We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional (1D) strongly attractive Fermi gases with SU(w) symmetry. These physical quantities ...We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional (1D) strongly attractive Fermi gases with SU(w) symmetry. These physical quantities provide a rigorous understanding on a universality class of quantum criticality characterized by the critical exponents z = 2 and correlation length exponent v= 1/2. Such a universality class of quantum criticality can occur when the Fermi sea of one branch of charge bound states starts to fill or becomes gapped at zero temperature. The quantum critical cone can be determined by the double peaks in specific heat, which serve to mark two crossover temperatures fanning out from the critical point. Our method opens to further study on quantum phases and phase transitions in strongly interacting fermions with large SU ( w) and non-SU ( w ) symmetries in one dimension.展开更多
The enhanced definition of Mechatronics involves the four underlying characteristics of integrated,unified,unique,and systematic approaches.In this realm,Mechatronics is not limited to electro-mechanical systems,in th...The enhanced definition of Mechatronics involves the four underlying characteristics of integrated,unified,unique,and systematic approaches.In this realm,Mechatronics is not limited to electro-mechanical systems,in the multi-physics sense,but involves other physical domains such as fluid and thermal.This paper summarizes the mechatronic approach to modeling.Linear graphs facilitate the development of state-space models of mechatronic systems,through this approach.The use of linear graphs in mechatronic modeling is outlined and an illustrative example of sound system modeling is given.Both time-domain and frequency-domain approaches are presented for the use of linear graphs.A mechatronic model of a multi-physics system may be simplified by converting all the physical domains into an equivalent single-domain system that is entirely in the output domain of the system.This approach of converting(transforming)physical domains is presented.An illustrative example of a pressure-controlled hydraulic actuator system that operates a mechanical load is given.展开更多
In this paper,we investigate the fifth-order modified Korteweg-de Vries(mKdV)equation on the half-line via the Fokas unified transformation approach.We show that the solution u(x,t)of the fifth-order mKdV equation can...In this paper,we investigate the fifth-order modified Korteweg-de Vries(mKdV)equation on the half-line via the Fokas unified transformation approach.We show that the solution u(x,t)of the fifth-order mKdV equation can be represented by the solution of the matrix Riemann-Hilbert problem constructed on the plane of complex spectral parameter θ.The jump matrix L(x,t,θ)has an explicit representation dependent on x,t and it can be represented exactly by the two pairs of spectral functions y(θ),z(θ)(obtained from the initial value u0(x))and Y(θ),Z(θ)(obtained from the boundary conditions v0(t),{vk(t)}_(1)^(4)).Furthermore,the two pairs of spectral functions y(θ),z(θ)and Y(θ),Z(θ)are not independent of each other,but are related to the compatibility condition,the so-called global relation.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 11374331the key NSFC under Grant No11534014partially supported by the Australian Research Council
文摘We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional (1D) strongly attractive Fermi gases with SU(w) symmetry. These physical quantities provide a rigorous understanding on a universality class of quantum criticality characterized by the critical exponents z = 2 and correlation length exponent v= 1/2. Such a universality class of quantum criticality can occur when the Fermi sea of one branch of charge bound states starts to fill or becomes gapped at zero temperature. The quantum critical cone can be determined by the double peaks in specific heat, which serve to mark two crossover temperatures fanning out from the critical point. Our method opens to further study on quantum phases and phase transitions in strongly interacting fermions with large SU ( w) and non-SU ( w ) symmetries in one dimension.
基金supported by research grants from the Natural Sciences and Engineering Research Council(NSERC)of Canada
文摘The enhanced definition of Mechatronics involves the four underlying characteristics of integrated,unified,unique,and systematic approaches.In this realm,Mechatronics is not limited to electro-mechanical systems,in the multi-physics sense,but involves other physical domains such as fluid and thermal.This paper summarizes the mechatronic approach to modeling.Linear graphs facilitate the development of state-space models of mechatronic systems,through this approach.The use of linear graphs in mechatronic modeling is outlined and an illustrative example of sound system modeling is given.Both time-domain and frequency-domain approaches are presented for the use of linear graphs.A mechatronic model of a multi-physics system may be simplified by converting all the physical domains into an equivalent single-domain system that is entirely in the output domain of the system.This approach of converting(transforming)physical domains is presented.An illustrative example of a pressure-controlled hydraulic actuator system that operates a mechanical load is given.
基金supported by the National Natural Science Foundation of China under Grant Nos.12147115 and 11835011the Natural Science Foundation of Anhui Province under Grant No.2108085QA09+3 种基金the University Natural Science Research Project of Anhui Province under Grant No.KJ2021A1094China Postdoctoral Science Foundation under Grant No.2022M712833the Program for Science and Technology Innovation Talents in Universities of Henan Province under Grant No.22HASTIT019the Natural Science Foundation of Henan Province under Grant No.202300410524
文摘In this paper,we investigate the fifth-order modified Korteweg-de Vries(mKdV)equation on the half-line via the Fokas unified transformation approach.We show that the solution u(x,t)of the fifth-order mKdV equation can be represented by the solution of the matrix Riemann-Hilbert problem constructed on the plane of complex spectral parameter θ.The jump matrix L(x,t,θ)has an explicit representation dependent on x,t and it can be represented exactly by the two pairs of spectral functions y(θ),z(θ)(obtained from the initial value u0(x))and Y(θ),Z(θ)(obtained from the boundary conditions v0(t),{vk(t)}_(1)^(4)).Furthermore,the two pairs of spectral functions y(θ),z(θ)and Y(θ),Z(θ)are not independent of each other,but are related to the compatibility condition,the so-called global relation.