According to the second law of thermodynamics, as currently understood, any given transit of a system along the reversible path proceeds with a total entropy change equal to zero. The fact that this condition is also ...According to the second law of thermodynamics, as currently understood, any given transit of a system along the reversible path proceeds with a total entropy change equal to zero. The fact that this condition is also the identifier of thermodynamic equilibrium, makes each and every point along the reversible path a state of equilibrium, and the reversible path, as expressed by a noted thermodynamic author, “a dense succession of equilibrium states”. The difficulties with these notions are plural. The fact, for example, that systems need to be forced out of equilibrium via the expenditure of work, would make any spontaneous reversible process a consumer of work, this in opposition to common thermodynamic wisdom that makes spontaneous reversible processes the most efficient transformers of work-producing-potential into actual work. The solution to this and other related impasses is provided by Dialectical Thermodynamics via its previously proved notion assigning a negative entropy change to the energy upgrading process represented by the transformation of heat into work. The said solution is here exemplified with the ideal-gas phase isomerization of butane into isobutane.展开更多
Mg-based hydrides are too stable and the kinetics of hydrogen absorption and desorption is not satisfactory.An efficient way to improve these shortcomings is to employ reactive ball milling to synthesize the nanocompo...Mg-based hydrides are too stable and the kinetics of hydrogen absorption and desorption is not satisfactory.An efficient way to improve these shortcomings is to employ reactive ball milling to synthesize the nanocomposite materials of Mg and additives.In this experiment,TiF_(3)was selected as an additive,and the mechanical milling method was employed to prepare the experimental alloys.The alloys used in this experiment were the as-cast Ce_(5)Mg_(85)Ni_(10),as-milled Ce_(5)Mg_(85)Ni_(10)and Ce_(5)Mg_(85)Ni_(10)+3 wt.%TiF3.The phase transformation,structural evolution,isothermal and non-isothermal hydrogenation and dehydrogenation performances of the alloys were inspected by XRD,SEM,TEM,Sievert apparatus,DSC and TGA.It revealed that nanocrystalline appeared in the as-milled samples.Compared with the as-cast alloy,ball milling made the particle dimension and grain size decrease dramatically and the defect density increase significantly.The addition of TiF_(3)made the surface of ball milling alloy particles markedly coarser and more irregular.Ball milling and adding TiF_(3)distinctly improved the activation and kinetics of the alloys.Moreover,ball milling along with TiF_(3)can decrease the onset dehydrogenation temperature of Mg-based hydrides and slightly ameliorate their thermodynamics.展开更多
We calculate the thermodynamic quantities in the quantum corrected Reissner-Nordstr?m-AdS(RN-AdS)black hole,and examine their quantum corrections.By analyzing the mass and heat capacity,we give the critical state and ...We calculate the thermodynamic quantities in the quantum corrected Reissner-Nordstr?m-AdS(RN-AdS)black hole,and examine their quantum corrections.By analyzing the mass and heat capacity,we give the critical state and the remnant state,respectively,and discuss their consistency.Then,we investigate the quantum tunneling from the event horizon of massless scalar particle by using the null geodesic method,and charged massive boson W^(±)and fermions by using the Hamilton-Jacob method.It is shown that the same Hawking temperature can be obtained from these tunneling processes of different particles and methods.Next,by using the generalized uncertainty principle(GUP),we study the quantum corrections to the tunneling and the temperature.Then the logarithmic correction to the black hole entropy is obtained.展开更多
It is found from textbooks and literature that there are three different statements for the third law of thermodynamics,i.e., the Nernst theorem, the unattainability statement of absolute zero temperature, and the hea...It is found from textbooks and literature that there are three different statements for the third law of thermodynamics,i.e., the Nernst theorem, the unattainability statement of absolute zero temperature, and the heat capacity statement. It is pointed out that such three statements correspond to three thermodynamic parameters, which are, respectively, the entropy,temperature, and heat capacity, and can be obtained by extrapolating the experimental results of different parameters at ultralow temperatures to absolute zero. It is expounded that because there is no need for additional assumptions in the derivation of the Nernst equation, the Nernst theorem should be renamed as the Nernst statement. Moreover, it is proved that both the Nernst statement and the heat capacity statement are mutually deducible and equivalent, while the unattainability of absolute zero temperature is only a corollary of the Nernst statement or the heat capacity statement so that it is unsuitably referred to as one statement of the third law of thermodynamics. The conclusion is that the Nernst statement and the heat capacity statement are two equivalent statements of the third law of thermodynamics.展开更多
Various metal-modified ZSM-5 zeolite adsorbents prepared by the impregnation method were applied to the removal of organic chlorides from model naphtha.The adsorption performance and regeneration stability were invest...Various metal-modified ZSM-5 zeolite adsorbents prepared by the impregnation method were applied to the removal of organic chlorides from model naphtha.The adsorption performance and regeneration stability were investigated by static adsorption experiments.The morphologies,structural features,and physicochemical properties of the adsorbents were characterized by X-ray diffraction,Brunauer-Emmett-Teller analysis,NH3 temperature-programmed desorption,scanning electron microscopy,transmission electron microscopy,and pyridine adsorption infrared spectroscopy.The Mg/ZSM-5 zeolite adsorbent possessed a relatively high specific surface area and good metal dispersion and exhibited the best dechlorination and regeneration performance.The characterization results revealed that introduction of the metal exerted a significant influence on the acidic properties of the catalyst surface.A decrease in the ratio of Brønsted acidic sites to Lewis acidic sites and an increase in the amount of moderately acidic sites were confirmed to be responsible for the excellent adsorption performance of the Mg-modified ZSM-5 zeolite.Furthermore,the Langmuir adsorption isotherm model was applied to study the adsorption equilibrium and thermodynamics of the Mg/ZSM-5 adsorbent under mild conditions.The results revealed that the removal of 1,2-dichloroethane by the Mg/ZSM-5 adsorbent was endothermic,spontaneous,disordered,and primarily involved physical adsorption.展开更多
2,4(5)-Dinitroimidazole(2,4(5)-DNI)is an important organic intermediate,and itself can also be used for energetic material.In this work,the solubility of 2,4(5)-DNI in(methanol+water,acetonitrile+water,acetone+water)b...2,4(5)-Dinitroimidazole(2,4(5)-DNI)is an important organic intermediate,and itself can also be used for energetic material.In this work,the solubility of 2,4(5)-DNI in(methanol+water,acetonitrile+water,acetone+water)binary solvents were measured by using a dynamic test method from 278.15 K to 323.15 K under 101.1 k Pa.The Jouyban–Acree model,van't Hoff–Jouyban–Acree model,Apelblat–Jouyb an–Acree model,Ma model,and Sun model were used to correlate the experimental data.The values of relative average deviation(RAD)and root-mean-square deviation(RMSD)were very small,indicating that the error between the experimental value and the correlated value was very small.The thermodynamic parameters such as dissolution enthalpy,dissolution entropy and Gibbs energy were calculated based on solubility data.High-purity of 2,4(5)-DNI was efficiently obtained by using cooling and dilution crystallization method.展开更多
In terms of security and privacy,mobile ad-hoc network(MANET)continues to be in demand for additional debate and development.As more MANET applications become data-oriented,implementing a secure and reliable data tran...In terms of security and privacy,mobile ad-hoc network(MANET)continues to be in demand for additional debate and development.As more MANET applications become data-oriented,implementing a secure and reliable data transfer protocol becomes a major concern in the architecture.However,MANET’s lack of infrastructure,unpredictable topology,and restricted resources,as well as the lack of a previously permitted trust relationship among connected nodes,contribute to the attack detection burden.A novel detection approach is presented in this paper to classify passive and active black-hole attacks.The proposed approach is based on the dipper throated optimization(DTO)algorithm,which presents a plausible path out of multiple paths for statistics transmission to boost MANETs’quality of service.A group of selected packet features will then be weighed by the DTO-based multi-layer perceptron(DTO-MLP),and these features are collected from nodes using the Low Energy Adaptive Clustering Hierarchical(LEACH)clustering technique.MLP is a powerful classifier and the DTO weight optimization method has a significant impact on improving the classification process by strengthening the weights of key features while suppressing the weights ofminor features.This hybridmethod is primarily designed to combat active black-hole assaults.Using the LEACH clustering phase,however,can also detect passive black-hole attacks.The effect of mobility variation on detection error and routing overhead is explored and evaluated using the suggested approach.For diverse mobility situations,the results demonstrate up to 97%detection accuracy and faster execution time.Furthermore,the suggested approach uses an adjustable threshold value to make a correct conclusion regarding whether a node is malicious or benign.展开更多
The internal energy change of ideal gas does not depend on the volume and pressure. The internal energy change of real gas has not any relation with the volume and pressure, which had been proved. If the internal ener...The internal energy change of ideal gas does not depend on the volume and pressure. The internal energy change of real gas has not any relation with the volume and pressure, which had been proved. If the internal energy change had not any relation with the volume and pressure, we could confirm the first law of thermodynamics in theory. Simultaneously, the internal energy change is the state function that shall be able to be proved in theory. If the internal energy change depended on the volume and pressure, we could not prove that the internal energy change is the state function and the chemical thermodynamics theory is right. The extended or modified Bernoulli equation can be derived from the energy conservation law, and the internal energy change, heat, and friction are all considered in the derivation procedure. The extended Bernoulli equation could be applied to the flying aircraft and mechanical motion on the gravitational field, for instance, the rocket and airplane and so on. This paper also revises some wrong ideas, viewpoints, or concepts about the thermodynamics theory and Bernoulli equation.展开更多
Inflationary spectral index from the Langevin equation is calculated under the frame of warm inflationary scenario with inflaton interacting with U(1) gauge fields through the Chern–Simons coupling ∝ФF_(μv)F^(μv)...Inflationary spectral index from the Langevin equation is calculated under the frame of warm inflationary scenario with inflaton interacting with U(1) gauge fields through the Chern–Simons coupling ∝ФF_(μv)F^(μv). Under the strong dissipative condition, the spectral index is calculated in terms of the ratio of Hubble parameter to temperature H/T. Then relation between H/T and other cosmic parameters is analytically expressed, based on which a spectral index related to the Chern–Simons coupling strength is further obtained. Numerical results show that cosmic temperature T closes to a constant during inflation and decreases after inflation without a reheating process. Meanwhile, the ratio H/T tends to a constant if the gauged coupling constant is less than a threshold. This phenomenon shows that cosmic temperature may be an important physical parameter with a special value and adiabatic approximation still holds. We obtain the estimate H/T ≤ 0.3377 during inflation from Planck data and other constraint conditions.展开更多
The formations of [NAPA-A(H<sub>2</sub>O)<sub>n</sub> (n = 1, 2, 3, 4)] complexes have been studied employing DFT/wB97XD/cc-pVTZ computational level to understand the kinetics and thermodynamic...The formations of [NAPA-A(H<sub>2</sub>O)<sub>n</sub> (n = 1, 2, 3, 4)] complexes have been studied employing DFT/wB97XD/cc-pVTZ computational level to understand the kinetics and thermodynamics for the hydration reactions of N-acetyl-phenylalaninylamide (NAPA). Thermodynamic parameters such as reaction energy (E), enthalpy (H), Gibb’s free energy (G), specific heat capacity (C<sub>v</sub>), entropy (S), and change of these parameters (ΔE<sub>r</sub>, ΔH<sub>r</sub>, ΔGr, ΔC<sub>r</sub>, and ΔS<sub>r</sub>) were studied using the explicit solvent model. The predicted values of H, G, C, and S increase with the sequential addition of water in NAPA-A due to the increase in the total number of vibrational modes. On the other hand, the value of ΔE<sub>r</sub>, ΔH<sub>r</sub>, and ΔG<sub>r</sub> increases (more negative to less negative) gradually for n = 1, 2, 3, and 4 that indicates an increase of hydration in NAPA-A makes exothermic to endothermic reactions. The barrier heights for the transition states (TS) of [NAPA-A(H<sub>2</sub>O)<sub>n</sub> (n = 1, 2, 3, 4)] complexes are predicted to lie at 4.41, 4.05, 3.72 and 2.26 kcal/mol respectively below the reactants. According to the calculations, the formations of [NAPA-A(H<sub>2</sub>O)<sub>1</sub>] and [NAPA-A(H<sub>2</sub>O)<sub>2</sub>] complexes are barrierless reactions because both water molecules are strongly bonded via two hydrogen bonds in the backbone of NAPA-A. On the contrary, the reactions of [NAPA-A(H<sub>2</sub>O)<sub>3</sub>] and [NAPA-A(H<sub>2</sub>O)<sub>4</sub>] complexation are endothermic and the barrier heights are predicted to stay at 6.30 and 10.54 kcal/mol respectively above the reactants. The free energy of activation (Δ<sup>‡</sup>G<sup>0</sup>) for the reaction of [NAPA-A(H<sub>2</sub>O)<sub>1</sub>], [NAPA-A(H<sub>2</sub>O)<sub>2</sub>], [NAPA-A(H<sub>2</sub>O)<sub>3</sub>], and [NAPA-A(H<sub>2</sub>O)<sub>4</sub>] complexation are 4.43, 4.28, 3.83 and 5.11 kcal/mol respectively which are very low. As well as the rates of reactions are 3.490 × 10<sup>9</sup> s<sup>-1</sup>, 4.514 × 10<sup>9</sup> s<sup>-1</sup>, 9.688 × 10<sup>9</sup> s<sup>-1</sup>, and 1.108 × 10<sup>9</sup> s<sup>-1</sup> respectively which are very fast and spontaneous.展开更多
Black holes contradict the Nernst-Planck (N/P) version of the 3rd law of thermodynamics, but agree with its unattainability (U) version. This happens without contradiction, because the N/P and U versions are not equiv...Black holes contradict the Nernst-Planck (N/P) version of the 3rd law of thermodynamics, but agree with its unattainability (U) version. This happens without contradiction, because the N/P and U versions are not equivalent, namely, N/P implies U but U does not imply N/P. So, black holes obey the weaker version of the 3rd law, but not the stronger one.展开更多
We creatively employ the shadow radius to study the thermodynamics of a charged Ad S black hole with a nonlinear electrodynamics(NLED)term.First,the connection between the shadow radius and event horizon is constructe...We creatively employ the shadow radius to study the thermodynamics of a charged Ad S black hole with a nonlinear electrodynamics(NLED)term.First,the connection between the shadow radius and event horizon is constructed with the aid of the geodesic analysis.It turns out that the black hole shadow radius shows a positive correlation as a function of the event horizon radius.Then in the shadow context,we find that the black hole temperature and heat capacity can be presented by the shadow radius.Further analysis shows that the shadow radius can work similarly to the event horizon in revealing black hole phase transition process.In this sense,we construct the thermal profile of the charged Ad S black hole with inclusion of the NLED effect.In the P<Pc case,it is found that the N-type trend of the temperature given by the shadow radius is always consistent with that obtained by using the event horizon.Thus,we can conclude for the charged Ad S black hole that the phase transition process can be intuitively presented as the thermal profile in the shadow context.Finally,the effects of NLED are carefully analyzed.展开更多
This paper combines a review of recent advances in quantum thermodynamics, including work on objective collapse (Zurek’s quantum Darwinism) and quantum gravity (Verlinde’s quantum gravity explanation), with a redefi...This paper combines a review of recent advances in quantum thermodynamics, including work on objective collapse (Zurek’s quantum Darwinism) and quantum gravity (Verlinde’s quantum gravity explanation), with a redefinition of entropy generation as systems’ change process. These concepts are used as systems’ behaviour analysis tools to allow us to revisit Hartle and Hawking’s 1983 quantum universe and develop a hypothesis for how physically a universe starting in a quantum state could evolve into our current universe, based on systems analysis. The outcome of this analysis raises a question: do we already have the elements of a “theory of everything” hiding in plain sight within recent advances in quantum thermodynamics?展开更多
The pseudo-rapidity distributions of the charged particles produced in the asymmetric collision systems p+Al,p+Au and ^(3)He+Au at√S_(NN)=200 GeV GeV are evaluated in the framework of a fireball model with Tsallis th...The pseudo-rapidity distributions of the charged particles produced in the asymmetric collision systems p+Al,p+Au and ^(3)He+Au at√S_(NN)=200 GeV GeV are evaluated in the framework of a fireball model with Tsallis thermodynamics.The fireball model assumes that the experimentally measured particles are produced by fireballs following the Tsallis distribution and it can effectively describe the experimental data.Our results as well as previous results for d+Au collisions at√S_(NN)=200 GeV GeV and p+Pb collisions at√S_(NN)=5.02 TeV TeV validate that the fireball model based on Tsallis thermodynamics can provide a universal framework for pseudo-rapidity distribution of the charged particles produced in asymmetric collision systems.We predict the centrality dependence of the total charged particle multiplicity in the p+Al,p+Au and 3He+Au collisions.Additionally,the dependences of the fireball model parameters(y_(0a),y_(0A),σ_(a) and σ_(A))on the centrality and system size are studied.展开更多
This paper proposes a novel approach and simplified model of Quantum Gravity based on the unification framework of Generalized Thermodynamics which suggests cross-related terms and modified equations of General Relati...This paper proposes a novel approach and simplified model of Quantum Gravity based on the unification framework of Generalized Thermodynamics which suggests cross-related terms and modified equations of General Relativity and Quantum Mechanics. To address the “background problem”, a metric tensor is introduced into stationary Schrödinger equations via curved coordinates yielding quantum spacetime variation term. Then quantum Lagrangian is added to Einstein-Hilbert functional yielding quantum stress-energy tensor. Obtained from one variational principle, two theories are linked by a common quantum spacetime field. The theory offers some interpretations of the quantum vacuum spacetime fluctuations, zero-point-fields, quantum fields shifting towards high spacetime densities, the quantum nature of spacetime, and black hole singularity.展开更多
In this paper,the data of Automatic Weather Stations(AWSs),ERA5 reanalysis,sounding,wind profile radar,and dual-polarization radar are used to study an extreme rainfall event in the south China Coast on 11 to 12 May 2...In this paper,the data of Automatic Weather Stations(AWSs),ERA5 reanalysis,sounding,wind profile radar,and dual-polarization radar are used to study an extreme rainfall event in the south China Coast on 11 to 12 May 2022 from the aspects of thermodynamics and microphysical characteristics under the influence of low-level jets(LLJs).Results show that:(1)The extreme rainfall event can be divided into two stages:the first stage(S1)from 0000 to 0600 LST on May 12 and the second stage(S2)from 0700 to 1700 LST on the same day.During S1,the rainfall is mainly caused by the upper-level shortwave trough and the boundary layer jet(BLJ),characterized by strong upward motion on the windward side of mountains.In S2,the combined influence of the BLJ and synoptic-system-related low-level jet(SLLJ)increases the vertical wind shear and vertical vorticity,strengthening the rainstorm.In combination with the effect of topography,a warm and humid southwest flow continuously transports water vapor to farther north,resulting in a significant increase in rainfall over the study area(on the terrain’s windward slope).From S1 to S2,the altitude of a divergence center in the upper air decreases obviously.(2)The rainfalls in the two stages are both associated with the mesoscale convergence line(MCL)on the surface,and the wind field from the mesoscale outflow boundary(MOB)in S1 is in the same direction as the environmental winds.Due to a small area of convergence that is left behind the MOB,convection moves eastward quickly and causes a short duration of heavy rainfall.In S2,the convergence along the MOB is enhanced,which strengthens the rainfall and leads to strong outflows,further enhancing the surface convergence near the MOB and forming a positive feedback mechanism.It results in a slow motion of convection and a long duration of heavy rainfall.(3)In terms of microphysics,the center of a strong echo in S1 is higher than in S2.The warm-rain process of the oceanic type characterizes both stages,but the convective intensity in S2 is significantly stronger than that in S1,featuring bigger drop sizes and lower concentrations.It is mainly due to the strengthening of LLJs,which makes small cloud droplets lift to melting levels,enhancing the ice phase process(riming process),producing large amounts of graupel particles and enhancing the melting and collision processes as they fall,resulting in the increase of liquid water content(LWC)and the formation of large raindrops near the surface.展开更多
Electrosynthesis of ammonia from the reduction of nitrogen is still confronted with the limited supply of gas reactant in dynamics as well as high activation barrier in thermodynamics.Unfortunately,despite tremendous ...Electrosynthesis of ammonia from the reduction of nitrogen is still confronted with the limited supply of gas reactant in dynamics as well as high activation barrier in thermodynamics.Unfortunately,despite tremendous efforts devoted to electrocatalysts themselves,they still fail to tackle the above two challenges simultaneously.Herein,we employ a heterogeneous catalyst adlayer-composed of crown ethers associated with Li^(+)ions-to achieve the dual promotion of dynamics and thermodynamics for ambient ammonia synthesis.Dynamically,the bound Li^(+)ions interact with the strong quadrupole moment of nitrogen,and trigger considerable reactant flux toward the catalyst.Thermodynamically,Li^(+)associated with the oxygen of crown ether achieves a higher density of states at the Fermi level for the catalyst,enabling effortless electron transfer from the catalysts to nitrogen and thus greatly reducing the activation barrier.As expected,the proof-of-concept system achieves an ammonia yield rate of 168.5μg h^(-1)mg^(-1)and a Faradaic efficiency of 75.3%at-0.3 V vs.RHE.This system-level approach opens up pathways for tackling the two key challenges that have limited the field of ammonia synthesis.展开更多
We examine thermodynamic phase transition(PT)of the charged Gauss-Bonnet Ad S black hole(BH)by utilizing the shadow radius.In this system,we rescale the corresponding Gauss-Bonnet coefficientαby a factor of 1/(D-4),a...We examine thermodynamic phase transition(PT)of the charged Gauss-Bonnet Ad S black hole(BH)by utilizing the shadow radius.In this system,we rescale the corresponding Gauss-Bonnet coefficientαby a factor of 1/(D-4),and ensure thatαis positive to avoid any singularity problems.The equation derived for the shadow radius indicates that it increases as the event horizon radius increases,making it an independent variable for determining BH temperature.By investigating the PT curve in relation to shadows,we can observe that the shadow radius can be used as an alternative to the event horizon radius in explaining the phenomenon of BH PT.Furthermore,the results indicate that an increase in the parameterαcorresponds to a decrease in the temperature of the BH.By utilizing the relationship between the temperature and the shadow radius,it is possible to obtain the thermal profile of the Gauss-Bonnet AdS BH.It is evident that there is an N-type variation in temperature for pressures P<P_(c).Additionally,as the parameterαincreases,the region covered by shadow expands while the temperature decreases.The utilization of BH shadows as a probe holds immense significance in gaining a deeper understanding of BH thermodynamic behavior.展开更多
Ground-based microwave radiometers(MWRs)operating in the K-and V-bands(20–60 GHz)can help us obtain temperature and humidity profiles in the troposphere.Aside from some soundings from local meteorological observatori...Ground-based microwave radiometers(MWRs)operating in the K-and V-bands(20–60 GHz)can help us obtain temperature and humidity profiles in the troposphere.Aside from some soundings from local meteorological observatories,the tropospheric atmosphere over the Tibetan Plateau(TP)has never been continuously observed.As part of the Chinese Second Tibetan Plateau Scientific Expedition and Research Program(STEP),the Tibetan Plateau Atmospheric Profile(TPPROFILE)project aims to construct a comprehensive MWR troposphere observation network to study the synoptic processes and environmental changes on the TP.This initiative has collected three years of data from the MWR network.This paper introduces the data information,the data quality,and data downloading.Some applications of the data obtained from these MWRs were also demonstrated.Our comparisons of MWR against the nearest radiosonde observation demonstrate that the TP-PROFILE MWR system is adequate for monitoring the thermal and moisture variability of the troposphere over the TP.The continuous temperature and moisture profiles derived from the MWR data provide a unique perspective on the evolution of the thermodynamic structure associated with the heating of the TP.The TP-PROFILE project reveals that the low-temporal resolution instruments are prone to large uncertainties in their vapor estimation in the mountain valleys on the TP.展开更多
Herein,a thermodynamic model aimed at describing deoxidation equilibria in liquid steel was developed.The model provides explicit forms of the activity coefficient of solutes in liquid steel,eliminating the need for t...Herein,a thermodynamic model aimed at describing deoxidation equilibria in liquid steel was developed.The model provides explicit forms of the activity coefficient of solutes in liquid steel,eliminating the need for the minimization of internal Gibbs energy preliminarily when solving deoxidation equilibria.The elimination of internal Gibbs energy minimization is particularly advantageous during the coupling of deoxidation equilibrium calculations with computationally intensive approaches,such as computational fluid dynamics.The model enables efficient calculations through direct embedment of the explicit forms of activity coefficient in the computing code.The proposed thermodynamic model was developed using a quasichemical approach with two key approximations:random mixing of metallic elements(Fe and oxidizing metal) and strong nonrandom pairing of metal and oxygen as nearest neighbors.Through these approximations,the quasichemical approach yielded the activity coefficients of solutes as explicit functions of composition and temperature without requiring the minimization of internal Gibbs energy or the coupling of separate programs.The model was successfully applied in the calculation of deoxidation equilibria of various elements(Al,B,C,Ca,Ce,Cr,La,Mg,Mn,Nb,Si,Ti,V,and Zr).The limitations of the model arising from these assumptions were also discussed.展开更多
文摘According to the second law of thermodynamics, as currently understood, any given transit of a system along the reversible path proceeds with a total entropy change equal to zero. The fact that this condition is also the identifier of thermodynamic equilibrium, makes each and every point along the reversible path a state of equilibrium, and the reversible path, as expressed by a noted thermodynamic author, “a dense succession of equilibrium states”. The difficulties with these notions are plural. The fact, for example, that systems need to be forced out of equilibrium via the expenditure of work, would make any spontaneous reversible process a consumer of work, this in opposition to common thermodynamic wisdom that makes spontaneous reversible processes the most efficient transformers of work-producing-potential into actual work. The solution to this and other related impasses is provided by Dialectical Thermodynamics via its previously proved notion assigning a negative entropy change to the energy upgrading process represented by the transformation of heat into work. The said solution is here exemplified with the ideal-gas phase isomerization of butane into isobutane.
基金the National Natural Science Foundation of China(Nos.51871125,51761032,52001005 and 51731002)Major Science and Technology Innovation Projects in Shandong Province(No.2019JZZY010320)for financial support of the work.
文摘Mg-based hydrides are too stable and the kinetics of hydrogen absorption and desorption is not satisfactory.An efficient way to improve these shortcomings is to employ reactive ball milling to synthesize the nanocomposite materials of Mg and additives.In this experiment,TiF_(3)was selected as an additive,and the mechanical milling method was employed to prepare the experimental alloys.The alloys used in this experiment were the as-cast Ce_(5)Mg_(85)Ni_(10),as-milled Ce_(5)Mg_(85)Ni_(10)and Ce_(5)Mg_(85)Ni_(10)+3 wt.%TiF3.The phase transformation,structural evolution,isothermal and non-isothermal hydrogenation and dehydrogenation performances of the alloys were inspected by XRD,SEM,TEM,Sievert apparatus,DSC and TGA.It revealed that nanocrystalline appeared in the as-milled samples.Compared with the as-cast alloy,ball milling made the particle dimension and grain size decrease dramatically and the defect density increase significantly.The addition of TiF_(3)made the surface of ball milling alloy particles markedly coarser and more irregular.Ball milling and adding TiF_(3)distinctly improved the activation and kinetics of the alloys.Moreover,ball milling along with TiF_(3)can decrease the onset dehydrogenation temperature of Mg-based hydrides and slightly ameliorate their thermodynamics.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China (Grant No.LY14A030001)。
文摘We calculate the thermodynamic quantities in the quantum corrected Reissner-Nordstr?m-AdS(RN-AdS)black hole,and examine their quantum corrections.By analyzing the mass and heat capacity,we give the critical state and the remnant state,respectively,and discuss their consistency.Then,we investigate the quantum tunneling from the event horizon of massless scalar particle by using the null geodesic method,and charged massive boson W^(±)and fermions by using the Hamilton-Jacob method.It is shown that the same Hawking temperature can be obtained from these tunneling processes of different particles and methods.Next,by using the generalized uncertainty principle(GUP),we study the quantum corrections to the tunneling and the temperature.Then the logarithmic correction to the black hole entropy is obtained.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12075197)the Fundamental Research Fund for the Central Universities of China (Grant No. 20720210020)。
文摘It is found from textbooks and literature that there are three different statements for the third law of thermodynamics,i.e., the Nernst theorem, the unattainability statement of absolute zero temperature, and the heat capacity statement. It is pointed out that such three statements correspond to three thermodynamic parameters, which are, respectively, the entropy,temperature, and heat capacity, and can be obtained by extrapolating the experimental results of different parameters at ultralow temperatures to absolute zero. It is expounded that because there is no need for additional assumptions in the derivation of the Nernst equation, the Nernst theorem should be renamed as the Nernst statement. Moreover, it is proved that both the Nernst statement and the heat capacity statement are mutually deducible and equivalent, while the unattainability of absolute zero temperature is only a corollary of the Nernst statement or the heat capacity statement so that it is unsuitably referred to as one statement of the third law of thermodynamics. The conclusion is that the Nernst statement and the heat capacity statement are two equivalent statements of the third law of thermodynamics.
基金This work was financially supported by the Natural Science Foundation of Shandong Province(ZR2021MB134 and ZR2022MB019)the National Natural Science Foundation of China(22008131)+1 种基金the Talent Fund for Province and Ministry Co-construction Collaborative Innovation Center of Eco-chemical Engineering(STHGYX2220)the Opening Fund of State Key Laboratory of Heavy Oil Processing(SKLOP202002002).
文摘Various metal-modified ZSM-5 zeolite adsorbents prepared by the impregnation method were applied to the removal of organic chlorides from model naphtha.The adsorption performance and regeneration stability were investigated by static adsorption experiments.The morphologies,structural features,and physicochemical properties of the adsorbents were characterized by X-ray diffraction,Brunauer-Emmett-Teller analysis,NH3 temperature-programmed desorption,scanning electron microscopy,transmission electron microscopy,and pyridine adsorption infrared spectroscopy.The Mg/ZSM-5 zeolite adsorbent possessed a relatively high specific surface area and good metal dispersion and exhibited the best dechlorination and regeneration performance.The characterization results revealed that introduction of the metal exerted a significant influence on the acidic properties of the catalyst surface.A decrease in the ratio of Brønsted acidic sites to Lewis acidic sites and an increase in the amount of moderately acidic sites were confirmed to be responsible for the excellent adsorption performance of the Mg-modified ZSM-5 zeolite.Furthermore,the Langmuir adsorption isotherm model was applied to study the adsorption equilibrium and thermodynamics of the Mg/ZSM-5 adsorbent under mild conditions.The results revealed that the removal of 1,2-dichloroethane by the Mg/ZSM-5 adsorbent was endothermic,spontaneous,disordered,and primarily involved physical adsorption.
文摘2,4(5)-Dinitroimidazole(2,4(5)-DNI)is an important organic intermediate,and itself can also be used for energetic material.In this work,the solubility of 2,4(5)-DNI in(methanol+water,acetonitrile+water,acetone+water)binary solvents were measured by using a dynamic test method from 278.15 K to 323.15 K under 101.1 k Pa.The Jouyban–Acree model,van't Hoff–Jouyban–Acree model,Apelblat–Jouyb an–Acree model,Ma model,and Sun model were used to correlate the experimental data.The values of relative average deviation(RAD)and root-mean-square deviation(RMSD)were very small,indicating that the error between the experimental value and the correlated value was very small.The thermodynamic parameters such as dissolution enthalpy,dissolution entropy and Gibbs energy were calculated based on solubility data.High-purity of 2,4(5)-DNI was efficiently obtained by using cooling and dilution crystallization method.
文摘In terms of security and privacy,mobile ad-hoc network(MANET)continues to be in demand for additional debate and development.As more MANET applications become data-oriented,implementing a secure and reliable data transfer protocol becomes a major concern in the architecture.However,MANET’s lack of infrastructure,unpredictable topology,and restricted resources,as well as the lack of a previously permitted trust relationship among connected nodes,contribute to the attack detection burden.A novel detection approach is presented in this paper to classify passive and active black-hole attacks.The proposed approach is based on the dipper throated optimization(DTO)algorithm,which presents a plausible path out of multiple paths for statistics transmission to boost MANETs’quality of service.A group of selected packet features will then be weighed by the DTO-based multi-layer perceptron(DTO-MLP),and these features are collected from nodes using the Low Energy Adaptive Clustering Hierarchical(LEACH)clustering technique.MLP is a powerful classifier and the DTO weight optimization method has a significant impact on improving the classification process by strengthening the weights of key features while suppressing the weights ofminor features.This hybridmethod is primarily designed to combat active black-hole assaults.Using the LEACH clustering phase,however,can also detect passive black-hole attacks.The effect of mobility variation on detection error and routing overhead is explored and evaluated using the suggested approach.For diverse mobility situations,the results demonstrate up to 97%detection accuracy and faster execution time.Furthermore,the suggested approach uses an adjustable threshold value to make a correct conclusion regarding whether a node is malicious or benign.
文摘The internal energy change of ideal gas does not depend on the volume and pressure. The internal energy change of real gas has not any relation with the volume and pressure, which had been proved. If the internal energy change had not any relation with the volume and pressure, we could confirm the first law of thermodynamics in theory. Simultaneously, the internal energy change is the state function that shall be able to be proved in theory. If the internal energy change depended on the volume and pressure, we could not prove that the internal energy change is the state function and the chemical thermodynamics theory is right. The extended or modified Bernoulli equation can be derived from the energy conservation law, and the internal energy change, heat, and friction are all considered in the derivation procedure. The extended Bernoulli equation could be applied to the flying aircraft and mechanical motion on the gravitational field, for instance, the rocket and airplane and so on. This paper also revises some wrong ideas, viewpoints, or concepts about the thermodynamics theory and Bernoulli equation.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11864030 and 62061037)Inner Mongolia Natural Science Foundation (Grant Nos. 2021LHBS01001 and 2020BS02011)the Scientific Research Funding Project for Introduced High Level Talents of IMNU (Grant No. 2020YJRC001)。
文摘Inflationary spectral index from the Langevin equation is calculated under the frame of warm inflationary scenario with inflaton interacting with U(1) gauge fields through the Chern–Simons coupling ∝ФF_(μv)F^(μv). Under the strong dissipative condition, the spectral index is calculated in terms of the ratio of Hubble parameter to temperature H/T. Then relation between H/T and other cosmic parameters is analytically expressed, based on which a spectral index related to the Chern–Simons coupling strength is further obtained. Numerical results show that cosmic temperature T closes to a constant during inflation and decreases after inflation without a reheating process. Meanwhile, the ratio H/T tends to a constant if the gauged coupling constant is less than a threshold. This phenomenon shows that cosmic temperature may be an important physical parameter with a special value and adiabatic approximation still holds. We obtain the estimate H/T ≤ 0.3377 during inflation from Planck data and other constraint conditions.
文摘The formations of [NAPA-A(H<sub>2</sub>O)<sub>n</sub> (n = 1, 2, 3, 4)] complexes have been studied employing DFT/wB97XD/cc-pVTZ computational level to understand the kinetics and thermodynamics for the hydration reactions of N-acetyl-phenylalaninylamide (NAPA). Thermodynamic parameters such as reaction energy (E), enthalpy (H), Gibb’s free energy (G), specific heat capacity (C<sub>v</sub>), entropy (S), and change of these parameters (ΔE<sub>r</sub>, ΔH<sub>r</sub>, ΔGr, ΔC<sub>r</sub>, and ΔS<sub>r</sub>) were studied using the explicit solvent model. The predicted values of H, G, C, and S increase with the sequential addition of water in NAPA-A due to the increase in the total number of vibrational modes. On the other hand, the value of ΔE<sub>r</sub>, ΔH<sub>r</sub>, and ΔG<sub>r</sub> increases (more negative to less negative) gradually for n = 1, 2, 3, and 4 that indicates an increase of hydration in NAPA-A makes exothermic to endothermic reactions. The barrier heights for the transition states (TS) of [NAPA-A(H<sub>2</sub>O)<sub>n</sub> (n = 1, 2, 3, 4)] complexes are predicted to lie at 4.41, 4.05, 3.72 and 2.26 kcal/mol respectively below the reactants. According to the calculations, the formations of [NAPA-A(H<sub>2</sub>O)<sub>1</sub>] and [NAPA-A(H<sub>2</sub>O)<sub>2</sub>] complexes are barrierless reactions because both water molecules are strongly bonded via two hydrogen bonds in the backbone of NAPA-A. On the contrary, the reactions of [NAPA-A(H<sub>2</sub>O)<sub>3</sub>] and [NAPA-A(H<sub>2</sub>O)<sub>4</sub>] complexation are endothermic and the barrier heights are predicted to stay at 6.30 and 10.54 kcal/mol respectively above the reactants. The free energy of activation (Δ<sup>‡</sup>G<sup>0</sup>) for the reaction of [NAPA-A(H<sub>2</sub>O)<sub>1</sub>], [NAPA-A(H<sub>2</sub>O)<sub>2</sub>], [NAPA-A(H<sub>2</sub>O)<sub>3</sub>], and [NAPA-A(H<sub>2</sub>O)<sub>4</sub>] complexation are 4.43, 4.28, 3.83 and 5.11 kcal/mol respectively which are very low. As well as the rates of reactions are 3.490 × 10<sup>9</sup> s<sup>-1</sup>, 4.514 × 10<sup>9</sup> s<sup>-1</sup>, 9.688 × 10<sup>9</sup> s<sup>-1</sup>, and 1.108 × 10<sup>9</sup> s<sup>-1</sup> respectively which are very fast and spontaneous.
文摘Black holes contradict the Nernst-Planck (N/P) version of the 3rd law of thermodynamics, but agree with its unattainability (U) version. This happens without contradiction, because the N/P and U versions are not equivalent, namely, N/P implies U but U does not imply N/P. So, black holes obey the weaker version of the 3rd law, but not the stronger one.
基金supported by the National Natural Science Foundation of China(Grant No.11903025)the Starting Fund of China West Normal University(Grant No.18Q062)+2 种基金the Sichuan Youth Science and Technology Innovation Research Team(Grant No.21CXTD0038)the Chongqing Science and Technology Bureau(Grant No.csts2022ycjh-bgzxm0161)the Natural Science Foundation of Sichuan Province(Grant No.2022NSFSC1833)。
文摘We creatively employ the shadow radius to study the thermodynamics of a charged Ad S black hole with a nonlinear electrodynamics(NLED)term.First,the connection between the shadow radius and event horizon is constructed with the aid of the geodesic analysis.It turns out that the black hole shadow radius shows a positive correlation as a function of the event horizon radius.Then in the shadow context,we find that the black hole temperature and heat capacity can be presented by the shadow radius.Further analysis shows that the shadow radius can work similarly to the event horizon in revealing black hole phase transition process.In this sense,we construct the thermal profile of the charged Ad S black hole with inclusion of the NLED effect.In the P<Pc case,it is found that the N-type trend of the temperature given by the shadow radius is always consistent with that obtained by using the event horizon.Thus,we can conclude for the charged Ad S black hole that the phase transition process can be intuitively presented as the thermal profile in the shadow context.Finally,the effects of NLED are carefully analyzed.
文摘This paper combines a review of recent advances in quantum thermodynamics, including work on objective collapse (Zurek’s quantum Darwinism) and quantum gravity (Verlinde’s quantum gravity explanation), with a redefinition of entropy generation as systems’ change process. These concepts are used as systems’ behaviour analysis tools to allow us to revisit Hartle and Hawking’s 1983 quantum universe and develop a hypothesis for how physically a universe starting in a quantum state could evolve into our current universe, based on systems analysis. The outcome of this analysis raises a question: do we already have the elements of a “theory of everything” hiding in plain sight within recent advances in quantum thermodynamics?
基金This work was supported in part by the National Natural Science Foundation of China(Nos.11905120,11947416)the Natural Science Foundation of Sichuan Province(No.2023NSFSC1322)+2 种基金the Natural Science Basic Research Plan in Shaanxi Province of China(No.2023-JC-YB-012)the United States Department of Energy(#DE-FG02-93ER40773)the NNSA(No.DENA0003841(CENTAUR)).
文摘The pseudo-rapidity distributions of the charged particles produced in the asymmetric collision systems p+Al,p+Au and ^(3)He+Au at√S_(NN)=200 GeV GeV are evaluated in the framework of a fireball model with Tsallis thermodynamics.The fireball model assumes that the experimentally measured particles are produced by fireballs following the Tsallis distribution and it can effectively describe the experimental data.Our results as well as previous results for d+Au collisions at√S_(NN)=200 GeV GeV and p+Pb collisions at√S_(NN)=5.02 TeV TeV validate that the fireball model based on Tsallis thermodynamics can provide a universal framework for pseudo-rapidity distribution of the charged particles produced in asymmetric collision systems.We predict the centrality dependence of the total charged particle multiplicity in the p+Al,p+Au and 3He+Au collisions.Additionally,the dependences of the fireball model parameters(y_(0a),y_(0A),σ_(a) and σ_(A))on the centrality and system size are studied.
文摘This paper proposes a novel approach and simplified model of Quantum Gravity based on the unification framework of Generalized Thermodynamics which suggests cross-related terms and modified equations of General Relativity and Quantum Mechanics. To address the “background problem”, a metric tensor is introduced into stationary Schrödinger equations via curved coordinates yielding quantum spacetime variation term. Then quantum Lagrangian is added to Einstein-Hilbert functional yielding quantum stress-energy tensor. Obtained from one variational principle, two theories are linked by a common quantum spacetime field. The theory offers some interpretations of the quantum vacuum spacetime fluctuations, zero-point-fields, quantum fields shifting towards high spacetime densities, the quantum nature of spacetime, and black hole singularity.
基金National Natural Science Foundation of China(U2242203,41975138,42275008)Natural Science Foundation of Guangdong Province(2019A1515010814,2021A1515011415)+1 种基金Science and Technology Development Fund Project of Guangdong Meteorological Bureau(GRMC2020M27)Jiangmen Young science and technology talents lifting Project(2022-2023)。
文摘In this paper,the data of Automatic Weather Stations(AWSs),ERA5 reanalysis,sounding,wind profile radar,and dual-polarization radar are used to study an extreme rainfall event in the south China Coast on 11 to 12 May 2022 from the aspects of thermodynamics and microphysical characteristics under the influence of low-level jets(LLJs).Results show that:(1)The extreme rainfall event can be divided into two stages:the first stage(S1)from 0000 to 0600 LST on May 12 and the second stage(S2)from 0700 to 1700 LST on the same day.During S1,the rainfall is mainly caused by the upper-level shortwave trough and the boundary layer jet(BLJ),characterized by strong upward motion on the windward side of mountains.In S2,the combined influence of the BLJ and synoptic-system-related low-level jet(SLLJ)increases the vertical wind shear and vertical vorticity,strengthening the rainstorm.In combination with the effect of topography,a warm and humid southwest flow continuously transports water vapor to farther north,resulting in a significant increase in rainfall over the study area(on the terrain’s windward slope).From S1 to S2,the altitude of a divergence center in the upper air decreases obviously.(2)The rainfalls in the two stages are both associated with the mesoscale convergence line(MCL)on the surface,and the wind field from the mesoscale outflow boundary(MOB)in S1 is in the same direction as the environmental winds.Due to a small area of convergence that is left behind the MOB,convection moves eastward quickly and causes a short duration of heavy rainfall.In S2,the convergence along the MOB is enhanced,which strengthens the rainfall and leads to strong outflows,further enhancing the surface convergence near the MOB and forming a positive feedback mechanism.It results in a slow motion of convection and a long duration of heavy rainfall.(3)In terms of microphysics,the center of a strong echo in S1 is higher than in S2.The warm-rain process of the oceanic type characterizes both stages,but the convective intensity in S2 is significantly stronger than that in S1,featuring bigger drop sizes and lower concentrations.It is mainly due to the strengthening of LLJs,which makes small cloud droplets lift to melting levels,enhancing the ice phase process(riming process),producing large amounts of graupel particles and enhancing the melting and collision processes as they fall,resulting in the increase of liquid water content(LWC)and the formation of large raindrops near the surface.
基金supported by the National Natural Science Foundation of China(U21A20332,52103226,52202275,52203314,and 12204253)the Distinguished Young Scholars Fund of Jiangsu Province(BK20220061)the Fellowship of China Postdoctoral Science Foundation(2021M702382)。
文摘Electrosynthesis of ammonia from the reduction of nitrogen is still confronted with the limited supply of gas reactant in dynamics as well as high activation barrier in thermodynamics.Unfortunately,despite tremendous efforts devoted to electrocatalysts themselves,they still fail to tackle the above two challenges simultaneously.Herein,we employ a heterogeneous catalyst adlayer-composed of crown ethers associated with Li^(+)ions-to achieve the dual promotion of dynamics and thermodynamics for ambient ammonia synthesis.Dynamically,the bound Li^(+)ions interact with the strong quadrupole moment of nitrogen,and trigger considerable reactant flux toward the catalyst.Thermodynamically,Li^(+)associated with the oxygen of crown ether achieves a higher density of states at the Fermi level for the catalyst,enabling effortless electron transfer from the catalysts to nitrogen and thus greatly reducing the activation barrier.As expected,the proof-of-concept system achieves an ammonia yield rate of 168.5μg h^(-1)mg^(-1)and a Faradaic efficiency of 75.3%at-0.3 V vs.RHE.This system-level approach opens up pathways for tackling the two key challenges that have limited the field of ammonia synthesis.
基金Project supported by the National Natural Science Foundation of China (Grant No.11903025)the starting fund of China West Normal University (Grant No.18Q062)+2 种基金the Sichuan Youth Science and Technology Innovation Research Team (Grant No.21CXTD0038)the Chongqing Science and Technology Bureau (Grant No.cstc2022ycjh-bgzxm0161)the Natural Science Foundation of Sichuan Province (Grant No.2022NSFSC1833)。
文摘We examine thermodynamic phase transition(PT)of the charged Gauss-Bonnet Ad S black hole(BH)by utilizing the shadow radius.In this system,we rescale the corresponding Gauss-Bonnet coefficientαby a factor of 1/(D-4),and ensure thatαis positive to avoid any singularity problems.The equation derived for the shadow radius indicates that it increases as the event horizon radius increases,making it an independent variable for determining BH temperature.By investigating the PT curve in relation to shadows,we can observe that the shadow radius can be used as an alternative to the event horizon radius in explaining the phenomenon of BH PT.Furthermore,the results indicate that an increase in the parameterαcorresponds to a decrease in the temperature of the BH.By utilizing the relationship between the temperature and the shadow radius,it is possible to obtain the thermal profile of the Gauss-Bonnet AdS BH.It is evident that there is an N-type variation in temperature for pressures P<P_(c).Additionally,as the parameterαincreases,the region covered by shadow expands while the temperature decreases.The utilization of BH shadows as a probe holds immense significance in gaining a deeper understanding of BH thermodynamic behavior.
基金supported by the Second Tibetan Plateau Scientific Expedition and Research Program(STEP)(Grant Nos.2019QZKK0103 and 2019QZKK0105)the National Natural Science Foundation of China(Grant Nos.41975009,42230610,41840650 and U2242208)the Youth Innovation Promotion Association of the Chinese Academy of Sciences(Wang Binbin,2022069).
文摘Ground-based microwave radiometers(MWRs)operating in the K-and V-bands(20–60 GHz)can help us obtain temperature and humidity profiles in the troposphere.Aside from some soundings from local meteorological observatories,the tropospheric atmosphere over the Tibetan Plateau(TP)has never been continuously observed.As part of the Chinese Second Tibetan Plateau Scientific Expedition and Research Program(STEP),the Tibetan Plateau Atmospheric Profile(TPPROFILE)project aims to construct a comprehensive MWR troposphere observation network to study the synoptic processes and environmental changes on the TP.This initiative has collected three years of data from the MWR network.This paper introduces the data information,the data quality,and data downloading.Some applications of the data obtained from these MWRs were also demonstrated.Our comparisons of MWR against the nearest radiosonde observation demonstrate that the TP-PROFILE MWR system is adequate for monitoring the thermal and moisture variability of the troposphere over the TP.The continuous temperature and moisture profiles derived from the MWR data provide a unique perspective on the evolution of the thermodynamic structure associated with the heating of the TP.The TP-PROFILE project reveals that the low-temporal resolution instruments are prone to large uncertainties in their vapor estimation in the mountain valleys on the TP.
文摘Herein,a thermodynamic model aimed at describing deoxidation equilibria in liquid steel was developed.The model provides explicit forms of the activity coefficient of solutes in liquid steel,eliminating the need for the minimization of internal Gibbs energy preliminarily when solving deoxidation equilibria.The elimination of internal Gibbs energy minimization is particularly advantageous during the coupling of deoxidation equilibrium calculations with computationally intensive approaches,such as computational fluid dynamics.The model enables efficient calculations through direct embedment of the explicit forms of activity coefficient in the computing code.The proposed thermodynamic model was developed using a quasichemical approach with two key approximations:random mixing of metallic elements(Fe and oxidizing metal) and strong nonrandom pairing of metal and oxygen as nearest neighbors.Through these approximations,the quasichemical approach yielded the activity coefficients of solutes as explicit functions of composition and temperature without requiring the minimization of internal Gibbs energy or the coupling of separate programs.The model was successfully applied in the calculation of deoxidation equilibria of various elements(Al,B,C,Ca,Ce,Cr,La,Mg,Mn,Nb,Si,Ti,V,and Zr).The limitations of the model arising from these assumptions were also discussed.