We study the energy relaxation process in one-dimensional(1D) lattices with next-nearestneighbor(NNN) couplings. This relaxation is produced by adding damping(absorbing conditions) to the boundary(free-end) of the lat...We study the energy relaxation process in one-dimensional(1D) lattices with next-nearestneighbor(NNN) couplings. This relaxation is produced by adding damping(absorbing conditions) to the boundary(free-end) of the lattice. Compared to the 1D lattices with on-site potentials, the properties of discrete breathers(DBs) that are spatially localized intrinsic modes are quite unusual with the NNN couplings included, i.e. these DBs are mobile, and thus they can interact with both the phonons and the boundaries of the lattice. For the interparticle interactions of harmonic and Fermi-Pasta-Ulam-Tsingou-β(FPUT-β) types, we find two crossovers of relaxation in general, i.e. a first crossover from the stretched-exponential to the regular exponential relaxation occurring in a short timescale, and a further crossover from the exponential to the power-law relaxation taking place in a long timescale. The first and second relaxations are universal, but the final power-law relaxation is strongly influenced by the properties of DBs, e.g. the scattering processes of DBs with phonons and boundaries in the FPUT-β type systems make the power-law decay relatively faster than that in the counterparts of the harmonic type systems under the same coupling. Our results present new information and insights for understanding the slow energy relaxation in cooling the lattices.展开更多
In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the...In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.展开更多
This paper investigates the electron-vibrational（e-V）energy exchange in nitrogencontaining plasma,which is very efficient in the case of gas discharge and high speed flow.Based on Harmonic oscillator approximation a...This paper investigates the electron-vibrational（e-V）energy exchange in nitrogencontaining plasma,which is very efficient in the case of gas discharge and high speed flow.Based on Harmonic oscillator approximation and the assumption of the e-V relaxation through a continuous series of Boltzmann distributions over the vibrational states,an analytic approach is derived from the proposed scaling relation of e-V transition rates.A full kinetic model is then investigated by numerically solving the state-to-state master equation for all vibrational levels.The analytical approach leads to a Landau-Teller（LT）-type equation for relaxation of vibrational energy,and predicts the relaxation time on the right order of magnitude.By comparison with the kinetic model,the LT-type equation is valid in typical electron temperatures in gas discharge.However,the analytical approach is not capable of describing the vibrational distribution function during the e-V process in which a full kinetic model is required.展开更多
Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time λ on start-up time ts of this flow is still not well understood. Especi...Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time λ on start-up time ts of this flow is still not well understood. Especially, there exist a series of jumps on the ts-λ. curve. In this paper we introduce a normalized mechanical energy by mode decomposition and mathematical analogy to describe the start-up process. An improved definition of start-up time is presented based on the normalized mechanical energy. It is proved that the ts-λ. curve contains a series of jumps if λ is larger than a critical value. The exact positions of the jumps are determined and the physical reason of the jumps is discussed.展开更多
In the present work the research of grain boundary (CB) energy versus angle of misorientation in fcc metals Al, Cu, An and Ni was carried out. An axis of CB misorientation is a direction [100], angle of misorientatio...In the present work the research of grain boundary (CB) energy versus angle of misorientation in fcc metals Al, Cu, An and Ni was carried out. An axis of CB misorientation is a direction [100], angle of misorientation makes from 2皍p in 23*. The interatomic interaction was opproximated by Morse' s pair semi-empirical potential. Two variants of relaxation technique were used: (1) rigid relax- ation with the change of atom quantity per a GB (vacancy relaxation ) and (2) full atomic relaxation by a molecular static method. The obtained orientation dependence has a good agreement with experi- ment. There are cusps on a curve in the range of special GB angles.The comparison of obtained curves with calculated ones in model Van der Merwe was carried out. Dependencies obtained in our investiga- tions are not smooth and have an oscillatory character. The oscillations reflect a discrete structure of a lattice.展开更多
The surface states of pyrite(Fe S2) were theoretically investigated using first principle calculation based on the density functional theory(DFT). The results indicate that both the(200) and(311) surfaces of pyrite un...The surface states of pyrite(Fe S2) were theoretically investigated using first principle calculation based on the density functional theory(DFT). The results indicate that both the(200) and(311) surfaces of pyrite undergo significant surface atom relaxation after geometry optimization, which results in a considerable distortion of the surface region. In the normal direction, i.e., perpendicular to the surface, S atoms in the first surface layer move outward from the bulk, while Fe atoms move toward the bulk, forming an S-rich surface. The surface relaxation processes are driven by electrostatic interaction, which is evidenced by a relative decrease in the surface energy after surface relaxation. Such a relaxation process is visually interpreted through the qualitative analysis of molecular mechanics. Atomic force microscopy(AFM) analysis reveals that only sulfur atom is visible on the pyrite surface. This result is consistent with the DFT data. Such S-rich surface has important influence on the flotation properties of pyrite.展开更多
To research the correlation between vibrational energy transition rates and acoustic relaxation processes in excitable gases, the vibrational relaxation theory provided by Tanczos [J. Chem. Phy3. 25, 439 （1956）] is ...To research the correlation between vibrational energy transition rates and acoustic relaxation processes in excitable gases, the vibrational relaxation theory provided by Tanczos [J. Chem. Phy3. 25, 439 （1956）] is applied to calculate the energy transition rates of Vibrational- Vibrational （V-V） and Vibrational-Translational （V-T） energy transfer in gas mixtures. The results of calculation for the multi-relaxation processes in various gas mixtures, consisting of carbon dioxide, methane, chlorine, nitrogen, and oxygen at room temperature, demonstrate that the acoustic energy stagnated in every vibrational mode is coupled with each other through V-V energy exchanges. The vibrational excitation energy will relax through the V-T de-excitation path of the lowest mode because of its fastest V-T transition rate, resulting in that only one absorption peak can be measured for most of excitable gas mixtures. Thus, an effective model is provided to analyze how the vibrational energy transition rates affect the characteristics of acoustic relaxation processes and acoustic propagation in excitable gas mixtures.展开更多
Chlorophyll a(naturally occurring Mg porphyrene)has been entrapped in nano/porous silica gel using sol-gel method at room temperature,producing a stable composite.HR TEM observationreveals regular nanoscale[around 15-...Chlorophyll a(naturally occurring Mg porphyrene)has been entrapped in nano/porous silica gel using sol-gel method at room temperature,producing a stable composite.HR TEM observationreveals regular nanoscale[around 15-20 nm diameter]distribution of aggregated polycrystalinechlorophylla within porous silica matrix.UV-vis study also corroborates the presence of variousaggregated chlorophyll a species within the system.Low field measurement shows almost 400times enhancement of dielectric constant(1700)with incorporation of only 0.125 mg/ml of chlorophyll and the loss is 0.5 at room temperature at 100 Hz.The dielectric constant of the composite reaches 2500 as chlorophyll concentration becomes 1 mg/ml.Observed strong space charge response to the external field and strong frequency dispersion of the dielectric properties ofthe composite can be attributed to the long-range electron delocalization[nomadic polarization]in chlorophyl a aggregates.The electric modulus(M*)formalism used in this study enabled us todistinguish and separate various relaxation processes.It is found that with increasing chlorophyll concentration D.C.relaxation time decreases exponentially at room temperature.It is shown that observed relaxations do not perfectly follow the Debye response in high frequency region due toheterogeneous distribution of chlorophyll aggregates.The low values of room temperature acti-vation energy calculated from Arrhenius plot reveal that polaronic hopping phenomena is absent at grain-interfacial region due to low thermal energy.展开更多
基金supported by the start-up fund of Minjiang university and NSF (Grant No. 2021J02051) of Fujian Province of Chinasupported by the start-up fund of Minjiang University+1 种基金supported by the NNSF (Grant No. 12105133) of ChinaNSF (Grant No. 2021J011030) of Fujian Province of China。
文摘We study the energy relaxation process in one-dimensional(1D) lattices with next-nearestneighbor(NNN) couplings. This relaxation is produced by adding damping(absorbing conditions) to the boundary(free-end) of the lattice. Compared to the 1D lattices with on-site potentials, the properties of discrete breathers(DBs) that are spatially localized intrinsic modes are quite unusual with the NNN couplings included, i.e. these DBs are mobile, and thus they can interact with both the phonons and the boundaries of the lattice. For the interparticle interactions of harmonic and Fermi-Pasta-Ulam-Tsingou-β(FPUT-β) types, we find two crossovers of relaxation in general, i.e. a first crossover from the stretched-exponential to the regular exponential relaxation occurring in a short timescale, and a further crossover from the exponential to the power-law relaxation taking place in a long timescale. The first and second relaxations are universal, but the final power-law relaxation is strongly influenced by the properties of DBs, e.g. the scattering processes of DBs with phonons and boundaries in the FPUT-β type systems make the power-law decay relatively faster than that in the counterparts of the harmonic type systems under the same coupling. Our results present new information and insights for understanding the slow energy relaxation in cooling the lattices.
基金Supported by the Chinese Postdoctoral Science Foundation, the Young Scientists Funds of NSF of China (10401019)the Tsinghua Basic Research Foundation.
文摘In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.
基金supported by National Natural Science Foundation of China(No.11505015)the National High-Tech Research and Development Program of China(863 Program)
文摘This paper investigates the electron-vibrational（e-V）energy exchange in nitrogencontaining plasma,which is very efficient in the case of gas discharge and high speed flow.Based on Harmonic oscillator approximation and the assumption of the e-V relaxation through a continuous series of Boltzmann distributions over the vibrational states,an analytic approach is derived from the proposed scaling relation of e-V transition rates.A full kinetic model is then investigated by numerically solving the state-to-state master equation for all vibrational levels.The analytical approach leads to a Landau-Teller（LT）-type equation for relaxation of vibrational energy,and predicts the relaxation time on the right order of magnitude.By comparison with the kinetic model,the LT-type equation is valid in typical electron temperatures in gas discharge.However,the analytical approach is not capable of describing the vibrational distribution function during the e-V process in which a full kinetic model is required.
文摘Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time λ on start-up time ts of this flow is still not well understood. Especially, there exist a series of jumps on the ts-λ. curve. In this paper we introduce a normalized mechanical energy by mode decomposition and mathematical analogy to describe the start-up process. An improved definition of start-up time is presented based on the normalized mechanical energy. It is proved that the ts-λ. curve contains a series of jumps if λ is larger than a critical value. The exact positions of the jumps are determined and the physical reason of the jumps is discussed.
文摘In the present work the research of grain boundary (CB) energy versus angle of misorientation in fcc metals Al, Cu, An and Ni was carried out. An axis of CB misorientation is a direction [100], angle of misorientation makes from 2皍p in 23*. The interatomic interaction was opproximated by Morse' s pair semi-empirical potential. Two variants of relaxation technique were used: (1) rigid relax- ation with the change of atom quantity per a GB (vacancy relaxation ) and (2) full atomic relaxation by a molecular static method. The obtained orientation dependence has a good agreement with experi- ment. There are cusps on a curve in the range of special GB angles.The comparison of obtained curves with calculated ones in model Van der Merwe was carried out. Dependencies obtained in our investiga- tions are not smooth and have an oscillatory character. The oscillations reflect a discrete structure of a lattice.
基金Project(51464029)supported by the National Natural Science Foundation of ChinaProject(2014M562343)supported by China Postdoctoral Science FoundationProject(KKSY201421110)supported by the Scholar Development Project of Yunnan Province,China
文摘The surface states of pyrite(Fe S2) were theoretically investigated using first principle calculation based on the density functional theory(DFT). The results indicate that both the(200) and(311) surfaces of pyrite undergo significant surface atom relaxation after geometry optimization, which results in a considerable distortion of the surface region. In the normal direction, i.e., perpendicular to the surface, S atoms in the first surface layer move outward from the bulk, while Fe atoms move toward the bulk, forming an S-rich surface. The surface relaxation processes are driven by electrostatic interaction, which is evidenced by a relative decrease in the surface energy after surface relaxation. Such a relaxation process is visually interpreted through the qualitative analysis of molecular mechanics. Atomic force microscopy(AFM) analysis reveals that only sulfur atom is visible on the pyrite surface. This result is consistent with the DFT data. Such S-rich surface has important influence on the flotation properties of pyrite.
基金supported by the National Natural Science Foundation of China(61461008,61371139,61571201,61540051)the China Scholarship Council Project(201708525058)+1 种基金the National Science Foundation of Guizhou Province,China(Qian Ke He J Zi[2015]2065),Qian Ke He LH Zi[2014]7361)the Recruitment Program of Guizhou Institute of Technology(XJGC20140601,XJGC20150107)
文摘To research the correlation between vibrational energy transition rates and acoustic relaxation processes in excitable gases, the vibrational relaxation theory provided by Tanczos [J. Chem. Phy3. 25, 439 （1956）] is applied to calculate the energy transition rates of Vibrational- Vibrational （V-V） and Vibrational-Translational （V-T） energy transfer in gas mixtures. The results of calculation for the multi-relaxation processes in various gas mixtures, consisting of carbon dioxide, methane, chlorine, nitrogen, and oxygen at room temperature, demonstrate that the acoustic energy stagnated in every vibrational mode is coupled with each other through V-V energy exchanges. The vibrational excitation energy will relax through the V-T de-excitation path of the lowest mode because of its fastest V-T transition rate, resulting in that only one absorption peak can be measured for most of excitable gas mixtures. Thus, an effective model is provided to analyze how the vibrational energy transition rates affect the characteristics of acoustic relaxation processes and acoustic propagation in excitable gas mixtures.
文摘Chlorophyll a(naturally occurring Mg porphyrene)has been entrapped in nano/porous silica gel using sol-gel method at room temperature,producing a stable composite.HR TEM observationreveals regular nanoscale[around 15-20 nm diameter]distribution of aggregated polycrystalinechlorophylla within porous silica matrix.UV-vis study also corroborates the presence of variousaggregated chlorophyll a species within the system.Low field measurement shows almost 400times enhancement of dielectric constant(1700)with incorporation of only 0.125 mg/ml of chlorophyll and the loss is 0.5 at room temperature at 100 Hz.The dielectric constant of the composite reaches 2500 as chlorophyll concentration becomes 1 mg/ml.Observed strong space charge response to the external field and strong frequency dispersion of the dielectric properties ofthe composite can be attributed to the long-range electron delocalization[nomadic polarization]in chlorophyl a aggregates.The electric modulus(M*)formalism used in this study enabled us todistinguish and separate various relaxation processes.It is found that with increasing chlorophyll concentration D.C.relaxation time decreases exponentially at room temperature.It is shown that observed relaxations do not perfectly follow the Debye response in high frequency region due toheterogeneous distribution of chlorophyll aggregates.The low values of room temperature acti-vation energy calculated from Arrhenius plot reveal that polaronic hopping phenomena is absent at grain-interfacial region due to low thermal energy.
