Hofstadter＇s Butterfly and Phase Transition of Checkerboard Superconducting Network in a Magnetic Field

We study the magnetic effect of the checkerboard superconducting wire network. Based on the de Gennes- Alexader theory, we obtain difference equations for superconducting order parameter in the wire network. Through solving these difference equations, we obtain the eigenvalues, linked to the coherence length, as a function of magnetic field. The diagram of eigenvalues shows a fractal structure, being so-called Hofstadter＇s butterfly. We also calculate and discuss the dependence of the transition temperature of the checkerboard superconducting wire network on the applied magnetic field, which is related to up-edge of the Hofstadter＇s butterfly spectrum.     

Novel Quantum Phases of Ultracold Bosonic Atoms in Honeycomb Optical Lattice

We study the quantum phase transition of ultracold atoms in the honeycomb optical lattice. The Hamiltonian of ultracold bosonic atoms in the honeycomb optical lattice is derived. We take the mean-field approximation and further solve the Hamiltonian with the numerical diagonalization method. We obtain the phase diagram and find that the Mort-insulator （MI）, density wave （DW） and modulated superfluid （MS） phases appear. Furthermore, the phase diagram is analyzed according to the order parameter and the average number of particles.     

Adomian Decomposition Method and Pade Approximants for Nonlinear Differential-Difference Equations

Combining Adomian decomposition method （ADM） with Pade approximants, we solve two differentiaidifference equations （DDEs）： the relativistic Toda lattice equation and the modified Volterra lattice equation. With the help of symbolic computation Maple, the results obtained by ADM-Pade technique are compared with those obtained by using ADM alone. The numerical results demonstrate that ADM-Pade technique give the approximate solution with faster convergence rate and higher accuracy and relative in larger domain of convergence than using ADM.     

Numerical Simulation of Antennae by Discrete Exterior Calculus

Numerical simulation of antennae is a topic in computational electromagnetism, which is concerned with the numerical study of Maxwell equations. By discrete exterior calculus and the lattice gauge theory with coefficient R, we obtain the Bianchi identity on prism lattice. By defining an inner product of discrete differential forms, we derive the source equation and continuity equation. Those equations compose the discrete Maxwell equations in vacuum case on discrete manifold, which are implemented on Java development platform to simulate the Gaussian pulse radiation on antennaes.     

Full period superconducting section physics design for injector Ⅱ of China-ADS

The China Accelerator Driven Subcritical System （China-ADS） project, which is a strategic plan and aims to design and build an ADS demonstration facility, has been proposed and launched actively in China. Injector Ⅱ as one of the parallel injectors of China-ADS, and is prompted by the Institute of Modern Physics （IMP）. In this paper, a new scheme with full period lattice structure for the SC section is proposed. In the new scheme, there are sixteen periods, with one superconducting solenoid and one superconducting cavity included in each period. All of the elements are contained in four eryomodules. The dreadful influence of the mismatch caused by period structural change can be avoided, and the beam quality is favorable. In addition, this new scheme has certain advantages in reducing the project＇s difficulty and construction risk. The details of the design and beam dynamic simulation for the full period lattice structure are given in this paper.     

Study on lattice vibrational properties and Raman spectra of Bi_2Te_3 based on density-functional perturbation theory

We present a variational density-functional perturbation theory(DFPT) to investigate the lattice dynamics and vibrational properties of single crystal bismuth telluride material. The phonon dispersion curves and phonon density of states(DOS) of the material were obtained. The phonon dispersions are divided into two fields by a phonon gap. In the lower field,atomic vibrations of both Bi and Te contribute to the DOS. In the higher field, most contributions come from Te atoms. The calculated Born effective charges and dielectric constants reveal a great anisotropy in the crystal. The largest Born effective charge generates a significant dynamic charge transferring along the c axis. By DFPT calculation, the greatest LO–TO splitting takes place in the infrared phonon modes and reaches 1.7 THz in the Brillouin zone center. The Raman spectra and peaks corresponding to respective atomic vibration modes were found to be in good agreement with the experimental data.     

A Backward-Looking Optimal Current Lattice Model

An optimai current lattice model with backward-looking effect is proposed to describe the motion of traffic flow on a single lane highway. The behavior of the new model is investigated anaiytically and numerically. The stability, neutrai stability, and instability conditions of the uniform flow are obtained by the use of linear stability theory. The stability of the uniform flow is strengthened effectively by the introduction of the backward-looking effect. The numerical simulations are carried out to verify the validity of the new model. The outcomes of the simulation are corresponding to the linearly analyticai results. The analytical and numerical results show that the performance of the new model is better than that of the previous models.     

Thermal properties of high-k Hf1-xSixO2

Classical atomistic simulations based on the lattice dynalnics theory and the Born core-shell model are performed to systematically study the crystal structure and thermal properties of high-k Hfl-xSixO2. The coefficients of thermal expansion, specific heat, Griineisen parameters, phonon densities of states and Debye temperatures are calculated at different temperatures and for different Si-doping concentrations. With the increase of the Si-doping concentration, the lattice constant decreases. At the same time, both the coefficient of thermal expansion and the specific heat at a constant volume of Hf1-mSixO2 also decreases. The Griineisen parameter is about 0.95 at temperatures less than 100 K. Compared with Si-doped HfO2, pure HfO2 has a higher Debye temperature when the temperature is less than 25 K, while it has lower Debye temperature when the temperature is higher than 50 K. Some simulation results fit well with the experimental data. We expect that our results will be helpful for understanding the local lattice structure and thermal properties of Hf1-mSixO2.     

Clock-transition spectrum of ^171yb atoms in a one-dimensional optical lattice

An optical atomic clock with 171Yb atoms is devised and tested. By using a two-stage Doppler cooling technique, the 171Yb atoms are cooled down to a temperature of 6 ± 3 μK, which is close to the Doppler limit. Then, the cold 171Yb atoms are loaded into a one-dimensional optical lattice with a wavelength of 759 nm in the Lamb-Dicke regime. Furthermore, these cold 171Yb atoms are excited from the ground-state 1S0 to the excited-state 3P0 by a clock laser with a wavelength of 578 nm. Finally, the 1S0-3P0 clock-transition spectrum of these 171Yb atoms is obtained by measuring the dependence of the population of the ground-state 1S0 upon the clock-laser detuning.     

Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems

A semi-direct sum of two Lie algebras of four-by-four matrices is presented, and a discrete four-by-four matrix spectral problem is introduced. A hierarchy of discrete integrable coupling systems is derived. The obtained integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discrete Hamiltonian systems.     

Zero-field splitting parameters and local structures for tetragonal Cr2＋ centers in Cr2＋-doped ZnSe semiconductors

The inter-relation between zero-field splitting （ZFS） parameters and local lattice structures of the （CrSe4）6 clusters in ZnSe semiconductors has been established by using the complete diagonalization （of the energy matrix） method. On the basis of this, the local lattice distortions, the ZFS parameters D, a, F and the optical spectrum for Cr2＋ ions doped into ZnSe are theoretically investigated, and the contributions of the spin singlets have been taken into account. The calculated ZFS parameters are in good agreement with the experimental values. From our calculations, the tetragonal distortion parameters AR = 0.091A and Aθ = 4.28° of Cr2＋ in ZnSe are acquired, and the results suggest that there exists a tetragonal expansion distortion for the local lattice structure of （CrSe4）6- clusters in ZnSe crystals. The influence of the spin singlets on ZFS parameters is also discussed, indicating that the contributions to ZFS parameters a and F cannot be ignored.     

Breather Lattice Solutions to Negative mKdV Equation

In this paper, dependent and independent variable transformations are introduced to solve the negative mKdV equation systematically by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different kinds of solutions can be obtained to the negative mKdV equation, including breather lattice solution and periodic wave solution.     

A Lattice Hydrodynamic Model for Traffic Flow Accounting for Driver Anticipation Effect of the Next-Nearest-Neighbor Site

In this paper, a new lattice hydrodynamic model is proposed by incorporating the driver anticipation effect of next-nearest-neighbor site. The linear stability analysis and nonlinear analysis show that the driver anticipation effect of next-nearest-neighbor site can enlarge the stable area of traffic flow. The space can be divided into three regions： stab/e, metastable, and unstable. Numerical simulation further illuminates that the driver anticipation effect of the next-neaxest-neighbor site can stabilize tramc flow in our modified lattice model, which is consistent with the analytical results.     

Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product

It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally.     

Symmetry Reductions and Exact Solutions of Blaszak-Marciniak Four-Field Lattice Equation

Applying the Lie group method to the differential-difference equation, the Lie point symmetry of Blaszak- Marciniak four-field Lattice equation is obtained. Using the obtained symmetry, the similarity reduction equations of Blaszak-Marciniak four-field Lattice equation are derived. Solving the reduction, we get the solution of Blaszak-Marciniak four-field Lattice equation which not only recovers one of the solutions obtained by Ma and Hu [J. Math. Phys. 40 （1999） 6071] but also has the singularity when we choose the arbitrary constants accurately.     

Relation between martensitic transformation temperature range and lattice distortion ratio of NiMnGaCoCu Heusler alloys

In order to study the relation between martensitic transformation temperature range AT （where AT is the difference between martensitic transformation start and finish temperature） and lattice distortion ratio （c/a） of martensitic transforma~ tion, a series of Ni46Mnz8_xGa22Co4Cux （x = 2-5） Heusler alloys is prepared by arc melting method. The vibration sample magnetometer （VSM） experiment results show that AT increases when x 〉 4 and decreases when x 〈 4 with x increasing, and the minimal AT （about 1 K） is found at x = 4. Ambient X-ray diffraction （XRD） results show that AT is proportional to c/a for non-modulated Ni46Mn28_xGa22Co4Cux （x = 2-5） martensites. The relation between AT and c/a is in agreement with the analysis result obtained from crystal lattice mismatch model. About 1000-ppm strain is found for the sample at x = 4 when heating temperature increases from 323 K to 324 K. These properties, which allow a modulation of AT and temperature-induced strain during martensitic transformation, suggest Ni46Mn24Ga22Co4Cu4 can be a promising actuator and sensor.     

New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology

We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology.Such problems are presented as nonlinear differential–difference equations.The proposed method is based on the Laplace transform with the homotopy analysis method(HAM).This method is a powerful tool for solving a large amount of problems.This technique provides a series of functions which may converge to the exact solution of the problem.A good agreement between the obtained solution and some well-known results is obtained.     

Lattice Dynamics at Zone-Center of Sulphide and Selenide Spinels

A rigid-ion model is used to calculate the force constants and effective dynamical charges of sulphide and selenide spinels. The Raman and infrared phonon modes of normal cubic sulphide spinels MCr2S4 （M = Mn, Co, Fe, Hg, Zn, and Cd） and selenide spinels MCr2Se4 （M = Hg, Zn, and Cd） are calculated at the first Brillouin zone-centre using above model, The significant outcome of the present work is （i） the interatomic interaction between Cr-S （Se） dominates over the Cr-S（Se） and S-S（Se-Se） type of interatomic interactions, （ii） the effective dynamical charges of the bivalent metal ions are nearly zero, and （iii） the selenide spinels are less ionic than the sulphide spinels and the ionicity decreases as MnCr2S4 〉 FeCr2S4 〉 CoCr2S4 〉 and CdOr2C4 〉 ZnCr2C4 〉 HgCr2C4 （C = S and Se）. The zone-center phonon frequencies, calculated using these parameters, are found to be in very good agreement with the observed results.     

Application of Exp-Function Method to Discrete Nonlinear SchrSdinger Lattice Equation with Symbolic Computation

In this paper, we present an extended Exp-function method to differential-difference equation（s）. With the help of symbolic computation, we solve discrete nonlinear Schrodinger lattice as an example, and obtain a series of general solutions in forms of Exp-function.     

Casoratian Solutions to Toda Lattice Via Its Backlund Transformation

Generalized Casoratian condition and Casoratian solutions of the Toda lattice are given in terms of its bilinear Bgcklund transformation. By choosing suitable Casoratian entries and parameter in the bilinear Bgcklund transformation, we can give transformations among many kinds of solutions.