Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for ...Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,展开更多
Physical and mathematical arguments are presented for equipartition as the statistical state achieved by a ran- dom field, independent of its sources, in the limit of enough scattering. The arguments are simplest for ...Physical and mathematical arguments are presented for equipartition as the statistical state achieved by a ran- dom field, independent of its sources, in the limit of enough scattering. The arguments are simplest for the case of thermally excited fields, but are shown to apply also, with caveats, in non-equilibrium acoustics and seismology. Practical implications are discussed.展开更多
We numerically study a one-dimensional,nonlinear lattice model which in the linear limit is relevant to the study of bending(flexural)waves.In contrast with the classic one-dimensional mass-spring system,the linear di...We numerically study a one-dimensional,nonlinear lattice model which in the linear limit is relevant to the study of bending(flexural)waves.In contrast with the classic one-dimensional mass-spring system,the linear dispersion relation of the considered model has different characteristics in the low frequency limit.By introducing disorder in the masses of the lattice particles,we investigate how different nonlinearities in the potential(cubic,quadratic,and their combination)lead to energy delocalization,equipartition,and chaotic dynamics.We excite the lattice using single site initial momentum excitations corresponding to a strongly localized linear mode and increase the initial energy of excitation.Beyond a certain energy threshold,when the cubic nonlinearity is present,the system is found to reach energy equipartition and total delocalization.On the other hand,when only the quartic nonlinearity is activated,the system remains localized and away from equipartition at least for the energies and evolution times considered here.However,for large enough energies for all types of nonlinearities we observe chaos.This chaotic behavior is combined with energy delocalization when cubic nonlinearities are present,while the appearance of only quadratic nonlinearity leads to energy localization.Our results reveal a rich dynamical behavior and show differences with the relevant Fermi–Pasta–Ulam–Tsingou model.Our findings pave the way for the study of models relevant to bending(flexural)waves in the presence of nonlinearity and disorder,anticipating different energy transport behaviors.展开更多
The extraction of the Earth＇s Green＇s function from field fluctuations is a rapidly growing area of research. The principle of Green＇s function extraction is often related to the requirement of equipartitioning, wh...The extraction of the Earth＇s Green＇s function from field fluctuations is a rapidly growing area of research. The principle of Green＇s function extraction is often related to the requirement of equipartitioning, which stipulates that the energy of field fluctuations is distributed evenly in some sense. We show the meaning of equipartitioning for a variety of different formulations for Green＇s function retrieval. We show that equipartitioning is not a sufficient condition, and provide several examples that illustrate this point. We discuss the implications of lack of equipartitioning for various schemes for the reconstruction of the Green＇s function in seismology. The theory for Green＇s function extraction is usually based on a statistical theory that relies on ensemble averages. Since there is only one Earth, one usually replaces the ensemble average with a time average. We show that such a replacement only makes sense when attenuation is taken into account, and show how the theory for Green＇s function extraction for oscillating systems can be extended to incorporate attenuation.展开更多
In this paper,we study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain（NSMC） indexed by Cayley tree with any finite states.The ...In this paper,we study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain（NSMC） indexed by Cayley tree with any finite states.The asymptotic equipartition properties with almost everywhere（a.e.） convergence for NSMC indexed by Cayley tree are obtained.This article generalizes a recent result.展开更多
We propose a cosmological scenario that describes the evolution of the universe based on particle creation and holographic equipartition. The model attempts to solve the inflation of the early universe and the acceler...We propose a cosmological scenario that describes the evolution of the universe based on particle creation and holographic equipartition. The model attempts to solve the inflation of the early universe and the accelerated expansion of the present universe without introducing the dark energy from the thermodynamical perspective.Throughout the evolution of the universe, we assume that the universe consistently creates particles, and that the holographic equipartition is always satisfied. Further, we set the creation rate of particles proportional to H^2 in the early universe and to H in the present and late universe, where H depicts the Hubble parameter. Consequently, we obtain the solutions a(t) ∝ e^αt/3 and a(t) ∝ t^1/2 for the early universe and solutions a(t) ∝ t^δ and a(t) ∝ e^Ht for the present and late universe, respectively, where α and δ are the parameters. Finally, we obtain and analyze two important thermodynamic properties for the present model.展开更多
The uniformity principle of temperature difference field is very useful in heat exchanger analyses and optimizations.In this paper,we analyze some other heat transfer optimization problems in the thermal management sy...The uniformity principle of temperature difference field is very useful in heat exchanger analyses and optimizations.In this paper,we analyze some other heat transfer optimization problems in the thermal management system of spacecrafts,including the cooling of thermal components,the one-stream series-wound heat exchanger network,the volume-to-point heat conduction problem,and the radiative heat transfer optimization problem,and have found that the uniformity principle of temperature difference field also holds.When the design objectives under the given constraints are achieved,the distributions of the temperature difference fields are uniform.The principle reflects the characteristic of the distribution of potential in the heat transfer optimization problems.It is also shown that the principle is consistent with the entransy theory.Therefore,although the principle is intuitive and phenomenological,the entransy theory can be the physical basis of the principle.展开更多
Fluctuations of energy and heat are investigated during the relaxation following the instantaneous temperature quench of an extended system. Results are obtained analytically for the Gaussian model and for the large N...Fluctuations of energy and heat are investigated during the relaxation following the instantaneous temperature quench of an extended system. Results are obtained analytically for the Gaussian model and for the large N model quenched below the critical temperature TC. The main finding is that fluctuations exceeding a critical threshold do condense. Though driven by a mechanism similar to that of Bose–Einstein condensation, this phenomenon is an out-of-equilibrium feature produced by the breaking of energy equipartition occurring in the transient regime. The dynamical nature of the transition is illustrated by phase diagrams extending in the time direction.展开更多
Statistical behavior of a classical φ4 Hamiltonian lattice is investigated from microscopic dynamics. Thelargest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the...Statistical behavior of a classical φ4 Hamiltonian lattice is investigated from microscopic dynamics. Thelargest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the system.It is found, for the first time, that for any large while finite system size there exist two critical couplings for the transitionsto equipartitions, and the scaling behaviors of these lower and upper critical couplings vs. the system size are numericallyobtained.展开更多
The empirically reported values of the critical current density (j<sub>c</sub>) of Bi-2212 as 2.4 × 10<sup>5</sup> (j<sub>c</sub><sub>1</sub>;Sample 1) and 1.0 ...The empirically reported values of the critical current density (j<sub>c</sub>) of Bi-2212 as 2.4 × 10<sup>5</sup> (j<sub>c</sub><sub>1</sub>;Sample 1) and 1.0 × 10<sup>6</sup> A/cm<sup>2</sup> (j<sub>c</sub><sub>2</sub>;Sample 2) are intriguing because both of them correspond to the same values of the temperature T = 4.2 K and the applied magnetic field H = 12 × 10<sup>4</sup> G. This difference is conventionally attributed to such factors—not all of which are quantifiable—as the geometry, dimensions and the nature of dopants and the manners of preparation of the samples which cause their granular structures, grain boundaries, alignment of the grains and so on to differ. Based on the premise that the chemical potential μ subsumes most of these features, given herein is a novel explanation of the said results in terms of the values of μ of the two samples. This paper revisits the problem that was originally addressed in [Malik G.P., Varma V.S. (2020) WJCMP, 10, 53-70] in the more accurate framework of a subsequent paper [Malik G.P., Varma V.S. (2021) JSNM, 34, 1551-1561]. Besides, it distinguishes between the contributions of the electro-electron (e-e) and the hole-hole (h-h) pairs to j<sub>c</sub>—a feature to which no heed was paid earlier. The essence of our findings is that the j<sub>c</sub>s of the two samples differ because they are characterized by different values of the primary variables μ<sub>i</sub><sub> </sub>and <img src="Edit_e1b831e9-dc51-4c3b-bd84-fa905e3e62b5.png" alt="" />, where <img src="Edit_1f775a80-30ab-447d-861f-afb4ba8fba6a.png" alt="" /> is the effective mass of a charge-carrier and m<sub>e</sub><sub> </sub>is the free-electron mass and i = 1 and 2 denote Sample 1 and Sample 2, respectively. In the scenario of the charge-carriers being predominantly h-h pairs, the values of these parameters are estimated to be: μ<sub>1</sub> ≈ 12.3 meV, η<sub>1</sub> ≈ 0.58;μ<sub>2</sub> ≈ 22.7 meV, η<sub>2</sub> ≈ 0.94. Following from these and similar estimates when the charge-carriers are e-e pairs, given below for each sample are the detailed results for the values of the secondary variables viz. the number density of the charge-carriers and their critical velocity, the number of occupied Landau levels and the magnetic interaction parameter.展开更多
In undergraduate statistical mechanics,we have learned that thermalization is the process of physical bodies reaching thermal equilibrium through mutual interaction.In general,the natural tendency of a system is towar...In undergraduate statistical mechanics,we have learned that thermalization is the process of physical bodies reaching thermal equilibrium through mutual interaction.In general,the natural tendency of a system is towards a state of equipartition of energy and uniform temperature that maximizes the system’s entropy.展开更多
In the environment,chemical pollutants always exist as mixtures.To evaluate mixture toxicity,we should ex-amine the concentration ratios and the concentration levels of mixture components as well as the interactive ti...In the environment,chemical pollutants always exist as mixtures.To evaluate mixture toxicity,we should ex-amine the concentration ratios and the concentration levels of mixture components as well as the interactive time between the components and testing organism.Selecting three pesticides,metribuzin(MET),dodine(DOD)and ri-domil(RID),as mixture components,Vibrio qinghaiensis sp.-Q67 as testing organism,and 96-well microplate as exposure experiment carrier,the luminescence inhibition toxicities of the pesticides and their binary mixtures at six exposure time points(0.25,2,4,8,12,and 16 h)were determined.The results showed that the three pesticides have different time-toxicity profiles.The toxicity of MET increases over time,and those of DOD and RID show a slight decrease or increase in the first 4 h,respectively,and then remain unchanged to 16 h.The toxicities of the binary mixtures consisting of the three pesticides depend on not only the mixture composition but also the exposure time.The time-toxicity profiles of all rays in MET-DOD mixture system are U-shaped curves,those in MET-RID system are basically monotonically increased and those in DOD-RID system are basically monotonically decreased.How-ever,our findings indicate that for the test substances,mixture toxicity can be predicted by the extended concentra-tion addition model.展开更多
基金Supported by National Basic Research Program of China(973 Program No.2007CBS14903)National Science Foundation of China(70671069)
文摘Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,
文摘Physical and mathematical arguments are presented for equipartition as the statistical state achieved by a ran- dom field, independent of its sources, in the limit of enough scattering. The arguments are simplest for the case of thermally excited fields, but are shown to apply also, with caveats, in non-equilibrium acoustics and seismology. Practical implications are discussed.
基金Supported by National Natural Science Foundation of China(11790325,11790320,11790321,11961131010,U1732138,11505056,11605054,U2067205,12105369,12047568,12147219)the Continuous Basic Scientific Research Project(WDJC-2019-09)。
文摘We numerically study a one-dimensional,nonlinear lattice model which in the linear limit is relevant to the study of bending(flexural)waves.In contrast with the classic one-dimensional mass-spring system,the linear dispersion relation of the considered model has different characteristics in the low frequency limit.By introducing disorder in the masses of the lattice particles,we investigate how different nonlinearities in the potential(cubic,quadratic,and their combination)lead to energy delocalization,equipartition,and chaotic dynamics.We excite the lattice using single site initial momentum excitations corresponding to a strongly localized linear mode and increase the initial energy of excitation.Beyond a certain energy threshold,when the cubic nonlinearity is present,the system is found to reach energy equipartition and total delocalization.On the other hand,when only the quartic nonlinearity is activated,the system remains localized and away from equipartition at least for the energies and evolution times considered here.However,for large enough energies for all types of nonlinearities we observe chaos.This chaotic behavior is combined with energy delocalization when cubic nonlinearities are present,while the appearance of only quadratic nonlinearity leads to energy localization.Our results reveal a rich dynamical behavior and show differences with the relevant Fermi–Pasta–Ulam–Tsingou model.Our findings pave the way for the study of models relevant to bending(flexural)waves in the presence of nonlinearity and disorder,anticipating different energy transport behaviors.
文摘The extraction of the Earth＇s Green＇s function from field fluctuations is a rapidly growing area of research. The principle of Green＇s function extraction is often related to the requirement of equipartitioning, which stipulates that the energy of field fluctuations is distributed evenly in some sense. We show the meaning of equipartitioning for a variety of different formulations for Green＇s function retrieval. We show that equipartitioning is not a sufficient condition, and provide several examples that illustrate this point. We discuss the implications of lack of equipartitioning for various schemes for the reconstruction of the Green＇s function in seismology. The theory for Green＇s function extraction is usually based on a statistical theory that relies on ensemble averages. Since there is only one Earth, one usually replaces the ensemble average with a time average. We show that such a replacement only makes sense when attenuation is taken into account, and show how the theory for Green＇s function extraction for oscillating systems can be extended to incorporate attenuation.
基金Supported by the National Natural Science Foundation of China (Grant No.10571076)
文摘In this paper,we study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain（NSMC） indexed by Cayley tree with any finite states.The asymptotic equipartition properties with almost everywhere（a.e.） convergence for NSMC indexed by Cayley tree are obtained.This article generalizes a recent result.
基金Supported by Doctoral Foundation of Zunyi Normal University(BS[2016]03)Education Department Foundation of Guizhou Province(QianjiaoheKYzi[2017]247)+1 种基金Major Research Project for Innovative Group of Education Department of Guizhou Province(KY[2018]028)the NNSF of China(11775187,11847031,11865018 and 11865019)。
文摘We propose a cosmological scenario that describes the evolution of the universe based on particle creation and holographic equipartition. The model attempts to solve the inflation of the early universe and the accelerated expansion of the present universe without introducing the dark energy from the thermodynamical perspective.Throughout the evolution of the universe, we assume that the universe consistently creates particles, and that the holographic equipartition is always satisfied. Further, we set the creation rate of particles proportional to H^2 in the early universe and to H in the present and late universe, where H depicts the Hubble parameter. Consequently, we obtain the solutions a(t) ∝ e^αt/3 and a(t) ∝ t^1/2 for the early universe and solutions a(t) ∝ t^δ and a(t) ∝ e^Ht for the present and late universe, respectively, where α and δ are the parameters. Finally, we obtain and analyze two important thermodynamic properties for the present model.
基金Project supported by the Science Fund for Creative Research Groups of National Natural Science Foundation of China(Grant No.51621062)
文摘The uniformity principle of temperature difference field is very useful in heat exchanger analyses and optimizations.In this paper,we analyze some other heat transfer optimization problems in the thermal management system of spacecrafts,including the cooling of thermal components,the one-stream series-wound heat exchanger network,the volume-to-point heat conduction problem,and the radiative heat transfer optimization problem,and have found that the uniformity principle of temperature difference field also holds.When the design objectives under the given constraints are achieved,the distributions of the temperature difference fields are uniform.The principle reflects the characteristic of the distribution of potential in the heat transfer optimization problems.It is also shown that the principle is consistent with the entransy theory.Therefore,although the principle is intuitive and phenomenological,the entransy theory can be the physical basis of the principle.
文摘Fluctuations of energy and heat are investigated during the relaxation following the instantaneous temperature quench of an extended system. Results are obtained analytically for the Gaussian model and for the large N model quenched below the critical temperature TC. The main finding is that fluctuations exceeding a critical threshold do condense. Though driven by a mechanism similar to that of Bose–Einstein condensation, this phenomenon is an out-of-equilibrium feature produced by the breaking of energy equipartition occurring in the transient regime. The dynamical nature of the transition is illustrated by phase diagrams extending in the time direction.
文摘Statistical behavior of a classical φ4 Hamiltonian lattice is investigated from microscopic dynamics. Thelargest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the system.It is found, for the first time, that for any large while finite system size there exist two critical couplings for the transitionsto equipartitions, and the scaling behaviors of these lower and upper critical couplings vs. the system size are numericallyobtained.
文摘The empirically reported values of the critical current density (j<sub>c</sub>) of Bi-2212 as 2.4 × 10<sup>5</sup> (j<sub>c</sub><sub>1</sub>;Sample 1) and 1.0 × 10<sup>6</sup> A/cm<sup>2</sup> (j<sub>c</sub><sub>2</sub>;Sample 2) are intriguing because both of them correspond to the same values of the temperature T = 4.2 K and the applied magnetic field H = 12 × 10<sup>4</sup> G. This difference is conventionally attributed to such factors—not all of which are quantifiable—as the geometry, dimensions and the nature of dopants and the manners of preparation of the samples which cause their granular structures, grain boundaries, alignment of the grains and so on to differ. Based on the premise that the chemical potential μ subsumes most of these features, given herein is a novel explanation of the said results in terms of the values of μ of the two samples. This paper revisits the problem that was originally addressed in [Malik G.P., Varma V.S. (2020) WJCMP, 10, 53-70] in the more accurate framework of a subsequent paper [Malik G.P., Varma V.S. (2021) JSNM, 34, 1551-1561]. Besides, it distinguishes between the contributions of the electro-electron (e-e) and the hole-hole (h-h) pairs to j<sub>c</sub>—a feature to which no heed was paid earlier. The essence of our findings is that the j<sub>c</sub>s of the two samples differ because they are characterized by different values of the primary variables μ<sub>i</sub><sub> </sub>and <img src="Edit_e1b831e9-dc51-4c3b-bd84-fa905e3e62b5.png" alt="" />, where <img src="Edit_1f775a80-30ab-447d-861f-afb4ba8fba6a.png" alt="" /> is the effective mass of a charge-carrier and m<sub>e</sub><sub> </sub>is the free-electron mass and i = 1 and 2 denote Sample 1 and Sample 2, respectively. In the scenario of the charge-carriers being predominantly h-h pairs, the values of these parameters are estimated to be: μ<sub>1</sub> ≈ 12.3 meV, η<sub>1</sub> ≈ 0.58;μ<sub>2</sub> ≈ 22.7 meV, η<sub>2</sub> ≈ 0.94. Following from these and similar estimates when the charge-carriers are e-e pairs, given below for each sample are the detailed results for the values of the secondary variables viz. the number density of the charge-carriers and their critical velocity, the number of occupied Landau levels and the magnetic interaction parameter.
基金supported by the US NSF under Grant No.PHY-2207283 and the Welch Foundation with Grant No.C-1669.
文摘In undergraduate statistical mechanics,we have learned that thermalization is the process of physical bodies reaching thermal equilibrium through mutual interaction.In general,the natural tendency of a system is towards a state of equipartition of energy and uniform temperature that maximizes the system’s entropy.
基金We are thankful to the National Natural Science Foundation of China(No.21177097)Specialized Research Fund for the Doctoral Program of Higher Education(No.20120072110052)for their financial support.
文摘In the environment,chemical pollutants always exist as mixtures.To evaluate mixture toxicity,we should ex-amine the concentration ratios and the concentration levels of mixture components as well as the interactive time between the components and testing organism.Selecting three pesticides,metribuzin(MET),dodine(DOD)and ri-domil(RID),as mixture components,Vibrio qinghaiensis sp.-Q67 as testing organism,and 96-well microplate as exposure experiment carrier,the luminescence inhibition toxicities of the pesticides and their binary mixtures at six exposure time points(0.25,2,4,8,12,and 16 h)were determined.The results showed that the three pesticides have different time-toxicity profiles.The toxicity of MET increases over time,and those of DOD and RID show a slight decrease or increase in the first 4 h,respectively,and then remain unchanged to 16 h.The toxicities of the binary mixtures consisting of the three pesticides depend on not only the mixture composition but also the exposure time.The time-toxicity profiles of all rays in MET-DOD mixture system are U-shaped curves,those in MET-RID system are basically monotonically increased and those in DOD-RID system are basically monotonically decreased.How-ever,our findings indicate that for the test substances,mixture toxicity can be predicted by the extended concentra-tion addition model.
