We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic po- tential and a constant magnetic field. Using an accurate density of states, we calculate analytically th...We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic po- tential and a constant magnetic field. Using an accurate density of states, we calculate analytically the thermodynamic potential and consequently various intriguing thermodynamic properties, including the Bose-Einstein transition tempera- ture, the specific heat, magnetization, and the corrections to these quantities due to the finite number of particles are also given explicitly. In contrast to the infinite number of particles scenarios, we show that those thermodynamic properties, particularly the Bose-Einstein transition temperature depends upon the strength of the magnetic field due to the finiteness of the particle numbers, and the collective effects of a finite number of particles become larger when the particle number decreases. Moreover, the magnetization varies with the temperature due to the finiteness of the particle number while it keeps invariant in the thermodynamic limit N -∞.展开更多
Analytical expressions for the thermodynamical properties of a two-dimensional electron gas in a perpendicular mag- netic field are derived. This is accomplished by first deriving the general expression for the thermo...Analytical expressions for the thermodynamical properties of a two-dimensional electron gas in a perpendicular mag- netic field are derived. This is accomplished by first deriving the general expression for the thermodynamical potential, and then employing this result to obtain the corresponding expression for the two-dimensional gas. The chemical potential and magnetization are studied as a function of temperature and magnetic field, and shown to be in agreement with prior work. It is also shown that the results are close to those obtained by assuming a Gaussian density of states for the Landau levels.展开更多
Phosphoric acid/phosphate solu-tions are commonly used as buffer solutions in the fundamental stud-ies in electrochemistry.Informa-tion on the nature of adsorbed(bi)phosphate as well as the do-main structures is of gr...Phosphoric acid/phosphate solu-tions are commonly used as buffer solutions in the fundamental stud-ies in electrochemistry.Informa-tion on the nature of adsorbed(bi)phosphate as well as the do-main structures is of great impor-tance in unveiling the impact on electrochemical processes occur-ring at electrode electrolyte interface.In this work,the pH effect on the adsorption of phosphate related species on Pd(111)electrode has been investigated by cyclic voltammetry over a broad pH range from 1 to 14.Af-ter carefully analyzing the related onset desorption potential of(bi)phosphate adsorbate to the thermodynamic equilibrium potential of the corresponding electrode reactions,three dif-ferent phosphate related adsorbates have been identified,which are highly pH-dependent.Our analysis reveals that the dominant phosphate anions in bulk solution undergo deprotona-tion upon adsorption.At pH<1.5,the main adsorbate on Pd(111)is;H_(2)PO_(4)^(λ_(1)^(-))in solutions with 1.5<pH<7,the main adsorbate changes into.HPO_(4)^(λ_2^(-))At higher pHs,PO_(4)^(λ_(3)^(-))on electrode surface dominates.The exact charging value ofλ_(i),which represents the true va-lence of the(bi)phosphate adsorbate,could be determined using theoretical calculations.In addition,our results can not rule out the possibility of co-adsorbed H_(3)PO_(4)molecules on Pd(111)at pH<1.5,which needs to be proved by infrared spectroscopy in the future.展开更多
This paper presents a deterministic model to predict the pit evolving morphology and crack initiation life of corrosion fatigue.Based on the semi-ellipsoidal pit assumption,the thermodynamic potential including elasti...This paper presents a deterministic model to predict the pit evolving morphology and crack initiation life of corrosion fatigue.Based on the semi-ellipsoidal pit assumption,the thermodynamic potential including elastic energy,surface energy and electrochemical energy of the cyclically stressed solid with an evolving pit is established,from which specific parameters that control the pit evolution are introduced and their influence on the pit evolution are evaluated.The critical pit size for crack nucleation is obtained from stress intensity factor criterion and the crack nucleation life is evaluated by Faraday's law.Meanwhile,this paper presents a numerical example to verify the proposed model and investigate the influence of cyclic load on the corrosion fatigue crack nucleation life.The corrosion pit appears approximately as a hemisphere in its early formation,and it gradually transits from semicircle to ellipsoid.The strain energy accelerates the morphology evolution of the pit,while the surface energy decelerates it.The higher the stress amplitude is,the smaller the critical pit size is and the shorter the crack initiation life is.展开更多
When initial radius R<sub>initial</sub> →0 if Stoica actually presents Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds....When initial radius R<sub>initial</sub> →0 if Stoica actually presents Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. We present entanglement entropy in the early universe with a shrinking scale factor, due to Muller and Lousto, and show that there are consequences due to initial entangled S<sub>Entropy</sub> = 0.3r<sup>2</sup><sub>h</sub>/a<sup>2 </sup>for a time dependent horizon radius r<sub>H</sub> = in cosmology, with (flat space conditions) for conformal time. Even if the 3 dimensional spatial length goes to zero, this construction preserves a minimum non-zero L vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if Rinitial</sub> →0 . We state that the presence of computational bits is necessary for cosmological evolution to commence.展开更多
A model for the morphological evolution of a void under thermal and mechanical loads is established, and the thermodynamics potential of the model is given based on energy principle. Thus, the path and the bifurcation...A model for the morphological evolution of a void under thermal and mechanical loads is established, and the thermodynamics potential of the model is given based on energy principle. Thus, the path and the bifurcation condition of the morphological evolution of the void are described, which gives some insight into the reliability of the interconnect under combined thermal and mechanical loads.展开更多
We propose a novel criterion to identify the first-order QCD phase transition and the critical end-point(CEP)via directly the netproton number fluctuations measured in relativistic heavy-ion collision(RHIC)experiments...We propose a novel criterion to identify the first-order QCD phase transition and the critical end-point(CEP)via directly the netproton number fluctuations measured in relativistic heavy-ion collision(RHIC)experiments.Using this method,we show that there has not yet been a direct signal of the CEP of QCD according to the currently available data accumulated in the beam energy scan experiments with√^(S)_(NN)≥7.7 GeV.However,there is still a possibility for the CEP to appear in the matter generated by the collisions with energy below 7.7 Ge V,and its identification requires future measurements with high statistics for the high-order cumulants at low collision energies.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11375090)the K.C.Wong Magna Foundation of Ningbo University,China
文摘We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic po- tential and a constant magnetic field. Using an accurate density of states, we calculate analytically the thermodynamic potential and consequently various intriguing thermodynamic properties, including the Bose-Einstein transition tempera- ture, the specific heat, magnetization, and the corrections to these quantities due to the finite number of particles are also given explicitly. In contrast to the infinite number of particles scenarios, we show that those thermodynamic properties, particularly the Bose-Einstein transition temperature depends upon the strength of the magnetic field due to the finiteness of the particle numbers, and the collective effects of a finite number of particles become larger when the particle number decreases. Moreover, the magnetization varies with the temperature due to the finiteness of the particle number while it keeps invariant in the thermodynamic limit N -∞.
基金Project supported by the National Natural Science Foundation of China(Grant No.11275100)the K.C.Wong Magna Foundation of Ningbo University,China
文摘Analytical expressions for the thermodynamical properties of a two-dimensional electron gas in a perpendicular mag- netic field are derived. This is accomplished by first deriving the general expression for the thermodynamical potential, and then employing this result to obtain the corresponding expression for the two-dimensional gas. The chemical potential and magnetization are studied as a function of temperature and magnetic field, and shown to be in agreement with prior work. It is also shown that the results are close to those obtained by assuming a Gaussian density of states for the Landau levels.
基金supported by the National Natural Science Foundation of China(No.22172151)。
文摘Phosphoric acid/phosphate solu-tions are commonly used as buffer solutions in the fundamental stud-ies in electrochemistry.Informa-tion on the nature of adsorbed(bi)phosphate as well as the do-main structures is of great impor-tance in unveiling the impact on electrochemical processes occur-ring at electrode electrolyte interface.In this work,the pH effect on the adsorption of phosphate related species on Pd(111)electrode has been investigated by cyclic voltammetry over a broad pH range from 1 to 14.Af-ter carefully analyzing the related onset desorption potential of(bi)phosphate adsorbate to the thermodynamic equilibrium potential of the corresponding electrode reactions,three dif-ferent phosphate related adsorbates have been identified,which are highly pH-dependent.Our analysis reveals that the dominant phosphate anions in bulk solution undergo deprotona-tion upon adsorption.At pH<1.5,the main adsorbate on Pd(111)is;H_(2)PO_(4)^(λ_(1)^(-))in solutions with 1.5<pH<7,the main adsorbate changes into.HPO_(4)^(λ_2^(-))At higher pHs,PO_(4)^(λ_(3)^(-))on electrode surface dominates.The exact charging value ofλ_(i),which represents the true va-lence of the(bi)phosphate adsorbate,could be determined using theoretical calculations.In addition,our results can not rule out the possibility of co-adsorbed H_(3)PO_(4)molecules on Pd(111)at pH<1.5,which needs to be proved by infrared spectroscopy in the future.
基金Project supported by the National Natural Science Foundation of China(No.10772116)the Fundamental Research Funds for the Central Universities(Nos.12CX04017B and 13CX02091A)
文摘This paper presents a deterministic model to predict the pit evolving morphology and crack initiation life of corrosion fatigue.Based on the semi-ellipsoidal pit assumption,the thermodynamic potential including elastic energy,surface energy and electrochemical energy of the cyclically stressed solid with an evolving pit is established,from which specific parameters that control the pit evolution are introduced and their influence on the pit evolution are evaluated.The critical pit size for crack nucleation is obtained from stress intensity factor criterion and the crack nucleation life is evaluated by Faraday's law.Meanwhile,this paper presents a numerical example to verify the proposed model and investigate the influence of cyclic load on the corrosion fatigue crack nucleation life.The corrosion pit appears approximately as a hemisphere in its early formation,and it gradually transits from semicircle to ellipsoid.The strain energy accelerates the morphology evolution of the pit,while the surface energy decelerates it.The higher the stress amplitude is,the smaller the critical pit size is and the shorter the crack initiation life is.
文摘When initial radius R<sub>initial</sub> →0 if Stoica actually presents Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. We present entanglement entropy in the early universe with a shrinking scale factor, due to Muller and Lousto, and show that there are consequences due to initial entangled S<sub>Entropy</sub> = 0.3r<sup>2</sup><sub>h</sub>/a<sup>2 </sup>for a time dependent horizon radius r<sub>H</sub> = in cosmology, with (flat space conditions) for conformal time. Even if the 3 dimensional spatial length goes to zero, this construction preserves a minimum non-zero L vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if Rinitial</sub> →0 . We state that the presence of computational bits is necessary for cosmological evolution to commence.
基金the National Natural Science Foundation of China(Nos.10602034,10572088)
文摘A model for the morphological evolution of a void under thermal and mechanical loads is established, and the thermodynamics potential of the model is given based on energy principle. Thus, the path and the bifurcation condition of the morphological evolution of the void are described, which gives some insight into the reliability of the interconnect under combined thermal and mechanical loads.
基金supported by the National Natural Science Foundation of China(Grant Nos.12175007,and 12247107)supported by the National Key Research and Development Program of China(Grant Nos.2022YFA1605501,2020YFE0202002,and 2018YFE0205201)+2 种基金the National Natural Science Foundation of China(Grant Nos.12122505,and 11890711)the Fundamental Research Funds of the Central China Normal University(Grant No.CCNU220N003)supported by the National Natural Science Foundation of China(Grant No.12135007)。
文摘We propose a novel criterion to identify the first-order QCD phase transition and the critical end-point(CEP)via directly the netproton number fluctuations measured in relativistic heavy-ion collision(RHIC)experiments.Using this method,we show that there has not yet been a direct signal of the CEP of QCD according to the currently available data accumulated in the beam energy scan experiments with√^(S)_(NN)≥7.7 GeV.However,there is still a possibility for the CEP to appear in the matter generated by the collisions with energy below 7.7 Ge V,and its identification requires future measurements with high statistics for the high-order cumulants at low collision energies.
