Showing papers in "International Journal of Modern Physics B in 2006"

Some asymptotic methods for strongly nonlinear equations

Abstract: This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modied perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are emphasized: (1) variational approaches, (2) parameter-expanding methods, (3) parameterized perturbation method, (4) homotopy perturbation method (5) iteration perturbation method, and ancient Chinese methods. The emphasis of this article is put mainly on the developments in this eld in China so the references, therefore, are not exhaustive.

Addendum:. New Interpretation of Homotopy Perturbation Method

Abstract: The present work constitutes a guided tour through the mathematics needed for a proper understanding of homotopy perturbation method as applied to various nonlinear problems. It gives a new interpretation of the concept of constant expansion in the homotopy perturbation method.

Phase transitions in self-gravitating systems

Abstract: We discuss the nature of phase transitions in self-gravitating systems. We show the connection between the binary star model of Padmanabhan, the thermodynamics of stellar systems and the thermodynamics of self-gravitating fermions. We stress the inequivalence of statistical ensembles for systems with long-range interactions, like gravity. In particular, we contrast the microcanonical evolution of stellar systems from the canonical evolution of self-gravitating Brownian particles. At low energies, self-gravitating Hamiltonian systems experience a gravothermal catastrophe in the microcanonical ensemble. At low temperatures, self-gravitating Brownian systems experience an isothermal collapse in the canonical ensemble. For classical particles, the gravothermal catastrophe leads to a binary star surrounded by a hot halo while the isothermal collapse leads to a Dirac peak containing all the mass. For self-gravitating fermions, the collapse stops when quantum degeneracy comes into play through the Pauli exclusio...

Dichotomous markov noise: exact results for out-of-equilibrium systems

Abstract: Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on analytically-solvable situations. In particular, it has escaped attention till recently that the standard results for the long-time properties of such systems cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present a few relevant applications — the hypersensitive transport, the rocking ratchet, and the stochastic Stokes' drift. These results reinforce the impression that dichotomous noise can be put on par with Gaussian white noise as far as obtaining analytical results is concerned. They convincingly illustrate the interplay between noise and nonlinearity in generating nontrivial behaviors of nonequilibrium systems and point to various practical applications.

Chaos synchronization of fractional-order differential systems

Abstract: Chaos synchronization of the Duffing, Lorenz and Rossler systems with fractional orders are studied theoretically and numerically. Three methods are applied in this paper: combination of active-passive decomposition (APD) and one-way coupling methods, Pecora–Carroll method, bidirectional coupling method. The sufficient conditions of achieving synchronization between two identical fractional systems are derived by using the Laplace transform theory. Numerical simulations demonstrate the effectiveness of the proposed synchronization schemes for these fractional systems.

Spin hall effect

Abstract: The intrinsic spin Hall effect in semiconductors has developed to a remarkably lively and rapidly growing branch of research in the field of semiconductor spintronics. In this article we give a pedagogical overview on both theoretical and experimental accomplishments and challenges. Emphasis is put on the the description of the intrinsic mechanisms of spin Hall transport in III-V zinc-blende semiconductors and on the effects of dissipation.

Simplified thermal lattice Boltzmann in incompressible limit

Abstract: In this paper, an incompressible thermohydrodynamics for the lattice Boltzmann scheme is developed. The basic idea is to solve the velocity field and the temperature field using two different distribution functions. A derivation of the lattice Boltzmann scheme from the continuous Boltzmann equation is discussed in detail. By using the same procedure as in the derivation of the discretised density distribution function, we found that a new lattice of four-velocity model for internal energy density distribution function can be developed where the viscous and compressive heating effects are negligible. This model is validated by the numerical simulation of the porous plate couette flow problem where the analytical solution exists and the natural convection flows in a square cavity.

Dimers on two-dimensional lattices

Abstract: We consider close-packed dimers, or perfect matchings, on two-dimensional regular lattices. We review known results and derive new expressions for the free energy, entropy, and the molecular freedom of dimers for a number of lattices including the simple-quartic, honeycomb, triangular, kagome, 3-12 and its dual, and 4-8 and its dual Union Jack lattices. The occurrence and nature of phase transitions are also elucidated and discussed in each case.

a SU(2) Recipe for Mutually Unbiased Bases

Abstract: A simple recipe for generating a complete set of mutually unbiased bases in dimension 2j + 1, with 2j integer and 2j + 1 prime, is developed from a single matrix Va acting on a space of constant angular momentum j and defined in terms of the irreducible characters of the cyclic group C2j + 1. This recipe yields an (apparently new) compact formula for the vectors spanning the various mutually unbiased bases. In dimension (2j + 1)e, with 2j integer, 2j + 1 prime and e positive integer, the use of direct products of matrices of type Va makes it possible to generate mutually unbiased bases. As two pending results, the matrix Va is used in the derivation of a polar decomposition of SU(2) and of a FFZ algebra.

Mean-Field Expansion in Bose-Einstein Condensates with Finite-Range Interactions

Abstract: We present a formal derivation of the mean-field expansion for dilute Bose–Einstein condensates with two-particle interaction potentials which are weak and finite-range, but otherwise arbitrary. The expansion allows for a controlled investigation of the impact of microscopic interaction details (e.g. the scaling behavior) on the mean-field approach and the induced higher-order corrections beyond the s-wave scattering approximation.

INTERPOLATING STATISTICS AND q-DEFORMED OSCILLATOR ALGEBRAS

Abstract: The idea that a system obeying interpolating statistics can be described by a deformed oscillator algebra, or quantum groups, has been an outstanding issue. We are able to demonstrate that a q-deformed oscillator algebra can be used to describe the statistics of particles which provide a continuous interpolation between Bose and Fermi statistics. We show that the generalized intermediate statistics splits into Boson-like and Fermion-like regimes, each described by a unique oscillator algebra. The thermostatistics of Boson-like particles is described by employing q-calculus based on the Jackson derivative while the Fermion-like particles are described by ordinary derivatives of thermodynamics. Thermodynamic functions for systems of both types are determined and examined.

The emission effects by the use of biodiesel fuel

Abstract: The smoke emission of diesel engine is being recognized as the main cause for the serious air pollution related problem affecting our environment. In this study, we investigated the possibility of biodiesel fuel to reduce smoke emission as an alternative fuel for diesel engine. Additionally, gas chromatography was used to analyze not only total amount of HC(hydrocarbon) but also the amount of HC components from C1 to C6 in the exhaust gas to determine the exact source responsible for the remarkable reduction in the amount of smoke emission. Because biodiesel fuel has about 10 vol-% oxygen content, the combustion process of the diesel engine is improved and exhausted smoke emission density especially decreased.

Limit Cycle and Conserved Dynamics

Abstract: We demonstrate here that the potential can coexist with limit cycle in nonlinear dissipative dynamics, where the potential plays the driving role for dynamics and determines the final steady state distribution in a manner similar to other situations in physics. First, we show the existence of limit cycle from a typical physics setting by an explicit construction: the potential is of the Mexican-hat shape, the strength of the magnetic field scales with that of the potential gradient near the limit cycle, and the friction goes to zero faster than that of potential gradient when approaching to the limit cycle. The dynamics at the limit cycle is conserved in this limit. The diffusion matrix is nevertheless finite at the limit cycle. Second, based on the physics knowledge, we construct the potential in the dynamics with limit cycle in a typical dynamical systems setting. Third, we argue that such a construction can be, in principle, carried out in a general situation combined with a novel method. Our present result may be useful in many applications, such as in the discussion of metastability of limit cycle and in the construction of Hopfield potential in the neural network computation.

Transport Equations from Liouville Equations for Fractional Systems

Abstract: We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the fractional systems are non-Hamiltonian. Generalized transport equation is derived from Liouville and Bogoliubov equations for fractional systems. Fractional generalization of average values and reduced distribution functions are dened. Gasdynamic equations for fractional systems are derived from the generalized transport equation.

Angular momentum and mutually unbiased bases

Abstract: The Lie algebra of the group SU2 is constructed from two deformed oscillator algebras for which the deformation parameter is a root of unity. This leads to an unusual quantization scheme, the {J2, Ur} scheme, an alternative to the familiar {J2, Jz} quantization scheme corresponding to common eigenvectors of the Casimir operator J2 and the Cartan operator Jz. A connection is established between the eigenvectors of the complete set of commuting operators {J2, Ur} and mutually unbiased bases in spaces of constant angular momentum.

Microscopic Quantum Mechanical Foundation of Fourier's Law

Abstract: Besides the growing interest in old concepts such as temperature and entropy at the nanoscale, theories of relaxation and transport have recently regained a lot of attention. With the electronic circuits and computer chips getting smaller and smaller, a fresh look on the equilibrium and nonequilibrium thermodynamics at small length scales far below the thermodynamic limit, i.e. on the theoretical understanding of original macroscopic processes, e.g. transport of energy, heat, charge, mass, magnetization, etc., should be appropriate. Only from the foundations of a theory its limits of applicability may be inferred. This review tries to give an overview on the background and recent developments in the field of nonequilibrium quantum thermodynamics, focusing on the transport of heat in small quantum systems.

Projected entangled states: properties and applications

Abstract: We present a new characterization of quantum states, what we call Projected Entangled-Pair States (PEPS). This characterization is based on constructing pairs of maximally entangled states in a Hilbert space of dimension D^2, and then projecting those states in subspaces of dimension d. In one dimension, one recovers the familiar matrix product states, whereas in higher dimensions this procedure gives rise to other interesting states. We have used this new parametrization to construct numerical algorithms to simulate the ground state properties and dynamics of certain quantum-many body systems in two dimensions.

Novel liquid crystalline phases in quantum hall systems

Abstract: Since 1999, experiments have shown a plethora of surprising results in the low-temperature magnetotransport in intermediate regions between quantum Hall (QH) plateaus: the extreme anisotropies observed for half-filling, or the re-entrant integer QH effects at quarter filling of high Landau levels (LL); or even an apparent melting of a Wigner Crystal (WC) at filling factor ν = 1/7 of the lowest LL. A large body of seemingly distinct experimental evidence has been successfully interpreted in terms of liquid crystalline phases in the two-dimensional electron system (2DES). In this paper, we present a review of the physics of liquid crystalline states for strongly correlated two-dimensional electronic systems in the QH regime. We describe a semi-quantitative theory for the formation of QH smectics (stripes), their zero-temperature melting onto nematic phases and ultimate anisotropic-isotropic transition via the Kosterlitz–Thouless (KT) mechanism. We also describe theories for QH-like states with various liquid crystalline orders and their excitation spectrum. We argue that resulting picture of liquid crystalline states in partially filled LL-s is a valuable starting point to understand the present experimental findings, and to suggest new experiments that will lead to further elucidation of this intriguing system.

Complexity and efficiency of beijing transit network

Abstract: Transit system has great impact on urban transportation, and it is especially important when the Olympic games take place in 2008. In this paper, Beijing Transit Network (BTN) is reconstructed based on Ref. 6, and the global and local efficiencies are given. Results show that the degree distribution exhibits broad-scale behavior, and there is a poor global and a good local efficiency in BTN. These results may lead to useful advice for the planning and redesigning of BTN.

Finite geometries in quantum theory: from galois (fields) to hjelmslev (rings)

Abstract: Geometries over Galois fields (and related finite combinatorial structures/algebras) have recently been recognized to play an ever-increasing role in quantum theory, especially when addressing properties of mutually unbiased bases (MUBs). The purpose of this contribution is to show that completely new vistas open up if we consider a generalized class of finite (projective) geometries, viz. those defined over Galois rings and/or other finite Hjelmslev rings. The case is illustrated by demonstrating that the basic combinatorial properties of a complete set of MUBs of a q-dimensional Hilbert space , q = pr with p being a prime and r a positive integer, are qualitatively mimicked by the configuration of points lying on a proper conic in a projective Hjelmslev plane defined over a Galois ring of characteristic p2 and rank r. The q vectors of a basis of correspond to the q points of a (so-called) neighbour class and the q + 1 MUBs answer to the total number of (pairwise disjoint) neighbour classes on the conic. Although this remarkable analogy is still established at the level of cardinalities only, we currently work on constructing an explicit mapping by associating a MUB to each neighbour class of the points of the conic and a state vector of this MUB to a particular point of the class. Further research in this direction may prove to be of great relevance for many areas of quantum information theory, in particular for quantum information processing.

Simple Minimal Informationally Complete Measurements for Qudits

Abstract: Simple minimal but informationally complete positive operator-valued measures are constructed out of the expectation-value representation for qudits. Upon suitable modification, the procedure transforms any set of d2 linearly independent hermitean operators into such an observable. Minor changes in the construction lead to closed-form expressions for informationally complete positive measures in the spaces ℂd.

Time-dependent current-density-functional theory applied to atoms and molecules

Abstract: We review time-dependent current-density-functional theory with the Vignale–Kohn (VK) functional. Historic background and an extensive discussion of the underlying theory is given. In particular, we focus on the application of VK to atoms and (large) molecules in electric fields. Results obtained with VK are shown and the successes and failures of this functional discussed.

EFFECT OF SINTERING TEMPERATURE ON DENSIFICATION AND DIELECTRIC PROPERTIES OF Pb(Zr0.44Ti0.56)O3 CERAMICS

Abstract: In this study, lead zirconate titanate (Pb(Zr0.44Ti0.56)O3) ceramics were fabricated with a mixed oxide synthetic route of lead oxide (PbO) and zirconium titanate (ZrTiO4) precursors. The effects of sintering temperature on phase formation, densification and dielectric responses of the ceramics have been investigated using XRD, SEM, EDX and dielectric measurement techniques. The densification of the PZT ceramics with density of 97% theoretical density can be achieved with appropriate sintering condition without any sintering additives. The optimized sintering condition has been identified as 1225°C for 4 h. More importantly, the dielectric properties are found to improve with increasing sintering temperature and grain size. However, when sintered over 1250°C, the dielectric properties of the ceramics are seen to deteriorate as a result of PbO vaporization, ZrO2 segregations and porosity.

Band collapse and the quantum hall effect in graphene

Abstract: The recent quantum Hall experiments in graphene have confirmed the theoretically well-understood picture of the quantum Hall (QH) conductance in fermion systems with continuum Dirac spectrum. In this paper we take into account the lattice and perform an exact diagonalization of the Landau problem on the hexagonal lattice. At very large magnetic fields the Dirac argument fails completely and the Hall conductance, given by the number of edge states present in the gaps of the spectrum, is dominated by lattice effects. As the field is lowered, the experimentally observed situation is recovered through a phenomenon which we call band collapse. As a corollary, for low magnetic fields, graphene will exhibit two qualitatively different QHE's: at low filling, the QHE will be dominated by the "relativistic" Dirac spectrum and the Hall conductance will be odd-integer; above a certain filling, the QHE will be dominated by a non-relativistic spectrum, and the Hall conductance will span all integers, even and odd.

Local invariants and pairwise entanglement in symmetric multiqubit system

Abstract: Pairwise entanglement properties of a symmetric multi-qubit system are analyzed through a complete set of two-qubit local invariants. Collective features of entanglement, such as spin squeezing, are expressed in terms of invariants and a classification scheme for pairwise entanglement is proposed. The invariant criteria given here are shown to be related to the recently proposed (Phys. Rev. Lett.95, 120502 (2005)) generalized spin squeezing inequalities for pairwise entanglement in symmetric multi-qubit states.

Adsorption of Polyatomics:. Theoretical Approaches in Model Systems and Applications

Abstract: The adsorption of polyatomics on one- and two-dimensional lattices is studied by combining theoretical modeling, Monte-Carlo (MC), simulations and their correspondence with experimental results. In one dimension, the rigorous statistical thermodynamics of interacting chains has been presented. With respect to two-dimensional adsorption, six different models to study non-interacting adsorbates have been discussed: (i) an extension to two dimensions of the exact thermodynamic functions obtained in one dimension; (ii) the Flory–Huggins's approximation and its modification to address linear adsorbates; (iii) the well-known Guggenheim–DiMarzio approximation; (iv) the fourth one is a new description of adsorption phenomena, based on Haldane's fractional statistics; (v) the so-called Occupation Balance, based on the expansion of the reciprocal of the fugacity; and (vi) a simple semi-empirical model obtained by combining exact one-dimensional calculations and Guggenheim–DiMarzio approach. In addition, the statistical thermodynamics of interacting polyatomics has been developed on a generalization in the spirit of the Bragg–Williams and the quasi-chemical approximations. Comparison with MC simulations and experimental adsorption isotherms are used to test the accuracy and reliability of the proposed models. Finally, applications to heterogeneous systems and multilayer adsorption are discussed.

4-vector fields and indefinite metrics

Abstract: We generalize the Stueckelberg formalism in the (1/2, 1/2) representation of the Lorentz Group, see Ref. 1–2. We analize the problem of the mass generation and of the indefinite metrics from the modern viewpoints, see Ref. 3–4. Some relations to other modern-physics models are found.

SCRATCH ADHESION EVALUATION OF ELECTROLESS NICKEL PLATING ON Mg AND Mg ALLOYS

Abstract: Magnesium (Mg) and its alloys are being used as structural components in industry because of their high strength-to-weight ratio and relatively high stiffness. A shortcoming of Mg based alloys is their poor corrosion and wear resistance. Therefore, coatings or surface treatment are needed for protection purpose. This paper reports our work on electroless plating of Ni-P on Mg alloys. Pure Mg, AZ31 and AZ91 Mg alloys were used as the substrates to investigate friction and adhesion properties of the electroless Ni-P coatings. The maximum friction coefficient (~0.3) was found on the electroless nickel coating of pure Mg substrate. The adhesion strengths of the coatings on AZ31 and AZ91 Mg alloys are higher than that on pure Mg. The critical load (a measure of adhesion strength) of AZ31 reached 13.1 N.

Prediction of the fatigue strength of nodular cast irons under combined loading

Abstract: A criterion was proposed for the prediction of the multiaxial fatigue strength of specimens containing small holes. The criterion was applied to nodular cast irons containing graphite nodules and small casting defects such as microshrinkage cavities. Combined axial and torsional fatigue tests were carried out to examine the influences of torsional shear stress amplitude, axial normal stress amplitude, the ratio of these stress amplitudes, phase difference, and mean stress. The materials investigated were nodular cast irons with a ferrite matrix, JIS FCD400, and a pearlite matrix, JIS FCD700. A method for the prediction of the lower bound of fatigue strength was presented. Reasonable agreement between predictions and experimental results was obtained.