of various plasma parameters on the reflection coefficient is presented. Under the one-dimensional case, transient electromagnetic propagation through various plasmas has been obtained, and the reflection coefficients of EM wave through various plasmas are calculated under different conditions. The results illustrate that a plasma cloaking system can successfully absorb the incident EM wave.

3D stability assessment of stepped slopes in inhomogeneous soils

Stability assessment of slopes has historically been performed assuming soils to be homogeneous in two-dimensional(2D) cases. In real cases, soils are usually inhomogeneous, and each slope collapse indicates a three-dimensional(3D) nature. Based on a 3D rotational failure mechanism, this work develops an approach to account for the impact of the vertical strength inhomogeneity on the 3D stability of stepped slopes. Seismic actions are taken into account by introducing the concept of a horizontal seismic coefficient. An upper-bound expression for stability factors is derived in the light of the kinematic approach, and the most critical solution is obtained from an optimization programming. In comparison with the previously published solutions, the validity of the proposed method is shown. A sensitivity analysis is carried out to discuss parametric effects on the stability of 3D stepped inhomogeneous slopes.

TEXTURE IN INHOMOGENEOUSLY ROLLED ALUMINIUM SHEET

The changs of stress state in cold rolled aluminium sheet with large pass reduction,the combining activation process of slip systems as well as the formation mechanism of corresponding shear textures were investigated.It is shown that the rolling deformation with large pass reduction produces not only the general rolling stresses but also a strong shear stress in aluminium sheet.With increasing additional shear stress the general rolling textures,i.e.{112}<111>,{123}<634>,{110}<1I2>and{110}<001>decrease,and the shear texture,i.e.{001}<110>as well as{111}fibre texture become stronger.The internal relation of these two kinds of textures was also discussed.

Analysis on nonlinear effect of unsteady percolation in the inhomogeneous shale gas reservoir

The nonlinear effects of unsteady multi-scale shale gas percolation,such as desorption,slippage,diffusion,pressure-dependent viscosity,and compressibility,are investigated by numerical simulation.A new general mathematical model of the problem is built,in which the Gaussian distribution is used to describe the inhomogeneous intrinsic permeability.Based on the Boltzmann transformation,an efficient semi-analytical method is proposed.The problem is then converted into a nonlinear equation in an integral form for the pressure field,and a related explicit iteration scheme is constructed by numerical discretization.The validation examples show that the proposed method has good convergence,and the simulation results also agree well with the results obtained from both numerical and actual data of two vertical fractured test wells in the literature.Desorption,slippage,and diffusion have significant influence on shale gas flows.The accuracy of the usual technique that the product of viscosity and compressibility is approximated as its value at the average formation pressure is examined.

Scattering of shear waves by an elliptical cavity in a radially inhomogeneous isotropic medium

Complex function and general conformal mapping methods are used to investigate the scattering of elastic shear waves by an elliptical cylindrical cavity in a radially inhomogeneous medium. The conformal mappings are introduced to solve scattering by an arbitrary cavity for the Helmholtz equation with variable coefficient through the transformed standard Helmholtz equation with a circular cavity. The medium density depends on the distance from the origin with a power-law variation and the shear elastic modulus is constant. The complex-value displacements and stresses of the in.homogeneous medium are explicitly obtained and the distributions of the dynamic stress for the case of an elliptical cavity are discussed. The accuracy of the present approach is verified by comparing the present solution results with the available published data. Numerical results demonstrate that the wave number, inhomogeneous parameters and different values of aspect ratio have significant influence on the dynamic stress concentration factors around the elliptical cavity.

Synchronization of spiral waves in a two-layer coupled inhomogeneous excitable system

We studied synchronization behaviours of spiral waves in a two-layer coupled inhomogeneous excitable system. It was found that phase synchronization can be observed under weak coupling strength. By increasing the coupling strength, the synchronization is broken down. With the further increase of the coupling strength, complete synchronization and phase synchronization occur again. We also found that the inhomogeneity in excitable systems is helpful to the synchronization.

Inhomogeneous Shadowing Effect in High-Energy p-A Drell-Yan Process:

Having studied the initial state energy loss versus nuclear shadowing for the Drell-Yan dimuon pairproduction in the color string model,the inhomogeneous shadowing effect is considered in this paper.We find thatthe inhomogeneous shadowing effect does amend the rate of energy loss per unit path length,-dE/dz.Finally,thetheoretical results for the Drell-Yan differential cross-section ratios are compared with the E772 and E866 data.It isfound that the theoretical results are in good agreement with the experimental data.

Selection of quantum path in high-order harmonics and isolated sub-100 attosecond generation in few-cycle spatially inhomogeneous laser fields

We theoretically study the selection of the quantum path in high-order harmonics（HHG） and isolated attosecond pulse generation from a one-dimensional（1D） model of a H_2~＋ molecule in few-cycle inhomogeneous laser fields.We show that the inhomogeneity of the laser fields play an important role in the HHG process.The cutoff of the harmonics can be extended remarkably,and the harmonic spectrum becomes smooth and has fewer modulations.We investigate the time-frequency profile of the time-dependent dipole,which shows that the short quantum path is enhanced and the long quantum path disappears in spatially inhomogeneous fields.The semi-classical three-step model is also applied to illustrate the physical mechanism of HHG.The influence of driving field carrier-envelop phase（CEP） on HHG is also discussed.By superposing a series of properly selected harmonics,an isolated attosecond pulse（IAP） with duration 53 as can be obtained by a 15-fs,1600-nm laser pulse with the parameter ε = 0.0013（e is the parameter that determines the order of inhomogeneity of the laser field）.