Analytical investigation velocity fields on mean and turbulent of a plane jet

This paper analyses the downstream developments of the mean and the turbulent velocity fields of a plane jet. Based on the conservation of mass and the conservation of momentum, the mean-velocity half width （reflecting the jet spread rate） and the relative mass flow rate （jet entrainment） are related to the decay rate of the centreline mean velocity. These relations are not subject to self-preservation. Both analytical and experimental results suggest that the jet spread rate （K1） and the entrainment rate （K3） （and thus the decay rate K2） can be well estimated from the centreline velocity, i.e., K1 ≈ 0.6K2 and K3 ∝K2. The effect of initial mean velocity and RMS velocity profiles on the downstream mean velocity field appears to be embodied in the constants K1 K2 and K3. The analytical relationship for the self-preserving Reynolds shear stress, obtained for the first time, works well.     

Slow decay of the finite Reynolds number effect of turbulence

The third-order structure function is used to study the finite Reynolds number (FRN) effect of turbulence, which refers to the deviation of turbulence statistics observed at finite Reynolds numbers from predictions of the Kolmogorov theories. It is found that the FRN effect decreases as CR(-mu)(lambda), when R(lambda) is high, and mu < or = 6/5. Here R(lambda) is the Taylor-microscale Reynolds number and C is a constant independent of R(lambda). From the exact spectral equations, the decay exponent mu and the constant C are determined for typical fully developed turbulent flows (freely decaying isotropic turbulence and shear flow turbulence), so that the quantitative prediction of the FRN effect is feasible.     

New Exact Periodic Solitary-Wave Solutions for New （2＋1）-Dimensional KdV Equation

The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions （including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions） for the new （2＋1）-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field.     

Fabrication and properties of the meander nanowires based on ultra-thin Nb films

We report the fabrication and the study of superconducting properties of ultra-thin Nb superconducting meander nanowires, which can be used as superconducting nanowire single-photon detectors （SNSPDs）. The ultra-thin （about 7- nm thick） Nb films are patterned into micro-bridges, and 100-nm wide meander nanowires by using e-beam lithography （EBL）. The average transition temperature （Tc） of the nanowires is about 4.8 K and the critical current density jc is about 2.8 × 10^6 A/cm2. Superconducting characteristics of the specimens at different applied magnetic fields up to 8 T （parallel or perpendicular to the specimen） are systematically investigated. The normalized temperature t （= T/Tc） dependences of the parallel critical field （HcⅡ） for both the micro-bridge and the meander nanowire are almost the same, following the Ginzburg and Landau （GL） formalism for ultra-thin films. However, in perpendicular field and in the vicinity of Tc （〉 0.95Tc）, the critical field Hc⊥ of the nanowire exhibits a down-turn curvature nonlinear temperature dependence while the micro-bridge displays a linear temperature dependence. The nonlinear behavior of Hc⊥ in the nanowire is believed to be due to the fact that in the vicinity of Tc the coherence length becomes larger than the line width. Additionally, the localization of carriers in the nanowire could also contribute to the nonlinear behavior. The resistive transitions could be described by the phase-slip model for quasi-one-dimensional system. Moreover, the hysteresis in I-V curve of the meander nanowires can be illustrated by a simple model of localized normal hotspot maintained by Joule heating.     

Analysis to Some Solutions Obtained by Modified Extended tanh-Function Method＊

First, two tanh-coth type solutions of a class of nonlinear wave equation are derived by using a simplified modified extended tanh-function method. Then, further analysis to some tanh-coth type solutions of nonlinear evolution equations are given. The results show that when balance number m is one or two, the tanh-eoth type solutions obtained by the modified extended tanh-funetion method can be obtained by using the hyperbolic-function method.     

Application of Extended Projective Riccati Equation Method to （2＋1）-Dimensional Broer-Kaup-Kupershmidt System

In this paper, extended projective Riccati equation method is presented for constructing more new exact solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the effect of the method, Broer Kaup Kupershmidt system is employed and Jacobi doubly periodic solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.     

Formation of epitaxial Tl_2Ba_2Ca_2Cu_3O_(10) superconducting films by dc-magnetron sputtering and triple post-annealing method

For obtaining pure phase T12Ba2Ca2Cu3O10 （T1-2223） films with good superconducting properties, the growth technique is improved by dc magnetron sputtering and a triple post-annealing process. The triple post-annealing process comprises annealing twice in argon and once in oxygen at different temperatures. In the first low-temperature annealing phase in argon, T12Ba2CaCu2O8 （T1-2212） is obtained to effectively minimize evaporation in the next step. With the increase of temperature in the second annealing stage in argon, the previously prepared T1-2212 inter-phase is converted into T1-2223 phase. An additional annealing in oxygen is also adopted to improve the properties of T1-2223 films, each containing an optimal oxygen content value. The results of X-ray diffraction （XRD） θ-2θ scans, 09 scans and rotational φ scans show that each of the T1-2223 films has a high phase purity and an epitaxial structure. Smooth films are observed by scanning electron microscopy （SEM）. The critical temperatures Tc of the films are measured to be about 120 K and the critical current densities Jc can reach 4.0 MA/cm2 at 77 K at self field.     

Lie group analysis,numerical and non-traveling wave solutions for the （2＋l）-dimensional diffusion-advection equation with variable coefficients

In this paper, the variable-coefficient diffusion-advection （DA） equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended （Gl/G）-expansion method is applied to the DA equation to construct some new non-traveling wave solutions.     

（G′/G）-Expansion Method Equivalent to Extended Tanh Function Method

In a recent article [Physics Letters A 372 （2008） 417], Wang et al. proposed a method, which is called the （G′/G）-expansion method, to look for travelling wave solutions of nonlinear evolution equations. The travelling wave solutions involving parameters of the KdV equation, the mKdV equation, the variant Boussinesq equations, and the Hirota-Satsuma equations are obtained by using this method. They think the （G′/G）-expansion method is a new method and more travelling wave solutions of many nonlinear evolution equations can be obtained. In this paper, we will show that the （G′/G）-expansion method is equivalent to the extended tanh function method.     

Various Methods for Constructing Auto-Baicklund Transformations for a Generalized Variable-Coefficient Korteweg-de Vries Model from Plasmas and Fluid Dynamics

In this paper, under the Painleve-integrable condition, the auto-Biicklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various methods including the Hirota method, truncated Painleve expansion method, extendedvariable-coefficient balancing-act method, and Lax pair. Additionally, the compatibility for the truncated Painleve expansion method and extended variable-coetfficient balancing-act method is testified.     

Critical phenomena in a disc-percolation model and their application to relativistic heavy ion collisions

By studying the critical phenomena in continuum-percolation of discs, we find a new approach to locate the critical point, i.e. using the inflection point of P∞ as an evaluation of the percolation threshold. The susceptibility, defined as the derivative of P∞, possesses a finite-size scaling property, where the scaling exponent is the reciprocal of v, the critical exponent of the correlation length. A possible application of this approach to the study of the critical phenomena in relativistic heavy ion collisions is discussed. The critical point for deconfinement can be extracted by the inflection point of PQGP -- the probability for the event with QGP formation. The finite-size scaling of its derivative can give the critical exponent v, which is a rare case that can provide an experimental measure of a critical exponent in heavy ion collisions.     

Critical behavior of a dynamical percolation model

The critical behavior of the dynamical percolation model,which realizes the molecular-aggregation conception and describes the crossover between the hadronic phase and the partonic phase,is studied in detail. The critical percolation distance for this model is obtained by using the probability P∞ of the appearance of an infinite cluster. Utilizing the finite-size scaling method the critical exponents γ/ν and τ are extracted from the distribution of the average cluster size and cluster number density. The influences of two model related factors,i.e. the maximum bond number and the definition of the infinite cluster,on the critical behavior are found to be small.     

Interplay of superconductivity and d-f correlation in CeFeAslPOl_yFy

The recent discovery of high-temperature superconductivity in iron-based pnictides （chalcogenides） not only trig- gers tremendous enthusiasm in searching for new superconducting materials, but also opens a new avenue to the study of the Kondo physics. CeFeAsO is a parent compound of the 1111-type iron-based superconductors. It shows 3d- antiferromagnetic （AFM） ordering below 139 K and 4f-AFM ordering below 4 K. On the other hand, the phosphide CeFePO is a ferromagnetically corelated heavy-fermion （HF） metal with Kondo scale TK 10 K. These properties set up a new platform for research of the interplay among magnetism, Kondo effect, and superconductivity （SC）. In this review, we present the recent progress in the study of chemical pressure effect in CeFeAsOl_yFy （y = 0 and 0.05）. This P/As-doping in CeFeAsO serves as an effective controlling parameter which leads to two magnetic critical points, Xcl -- 0.4 and Xc2 - 0.92, associated with suppression of 3d and 4f magnetism, respectively. We also observe a turning point of AFM-FM ordering of Ce3＋ moment at Xc3 - 0.37. The SC is absent in the phase diagram, which is attributed to the destruction to Cooper pair by Ce-FM fluctuations in the vicinity of Xcl. We continue to investigate CeFeAsl-xPxO0.95Fo.os. With the separation of xcl and xc3, this chemical pressure results in a broad SC region 0〈 x 〈 0.53, while the original HF behavior is driven away by 5% F- doping. Different roles of P and F dopings are addressed, and the interplay between SC and Ce-4f magnetism is also discussed.     

Exploring FeSe-based superconductors by liquid ammonia method

Our recent progress on the preparation of a series of new FeSe-based superconductors and the clarification of SC phases in potassium-intercalated iron selenides are reviewed here. By the liquid ammonia method, metals Li, Na, Ca, Sr, Ba, Eu, and Yb are intercalated in between FeSe layers and form superconductors with transition temperatures of 30 K～46 K, which cannot be obtained by high-temperature routes. In the potassium-intercalated iron selenides, we demonstrate that at least two SC phases exist, K x Fe 2 Se 2 (NH 3 ) y (x ≈ 0.3 and 0.6), determined mainly by the concentration of potassium. NH 3 has little, if any, effect on superconductivity, but plays an important role in stabilizing the structures. All these results provide a new starting point for studying the intrinsic properties of this family of superconductors, especially for their particular electronic structures.     

Phase diagrams of spin-3/2 Ising model in the presence of random crystal field within the effective field theory based on two approximations

The bimodal random crystal field （A） effects are investigated on the phase diagrams of spin-3/2 Ising model by using the effective-field theory with correlations based on two approximations： the general van der Waerden identity and the approximated van der Waerden identity. In our approach, the crystal field is either turned on or turned off randomly for a given probability p or q = 1 -p, respectively. Then the phase diagrams are constructed on the （A,kT/J） and （p,kT/J） planes for given p and A, respectively, when the coordination number is z = 3. Furthermore, the effect of randomization of the crystal field is illustrated on the （△,kT/J） plane for p = 0.5 when z - 3,4, and 6. All these are carried out for both approximations and then the results are compared to point out the differences. In addition to the lines of second-order phase transitions, the model also exhibits first-order phase transitions and the lines of which terminate at the isolated critical points for high p values.     

Criticality in Two-Variable Earthquake Model on a Random Graph

A two-variable earthquake model on a quenched random graph is established here. It can be seen as a generalization of the OFC models. We numerically study the critical behavior of the model when the system is nonconservative： the result indicates that the model exhibits self-organized criticality deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling. We compare our mode/with the mode/ introduced by Stefano Lise and Maya Paczuski [Phys. Rev. Lett. 88 （2002） 228301], it is proved that they are not in the same universality class.     

Cumulants in the 3-dimensional Ising,O（2） and O（4） spin models

Based on the universal properties of a critical point in different systems and that the QCD phase transitions fall into the same universality classes as the 3-dimensional Ising, O（2） or O（4） spin models, the critical behavior of cumulants and higher cumulant ratios of the order parameter from the three kinds of spin models is studied. We found that all higher cumulant ratios change dramatically the sign near the critical temperature. The qualitative critical behavior of the same order cumulant ratio is consistent in these three models.     

High order Lagrangian velocity statistics in turbulence

We report measurements of the Lagrangian velocity structure functions of orders 1 through 10 in a high Reynolds number (Taylor microscale Reynolds numbers of up to R(lambda) = 815 ) turbulence experiment. Passive tracer particles are tracked optically in three dimensions and in time, and velocities are calculated from the particle tracks. The structure function anomalous scaling exponents are measured both directly and using extended self-similarity and are found to be more intermittent than their Eulerian counterparts. Classical Kolmogorov inertial range scaling is also found for all structure function orders at times that trend downward as the order increases. The temporal shift of this classical scaling behavior is observed to saturate as the structure function order increases at times shorter than the Kolmogorov time scale.     

Early warning signals of abrupt temperature change in different regions of China over the past 50 years

In this paper, the early warning signals of abrupt temperature change in different regions of China are investigated. Seven regions are divided on the basis of different climate temperature patterns, obtained through the rotated empirical orthogonal function, and the signal-to-noise temperature ratios for each region are then calculated. Based on the concept of critical slowing down, the temperature data that contain noise in the different regions of China are preprocessed to study the early warning signals of abrupt climate change. First, the Mann-Kendall method is used to identify the instant of abrupt climate change in the temperature data. Second, autocorrelation coefficients that can identify critical slowing down are calculated. The results show that the critical slowing down phenomenon appeared in temperature data about 5-10 years before abrupt climate change occurred, which indicates that the critical slowing down phenomenon is a possible early warning signal for abrupt climate change, and that noise has less influence on the detection results of the early warning signals. Accordingly, this demonstrates that the model is reliable in identifying the early warning signals of abrupt climate change based on detecting the critical slowing down phenomenon, which provides an experimental basis for the actual application of the method.     

Investigation of a wake decay behind a circular disk in a hydro channel at high Reynolds numbers

LDA and PIV techniques were used to study the decay of an axisymmetrical turbulent wake originated downstream an immobile disk in a water flume for Reynolds numbers Re = 1.5?2.4?10⁵. Data were compared with experiments performed with a set of thermo-anemometers behind a disk in a wind tunnel at lower Reynolds numbers (Re = 1.3?2.6?10⁴). Observations for a new range of Reynolds number confirmed that the velocity distribution in the disk wake keeps self-similarity. The decay of a wake by the power law ?2/3 in the presented experiments remains until the maximum deficit of velocity becomes comparable with the turbulent pulsation level in the free-stream (less than 2 %).