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
The development of vertical vorticity under adiabatic condition is investigated by virtue of the view of potential vorticity and potential temperature （PV-θ） and from a Lagrangian perspective. A new concept of gene...The development of vertical vorticity under adiabatic condition is investigated by virtue of the view of potential vorticity and potential temperature （PV-θ） and from a Lagrangian perspective. A new concept of generalized slantwise vorticity development （GSVD） is introduced for adiabatic condition. The GSVD is a coordinate independent framework of vorticity development （VD）, which includes slantwise vorticity development （SVD） when a particle is sliding down the concave slope or up the convex slope of a sharply tilting isentropic surface under stable or unstable condition. The SVD is a special VD for studying the severe weather systems with rapid development of vertical vorticity. In addition, the GSVD clarifies VD and SVD. The criteria for VD and SVD demonstrate that the demand for SVD is much more restricted than the demand for VD. When an air parcel is moving down the concave slope or up the convex slope Of a sharply tilting isentropic surface in a stable stratified atmosphere with its stability decreasing, or in an unstable atmosphere with its stability increasing, i.e., its stability θz approaches zero, its vertical vorticity can develop rapidly if its CD is decreasing. The theoretical results are employed to analyze a Tibetan Plateau （TP） vortex （TPV）, which appeared over the TP, then slid down and moved eastward in late July 2008, resulting in heavy rainfall in Sichuan Province and along the middle and lower reaches of the Yangtze River. The change of PV2 contributed to the intensification of the TPV from 0000 to 0600 UTC 22 July 2008 when it slid upward on the upslope of the northeastern edge of the Sichuan basin, since the changes in both horizontal vorticity ~？~ and baroclinity Os have positive effects on the development of vertical vorticity. At 0600 UTC 22 July 2008, the criterion for SVD at 300 K isentropic surface is satisfied, meaning that SVD occurred and contributed significantly to the development of vertical vorticity. The appearance of the stronger signals concerni展开更多
In this paper, we prove the global existence of generalized solutions of Cauchy problem for transportation equations; moreover, we construct the solution by generalized potential.
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
The literature reports that equality of temperature, equality of potential and equality of pressure between a system and a reservoir are necessary conditions for the stable equilibrium of the system-reservoir composit...The literature reports that equality of temperature, equality of potential and equality of pressure between a system and a reservoir are necessary conditions for the stable equilibrium of the system-reservoir composite or, in the opposite and equivalent logical inference, that stable equilibrium is a sufficient condition for equality. The aim and the first novelty of the present study is to prove that equality of temperature, potential and pressure is also a sufficient condition for stable equilibrium, in addition to necessity, implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality. The second novelty is that the proof of the sufficiency of equality (or the necessity of stable equilibrium) is attained by means of the generalization of the entropy property, derived from the generalization of exergy property, which is used to demonstrate that stable equilibrium is a logical consequence of equality of generalized potential. This proof is underpinned by the Second Law statement and the Maximum-Entropy Principle based on generalized entropy which depends on temperature, potential and pressure of the reservoir. The conclusion, based on these two novel concepts, consists of the theorem of necessity and sufficiency of stable equilibrium for equality of generalized potentials within a composite constituted by a system and a reservoir.展开更多
A new invariant called the generalized Ertel Rossby invariant （GER） was developed in this study. The new invariant is given by the dot product of the generalized vorticity and the generalized velocity. The generaliz...A new invariant called the generalized Ertel Rossby invariant （GER） was developed in this study. The new invariant is given by the dot product of the generalized vorticity and the generalized velocity. The generalized vortieity is the absolute vorticity minus the cross product of the gradient of Lagrangian--time integrated temperature and the gradient of entropy. The generalized velocity is the absolute velocity minus the sum of the gradient of Lagrangian-time integrated kinetic potential and the Lagrangian time integrated temperature multiplied by the gradient of entropy. In addition to the traditional potential vorticity, the GER invariant may provide another useful tool to study the atmospheric dynamic processes for weather phenomena ranging from large scales to small scales.展开更多
We perform benchmark calculations of the p-wave resonances in the exponentially cosine screened Coulomb potential using the uniform complex-scaling generalized pseudo-spectral method.The present results show significa...We perform benchmark calculations of the p-wave resonances in the exponentially cosine screened Coulomb potential using the uniform complex-scaling generalized pseudo-spectral method.The present results show significant improvement in calculation accuracy compared to previous predictions and correct the misidentification of resonance electron configuration in previous works.It is found that the resonance states approximately follow an n^(2)-scaling law which is similar to the bound counterparts.The birth of a new resonance would distort the trajectory of an adjacent higher-lying resonance.展开更多
The performance of a two-state quantum engine under different conditions is analyzed. It is shown that the efficiency of the quantum engine can be enhanced by superposing the eigenstates at the beginning of the cycle....The performance of a two-state quantum engine under different conditions is analyzed. It is shown that the efficiency of the quantum engine can be enhanced by superposing the eigenstates at the beginning of the cycle. By employing the finite-time movement of the potential wall, the power output of the quantum engine as well as the efficiency at the maximum power out- put （EMP） can be obtained. A generalized potential is adopted to describe a class of two-level quantum engines in a unified way. The results obtained show clearly that the performances of these engines depend on the external potential, the geometric configuration of the quantum engines, and the superposition effect. Moreow^r, it is found that the superposition effect will en- large the optimally operating region of quantum engines.展开更多
By means of expansions of rapidly in infinity decreasing functions in delta functions and their derivatives, we derive generalized boundary conditions of the Sturm-Liouville equation for transitions and barriers or we...By means of expansions of rapidly in infinity decreasing functions in delta functions and their derivatives, we derive generalized boundary conditions of the Sturm-Liouville equation for transitions and barriers or wells between two asymptotic potentials for which the solutions are supposed as known. We call such expansions “moment series” because the coefficients are determined by moments of the function. An infinite system of boundary conditions is obtained and it is shown how by truncation it can be reduced to approximations of a different order (explicitly made up to third order). Reflection and refraction problems are considered with such approximations and also discrete bound states possible in nonsymmetric and symmetric potential wells are dealt with. This is applicable for large wavelengths compared with characteristic lengths of potential changes. In Appendices we represent the corresponding foundations of Generalized functions and apply them to barriers and wells and to transition functions. The Sturm-Liouville equation is not only interesting because some important second-order differential equations can be reduced to it but also because it is easier to demonstrates some details of the derivations for this one-dimensional equation than for the full three-dimensional vectorial equations of electrodynamics of media. The article continues a paper that was made long ago.展开更多
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 existen...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.展开更多
Based on μ-, T- and H-dependent pairing and number equations and the premise that μ(T) is predominantly the cause of the variation of the upper critical field H<sub>c</sub><sub>2</sub>(T), wh...Based on μ-, T- and H-dependent pairing and number equations and the premise that μ(T) is predominantly the cause of the variation of the upper critical field H<sub>c</sub><sub>2</sub>(T), where μ, T and H denote the chemical potential, temperature and the applied field, respectively, we provide in this paper fits to the empirical H<sub>c</sub><sub>2</sub>(T) data of H<sub>3</sub>S reported by Mozaffari, et al. (2019) and deal with the issue of whether or not H<sub>3</sub>S exhibits the Meissner effect. Employing a variant of the template given by Dogan and Cohen (2021), we examine in detail the results of Hirsch and Marsiglio (2022) who have claimed that H<sub>3</sub>S does not exhibit the Meissner effect and Minkov, et al. (2023) who have claimed that it does. We are thus led to suggest that monitoring the chemical potential (equivalently, the number density of Cooper pairs N<sub>s</sub> at T = T<sub>c</sub>) should shed new light on the issue being addressed.展开更多
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
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
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.
基金Supported by the National Basic Research and Development(973)Program of China(2012CB417203 and 2010CB950403)National Natural Science Foundation of China(40875034 and 40925015)
文摘The development of vertical vorticity under adiabatic condition is investigated by virtue of the view of potential vorticity and potential temperature （PV-θ） and from a Lagrangian perspective. A new concept of generalized slantwise vorticity development （GSVD） is introduced for adiabatic condition. The GSVD is a coordinate independent framework of vorticity development （VD）, which includes slantwise vorticity development （SVD） when a particle is sliding down the concave slope or up the convex slope of a sharply tilting isentropic surface under stable or unstable condition. The SVD is a special VD for studying the severe weather systems with rapid development of vertical vorticity. In addition, the GSVD clarifies VD and SVD. The criteria for VD and SVD demonstrate that the demand for SVD is much more restricted than the demand for VD. When an air parcel is moving down the concave slope or up the convex slope Of a sharply tilting isentropic surface in a stable stratified atmosphere with its stability decreasing, or in an unstable atmosphere with its stability increasing, i.e., its stability θz approaches zero, its vertical vorticity can develop rapidly if its CD is decreasing. The theoretical results are employed to analyze a Tibetan Plateau （TP） vortex （TPV）, which appeared over the TP, then slid down and moved eastward in late July 2008, resulting in heavy rainfall in Sichuan Province and along the middle and lower reaches of the Yangtze River. The change of PV2 contributed to the intensification of the TPV from 0000 to 0600 UTC 22 July 2008 when it slid upward on the upslope of the northeastern edge of the Sichuan basin, since the changes in both horizontal vorticity ~？~ and baroclinity Os have positive effects on the development of vertical vorticity. At 0600 UTC 22 July 2008, the criterion for SVD at 300 K isentropic surface is satisfied, meaning that SVD occurred and contributed significantly to the development of vertical vorticity. The appearance of the stronger signals concerni
文摘In this paper, we prove the global existence of generalized solutions of Cauchy problem for transportation equations; moreover, we construct the solution by generalized potential.
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The literature reports that equality of temperature, equality of potential and equality of pressure between a system and a reservoir are necessary conditions for the stable equilibrium of the system-reservoir composite or, in the opposite and equivalent logical inference, that stable equilibrium is a sufficient condition for equality. The aim and the first novelty of the present study is to prove that equality of temperature, potential and pressure is also a sufficient condition for stable equilibrium, in addition to necessity, implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality. The second novelty is that the proof of the sufficiency of equality (or the necessity of stable equilibrium) is attained by means of the generalization of the entropy property, derived from the generalization of exergy property, which is used to demonstrate that stable equilibrium is a logical consequence of equality of generalized potential. This proof is underpinned by the Second Law statement and the Maximum-Entropy Principle based on generalized entropy which depends on temperature, potential and pressure of the reservoir. The conclusion, based on these two novel concepts, consists of the theorem of necessity and sufficiency of stable equilibrium for equality of generalized potentials within a composite constituted by a system and a reservoir.
基金supported by the National Natural Science Foundation ofChina(Grant Nos.40921160379,40930950,and41075043)State Key Laboratory of Severe Weather(LaSW)Chinese Academy of Meteorological Sciences(Grant No.2011LASW-A01)
文摘A new invariant called the generalized Ertel Rossby invariant （GER） was developed in this study. The new invariant is given by the dot product of the generalized vorticity and the generalized velocity. The generalized vortieity is the absolute vorticity minus the cross product of the gradient of Lagrangian--time integrated temperature and the gradient of entropy. The generalized velocity is the absolute velocity minus the sum of the gradient of Lagrangian-time integrated kinetic potential and the Lagrangian time integrated temperature multiplied by the gradient of entropy. In addition to the traditional potential vorticity, the GER invariant may provide another useful tool to study the atmospheric dynamic processes for weather phenomena ranging from large scales to small scales.
基金supported by the National Natural Science Foundation of China(Grant No.12174147)the Chinese Scholarship Council(Grant Nos.202108210152 and 202006175016).
文摘We perform benchmark calculations of the p-wave resonances in the exponentially cosine screened Coulomb potential using the uniform complex-scaling generalized pseudo-spectral method.The present results show significant improvement in calculation accuracy compared to previous predictions and correct the misidentification of resonance electron configuration in previous works.It is found that the resonance states approximately follow an n^(2)-scaling law which is similar to the bound counterparts.The birth of a new resonance would distort the trajectory of an adjacent higher-lying resonance.
基金supported by the National Natural Science Foundation of China(Grant No.11005041)the Program for Prominent Young Talents in Fujian Province University(Grant No.JA12001)+2 种基金the Natural Science Foundation of Fujian Province(Grant Nos.2010J05007 and 2011J01012)the Fundamental Research Funds for the Central Universities(Grant No.JB-SJ1005)the Science Research Fund of Huaqiao University(Grant No.09BS510)
文摘The performance of a two-state quantum engine under different conditions is analyzed. It is shown that the efficiency of the quantum engine can be enhanced by superposing the eigenstates at the beginning of the cycle. By employing the finite-time movement of the potential wall, the power output of the quantum engine as well as the efficiency at the maximum power out- put （EMP） can be obtained. A generalized potential is adopted to describe a class of two-level quantum engines in a unified way. The results obtained show clearly that the performances of these engines depend on the external potential, the geometric configuration of the quantum engines, and the superposition effect. Moreow^r, it is found that the superposition effect will en- large the optimally operating region of quantum engines.
文摘By means of expansions of rapidly in infinity decreasing functions in delta functions and their derivatives, we derive generalized boundary conditions of the Sturm-Liouville equation for transitions and barriers or wells between two asymptotic potentials for which the solutions are supposed as known. We call such expansions “moment series” because the coefficients are determined by moments of the function. An infinite system of boundary conditions is obtained and it is shown how by truncation it can be reduced to approximations of a different order (explicitly made up to third order). Reflection and refraction problems are considered with such approximations and also discrete bound states possible in nonsymmetric and symmetric potential wells are dealt with. This is applicable for large wavelengths compared with characteristic lengths of potential changes. In Appendices we represent the corresponding foundations of Generalized functions and apply them to barriers and wells and to transition functions. The Sturm-Liouville equation is not only interesting because some important second-order differential equations can be reduced to it but also because it is easier to demonstrates some details of the derivations for this one-dimensional equation than for the full three-dimensional vectorial equations of electrodynamics of media. The article continues a paper that was made long ago.
文摘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.
文摘Based on μ-, T- and H-dependent pairing and number equations and the premise that μ(T) is predominantly the cause of the variation of the upper critical field H<sub>c</sub><sub>2</sub>(T), where μ, T and H denote the chemical potential, temperature and the applied field, respectively, we provide in this paper fits to the empirical H<sub>c</sub><sub>2</sub>(T) data of H<sub>3</sub>S reported by Mozaffari, et al. (2019) and deal with the issue of whether or not H<sub>3</sub>S exhibits the Meissner effect. Employing a variant of the template given by Dogan and Cohen (2021), we examine in detail the results of Hirsch and Marsiglio (2022) who have claimed that H<sub>3</sub>S does not exhibit the Meissner effect and Minkov, et al. (2023) who have claimed that it does. We are thus led to suggest that monitoring the chemical potential (equivalently, the number density of Cooper pairs N<sub>s</sub> at T = T<sub>c</sub>) should shed new light on the issue being addressed.
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.
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.
