Yang-Yang thermodynamics of one-dimensional Bose gases with anisotropic transversal confinement

By combining the thermodynamic Bethe ansatz and local density approximation, we investigate the Yang-Yang thermodynamics of interacting one-dimensional Bose gases with anisotropic transversal confinement. It is shown that with the increase of anisotropic parameter at low temperature, the Bose atoms are distributed over a wider region, while at high temperature the density distribution is not affected obviously. Both the temperature and transversal confinement can strengthen the local pressure of the Dose gases.

Functional Integral Approach to Transition Temperature of a Homogeneous ImperfectBose Gas

A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresponding ideal gas. We obtain the expression of the transition temperature shift as , where n is the density of particle number and a is the scattering length. The result has never been reported in the literature.

Dynamics of an Ultracold Bose Gas in Funnel-Shaped Potential

In this paper we develop a variational theory to study the dynamic properties of ultracold Bose gas ina funnel external potential.We obtain one-dimensional nonlinear equation which describes the dynamics of transversetight confined bosonic gas from three-dimension to one-dimension,and find one-dimensional s-wave scattering lengthwhich depends on the shape of transverse confining potential.If the funnel trapping potential is strong enough at zerotemperature,all transverse excitations are frozen.We find the dynamic equation which describes the Tonks-Girardeaugas and present a qualitative analysis of the experimental accessibility of the Tonks-Girardeau gas with funnel-trappedalkalic atoms.

A Quasi-1D Potential for Bose Gas Phase Fluctuations

An elongated trap potential for cold atoms is designed based on a quadrupole-Ioffe configuration.Phase fluctuations in a Bose-Einstein condensate(BEC),which is confined by the trap,are studied.We simulate the atom density distribution induced by fluctuation after time of flight from this elongated trap potential and study the temperature measurement method related to the distribution.Furthermore,taking advantage of the tight confinement and radio frequency dressing technique,we propose a double well potential for splitting BECs.Our results are helpful for improving understanding of low-dimensional quantum gases and provide important guidance for atomic interferometry.

Effects of a finite number of particles on the thermodynamic properties of a harmonically trapped ideal charged Bose gas in a constant magnetic field

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 -∞.

Optimal preparation of Bose and Fermi atomic gas mixtures of ^(87)Rb and ^(40)K in a crossed optical dipole trap

We report on the optimal production of the Bose and Fermi mixtures with ^(87) Rb and ^(40)K in a crossed optical dipole trap(ODT).We measure the atomic number and lifetime of the mixtures in combination of the spin state |F=9/2,m_(F)=9/2> of^(40)K and |1,1>of ^(87) Rb in the ODT,which is larger and longer compared with the combination of the spin state |9/2,9/2> of^(40)K and 12,2) of ^(87)Rb in the ODT.We observe the atomic numbers of ^(87)Rb and ^(40)K shown in each stage of the sympathetic cooling process while gradually reducing the depth of the optical trap.By optimizing the relative loading time of atomic mixtures in the MOT,we obtain the large atomic number of ^(40)K(~6 ×10^(6)) or the mixtures of atoms with an equal number(~1.6 × 10^(6)) at the end of evaporative cooling in the ODT.We experimentally investigate the evaporative cooling in an enlarged volume of the ODT via adding a third laser beam to the crossed ODT and found that more atoms(8 × 10^(6)) and higher degeneracy(T/T_(F)=0.25) of Fermi gases are obtained.The ultracold atomic gas mixtures pave the way to explore phenomena such as few-body collisions and the Bose-Fermi Hubbard model,as well as for creating ground-state molecules of ^(87)Rb^(40)K.

Investigations of methane adsorption characteristics on marine-continental transitional shales and gas storage capacity models considering pore evolution

Methane adsorption is a critical assessment of the gas storage capacity(GSC)of shales with geological conditions.Although the related research of marine shales has been well-illustrated,the methane adsorption of marine-continental transitional(MCT)shales is still ambiguous.In this study,a method of combining experimental data with analytical models was used to investigate the methane adsorption characteristics and GSC of MCT shales collected from the Qinshui Basin,China.The Ono-Kondo model was used to fit the adsorption data to obtain the adsorption parameters.Subsequently,the geological model of GSC based on pore evolution was constructed using a representative shale sample with a total organic carbon(TOC)content of 1.71%,and the effects of reservoir pressure coefficient and water saturation on GSC were explored.In experimental results,compared to the composition of the MCT shale,the pore structure dominates the methane adsorption,and meanwhile,the maturity mainly governs the pore structure.Besides,maturity in the middle-eastern region of the Qinshui Basin shows a strong positive correlation with burial depth.The two parameters,micropore pore volume and non-micropore surface area,induce a good fit for the adsorption capacity data of the shale.In simulation results,the depth,pressure coefficient,and water saturation of the shale all affect the GSC.It demonstrates a promising shale gas potential of the MCT shale in a deeper block,especially with low water saturation.Specifically,the economic feasibility of shale gas could be a major consideration for the shale with a depth of<800 m and/or water saturation>60%in the Yushe-Wuxiang area.This study provides a valuable reference for the reservoir evaluation and favorable block search of MCT shale gas.

Machine learning prediction of methane,ethane,and propane solubility in pure water and electrolyte solutions:Implications for stray gas migration modeling

Hydraulic fracturing is an effective technology for hydrocarbon extraction from unconventional shale and tight gas reservoirs.A potential risk of hydraulic fracturing is the upward migration of stray gas from the deep subsurface to shallow aquifers.The stray gas can dissolve in groundwater leading to chemical and biological reactions,which could negatively affect groundwater quality and contribute to atmospheric emissions.The knowledge oflight hydrocarbon solubility in the aqueous environment is essential for the numerical modelling offlow and transport in the subsurface.Herein,we compiled a database containing 2129experimental data of methane,ethane,and propane solubility in pure water and various electrolyte solutions over wide ranges of operating temperature and pressure.Two machine learning algorithms,namely regression tree(RT)and boosted regression tree(BRT)tuned with a Bayesian optimization algorithm(BO)were employed to determine the solubility of gases.The predictions were compared with the experimental data as well as four well-established thermodynamic models.Our analysis shows that the BRT-BO is sufficiently accurate,and the predicted values agree well with those obtained from the thermodynamic models.The coefficient of determination(R2)between experimental and predicted values is 0.99 and the mean squared error(MSE)is 9.97×10^(-8).The leverage statistical approach further confirmed the validity of the model developed.

Critical temperature of Bose-Einstein condensation for weakly interacting bose gas in a potential trap

The critical temperature of Bose-Einstein condensation at minimum momentum state for weakly interacting Bose gases in a power-law potential and the deviation of the critical temperature from ideal bose gas are studied.The effect of interaction on the critical temperature is ascribed to the ratiaoα/I_(c),whereαis the scattering length for s wave andI_(c) is de Broglie wavelength at critical temperature.Asα/I_(c)<<1/(2p)^(2),the interaction is negligible.The presented deviation of the critical temperature for three dimensional harmonI_(c) potential is well in agreement with recent measurement of critical temperature for ^(87)Rb bose gas trapped in a harmonI_(c) well.

Dynamics of momentum distribution and structure factor in a weakly interacting Bose gas with a periodical modulation

The momentum distribution and dynamical structure factor in a weakly interacting Bose gas with a time-dependent periodic modulation in terms of the Bogoliubov treatment are investigated.The evolution equation related to the Bogoliubov weights happens to be a solvable Mathieu equation when the coupling strength is periodically modulated.An exact relation between the time derivatives of momentum distribution and dynamical structure factor is derived,which indicates that the single-particle property is strongly related to the two-body property in the evolutions of Bose–Einstein condensates.It is found that the momentum distribution and dynamical structure factor cannot display periodical behavior.For stable dynamics,some particular peaks in the curves of momentum distribution and dynamical structure factor appear synchronously,which is consistent with the derivative relation.

On the ground state energy of the inhomogeneous Bose gas

Within the self-consistent Hartree^Fock approximation, an explicit in this approximation expression for the ground state energy of inhomogeneous Bose gas is derived as a functional of the inhomogeneous density of the Bose-Einstein condensate. The results obtained are based on existence of the off-diagonal long-range order in the single-particle density matrix for systems with a Bose-Einstein condensate. This makes it possible to avoid the use of anomalous averages. The explicit form of the kinetic energy, which differs from one in the Gross-Pitaevski approach, is found. The obtained form of kinetic energy is valid beyond the Hartree--Fock approximation and can be applied for arbitrary strong interparticle interaction.

A theoretical insight about co-pyrolysis reaction of natural gas and coal

The co-pyrolysis of natural gas and coal is a promising way for the production of acetylene due to its high efficiency for energy and hydrogen utilization.This work investigated the thermodynamics for the copyrolysis reaction of natural gas and coal using density functional theory.The favorable reaction conditions are presented in the form of phase diagrams.The calculation results show that the extra amount of methane may benefit the production of acetylene in the co-pyrolysis reaction,and the C/H ratio of 1:1,temperature around 3000 K and pressure at 0.1 MPa are most favorable.The results would provide basic data for related industrial process for the production of acetylene.

Thermodynamics of Criticality: Percolation Loci, Mesophases and a Critical Dividing Line in Binary-Liquid and Liquid-Gas Equilibria

High-temperature and pressure boundaries of the liquid and gas states have not been defined thermodynamically. Standard liquid-state physics texts use either critical isotherms or isobars as ad hoc boundaries in phase diagrams. Here we report that percolation transition loci can define liquid and gas states, extending from super-critical temperatures or pressures to “ideal gas” states. Using computational methodology described previously we present results for the thermodynamic states at which clusters of excluded volume (VE) and pockets of available volume (VA), for a spherical molecule diameter σ, percolate the whole volume (V = VE + VA) of the ideal gas. The molecular-reduced temperature (T)/pressure(p) ratios ( ) for the percolation transitions are = 1.495 ± 0.015 and = 1.100 ± 0.015. Further MD computations of percolation loci, for the Widom-Rowlinson (W-R) model of a partially miscible binary liquid (A-B), show the connection between the ideal gas percolation transitions and the 1st-order phase-separation transition. A phase diagram for the penetrable cohesive sphere (PCS) model of a one-component liquid-gas is then obtained by analytic transcription of the W-R model thermodynamic properties. The PCS percolation loci extend from a critical coexistence of gas plus liquid to the low-density limit ideal gas. Extended percolation loci for argon, determined from literature equation-of-state measurements exhibit similar phenomena. When percolation loci define phase bounds, the liquid phase spans the whole density range, whereas the gas phase is confined by its percolation boundary within an area of low T and p on the density surface. This is contrary to a general perception and opens a debate on the definitions of gaseous and liquid states.

Removal of phosphorus from metallurgical grade silicon by Ar-H_2O gas mixtures

The removal of phosphorus in metallurgical grade silicon （MG-Si） by water vapor carried with high purity argon was examined. The effect of the nozzle types, refining time, refining temperature, refining gas temperature and refining gas flow rate on the phosphorus removed was investigated by the self-designed gas blowing device. The optimal refining conditions are nozzle type of holes at bottom and side, refining time of 3 h, refining temperature of 1793 K, refining gas temperature of 373 K, refining gas flow rate of 2 L/min. Under these optimal conditions, the phosphorus content in MG-Si is reduced from 94×10^-6 initially to 11×10-6 （mass fraction）, which indicates that gas blowing refining is very effective to remove phosphorus in MG-Si.

The universal sound velocity formula for the strongly interacting unitary Fermi gas

Due to the scale invariance, the thermodynamic laws of strongly interacting limit unitary Fermi gas can be similar to those of non-interacting ideal gas. For example, the virial theorem between pressure and energy density of the ideal gas P = 2E/aV is still satisfied by the unitary Fermi gas. This paper analyses the sound velocity of unitary Fermi gases with the quasi-linear approximation. For comparison, the sound velocities for the ideal Boltzmann, Bose and Fermi gas are also given. Quite interestingly, the sound velocity formula for the ideal non-interacting gas is found to be satisfied by the unitary Fermi gas in different temperature regions.

Study of dynamical behaviour and fermionization of a bosonic gas in funnel potential

This paper presents a funnel external potential model to investigate dynamic properties of ultracold Bose gas. By using variational method, we obtain the ground-state energy and density properties of ultracold Bose atoms. The results show that the ultracold Bose gas confined in a funnel potential experiences the transition from three-dimensional regime to quasi-one-dimensional regime in a small aspect ratio, and undergoes fermionization process as the aspect ratio increases.

The Cloud Model for Climate Change

In 1995, the Intergovernmental Panel on Climate Change (IPCC) released a thermodynamic model based on the Greenhouse Effect, aiming to forecast global temperatures. This study delves into the intricacies of that model. Some interesting observations are revealed. The IPCC model equated average temperatures with average energy fluxes, which can cause significant errors. The model assumed that all energy fluxes remained constant, and the Earth emitted infrared radiation as if it were a blackbody. Neither of those conditions exists. The IPCC’s definition of Climate Change only includes events caused by human actions, excluding most causes. Satellite data aimed at the tops of clouds may have inferred a high Greenhouse Gas absorption flux. The model showed more energy coming from the atmosphere than absorbed from the sun, which may have caused a violation of the First and Second Laws of Thermodynamics. There were unexpectedly large gaps in the satellite data that aligned with various absorption bands of Greenhouse Gases, possibly caused by photon scattering associated with re-emissions. Based on science, we developed a cloud-based climate model that complied with the Radiation Laws and the First and Second Laws of Thermodynamics. The Cloud Model showed that 81.3% of the outgoing reflected and infrared radiation was applicable to the clouds and water vapor. In comparison, the involvement of CO2 was only 0.04%, making it too minuscule to measure reliably.

Simulation Modelling and Techno-Economics of Supercritical Carbon Dioxide Recompression Closed Brayton Cycle

In recent years, there has been global interest in meeting targets relating to energy affordability and security while taking into account greenhouse gas emissions. This has heightened major interest in potential investigations into the use of supercritical carbon dioxide (sCO2) power cycles. Climate change mitigation is the ultimate driver for this increased interest;other relevant issues include the potential for high cycle efficiency and a circular economy. In this study, a 25 MWe recompression closed Brayton cycle (RCBC) has been assessed, and sCO2 has been proposed as the working fluid for the power plant. The methodology used in this research work comprises thermodynamic and techno-economic analysis for the prospective commercialization of this sCO2 power cycle. An evaluated estimation of capital expenditure, operational expenditure, and cost of electricity has been considered in this study. The ASPEN Plus simulation results have been compared with theoretical and mathematical calculations to assess the performance of the compressors, turbine, and heat exchangers. The results thus reveal that the cycle efficiency for this prospective sCO2 recompression closed Brayton cycle increases (39% - 53.6%) as the temperature progressively increases from 550˚C to 900˚C. Data from the Aspen simulation model was used to aid the cost function calculations to estimate the total capital investment cost of the plant. Also, the techno-economic results have shown less cost for purchasing equipment due to fewer components being required for the cycle configuration as compared to the conventional steam power plant.

Thermodynamic behaviors of SiCl_2 in silicon deposition by gas phase zinc reduction of silicon tetrachloride

The modified Siemens process,which is the major process of producing polycrystalline silicon through current technologies,is a high temperature,slow,semi-batch process and the product is expensive primarily due to the large energy consumption.Therefore,the zinc reduction process,which can produce solar-grade silicon in a cost effective manner,should be redeveloped for these conditions.The SiCl2 generation ratio,which stands for the degree of the side reactions,can be decomposed to SiCl4 and ZnCl2 in gas phase zinc atmosphere in the exit where the temperature is very low.Therefore,the lower SiCl2 generation ratio is profitable with lower power consumption.Based on the thermodynamic data for the related pure substances,the relations of the SiCl2 generation ratio and pressure,temperature and the feed molar ratio（n（Zn）/n（SiCl4） are investigated and the graphs thereof are plotted.And the diagrams of Kpθ-T at standard atmosphere pressure have been plotted to account for the influence of temperature on the SiCl2 generation ratio.Furthermore,the diagram of Kpθ-T at different pressures have also been plotted to give an interpretation of the influence of pressure on the SiCl2 generation ratio.The results show that SiCl2 generation ratio increases with increasing temperature,and the higher pressure and excess gas phase zinc can restrict SiCl2 generation ratio.Finally,suitable operational conditions in the practical process of polycrystalline silicon manufacture by gas phase zinc reduction of SiCl4 have been established with 1200 K,0.2 MPa and the feed molar ratio（n（Zn） /n（SiCl4）） of 4 at the entrance.Under these conditions,SiCl2 generation ratio is very low,which indicates that the side reactions can be restricted and the energy consumption is reasonable.

Memory effect on the pressure-temperature condition and induction time of gas hydrate nucleation

The focus of this study is to investigate the influence of memory effect and the relation of its existence with the dissociation temperature,using gas hydrate formation and dissociation experiments.This is beneficial because memory effect is considered as an effective approach to promote the thermodynamic and dynamic conditions of gas hydrate nucleation.Seven experimental systems （twenty tests in total） were performed in a 1 L pressure cell.Three types of hydrate morphology,namely massive,whiskery and jelly crystals were present in the experiments.The pressures and temperatures at the time when visual hydrate crystals appeared were measured.Furthermore,the influence of memory effect was quantified in terms of pressure-temperature-time （p-T-t） relations.The results revealed that memory effect could promote the thermodynamic conditions and shorten the induction time when the dissociation temperature was not higher than 25℃.In this study,the nucleation superpressure and induction time decrease gradually with time of tests,when the earlier and the later tests are compared.It is assumed that the residual structure of hydrate dissociation,as the source of the memory effect,provides a site for mass transfer between host and guest molecules.Therefore,a driving force is created between the residual structures and its surrounding bulk phase to promote the hydrate nucleation.However,when the dissociation temperature was higher than 25 ℃,the memory effect vanished.These findings provide references for the application of memory effect in hydrate-based technology.