Search

High-quality superconducting Ca1−x Na x Fe2As2 single crystals have been successfully grown by the NaAs-flux method, with sodium doping level x = 0.4–0.64. The typical sizes of these crystals are more than 10 mm in ab-plane and ∼ 0.1 mm along c-axis in thickness. X-ray diffraction, resistance and magnetization measurements are carried out to characterize the quality of these crystals. While no signature of magnetic phase transitions is detected in the normal state, bulk superconductivity is found for these samples, with a sharp transition at T c ranging from 19.8 K (x = 0.4) to 34.8 K (x = 0.64). The doping dependences of the c-axis parameter and T c are consistent with previous reports, suggesting a possible connection between the lattice parameters and superconductivity.

The solitary waves of a viscous plasma confined in a cuboid under the three types of boundary condition are theoretically investigated in the present paper. By introducing a three-dimensional rectangular geometry and employing the reductive perturbation theory, a quasi-KdV equation is derived in the viscous plasma and a damping solitary wave is obtained. It is found that the damping rate increases as the viscosity coefficient increases, or increases as the length and width of the rectangle decrease, for all kinds of boundary condition. Nevertheless, the magnitude of the damping rate is dominated by the types of boundary condition. We thus observe the existence of a damping solitary wave from the fact that its amplitude disappears rapidly for a → 0 and b → 0, or v' → + ∞.

A general small amplitude wave equations are proposed for the granular material. It is shown that the wave is localized in a certain region which is in agreement with that found in both the analytical and the simulation results. The localization region depends on the wave frequency and the parameters of the granular material such as the bead radius, the magnitude of the initial prestress, the Young’s modulus and the bead mass. Several examples are given which indicate that the attenuation rate of the wave depend on the permutation of the bead. It also depends on whether the wave is longitudinal or tangential.

The modulational instability of two-component Bose–Einstein condensates (BECs) under an external parabolic potential is discussed. Based on the trapped two-component Gross–Pitaevskill equations, a time-dependent dispersion relation is obtained analytically by means of the modified lens-type transformation and linear stability analysis. It is shown that a modulational unstable time scale exists for trapped two-component BECs. The modulational properties—which are determined by the wave number, external trapping parameter, intra- and inter-species atomic interactions—are modified significantly. The analytical results are confirmed by direct numerical simulation. Our results provide a criterion for judging the occurrence of instability of the trapped two-component BECs in experiment.

Starting from the governing equations for a quantum magnetoplasma including the electron spin −1/2 effects and quantum Bohm potential, we derive Korteweg-de Vries (KdV) equation of the system of quantum magnetohydrodynamics (QMHD). The amplitude and width of magnetosonic soliton with different parameters in the system are studied. It is found that the normalized Zeeman energy E plays a crucial role, for E ≥ 1 the amplitude rmξ and the width wξ of solitary wave all decrease as E increases. That is, the introduction of spin quantum force modifies the shape of solitary magnetosonic waves and makes them more narrower and shallower.

Driven dynamics of a two-dimensional Frenkel-Kontorova model is studied in the paper. In our numerical simulations, it is found that the movement direction of the center of mass is not consistent with that of the external driving force except for some special symmetric directions at the lower driving force. Our results also indicate that the movement direction of the center of mass strongly depends on both the magnitude and the direction of the external driving force as well as the misfit angle between two layers.

The dry friction force between two contacting surface layers is studied. The upper layer is arranged on a two-dimensional square lattice and driven by an external driving force. The lower layer is approximated by a two-dimensional periodic substrate potential. This model, usually called two-dimensional Frenkel–Kontorova model, is applied to study the friction forces in this paper. The behaviors of different substrate potential strongly affect the static friction force. It is found that the system has strong anisotropic character. The possibility to obtain superlubricity is suggested.

We investigate the macroscopic quantum self-trapping (MQST) phenomenon of a spin–orbit-coupled Bose–Einstein condensate (BEC) in a double-well potential, emphasizing the critical behavior at the transition to MQST. We show that as the nonlinear parameter characterizing the atomic interaction increases, the spin–orbit-coupled BEC appears as MQST, manifesting an asymmetric distribution of the atom in two wells. Then, the effect of the initial condition on the critical behavior at the transition to MQST is given. Analytic expressions for the dependence of the transition parameters on the system parameters and the initial condition are derived, which are in agreement with our numerical simulations.

A nonlinear Schroodinger equation in one-dimensional bead chain is first obtained and an envelope solitary wave of the system is verified numerically in this system. The reflection and the transmission of an incident envelope solitary wave due to impurities has also been investigated. It is found that the magnitudes of both the reflection and the transmission not only depend on the characters of impurity materials, the wave number, the incident wave amplitude, but also on the impurity number. This can be used to detect the character and the number of the impurity materials in the bead chain by measuring the reflection and the transmission of an incident pulse.

By means of the multiple-scale expansion method, the coupled nonlinear Schrodinger equations without an explicit external potential are obtained in two-dimensional geometry for a self-attractive Bose–Einstein condensate composed of different hyperfine states. The modulational instability of two-component condensate is investigated by using a simple technique. Based on the discussion about two typical cases, the explicit expression of the growth rate for a purely growing modulational instability and the optimum stable conditions are given and analysed analytically. The results show that the modulational instability of this two-dimensional system is quite different from that in a one-dimensional system.

We study the Landau?Zener tunneling of a nonlinear two-level system by applying a periodic modulation on its energy bias. We find that the two levels are splitting at the zero points of the zero order Bessel function for high-frequency modulation. Moreover, we obtain the effective coupling constant between two levels at the zero points of the zero order Bessel function by calculating the final tunneling probability at these points. It seems that the effective coupling constant can be regarded as the approximation of the higher order Bessel function at these points. For the low-frequency modulation, we find that the final tunneling probability is a function of the interaction strength. For the weak inter-level coupling case, we find that the final tunneling probability is more disordered as the interaction strength becomes larger.

In order to investigate the effect of an arbitrary dust size distribution for vortex-like ion distribution dusty plasma, we use a reasonable polynomial-expressed function to represent an arbitrary dust size distribution. The numerical results of linear dispersion relation, nonlinear solitary wave amplitude, width and velocity for polynomial expressed dust size distribution dusty plasma with vortex-like ion distribution have been studied.

Linear dispersion relation for linear wave and a Kadomtsev–Petviashvili (KP) equation for nonlinear wave are given for the unmagnetized two-ion-temperature cold dusty plasma with many different dust grain species. The numerical results of variations of linear dispersion with respect to the different dust size distribution are given. Moreover, how the amplitude, width, and propagation velocity of solitary wave vary vs different dust size distribution is also studied numerically in this paper.

A (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation for nonlinearly interacting intense laser pulses with an electron-positron (e-p) plasma is derived. Taking into account the combined action of the relativistic particle mass increase and the relativistic light ponderomotive force, using the perturbation method, and allowing different types solution, we discuss the analytical solution of (3+1)-dimensional KP-I equation, and give the approximate solutions of vector potential of the intense laser pulse in e-p plasma. Our results may be significantly useful in understanding the nonlinear wave propagation and interaction of intense laser beams in an e-p plasma.

We study the propagation and interaction of ion-acoustic solitary waves in a simple two-dimensional plasma by using the extended Poincare–Lighthill–Kuo perturbation method. We consider the interaction between two ion-acoustic solitary waves with different propagation directions in such a system, and obtain two Korteweg-de Vries equations for small but finite amplitude solitary waves along both ξ and η trajectories. The effects of the ratio of ion temperature σ, the ratio of heat capacity γ and the colliding angle α. on the amplitude, the width of the new nonlinear wave created by the collision between two solitary waves are studied. The effects of these parameters on both the colliding solitary waves are examined as well. It is found that all the above-mentioned parameters have significant effects on the properties of these nonlinear waves.

Based on active control theory, anti-synchronization between two different hyperchaotic systems is investigated. The sufficient conditions for achieving anti-synchronization of two different hyperchaotic systems are derived. Moreover, numerical simulations are presented for hyperchaotic Lorenz–Chen system, hyperchaotic Lorenz–Lu system, and hyperchaotic Chen–Lu system to verify the effectiveness and feasibility of the proposed anti-synchronization scheme.

For two-component disk-shaped Bose–Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a Kadomtsev–Petviashvili-I equation at the lowest order from the original coupled Gross–Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev–Petviashvili-I equation are given, therefore, the wave functions of both atomic gases are obtained as well. The instability of a soliton under higher-order long wavelength disturbance has been investigated. It is found that the instability depends on the angle between two directions of both soliton and disturbance.

A one-dimensional (1D) Frenkel–Kontorova (FK) model is studied numerically in this paper, and two new analytical solutions (a supersonic kink and a nonlinear periodic wave) of the Sine–Gordon (SG) equation (continuum limit approximation of the FK model) are obtained by using the Jacobi elliptic function expansion method. Taking these new solutions as initial conditions for the FK model, we numerically find there exist the supersonic kink and the nonlinear periodic wave in these systems and obtain a lot of interesting and significant results. Moreover, we also investigate the subsonic kink and the breather in these systems and obtain some new feature.

This paper investigates the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice. By using the extended Poincare–Lighthill–Kuo perturbation method, it obtains two Korteweg–de Vries equations for nonlinear waves in both the ξ and η directions, respectively, and derives the analytical phase shifts after the collision of two nonlinear waves. Finally, the solution of u(υ) up to O(e3) order is given.

We discuss the possible nonlinear waves of atomic matter waves in a cigar-shaped Bose-Einstein condensate with dissipation. The waves can be described by a KdV-type equation. The KdV-type equation has a solitary wave solution. The amplitude, speed, and width of the wave vary exponentially with time t. The dissipative term of γ plays an important role for the wave amplitude, speed, and width. Comparisons have been given between the analytical solutions and the numerical results. It is shown that both are in good agreement.

Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the (3+1)-dimensional Jimbo–Miwa equation is analytically obtained by choosing the Jacobi elliptic functions and their combinations. Limit cases are considered and some new solitary structures (new dromions) are derived. The interaction properties of periodic waves are numerically studied and found to be inelastic. Under long wave limit, two sets of new solution structures (dromions) are given. The interaction properties of these solutions reveal that some of them are completely elastic and some are inelastic.

By using the reductive perturbation method, a Kadomtsev–Petviashvili (KP) equation has been derived for the dust acoustic waves (DAW) in an unmagnetized, collisionless and cold dusty plasma with nonthermal ions. It is found that the different dust size distributions have some important effect on the propagating character for dust acoustic solitary waves (DASW) in this system. Meanwhile, it is shown that the velocity of soliton in dusty plasma with power law dust size distribution is larger than that of dusty plasma with mono-sized dust particles. On the other hand, the influence of nonthermal ions on the amplitude and the width of soliton have also been investigated in this paper.

The dust acoustic solitary waves propagating in two different directions in two-dimensional dusty plasma are investigated. In order to study the soliton interactions in multi-dimensional systems, we extend the reductive perturbation method and obtain two Korteweg–de Vries equations for nonlinear waves in both the ξ and η directions, respectively. The phase shifts after collision of two solitons with arbitrary angle are given. Finally, the solution of nd up to O(4) order is obtained.

An effective fluence concept was employed to make forward dose calculations to investigate the effects of a distorted fluence map on dose plans. Fluence changes caused by organ motion were calculated using Chui's algorithm (2003 Med. Phys. 30 1736). In two test cases with various fluence maps, the effects of motion were simulated using a maximal displacement from 5 mm to 25 mm; 108 fluence maps that were calculated from 16 IMRT plans for eight liver cancer patients were analyzed and compared with and without gating. Fluoroscopic measurements were made of a moving diaphragm in this study. Fluence changes associated with superior-inferior organ motion, perpendicular to the moving MLC, were also examined. The effects of motion on the fluence maps were evaluated from both the fluence differences between static and motion and the chi function. The maximum displacements of the organs in all of these cases were analyzed and correlated with the change in fluence generated from the liver IMRT plans. The dosimetric effects on the target coverage were evaluated for each plan. The results indicate that, for the same fluence map, the mean fluence intensity error or the percentage of the fluence points that have an unacceptable error is linearly related to the extent of motion. For different fluence maps, the degree to which the fluence is distorted by motion is strongly related to the product of the motion extent and the fluence gradient in the direction of diaphragm motion. For eight liver patients and 16 IMRT plans in this work (with gated technique, motion extent from 0.5 cm to 1.0 cm; without gated technique, motion extent from 0.9 cm to 1.8 cm), the fluence modulations are mild, such that the respiratory motion of each patient did not strongly affect the CTV coverage. The mean dose error is 1.5% for free motion (0.9-1.8 cm) and is around 1% for gated motion (0.5-1 cm).

In this paper, (2+1)-dimensional electron acoustic waves (EAW) in an unmagnetized collisionless plasma have been studied by the linearized method and the reductive perturbation technique, respectively. The dispersion relation and a modified Kadomtsev–Petviashvili (KP) equation have been obtained for the EAW in the plasma considering a cold electron fluid and a vortex-like hot electrons. It is found from some numerical results that the parameter β (the ratio of the free hot electron temperature to the hot trapped electron temperature) effects on the amplitude and the width of the electron acoustic solitary waves (EASW). It can be indicated that the free hot electron temperature and the hot trapped electron temperature have very important effect on the characters of the propagation for the EASW.

A modified Zakharov–Kuznetsov equation for small but finite amplitude dust acoustic waves in a magnetized votex-like ion distribution dusty plasma is obtained in this paper. It seems that there are instability for a soliton under higher-order transverse perturbations in this system. There is a certain critical value 4λ0. If the ratio of the wave length of the higher-order perturbations to the width of the soliton is larger than this critical value, the solitary wave is unstable, otherwise it is stable.

We discuss the possible nonlinear waves of atomic matter wave in a Bose–Einstein condensate. One and two of two-dimensional (2D) dark solitons in the Bose–Einstein condensed system are investigated. A rich dynamics is studied for the interactions between two solitons. The interaction profiles of two solitons are greatly different if the angle between them are different. If the angle is small enough, the maximum amplitude during the interaction between two solitons is even less than that of a single soliton. However, if the angle is large enough, the maximum amplitude of two solitons can gradually attend to the sum of two soliton amplitudes.

In this paper, the Fisher equation is analysed. One of its travelling wave solution is obtained by comparing it with KdV–Burgers (KdVB) equation. Its amplitude, width and speed are investigated. The instability for the higher order disturbances to the solution of the Fisher equation is also studied.

With the aid of computerized symbolic computation, the new modified Jacobi elliptic function expansion method for constructing exact periodic solutions of nonlinear mathematical physics equation is presented by a new general ansatz. The proposed method is more powerful than most of the existing methods. By use of the method, we not only can successfully recover the previously known formal solutions but also can construct new and more general formal solutions for some nonlinear evolution equations. We choose the (3+1)-dimensional Kadomtsev–Petviashvili equation to illustrate our method. As a result, twenty families of periodic solutions are obtained. Of course, more solitary wave solutions, shock wave solutions or triangular function formal solutions can be obtained at their limit condition.

The governing equation of the dust fluid with non-thermal ions and variable dust charge on dust particles in hot dust plasmas is obtained. Both the compressive and rarefactive waves in this system are investigated. They can be determined by plasma parameters including the temperatures of dust fluid, ions and electrons, as well as the non-thermal parameter of ions, and the number densities of the dust particles, the ions and the electrons, etc.

Cu/MgO/La0.9Sr0.1MnO3 pillars are fabricated on SrTiO3 (001) substrates by the micro-fabrication patterning processes. Their electric transport properties have been measured in the temperature range from the temperature smaller than the Curie one to 300K. At 125K there emerges abrupt breaks of output voltage in voltage-current (V-I) curves, corresponding to switching in resistance to metastable states, and finally two closed loops are formed with double threshold biases. Around room temperature the V-I characteristics are non-ohmic and show some gradual hysteresis when sweeping the current in a round-trip scan. A large current-induced resistive change Delta R/R-o, similar to -63.2%, is obtained under a current density of 1.0 x 10(4) Acm(-2). Especially, Delta R/R-0 depends linearly on the applied current and is independent of the applied magnetic field. The current-induced resistive effect should be of interest for various applications such as switching and field effect devices.

The dispersion relation is derived for three-dimensional dust-acoustic waves in a current-driven dusty plasmas with both positively and negatively charged dust particles. The dependencies of the frequency and the growth rate on the wave number K, the intensity of magnetic field B, and the inclination angle θ have been numerically shown in this paper. The growth rate is negative for the laboratory dusty plasma, but it is positive for the cosmic dusty plasma. It is found that when the inclination angle θ = π/2, there is no instability. The effect of the electrostatic field E0 has also been studied in this paper.

By using the equivalent particle theory, the adiabatic approximation solutions of the Korteweg–de Vries type equation (including KdV equation, cylindrical KdV equation and spherical KdV equation) in dust ion-acoustic solitary waves were obtained. The method can be extended to other nonlinear evolution equations.