A description of inverse energy cascade(from small scale to large scale)in homogeneous isotropic turbulence is introduced by using an eigenvalue method.We show a special isotropic turbulence,in which the initial condi...A description of inverse energy cascade(from small scale to large scale)in homogeneous isotropic turbulence is introduced by using an eigenvalue method.We show a special isotropic turbulence,in which the initial condition is constructed by reversing the velocity field in space,i.e.,the time-reversed turbulence.It is shown that the product of eigenvalues of the rate-of-strain tensor can quantitatively describe the backward energy transfer process.This description is consistent to the velocity derivative skewness Sk.However,compared with Sk,it is easier to be obtained,and it is expected to be extended to anisotropic turbulence.Furthermore,this description also works for the resolved velocity field,which means that it can be used in engineering turbulent flows.The description presented here is desired to inspire future investigation for the modeling of the backward energy transfer process and lay the foundation for the accurate prediction of complex flows.展开更多
In this paper, we consider the two-dimensional complex Ginzburg–Landau equation(CGLE) as the spatiotemporal model, and an expression of energy eigenvalue is derived by using the phase-amplitude representation and the...In this paper, we consider the two-dimensional complex Ginzburg–Landau equation(CGLE) as the spatiotemporal model, and an expression of energy eigenvalue is derived by using the phase-amplitude representation and the basic ideas from quantum mechanics. By numerical simulation, we find the energy eigenvalue in the CGLE system can be divided into two parts, corresponding to spiral wave and bulk oscillation. The energy eigenvalue of spiral wave is positive, which shows that it propagates outwardly; while the energy eigenvalue of spiral wave is negative, which shows that it propagates inwardly. There is a necessary condition for generating a spiral wave that the energy eigenvalue of spiral wave is greater than bulk oscillation. A wave with larger energy eigenvalue dominates when it competes with another wave with smaller energy eigenvalue in the space of the CGLE system. At the end of this study, a tentative discussion of the relationship between wave propagation and energy transmission is given.展开更多
A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential c...A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.展开更多
We compute the dark energy and ordinary energy density of the cosmos as a double Eigenvalue problem. In addition, we validate the result using two different theories. The first theory is based on Witten’s 11 dimensio...We compute the dark energy and ordinary energy density of the cosmos as a double Eigenvalue problem. In addition, we validate the result using two different theories. The first theory is based on Witten’s 11 dimensional spacetime and the second is based on ‘tHooft’s fractal renormalization spacetime. In all cases, the robust result is E(O) = mc2/22 for ordinary energy and E(D) = mc2(21/22) for dark energy. Adding E(O) to E(D) we obtain Einstein’s famous equation which confirms special relativity, although it adds a quantum twist to its interpretation. This new interpretation is vital because it brings relativity theory in line with modern cosmological measurements and observations. In particular, we replace calculus by Weyl scaling in all computation which is essentially transfinite discrete.展开更多
There is no any spin rotational construction for zero spin particle, Casimir operator and the thired component of zero spin particle areandrespectively. Further, there are no spin interactions between zero spin partic...There is no any spin rotational construction for zero spin particle, Casimir operator and the thired component of zero spin particle areandrespectively. Further, there are no spin interactions between zero spin particle and other spin particles. This paper shows: in Spin Topological Space, STS [1], the third component of zero spin particle possesses non-zero eigenvalues besides original zero value, this leads to a miraculous spin interaction phenomenon between zero spin particle and other spin particles. In STS, zero spin particle could "dissolve other spin particles", degrade the values of their Casimir operator, and decay these spin particles into other forms of spin particle.展开更多
This paper proves that if the energy density of a harmonic map to a unit sphere varies between two successive half eigenvalues, then it must be one of them. Applying this result to the Gaussian maps of some submanifol...This paper proves that if the energy density of a harmonic map to a unit sphere varies between two successive half eigenvalues, then it must be one of them. Applying this result to the Gaussian maps of some submanifolds, the quantum phenomena of the square length of the second fundamental forms of these submanifolds is obtained. Some related topics are discussed in this note.展开更多
Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the f...Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.展开更多
Let G be a simple graph with n vertices and m edges. Let λ1, λ2,…, λn, be the adjacency spectrum of G, and let μ1, μ2,…, μn be the Laplacian spectrum of G. The energy of G is E（G） = n∑i=1｜λi｜, while the ...Let G be a simple graph with n vertices and m edges. Let λ1, λ2,…, λn, be the adjacency spectrum of G, and let μ1, μ2,…, μn be the Laplacian spectrum of G. The energy of G is E（G） = n∑i=1｜λi｜, while the Laplacian energy of G is defined as LE（G） = n∑i=1｜μi-2m/n｜ Let γ1, γ2, ~ …, γn be the eigenvalues of Hermite matrix A. The energy of Hermite matrix as HE（A） = n∑i=1｜γi-tr（A）/n｜ is defined and investigated in this paper. It is a natural generalization of E（G） and LE（G）. Thus all properties about energy in unity can be handled by HE（A）.展开更多
A new adaptive technique of r-and h-version for vibration problemsutilizing the matrix per- turbation theory and element energy ratiois proposed. In structural vibration analysis, through the r-conver-gence adaptvie f...A new adaptive technique of r-and h-version for vibration problemsutilizing the matrix per- turbation theory and element energy ratiois proposed. In structural vibration analysis, through the r-conver-gence adaptvie finite element process, mesh optimization can berealized. In the light of the judgement on the changes in themagnitude of the element energy ratio, local refinement can beachieved in the process of h- convergence adaptive finite element sothat more accurate finite element solutions can be obtained with asfew meshes as possible. Many numerical examples are given and theproposed approach is shown to be feasible and effective.展开更多
For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is C...For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. In this note, we establish lower bounds for the distance energy of circulant graphs. In particular, we discuss upper bound of distance energy for the 4-circulant graph.展开更多
Complex networks have been a prominent topic of research for several years,spanning a wide range of fields from mathematics to computer science and also to social and biological sciences.The eigenvalues of the Seidel ...Complex networks have been a prominent topic of research for several years,spanning a wide range of fields from mathematics to computer science and also to social and biological sciences.The eigenvalues of the Seidel matrix,Seidel Signless Laplacian matrix,Seidel energy,Seidel Signless Laplacian energy,Maximum and Minimum energy,Degree Sum energy and Distance Degree energy of the Unitary Cayley graphs[UCG]have been calculated.Low-power devices must be able to transfer data across long distances with low delay and reliability.To overcome this drawback a small-world network depending on the unitary Cayley graph is proposed to decrease the delay and increase the reliability and is also used to create and analyze network communication.Small-world networks based on the Cayley graph have a basic construction and are highly adaptable.The simulation result shows that the small-world network based on unitary Cayley graphs has a shorter delay and is more reliable.Furthermore,the maximum delay is lowered by 40%.展开更多
Randićenergy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randićenergy RE<sub>C</sub> (G) of a graph G in this paper. This p...Randićenergy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randićenergy RE<sub>C</sub> (G) of a graph G in this paper. This paper contains computation of minimum covering Randićenergies for some standard graphs like star graph, complete graph, thorn graph of complete graph, crown graph, complete bipartite graph, cocktail graph and friendship graphs. At the end of this paper, upper and lower bounds for minimum covering Randićenergy are also presented.展开更多
In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ,?,?NCN-energy for some standard graphs is obtained and an upper bound for ?is found when G is a strongly regular graph....In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ,?,?NCN-energy for some standard graphs is obtained and an upper bound for ?is found when G is a strongly regular graph. Also the relation between common neigh-bourhood energy and non-common neighbourhood energy of a graph is established.展开更多
With the rapid integration of renewable energy,wide-band oscillations caused by interactions between power electronic equipment and grids have emerged as one of the most critical stability issues.Existing methods are ...With the rapid integration of renewable energy,wide-band oscillations caused by interactions between power electronic equipment and grids have emerged as one of the most critical stability issues.Existing methods are usually studied for local power systems with around one hundred nodes.However,for a large-scale power system with tens of thousands of nodes,the dimension of transfer function matrix or the order of characteristic equation is much higher.In this case,the existing methods such as eigenvalue analysis method and impedance-based method have difficulty in computation and are thus hard to utilize in practice.To fill this gap,this paper proposes a novel method named the smallest eigenvalues based logarithmic derivative(SELD)method.It obtains the dominant oscillation modes by the logarithmic derivative of the k-smallest eigenvalue curves of the sparse extended nodal admittance matrix(NAM).An oscillatory stability analysis tool is further developed based on this method.The effectiveness of the method and the tool is validated through a local power system as well as a large-scale power system.展开更多
基金the National Natural Science Foundation of China(Nos.12002318 and51976203)the Central Government Guides Local Science and Technology Development Fund Projects(No.YDZX20191400002850)the Science Foundation of North University of China(No.XJJ201929)。
文摘A description of inverse energy cascade(from small scale to large scale)in homogeneous isotropic turbulence is introduced by using an eigenvalue method.We show a special isotropic turbulence,in which the initial condition is constructed by reversing the velocity field in space,i.e.,the time-reversed turbulence.It is shown that the product of eigenvalues of the rate-of-strain tensor can quantitatively describe the backward energy transfer process.This description is consistent to the velocity derivative skewness Sk.However,compared with Sk,it is easier to be obtained,and it is expected to be extended to anisotropic turbulence.Furthermore,this description also works for the resolved velocity field,which means that it can be used in engineering turbulent flows.The description presented here is desired to inspire future investigation for the modeling of the backward energy transfer process and lay the foundation for the accurate prediction of complex flows.
基金Supported by the Basic Research Project of Shenzhen,China under Grant Nos.JCYJ 20140418181958489 and 20160422144751573
文摘In this paper, we consider the two-dimensional complex Ginzburg–Landau equation(CGLE) as the spatiotemporal model, and an expression of energy eigenvalue is derived by using the phase-amplitude representation and the basic ideas from quantum mechanics. By numerical simulation, we find the energy eigenvalue in the CGLE system can be divided into two parts, corresponding to spiral wave and bulk oscillation. The energy eigenvalue of spiral wave is positive, which shows that it propagates outwardly; while the energy eigenvalue of spiral wave is negative, which shows that it propagates inwardly. There is a necessary condition for generating a spiral wave that the energy eigenvalue of spiral wave is greater than bulk oscillation. A wave with larger energy eigenvalue dominates when it competes with another wave with smaller energy eigenvalue in the space of the CGLE system. At the end of this study, a tentative discussion of the relationship between wave propagation and energy transmission is given.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60877055 and 60806041)the Shanghai Rising-Star Program,China (Grant No. 08QA14030)+1 种基金the Innovation Funds for Graduates of Shanghai University,China (Grant No. SHUCX092021)the Foundation of the Science and Technology Commission of Shanghai Municipality,China (Grant No. 08JC14097)
文摘A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.
文摘We compute the dark energy and ordinary energy density of the cosmos as a double Eigenvalue problem. In addition, we validate the result using two different theories. The first theory is based on Witten’s 11 dimensional spacetime and the second is based on ‘tHooft’s fractal renormalization spacetime. In all cases, the robust result is E(O) = mc2/22 for ordinary energy and E(D) = mc2(21/22) for dark energy. Adding E(O) to E(D) we obtain Einstein’s famous equation which confirms special relativity, although it adds a quantum twist to its interpretation. This new interpretation is vital because it brings relativity theory in line with modern cosmological measurements and observations. In particular, we replace calculus by Weyl scaling in all computation which is essentially transfinite discrete.
文摘There is no any spin rotational construction for zero spin particle, Casimir operator and the thired component of zero spin particle areandrespectively. Further, there are no spin interactions between zero spin particle and other spin particles. This paper shows: in Spin Topological Space, STS [1], the third component of zero spin particle possesses non-zero eigenvalues besides original zero value, this leads to a miraculous spin interaction phenomenon between zero spin particle and other spin particles. In STS, zero spin particle could "dissolve other spin particles", degrade the values of their Casimir operator, and decay these spin particles into other forms of spin particle.
基金Research supported by the NNSF of China (10071021)
文摘This paper proves that if the energy density of a harmonic map to a unit sphere varies between two successive half eigenvalues, then it must be one of them. Applying this result to the Gaussian maps of some submanifolds, the quantum phenomena of the square length of the second fundamental forms of these submanifolds is obtained. Some related topics are discussed in this note.
文摘Using the asymptotic iteration method, we obtain the S-wave solution for a short-range three-parameter central potential with 1/r singularity and with a non-orbital barrier. To the best of our knowledge, this is the first attempt at calculating the energy spectrum for this potential, which was introduced by H. Bahlouli and A. D. Alhaidari and for which they obtained the “potential parameter spectrum”. Our results are also independently verified using a direct method of diagonalizing the Hamiltonian matrix in the J-matrix basis.
基金supported by the National Natural Science Foundation of China(10771080)
文摘Let G be a simple graph with n vertices and m edges. Let λ1, λ2,…, λn, be the adjacency spectrum of G, and let μ1, μ2,…, μn be the Laplacian spectrum of G. The energy of G is E（G） = n∑i=1｜λi｜, while the Laplacian energy of G is defined as LE（G） = n∑i=1｜μi-2m/n｜ Let γ1, γ2, ~ …, γn be the eigenvalues of Hermite matrix A. The energy of Hermite matrix as HE（A） = n∑i=1｜γi-tr（A）/n｜ is defined and investigated in this paper. It is a natural generalization of E（G） and LE（G）. Thus all properties about energy in unity can be handled by HE（A）.
基金the National Natural Science Foundation of China (No.19872029)
文摘A new adaptive technique of r-and h-version for vibration problemsutilizing the matrix per- turbation theory and element energy ratiois proposed. In structural vibration analysis, through the r-conver-gence adaptvie finite element process, mesh optimization can berealized. In the light of the judgement on the changes in themagnitude of the element energy ratio, local refinement can beachieved in the process of h- convergence adaptive finite element sothat more accurate finite element solutions can be obtained with asfew meshes as possible. Many numerical examples are given and theproposed approach is shown to be feasible and effective.
基金Project Supported by Scientific Research Fund of Hunan Provincial Education Department(15C1235)
文摘For a connected graph G, the distance energy of G is a recently developed energytype invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix G. A graph is called circulant if it is Cayley graph on the circulant group, i.e., its adjacency matrix is circulant. In this note, we establish lower bounds for the distance energy of circulant graphs. In particular, we discuss upper bound of distance energy for the 4-circulant graph.
文摘Complex networks have been a prominent topic of research for several years,spanning a wide range of fields from mathematics to computer science and also to social and biological sciences.The eigenvalues of the Seidel matrix,Seidel Signless Laplacian matrix,Seidel energy,Seidel Signless Laplacian energy,Maximum and Minimum energy,Degree Sum energy and Distance Degree energy of the Unitary Cayley graphs[UCG]have been calculated.Low-power devices must be able to transfer data across long distances with low delay and reliability.To overcome this drawback a small-world network depending on the unitary Cayley graph is proposed to decrease the delay and increase the reliability and is also used to create and analyze network communication.Small-world networks based on the Cayley graph have a basic construction and are highly adaptable.The simulation result shows that the small-world network based on unitary Cayley graphs has a shorter delay and is more reliable.Furthermore,the maximum delay is lowered by 40%.
文摘Randićenergy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randićenergy RE<sub>C</sub> (G) of a graph G in this paper. This paper contains computation of minimum covering Randićenergies for some standard graphs like star graph, complete graph, thorn graph of complete graph, crown graph, complete bipartite graph, cocktail graph and friendship graphs. At the end of this paper, upper and lower bounds for minimum covering Randićenergy are also presented.
文摘In this paper, we introduce a new type of graph energy called the non-common-neighborhood energy ,?,?NCN-energy for some standard graphs is obtained and an upper bound for ?is found when G is a strongly regular graph. Also the relation between common neigh-bourhood energy and non-common neighbourhood energy of a graph is established.
基金supported by the National Natural Science Foundation of China(No.52321004)the Delta Power Electronics Science and Education Development Program of Delta Group.
文摘With the rapid integration of renewable energy,wide-band oscillations caused by interactions between power electronic equipment and grids have emerged as one of the most critical stability issues.Existing methods are usually studied for local power systems with around one hundred nodes.However,for a large-scale power system with tens of thousands of nodes,the dimension of transfer function matrix or the order of characteristic equation is much higher.In this case,the existing methods such as eigenvalue analysis method and impedance-based method have difficulty in computation and are thus hard to utilize in practice.To fill this gap,this paper proposes a novel method named the smallest eigenvalues based logarithmic derivative(SELD)method.It obtains the dominant oscillation modes by the logarithmic derivative of the k-smallest eigenvalue curves of the sparse extended nodal admittance matrix(NAM).An oscillatory stability analysis tool is further developed based on this method.The effectiveness of the method and the tool is validated through a local power system as well as a large-scale power system.
