A Brief Report of Graphic Explanations for Generalized Potential Temperature in the Non-Uniformly Saturated Atmosphere

Compared to potential temperature （θ） in the dry atmosphere and equivalent potential temperature （θc） in the saturated atmosphere, generalized potential tem- perature （θ＂） has already proven a better thermodynamic parameter in describing the non-uniformly saturated real atmosphere. To add otherwise absent graphic explanations, this paper first presents the physical definition of θ through a tephigram. Then, the utility of the measurement in identifying and forecasting the locations of precipita- tion maxima and heat wave areas with diagnostic com- parison studies and traditionally used thermodynamic parameters is shown.

Numerical verification of similar Cam-clay model based on generalized potential theory

From the mathematical principles, the generalized potential theory can be employed to create constitutive model of geomaterial directly. The similar Cam-clay model, which is created based on the generalized potential theory, has less assumptions,clearer mathematical basis, and better computational accuracy. Theoretically, it is more scientific than the traditional Cam-clay models. The particle flow code PFC3 D was used to make numerical tests to verify the rationality and practicality of the similar Cam-clay model. The verification process was as follows: 1) creating the soil sample for numerical test in PFC3 D, and then simulating the conventional triaxial compression test, isotropic compression test, and isotropic unloading test by PFC3D; 2)determining the parameters of the similar Cam-clay model from the results of above tests; 3) predicting the sample's behavior in triaxial tests under different stress paths by the similar Cam-clay model, and comparing the predicting results with predictions by the Cam-clay model and the modified Cam-clay model. The analysis results show that the similar Cam-clay model has relatively high prediction accuracy, as well as good practical value.

A Comparative study on generalized Manev potential and Newtonian potential in perturbed restricted four-body problem

The motion of a test particle within the context of the restricted four-body problem(R4BP)driven by a new kind of potential,called the generalized Manev potential,with perturbations in the Coriolis and centrifugal forces is considered in this study.The system possesses eight libration points which were distributed on its plane of motion in different manner from those of the usual Newtonian potential.Unlike the case of the perturbed R4BP under Newtonian potential,where two of these librations are stable,all of them are unstable in linear sense under Manev potential.We found that a gradual perturbation in the centrifugal force causes the trajectories of motion to drift inward but the Coriolis force was proven to have no effect on the location of the libration points of the system.Using first order Lyapunov characteristic exponents,the dynamical behavior of the system is found irregular.We experimented with a high velocity stellar system(82 G.Eridani)to establish the applicability of the model in astrophysics.

Generalized Available Potential Energy

The kinetic energy generation in either the dry or moist atmosphere may be estimated by the same relationships if we introduce the new concept of generalized available potential energy. The largest magnitude of generalized available potential energy and corresponding reference state of either dry or moist atmosphere are calculated in terms of the mitial conditions and entropy variation of the atmosphere. The obtained relationships are applicable for the statically unstable atmosphere as well. The generalized available potential energy associated with reversible processes reaches the maximum with respect to same initial state. While the generation of kinetic energy in irreversible processes is characterized by sudden changes. When the reference state is assumed to be saturated, we may predict the final temperature and moisture fields corresponding to provided initial state and entropy variation.

APPROXIMATION OF GENERALIZED BI－AXIALLY SYMMETRIC POTENTIALS WITH FAST RATES OF GROWTH

The paper deals with growth and approximation of solutions (not necessarily entire) of certain elliptic partial differential equations. These solutions are called Generalized Bi-axially Symmetric Potentials (GBSP's). The GBSP's are taken to be regular in a finite hyperball and influence of the growth of their maximum moduli on the rate of decay of their approximation errors in sup norm is studied. The authors obtain the characterizations of the q-type and lower q-type of a GBSP H ∈ HP,0 < R < ∞, in terms of rate of decay of approximation error E.(H,R0), 0 < R0<R <∞.

Bound State Solutions of Schrodinger Equation for Generalized Morse Potential with Position-Dependent Mass

The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.

The scattering states of the generalized Hulthén potential with an improved new approximate scheme for the centrifugal term

This paper finds the approximate analytical scattering state solutions of the arbitrary 1-wave Schrodinger equation for the generalized Hulthen potential by taking an improved new approximate scheme for the centrifugal term. The normalized analytical radial wave functions of the 1-wave SchrSdinger equation for the generalized Hulthen potential are presented and the corresponding calculation formula of phase shifts is derived. Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulthen potential and Woods-Saxon potential are also studied briefly.

Groundstate with Zero Eigenvalue for Generalized Sombrero-Shaped Potential in N-Dimensional Space

Based on an iterative method for solving the groundstate of Schrodinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The restrictions on the parameters in the potential are discussed.

Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential

A bound state solution is a quantum state solution of a particle subjected to a potential such that the particle＇s energy is less than the potential at both negative and positive infinity. The particle＇s energy may also be negative as the potential approaches zero at infinity. It is characterized by the discretized eigenvalues and eigenfunctions, which contain all the necessary information regarding the quantum systems under consideration. The bound state problems need to be extended using a more precise method and approximation scheme. This study focuses on the non-relativistic bound state solutions to the generalized inverse quadratic Yukawa potential. The expression for the non-relativistic energy eigenvalues and radial eigenfunctions are derived using proper quantization rule and formula method, respectively. The results reveal that both the ground and first excited energy eigenvalues depend largely on the angular momentum numbers, screening parameters, reduced mass, and the potential depth. The energy eigenvalues, angular momentum numbers, screening parameters, reduced mass, and the potential depth or potential coupling strength determine the nature of bound state of quantum particles. The explored model is also suitable for explaining both the bound and continuum states of quantum systems.

Relativistic Study of Spinless Particles for Generalized Hylleraas Potential with Position Dependent Mass

The relativistic study of spinless particles under a special case of equal scalar and vector generalized Hylleraas potential with position dependent mass has been studied. The energy eigenvalues and the corresponding wave functions expressed in terms ofa Jacobi polynomial are obtained using the parametric generalization of NU （Nikiforo-Uvarov） method. In obtaining the solutions for this system, we have used an approximation scheme to evaluate the centrifugal term （potential barrier）. To test the accuracy of the result, we compared the approximation scheme with the centrifugal term and the result shows a good agreement with the centrifugal term for a short-range potential. The results obtained in this work would have many applications in semiconductor quantum well structures, quantum dots, quantum liquids. Under limiting cases, the results could be used to study the binding energy and interaction of some diatomic molecules which is of great applications in nuclear physics, atomic and molecular physics and other related areas. We have also discussed few special cases of generalized Hylleraas potential such as Rosen-Morse, Woods-Saxon and Hulthen potentials.

Relativistic Treatment of Massive Klein-Gordon Particle by Modified Generalized Hulthen Potential

Approximate bound state solutions of spinless particles with a special case of equal scalar and vector modified generalized Hulthen potential has been obtained under the massive Klein-Gordon equation. The energy eigenvalues and the corresponding wave functions expressed in terms of a Jacobi polynomial are also obtained using the parametric generalization of the Nikiforov-Uvarov （NU） method. Under limiting cases our result are in agreement with the existing literature. Our results could be used to study the interactions and binding energies of the central potential for diatomic molecules in the relativistic framework which have many applications in physics and some others related disciplines.

UNIQUENESS OF GENERALIZED SOLUTION FOR THE CAUCHY PROBLEM OF TRANSPORTATTION EQUATIONS

In this paper, we prove the uniqueness of generalized solution defined by Lebesgue-Stieltjes integral for the Cauchy problem of transportation equations. Our results are based on the discussions for linear system with discontinuous coefficient.

GENERALIZED VARIATIONAL PRINCIPLES OF THE VISCOELASTIC BODY WITH VOIDS AND THEIR APPLICATIONS

From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and the initial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.

A Generalized Statement of Highest-Entropy Principle for Stable Equilibrium and Non-Equilibrium in Many-Particle Systems

Among all statements of Second Law, the existence and uniqueness of stable equilibrium, for each given value of energy content and composition of constituents of any system, have been adopted to define thermodynamic entropy by means of the impossibility of Perpetual Motion Machine of the Second Kind (PMM2) which is a consequence of the Second Law. Equality of temperature, chemical potential and pressure in many-particle systems are proved to be necessary conditions for the stable equilibrium. The proofs assume the stable equilibrium and derive, by means of the Highest-Entropy Principle, equality of temperature, chemical potential and pressure as a consequence. A first novelty of the present research is to demonstrate that equality is also a sufficient condition, in addition to necessity, for stable equilibrium implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality of temperature potential and pressure addressed to as generalized potential. The second novelty is that the proof of sufficiency of equality, or necessity of stable equilibrium, is achieved by means of a generalization of entropy property, derived from a generalized definition of exergy, both being state and additive properties accounting for heat, mass and work interactions of the system underpinning the definition of Highest-Generalized-Entropy Principle adopted in the proof.

A study on assessment of hydrocarbon potential of the lignite deposits of Saurashtra basin, Gujarat （Western India）

In the present investigation, Bhavnagar lignites of the Saurashtra basin （Gujarat） have been studied to assess their hydrocarbon generating potential. The samples of upper as well as lower lignite seams have been studied through microscopy and subjected to various chemical analyses viz. proximate analysis, ultimate analysis and Rock-Eval Pyrolysis. These lignites have high moisture and low to moderate ash yield but are characterized by high volatile matter. Petro- graphically they comprise predominantly of huminite group maceral while liptinite and inertinite groups occur in sub- ordinated amount. Huminite is chiefly composed of detrohuminite and telohuminite. The Tma~ （av. 416.23 ~C） and huminite reflectivity （0.28%-0.30%） indicate a low degree of maturity for these lignites which is also substantiated by the T,n~~ versus hydrogen index plot. The organic matter is subjugated by kerogen Type-III with a potential to expel hydrocarbon on liquefaction. Study further reveals that the fixed hydrocarbon is several folds higher than the free hydrocarbons. Being high in reactive maceral content, a high ＇conversion＇ and good ＇oil yield＇ values for these lignites were observed. Thus, the empirically derived values match well with those obtained through the experimental values of Rock-Eval Pyrolysis and validate their hydrocarbon generating potential.

ELASTO-PLASTIC CONSTITUTIVE MODEL OF SOIL-STRUCTURE INTERFACE IN CONSIDERATION OF STRAIN SOFTENING AND DILATION

The behavior of soil-structure interface plays a major role in the definition of soil-structure interaction. In this paper a bi-potential surface elasto-plastic model for soil-structure interface is proposed in order to describe the interface deformation behavior,including strain softening and normal dilatancy. The model is formulated in the framework of generalized potential theory,in which the soil-structure interface problem is regard as a two-dimensional mathematical problem in stress field,and plastic state equations are used to replace the traditional field surface. The relation curves of shear stress and tangential strain are fitted by a piecewise function composed by hyperbolic functions and hyperbolic secant functions,while the relation curves of normal strain and tangential strain are fitted by another piecewise function composed by quadratic functions and hyperbolic secant functions. The approach proposed has the advantage of deriving an elastoplastic constitutive matrix without postulating the plastic potential functions and yield surface. Moreover,the mathematical principle is clear,and the entire model parameters can be identified by experimental tests. Finally,the predictions of the model have been compared with experimental results obtained from simple shear tests under normal stresses,and results show the model is reasonable and practical.

An elasto-plastic constitutive model incorporating strain softening and dilatancy for interface thin-layer element and its verification

The mechanical behaviors of the interface between coarse-grained soil and concrete were investigated by simple shear tests under condition of mixed soil slurry (bentonite mixed with cement grout).For comparison,the interfaces both without slurry and with bentonite slurry were analyzed.The experimental results show that different slurries exert much influence on the strength and deformation of soil/structure interface.Under mixed soil slurry,strain softening and shear dilatation are observed,while shear dilatation appears under the small normal stress of the interface without slurry,and shear contraction is significant under the condition of the bentonite slurry.The thickness of the interface was determined by analyzing the disturbed height of the sample with both simple shear test and particle flow code (PFC).An elasto-plastic constitutive model incorporating strain softening and dilatancy for thin layer element of interface was formulated in the framework of generalized potential theory.The relation curves of shear stress and shear strain,as well as the relation curves of normal strain and shear strain,were fitted by a piecewise function composed by hyperbolic functions and resembling normal functions.The entire model parameters can be identified by tests.The new model is verified by comparing the measured data of indoor cut-off wall model tests with the predictions from finite element method (FEM).The FEM results indicate that the stress of wall calculated by using Goodman element is too large,and the maximum deviation between the test data and prediction is about 45%.While the prediction from the proposed model is close to the measured data,and the error is generally less than 10%.

NOETHER’S THEORY FOR NONHOLONOMIC DYNAMICAL SYSTEMS RELATIVE TO NON-INERTIAL REFERENCE FRAME

The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's theorem and Naether's inverse theorem of the system above is presented and proved. Finally, one example is given to illustrate the application.

UNIQUENESS ON ZERO PRESSURE GAS DYNAMICS

By introducing a new idea, the authors prove the uniqueness of weak solution of pressureless gases with the large initial data. In particular, uniqueness theorem is obtained in the same functional space as the existence theorem.

Diagnostic Analysis of Wave Action Density During Heavy Rainfall Caused by Landfalling Typhoon

Based on prior investigation,this work defined a new thermodynamic shear advection parameter,which combines the vertical component of convective vorticity vector,horizontal divergence,and vertical gradient of generalized potential temperature.The interaction between waves and fundamental states was computed for the heavyrainfall event generated by landfalling typhoon“Morakot”.The analysis data was produced by ADAS[ARPS(Advanced Regional Prediction System)Data Analysis System]combined with the NCEP/NCAR final analysis data(1°×1°,26 vertical pressure levels and 6-hour interval)with the routine observations of surface and sounding.Because it may describe the typical vertical structure of dynamical and thermodynamic fields,the result indicates that the parameter is intimately related to precipitation systems.The parameter’s positive high-value area closely matches the reported 6-hour accumulated surface rainfall.And the statistical analysis reveals a certain correspondence between the thermodynamic shear advection parameter and the observed 6-hour accumulated surface rainfall in the summer of 2009.This implies that the parameter can predict and indicate the rainfall area,as well as the initiation and evolution of precipitation systems.