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
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
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
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
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.
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.
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.
