Nonlocal Effects of Low-Energy Excitations in Quantum-Spin-Liquid Candidate Cu_3Zn(OH)_6FBr

We systematically study the low-temperature specific heats for the two-dimensional kagome antiferromagnet,Cu_3Zn(OH)_6FBr.The specific heat exhibits a T~(1.7) dependence at low temperatures and a shoulder-like feature above it.We construct a microscopic lattice model of Z_2 quantum spin liquid and perform large-scale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic impurities.Surprisingly,we find the entropy associated with the shoulder decreases quickly with grain size d,although the system is paramagnetic to the lowest temperature.While this can be simply explained by a core-shell picture in that the contribution from the interior state disappears near the surface,the 5.9-nm shell width precludes any trivial explanations.Such a large length scale signifies the coherence length of the nonlocality of the quantum entangled excitations in quantum spin liquid candidate,similar to Pippard's coherence length in superconductors.Our approach therefore offers a new experimental probe of the intangible quantum state of matter with topological order.     

Bäcklund transformations and abundant exact explicit solutions of the Sharma-Tasso-Olver equation

By using an extension of the homogeneous balance method and Maple, the Bäcklund transformations for the Sharma-Tasso-Olver equation are derived. The connections between the Sharma-Tasso-Olver equation and some linear partial differential equations are found. With the aid of the transformations given here and the computer program Maple 12, abundant exact explicit special solutions to the Sharma-Tasso-Olver equation are constructed. In addition to all known solutions re-deriving in a systematic way, several entirely new and more general exact explicit solitary wave solutions can also be obtained. These solutions include (a) the algebraic solitary wave solution of rational function, (b) single-soliton solutions, (c) double-soliton solutions, (d) N-soliton solutions, (e) singular traveling solutions, (f) the periodic wave solutions of trigonometric function type, and (g) many non-traveling solutions. By using the Airy’s function and the Bäcklund transformations obtained here, the exact explicit solution of the initial value problem for the STO equation is presented. The variety of the structure of the solutions for the Sharma-Tasso-Olver equation is illustrated.     

Global existence of strong solutions of Navier–Stokes equations with non-Newtonian potential for one-dimensional isentropic compressible fluids

We consider strong solutions to the initial boundary value problems for the isentropic compressible Navier–Stokes equations in one dimension: $$\rho\left\{\begin{array}{lll} t+(\rho u)_x=0\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\, {\rm in}\,(0,T)\times(0,1)\\ (\rho u )_t+(\rho u^2)_x+\rho \Phi_x-(\mu( \rho )u_x)_x+P_x=0\quad\quad {\rm in}\,(0,T)\times(0,1) \\\left(\left(\frac{\delta(\Phi_x)^2\,+\,1}{(\Phi_x)^2\,+\,\delta}\right)^{\frac{2-p}{2}}\Phi_x\right)_x=4\pi g(\rho-\frac{1}{|\Omega|}\int\nolimits_\Omega \rho dx\,\,\,\, )\quad\,\, {\rm in}\,(0,T)\times(0,1)\end{array}\right.$$ Here, the Φ is a non-Newtonian potential and strong solutions of the problem and obtains the uniqueness under the compatibility condition.     

Time-clustering behavior of sharp fluctuation sequences in Chinese stock markets

Sharp fluctuations (in particular, extreme fluctuations) of asset prices have a great impact on financial markets and risk management. Therefore, investigating the time dynamics of sharp fluctuation is a challenge in the financial fields. Using two different representations of the sharp fluctuations (inter-event times and series of counts), the time clustering behavior in the sharp fluctuation sequences of stock markets in China is studied with several statistical tools, including coefficient of variation, Allan Factor, Fano Factor as well as R/S (rescaled range) analysis. All of the empirical results indicate that the time dynamics of the sharp fluctuation sequences can be considered as a fractal process with a high degree of time-clusterization of the events. It can help us to get a better understanding of the nature and dynamics of sharp fluctuation of stock price in stock markets.     

Spin-polarized transport in zigzag graphene nanoribbons adsorbing nonmagnetic atomic chain

We theoretically study the electron transport properties in a ferromagnetic/normal/ferromagnetic tunnel junction, which is deposited on the top of a topological surface. The conductance at the parallel (P) configuration can be much bigger than that at the antiparallel (AP) configuration. Compared P with AP configuration, there exists a shift of phase which can be tuned by gate voltage. We find that the exchange field weakly affects the conductance of carriers for P configuration but can dramatically suppress the conductance of carriers for AP configuration. This controllable electron transport implies anomalous magnetoresistance in this topological spin valve, which may contribute to the development of spintronics. In addition, there shows an existence of Fabry-Perot-like electron interference in our model based on the topological insulator, which does not appear in the same model based on the two dimensional electron gas.     

Optimization of Cockpit Ventilation for Polar Cruise Ships in Combination with Windscreen Defogging and Cabin Comfort Considerations

Polar cruise ships are exposed to extreme external conditions during voyages, resulting in cockpit windscreens that are prone to fogging and frosting, seriously affecting the driver’s vision and even threatening navigation safety. However, the current research mainly focuses on cabin comfort, ignoring the coupling of defogging and comfort. Accordingly, this paper combines cockpit-windshield-defogging design and cockpit comfort considerations, and proposes 108 orthogonal-ventilation design parameters based on the four basic ventilation methods. The effects of different air supply parameters on comfort and anti-fog characteristics are investigated by using fluid dynamics simulation methods. The entropy weight–TOPSIS algorithm is employed to find the optimal ventilation parameters. The results show that the “Down-supply up-return type vertical jet” air supply method corresponding to an air supply velocity of 1 m/s, an air supply temperature of 297 K, and an air supply relative humidity of 30% has the smallest Euclidean distance di+ from the positive ideal solution, and the largest Euclidean distance di− from the negative ideal solution; thus, it obtains a higher ci and the highest priority. This air supply method provides the best thermal comfort for the drivers, as well as the best anti-fogging and defogging effect. The results can be useful to provide suggestions for the future design of the air-conditioning systems in polar cruise ships.     

Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation

Applying the method of normalized systems of functions we construct solutions of the generalized Dirichlet problem for the iterated slice Dirac operator in Clifford analysis. This problem is a natural generalization of the Dirichlet problem.

     

Elastic,mechanical, electronic properties and hardness of Nb2AsC from first principles

The study aims at the elastic, mechanical, electronic properties and hardness of Nb₂AsC using first principles based on the density functional theory method within the generalised gradient approximation. The calculated lattice parameters of Nb₂AsC are in good agreement with the experimental data. The five independent elastic constants are firstly calculated as a function of pressure, and our results indicate that it is mechanically stable in the applied pressure. The elastic anisotropy is examined through the computation of the direction dependence of Young's modulus. The pressure dependences of the bulk modulus, shear modulus, average velocity of acoustic waves and Debye temperature of Nb₂AsC are systematically investigated. The band structure and density of states are discussed, and the results show that the strong hybridisations C p–Nb d and As p–Nb d would be beneficial to the structure stability of Nb₂AsC. Based on the Mulliken population analysis, the hardness of Nb₂AsC is predicted.     

Constructive methods of approximation by ridge functions and radial functions

Let be a univariant function, and letg(x) be the average of (x,u) asu runs over the unit sphere in ⁿ . We give a necessary and sufficient condition forg to be a kernel function, i.e., thatg be inL ¹ ( ⁿ ) and have integral 1. The result is used to give a constructive proof of the density of the ridge functions based upon the function .     

Influence of the structure parameters on the gain and noise figure in silicon parametric amplifiers based on SOI Rib waveguides

Gain and Noise figure (NF) characteristics in dual-pump parametric amplifier based on silicon on insulator (SOI) Rib waveguides are numerically investigated in the presence of nonlinear losses. The impact of structure parameters of the silicon optical parametric amplifiers (SOPAs) on the gain and the NF are also analyzed. The results show that both the height and the width of the silicon on insulator (SOI) can affect the gain and the NF of SOPAs. 354 nm bandwidth (3 dB) and 8.135 maximum gain can be achieved by tailoring the structure parameters of the SOI rib waveguides. Moreover, the dispersion and the effective mode area of SOI are also analyzed.