Fresnel Equations Derived Using a Non-Local Hidden-Variable Particle Theory

Problem: The Fresnel equations describe the proportions of reflected and transmitted light from a surface, and are conventionally derived from wave theory continuum mechanics. Particle-based derivations of the Fresnel equations appear not to exist. Approach: The objective of this work was to derive the basic optical laws from first principles from a particle basis. The particle model used was the Cordus theory, a type of non-local hidden-variable (NLHV) theory that predicts specific substructures to the photon and other particles. Findings: The theory explains the origin of the orthogonal electrostatic and magnetic fields, and re-derives the refraction and reflection laws including Snell’s law and critical angle, and the Fresnel equations for s and p-polarisation. These formulations are identical to those produced by electromagnetic wave theory. Contribution: The work provides a comprehensive derivation and physical explanation of the basic optical laws, which appears not to have previously been shown from a particle basis. Implications: The primary implications are for suggesting routes for the theoretical advancement of fundamental physics. The Cordus NLHV particle theory explains optical phenomena, yet it also explains other physical phenomena including some otherwise only accessible through quantum mechanics (such as the electron spin g-factor) and general relativity (including the Lorentz and relativistic Doppler). It also provides solutions for phenomena of unknown causation, such as asymmetrical baryogenesis, unification of the interactions, and reasons for nuclide stability/instability. Consequently, the implication is that NLHV theories have the potential to represent a deeper physics that may underpin and unify quantum mechanics, general relativity, and wave theory.

Existence and Uniqueness of Solution for a Fractional Order Integro-Differential Equation with Non-Local and Global Boundary Conditions

In this paper, we prove an important existence and uniqueness theorem for a fractional order Fredholm – Volterra integro-differential equation with non-local and global boundary conditions by converting it to the corresponding well known Fredholm integral equation of second kind. The considered in this paper has been solved already numerically in [1].

On the Properties of Solutions of Non-local Parabolic Equations

In this short note, we investigate the properties of positive solutions for some non-local parabolic equations. The conditions on the global existence and blow-up in finite time of solution are given.

Continuity Equation in Presence of a Non-Local Potential in Non-Commutative Phase-Space

We studied the continuity equation in presence of a local potential, and a non-local potential arising from electron-electron interaction in both commutative and non-commutative phase-space. Furthermore, we examined the influence of the phase-space non-commutativity on both the locality and the non-locality, where the definition of current density in commutative phase-space cannot satisfy the condition of current conservation, but with the steady state, in order to solve this problem, we give a new definition of the current density including the contribution due to the non-local potential. We showed that the calculated current based on the new definition of current density maintains the current. As well for the case when the non- commutativity in phase-space considered, we found that the conservation of the current density completely violated;and the non-commutativity is not suitable for describing the current density in presence of non-local and local potentials. Nevertheless, under some conditions, we modified the current density to solve this problem. Subsequently, as an application we studied the Frahn-Lemmer non-local potential, taking into account that the employed methods concerning the phase-space non-commutativity are both of Bopp-shift linear transformation through the Heisenberg-like commutation relations, and the Moyal-Weyl product.

Integrated Approach of Universal Soil Loss Equation (USLE) and Geographical Information System (GIS) for Soil Loss Risk Assessment in Upper South Koel Basin, Jharkhand

Soil erosion is a growing problem especially in areas of agricultural activity where soil erosion not only leads to decreased agricultural productivity but also reduces water availability. Universal Soil Loss Equation (USLE) is the most popular empirically based model used globally for erosion prediction and control. Remote sensing and GIS techniques have become valuable tools specially when assessing erosion at larger scales due to the amount of data needed and the greater area coverage. The present study area is a part of Chotanagpur plateau with undulating topography, with a very high risk of soil erosion. In the present study an attempt has been made to assess the annual soil loss in Upper South Koel basin using Universal Soil Loss Equation (USLE) in GIS framework. Such information can be of immense help in identifying priority areas for implementation of erosion control measures. The soil erosion rate was determined as a function of land topography, soil texture, land use/land cover, rainfall erosivity, and crop management and practice in the watershed using the Universal Soil Loss Equation (for Indian conditions), remote sensing imagery, and GIS techniques. The rainfall erosivity R-factor of USLE was found as 546 MJ mm/ha/hr/yr and the soil erodibility K-factor varied from 0.23 - 0.37. Slopes in the catchment varied between 0% and 42% having LS factor values ranging from 0 - 21. The C factor was computed from NDVI (Normalized Difference Vegetative Index) values derived from Landsat-TM data. The P value was computed from existing cropping patterns in the catchment. The annual soil loss estimated in the watershed using USLE is 12.2 ton/ha/yr.

A Phenomenological Gradient Approach to Generalized Constitutive Equations for Isotropic Fluids

An extension of the linear irreversible thermodynamics is proposed through the inclusion of the first gradients of velocity and of the classical local state parameters as additional independent variables in the fundamental energy state equation of a fluid system. We show that consistency of this hypothesis with the energy balance equation leads to generalized nonlinear constitutive equations, which we discuss in terms of an isotropic non-Newtonian viscous fluid.

基于CSLE与GIS的高州市土壤侵蚀特征研究

文章应用中国土壤流失方程(CSLE)与GIS地理空间分析技术,分析研究了高州市土壤侵蚀空间分布特征及其与土地利用之间的关系。研究结果显示:高州市土壤侵蚀以轻度自然侵蚀为主,主要分布在中部及北部,少量生产建设项目人为水土流失零星分布于南部城镇区域,不同强度的土壤侵蚀大部分发生在园地及林地,其次为耕地和建设用地;研究成果可为高州市进行水土保持规划、合理开发利用水土资源提供决策参考。

Estimation of soil erosion risk within a small mountainous sub-watershed in Kerala,India,using Revised Universal Soil Loss Equation(RUSLE) and geo-information technology

A comprehensive methodology that integrates Revised Universal Soil Loss Equation （RUSLE） model and Geographic Information System （GIS） techniques was adopted to determine the soil erosion vulner- ability of a forested mountainous sub-watershed in Kerala, India. The spatial pattern of annual soil erosion rate was obtained by integrating geo-environmental variables in a raster based GIS method. GIS data layers including, rainfall erosivity （R）, soil erodability （K）, slope length and steepness （LS）, cover management （C） and conservation practice （P） factors were computed to determine their effects on average annual soil loss in the area. The resultant map of annual soil erosion shows a maximum soil loss of 17.73 t h-1 y i with a close relation to grass land areas, degraded forests and deciduous forests on the steep side-slopes （with high LS ）. The spatial erosion maps generated with RUSLE method and GIS can serve as effective inputs in deriving strategies for land planning and management in the environmentally sensitive mountainous areas.

Improved gradient iterative algorithms for solving Lyapunov matrix equations

In this paper, an improved gradient iterative （GI） algorithm for solving the Lyapunov matrix equations is studied. Convergence of the improved method for any initial value is proved with some conditions. Compared with the GI algorithm, the improved algorithm reduces computational cost and storage. Finally, the algorithm is tested with GI several numerical examples.

INVESTIGATION OF THE SCATTERING OF HARMONIC ELASTIC WAVES BY TWO COLLINEAR SYMMETRIC CRACKS USING THE NON-LOCAL THEORY

The scattering of harmonic waves by two collinear symmetric cracks is studied using the non-local theory. A one-dimensional non-local kernel was used to replace a two-dimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt's method. This method is more exact and more reasonable than Eringen's for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.

Soliton Solutions to the Coupled Gerdjikov-Ivanov Equation with Rogue-Wave-Like Phenomena

Bilinear forms of the coupled Gerdjikov–Ivanov equation are derived. The $N$-soliton solutions to the equation are obtained by Hirota＇s method. It is interesting that the two-soliton solutions can generate the rogue-wave-like phenomena by selecting special parameters. The equation can be reduced to the Gerdjikov–Ivanov equation as well as its bilinear forms and its solutions.

REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH JUMPS AND VISCOSITY SOLUTION OF SECOND ORDER INTEGRO-DIFFERENTIAL EQUATION WITHOUT MONOTONICITY CONDITION: CASE WITH THE MEASURE OF LéVY INFINITE

We consider the problem of viscosity solution of integro-partial differential equation( IPDE in short) with one obstacle via the solution of reflected backward stochastic dif ferential equations(RBSDE in short) with jumps. We show the existence and uniqueness of a continuous viscosity solution of equation with non local terms, if the generator is not monotonous and Levy's measure is infinite.

Analysis of anomalous transport based on radial fractional diffusion equation

Anomalous transport in magnetically confined plasmas is investigated by radial fractional transport equations.It is shown that for fractional transport models,hollow density profiles are formed and uphill transports can be observed regardless of whether the fractional diffusion coefficients(FDCs)are radially dependent or not.When a radially dependent FDC<D_(α)(r)1 is imposed,compared with the case under=D_(α)(r)1.0,it is observed that the position of the peak of the density profile is closer to the core.Further,it is found that when FDCs at the positions of source injections increase,the peak values of density profiles decrease.The non-local effect becomes significant as the order of fractional derivative a 1 and causes the uphill transport.However,as a 2,the fractional diffusion model returns to the standard model governed by Fick’s law.

INVESTIGATION OF A GRIFFITH CRACK SUBJECT TO UNIFORM TENSION USING THE NON-LOCAL THEORY BY A NEW METHOD

Field equations of the non-local elasticity are solved to determine the state of stress in a plate with a Griffith crack subject to uniform tension. Then a set of dual-integral equations is solved using a new method, namely Schmidt's method. This method is more exact and more reasonable than Eringen's a one Sor solving this kind of problem. Contrary to the solution of classical elasticity, it is found that no stress singularity is present ar the crack tip. The significance of this result is that the fracture criteria are unified at both the macroscopic and the microscopic scales. The finite hoop stress at the crack tip depends on the crack length.

THE SCATTERING OF HARMONIC ELASTIC ANTI-PLANE SHEAR WAVES BY A FINITE CRACK IN INFINITELY LONG STRIP USING THE NON-LOCAL THEORY

In this paper, the scattering of harmonic anti-plane shear wavesby a finite crack in infinitely long strip is studied using thenon-local theory. The Fourier transform is applied and a mixedboundary value problem is formulated. Then a set of dual integralequations is solved using the Schmidt method instead of the first orthe second integral equation method. A one-dimensional non-localkernel is used instead of a two-di- mensional one for the anti-planedynamic problem to obtain the stress occurring at the crack tips.Contrary to the classical elasticity solution, it is found that nostress singularity is present at the crack tip. The non-local dynamicelastic solutions yield a finite hoop stress at the crack tip, thusallowing for a fracture criterion based on the maximum dynamic stresshypothesis. The finite hoop stress at the crack tip depends on thecrack length, the width of the strip and the lattice parameters.

GLOBAL BLOWUP AND BLOWUP RATE ESTIMATES OF SOLUTIONS FOR A CLASS OF NONLINEAR NON-LOCAL REACTION-DIFFUSION PROBLEMS

In this paper, the global blowup properties of solutions for a class of nonlinear non-local reaction-diffusion problems are investigated by the methods of the prior estimates. Moreover, the blowup rate estimate of the solution is given.

THE ANALYSIS OF CRACK PROBLEMS WITHNON-LOCAL ELASTICITY

In this pager, the displacement discontinuity fundamental solutions ( DDFS) corresponding to the unit concentrated displacement discontinuity for plane problems of non-local elasticity are obtained. Based on the displacement discontinuity boundary integral equation (DDBIE) and boundary element method (BEM), a method of analysis of crack problems in non-local elasticity with generalized purpose is proposed. By using this method, several important problems in fracture mechanics such as edge crack are studied. The study of edge crack shows that the stress concentration factor (SCF) near the crack tip is not a constant but varies with the crack length. With this result the effect of crack length on the fracture roughness K (I c) is studied. The results obtained in this paper are in accordance with the published ones.

Uniqueness Theorem for the Non-Local Ionization Source in Glow Discharge and Hollow Cathode

The paper is devoted to the proof of the uniqueness theorem for solution of the equation for the non-local ionization source in a glow discharge and a hollow cathode in general 3D geometry. The theorem is applied to wide class of electric field configurations, and to the walls of discharge volume, which have a property of incomplete absorption of the electrons. Cathode is regarded as interior singular source, which is placed arbitrarily close to the wall. The existence of solution is considered also. During the proof of the theorem many of useful structure formulae are obtained. Elements of the proof structure, which have arisen, are found to have physical sense. It makes clear physical construction of non-local electron avalanche, which builds a source of ionization in glow discharge at low pressures. Last has decisive significance to understand the hollow cathode discharge configuration and the hollow cathode effect.

基于GIS丘陵土壤分区的水稻施肥配方研究

【目的】分析弋阳县土壤养分分布状况,划分弋阳县土壤肥力等别,绘制肥力等别图;创建施肥建议模型,得出各区明确而可行的水稻最佳经济效益施肥方案并得到相应施肥方案图。【方法】基于弋阳县2006—2008三年测土数据和基础地理数据,结合GIS软件形成养分专题图、坡度图和高程图,分析丘陵县域土壤养分含量分布与地形的关系。结合耕地地力调查数据,进一步对该县土壤进行养分综合等级分区。在分区的基础上,选取能代表各区土壤肥力特性的水稻"3414"肥料试验,利用SAS软件对各"3414"试验数据进行肥料效应方程的拟合,结合方程求解各区水稻最佳经济效益和对应的施肥量、施肥比例。【结果】中、高含量的碱解氮、有效磷和速效钾主要分布在平原及低坡度区;低含量的碱解氮、有效磷和速效钾主要分布在丘陵、低山、岗埠地带。弋阳县耕地主要肥力等别区共9区,各区水稻最佳经济效益为8 313—13 500元/hm2,对应的氮、磷、钾施肥量高低有别,施用比例为1.0﹕0.18—0.49﹕0.48—0.85。【结论】丘陵县域土壤养分含量分布变异较大,与地形分布相关。采用宏观GIS和建模技术,结合土壤分析数据和田间试验数据,针对不同分区提出各区的施肥建议。

基于GIS和USLE的土壤侵蚀定量分析研究——以四川省洪雅县为例

以四川省洪雅县为研究对象,运用GIS方法和USLE土壤侵蚀模型,分析与评价该区域的土壤侵蚀状况。结果表明:洪雅县土地利用单元的侵蚀强度存在显著差异,不同的土地利用类型与土壤侵蚀强度强弱有较为密切的联系。根据洪雅县的土地利用和自然经济状况,洪雅县可分为北部轻度侵蚀区、中部微度侵蚀区和西南部无明显侵蚀区3类土壤侵蚀强度类型区,并针对各区不同的情况模拟制定了相应的水土保持治理措施,为当地政府开展水土保持规划工作提供科学依据。