Constructing N-soliton solution for the mKdV equation through constrained flows

Based on the factorization of soliton equations into two commuting integrable x- and t-constrained flows, we derive N-soliton solutions for mKdV equation via its x- and t-constrained flows. It shows that soliton solution for soliton equations can be constructed directly from the constrained flows.Comment: 10 pages, Latex, to be published in "J. Phys. A: Math. Gen.

Enantiospecific Detection of Chiral Nanosamples Using Photoinduced Force

We propose a high-resolution microscopy technique for enantiospecific detection of chiral samples down to sub-100-nm size based on force measurement. We delve into the differential photoinduced optical force ΔF exerted on an achiral probe in the vicinity of a chiral sample when left and right circularly polarized beams separately excite the sample-probe interactive system. We analytically prove that ΔF is entangled with the enantiomer type of the sample enabling enantiospecific detection of chiral inclusions. Moreover, we demonstrate that ΔF is linearly dependent on both the chiral response of the sample and the electric response of the tip and is inversely related to the quartic power of probe-sample distance. We provide physical insight into the transfer of optical activity from the chiral sample to the achiral tip based on a rigorous analytical approach. We support our theoretical achievements by several numerical examples highlighting the potential application of the derived analytic properties. Lastly, we demonstrate the sensitivity of our method to enantiospecify nanoscale chiral samples with chirality parameter on the order of 0.01 and discuss how the sensitivity of our proposed technique can be further improved

Higher Order Potential Expansion for the Continuous Limits of the Toda Hierarchy

A method for introducing the higher order terms in the potential expansion to study the continuous limits of the Toda hierarchy is proposed in this paper. The method ensures that the higher order terms are differential polynomials of the lower ones and can be continued to be performed indefinitly. By introducing the higher order terms, the fewer equations in the Toda hierarchy are needed in the so-called recombination method to recover the KdV hierarchy. It is shown that the Lax pairs, the Poisson tensors, and the Hamiltonians of the Toda hierarchy tend towards the corresponding ones of the KdV hierarchy in continuous limit.Comment: 20 pages, Latex, to be published in Journal of Physics

Negaton and Positon solutions of the soliton equation with self-consistent sources

The KdV equation with self-consistent sources (KdVES) is used as a model to illustrate the method. A generalized binary Darboux transformation (GBDT) with an arbitrary time-dependent function for the KdVES as well as the formula for $N$-times repeated GBDT are presented. This GBDT provides non-auto-B\"{a}cklund transformation between two KdV equations with different degrees of sources and enable us to construct more general solutions with $N$ arbitrary $t$-dependent functions. By taking the special $t$-function, we obtain multisoliton, multipositon, multinegaton, multisoliton-positon, multinegaton-positon and multisoliton-negaton solutions of KdVES. Some properties of these solutions are discussed.Comment: 13 pages, Latex, no figues, to be published in J. Phys. A: Math. Ge

Thermodynamic Properties of Kagome Antiferromagnets with different Perturbations

We discuss the results of several small perturbations to the thermodynamic properties of Kagome Lattice Heisenberg Model (KLHM) at high and intermediate temperatures, including Curie impurities, dilution, in-plane and out of plane Dzyaloshinski-Moria (DM) anisotropies and exchange anisotropy. We examine the combined role of Curie impurities and dilution in the behavior of uniform susceptibility. We also study the changes in specific heat and entropy with various anisotropies. Their relevance to newly discovered materials ZnCu3(OH)6Cl2 is explored. We find that the magnetic susceptibility is well described by about 6 percent impurity and dilution. We also find that the entropy difference between the material and KLHM is well described by the DM parameter D_z/J~0.1.Comment: 6 pages, 3 figures, proceedings of the HFM 2008 Conferenc

On the Numerical Dispersion of Electromagnetic Particle-In-Cell Code : Finite Grid Instability

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the electromagnetic PIC algorithm to analyze the origin of these instabilities. We rigorously derive the faithful 3D numerical dispersion of the PIC algorithm, and then specialize to the Yee FDTD scheme. In particular, we account for the manner in which the PIC algorithm updates and samples the fields and distribution function. Temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme are also explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical 1D modes admitted in the system and their aliases. The most significant interaction is due critically to the correct represenation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction.Comment: 25 pages, 6 figure