New Explicit Rational Solitary Wave Solutions for Discretized mKdV Lattice Equation

In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.     

Very-high-order weno schemes

We study weno(2r − 1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving weno schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452], with the mapping (wenom) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542–567], which we extend up to weno17 (r=9)$(r=9)$. We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent cfl limitation (cfl∈[0.8,1])$(\text{<small-caps>cfl</small-caps>}\in [0.8\text{,}1])$, for scalar hyperbolic problems (both linear and scalar conservation laws), provided that the exponent p_β$p_{\beta }$ in the definition of the Jiang–Shu [G.S. Jiang, C.W. Shu, Efficient implementation of weighted eno schemes, J. Comput. Phys. 126 (1996) 202–228] nonlinear weights be taken as p_β=r$p_{\beta }=r$, as originally proposed by Liu et al. [X.D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200–212], instead of p_β=2$p_{\beta }=2$ (this is valid both for weno and wenom reconstructions), although the optimal value of the exponent is probably p_β(r)∈[2,r]$p_{\beta }(r)\in [2\text{,}r]$. Then, we apply the family of very-high-order wenom_pβ=r${\text{<small-caps>wenom</small-caps>}}_{p_{\beta }=r}$ reconstructions to the Euler equations of gasdynamics, by combining local characteristic decomposition [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes iii, J. Comput. Phys. 71 (1987) 231–303], with recursive-order-reduction (ror) aiming at aleviating the problems induced by the nonlinear interactions of characteristic fields within the stencil. The proposed ror algorithm, which generalizes the algorithm of Titarev and Toro [V.A. Titarev, E.F. Toro, Finite-volume weno schemes for 3-D conservation laws, J. Comput. Phys. 201 (2004) 238–260], is free of adjustable parameters, and the corresponding rorwenom_pβ=r${\text{<small-caps>rorwenom</small-caps>}}_{p_{\beta }=r}$ schemes are essentially nonoscillatory, as Δx→0$\mathrm{\Delta }x\to 0$, up to r=9$r=9$, for all of the test-cases studied. Finally, the unsplit linewise 2-D extension of the schemes is evaluated for several test-cases.     

Analysis of detection limit to time-resolved coherent anti-Stokes Raman scattering nanoscopy

In the implementation of CARS nanoscopy, signal strength decreases with focal volume size decreasing. A crucial problem that remains to be solved is whether the reduced signal generated in the suppressed focal volume can be detected. Here reported is a theoretical analysis of detection limit （DL） to time-resolved CARS （T-CARS） nanoscopy based on our proposed additional probe-beam-induced phonon depletion （APIPD） method for the low concentration samples. In order to acquire a detailed shot-noise limited signal-to-noise （SNR） and the involved parameters to evaluate DL, the T-CARS process is described with full quantum theory to estimate the extreme power density levels of the pump and Stokes beams determined by saturation behavior of coherent phonons, which are both actually on the order of ~ 109 W/cm2. When the pump and Stokes intensities reach such values and the total intensity of the excitation beams arrives at a maximum tolerable by most biological samples in a certain suppressed focal volume （40-nm suppressed focal scale in APIPD method）, the DL correspondingly varies with exposure time, for example, DL values are 103 and 102 when exposure times are 20 ms and 200 ms respectively.     

The master equation for a two-level atom in a laser field with squeezing-like terms

In this paper, we derive the time dependent solution of the effective master equation for the reduced density matrix operator of a two-level atom driven by a strong classical field and damped into a “modelled” reservoir with non-flat density of modes. The effects of different parameters on the atomic inversion, the von Neumann entropy and the entropy squeezing are discussed.     

Long-time fidelity and chaos for a kicked nonlinear oscillator system

We deal with a system comprising a nonlinear (Kerr-like) oscillator excited by a series of ultra-short external pulses. We introduce the fidelity-based entropic parameter that can be used as an indicator of quantum chaos. Moreover, we propose to use the fidelity-like parameter comprising the information about the mean number of photons in the system. We shall concentrate on the long-time behaviour of the parameters discussed, showing that for deep chaos cases the quantum fidelities behave chaotically in the classical sense despite their strictly quantum character.     

Stability in a general coupled laser array

For the first time we have presented a method to investigate the stability of quiescent state in a coupled laser array. By introducing tiny perturbation, stability of quiescent state can be known by investigating eigenvalues of coefficient matrix of the corresponding linear differential equations. Only when real parts of the eigenvalues were all negative or zero, the corresponding quiescent state is stable. Two tapes of coupled laser array with loop and linear topological structure were studied respectively. It was found that there were innumerable quiescent states and they could be divided into several types based on phase relation. Some types were stable and others were unstable. Topological structure affects the stability of quiescent state in a coupled laser array.     

Melting and unzipping of DNA

Existing experimental studies of the thermal denaturation of DNA yield sharp steps in the melting curve suggesting that the melting transition is first order. This transition has been theoretically studied since the early sixties, mostly within an approach in which the microscopic configurations of a DNA molecule consist of an alternating sequence of non-interacting bound segments and denaturated loops. Studies of these models neglect the repulsive, self-avoiding, interaction between different loops and segments and have invariably yielded continuous denaturation transitions. In the present study we take into account in an approximate way the excluded-volume interaction between denaturated loops and the rest of the chain. This is done by exploiting recent results on scaling properties of polymer networks of arbitrary topology. We also ignore the heterogeneity of the polymer. We obtain a first-order melting transition in d = 2 dimensions and above, consistent with the experimental results. We also consider within our approach the unzipping transition, which takes place when the two DNA strands are pulled apart by an external force acting on one end. We find that the under equilibrium condition the unzipping transition is also first order. Although the denaturation and unzipping transitions are thermodynamically first order, they do exhibit critical fluctuations in some of their properties. For instance, the loop size distribution decays algebraically at the transition and the length of the denaturated end segment diverges as the transition is approached. We evaluate these critical properties within our approach. Received 21 August 2001 and Received in final form 26 January 2002     

Coupling coefficients evaluation of a directional coupler using gain guided and index antiguided fibers

In this paper, we have investigated the mutual and self coupling characteristics of directional couplers using two individual gain guided and index antiguided fibers, which can deliver robust single mode operation with large mode area, respectively owing to the combined adequately large gain coefficients in the core; Some interesting and distinguishing properties from conventional index guided fiber couplers are obtained that: The variations of coupling coefficients are complex-valued and spatially damping oscillated, but not exponential-like decreasing as conventional index guided couplers.     

Polarization-encoded all-optical quaternary multiplexer and demultiplexer - A proposal

Multi-valued logic is positioned as a coming generation technology that can execute arithmetic functions faster and with less interconnect than binary logic. Furthermore, nonbinary data storage would require less physical space than binary data. The application of multi-valued digital signals can provide considerable relief of capacity constraints. In electronics many proposals have already been reported. But, here for the first time we propose an all-optical circuit for designing quaternary (four-valued) multiplexer and demultiplexer with the help of some polarization-encoded basic quaternary logic gates (quaternary min and quaternary delta literal). Nonlinear interferometer-based optical switch can take an important role here. The principles and possibilities of design of all-optical quaternary multi-valued multiplexer and demultiplexer circuits are proposed and described.     

Comparative atomistic and coarse-grained study of water: What do we lose by coarse-graining?

We employ the inverse Boltzmann method to coarse-grain three commonly used three-site water models (TIP3P, SPC and SPC/E) where one molecule is replaced with one coarse-grained particle with isotropic two-body interactions only. The shape of the coarse-grained potentials is dominated by the ratio of two lengths, which can be rationalized by the geometric constraints of the water clusters. It is shown that for simple two-body potentials either the radial distribution function or the geometrical packing can be optimized. In a similar way, as needed for multiscale methods, either the pressure or the compressibility can be fitted to the all atom liquid. In total, a speed-up by a factor of about 50 in computational time can be reached by this coarse-graining procedure.