We study nonlinear mid-IR crystals and assess their potential for ultrafast cascaded nonlinearities in the type 0 phase-matching interaction. Few-cycle, broadband energetic mid-IR pulses can be generated from compressing multi-cycle mid-IR pulses with self-defocusing solitons. Ultrashort mid-IR pulses is currently a hot topic since they can be used for probing and even manipulating the ultra-fa...

We examine the scale dependence of dark matter halo and galaxy clustering on very large scales (0:01 < k‰h Mpc ÿ1 Š < 0:15), due to nonlinear effects from dynamics and halo bias. We pursue a two line offensive: high-resolution numerical simulations are used to establish some old and some new results, and an analytic model is developed to understand their origins. Our simulations show: (i) that ...

in an ordered Banach space E with positive cone K, where M >0 is a constant, f : [0, 1] × K × K ® K is continuous, S : C([0, 1], K) ® C([0, 1], K) is a Fredholm integral operator with positive kernel. Under more general order conditions and measure of noncompactness conditions on the nonlinear term f, criteria on existence of positive solutions are obtained. The argument is based on the fixed p...

Single crystals of nonlinear optical material bis (guanidinium) hydrogen phosphate monohydrate (G2HP) belonging to non centrosymmetric space group P 21c were successfully grown by the slow evaporation method. Optical transmittance and second harmonic generation of the grown crystals have been studied by UV-vis-NIR spectrum and Kurtz powder technique respectively. The transmittance of G2HP cryst...

We determine optimal L-properties for the solutions of the general nonlinear elliptic system in the plane of the form fz = H(z, fz), h ∈ L(C), where H is a measurable function satisfying |H(z,w1) − H(z,w2)| ≤ k|w1 − w2| and k is a constant k < 1. We also establish the precise invertibility and spectral properties in L(C) for the operators I − T μ, I − μT, and T − μ, where T is the Beurling tran...

Abstract. In this paper, the analysis of the superconvergence property of the discontinuous Galerkin (DG) method applied to one-dimensional time-dependent nonlinear scalar conservation laws is carried out. We prove that the error between the DG solution and a particular projection of the exact solution achieves (k+ 3 2 )-th order superconvergence when upwind fluxes are used. The results hold tr...

The specific heat of liquid helium was calculated theoretically in the Landau theory . The results deviate from experimental data in the temperature region of 1.3 2.1 K. Many theorists subsequently improved the results of the Landau theory by applying temperature dependence of the elementary excitation energy , . As well known, many-body system has a total energy of Galilean covariant form. The...

In this paper, a possible solution of the basic nonlinear quadratic matrix equation was proposed. The solution is crucial in the formulation of the particular criteria for the delay-dependent finite time stability of discrete time delay systems represented as x(k+1) = A0(k) + A1x(k–h). The time delay-dependent criteria have been derived. In addition, the significance of the nonlinear discrete p...

In this article, we study the periodicity, the boundedness and the global stability of the positive solutions of the following nonlinear difference equation xn+1 = Axn +Bxn−k +Cxn−l +Dxn−σ + bxn−k [dxn−k − exn−l ] , n = 0,1,2, ....., where the coefficients A,B,C,D,b,d,e ∈ (0,∞), while k, l and σ are positive integers. The initial conditions x−σ ,...,x−l ,...,x−k, ...,x−1,x0 are arbitrary positi...

We consider the dynamics of N boson systems interacting through a pair potential N−1Va(xi− xj) where Va(x) = a V (x/a). We denote the solution to the N -particle Schrödinger equation by ψN,t. Recall that the Gross-Pitaevskii (GP) equation is a nonlinear Schrödinger equation and the GP hierarchy is an infinite BBGKY hierarchy of equations so that if ut solves the GP equation, then the family of ...