Algebraic structure and Poisson＇s theory of mechanico-electrical systems

The algebraic structure and Poisson's integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson's integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson's integral theory of the Lagrange--Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.     

q → ∞ limit of the quasitriangular WZW model

Abstract

We study the q → ∞ limit of the q-deformation of the WZW model on a compact simple and simply connected target Lie group. We show that the commutation relations of the q → ∞ current algebra are underlied by certain affine Poisson structure on the group of holomorphic maps from the disc into the complexification of the target group. The Lie algebroid corresponding to this affine Poisson structure can be integrated to a global symplectic groupoid which turns out to be nothing but the phase space of the q → ∞ limit of the q-WZW model. We also show that this symplectic grupoid admits a chiral decomposition compatible with its (anomalous) Poisson-Lie symmetries. Finally, we dualize the chiral theory in a remarkable way and we evaluate the exchange relations for the q → ∞ chiral WZW fields in both the original and the dual pictures.     

The effect of the polytropic index γ on the structure of gaseous detonations

The present study aims to clarify the effect of the polytropic index (i.e., the ratio of specific heats in the context of a perfect gas) on the detonation structure. This is addressed by two-dimensional numerical simulations. To ease the clarification of the role of gasdynamics, a simple Arrhenius kinetic law is used for the chemical model. The activation energy, normalized by the shock temperature, is kept constant to obtain the same reaction rate sensitivity to temperature in all considered mixtures. This procedure dissociates the gasdynamic effects from the chemistry effects. The numerical results reveal that in mixtures with low polytropic indicies, the convective mixing is enhanced compared to mixtures with higher polytropic indicies. The mixing is evaluated using Lagrangian tracers. Moreover, mixtures with low polytropic indicies are found to have a shorter reaction length than mixtures with high polytropic indicies. Also, for the range of parameters considered in this study the results indicate that Mach stem bifurcation in detonations due to jetting is primarily a gasdynamic driven mechanism.     

Kontsevich and Takhtajan Construction of Star Product on the Poisson–Lie Group GL(2)

Comparing the star product defined by Takhtajan on the Poisson–Lie group GL(2) and any star product calculated from the Kontsevich's graphs (any K-star product) on the same group, we show, by direct computation, that the Takhtajan star product on GL(2) can't be written as a K-star product.     

The effect of α, β crystalline structure on the mechanical properties of polypropylene

In order to study the effect of the α,β crystalline structure of polypropylene (PP) on its mechanical properties, it is necessary to prepare samples with variable α/β-phase content but with constant crystallinity and constant spherulite size. With this objective, heat treatment was first defined to be applied to an isotactic PP containing a β nucleating agent in order to achieve these conditions. Then study of the effect of the β-phase content on the tensile properties and fracture behaviour has been done at room temperature. The mechanical properties at fracture were assessed by three-point bending tests and were analysed on the basis of the “Essential Work of Fracture” (EWF). The results show that the elongation at fracture under tensile stress and the “near” Plane-Strain Essential Work of Fracture, w _Ie, increase substantially with the β-phase content. Besides, Young's modulus and the yield stress in tensile tests decrease slowly with the β-phase content. Finally, these results are analysed taking account the differences in structure of the α and β spherulites. Received 18 September 2000 and Received in final form 19 December 2000     

The Hamiltonian dynamics of the soliton of the discrete nonlinear Schrödinger equation

Hamiltonian equations are formulated in terms of collective variables describing the dynamics of the soliton of an integrable nonlinear Schrödinger equation on a 1D lattice. Earlier, similar equations of motion were suggested for the soliton of the nonlinear Schrödinger equation in partial derivatives. The operator of soliton momentum in a discrete chain is defined; this operator is unambiguously related to the velocity of the center of gravity of the soliton. The resulting Hamiltonian equations are similar to those for the continuous nonlinear Schrödinger equation, but the role of the field momentum is played by the summed quasi-momentum of virtual elementary system excitations related to the soliton.     

The influence of molecular structure of protein on the acoustic nonlinearity parameter B/A

I.IntroductionAcousticnonlinearityparameterB/Adescrjbesthenonlilleareffectsofasoundwavetrav-ellingthroughamedium.Withtheapplicationofhighmowerultrasonicwavetomedicine,thenonlineareffectsbecomemoreandmoreimportant.EspeciallybecauseB/Aissensitivetothepathologicalstateofbiologicaltissues[1-2])thisprovidesprospectiveapplicationinmedicaldiagnosis.Atpresent,thestudyinthisareaemphasizesontwoaspects.OneistodevelopnewmedicalimagingtechniquesbyusingthisnonlinearityparameterB/Al1'3-'];theotheristostu…     

The effect of laser surface treatment of Al-Si alloy on the surface hardness and structure

In this paper, some samples of Al-Si alloy with various silicon content were treated by laser beam. The effects on structure, hardness and substructure of samples were investigated. The experimental results show that the primary crystal Al and eutectic silicon in the laser treated samples is got thinning obviously, the mosaic dimension is decreased and the dislocation density is increased.     

The effect of frenkel defects on the electronic structure of 1T−TiSe2

Using a tight binding formalism the wave vector resolved electronic density of states has been calculated in the coherent potential approximation for an 1 T–TiSe₂ crystal containing Frenkel defects. Additional structure originating from disorder is discussed. An extra peak in the A direction at 1.5 eV binding energy can be traced back to a resonance caused by titanium vacancies.     

New results on the moments of the eigenvalues of the Schrödinger Hamiltonian and applications

We show that the moments of order of the eigenvalues of the Schrödinger Hamiltonian inn dimensions can be related to moments of order less than or equal to -1/2 inn+1 dimensions. This makes it possible to improved the bounds on the sum of the eigenvalues in three dimensions and consequently the Lieb-Thiirng bound on the binding energy of matter.     

Influence of structure disorders and temperaturesof systems on the bio-energy transport in proteinmolecules (Ⅱ)

The influence of molecular structure disorders and physiological temperature on the states and properties of solitons as transporters of bio-energy are numerically studied through the fourth-order Runge-Kutta method and a new theory based on my paper [Front. Phys. China, 2007, 2(4): 469]. The structure disorders include fluctuations in the characteristic parameters of the spring constant, dipole-dipole interaction constant and exciton-phonon coupling constant, as well as the chain-chain interaction coefficient among the three channels and ground state energy resulting from the disorder distributions of masses of amino acid residues and impurities. In this paper, we investigate the behaviors and states of solitons in a single protein molecular chain, and in α-Helix protein molecules with three channels. In the former we prove first that the new solitons can move without dispersion, retaining its shape, velocity and energy in a uniform and periodic protein molecule. In this case of structure disorder, the fluctuations of the spring constant, dipole-dipole interaction constant and exciton-phonon coupling constant, as well as the ground state energy and the disorder distributions of masses of amino acid residues of the proteins influence the states and properties of motion of solitons. However, they are still quite stable and are very robust against these structure disorders, even in the presence of larger disorders in the sequence of masses, spring constants and coupling constants. Still, the solitons may disperse or be destroyed when the disorder distribution of the masses and fluctuations of structure parameters are quite great. If the effect of thermal perturbation of the environment on the soliton in nonuniform proteins is considered again, it is still thermally stable at the biological temperature of 300 K, and at the longer time period of 300 ps and larger spacing of 400 amino acids. The new soliton is also thermally stable in the case of motion over a long time period of 300 ps in the region of 300–320 K under the influence of the above structure disorders. However, the soliton disperses in the case of a higher temperature of 325 K and in larger structure disorders. Thus, we determine that the soliton’s lifetime and critical temperature are 300 ps and 300–320 K, respectively. These results are also consistent with analytical data obtained via quantum perturbed theory. In α-Helix protein molecules with three channels, results obtained show that these structure disorders and quantum fluctuations can change the states and features of solitons, decrease their amplitudes, energies and velocities, but they still cannot destroy the solitons, which can still transport steadily along the molecular chains while retaining energy and momentum when the quantum fluctuations are small, such as in structure disorders and quantum fluctuations of and and . Therefore, the solitons in the improved model are quite robust against these disorder effects. However, the solitons may be dispersed or disrupted in cases of very large structure disorders. When the influence of temperature on solitons is considered, we find that the new solitons can transport steadily over 333 amino acid residues in the case of motion over a long time period of 120 ps, and can retain their shapes and energies to travel forward along protein molecules after mutual collision of the solitons at the biological temperature of 300 K. Therefore, the soliton is also very robust against thermal perturbation of the α-helix protein molecules at 300 K. However, the soliton disperses in cases of higher temperatures at 325 K and in larger structure disorders. Thus, their critical temperature is about 320 K. When the effects of structure disorder and temperature are considered simultaneously, the soliton has high thermal stability and can transport for a long time along the protein molecular chains while retaining its amplitude, energy and velocity, even though the fluctuations of the structure parameters and temperature of the medium increase continually. However, the soliton disperses in the larger fluctuations of and at T=300 K, and at temperatures higher than 315 K when the fluctuations are and . This means that the critical temperature of the soliton is only 315 K in this condition. In a word, we can conclude from the above investigations that the soliton in the improved model is very robust against the structure disorders and thermal perturbation of proteins at the biological temperature of 300 K in α-helix protein molecules, and is a possible bio-energy transport carrier; the improved model is a possible candidate for the mechanism of this transport.      

The threshold photoproduction of π0 on nucleons and on few-nucleon systems

The absolute value of the π⁰ photoproduction cross section on the proton recently measured near threshold enables to reanalyze previous data collected on ²H, ³He, and ⁴He relatively to the proton. Absolute cross sections are presented for these nuclei in the energy region extending up to 10 MeV above threshold. The threshold s-wave amplitudes for ²H and ³He thus obtained are discussed in relation with the neutron threshold amplitude E^(nπ0)₀₊ value.     

On the hopf structure of U p,q (gl(1∣1)) and the universal T-matrix of fun p,q (GL(1∣1))

The dually conjugate Hopf superalgebras Fun _p,q (GL(11)) and U _p,q (gl(11)) are studied using the Frønsdal-Galindo approach and the full Hopf structure of U _p,q (gl(11)) is extracted. A finite expression for the universal T-matrix, identified with the dual form and expressing the generalization of the exponential map of the classical groups, is obtained for Fun _p,q (GL(11)). In a representation with a colour index, the T-matrix assumes a form that satisfies a coloured graded Yang-Baxter equation.     

Quantum-size effects in the electronic structure of low-dimensional metallic systems

By angle-resolved photoemission the electronic structure of quantum films of Mg, Ag, and Au has been compared on W(110) and Mo(110) substrates which are structurally and electronically very similar but differ in atomic number. In all cases, substrate-induced states with characteristic dispersions are observed in the region of a bulk band gap of the substrate. Based on the comparison between Mo and W, we can exclude that previously observed Mg states are spin-orbit split but observe a spin-orbit splitting in Ag and Au monolayers. This splitting is mainly caused by the substrate because it does not differ much between Ag and Au overlayers despite the large difference in atomic number.     

Integrable Hamiltonian systems related to the Hilbert–Schmidt ideal

By the application of the coinduction method as well as the Magri method to the ideal of real Hilbert–Schmidt operators we construct the hierarchies of integrable Hamiltonian systems on Banach Lie–Poisson spaces which consist of such types of operators. We also discuss their algebraic and analytic properties and solve them in dimensions, N=2,3,4$N=2,3,4$.     

On bi-hamiltonian structure of some integrable systems on so* (4)

Abstract

We classify quadratic Poisson structures on so*(4) and e*(3), which have the same foliations by symplectic leaves as canonical Lie-Poisson tensors. The separated variables for some of the corresponding bi-integrable systems are constructed.