Examples of heat transfer and heat-work conversion are optimized with entropy generation and entransy loss,respectively based on the generalized heat transfer law in this paper.The applicability of entropy generation ...Examples of heat transfer and heat-work conversion are optimized with entropy generation and entransy loss,respectively based on the generalized heat transfer law in this paper.The applicability of entropy generation and entransy loss evaluation in these optimization problems is analyzed and discussed.The results show that the entransy loss rate reduces to the entransy dissipation rate in heat transfer processes,and that the entransy loss evaluation is effective for heat transfer optimization.However,the maximum heat transfer rate does not correspond to the minimum entropy generation rate with prescribed heat transfer temperature difference,which indicates that the entropy generation minimization is not always appropriate to heat transfer optimization.For heat-work conversion processes,the maximum entransy loss rate and the minimum entropy generation rate both correspond to the maximum output power,and they are both appropriate to the optimization of the heat-work conversion processes discussed in this paper.展开更多
In recent years, a new fundamental equation of nonequilibrium statistical physics was proposed in place of the Liouville equation. That is the anomalous Langevin equation in (?) space or its equivalent Liouville diffu...In recent years, a new fundamental equation of nonequilibrium statistical physics was proposed in place of the Liouville equation. That is the anomalous Langevin equation in (?) space or its equivalent Liouville diffusion equation of time-reversal asymmetry. This equation reflects that the form of motion of particles in statistical thermody-namic systems has the drift-diffusion duality and the law of motion of statistical thermodynamics is stochastic in essence, but does not obey the Newton equation of motion, though it is also constrained by dynamics. The stochastic diffusion of the particles is the microscopic origin of macroscopic irre-versibility. Starting from this equation, the BBGKY diffusion equation hierarchy was presented, the hydrodynamic equations, such as the generalized Navier-Stokes equation, the mass drift-diffusion equation and the thermal conductivity equation have been derived succinctly. The unified description of all three level equations of microscopic, kinetic and hydrodynamic展开更多
We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
In complex networks,identifying influential spreader is of great significance for improving the reliability of networks and ensuring the safe and effective operation of networks.Nowadays,it is widely used in power net...In complex networks,identifying influential spreader is of great significance for improving the reliability of networks and ensuring the safe and effective operation of networks.Nowadays,it is widely used in power networks,aviation networks,computer networks,and social networks,and so on.Traditional centrality methods mainly include degree centrality,closeness centrality,betweenness centrality,eigenvector centrality,k-shell,etc.However,single centrality method is onesided and inaccurate,and sometimes many nodes have the same centrality value,namely the same ranking result,which makes it difficult to distinguish between nodes.According to several classical methods of identifying influential nodes,in this paper we propose a novel method that is more full-scaled and universally applicable.Taken into account in this method are several aspects of node’s properties,including local topological characteristics,central location of nodes,propagation characteristics,and properties of neighbor nodes.In view of the idea of the multi-attribute decision-making,we regard the basic centrality method as node’s attribute and use the entropy weight method to weigh different attributes,and obtain node’s combined centrality.Then,the combined centrality is applied to the gravity law to comprehensively identify influential nodes in networks.Finally,the classical susceptible-infected-recovered(SIR)model is used to simulate the epidemic spreading in six real-society networks.Our proposed method not only considers the four topological properties of nodes,but also emphasizes the influence of neighbor nodes from the aspect of gravity.It is proved that the new method can effectively overcome the disadvantages of single centrality method and increase the accuracy of identifying influential nodes,which is of great significance for monitoring and controlling the complex networks.展开更多
From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that...From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that Benford’s distribution fits to calculate the rank probabilities of distinguishable objects. i.e. in the distribution of words in long texts all the words in a given rank are identical, therefore, the rank distribution is Zipfian. In logarithmic tables, the objects with identical 1st digits are distinguishable as there are many different digits in the 2nd, 3rd… places, etc., and therefore the distribution is according to Benford’s law. Pareto 20 - 80 rule is shown to be an outcome of Benford’s distribution as when the number of ranks is about 10 the probability of 20% of the high probability ranks is equal to the probability of the rest of 80% low probability ranks. It is argued that all these distributions, including the central limit theorem, are outcomes of Planck’s law and are the result of the quantization of energy. This argumentation may be considered a physical origin of probability.展开更多
High-entropy diborides(HEBs)have attracted extensive research due to their potential ultra-high hardness.In the present work,the effects of transition metals(TM)on lattice parameters,electron work function(EWF),bondin...High-entropy diborides(HEBs)have attracted extensive research due to their potential ultra-high hardness.In the present work,the effects of transition metals(TM)on lattice parameters,electron work function(EWF),bonding charge density,and hardness of HEBs are comprehensively investigated by the first-principles calculations,including(TiZrHfNbTa)B_(2),(TiZrHfNbMo)B_(2),(TiZrHfTaMo)B_(2),(TiZrNbTaMo)B_(2),and(TiHfNbTaMo)B_(2).It is revealed that the disordered TM atoms result in a severe local lattice distortion and the formation of weak spots.In view of bonding charge density,it is understood that the degree of electron contribution of TM atoms directly affects the bonding strength of the metallic layer,contributing to the optimized hardness of HEBs.Moreover,the proposed power-law-scaled relationship integrating the EWF and the grain size yields an excellent agreement between our predicted results and those reported experimental ones.It is found that the HEBs exhibit relatively high hardness which is higher than those of single transition metal diborides.In particular,the hardness of(TiZrNbTaMo)B_(2)and(TiHfNbTaMo)B_(2)can be as high as29.15 and 28.02 GPa,respectively.This work provides a rapid strategy to discover/design advanced HEBs efficiently,supported by the coupling hardening mechanisms of solid solution and grain refinement based on the atomic and electronic interactions.展开更多
基金supported by the Natural Science Foundation of China(Grant No. 51136001)the Tsinghua University Initiative ScientificResearch Program
文摘Examples of heat transfer and heat-work conversion are optimized with entropy generation and entransy loss,respectively based on the generalized heat transfer law in this paper.The applicability of entropy generation and entransy loss evaluation in these optimization problems is analyzed and discussed.The results show that the entransy loss rate reduces to the entransy dissipation rate in heat transfer processes,and that the entransy loss evaluation is effective for heat transfer optimization.However,the maximum heat transfer rate does not correspond to the minimum entropy generation rate with prescribed heat transfer temperature difference,which indicates that the entropy generation minimization is not always appropriate to heat transfer optimization.For heat-work conversion processes,the maximum entransy loss rate and the minimum entropy generation rate both correspond to the maximum output power,and they are both appropriate to the optimization of the heat-work conversion processes discussed in this paper.
文摘In recent years, a new fundamental equation of nonequilibrium statistical physics was proposed in place of the Liouville equation. That is the anomalous Langevin equation in (?) space or its equivalent Liouville diffusion equation of time-reversal asymmetry. This equation reflects that the form of motion of particles in statistical thermody-namic systems has the drift-diffusion duality and the law of motion of statistical thermodynamics is stochastic in essence, but does not obey the Newton equation of motion, though it is also constrained by dynamics. The stochastic diffusion of the particles is the microscopic origin of macroscopic irre-versibility. Starting from this equation, the BBGKY diffusion equation hierarchy was presented, the hydrodynamic equations, such as the generalized Navier-Stokes equation, the mass drift-diffusion equation and the thermal conductivity equation have been derived succinctly. The unified description of all three level equations of microscopic, kinetic and hydrodynamic
文摘We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
基金Project support by the National Key Research and Development Program of China(Grant No.2018YFF0301000)the National Natural Science Foundation of China(Grant Nos.71673161 and 71790613)。
文摘In complex networks,identifying influential spreader is of great significance for improving the reliability of networks and ensuring the safe and effective operation of networks.Nowadays,it is widely used in power networks,aviation networks,computer networks,and social networks,and so on.Traditional centrality methods mainly include degree centrality,closeness centrality,betweenness centrality,eigenvector centrality,k-shell,etc.However,single centrality method is onesided and inaccurate,and sometimes many nodes have the same centrality value,namely the same ranking result,which makes it difficult to distinguish between nodes.According to several classical methods of identifying influential nodes,in this paper we propose a novel method that is more full-scaled and universally applicable.Taken into account in this method are several aspects of node’s properties,including local topological characteristics,central location of nodes,propagation characteristics,and properties of neighbor nodes.In view of the idea of the multi-attribute decision-making,we regard the basic centrality method as node’s attribute and use the entropy weight method to weigh different attributes,and obtain node’s combined centrality.Then,the combined centrality is applied to the gravity law to comprehensively identify influential nodes in networks.Finally,the classical susceptible-infected-recovered(SIR)model is used to simulate the epidemic spreading in six real-society networks.Our proposed method not only considers the four topological properties of nodes,but also emphasizes the influence of neighbor nodes from the aspect of gravity.It is proved that the new method can effectively overcome the disadvantages of single centrality method and increase the accuracy of identifying influential nodes,which is of great significance for monitoring and controlling the complex networks.
文摘From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that Benford’s distribution fits to calculate the rank probabilities of distinguishable objects. i.e. in the distribution of words in long texts all the words in a given rank are identical, therefore, the rank distribution is Zipfian. In logarithmic tables, the objects with identical 1st digits are distinguishable as there are many different digits in the 2nd, 3rd… places, etc., and therefore the distribution is according to Benford’s law. Pareto 20 - 80 rule is shown to be an outcome of Benford’s distribution as when the number of ranks is about 10 the probability of 20% of the high probability ranks is equal to the probability of the rest of 80% low probability ranks. It is argued that all these distributions, including the central limit theorem, are outcomes of Planck’s law and are the result of the quantization of energy. This argumentation may be considered a physical origin of probability.
基金financially supported by the Science Challenge Project(No.TZ 2018002)。
文摘High-entropy diborides(HEBs)have attracted extensive research due to their potential ultra-high hardness.In the present work,the effects of transition metals(TM)on lattice parameters,electron work function(EWF),bonding charge density,and hardness of HEBs are comprehensively investigated by the first-principles calculations,including(TiZrHfNbTa)B_(2),(TiZrHfNbMo)B_(2),(TiZrHfTaMo)B_(2),(TiZrNbTaMo)B_(2),and(TiHfNbTaMo)B_(2).It is revealed that the disordered TM atoms result in a severe local lattice distortion and the formation of weak spots.In view of bonding charge density,it is understood that the degree of electron contribution of TM atoms directly affects the bonding strength of the metallic layer,contributing to the optimized hardness of HEBs.Moreover,the proposed power-law-scaled relationship integrating the EWF and the grain size yields an excellent agreement between our predicted results and those reported experimental ones.It is found that the HEBs exhibit relatively high hardness which is higher than those of single transition metal diborides.In particular,the hardness of(TiZrNbTaMo)B_(2)and(TiHfNbTaMo)B_(2)can be as high as29.15 and 28.02 GPa,respectively.This work provides a rapid strategy to discover/design advanced HEBs efficiently,supported by the coupling hardening mechanisms of solid solution and grain refinement based on the atomic and electronic interactions.
