A generalised cole-hopf transformation for nonlinear parabolic and hyperbolic equations

The Cole-Hopf transformation has been generalized to generate a large class of nonlinear parabolic and hyperbolic equations which are exactly linearizable. These include model equations of exchange processes and turbulence. The methods to solve the corresponding linear equations have also been indicated.La transformation de Cole et de Hopf a été généralisée en vue d'engendrer une classe d'équations nonlinéaires paraboliques et hyperboliques qui peuvent être rendues linéaires de façon exacte. Elles comprennent des équations modèles de procédés d'échange et de turbulence. Les méthodes pour résoudre les équations linéaires correspondantes ont également été indiquées.

Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT)

System of kinematical conservation laws (KCL) govern evolution of a curve in a plane or a surface in space, even if the curve or the surface has singularities on it. In our recent publication K. R. Arun, P. Prasad, 3-D kinematical conservation laws (KCL): evolution of a surface in R-3-in particular propagation of a nonlinear wavefront, Wave Motion 46 (2009) 293-311] we have developed a mathematical theory to study the successive positions and geometry of a 3-D weakly nonlinear wavefront by adding an energy transport equation to KCL. The 7 x 7 system of equations of this KCL based 3-D weakly nonlinear ray theory (WNLRT) is quite complex and explicit expressions for its two nonzero eigenvalues could not be obtained before. In this short note, we use two different methods: (i) the equivalence of KCL and ray equations and (ii) the transformation of surface coordinates, to derive the same exact expressions for these eigenvalues. The explicit expressions for nonzero eigenvalues are important also for checking stability of any numerical scheme to solve 3-D WNLRT. (C) 2010 Elsevier Inc. All rights reserved.

Graphene analogue BCN: Femtosecond nonlinear optical susceptibility and hot carrier dynamics

Third-order nonlinear absorption and refraction coefficients of a few-layer boron carbon nitride (BCN) and reduced graphene oxide (RGO) suspensions have been measured at 3.2 eV in the femtosecond regime. Optical limiting behavior is exhibited by BCN as compared to saturable absorption in RGO. Nondegenerate time-resolved differential transmissions from BCN and RGO show different relaxation times. These differences in the optical nonlinearity and carrier dynamics are discussed in the light of semiconducting electronic band structure of BCN vis-a-vis the Dirac linear band structure of graphene. (C) 2010 Elsevier B.V. All rights reserved.

Nonlinear fracture properties of concrete-concrete interfaces

The fracture properties of different concrete-concrete interfaces are determined using the Bazant's size effect model. The size effect on fracture properties are analyzed using the boundary effect model proposed by Wittmann and his co-workers. The interface properties at micro-level are analyzed through depth sensing micro-indentation and scanning electron microscopy. Geometrically similar beam specimens of different sizes having a transverse interface between two different strengths of concrete are tested under three-point bending in a closed loop servo-controlled machine with crack mouth opening displacement control. The fracture properties such as, fracture energy (G(f)), length of process zone (c(f)), brittleness number (beta), critical mode I stress intensity factor (K-ic), critical crack tip opening displacement CTODc (delta(c)), transitional ligament length to free boundary (a(j)), crack growth resistance curve and micro-hardness are determined. It is seen that the above fracture properties decrease as the difference between the compressive strength of concrete on either side of the interface increases. (C) 2010 Elsevier Ltd. All rights reserved.

Invariant norm quantifying nonlinear content of Hamiltonian systems

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm has several potential applications. (C) 2010 Elsevier Inc. All rights reserved.

Weber-Fechner type nonlinear behavior in zigzag edge graphene nanoribbons

Using a continuum Dirac theory, we study the density and spin response of zigzag edge-terminated graphene ribbons subjected to edge potentials and Zeeman fields. Our analytical calculations of the density and spin responses of the closed system (fixed particle number) to the static edge fields, show a highly nonlinear Weber-Fechner type behavior where the response depends logarithmically on the edge potential. The dependence of the response on the size of the system (e.g., width of a nanoribbon) is also uncovered. Zigzag edge graphene nanoribbons, therefore, provide a realization of response of organs such as the eye and ear that obey Weber-Fechner law. We validate our analytical results with tight-binding calculations. These results are crucial in understanding important effects of electron-electron interactions in graphene nanoribbons such as edge magnetism, etc., and also suggest possibilities for device applications of graphene nanoribbons.

A DC-to-Three-Phase-AC High-Frequency Link Converter With Compensation for Nonlinear Distortion

This paper focuses on a new high-frequency (HF) link dc-to-three-phase-ac power converter. The least number of switching devices among other HF link dc-to-three-phase-ac converters, improved power density due to the absence of devices of bidirectional voltage-blocking capability, simple commutation requirements, and isolation between input and output are the integral features of this topology. The commutation process of the converter requires zero portions in the link voltage. This causes a nonlinear distortion in the output three-phase voltages. The mathematical analysis is carried out to investigate the problem, and suitable compensation in modulating signal is proposed for different types of carrier. Along with the modified modulator structure, a synchronously rotating reference-frame-based control scheme is adopted for the three-phase ac side in order to achieve high dynamic performance. The effectiveness of the proposed scheme has been investigated and verified through computer simulations and experimental results with 1-kVA prototype.

Structure and representation of correlation functions and the density matrix for a statistical wave field in optics

A systematic structure analysis of the correlation functions of statistical quantum optics is carried out. From a suitably defined auxiliary two‐point function we are able to identify the excited modes in the wave field. The relative simplicity of the higher order correlation functions emerge as a byproduct and the conditions under which these are made pure are derived. These results depend in a crucial manner on the notion of coherence indices and of unimodular coherence indices. A new class of approximate expressions for the density operator of a statistical wave field is worked out based on discrete characteristic sets. These are even more economical than the diagonal coherent state representations. An appreciation of the subtleties of quantum theory obtains. Certain implications for the physics of light beams are cited.

Studies on nonlinear optical materials: structure of diphenylmethyl (Z)-1-(1-methylthio-2-nitrovinyl)tetrahydropyrrole-2-carboxylate

C21H22N2045, M r = 398.5, orthorhombic, P212~21, a = 9.799 (1), b = 11.853 (1), c = 17.316(2)/~, V=2011.4A 3, Z=4, Dm=l.320, Dx=1.314Mgm -3, CuKa, A=1.5418A, Iz= 1.63 ram-1, F(000) = 840.0, T = 293 K, R = 0.055 for 1735 significant reflections. In the 1-methylthio-2- nitrovinyl moiety the C--C bond, 1.368 (7)A, is significantly longer than in ethylene, 1.336 (2)/~. The second harmonic generation (SHG) efficiency of this compound is only 0.25 of the urea standard. The correlation between the molecular packing and SHG is discussed.

A mathematical analysis of nonlinear waves in a fluid filled visco-elastic tube

Our investigations in this paper are centred around the mathematical analysis of a ldquomodal waverdquo problem. We have considered the axisymmetric flow of an inviscid liquid in a thinwalled viscoelastic tube under certain simplifying assumptions. We have first derived the propagation space equations in the long wave limit and also given a general procedure to derive these equations for arbitrary wave length, when the flow is irrotational. We have used the method of operators of multiple scales to derive the nonlinear Schrödinger equation governing the modulation of periodic waves and we have elaborated on the ldquolong modulated wavesrdquo and the ldquomodulated long wavesrdquo. We have also examined the existence and stability of Stokes waves in this system. This is followed by a discussion of the progressive wave solutions of the long wave equations. One of the most important results of our paper is that the propagation space equations are no longer partial differential equations but they are in terms of pseudo-differential operators.Die vorliegenden Untersuchungen beziehen sich auf die mathematische Behandlung des ldquorModalwellenrdquo-Problems. Die achsensymmetrische Strömung einer nichtviskosen Flüssigkeit in einem dünnwandigen viskoelastischen Rohr, unter bestimmten vereinfachenden Annahmen, wird betrachtet. Zuerst werden die Gleichungen des Ausbreitungsraumes im Langwellenbereich abgeleitet und eine allgemeine Methode zur Herleitung dieser Gleichungen für beliebige Wellenlängen bei nichtrotierender Strömung angegeben. Eine Operatorenmethode mit multiplem Maßstab wird verwendet zur Herleitung der nichtlinearen Schrödinger-Gleichung für die Modulation der periodischen Wellen, und die ldquorlangmodulierten Wellenrdquo sowie die ldquormodulierten Langwellenrdquo werden aufgezeigt. Weiters wird die Existenz und die Stabilität der Stokes-Wellen im System untersucht. Anschließend werden die progressiven Wellenlösungen der Langwellengleichungen diskutiert. Eines der wichtigsten Ergebnisse dieser Arbeit ist, daß die Gleichungen des Ausbreitungsraumes keine partiellen Differentialgleichungen mehr sind, sondern Ausdrücke von Pseudo-Differentialoperatoren.

Nonlinear Transport in Hybrid Polypyrrole-Gold Nanostructures

We have studied charge transport in nanometer scale films of polypyrrole (PPy) that were grown electrochemically onto discontinuous ultrathin films of gold. The gold films consisted of 100 nm size islands, separated from each other by nanometer-size gaps. The thickness of PPy can be varied from 30 to 200 nm. The I-V characteristics of these hybrid PPy-Au nanostructures show strong non-linearity at low temperatures, and in particular for the more insulating samples. The hopping transport is further verified from the log / versus V-1/4 plots. Furthermore, the I-V data follow an empirical relation dlog//dV(1/4) similar to T-1/2.

Application of nonlinear filtering to credit risk

Merton's model views equity as a call option on the asset of the firm. Thus the asset is partially observed through the equity. Then using nonlinear filtering an explicit expression for likelihood ratio for underlying parameters in terms of the nonlinear filter is obtained. As the evolution of the filter itself depends on the parameters in question, this does not permit direct maximum likelihood estimation, but does pave the way for the `Expectation-Maximization' method for estimating parameters. (C) 2010 Elsevier B.V. All rights reserved.

Analysis of Nonlinear Optical Properties of Photonic Crystal Beam-splitters

The paper analyses electromagnetic wave propagation through nonlinear photonic crystal beam-splitters. Different lattice configurations of Y-junction beam-splitters are simulated and propagation properties are investigated with introducing nonlinearity with varying the rod size in crystal lattice. It is seen that nonlinear photonic crystal shows a considerable band-gap even at low refractive contrast. The division of power in both arms of beam-splitters can be controlled by varying the nonlinearity.

Minimal three-component SU(2) gadget for polarization optics

Two identities involving quarter-wave plates and half-wave plates are established. These are used to improve on an earlier gadget involving four wave plates leading to a new gadget involving just three plates, a half-wave plate and two quarter-wave plates, which can realize all SU(2) polarization transformations. This gadget is shown to involve the minimum number of quarter-wave and half-wave plates. The analysis leads to a decomposition theorem for SU (2) matrices in terms of factors which are symmetric fourth and eighth roots of the identity.