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 thermod...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.展开更多
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 ...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.展开更多
Introducing PT-symmetric generalized Scarf-Ⅱpotentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seek stable soliton states in quasi-onedimensional spin-1 Bose-Einstein condensat...Introducing PT-symmetric generalized Scarf-Ⅱpotentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seek stable soliton states in quasi-onedimensional spin-1 Bose-Einstein condensates.In scenarios where the spin-independent parameter c_(0)and the spin-dependent parameter c_(2)vary,we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross-Pitaevskii equations with PT-symmetric generalized Scarf-Ⅱpotentials.We obtain analytical soliton states and find that simply modulating c_(2)may change the analytical soliton states from unstable to stable.Additionally,we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations,exhibiting distinct behavior in energy exchange.For further investigation,we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components.These findings may contribute to a deeper understanding of solitons in Bose-Einstein condensates with PT-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.展开更多
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 genera...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.展开更多
In this paper,based on physics-informed neural networks(PINNs),a good deep learning neural network framework that can be used to effectively solve the nonlinear evolution partial differential equations(PDEs)and other ...In this paper,based on physics-informed neural networks(PINNs),a good deep learning neural network framework that can be used to effectively solve the nonlinear evolution partial differential equations(PDEs)and other types of nonlinear physical models,we study the nonlinear Schrodinger equation(NLSE)with the generalized PT-symmetric Scarf-Ⅱpotential,which is an important physical model in many fields of nonlinear physics.Firstly,we choose three different initial values and the same Dinchlet boundaiy conditions to solve the NLSE with the generalized PT-symmetric Scarf-Ⅱpotential via the PINN deep learning method,and the obtained results are compared with ttose denved by the toditional numencal methods.Then,we mvestigate effect of two factors(optimization steps and activation functions)on the performance of the PINN deep learning method in the NLSE with the generalized PT-symmetric Scarf-Ⅱpotential.Ultimately,the data-driven coefficient discovery of the generalized PT-symmetric Scarf-Ⅱpotential or the dispersion and nonlinear items of the NLSE with the generalized PT-symmetric Scarf-Ⅱpotential can be approximately ascertained by using the PINN deep learning method.Our results may be meaningful for further investigation of the nonlinear Schrodmger equation with the generalized PT-symmetric Scarf-Ⅱpotential in the deep learning.展开更多
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'...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 <∞.展开更多
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. T...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.展开更多
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 centrifuga...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.展开更多
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 for...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.展开更多
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 res...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.展开更多
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 ...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.展开更多
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 ...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.展开更多
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 eigen...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.展开更多
The paper deals with growth estimates and approximation（not necessarily entire） of solutions of certain elliptic partial differential equations. These solutions are called generalized bi-axially symmetric potentials...The paper deals with growth estimates and approximation（not necessarily entire） of solutions of certain elliptic partial differential equations. These solutions are called generalized bi-axially symmetric potentials（GBASP＇s）. To obtain more refined measure of growth, we have defined q-proximate order and obtained the characterization of generalized q-type and generalized lower q-type with respect to q-proximate order of a GBASP in terms of approximation errors and ratio of these errors in sup norm.展开更多
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...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.展开更多
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....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.展开更多
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 e...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.展开更多
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 st...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.展开更多
In this study, we reveal the difference between Woods-Saxon(WS) and Generalized Symmetric WoodsSaxon(GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schr¨odinger eq...In this study, we reveal the difference between Woods-Saxon(WS) and Generalized Symmetric WoodsSaxon(GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schr¨odinger equation for the two potentials. The additional term squeezes the WS potential well, which leads an upward shift in the spectrum, resulting in a more realistic picture. The resulting GSWS potential does not merely accommodate extra quasi bound states, but also has modified bound state spectrum. As an application, we apply the formalism to a real problem,an α particle confined in Bohrium-270 nucleus. The thermodynamic functions Helmholtz energy, entropy, internal energy,specific heat of the system are calculated and compared for both wells. The internal energy and the specific heat capacity increase as a result of upward shift in the spectrum. The shift of the Helmholtz free energy is a direct consequence of the shift of the spectrum. The entropy decreases because of a decrement in the number of available states.展开更多
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 ...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.展开更多
基金supported by the National Basic Research Program of China (2009CB421505)the National Natural Science Foundation of China (41075044 and 41075079)
文摘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.
基金Projects(51378131,51378403)supported by the National Natural Science Foundation of ChinaProject(2012210020203)supported by the Fundamental Research Funds for the Central Universities,China
文摘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.
基金supported by NSFC under Grant No.12272403Beijing Training Program of Innovation under Grant No.S202410019024。
文摘Introducing PT-symmetric generalized Scarf-Ⅱpotentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seek stable soliton states in quasi-onedimensional spin-1 Bose-Einstein condensates.In scenarios where the spin-independent parameter c_(0)and the spin-dependent parameter c_(2)vary,we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross-Pitaevskii equations with PT-symmetric generalized Scarf-Ⅱpotentials.We obtain analytical soliton states and find that simply modulating c_(2)may change the analytical soliton states from unstable to stable.Additionally,we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations,exhibiting distinct behavior in energy exchange.For further investigation,we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components.These findings may contribute to a deeper understanding of solitons in Bose-Einstein condensates with PT-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.
文摘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.
基金supported by the National Natural Science Foundation of China under Grant Nos.11775121,11435005the K.C.Wong Magna Fund of Ningbo University。
文摘In this paper,based on physics-informed neural networks(PINNs),a good deep learning neural network framework that can be used to effectively solve the nonlinear evolution partial differential equations(PDEs)and other types of nonlinear physical models,we study the nonlinear Schrodinger equation(NLSE)with the generalized PT-symmetric Scarf-Ⅱpotential,which is an important physical model in many fields of nonlinear physics.Firstly,we choose three different initial values and the same Dinchlet boundaiy conditions to solve the NLSE with the generalized PT-symmetric Scarf-Ⅱpotential via the PINN deep learning method,and the obtained results are compared with ttose denved by the toditional numencal methods.Then,we mvestigate effect of two factors(optimization steps and activation functions)on the performance of the PINN deep learning method in the NLSE with the generalized PT-symmetric Scarf-Ⅱpotential.Ultimately,the data-driven coefficient discovery of the generalized PT-symmetric Scarf-Ⅱpotential or the dispersion and nonlinear items of the NLSE with the generalized PT-symmetric Scarf-Ⅱpotential can be approximately ascertained by using the PINN deep learning method.Our results may be meaningful for further investigation of the nonlinear Schrodmger equation with the generalized PT-symmetric Scarf-Ⅱpotential in the deep learning.
文摘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 <∞.
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
文摘The paper deals with growth estimates and approximation（not necessarily entire） of solutions of certain elliptic partial differential equations. These solutions are called generalized bi-axially symmetric potentials（GBASP＇s）. To obtain more refined measure of growth, we have defined q-proximate order and obtained the characterization of generalized q-type and generalized lower q-type with respect to q-proximate order of a GBASP in terms of approximation errors and ratio of these errors in sup norm.
文摘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.
文摘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.
文摘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.
文摘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.
基金Supported by the Turkish Science and Research Council(TBTAK)Akdeniz University
文摘In this study, we reveal the difference between Woods-Saxon(WS) and Generalized Symmetric WoodsSaxon(GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schr¨odinger equation for the two potentials. The additional term squeezes the WS potential well, which leads an upward shift in the spectrum, resulting in a more realistic picture. The resulting GSWS potential does not merely accommodate extra quasi bound states, but also has modified bound state spectrum. As an application, we apply the formalism to a real problem,an α particle confined in Bohrium-270 nucleus. The thermodynamic functions Helmholtz energy, entropy, internal energy,specific heat of the system are calculated and compared for both wells. The internal energy and the specific heat capacity increase as a result of upward shift in the spectrum. The shift of the Helmholtz free energy is a direct consequence of the shift of the spectrum. The entropy decreases because of a decrement in the number of available states.
基金supported by the National Natural Science Foundation of ChinaYalona River Hydropower Development of Ertan Hydropower Development Company (No.50639050)
文摘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.
