Table of contents

Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry under the infinitesimal transformations is provided. Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.

Basing on the direct method developed by Clarkson and Kruskal, the nonisospectral BKP equation can be reduced to three types of (1+1)-dimensional variable coefficients partial differential equations (PDEs). Furthermore, on the basis of the idea of the symmetry group direct method by Lou et al., three types of reduction PDEs are all reduced to the related constant coefficients PDEs by some transformations.

Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomic mechanic systems with unilateral constraints are established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups are also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.

Vortices in the N-gap (N ≥ 1) superconductor is studied by Dirac δ function. The topological structure of vortices can be characterized by Brouwer degree and Hopf index, i.e. (β₁η₁, ..., β_Nη_N). The magnetic flux and circulation of vortices without London approximation in the N-gap superconductor are calculated. The universal modified London equation is given for the case that each individual condensate is conserved or not conserved.

Lie point symmetry analysis is performed to a recently proposed (2+1)-dimensional nonlinear system, the resonant Davey–Stewartson equation. Some similarity solutions of the RDS equation are thus obtained.

We propose a scheme for generating a four-particle cluster state in an ion-trap system. The scheme is insensitive to the thermal motion of the ions, and needs less operations than previous ones. With such a setup, we also demonstrate a procedure for perfectly teleporting an arbitrary two-particle state via a single multipartite entanglement channel, a four-particle cluster state.

We present a (t, n) threshold multiparty controlled quantum teleportation protocol of an arbitrary m-qubit quantum state between two remote parties. The unknown m-qubit quantum state can be recovered by the receiver under control of a subset of the n controllers if the number of the subset is larger than or equal to a threshold, say, t, but not for any t – 1 or fewer controllers. Our scheme seems to be more practical and more flexible than other existing protocols. The quantum resource required is just m Einstein–Podolsky–Rosen (EPR) pairs plus some single photons. The techniques required are only Bell state measurement, single-qubit unitary operation and von Neumann measurement. So our scheme is also feasible with present-day technique.

We present an optical scheme to almost completely teleport a bipartite entangled coherent state using a four-partite cluster-type entangled coherent state as quantum channel. The scheme is based on optical elements such as beam splitters, phase shifters, and photon detectors. We also obtain the average fidelity of the teleportation process. It is shown that the average fidelity is quite close to unity if the mean photon number of the coherent state is not too small.

On the condition of electric-LO phonon strong coupling in a parabolic quantum dot, we obtain the eigenenergy and the eigenfunctions of the ground state and the first-excited state using the variational method of Pekar type. This system in a quantum dot may be employed as a two-level quantum system-qubit. When the electron is in the superposition state of the ground state and the first-excited state, we obtain the time evolution of the electron density. The relations of the probability density of electron on the temperature and the electron-LO-phonon coupling constant and the relations of the period of oscillation on the temperature, the electron-LO-phonon coupling constant, the Coulomb binding parameter and the confinement length are derived. The results show that the probability density of electron oscillates with a period when the electron is in the superposition state of the ground and the first-excited state, and show that there are different laws that the probability density of electron and the period of oscillation change with the temperature and the electron-LO-phonon coupling constant when the temperature is lower or higher. And it is obtained that the period of oscillation decreases with increasing the Coulomb bound potential and increases with increasing the confinement length not only at lower temperatures but also at higher temperatures.

A four-party scheme is put forward for a sender to partition arbitrary single-qubit information among three receivers by utilizing a class of asymmetric four-qubit W state as quantum channels. In the scheme the sender's quantum information can be recovered by the three receivers if and only if they collaborate together. Specifically, they collaborate to perform first two different 2-qubit collective unitary operations and then a single-qubit unitary operation. The scheme is symmetric and (3,3)-threshold with regard to the reconstruction, for any receiver can be assigned to conclusively recover the quantum information with the other two's assistances.

We study superfluidity of paired Bosonic atoms in optical lattices. The atoms have strong repulsive on-site energy. Single atom tunneling is severely suppressed while the atom-pair may co-tunnel by the second order quantum transition, which induces paired superfluidity as repulsive nearest-neighbor interactions are included. The mean-field phase diagram and low energy excitations are explored for a square lattice system.

We present the logistic growth model to study the stochastic resonance (SR) in a bacterium growth system under the simultaneous action of two external multiplicative cross-correlation noises and periodic external forcing. The expression of the signal-to-noise ratio (SNR) for a bacterium growth system is derived by using the theory of SNR in the adiabatic limit. Based on SNR, we discuss the effects of self-correlation time τ₁ and τ₂, cross-correlation time τ₃ and cross-correlation strength λ on the SNR. It is found that the self-correlation time τ₁ and τ₂, and cross-correlation strength λ enhance the SR of the bacterium growth system, while cross-correlation time τ₃ weakens the SR of the bacterium growth system.

By extending the Parikh–Wilczek tunneling framework, we investigate the tunneling radiation of uncharged massless particles from a static spherically symmetric black hole surrounded by quintessence. The results are consistent with an underlying unitary theory.

We propose a three-species aggregation model with catalysis-driven decomposition. Based on the mean-field rate equations, we investigate the evolution behavior of the system with the size-dependent catalysis-driven decomposition rate J(i; j; k) = Jijk^v and the constant aggregation rates. The results show that the cluster size distribution of the species without decomposition can always obey the conventional scaling law in the case of 0 ≤ v ≤ 1, while the kinetic evolution of the decomposed species depends crucially on the index v. Moreover, the total size of the species without decomposition can keep a nonzero value at large times, while the total size of the decomposed species decreases exponentially with time and vanishes finally.

In the paper, we consider the transport of a two-dimensional random walk. The velocity and the dispersion of this two-dimensional random walk are derived. It mainly show that: (i) by controlling the values of the transition rates, the direction of the random walk can be reversed; (ii) for some suitably selected transition rates, our two-dimensional random walk can be efficient in comparison with the one-dimensional random walk. Our work is motivated in part by the challenge to explain the unidirectional transport of motor proteins. When the motor proteins move at the turn points of their tracks (i.e., the cytoskeleton filaments and the DNA molecular tubes), some of our results in this paper can be used to deal with the problem.

In this paper, we design a feedback controller, and analytically determine a control criterion so as to control the codimension-2 Bautin bifurcation in the chaotic Lü system. According to the control criterion, we determine a potential Bautin bifurcation region (denoted by P) of the controlled system. This region contains the Bautin bifurcation region (denoted by Q) of the uncontrolled system as its proper subregion. The controlled system can exhibit Bautin bifurcation in P or its proper subregion provided the control gains are properly chosen. Particularly, we can control the appearance of Bautin bifurcation at any appointed point in the region P. Due to the relationship between Bautin bifurcation and Hopf bifurcation, the control scheme thereby is also viable for controlling the creation and stability of the Hopf bifurcation. In the controller, there are two terms: a linear term and a nonlinear cubic term. We show that the former determines the location of the Hopf bifurcation while the latter regulates its criticality. We also carry out numerical studies, and the simulation results confirm our analytical predictions.

In this paper exact solutions of a new modified nonlinearly dispersive equation (simply called mK(m, n, a, b) equation), u^m–1u_t + α(uⁿ)_x + β(u^a(u^b)_xx)_x = 0, is investigated by using some direct algorithms. As a result, abundant new compacton solutions (solitons with the absence of infinite wings) and solitary pattern solutions (having infinite slopes or cusps) are obtained.

In this short note, a new projective equation (φ' = σφ + φ²) is used to obtain the variable separation solutions with two arbitrary functions of the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli system (BLMP). Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as multi dromion-solitoffs and fractal-solitons are investigated.

In this article, we study traffic flow in the presence of speed breaking structures. The speed breakers are typically used to reduce the local speed of vehicles near certain institutions such as schools and hospitals. Through a cellular automata model we study the impact of such structures on global traffic characteristics. The simulation results indicate that the presence of speed breakers could reduce the global flow under moderate global densities. However, under low and high global density traffic regime the presence of speed breakers does not have an impact on the global flow. Further the speed limit enforced by the speed breaker creates a phase distinction. For a given global density and slowdown probability, as the speed limit enforced by the speed breaker increases, the traffic moves from the reduced flow phase to maximum flow phase. This underlines the importance of proper design of these structures to avoid undesired flow restrictions.

As a sister work of [Phys. Rev. D 79 (2009) 094004], we incorporate the color-screening effect due to light quark pair creation into the heavy quark-antiquark potential, and investigate the effects of screened potential on the spectrum of bottomonium. We calculate the masses, electromagnetic decays, and E1 transitions of bottomonium states. We find that the fine splittings between χ_bJ (J = 0, 1, 2) states are in good agreement with experimental data, and the E1 transition rates of γ(2S) → γχ_bJ (1P) and γ(3S) → γχ_bJ (2P) (J = 0, 1, 2) all agree with data within experimental errors. In particular, the mass of γ(6S) is lowered down to match that of the γ(11020), which is smaller than the predictions of the linear potential models by more than 100 MeV. Comparison between charmonium and bottomonium in some related problems is also discussed.

We study the one-loop contribution of the effective flavor changing neutral couplings (FCNC) tcZ on the charm quark electric dipole moment. Using the known limits on the top and charm quarks electric dipole moments, we place limits on these FCNC anomalous couplings.

The QCD deconfinement phase transition in pure SU(3) gauge theory is studied on an anisotropic lattice. The critical temperature is determined to be T_c ≈ 285 MeV. The relation between the deconfinement phase transition and the breakdown of Z(3) center symmetry is also discussed.

By using Total Routhian Surface (TRS) method the deformation of the nucleus ¹⁶⁰Yb is studied. The result shows that the triaxial superdeformed state exists with deformation parameters ∊₂ = 0.38 and γ = 21°, where proton shell correction energy plays a key role, and the sum of two quasi-proton particle energies gives an additional driving effect. The rotational energy also has an additional role in the formation of triaxial superdeformed.

A systematic study on the structures and electronic properties of copper clusters has been performed using the density functional theory. In the calculation, there are many isomers near the ground state for small copper clusters. Our results show that the three-dimensional isomers of copper clusters start from Cu₇ cluster and then show a tendency to form more compact structures. The results of the formation energy and the second derivative of binding energy with cluster size show that besides N = 8, N = 11 is also a magic number. Furthermore, it is the first time to find that the ground state of 11-atom clusters is a biplanar structure as same as the 13-atom cluster. The clear odd-even alternation as cluster size for the formation energy indicates the stability of electronic close shell existed in the range studied.

We present a highly efficient lattice Boltzmann model for simulating compressible flows. This model is based on the combination of an appropriate finite difference scheme, a 16-discrete-velocity model [Kataoka and Tsutahara, Phys. Rev. E 69 (2004) 035701(R)] and reasonable dispersion and dissipation terms. The dispersion term effectively reduces the oscillation at the discontinuity and enhances numerical precision. The dissipation term makes the new model more easily meet with the von Neumann stability condition. This model works for both high-speed and low-speed flows with arbitrary specific-heat-ratio. With the new model simulation results for the well-known benchmark problems get a high accuracy compared with the analytic or experimental ones. The used benchmark tests include (i) Shock tubes such as the Sod, Lax, Sjogreen, Colella explosion wave, and collision of two strong shocks, (ii) Regular and Mach shock reflections, and (iii) Shock wave reaction on cylindrical bubble problems. With a more realistic equation of state or free-energy functional, the new model has the potential tostudy the complex procedure of shock wave reaction on porous materials.

This paper studies the phase effect in mode coupling of Kelvin–Helmholtz instability in two-dimensional incompressible fluid. It is found that there is an important growth phenomenon of every mode in the mode coupling process. The growth changes periodically with phase difference and in the condition of our simulation the period is about 0.7π. The period characteristic is apparent in all stage of the mode coupling process, especially in the relatively later stage.

Recently F. Huang [Commun. Theor. Phys. 42 (2004) 903] and X. Tang and P.K. Shukla [Commun. Theor. Phys. 49 (2008) 229] investigated symmetry properties of the barotropic potential vorticity equation without forcing and dissipation on the beta-plane. This equation is governed by two dimensionless parameters, F and β, representing the ratio of the characteristic length scale to the Rossby radius of deformation and the variation of earth' angular rotation, respectively. In the present paper it is shown that in the case F ≠ 0 there exists a well-defined point transformation to set β = 0. The classification of one- and two-dimensional Lie subalgebras of the Lie symmetry algebra of the potential vorticity equation is given for the parameter combination F ≠ 0 and β = 0. Based upon this classification, distinct classes of group-invariant solutions are obtained and extended to the case β ≠ 0.

First-principles study of structural, elastic, and electronic properties of the B20 structure OsSi has been reported using the plane-wave pseudopotential density functional theory method. The calculated equilibrium lattice and elastic constants are in good agreement with the experimental data and other theoretical results. The dependence of the elastic constants, the aggregate elastic modulus, the deviation from the Cauchy relation, the elastic wave velocities in different directions and the elastic anisotropy on pressure have been obtained and discussed. This could be the first quantitative theoretical prediction of the elastic properties under high pressure of OsSi compound. Moreover, the electronic structure calculations show that OsSi is a degenerate semiconductor with the gap value of 0.68 eV, which is higher than the experimental value of 0.26 eV. The analysis of the PDOS reveals that hybridization between Os d and Si p states indicates a certain covalency of the Os-Si bonds.

We studied the electronic structure of the two new transition-metal carbodiimides CoNCN and NiNCN using first-principles method, which is based on density-functional theory (DFT). The density of states (DOS), the total energy of the cell and the spin magnetic moment of CoNCN and NiNCN were calculated. The calculations reveal that the compound CoNCN and NiNCN have half-metallic properties in ferromagnetic ground state, and the spin magnetic moment per molecule is about 7.000 μ_B and 6.000 μ_B for CoNCN and NiNCN, respectively.

Using the configuration-integration methods (CI) [Phys. Rev. B 45 (1992) 19], we report the results of the Hydrogenic-impurity ground state in a GaAs/AlAs spherical quantum dot under an electric field. We discuss the variations of the binding energies of the Hydrogenic-impurity ground state as a function of the position of impurity D, the radius R of the quantum dot, and also as a function of electric field F. We find that the ground energy and binding energy of impurity placed anywhere depend strongly on the position of impurity. Also, electric field can largely change the Hydrogenic-impurity ground state only limiting to the big radius of quantum dot. And the differences in energy level and binding energy are observed from the center donor and off-center donor.

We study the temperature T and the phase of the Josephson critical current I(Φ) by taking into account the roughness scattering effect at inerface in an f-wave superconductor (S)/Insulator layer (I)/f-wave superconductor (S) junction. It is found that the Josephson critical currents in f-wave S/f-wave S, the barrier strength and the roughness strength at inerface always suppress the Andreev reflection. When α = β, the phase dependence of the Josephson current I(φ) between two f-wave S is predicted to be sin φ; particularly, when α ≠ β, the phase dependence of the Josephson current I(φ) between two f-wave superconductors is not predicted to be sin φ and with the barrier strength increasing, the period of the I(φ) turns decrease.

The Bogoliubov de Gennes equation is applied to the study of coherence effects in the ferromagnetic superconductor/insulator/normal metal/insulator/ferromagnetic/superconductor (FS/I/N/I/FS) junction. We calculated the Josephson current in FS/I/N/I/FS as a function of exchange field in ferromagnetic superconductor, temperature, and normal metal thickness. It is found that the Josephson critical current in FS/I/N/I/FS exhibits oscillations as a function of the length of normal metal. The exchange field always suppresses the Josephson critical current I_p for a parallel configuration of the magnetic moments of two ferromagnetic superconductor (FS) electrodes. In the antiparallel configuration, the Josephson critical current I_Ap at the minimum values of oscillation increases with the exchange field for strong barrier strength and at low temperatures.

The relaxation property of both Eigen model and Crow–Kimura model with a single peak fitness landscape is studied from phase transition point of view. We first analyze the eigenvalue spectra of the replication mutation matrices. For sufficiently long sequences, the almost crossing point between the largest and second-largest eigenvalues locates the error threshold at which critical slowing down behavior appears. We calculate the critical exponent in the limit of infinite sequence lengths and compare it with the result from numerical curve fittings at sufficiently long sequences. We find that for both models the relaxation time diverges with exponent 1 at the error (mutation) threshold point. Results obtained from both methods agree quite well. From the unlimited correlation length feature, the first order phase transition is further confirmed. Finally with linear stability theory, we show that the two model systems are stable for all ranges of mutation rate. The Eigen model is asymptotically stable in terms of mutant classes, and the Crow–Kimura model is completely stable.

A competition model of three species in exchange-driven aggregation growth is proposed. In the model, three distinct aggregates grow by exchange of monomers and in parallel, birth of species A is catalyzed by species B and death of species A is catalyzed by species C. The rates for both catalysis processes are proportional to kj^ν and kj^ω respectively, where ν(Ω) is a parameter reflecting the dependence of the catalysis reaction rate of birth (death) on the catalyst aggregate's size. The kinetic evolution behaviors of the three species are investigated by the rate equation approach based on the mean-field theory. The form of the aggregate size distribution of A-species a_k(t) is found to be dependent crucially on the two catalysis rate kernel parameters. The results show that (i) in case of μ ≤ 0, the form of a_k(t) mainly depends on the competition between self-exchange of species A and species-C-catalyzed death of species A; (ii) in case of ν > 0, the form of a_k(t) mainly depends on the competition between species-B-catalyzed birth of species A and species-C-catalyzed death of species A.

The holographic dark energy (HDE) is now an interesting candidate of dark energy, which has been studied extensively in the literature. In the derivation of HDE, the black hole entropy plays an important role. In fact, the entropy-area relation can be modified due to loop quantum gravity or other reasons. With the modified entropy-area relation, we propose the so-called "entropy-corrected holographic dark energy" (ECHDE) in the present work. We consider many aspects of ECHDE and find some interesting results. In addition, we briefly consider the so-called "entropy-corrected agegraphic dark energy" (ECADE).

In this article, we report the principle and conceptual design of a fundamentally different technology in fabricating high precision aberration free optical devices. The tip-tilt of facet in a mirror array is produced by digitally controlled line-tilts of rows and columns. It has not only provided a cost-effective designing methodology in optical physics but also led to a much finer precision of 1 mili arc sec or less. As examples of the application of the proposed digitalised optics, two case studies have been given: a 10 m Schmidt telescope (off-axis) and an 8 m Cassegrain telescope (on-axis).

In this paper, we investigate the new agegraphic dark energy model in the framework of Brans–Dicke theory, which is a natural extension of the Einstein's general relativity. In this framework the form of the new agegraphic dark energy density takes as ρ_q = 3n² Φ(t)η⁻², where η is the conformal age of the universe and Φ(t) is the Brans–Dicke scalar field representing the inverse of the time-variable Newton's constant. We derive the equation of state of the new agegraphic dark energy and the deceleration parameter of the universe in the Brans–Dicke theory. It is very interesting to find that in the Brans–Dicke theory the agegraphic dark energy realizes quintom-like behavior, i.e., its equation of state crosses the phantom divide w = –1 during the evolution. We also compare the situation of the agegraphic dark energy model in the Brans–Dicke theory with that in the Einstein's theory. In addition, we discuss the new agegraphic dark energy model with interaction in the framework of the Brans–Dicke theory.