We investigate the finite-time performance of a quantum endoreversible Carnot engine cycle and its inverse operation-Carnot refrigeration cycle,employing a spin-1/2 system as the working substance.The thermal machine ...We investigate the finite-time performance of a quantum endoreversible Carnot engine cycle and its inverse operation-Carnot refrigeration cycle,employing a spin-1/2 system as the working substance.The thermal machine is alternatively driven by a hot boson bath of inverse temperatureβ_(h)and a cold boson bath at inverse temperatureβ_(c)(>βh).While for the engine model the hot bath is constructed to be squeezed,in the refrigeration cycle the cold bath is established to be squeezed,with squeezing parameter r.We obtain the analytical expressions for both efficiency and power in heat engines and for coefficient of performance and cooling rate in refrigerators.We find that,in the high-temperature limit,the efficiency at maximum power is bounded by the analytical valueη_(+)=√sech(2r)(1-η_(C)),and the coefficient of performance at the maximum figure of merit is limited byε_(+)=√sech(2r)(1+ε_(C))/sech(2r)(1+ε_(C))-εC)-1,whereη_(C)=1-β_(h)/β_(c)andε_(C)=β_(h)/(β_(c)-β_(h))are the respective Carnot values of the engines and refrigerators.These analytical results are identical to those obtained from the Carnot engines based on harmonic systems,indicating that the efficiency at maximum power and coefficient at maximum figure of merit are independent of the working substance.展开更多
In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimens...In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.展开更多
Taking the output power, thermal efficiency, and thermo-economic performance as the optimization objectives, we optimize the operation parameters of a thermodynamic system with combined endoreversible Carnot heat engi...Taking the output power, thermal efficiency, and thermo-economic performance as the optimization objectives, we optimize the operation parameters of a thermodynamic system with combined endoreversible Carnot heat engines in this paper. The applicabilities of the entropy generation minimization and entransy theory to the optimizations are discussed. For the discussed cases, only the entransy loss coefficient is always agreeable to the optimization of thermal efficiency. The applicabilities of the other discussed concepts to the optimizations are conditional. Different concepts and principles are needed for different optimization objectives, and the optimization principles have their application preconditions. When the preconditions are not satisfied, the principles may be not applicable.展开更多
In this paper, we investigate a horizontal Laplacian version of the clamped plate problem on Carnot groups and obtain some universal inequalities. Furthermore, for the lower order eigenvalues of this eigenvalue proble...In this paper, we investigate a horizontal Laplacian version of the clamped plate problem on Carnot groups and obtain some universal inequalities. Furthermore, for the lower order eigenvalues of this eigenvalue problem on carnot groups, we also give some universal inequalities.展开更多
In this paper, an endoreversible Carnot heat engine with irreversible heat transfer processes is analyzed based on generalized heat transfer law. The applicability of the entropy generation minimization, exergy analys...In this paper, an endoreversible Carnot heat engine with irreversible heat transfer processes is analyzed based on generalized heat transfer law. The applicability of the entropy generation minimization, exergy analyses method, and entransy theory to the analyses is discussed. Three numerical cases are presented. It is shown that the results obtained from the entransy theory are different from those from the entropy generation minimization, which is equivalent to the exergy analyses method. For the first case in which the application preconditions of the entropy generation minimization and entransy loss maximization are satisfied, both smaller entropy generation rate and larger entransy loss rate lead to larger output power. For the second and third cases in which the preconditions are not satisfied, the entropy generation minimization does not lead to the maximum output power, while larger entransy loss rate still leads to larger output power in the third case. For the discussed cases, the concept of entransy dissipation is not applicable for the analyses of output power.The problems in the negative comments on the entransy theory are pointed out and discussed. The related researchers are advised to focus on some new specific application cases to show if the entransy theory is the same as some other theories.展开更多
基金the National Natural Science Foundation of China(Grant No.11875034)the Opening Project of Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology.
文摘We investigate the finite-time performance of a quantum endoreversible Carnot engine cycle and its inverse operation-Carnot refrigeration cycle,employing a spin-1/2 system as the working substance.The thermal machine is alternatively driven by a hot boson bath of inverse temperatureβ_(h)and a cold boson bath at inverse temperatureβ_(c)(>βh).While for the engine model the hot bath is constructed to be squeezed,in the refrigeration cycle the cold bath is established to be squeezed,with squeezing parameter r.We obtain the analytical expressions for both efficiency and power in heat engines and for coefficient of performance and cooling rate in refrigerators.We find that,in the high-temperature limit,the efficiency at maximum power is bounded by the analytical valueη_(+)=√sech(2r)(1-η_(C)),and the coefficient of performance at the maximum figure of merit is limited byε_(+)=√sech(2r)(1+ε_(C))/sech(2r)(1+ε_(C))-εC)-1,whereη_(C)=1-β_(h)/β_(c)andε_(C)=β_(h)/(β_(c)-β_(h))are the respective Carnot values of the engines and refrigerators.These analytical results are identical to those obtained from the Carnot engines based on harmonic systems,indicating that the efficiency at maximum power and coefficient at maximum figure of merit are independent of the working substance.
基金Supported by National Natural Science Foundation of China(11271299,11001221)Northewstern Polytechnical University jichu yanjiu jijin tansuo xiangmu(JC201124)
基金Supported by Natural Science Foundations of China(1126104111271045+2 种基金11461053)Natural Science Foundations of Ningxia(NZ15055)Research Starting Funds for Imported Talents of Ningxia University
基金Supported by National Natural Science Foundation of China(11001130)Fundamental Research Funds for the Central Universities(30917011335)Scientific Research Innovation Project of Jiangsu Province(KYCX17-0327)。
基金partially supported by the grant of Ahi Evran University Scientific Research Projects(FEN 4001.12.0018)partially supported by the grant of Ahi Evran University Scientific Research Projects(FEN 4001.12.0019)+1 种基金by the grant of Science Development Foundation under the President of the Republic of Azerbaijan project EIF-2010-1(1)-40/06-1partially supported by the Scientific and Technological Research Council of Turkey(TUBITAK Project No:110T695)
文摘In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.
基金Project supported by the National Natural Science Foundation of China(Grant No.51376101)the Science Fund for Creative Research Groups,China(Grant No.51321002)
文摘Taking the output power, thermal efficiency, and thermo-economic performance as the optimization objectives, we optimize the operation parameters of a thermodynamic system with combined endoreversible Carnot heat engines in this paper. The applicabilities of the entropy generation minimization and entransy theory to the optimizations are discussed. For the discussed cases, only the entransy loss coefficient is always agreeable to the optimization of thermal efficiency. The applicabilities of the other discussed concepts to the optimizations are conditional. Different concepts and principles are needed for different optimization objectives, and the optimization principles have their application preconditions. When the preconditions are not satisfied, the principles may be not applicable.
基金partially supported by the NSF of China(11171096,11401131)NSF of Hubei Provincial Department of Education(Q20154301)CNPq,Brazil
文摘In this paper, we investigate a horizontal Laplacian version of the clamped plate problem on Carnot groups and obtain some universal inequalities. Furthermore, for the lower order eigenvalues of this eigenvalue problem on carnot groups, we also give some universal inequalities.
基金Project supported by the Youth Programs of Chongqing Three Gorges University,China(Grant No.13QN18)
文摘In this paper, an endoreversible Carnot heat engine with irreversible heat transfer processes is analyzed based on generalized heat transfer law. The applicability of the entropy generation minimization, exergy analyses method, and entransy theory to the analyses is discussed. Three numerical cases are presented. It is shown that the results obtained from the entransy theory are different from those from the entropy generation minimization, which is equivalent to the exergy analyses method. For the first case in which the application preconditions of the entropy generation minimization and entransy loss maximization are satisfied, both smaller entropy generation rate and larger entransy loss rate lead to larger output power. For the second and third cases in which the preconditions are not satisfied, the entropy generation minimization does not lead to the maximum output power, while larger entransy loss rate still leads to larger output power in the third case. For the discussed cases, the concept of entransy dissipation is not applicable for the analyses of output power.The problems in the negative comments on the entransy theory are pointed out and discussed. The related researchers are advised to focus on some new specific application cases to show if the entransy theory is the same as some other theories.
