The superheavy nucleus 270Hs is expected to be a “double-magic” deformed nucleus. We have calculated its cross sections of evaporation residue for the reactions 248Cm(26Mg,4n)270Hs, 244Pu(30Si,4n)270Hs, 238U(36S,4n)...The superheavy nucleus 270Hs is expected to be a “double-magic” deformed nucleus. We have calculated its cross sections of evaporation residue for the reactions 248Cm(26Mg,4n)270Hs, 244Pu(30Si,4n)270Hs, 238U(36S,4n)270Hs and 226Ra(48Ca,4n)270Hs using a two-parameter Smoluchowski equation. It is found from our results that 226Ra(48Ca,4n)270Hs and 238U(36S,4n)270Hs are two optimal reactions for the synthesis of the superheavy nucleus 270Hs due to their large negative Q-values.展开更多
The particle migration and coalescence(PMC) kinetics of a supported metal are the main deactivation mechanisms restricting the successful industrialization of nanoparticles, but the theoretical insights regarding thes...The particle migration and coalescence(PMC) kinetics of a supported metal are the main deactivation mechanisms restricting the successful industrialization of nanoparticles, but the theoretical insights regarding these kinetics are lacking. One key issue is the lack of a physical model to predict the effects of metal-support interaction(MSI) on PMC kinetics. In this paper, we report a theoretical study of PMC kinetics and their dependence on MSI. A new particle diffusion model is proposed based on the surface premelting hypothesis that considers the contact angle of a hemispherical particle on the support. Enhanced MSI suppresses PMC by increasing the radius of curvature and the interfacial adhesion energy, even though the accompanying reduction in the geometry factor partially promotes PMC kinetics. The increased surface energy increases the chemical potential of the atoms in the particle, which is conducive to PMC; an increased surface energy also results in enhanced MSI, which suppresses PMC. The competition between these two contradictory effects leads to a critical contact angle where the surface energy has no influence on the diffusion and resulting PMC kinetics. The proposed diffusion theory mode lincluding the effects of the support and the corresponding kinetic simulations, shed light onto the support-dependence of PMC kinetics and provide a foundation for further optimization and design of supported particles with better stability.展开更多
Non-equilibrium fission has been described by diffusion model. In order to describe the diffusion process analytically, the analytical solution of Smoluchowski equation in harmonic oscillator potential is obtained. Th...Non-equilibrium fission has been described by diffusion model. In order to describe the diffusion process analytically, the analytical solution of Smoluchowski equation in harmonic oscillator potential is obtained. This analytical solution is able to describe the probability distribution and the diffusive current with the variable x and t. The results indicate that the probability distribution and the diffusive current are relevant to the initial distribution shape, initial position, and the nuclear temperature T; the time to reach the quasi-stationary state is proportional to friction coefficient beta, but is independent of the initial distribution status and the nuclear temperature T. The prerequisites of negative diffusive current are justified. This method provides an approach to describe the diffusion process for fissile process in complicated potentials analytically.展开更多
Some models dealing with fibers and liquid crystals can be formulated probabilistically in terms of orientation distributions. Since the orientation of a thin object can be specified by a point in a real projective pl...Some models dealing with fibers and liquid crystals can be formulated probabilistically in terms of orientation distributions. Since the orientation of a thin object can be specified by a point in a real projective plane this approach leads to elliptic and parabolic problems in the real projective plane. In most previous works these kind of problems have been considered on the unit sphere which is a double cover of the real projective plane. However, numerically this is inefficient because the resulting systems of equations are unnecessarily big. We formulate the problem directly in the real projective plane using a certain parametrization with three coordinate domains. After reducing the computations to the coordinate domains we can then use finite elements almost in a standard way. In particular the standard error estimates with usual Sobolev spaces remain valid in this setting. We consider both elliptic and parabolic cases, and demonstrate the validity of our approach.展开更多
In this paper, we prove the global existence and uniqueness of non-negative classical solutions of the Smoluchowski equation with viscosity ε>0. The existence of weak solutions when ε=0 is also obtained.
The cross sections for the production of nuclides of element 108 via hot fusion evaporation reactions are studied using a two-parameter Smoluchowski equation. The optimal reactions for the synthesis of new nuclides of...The cross sections for the production of nuclides of element 108 via hot fusion evaporation reactions are studied using a two-parameter Smoluchowski equation. The optimal reactions for the synthesis of new nuclides of element 108 with mass numbers from 266 to 271 are suggested. The macroscopic-microscopic approach predicts a strong deformed shell closure at Z ≈ 108 and N = 162. The synthesis of more nuclides of element 108 is meaningful to the confirmation of the existence of this deformed shell closure.展开更多
In this paper, we investigate the escape of Brownian particles and stochastic resonance (SR) with low-temperatures quantum fluctuations by using the quantum Smoluchowski equations at low-temperature. Two specific exam...In this paper, we investigate the escape of Brownian particles and stochastic resonance (SR) with low-temperatures quantum fluctuations by using the quantum Smoluchowski equations at low-temperature. Two specific examples have been considered: one is the example of bistable system, and the other is the example of metastable system. The explicit expressions of the mean-first passage time (MFPT) and signal-to-noise ratio (SNR) for both specific examples are obtained, respectively. Based on the numerical computations, we compare the quantum case with its classical counterpart. Our research results show that: (i) the quantum effect accelerates the escape of the Brownian particle in comparison with the classical result and (ii) the quantum effect enhances the SR in the SNR as a function of β for a bistable system (i.e., β = 1/kBT, kB is the Boltzmann constant and T is the temperature), while for a metastable system, the β amplifies the quantum effects, and the quantum effect weakens the SNR as a function of β.展开更多
The shell effects on the particle evaporation prior to fission for three Pb isotopes, ^204Pb, ^208Pb, and ^212pb,as well as three Sn isotopes, ^128Sn, ^132Sn, and ^136Sn, are explored by a diffusion model. Calculation...The shell effects on the particle evaporation prior to fission for three Pb isotopes, ^204Pb, ^208Pb, and ^212pb,as well as three Sn isotopes, ^128Sn, ^132Sn, and ^136Sn, are explored by a diffusion model. Calculations show that the magnitude of shell effects in the emission of particles changes with the neutron-to-proton ratio N/Z of these fissioning nuclei, and this change is affected significantly by the spin and excitation energy of the system. It is shown that high angular momentum enhances the dependence of shell effects on the N/Z while high excitation energy weakens such a dependence.展开更多
Understanding the dynamic process of black hole thermodynamic phase transitions at a triple point is a huge challenge. In this paper, we conduct the first investigation of dynamic phase behavior at a black hole triple...Understanding the dynamic process of black hole thermodynamic phase transitions at a triple point is a huge challenge. In this paper, we conduct the first investigation of dynamic phase behavior at a black hole triple point. By numerically solving the Smoluchowski equation near the triple point for a six-dimensional charged Gauss-Bonnet anti-de Sitter black hole, we report that initial small, intermediate, or large black holes can transit to the other two coexistent phases at the triple point, indicating that thermodynamic phase transitions can indeed occur dynamically. More significantly, we observe characteristic weak and strong oscillatory behavior in this dynamic process, which can be understood from an investigation of the rate of first passage from one phase to another. Our results further an understanding of the dynamic process of black hole thermodynamic phase transitions.展开更多
The goal of this paper is to present a numerical method for the Smoluchowski equation,a drift-diffusion equation on the sphere,arising in the modelling of particle dynamics.The numerical method uses radial basis funct...The goal of this paper is to present a numerical method for the Smoluchowski equation,a drift-diffusion equation on the sphere,arising in the modelling of particle dynamics.The numerical method uses radial basis functions(RBF).This is a relatively new approach,which has recently mainly been used for geophysical applications.For a simplified model problem we compare the RBF approach with a spectral method,i.e.the standard approach used in related physical applications.This comparison as well as our other accuracy studies show that RBF methods are an attractive alternative for these kind of models.展开更多
We prove the global existence of classical solutions to a fluid-particle interaction model in R^3, namely, compressible Navier-Stokes-Smoluchowski equations, when the initial data are close to the stationary state(ρ*...We prove the global existence of classical solutions to a fluid-particle interaction model in R^3, namely, compressible Navier-Stokes-Smoluchowski equations, when the initial data are close to the stationary state(ρ*, 0, η*) and the external potential satisfies the smallness assumption. Furthermore, optimal decay rates of classical solutions in H^3-framework are obtained.展开更多
基金This work was supported by the National Natural Science Founda tion of China (Grant Nos.10235020 and 10235030).
文摘The superheavy nucleus 270Hs is expected to be a “double-magic” deformed nucleus. We have calculated its cross sections of evaporation residue for the reactions 248Cm(26Mg,4n)270Hs, 244Pu(30Si,4n)270Hs, 238U(36S,4n)270Hs and 226Ra(48Ca,4n)270Hs using a two-parameter Smoluchowski equation. It is found from our results that 226Ra(48Ca,4n)270Hs and 238U(36S,4n)270Hs are two optimal reactions for the synthesis of the superheavy nucleus 270Hs due to their large negative Q-values.
基金supported by the National Key R&D Program of China(Grant Nos.2018YFA0208603,2017YFB0602205)the Chinese Academy of Sciences(Grant No.QYZDJ-SSW-SLH054)the National Natural Science Foundation of China(Grant No.91645202)
文摘The particle migration and coalescence(PMC) kinetics of a supported metal are the main deactivation mechanisms restricting the successful industrialization of nanoparticles, but the theoretical insights regarding these kinetics are lacking. One key issue is the lack of a physical model to predict the effects of metal-support interaction(MSI) on PMC kinetics. In this paper, we report a theoretical study of PMC kinetics and their dependence on MSI. A new particle diffusion model is proposed based on the surface premelting hypothesis that considers the contact angle of a hemispherical particle on the support. Enhanced MSI suppresses PMC by increasing the radius of curvature and the interfacial adhesion energy, even though the accompanying reduction in the geometry factor partially promotes PMC kinetics. The increased surface energy increases the chemical potential of the atoms in the particle, which is conducive to PMC; an increased surface energy also results in enhanced MSI, which suppresses PMC. The competition between these two contradictory effects leads to a critical contact angle where the surface energy has no influence on the diffusion and resulting PMC kinetics. The proposed diffusion theory mode lincluding the effects of the support and the corresponding kinetic simulations, shed light onto the support-dependence of PMC kinetics and provide a foundation for further optimization and design of supported particles with better stability.
文摘Non-equilibrium fission has been described by diffusion model. In order to describe the diffusion process analytically, the analytical solution of Smoluchowski equation in harmonic oscillator potential is obtained. This analytical solution is able to describe the probability distribution and the diffusive current with the variable x and t. The results indicate that the probability distribution and the diffusive current are relevant to the initial distribution shape, initial position, and the nuclear temperature T; the time to reach the quasi-stationary state is proportional to friction coefficient beta, but is independent of the initial distribution status and the nuclear temperature T. The prerequisites of negative diffusive current are justified. This method provides an approach to describe the diffusion process for fissile process in complicated potentials analytically.
文摘Some models dealing with fibers and liquid crystals can be formulated probabilistically in terms of orientation distributions. Since the orientation of a thin object can be specified by a point in a real projective plane this approach leads to elliptic and parabolic problems in the real projective plane. In most previous works these kind of problems have been considered on the unit sphere which is a double cover of the real projective plane. However, numerically this is inefficient because the resulting systems of equations are unnecessarily big. We formulate the problem directly in the real projective plane using a certain parametrization with three coordinate domains. After reducing the computations to the coordinate domains we can then use finite elements almost in a standard way. In particular the standard error estimates with usual Sobolev spaces remain valid in this setting. We consider both elliptic and parabolic cases, and demonstrate the validity of our approach.
基金This research is supported by the National Natural Science Foundation of China
文摘In this paper, we prove the global existence and uniqueness of non-negative classical solutions of the Smoluchowski equation with viscosity ε>0. The existence of weak solutions when ε=0 is also obtained.
基金Project supported by the National Natural Science Foundation of China （Grants Nos 10235020 and 10235030）.
文摘The cross sections for the production of nuclides of element 108 via hot fusion evaporation reactions are studied using a two-parameter Smoluchowski equation. The optimal reactions for the synthesis of new nuclides of element 108 with mass numbers from 266 to 271 are suggested. The macroscopic-microscopic approach predicts a strong deformed shell closure at Z ≈ 108 and N = 162. The synthesis of more nuclides of element 108 is meaningful to the confirmation of the existence of this deformed shell closure.
基金supported by the Natural Science Foundation of Yunnan Province (Grant No. 2010CD031)the National Natural Science Foun-dation of China (Grant Nos. 50906035, 51066002 and U0937604)
文摘In this paper, we investigate the escape of Brownian particles and stochastic resonance (SR) with low-temperatures quantum fluctuations by using the quantum Smoluchowski equations at low-temperature. Two specific examples have been considered: one is the example of bistable system, and the other is the example of metastable system. The explicit expressions of the mean-first passage time (MFPT) and signal-to-noise ratio (SNR) for both specific examples are obtained, respectively. Based on the numerical computations, we compare the quantum case with its classical counterpart. Our research results show that: (i) the quantum effect accelerates the escape of the Brownian particle in comparison with the classical result and (ii) the quantum effect enhances the SR in the SNR as a function of β for a bistable system (i.e., β = 1/kBT, kB is the Boltzmann constant and T is the temperature), while for a metastable system, the β amplifies the quantum effects, and the quantum effect weakens the SNR as a function of β.
基金国家自然科学基金，Teaching and Researching Foundation for the Excellent Teachers of Southeast University
文摘The shell effects on the particle evaporation prior to fission for three Pb isotopes, ^204Pb, ^208Pb, and ^212pb,as well as three Sn isotopes, ^128Sn, ^132Sn, and ^136Sn, are explored by a diffusion model. Calculations show that the magnitude of shell effects in the emission of particles changes with the neutron-to-proton ratio N/Z of these fissioning nuclei, and this change is affected significantly by the spin and excitation energy of the system. It is shown that high angular momentum enhances the dependence of shell effects on the N/Z while high excitation energy weakens such a dependence.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12075103, 11675064, 11875151, and 12047501)the Natural Sciences and Engineering Research Council of Canada。
文摘Understanding the dynamic process of black hole thermodynamic phase transitions at a triple point is a huge challenge. In this paper, we conduct the first investigation of dynamic phase behavior at a black hole triple point. By numerically solving the Smoluchowski equation near the triple point for a six-dimensional charged Gauss-Bonnet anti-de Sitter black hole, we report that initial small, intermediate, or large black holes can transit to the other two coexistent phases at the triple point, indicating that thermodynamic phase transitions can indeed occur dynamically. More significantly, we observe characteristic weak and strong oscillatory behavior in this dynamic process, which can be understood from an investigation of the rate of first passage from one phase to another. Our results further an understanding of the dynamic process of black hole thermodynamic phase transitions.
文摘The goal of this paper is to present a numerical method for the Smoluchowski equation,a drift-diffusion equation on the sphere,arising in the modelling of particle dynamics.The numerical method uses radial basis functions(RBF).This is a relatively new approach,which has recently mainly been used for geophysical applications.For a simplified model problem we compare the RBF approach with a spectral method,i.e.the standard approach used in related physical applications.This comparison as well as our other accuracy studies show that RBF methods are an attractive alternative for these kind of models.
基金supported by the National Natural Science Foundation of China(11371152,11771155,11571117 and 11871005)the Natural Science Foundation of Guangdong Province(2017A030313003)+2 种基金supported by the Natural Science Foundation of Guangdong Province(2018A030310008)the Doctoral Scientific Research Foundation of Hanshan Normal University(QD20171002)the Educational Commission of Guangdong Province(2017KTSCX124)
文摘We prove the global existence of classical solutions to a fluid-particle interaction model in R^3, namely, compressible Navier-Stokes-Smoluchowski equations, when the initial data are close to the stationary state(ρ*, 0, η*) and the external potential satisfies the smallness assumption. Furthermore, optimal decay rates of classical solutions in H^3-framework are obtained.
