Sample records for cubic nonlinear schroedinger

  1. Cubic nonlinear Schroedinger equation with vorticity

    Energy Technology Data Exchange (ETDEWEB)

    Caliari, M; Morato, L M; Zuccher, S [Dipartimento di Informatica, Universita di Verona, Ca' Vignal 2, Strada Le Grazie 15, 37134 Verona (Italy); Loffredo, M I [Dipartimento di Scienze Matematiche ed Informatiche, Universita di Siena, Pian dei Mantellini 44, 53100 Siena (Italy)], E-mail:, E-mail:, E-mail:, E-mail:


    In this paper, we introduce a new class of nonlinear Schroedinger equations (NLSEs), with an electromagnetic potential (A,{phi}), both depending on the wavefunction {psi}. The scalar potential {phi} depends on |{psi}|{sup 2}, whereas the vector potential A satisfies the equation of magnetohydrodynamics with coefficient depending on {psi}. In Madelung variables, the velocity field comes to be not irrotational in general and we prove that the vorticity induces dissipation, until the dynamical equilibrium is reached. The expression of the rate of dissipation is common to all NLSEs in the class. We show that they are a particular case of the one-particle dynamics out of dynamical equilibrium for a system of N identical interacting Bose particles, as recently described within stochastic quantization by Lagrangian variational principle. The cubic case is discussed in particular. Results of numerical experiments for rotational excitations of the ground state in a finite two-dimensional trap with harmonic potential are reported.

  2. Study of nonlinear waves described by the cubic Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Walstead, A.E.


    The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables.

  3. Ultrashort self-similar solutions of the cubic-quintic nonlinear Schroedinger equation with distributed coefficients in the inhomogeneous fiber

    Energy Technology Data Exchange (ETDEWEB)

    Dai Chaoqing; Wang Yueyue; Wang Xiaogang, E-mail: [School of Sciences, Zhejiang A and F University, Lin' an, Zhejiang 311300 (China)


    By means of the similarity transformation, we obtain exact self-similar solutions (similaritons) of the generalized cubic-quintic (CQ) nonlinear Schroedinger equation with spatially inhomogeneous group velocity dispersion, CQ nonlinearity and amplification or attenuation. Exact balance conditions between the dispersion, nonlinearity and the gain/loss have been obtained. As an example, we investigate their propagation dynamics in the dispersion decreasing fiber (DDF). Considering the fluctuation of the fiber parameter in real application, the exact balance conditions do not satisfy, and so we perform direct numerical analysis with initial 10% white noise for the bright similariton in both the DDF and the periodic distributed amplification system. Numerical calculations indicate stable propagation of the bright similariton over tens of dispersion lengths. These ultrashort self-similar optical waves are potentially useful for all-optical data-processing schemes and the design of beam compressors and amplifiers.

  4. A reliable treatment for nonlinear Schroedinger equations

    Energy Technology Data Exchange (ETDEWEB)

    Khani, F. [Department of Mathematics, Ilam University, PO Box 69315516, Ilam (Iran, Islamic Republic of); Department of Mathematics, Bakhtar Institute of Higher Education, PO Box 696, Ilam (Iran, Islamic Republic of)], E-mail:; Hamedi-Nezhad, S. [Department of Mathematics, Bakhtar Institute of Higher Education, PO Box 696, Ilam (Iran, Islamic Republic of)], E-mail:; Molabahrami, A. [Department of Mathematics, Ilam University, PO Box 69315516, Ilam (Iran, Islamic Republic of)], E-mail:


    Exp-function method is used to find a unified solution of nonlinear wave equation. Nonlinear Schroedinger equations with cubic and power law nonlinearity are selected to illustrate the effectiveness and simplicity of the method. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equation.

  5. Orbital stability of standing waves for some nonlinear Schroedinger equations

    Energy Technology Data Exchange (ETDEWEB)

    Cazenave, T.; Lions, P.L.


    We present a general method which enables as to prove the orbital stability of some standing waves in nonlinear Schroedinger equations. For example, we treat the cases of nonlinear Schroedinger equations arising in laser beams, of time-dependent Hartree equations.

  6. Analytic doubly periodic wave patterns for the integrable discrete nonlinear Schroedinger (Ablowitz-Ladik) model

    Energy Technology Data Exchange (ETDEWEB)

    Chow, K.W. [Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong (China)]. E-mail:; Conte, Robert [Service de Physique de l' etat Condense (URA 2464), CEA-Saclay, F-91191 Gif-sur-Yvette Cedex (France)]. E-mail:; Xu, Neil [Department of Mathematics, California Institute of Technology, Pasadena, CA 91125 (United States)]. E-mail:


    We derive two new solutions in terms of elliptic functions, one for the dark and one for the bright soliton regime, for the semi-discrete cubic nonlinear Schroedinger equation of Ablowitz and Ladik. When considered in the complex plane, these two solutions are identical. In the continuum limit, they reduce to known elliptic function solutions. In the long wave limit, the dark one reduces to the collision of two discrete dark solitons, and the bright one to a discrete breather.

  7. Blow-up in nonlinear Schroedinger equations. II. Similarity structure of the blow-up singularity

    DEFF Research Database (Denmark)

    Rypdal, K.; Juul Rasmussen, Jens


    A critical review of the literature on similarity solutions of nonlinear Schroedinger equations is presented. We demonstrate that the self-similar blow-up solutions discovered hitherto are all associated either with a simple stretching invariance, or with a slightly more complicated conformal...... invariance and generalizations of the latter. This generalized "quasi-invariance" reveals the nature of the blow-up singularity and resolves an old controversy. Most of the previous work has been done on the cubic nonlinearity. We generalize the results to an arbitrary power nonlinearity....

  8. Ehrenfest theorem, Galilean invariance and nonlinear Schroedinger equations

    Energy Technology Data Exchange (ETDEWEB)

    Kaelbermann, G [Soil and Water Department, Faculty of Agriculture, Rehovot 76100 (Israel)


    We prove that Galilean invariant Schroedinger equations derived from Lagrangian densities necessarily obey the Ehrenfest theorem for velocity-independent potentials. The conclusion holds as well for Lagrangians describing nonlinear self-interactions. An example of Doebner and Goldin motivates the result.

  9. Cubication of Conservative Nonlinear Oscillators (United States)

    Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada


    A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…

  10. Derivation of an applied nonlinear Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Pitts, Todd Alan [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Laine, Mark Richard [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Schwarz, Jens [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Rambo, Patrick K. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Karelitz, David B. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)


    We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release

  11. Asymptotics of weakly collapsing solutions of nonlinear Schroedinger equation

    CERN Document Server

    Ovchinnikov, Yu N


    One studied possible types of asymptotic behavior of weakly collapsing solution of the 3-rd nonlinear Schroedinger equation. It is shown that within left brace A, C sub 1 right brace parameter space there are two neighboring lines along which the amplitude of oscillation terms is exponentially small as to C sub 1 parameter. The same lines locates values of left brace A, C sub 1 right brace parameters at which the energy is equal to zero. With increase of C sub 1 parameter the accuracy of numerical determination of points with zero energy drops abruptly

  12. Cubication of conservative nonlinear oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Belendez, Augusto; Alvarez, Mariela L [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, Elena; Pascual, Inmaculada [Departamento de Optica, FarmacologIa y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail:


    A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.

  13. Rapidly decaying solutions of the nonlinear Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Cazenave, T. (Paris-6 Univ., 75 (France). Lab. d' Analyse Numerique); Weissler, F.B. (ENS, 94 - Cachan (France). Centre de Mathematiques Paris-7 Univ., 94 - Creteil (France). UFR de Sciences)


    We consider global solutions of the nonlinear Schroedinger equation iu{sub t}+{Delta}u={lambda}vertical strokeuvertical stroke{sup {alpha}}u, in R{sup N}, (NLS) where {lambda}{epsilon}R and 0<{alpha}< 4/N-2. In particular, for {alpha}>{alpha}{sub 0}=(2-N+{radical}(N{sup 2}+12N+4))/2N, we show that for every ({phi}{epsilon}H{sup 1}(R{sup N}) such that x{phi}(x){epsilon}L{sup 2}(R{sup N}), the solution of (NLS) with initial value {phi}(x)e{sup i(bvertical} {sup strokexvertical} {sup stroke2/4)} is global and rapidly decaying as t{yields}{infinity} if b is large enough. Furthermore, by applying the pseudo-conformal transformation and studying the resulting nonautonomous nonlinear Schroedinger equation, we obtain both new results and simpler proofs of some known results concerning the scattering theory. In particular, we construct the wave operators for 4/N+2<{alpha}<4/N-2. Also, we establish a low energy scattering theory for the same range of {alpha} and show that, at least for {lambda}<0, the lower bound on {alpha} is optimal. Finally, if {lambda}>0, we prove asymptotic completeness for {alpha}{sub 0}{<=}{alpha}<4/N-2. (orig.).

  14. Breathers and solitons of generalized nonlinear Schroedinger equations as degenerations of algebro-geometric solutions

    Energy Technology Data Exchange (ETDEWEB)

    Kalla, C, E-mail: [Institut de Mathematiques de Bourgogne, Universite de Bourgogne, 9 avenue Alain Savary, 21078 Dijon (France)


    We present new solutions in terms of elementary functions of the multi-component nonlinear Schroedinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These solutions are given in a simple determinantal form and are obtained as limiting cases in suitable degenerations of previously derived algebro-geometric solutions. In particular, we present for the first time breather and rational breather solutions of the multi-component nonlinear Schroedinger equations.

  15. Solitons on nanotubes and fullerenes as solutions of a modified non-linear Schroedinger equation


    Brihaye, Yves; Hartmann, Betti


    Fullerenes and nanotubes consist of a large number of carbon atoms sitting on the sites of a regular lattice. For pratical reasons it is often useful to approximate the equations on this lattice in terms of the continuous equation. At the moment, the best candidate for such an equation is the modified non-linear Schroedinger equation. In this paper, we study the modified non-linear Schroedinger equation, which arises as continuous equation in a system describing an excitation on a hexagonal l...

  16. Analytical solutions to a class of nonlinear Schroedinger equations with PT-like potentials

    Energy Technology Data Exchange (ETDEWEB)

    Musslimani, Ziad H [Department of Mathematics, Florida State University, Tallahassee, 32306-4510 FL (United States); Makris, Konstantinos G; El-Ganainy, Ramy; Christodoulides, Demetrios N [College of Optics and Photonics-CREOL, University of Central Florida, Orlando, 32816 FL (United States)


    We present closed form solutions to a certain class of one- and two-dimensional nonlinear Schroedinger equations involving potentials with broken and unbroken PT symmetry. In the one-dimensional case, these solutions are given in terms of Jacobi elliptic functions, hyperbolic and trigonometric functions. Some of these solutions are possible even when the corresponding PT-symmetric potentials have a zero threshold. In two-dimensions, hyperbolic secant type solutions are obtained for a nonlinear Schroedinger equation with a non-separable complex potential.

  17. Blow-up in nonlinear Schroedinger equations. I. A general review

    DEFF Research Database (Denmark)

    Juul Rasmussen, Jens; Rypdal, K.


    The general properties of a class of nonlinear Schroedinger equations: iut + p:∇∇u + f(|u|2)u = 0 are reviewed. Conditions for existence, uniqueness, and stability of solitary wave solutions are presented, along with conditions for blow-up and global existence for the Cauchy problem.......The general properties of a class of nonlinear Schroedinger equations: iut + p:∇∇u + f(|u|2)u = 0 are reviewed. Conditions for existence, uniqueness, and stability of solitary wave solutions are presented, along with conditions for blow-up and global existence for the Cauchy problem....

  18. Asymptotic stability of multi-soliton solutions for nonlinear Schroedinger eqations


    Perelman, G.


    We consider the Cauchy problem for the nonlinear Schroedinger eqiation with initial data close to a sum of N decoupled solitons. Under some suitable assumptions on the spectral structure of the one soliton linearizations we prove that for large time the asymptotics of the solution is given by a sum of solitons with slightly modified parameters and a small dispersive term.

  19. A study on the d-dimensional Schroedinger equation with a power-law nonlinearity

    Energy Technology Data Exchange (ETDEWEB)

    Shidfar, A. [Department of Mathematics, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of)], E-mail:; Molabahrami, A. [Department of Mathematics, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of); Department of Mathematics, Ilam University, PO Box 69315516, Ilam (Iran, Islamic Republic of)], E-mail:; Babaei, A.; Yazdanian, A. [Department of Mathematics, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of)


    In this paper, the homotopy perturbation method (HPM) is applied to obtain series pattern solutions of the Cauchy problem for the d-dimensional Schroedinger equation with a power-law nonlinearity. We introduce the recurrent relation to solve the mentioned Cauchy problem. For some cases of given initial condition, we obtain the closed form of the exact solutions.

  20. On the effect of random inhomogeneities in Kerr media modelled by a nonlinear Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Villarroel, Javier [Facultad de Ciencias, Universidad de Salamanca, Plaza Merced s/n, E-37008 Salamanca (Spain); Montero, Miquel, E-mail: javier@usal.e, E-mail: miquel.montero@ub.ed [Departament de FIsica Fonamental, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona (Spain)


    We consider the propagation of optical beams under the interplay of dispersion and Kerr nonlinearity in optical fibres with impurities distributed at random uniformly on the fibre. By using a model based on the nonlinear Schroedinger equation we clarify how such inhomogeneities affect different aspects such as the number of solitons present and the intensity of the signal. We also obtain the mean distance for the signal to dissipate to a given level.

  1. TOPICAL REVIEW: Nonlinear photonic crystals: III. Cubic nonlinearity (United States)

    Babin, Anatoli; Figotin, Alexander


    Weakly nonlinear interactions between wavepackets in a lossless periodic dielectric medium are studied based on the classical Maxwell equations with a cubic nonlinearity. We consider nonlinear processes such that: (i) the amplitude of the wave component due to the nonlinearity does not exceed the amplitude of its linear component; (ii) the spatial range of a probing wavepacket is much smaller than the dimension of the medium sample, and it is not too small compared with the dimension of the primitive cell. These nonlinear processes are naturally described in terms of the cubic interaction phase function based on the dispersion relations of the underlying linear periodic medium. It turns out that only a few quadruplets of modes have significant nonlinear interactions. They are singled out by a system of selection rules including the group velocity, frequency and phase matching conditions. It turns out that the intrinsic symmetries of the cubic interaction phase stemming from assumed inversion symmetry of the dispersion relations play a significant role in the cubic nonlinear interactions. We also study canonical forms of the cubic interaction phase leading to a complete quantitative classification of all possible significant cubic interactions. The classification is ultimately based on a universal system of indices reflecting the intensity of nonlinear interactions.

  2. Baecklund transformations and exact soliton solutions for nonlinear Schroedinger-type equations

    Energy Technology Data Exchange (ETDEWEB)

    Khater, A. H. [Cairo Univ. (Egypt). Faculty of science, Dept. of Mathematics]|[Antwerp Univ. (Belgium). Dept. of Physics; Callebaut, D. K. [Antwerp Univ. (Belgium). Dept. of Physics; El-Kalaawy, O. H. [Cairo Univ. (Egypt). Faculty of science, Dept. of Mathematics


    Using the Baecklund transformations (BTs) and the Darboux-Bargmann technique, the Authors consider the nonlinear Schroedinger-type (NLS-type) equations solvable by the inverse scattering method of Zakharov-Shabat/Ablowitz-Kaup-Newell-Segur (ZS/AKNS) system and the ZS/AKNS wave functions corresponding to the soliton solutions of NLS-type equations. Thus, families of new soliton solutions for NLS- type equations are obtained.

  3. General soliton solutions of an n-dimensional nonlinear Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Khater, A. H.; Seadawy, A. R. [Cairo Univ., Cairo (Egypt). Faculty of Science, Mathematics Dept.; Helal, M. A. [Cairo Univ., Cairo (Egypt). Faculty of Science, Mathematics Dept.


    Applying the function transformation method, an n-dimensional nonlinear Schroedinger (NDNLS) equation is transformed into a sinh-Gordon equation and other equations, which depend only on one function {zeta} leads to a general soliton solution of the NDNLS equation. It contains some interesting specific solutions such as the N multiple solitons, the propagational breathers and the quadric solitons. Their properties are simply discussed.

  4. Instability of stationary states in nonlinear Schroedinger or Klein-Gordon equations

    Energy Technology Data Exchange (ETDEWEB)

    Berestycki, H.; Cazenave, T. (Universite Pierre et Marie Curie, Paris (France))


    In this note, we prove the instability of stationary states for the Schroedinger equation and for the Klein-Gordon equation. Here, u(x) is a ground state solution of the nonlinear scalar field equation in Rsup(N). Indeed, under certain assumptions on g, we show that there exist initial conditions, arbitrarily close to the stationary states, such that the solutions of these equations blow up in finite time.

  5. Strong correlations in model of the scale-invariance (2+1) dimensional nonlinear Schroedinger equation

    CERN Document Server

    Protogenov, A P


    The brief review of events, conditioned by the nonlinear modes strong correlations in the planar systems is presented. The analysis is limited by the Schroedinger nonlinear equation model. The fields stationary distributions are determined. The dependence of the particles number on the parameter characterizing the degree of looking, of the universal oscillation lines, is obtained. It is shown that by small values of this parameter there exists on the two-dimensional lattice the universal gravitation, which may be the dynamic cause of transition to the coherent state. The connection of the chiral nonlinear boundary modes with the violations of the Galilean-invariance of the considered system is discussed

  6. Cole-Hopf-like transformation for Schroedinger equations containing complex nonlinearities

    Energy Technology Data Exchange (ETDEWEB)

    Kaniadakis, G.; Scarfone, A.M. [Dipartimento di Fisica, Politecnico di Torino, Torino (Italy) and Istituto Nazionale di Fisica della Materia, Unita del Politecnico di Torino, Torino (Italy)]. E-mails:;


    We consider systems which conserve the particle number and are described by Schroedinger equations containing complex nonlinearities. In the case of canonical systems, we study their main symmetries and conservation laws. We introduce a Cole-Hopf-like transformation both for canonical and noncanonical systems, which changes the evolution equation into another one containing purely real nonlinearities, and reduces the continuity equation to the standard form of the linear theory. This approach allows us to treat, in a unifying scheme, a wide variety of canonical and noncanonical nonlinear systems, some of them already known in the literature. (author)

  7. Embedded solitons in the third-order nonlinear Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Pal, Debabrata; Ali, Sk Golam; Talukdar, B [Department of Physics, Visva-Bharati University, Santiniketan 731235 (India)], E-mail:


    We work with a sech trial function with space-dependent soliton parameters and envisage a variational study for the nonlinear Schoedinger (NLS) equation in the presence of third-order dispersion. We demonstrate that the variational equations for pulse evolution in this NLS equation provide a natural basis to derive a potential model which can account for the existence of a continuous family of embedded solitons supported by the third-order NLS equation. Each member of the family is parameterized by the propagation velocity and co-efficient of the third-order dispersion.

  8. Light bullets in the spatiotemporal nonlinear Schroedinger equation with a variable negative diffraction coefficient

    Energy Technology Data Exchange (ETDEWEB)

    Zhong Weiping [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Belic, Milivoj [Texas A and M University at Qatar, 23874 Doha (Qatar); Institute of Physics, University of Belgrade, P. O. Box 68, 11001 Belgrade (Serbia); Assanto, Gaetano [NooEL, Nonlinear Optics and OptoElectronics Lab, University of Rome ' ' Roma Tre,' ' I-00146 Rome (Italy); Malomed, Boris A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona) (Spain); Huang, Tingwen [Texas A and M University at Qatar, 23874 Doha (Qatar)


    We report approximate analytical solutions to the (3+1)-dimensional spatiotemporal nonlinear Schroedinger equation, with the uniform self-focusing nonlinearity and a variable negative radial diffraction coefficient, in the form of three-dimensional solitons. The model may be realized in artificial optical media, such as left-handed materials and photonic crystals, with the anomalous sign of the group-velocity dispersion (GVD). The same setting may be realized through the interplay of the self-defocusing nonlinearity, normal GVD, and positive variable diffraction. The Hartree approximation is utilized to achieve a suitable separation of variables in the model. Then, an inverse procedure is introduced, with the aim to select a suitable profile of the modulated diffraction coefficient supporting desirable soliton solutions (such as dromions, single- and multilayer rings, and multisoliton clusters). The validity of the analytical approximation and stability of the solutions is tested by means of direct simulations.

  9. Ultrasonic harmonic generation from materials with up to cubic nonlinearity. (United States)

    Kube, Christopher M; Arguelles, Andrea P


    This letter considers the combined effects of quadratic and cubic nonlinearity on plane wave propagation in generally anisotropic elastic solids. Displacement solutions are derived that represent the fundamental, second-, and third-harmonic waves. In arriving at the solutions, the quadratic and cubic nonlinearity parameters for generally anisotropic materials are defined. The effects of quadratic and cubic nonlinearity are shown to influence the amplitude and phase of the fundamental wave. In addition, the phase of the third-harmonic depends on a simple combination of the quadratic and cubic nonlinearity parameters. Nonlinearity parameters are given explicitly for materials having isotropic and cubic symmetry. Lastly, acoustic nonlinearity surfaces are introduced, which illustrate the nonlinearity parameters as a function of various propagation directions in anisotropic materials.

  10. Parametric resonance for solitons in the nonlinear Schroedinger equation model with time-dependent harmonic oscillator potential

    Energy Technology Data Exchange (ETDEWEB)

    Hernandez-Tenorio, C. [Benemerita Universidad Autonoma de Puebla, 7200 Puebla (Mexico) and Universidad Autonoma del Estado de Mexico (Mexico)]. E-mail:; Belyaeva, T.L. [Universidad Autonoma del Estado de Mexico (Mexico); Serkin, V.N. [Benemerita Universidad Autonoma de Puebla, 7200 Puebla (Mexico)


    The dynamics of nonlinear solitary waves is studied in the framework of the nonlinear Schroedinger equation model with time-dependent harmonic oscillator potential. The model allows one to analyse on general basis a variety of nonlinear phenomena appearing both in Bose-Einstein condensate, condensed matter physics, nonlinear optics, and biophysics. The soliton parametric resonance is investigated by using two complementary methods: the adiabatic perturbation theory and direct numerical experiments. Conditions for reversible and irreversible denaturation of soliton bound states are also considered.

  11. Global Well-Posedness for Cubic NLS with Nonlinear Damping

    KAUST Repository

    Antonelli, Paolo


    We study the Cauchy problem for the cubic nonlinear Schrödinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we treat the energy-critical case of a quintic dissipation in three space dimensions. © Taylor & Francis Group, LLC.

  12. A cubic interpolation algorithm for solving non-linear equations ...

    African Journals Online (AJOL)

    A new Algorithm - based on cubic interpolation have been developed for solving non-linear algebraic equations. The Algorithm is derived from LaGrange's interpolation polynomial. The method discussed here is faster than the \\"Regular Falsi\\" which is based on linear interpolation. Since this new method does not involve ...

  13. The initial value problem, scattering and inverse scattering, for Schroedinger equations with a potential and a non-local nonlinearity

    Energy Technology Data Exchange (ETDEWEB)

    Romero, MarIa de los Angeles Sandoval; Weder, Ricardo [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-726, Mexico DF 01000 (Mexico)


    We consider nonlinear Schroedinger equations with a potential, and non-local nonlinearities, that are models in mesoscopic physics, for example of a quantum capacitor, and that are also models of molecular structure. We study in detail the initial value problem for these equations, in particular, existence and uniqueness of local and global solutions, continuous dependence on the initial data and regularity. We allow for a large class of unbounded potentials. We have no restriction on the growth at infinity of the positive part of the potential. We also construct the scattering operator in the case of potentials that go to zero at infinity. Furthermore, we give a method for the unique reconstruction of the potential from the small amplitude limit of the scattering operator. In the case of the quantum capacitor, our method allows us to uniquely reconstruct all the physical parameters from the small amplitude limit of the scattering operator.

  14. Cubic nonlinear Schrödinger equation with vorticity (United States)

    Caliari, M.; Loffredo, M. I.; Morato, L. M.; Zuccher, S.


    In this paper, we introduce a new class of nonlinear Schrödinger equations (NLSEs), with an electromagnetic potential (\\mathcal A,\\Phi) , both depending on the wavefunction Ψ. The scalar potential Φ depends on |Ψ|2, whereas the vector potential \\mathcal A satisfies the equation of magnetohydrodynamics with coefficient depending on Ψ. In Madelung variables, the velocity field comes to be not irrotational in general and we prove that the vorticity induces dissipation, until the dynamical equilibrium is reached. The expression of the rate of dissipation is common to all NLSEs in the class. We show that they are a particular case of the one-particle dynamics out of dynamical equilibrium for a system of N identical interacting Bose particles, as recently described within stochastic quantization by Lagrangian variational principle. The cubic case is discussed in particular. Results of numerical experiments for rotational excitations of the ground state in a finite two-dimensional trap with harmonic potential are reported.

  15. Semiclassical Limit of the Non-linear Schroedinger-Poisson Equation With Subcritical Initial Data (United States)


    lim ∇xargψ. As noted earlier, this argument is self - consistent as long as the solution of the Euler- Poisson system (1.5)-(1.6) remains classical...00-2003 to 00-00-2003 4. TITLE AND SUBTITLE Semiclassical Limit of the Non-linear Schrodinger - Poisson Equation with Subcritical Initial Data 5a...classical limit of a self - consistent quantum-Vlasov equation in 3-D, Math. Models Methods Appl. Sci., 3 (1993), pp. 109–124. [SMM] C. Sparber, P. Markowich

  16. Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices (United States)

    Gao, Xuzhen; Zeng, Jianhua


    The nonlinear lattice — a new and nonlinear class of periodic potentials — was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting — the cubic and quintic model — by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully "nonlinear quasi-crystal". A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted Vakhitov-Kolokolov stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode — the fundamental and vortex solitons — are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross-Pitaevskii equation or nonlinear Schrödinger equation, the predicted localized modes thus may be implemented in Bose-Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.

  17. Schroedinger equation for bosons and fermions

    Energy Technology Data Exchange (ETDEWEB)

    Kaniadakis, G. [Politecnico di Torino (Italy). Dipt. di Fisica]|[Istituto Nazionale di Fisica della Materia, Unita del Politecnico di Torino, Turin (Italy)]|[Istituto Nazionale di Fisica Nucleare, Turin (Italy)


    We propose a non-linear Schroedinger equation describing the dynamics of bosons or fermions in an effective external force field. This equation is obtained by quantization of a stochastic Markovian process obeying a generalized exclusion principle. (orig.).

  18. A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities

    Directory of Open Access Journals (Sweden)

    S.H. Chen


    Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.

  19. Solving nonlinear Benjamin-Bona-Mahony equation using cubic B-spline and cubic trigonometric B-spline collocation methods (United States)

    Rahan, Nur Nadiah Mohd; Ishak, Siti Noor Shahira; Hamid, Nur Nadiah Abd; Majid, Ahmad Abd.; Azmi, Amirah


    In this research, the nonlinear Benjamin-Bona-Mahony (BBM) equation is solved numerically using the cubic B-spline (CuBS) and cubic trigonometric B-spline (CuTBS) collocation methods. The CuBS and CuTBS are utilized as interpolating functions in the spatial dimension while the standard finite difference method (FDM) is applied to discretize the temporal space. In order to solve the nonlinear problem, the BBM equation is linearized using Taylor's expansion. Applying the von-Neumann stability analysis, the proposed techniques are shown to be unconditionally stable under the Crank-Nicolson scheme. Several numerical examples are discussed and compared with exact solutions and results from the FDM.

  20. Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier

    DEFF Research Database (Denmark)

    Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel


    We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system...

  1. Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schroedinger model

    Energy Technology Data Exchange (ETDEWEB)

    Kozlowski, K.K.


    Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear Schroedinger model. This representation allows one to read-off straightforwardly the long-time/large-distance asymptotic behavior of this correlator. Our method of analysis reduces the complexity of the computation of the asymptotic behavior of correlation functions in the so-called interacting integrable models, to the one appearing in free fermion equivalent models. We compute explicitly the first few terms appearing in the asymptotic expansion. Part of these terms stems from excitations lying away from the Fermi boundary, and hence go beyond what can be obtained by using the CFT/Luttinger liquid based predictions. (orig.)

  2. Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schroedinger model

    Energy Technology Data Exchange (ETDEWEB)

    Kozlowski, K.K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Terras, V. [CNRS, ENS Lyon (France). Lab. de Physique


    We present a new method allowing us to derive the long-time and large-distance asymptotic behavior of the correlations functions of quantum integrable models from their exact representations. Starting from the form factor expansion of the correlation functions in finite volume, we explain how to reduce the complexity of the computation in the so-called interacting integrable models to the one appearing in free fermion equivalent models. We apply our method to the time-dependent zero-temperature current-current correlation function in the non-linear Schroedinger model and compute the first few terms in its asymptotic expansion. Our result goes beyond the conformal field theory based predictions: in the time-dependent case, other types of excitations than the ones on the Fermi surface contribute to the leading orders of the asymptotics. (orig.)

  3. A note on the prolongation structure of the cubically nonlinear integrable Camassa-Holm type equation

    Energy Technology Data Exchange (ETDEWEB)

    Stalin, S. [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamil Nadu (India); Senthilvelan, M., E-mail: [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamil Nadu (India)


    In this Letter, we formulate an exterior differential system for the newly discovered cubically nonlinear integrable Camassa-Holm type equation. From the exterior differential system we establish the integrability of this equation. We then study Cartan prolongation structure of this equation. We also discuss the method of identifying conservation laws and Baecklund transformation for this equation from the identified exterior differential system. -- Highlights: → An exterior differential system for a cubic nonlinear integrable equation is given. → The conservation laws from the exterior differential system is derived. → The Baecklund transformation from the Cartan-Ehresmann connection is obtained.

  4. Drag force in bimodal cubic-quintic nonlinear Schr\\"odinger equation

    CERN Document Server

    Feijoo, David; Paredes, Ángel; Michinel, Humberto


    We consider a system of two cubic-quintic non-linear Schr\\"odinger equations in two dimensions, coupled by repulsive cubic terms. We analyse situations in which a probe lump of one of the modes is surrounded by a fluid of the other one and analyse their interaction. We find a realization of D'Alembert's paradox for small velocities and non-trivial drag forces for larger ones. We present numerical analysis including the search of static and traveling form-preserving solutions along with simulations of the dynamical evolution in some representative examples.

  5. Accuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic Nonlinearities

    Directory of Open Access Journals (Sweden)

    Akira Abe


    and are the driving and natural frequencies, respectively. The application of Galerkin's procedure to the equation of motion yields nonlinear ordinary differential equations with quadratic and cubic nonlinear terms. The steady-state responses are obtained by using the discretization approach of the MMS in which the definition of the detuning parameter, expressing the relationship between the natural frequency and the driving frequency, is changed in an attempt to improve the accuracy of the solutions. The validity of the solutions is discussed by comparing them with solutions of the direct approach of the MMS and the finite difference method.

  6. On the reflection of solitons of the cubic nonlinear Schrödinger equation

    KAUST Repository

    Katsaounis, Theodoros


    In this paper, we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D cubic nonlinear Schrödinger equation as the underlying mathematical model, and we use an implicit-explicit type Crank-Nicolson finite element scheme for its numerical solution. After verifying the perfect reflection of the solitons on a vertical wall, we present the imperfect reflection of a dark soliton on a diagonal wall.

  7. Inelastic collision of two solitons for generalized BBM equation with cubic nonlinearity

    Directory of Open Access Journals (Sweden)

    Jingdong Wei


    Full Text Available We study the inelastic collision of two solitary waves of different velocities for the generalized Benjamin-Bona-Mahony (BBM equation with cubic nonlinearity. It shows that one solitary wave is smaller than the other one in the H^1(R energy space. We explore the sharp estimates of the nonzero residue due to the collision, and prove the inelastic collision of two solitary waves and nonexistence of a pure 2-soliton solution.

  8. Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schrödinger equation

    KAUST Repository

    Crosta, M.


    We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.

  9. Distributed nonlinear optical response

    DEFF Research Database (Denmark)

    Nikolov, Nikola Ivanov


    of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....

  10. Single-particle And Collective Effects Of Cubic Nonlinearity In The Beam Dynamics Of Proton Synchrotrons

    CERN Document Server

    Tran Hy, J


    This thesis describes some new studies of the effects of cubic nonlinearities arising from image-charge forces and octupole magnets on the transverse beam dynamics of proton synchrotrons and storage rings, and also a study of the damping of coherent oscillations using a feed-back damper. In the latter case, various corrective algorithms were modeled using linear one-turn maps. Kicks of fixed amplitude but appropriate sign were shown to provide linear damping and no coherent tune shift, though the rate predicted analytically was somewhat higher than that observed in simulations. This algorithm gave much faster damping (for equal power) than conventional proportional kicks, which damp exponentially. Two single-particle effects of the image-change force were investigated: distortion of the momentum dispersion function and amplitude dependence of the betatron tunes (resulting in tune spread). The former is calculated using transfer maps and the method of undetermined coefficients, the latter by solving the cubic ...

  11. Wave propagation properties in oscillatory chains with cubic nonlinearities via nonlinear map approach

    Energy Technology Data Exchange (ETDEWEB)

    Romeo, Francesco [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail:; Rega, Giuseppe [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail:


    Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration.

  12. Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity

    Directory of Open Access Journals (Sweden)

    Alberto Lastra


    Full Text Available We study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter $\\epsilon$. This is a continuation of the precedent work [22] by the first author. We construct two families of sectorial meromorphic solutions obtained as a small perturbation in $\\epsilon$ of two branches of an algebraic slow curve of the equation in time scale. We show that the nonsingular part of the solutions of each family shares a common formal power series in $\\epsilon$ as Gevrey asymptotic expansion which might be different one to each other, in general.

  13. Chirped self-similar waves for quadratic-cubic nonlinear Schrödinger equation (United States)

    Pal, Ritu; Loomba, Shally; Kumar, C. N.


    We have constructed analytical self-similar wave solutions for quadratic-cubic Nonlinear Schrödinger equation (QC-NLSE) by means of similarity transformation method. Then, we have investigated the role of chirping on these self-similar waves as they propagate through the tapered graded index waveguide. We have revealed that the chirping leads to interesting features and allows us to control the propagation of self-similar waves. This has been demonstrated for two cases (i) periodically distributed system and (ii) constant choice of system parameters. We expect our results to be useful in designing high performance optical devices.

  14. Dendrimers Containing Ferrocene and Porphyrin Moieties: Synthesis and Cubic Non-Linear Optical Behavior

    Directory of Open Access Journals (Sweden)

    Eric G. Morales-Espinoza


    Full Text Available Dendrons with ferrocenyl ended groups joined by styryl moieties were attached to a porphyrin core. All the dendrons used for dendrimer synthesis showed trans configuration. The chemical structure of the first generation dendron was confirmed by X-ray crystallographic studies. The structure of the synthesized dendrimers was confirmed by 1H- and 13C-NMR, electrospray mass spectrometry and elemental analysis. Cubic non-linear optical behavior of the ferrocene and porphyrin-containing dendrimers was studied in solid thin films by THG Maker-Fringe technique at 1,260 nm.

  15. A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control


    Vaidyanathan Sundarapandian


    This paper presents a new seven-term 3-D jerk chaotic system with two cubic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0:2974, L2 = 0 and L3 = −3:8974. Since the sum of the Lyapunov exponents of the jerk cha...

  16. Dynamics of solitons and quasisolitons of the cubic third-order nonlinear Schrödinger equation

    DEFF Research Database (Denmark)

    Karpman, V.I.; Juul Rasmussen, J.; Shagalov, A.G.


    The dynamics of soliton and quasisoliton solutions of the cubic third-order nonlinear Schrodinger equation is studied. Regular solitons exist due to a balance between the nonlinear terms and (linear) third-order dispersion; they are not important at small alpha (3) (alpha (3) is the coefficient...

  17. Chirped femtosecond pulses in the higher-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities (United States)

    Triki, Houria; Biswas, Anjan; Milović, Daniela; Belić, Milivoj


    We consider a high-order nonlinear Schrödinger equation with competing cubic-quintic-septic nonlinearities, non-Kerr quintic nonlinearity, self-steepening, and self-frequency shift. The model describes the propagation of ultrashort (femtosecond) optical pulses in highly nonlinear optical fibers. A new ansatz is adopted to obtain nonlinear chirp associated with the propagating femtosecond soliton pulses. It is shown that the resultant elliptic equation of the problem is of high order, contains several new terms and is more general than the earlier reported results, thus providing a systematic way to find exact chirped soliton solutions of the septic model. Novel soliton solutions, including chirped bright, dark, kink and fractional-transform soliton solutions are obtained for special choices of parameters. Furthermore, we present the parameter domains in which these optical solitons exist. The nonlinear chirp associated with each of the solitonic solutions is also determined. It is shown that the chirping is proportional to the intensity of the wave and depends on higher-order nonlinearities. Of special interest is the soliton solution of the bright and dark type, determined for the general case when all coefficients in the equation have nonzero values. These results can be useful for possible chirped-soliton-based applications of highly nonlinear optical fiber systems.

  18. 3D computation of non-linear eddy currents: Variational method and superconducting cubic bulk (United States)

    Pardo, Enric; Kapolka, Milan


    Computing the electric eddy currents in non-linear materials, such as superconductors, is not straightforward. The design of superconducting magnets and power applications needs electromagnetic computer modeling, being in many cases a three-dimensional (3D) problem. Since 3D problems require high computing times, novel time-efficient modeling tools are highly desirable. This article presents a novel computing modeling method based on a variational principle. The self-programmed implementation uses an original minimization method, which divides the sample into sectors. This speeds-up the computations with no loss of accuracy, while enabling efficient parallelization. This method could also be applied to model transients in linear materials or networks of non-linear electrical elements. As example, we analyze the magnetization currents of a cubic superconductor. This 3D situation remains unknown, in spite of the fact that it is often met in material characterization and bulk applications. We found that below the penetration field and in part of the sample, current flux lines are not rectangular and significantly bend in the direction parallel to the applied field. In conclusion, the presented numerical method is able to time-efficiently solve fully 3D situations without loss of accuracy.

  19. The Schroedinger eigenvalue march

    Energy Technology Data Exchange (ETDEWEB)

    Tannous, C; Langlois, J, E-mail: [Laboratoire de Magnetisme de Bretagne, CNRS-FRE 3117, Universite de Bretagne Occidentale, BP: 809 Brest CEDEX 29285 (France)


    A simple numerical method for the determination of Schroedinger equation eigenvalues is introduced. It is based on a marching process that starts from an arbitrary point, proceeds in two opposite directions simultaneously and stops after a tolerance criterion is met. The method is applied to solving several 1D potential problems including symmetric double-well (ammonia inversion problem) and Johnson asymmetric potentials, 3D hydrogen atom and Morse potential. Band structure calculation can equally be tackled by extending marching to the complex plane as illustrated with the Kronig-Penney problem.

  20. The nonlinear aeroelastic characteristics of a folding wing with cubic stiffness (United States)

    Hu, Wei; Yang, Zhichun; Gu, Yingsong; Wang, Xiaochen


    This paper focuses on the nonlinear aeroelastic characteristics of a folding wing in the quasi-steady condition (namely at fixed folding angles) and during the morphing process. The structure model of the folding wing is formulated by the Lagrange equations, and the constraint equation is used to describe the morphing strategy. The aerodynamic influence coefficient matrices at several folding angles are calculated by the Doublet Lattice method, and described as rational functions in the Laplace domain by the rational function approximation, and then the Kriging agent model technique is adopted to interpolate the coefficient matrices of the rational functions, and the aerodynamics model of the folding wing during the morphing process is built. The aeroelastic responses of the folding wing with cubic stiffness are simulated, and the results show that the motion types of aeroelastic responses in the quasi-steady condition and during the morphing process are all sensitive to the initial condition and folding angle. During the morphing process, the transition of the motion types is observed. And apart from the period of transition, the aeroelastic response at some folding angles may exhibit different motion types, which can be found from the results in the quasi-steady condition.

  1. A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

    Directory of Open Access Journals (Sweden)

    Vaidyanathan Sundarapandian


    Full Text Available This paper presents a new seven-term 3-D jerk chaotic system with two cubic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0:2974, L2 = 0 and L3 = −3:8974. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the new jerk chaotic system is found as DKY = 2:0763. Next, an adaptive backstepping controller is designed to globally stabilize the new jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations are shown to illustrate all the main results derived in this work.

  2. Solving the nonlinear Schrödinger equation using cubic B-spline interpolation and finite difference methods (United States)

    Ahmad, Azhar; Azmi, Amirah; Majid, Ahmad Abd.; Hamid, Nur Nadiah Abd


    In this paper, Nonlinear Schrödinger (NLS) equation with Neumann boundary conditions is solved using finite difference method (FDM) and cubic B-spline interpolation method (CuBSIM). First, the approach is based on the FDM applied on the time and space discretization with the help of theta-weighted method. However, our main interest is the second approach, whereby FDM is applied on the time discretization and cubic B-spline is utilized as an interpolation function in the space dimension with the same help of theta-weighted method. The CuBSIM is shown to be stable by using von Neumann stability analysis. The proposed method is tested on a test problem with single soliton motion of the NLS equation. The accuracy of the numerical results is measured by the Euclidean-norm and infinity-norm. CuBSIM is found to produce more accurate results than the FDM.

  3. Bright-dark and dark-dark solitons for the coupled cubic-quintic nonlinear Schrödinger equations in a twin-core nonlinear optical fiber (United States)

    Yuan, Yu-Qiang; Tian, Bo; Liu, Lei; Chai, Han-Peng


    In this paper, we investigate the coupled cubic-quintic nonlinear Schrödinger equations, which can describe the effects of quintic nonlinearity on the ultrashort optical soliton pulse propagation in a twin-core nonlinear optical fiber. Through the Kadomtsev-Petviashvili hierarchy reduction, we present the bright-dark and dark-dark soliton solutions in terms of the Grammian for such equations. With the help of analytic and graphic analysis, head-on and overtaking elastic interactions between the two solitons are presented, as well as the bound-state solitons. Particularly, we find the inelastic interaction between the bright-dark two solitons. One of the electromagnetic fields presents the V-shape profile, while the other one presents the Y-shape profile.

  4. Computer simulation of solitary waves in a common or auxetic elastic rod with both quadratic and cubic nonlinearities

    Energy Technology Data Exchange (ETDEWEB)

    Bui Dinh, T. [Institute of Physics, University of Zielona Gora, ul. Prof. A. Szafrana 4a, 65-516 Zielona Gora (Poland); Vinh University, 182 Duong Le Duan, Nghe An (Viet Nam); Long, V. Cao [Institute of Physics, University of Zielona Gora, ul. Prof. A. Szafrana 4a, 65-516 Zielona Gora (Poland); Xuan, K. Dinh [Vinh University, 182 Duong Le Duan, Nghe An (Viet Nam); Wojciechowski, K.W. [Institute of Molecular Physics, Polish Academy of Sciences, ul. Smoluchowskiego 17, 60-179 Poznan (Poland)


    Results of numerical simulations are presented for propagation of solitary waves in an elastic rod of positive or negative Poisson's ratio, i.e. of a common or auxetic material. Splitting of various initial pulses during propagation into a sequence of solitary waves is considered in frames of a model which contains both quadratic and cubic nonlinear terms. The obtained results are compared with some exact analytic solutions, called solitons, what leads to the conclusion that the solitons describe well the more complicated wave fields which are obtained by numerical simulations. This is because the analytic solutions reflect complete balance between various orders of nonlinearity and dispersion. Collisions between some obtained solitary waves are also presented. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  5. Interaction of elliptically polarised cross-degenerate cnoidal waves in an isotropic gyrotropic medium with spatial dispersion of cubic nonlinearity (United States)

    Makarov, V. A.; Petnikova, V. M.; Shuvalov, V. V.


    Three unusual classes of particular analytical solutions to a system of four nonlinear equations are found for slowly varying complex amplitudes of circularly polarised components of the electric field. The system describes the self-action and interaction of two elliptically polarised plane waves collinearly propagating in an isotropic medium with second-order frequency dispersion and spatial dispersion of cubic nonlinearity. The solutions correspond to self-consistent combinations of two elliptically polarised cnoidal waves whose mutually orthogonal polarisation components vary in accordance with pairwise identical laws during propagation. At the same time, the amplitudes of the component with the same circular polarisation are proportional to two different elliptic Jacobi functions with the same periods.

  6. Solution of (3+1-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method

    Directory of Open Access Journals (Sweden)

    Hassan A. Zedan


    Full Text Available Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.

  7. Asymmetric induced cubic nonlinearities in homogeneous and quasi-phase-matched quadratic materials: signature and importance

    DEFF Research Database (Denmark)

    Bang, Ole; Corney, Joel Frederick


    In continuous-wave operation asymmetric induced nonlinearities induce an intensity-dependent phase mismatch that implies a nonzero so-called separatrix intensity, the crossing of which changes the one-period phase shift of the fundamental by Pi , with obvious use in switching applications.We deri...

  8. An Eight-Term Novel Four-Scroll Chaotic System with Cubic Nonlinearity and its Circuit Simulation

    Directory of Open Access Journals (Sweden)

    S. Sampath


    Full Text Available This research work proposes an eight-term novel four-scroll chaotic system with cubic nonlinearity and analyses its fundamental properties such as dissipativity, equilibria, symmetry and invariance, Lyapunov exponents and KaplanYorke dimension. The phase portraits of the novel chaotic system, which are obtained in this work by using MATLAB, depict the four-scroll attractor of the system. For the parameter values and initial conditions chosen in this work, the Lyapunov exponents of the novel four-scroll chaotic system are obtained as L1 = 0.75335, L2 = 0 and L3 = −22.43304. Also, the Kaplan-Yorke dimension of the novel four-scroll chaotic system is obtained as DKY = 2.0336. Finally, an electronic circuit realization of the novel four-scroll chaotic system is presented by using SPICE to confirm the feasibility of the theoretical model.

  9. Dynamical behaviors, control and synchronization of a new chaotic model with complex variables and cubic nonlinear terms (United States)

    Mahmoud, Emad E.; Al-Adwani, Madeha A.

    A novel chaotic model with complex variables and cubic non-linear terms was proposed. The new system is a six dimensional continuous real autonomous chaotic system. The characteristics of this system containing invariance, dissipation, equilibria and their stability, Lyapunov exponents, Lyapunov dimension, bifurcation diagrams and chaotic achievement are studied. Converting and turning the system chaotic behavior to its unstable trivial fixed point via the Lyapunov stability theorem. An approach proposed to analyze the system chaos synchronization. Analytical expressions are derived for control functions. The chaos synchronization results were employed to develop a simple application in secure communication. Numerical effects computed to experiment the control forces scientific expressions gravity and to show the chaos synchronization of a chaotic system.

  10. Optical soliton solutions for the higher-order dispersive cubic-quintic nonlinear Schrödinger equation (United States)

    Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru


    In this paper, we analyze new optical soliton solutions to the higher-order dispersive cubic-quintic nonlinear Schrödinger equation (NLSE) using three integration schemes. The schemes used in this paper are modified tanh-coth (MTC), extended Jacobi elliptic function expansion (EJEF), and two variable (G‧ / G , 1 / G) -expansion methods. We obtain new solutions that to the best of our knowledge do not exist previously. The obtained solutions includes bright, dark, combined bright-dark, singular as well as periodic waves solitons. The obtained solutions may be used to explain and understand the physical nature of the wave spreads in the most dispersive optical medium. Some interesting figures for the physical interpretation of the obtained solutions are also presented.

  11. Magnetic virial identities and applications to blow-up for Schroedinger and wave equations

    Energy Technology Data Exchange (ETDEWEB)

    Garcia, Andoni, E-mail: [Departamento de Matematicas, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao (Spain)


    We prove blow-up results for the solution of the initial-value problem with negative energy of the focusing mass-critical and supercritical nonlinear Schroedinger and the focusing energy-subcritical nonlinear wave equations with electromagnetic potential. (paper)

  12. Linear and Non-Linear Piezoresistance Coefficients in Cubic Semiconductors. I. Theoretical Formulations (United States)

    Durand, S.; Tellier, C. R.


    This paper constitutes the first part of a work devoted to applications of piezoresistance effects in germanium and silicon semiconductors. In this part, emphasis is placed on a formal explanation of non-linear effects. We propose a brief phenomenological description based on the multi-valleys model of semiconductors before to adopt a macroscopic tensorial model from which general analytical expressions for primed non-linear piezoresistance coefficients are derived. Graphical representations of linear and non-linear piezoresistance coefficients allows us to characterize the influence of the two angles of cut and of directions of alignment. The second part will primarily deal with specific applications for piezoresistive sensors. Cette publication constitue la première partie d'un travail consacré aux applications des effets piézorésistifs dans les semiconducteurs germanium et silicium. Cette partie traite essentiellement de la modélisation des effets non-linéaires. Après une description phénoménologique à partir du modèle de bande des semiconducteurs nous développons un modèle tensoriel macroscopique et nous proposons des équations générales analytiques exprimant les coefficients piézorésistifs non-linéaires dans des repères tournés. Des représentations graphiques des variations des coefficients piézorésistifs linéaires et non-linéaires permettent une pré-caractérisation de l'influence des angles de coupes et des directions d'alignement avant l'étude d'applications spécifiques qui feront l'objet de la deuxième partie.

  13. Self-organization of frozen light in near-zero-index media with cubic nonlinearity (United States)

    Marini, A.; García de Abajo, F. J.


    Optical beams are generally unbound in bulk media, and propagate with a velocity approximately amounting to the speed of light in free-space. Guidance and full spatial confinement of light are usually achieved by means of waveguides, mirrors, resonators, and photonic crystals. Here we theoretically demonstrate that nonlinear self-organization can be exploited to freeze optical beams in bulk near-zero-index media, thus enabling three-dimensional self-trapping of still light without the need of optical resonators. Light is stopped to a standstill owing to the divergent wavelength and the vanishing group velocity, effectively rendering, through nonlinearity, a positive-epsilon trapping cavity carved in an otherwise slightly-negative-epsilon medium. By numerically solving Maxwell’s equations, we find a soliton-like family of still azimuthal doughnuts, which we further study through an adiabatic perturbative theory that describes soliton evaporation in lossy media or condensation in actively pumped materials. Our results suggest applications in optical data processing and storage, quantum optical memories, and soliton-based lasers without cavities. Additionally, near-zero-index conditions can also be found in the interplanetary medium and in the atmosphere, where we provide a complementary explanation to the rare phenomenon of ball-lightning.

  14. Effective Schroedinger equations on submanifolds

    Energy Technology Data Exchange (ETDEWEB)

    Wachsmuth, Jakob


    In this thesis the time dependent Schroedinger equation is considered on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When the potential is scaled in the directions normal to C by a small parameter epsilon, the solutions concentrate in an epsilon-neighborhood of the submanifold. An effective Schroedinger equation on the submanifold C is derived and it is shown that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order {epsilon}{sup 3} vertical stroke t vertical stroke at time t. Furthermore, it is proved that, under reasonable conditions, the eigenvalues of the corresponding Hamiltonians below a certain energy coincide upto errors of order {epsilon}{sup 3}. These results holds in the situation where tangential and normal energies are of the same order, and where exchange between normal and tangential energies occurs. In earlier results tangential energies were assumed to be small compared to normal energies, and rather restrictive assumptions were needed, to ensure that the separation of energies is maintained during the time evolution. The most important consequence of this thesis is that now constraining potentials that change their shape along the submanifold can be treated, which is the typical situation in applications like molecular dynamics and quantum waveguides.

  15. Schroedinger's Cat is not Alone

    CERN Document Server

    Gato, Beatriz


    We introduce the `Complete Wave Function' and deduce that all living beings, not just Schroedinger's cat, are actually described by a superposition of `alive' and `dead' quantum states; otherwise they would never die. Therefore this proposal provides a quantum mechanical explanation to the world-wide observation that we all pass away. Next we consider the Measurement problem in the framework of M-theory. For this purpose, together with Schroedinger's cat we also place inside the box Rasputin's cat, which is unaffected by poisson. We analyse the system identifying its excitations (catons and catinos) and we discuss its evolution: either to a classical fight or to a quantum entanglement. We also propose the $BSV\\Psi$ scenario, which implements the Complete Wave Function as well as the Big Bang and the String Landscape in a very (super)natural way. Then we test the gravitational decoherence of the entangled system applying an experimental setting due to Galileo. We also discuss the Information Loss paradox. For ...

  16. Erwin Schroedinger, Francis Crick and epigenetic stability

    Directory of Open Access Journals (Sweden)

    Ogryzko Vasily V


    Full Text Available Abstract Schroedinger's book 'What is Life?' is widely credited for having played a crucial role in development of molecular and cellular biology. My essay revisits the issues raised by this book from the modern perspective of epigenetics and systems biology. I contrast two classes of potential mechanisms of epigenetic stability: 'epigenetic templating' and 'systems biology' approaches, and consider them from the point of view expressed by Schroedinger. I also discuss how quantum entanglement, a nonclassical feature of quantum mechanics, can help to address the 'problem of small numbers' that led Schroedinger to promote the idea of a molecular code-script for explaining the stability of biological order.

  17. Erwin Schroedinger, Francis Crick and epigenetic stability. (United States)

    Ogryzko, Vasily V


    Schroedinger's book 'What is Life?' is widely credited for having played a crucial role in development of molecular and cellular biology. My essay revisits the issues raised by this book from the modern perspective of epigenetics and systems biology. I contrast two classes of potential mechanisms of epigenetic stability: 'epigenetic templating' and 'systems biology' approaches, and consider them from the point of view expressed by Schroedinger. I also discuss how quantum entanglement, a nonclassical feature of quantum mechanics, can help to address the 'problem of small numbers' that led Schroedinger to promote the idea of a molecular code-script for explaining the stability of biological order.

  18. Spectral Target Detection using Schroedinger Eigenmaps (United States)

    Dorado-Munoz, Leidy P.

    Applications of optical remote sensing processes include environmental monitoring, military monitoring, meteorology, mapping, surveillance, etc. Many of these tasks include the detection of specific objects or materials, usually few or small, which are surrounded by other materials that clutter the scene and hide the relevant information. This target detection process has been boosted lately by the use of hyperspectral imagery (HSI) since its high spectral dimension provides more detailed spectral information that is desirable in data exploitation. Typical spectral target detectors rely on statistical or geometric models to characterize the spectral variability of the data. However, in many cases these parametric models do not fit well HSI data that impacts the detection performance. On the other hand, non-linear transformation methods, mainly based on manifold learning algorithms, have shown a potential use in HSI transformation, dimensionality reduction and classification. In target detection, non-linear transformation algorithms are used as preprocessing techniques that transform the data to a more suitable lower dimensional space, where the statistical or geometric detectors are applied. One of these non-linear manifold methods is the Schroedinger Eigenmaps (SE) algorithm that has been introduced as a technique for semi-supervised classification. The core tool of the SE algorithm is the Schroedinger operator that includes a potential term that encodes prior information about the materials present in a scene, and enables the embedding to be steered in some convenient directions in order to cluster similar pixels together. A completely novel target detection methodology based on SE algorithm is proposed for the first time in this thesis. The proposed methodology does not just include the transformation of the data to a lower dimensional space but also includes the definition of a detector that capitalizes on the theory behind SE. The fact that target pixels and

  19. Linear and nonlinear behaviour of near-IR intersubband transitions of cubic GaN/AlN multi quantum well structures (United States)

    Wecker, T.; Jostmeier, T.; Rieger, T.; Neumann, E.; Pawlis, A.; Betz, M.; Reuter, D.; As, D. J.


    The linear and nonlinear behaviour of intersubband transitions of cubic GaN/AlN multi quantum well (QW) structures in the IR spectral region is investigated. In this study photoluminescence, IR absorption as well as pump-probe measurements are done. Two cubic GaN/AlN multi quantum wells with Si content of NSi 1019 cm-3 in the cubic GaN quantum wells were grown on 3C-SiC (001) substrate by radio-frequency plasma-assisted molecular beam epitaxy. A broad IR absorption with a FWHM of 370 meV was found with a maximum at 0.7 eV, corresponding to the intersubband transition of the multi quantum wells. The nonlinear optical measurement reveals a clear change of transmission for a pump pulse with an angle of incidence of 65°. Furthermore, transmission electron microscopy measurements are used to determine the real layer thicknesses. These thickness values are exploited in the calculation with the Schrödinger-Poisson solver nextnano³. The simulated transition energies agree very well with the experimental data for the photoluminescence and the absorption measurement.

  20. Solving the nonlinear Schrödinger equation using cubic B-spline interpolation and finite difference methods on dual solitons (United States)

    Ahmad, Azhar; Azmi, Amirah; Majid, Ahmad Abd.; Hamid, Nur Nadiah Abd


    In this paper, Nonlinear Schrödinger (NLS) equation with Neumann boundary conditions is solved using cubic B-spline interpolation method (CuBSIM) and finite difference method (FDM). Firstly, FDM is applied on the time discretization and cubic B-spline is utilized as an interpolation function in the space dimension with the help of theta-weighted method. The second approach is based on the FDM applied on the time and space discretization with the help of theta-weighted method. The CuBSIM is shown to be stable by using von Neumann stability analysis. The proposed method is tested on the interaction of the dual solitons of the NLS equation. The accuracy of the numerical results is measured by the Euclidean-norm and infinity-norm. CuBSIM is found to produce more accurate results than the FDM.

  1. Study on TVD parameters sensitivity of a crankshaft using multiple scale and state space method considering quadratic and cubic non-linearities

    Directory of Open Access Journals (Sweden)

    R. Talebitooti

    Full Text Available In this paper the effect of quadratic and cubic non-linearities of the system consisting of the crankshaft and torsional vibration damper (TVD is taken into account. TVD consists of non-linear elastomer material used for controlling the torsional vibration of crankshaft. The method of multiple scales is used to solve the governing equations of the system. Meanwhile, the frequency response of the system for both harmonic and sub-harmonic resonances is extracted. In addition, the effects of detuning parameters and other dimensionless parameters for a case of harmonic resonance are investigated. Moreover, the external forces including both inertia and gas forces are simultaneously applied into the model. Finally, in order to study the effectiveness of the parameters, the dimensionless governing equations of the system are solved, considering the state space method. Then, the effects of the torsional damper as well as all corresponding parameters of the system are discussed.

  2. Philosophy of Erwin Schroedinger: a diachronic view of Schroedinger's thoughts

    Energy Technology Data Exchange (ETDEWEB)

    Melgar, M.F.


    There is no agreement within the scientific community about the philosophy of Schroedinger. Some people think that he was a realist, while others defend him as an idealist. In this paper we study a number of Schroedinger's works and we show that the epithets of realist and idealist do not do him justice. Toward the end we conclude that it would be more adequate to place him in the trend known as the philosophy of immanence.

  3. Elliptic function and solitary wave solutions of the higher-order nonlinear Schrödinger dynamical equation with fourth-order dispersion and cubic-quintic nonlinearity and its stability (United States)

    Arshad, M.; Seadawy, Aly R.; Lu, Dianchen


    The higher-order nonlinear Schrödinger equation (NLSE) with fourth-order dispersion, cubic-quintic terms, self-steepening and nonlinear dispersive terms describes the propagation of extremely short pulses in optical fibers. In this paper, the elliptic function, bright and dark solitons and solitary wave solutions of higher-order NLSE are constructed by employing a modified extended direct algebraic method, which has important applications in applied mathematics and physics. Furthermore, we also present the formation conditions of the bright and dark solitons for this equation. The modulation instability is utilized to discuss the stability of these solutions, which shows that all solutions are exact and stable. Many other higher-order nonlinear evolution equations arising in applied sciences can also be solved by this powerful, effective and reliable method.

  4. Schroedinger upper bounds to semirelativistic eigenvalues

    Energy Technology Data Exchange (ETDEWEB)

    Hall, Richard L [Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec, H3G 1M8 (Canada); Lucha, Wolfgang [Institut fuer Hochenergiephysik, Oesterreichische Akademie der Wissenschaften, Nikolsdorfergasse 18, A-1050 Vienna (Austria)


    Problems posed by semirelativistic Hamiltonians of the form H = {radical}(m{sup 2} + p{sup 2}) + V(r) are studied. It is shown that energy upper bounds can be constructed in terms of certain related Schroedinger operators; these bounds include free parameters which can be chosen optimally.

  5. New travelling wave solutions of the (1 + 1-dimensional cubic nonlinear Schrodinger equation using novel (G′/G-expansion method

    Directory of Open Access Journals (Sweden)

    M.G. Hafez


    Full Text Available In this paper, the novel (G′/G-expansion method is applied to construct exact travelling wave solutions of the cubic nonlinear Schrodinger equation. This technique is straightforward and simple to use, and gives more new general solutions than the other existing methods. Various types of solitary and periodic wave solutions of this equation are derived. The obtained results may be helpful to describe the wave propagation in soliton physics, such as soliton propagation in optical fibers, modulus instability in plasma physics, etc. and provided us the firm mathematical foundation in soliton physics or any varied instances. Furthermore, three-dimensional modules plot of the solutions are also given to visualize the dynamics of the equation.

  6. A life of Erwin Schroedinger. 2. ed.; Erwin Schroedinger. Eine Biographie

    Energy Technology Data Exchange (ETDEWEB)

    Moore, Walter J.


    Erwin Schroedinger (1887-1961) was a pioneer of quantum physics, one of the most important scientist of the 20th century at all and a charming Austrian. He was a man with a passionate interest for men and ideas. Mostly known he became by his representation of quantum theory in the form of wave mechanics, for which he obtained the Nobel prize for physics and naturally by the famous thought experiment ''Schroedingers cat''. Walter Moore's biography is quite near to the person of Schroedinger and presents his scientific work in the context of his friendships, his interset for mysticism, and in front of the moving background of the political events in Germany and Austria.

  7. Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection. (United States)

    Sabelnikov, V A; Lipatnikov, A N


    The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.

  8. The Schroedinger-Virasoro algebra. Mathematical structure and dynamical Schroedinger symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Unterberger, Jeremie [Henri Poincare Univ., Vandoeuvre-les-Nancy (France). Inst. Elie Cartan; Roger, Claude [Lyon I Univ., Villeurbanne (France). Dept. de Mathematiques


    This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure the Schroedinger-Virasoro algebra. Just as Poincare invariance or conformal (Virasoro) invariance play a key role in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence. The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schroedinger operators. (orig.)

  9. Schroedinger operators and evolutionary strategies; Schroedinger-Operatoren und Evolutionaere Strategien

    Energy Technology Data Exchange (ETDEWEB)

    Asselmeyer, T.


    First we introduce a simple model for the description of evolutionary algorithms, which is based on 2nd order partial differential equations for the distribution function of the individuals. Then we turn to the properties of Boltzmann's and Darwin's strategy. the next chapter is dedicated to the mathematical properties of Schroedinger operators. Both statements on the spectral density and their reproducibility during the simulation are summarized. The remaining of this chapter are dedicated to the analysis of the kernel as well as the dependence of the Schroedinger operator on the potential. As conclusion from the results of this chapter we obtain the classification of the strategies in dependence of the fitness. We obtain the classification of the evolutionary strategies, which are described by a 2nd order partial differential equation, in relation to their solution behaviour. Thereafter we are employed with the variation of the mutation distribution.

  10. Electronic levels of cubic quantum dots

    Energy Technology Data Exchange (ETDEWEB)

    Aristone, Flavio [Federal De Mato Grosso Do Sul Univ., Campo Grande (Brazil); Sanchez-Dehesa, Jose [Autonoma De Madrid Univ., Madrid (Spain); Marques, Gilmar E. [Federal De Sao Carlos Univ., Sao Carlos (Brazil)


    We introduce an efficient variational method to solve the three-dimensional Schroedinger equation for any arbitrary potential V(x,y,z). The method uses a basis set of localized functions which are build up as products of one-dimensional cubic {beta}-splines. We calculated the energy levels of GaAs/AlGaAs cubic quantum dots and make a comparison with the results from two well-known simplification schemes based on a decomposition of the full potential problem into three separate one-dimensional problems. We show that the scheme making a sequential decomposition gives eigenvalues in better agreement with the ones obtained variationally, but an exact solution is necessary when looking for highly precise values.


    Directory of Open Access Journals (Sweden)

    L. S. Konev


    Full Text Available Numerical method for calculation of forward and backward waves of intense few-cycle laser pulses propagating in an optical waveguide with dispersion and cubic nonlinearity of electronic and electronic-vibration nature is described. Simulations made with the implemented algorithm show that accounting for Raman nonlinearity does not lead to qualitative changes in behavior of the backward wave. Speaking about quantitative changes, the increase of efficiency of energy transfer from the forward wave to the backward wave is observed. Presented method can be also used to simulate interaction of counterpropagating pulses.

  12. Diophantine approximation and the solubility of the Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Kristensen, Simon


    We characterise the set of periods for which number theoretical obstructions prevent us from finding periodic solutions of the Schroedinger equation on a two-dimensional torus as well as the asymptotic occurrence of possible resonances.

  13. Random discrete Schroedinger operators from random matrix theory

    Energy Technology Data Exchange (ETDEWEB)

    Breuer, Jonathan [Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Forrester, Peter J [Department of Mathematics and Statistics, University of Melbourne, Parkville, Vic 3010 (Australia); Smilansky, Uzy [Department of Physics of Complex Systems, Weizmann Institute, Rehovot 76100 (Israel)


    We investigate random, discrete Schroedinger operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature {beta}. They are similar to the class of 'critical' random Schroedinger operators with random potentials which diminish as vertical bar x vertical bar{sup -1/2}. We show that as a function of {beta} they undergo a transition from a regime of (power-law) localized eigenstates with a pure point spectrum for {beta} < 2 to a regime of extended states with a singular continuous spectrum for {beta} {>=} 2. (fast track communication)

  14. Intertwining operator method and supersymmetry for effective mass Schroedinger equations

    Energy Technology Data Exchange (ETDEWEB)

    Suzko, A.A. [Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); JIPENP, National Academy of Sciences of Belarus, Minsk (Belarus)], E-mail:; Schulze-Halberg, A. [Mathematics Department, University of Colima, Bernal Diaz del Castillo 340, Colima 28045 (Mexico)], E-mail:


    By application of the intertwining operator method to Schroedinger equations with position-dependent (effective) mass, we construct Darboux transformations, establish the supersymmetry factorization technique and show equivalence of both formalisms. Our findings prove equivalence of the intertwining technique and the method of point transformations.

  15. Evaluation of eigenvalues of a smooth potential via Schroedinger ...

    Indian Academy of Sciences (India)

    Evaluation of eigenvalues of a smooth potential via Schroedinger transmission across multi-step potential. BASUDEB SAHU1,∗, BIDHUBHUSAN SAHU1 and SANTOSH K AGARWALLA2. 1Department of Physics, North Orissa University, Baripada 757 003, India. 2Department of Applied Physics and Ballistics, Fakir Mohan ...

  16. On Galilean invariance and nonlinearity in electrodynamics and quantum mechanics


    Goldin, Gerald A.; Shtelen, Vladimir


    Recent experimental results on slow light heighten interest in nonlinear Maxwell theories. We obtain Galilei covariant equations for electromagnetism by allowing special nonlinearities in the constitutive equations only, keeping Maxwell's equations unchanged. Combining these with linear or nonlinear Schroedinger equations, e.g. as proposed by Doebner and Goldin, yields a Galilean quantum electrodynamics.

  17. Representations of the Schroedinger group and matrix orthogonal polynomials

    Energy Technology Data Exchange (ETDEWEB)

    Vinet, Luc [Centre de recherches mathematiques, Universite de Montreal, CP 6128, succ. Centre-ville, Montreal, QC H3C 3J7 (Canada); Zhedanov, Alexei, E-mail:, E-mail: [Donetsk Institute for Physics and Technology, Donetsk 83114 (Ukraine)


    The representations of the Schroedinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrix orthogonal polynomials in a discrete variable that have Charlier and Meixner polynomials as building blocks. The underlying Lie-theoretic framework allows for a systematic derivation of the structural formulas (recurrence relations, difference equations, Rodrigues' formula, etc) that these matrix orthogonal polynomials satisfy. (paper)

  18. Solution of the Schroedinger equation in two and three dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Hajj, F.Y. (National Council for Scientific Research, Beirut (Lebanon))


    Eigenvalues and eigenfunctions of the Schroedinger equation are computed by a finite-difference method that is very simple and fast. In two dimensions, the ground state of helium and that of the hydride ion are computed in the S-limit approximation. In three dimensions, the computations include the ground state of the unapproximated helium atom and that of the lithium atom in the S-limit approximation.

  19. Integrability of the higher-order nonlinear Schrödinger equation revisited

    CERN Document Server

    Sakovich, S Yu


    Only the known integrable cases of the Kodama-Hasegawa higher-order nonlinear Schroedinger equation pass the Painleve test. Recent results of Ghosh and Nandy add no new integrable cases of this equation.

  20. Schroedinger invariant solutions of type IIB with enhanced supersymmetry

    Energy Technology Data Exchange (ETDEWEB)

    Donos, Aristomenis [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gauntlett, Jerome P. [Imperial College, London (United Kingdom). Theoretical Physics Group; Imperial College, London (United Kingdom). Inst. for Mathematical Sciences


    We construct the Killing spinors for a class of supersymmetric solutions of type IIB supergravity that are invariant under the non-relativistic Schroedinger algebra. The solutions depend on a five-dimensional Sasaki- Einstein space and it has been shown that they admit two Killing spinors. Here we will show that, for generic Sasaki-Einstein space, there are special subclasses of solutions which admit six Killing spinors and we determine the corresponding superisometry algebra. We also show that for the special case that the Sasaki-Einstein space is the round five-sphere, the number of Killing spinors can be increased to twelve. (orig.)

  1. Numerical stochastic perturbation theory in the Schroedinger functional

    Energy Technology Data Exchange (ETDEWEB)

    Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk [Parma Univ. (Italy); INFN, Parma (Italy); Dalla Brida, Mattia [Trinity College Dublin (Ireland). School of Mathematics; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC


    The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

  2. A new method for the solution of the Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima, Colima (Mexico); Aranda, Alfredo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima, Colima (Mexico); De Pace, Arturo [Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P Giuria 1, I-10125, Torino (Italy)


    We present a new method for the solution of the Schroedinger equation applicable to problems of a non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: an asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wavefunction; and, finally, a short distance scale, in which the wavefunction is sizable. The notion of optimized perturbation is then used in the last two regimes. We apply the method to the quantum anharmonic oscillator and find it suitable to treat both energy eigenvalues and wavefunctions, even for strong couplings.

  3. A numerical study of the Schroedinger-Newton equations

    CERN Document Server

    Harrison, R I


    and added perturbations oscillate at frequencies determined by the linear perturbation theory. The higher states are shown to be unstable, emitting scatter and leaving a rescaled ground state. The rate at which they decay is controlled by the complex eigenvalues of the linear perturbation. Next we consider adding another dimension in two different ways: by considering the axisymmetric case and the 2-D equations. The stationary solutions are found. We modify the evolution method and find that the higher states are unstable. In 2-D case we consider rigidly rotating solutions and show they exist and are unstable. The Schroedinger-Newton (S-N) equations were proposed by Penrose [18] as a model for gravitational collapse of the wave-function. The potential in the Schroedinger equation is the gravity due to the density of vertical bar psi vertical bar sup 2 , where psi is the wave-function. As with normal Quantum Mechanics the probability, momentum and angular momentum are conserved. We first consider the spherical...

  4. Generalized Born--Infeld Actions and Projective Cubic Curves

    CERN Document Server

    Ferrara, S; Sagnotti, A; Stora, R; Yeranyan, A


    We investigate $U(1)^{\\,n}$ supersymmetric Born-Infeld Lagrangians with a second non-linearly realized supersymmetry. The resulting non-linear structure is more complex than the square root present in the standard Born-Infeld action, and nonetheless the quadratic constraints determining these models can be solved exactly in all cases containing three vector multiplets. The corresponding models are classified by cubic holomorphic prepotentials. Their symmetry structures are associated to projective cubic varieties.

  5. Purely cubic action for string field theory (United States)

    Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.


    It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.

  6. The Schroedinger representation and its relation to the holomorphic representation in linear and affine field theory

    Energy Technology Data Exchange (ETDEWEB)

    Oeckl, Robert [Centro de Ciencias Matematicas, Universidad Nacional Autonoma de Mexico, Campus Morelia, C.P. 58190, Morelia, Michoacan (Mexico)


    We establish a precise isomorphism between the Schroedinger representation and the holomorphic representation in linear and affine field theory. In the linear case, this isomorphism is induced by a one-to-one correspondence between complex structures and Schroedinger vacua. In the affine case we obtain similar results, with the role of the vacuum now taken by a whole family of coherent states. In order to establish these results we exhibit a rigorous construction of the Schroedinger representation and use a suitable generalization of the Segal-Bargmann transform. Our construction is based on geometric quantization and applies to any real polarization and its pairing with any Kaehler polarization.

  7. Soliton-like solutions to the ordinary Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Zamboni-Rached, Michel [Universidade Estadual de Campinas (DMO/FEEC/UNICAMP), Campinas, SP (Brazil). Fac. de Engenharia Eletrica e de Computacao. Dept. de Microondas e Optica; Recami, Erasmo, E-mail: recami@mi.infn.i [Universita Statale di Bergamo, Bergamo (Italy). Facolta di Ingegneria


    In recent times it has been paid attention to the fact that (linear) wave equations admit of soliton-like solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G or Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation within standard Quantum Mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we show therefore how to obtain nite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. (author)

  8. From qubits and actions to the Pauli-Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Mizrahi, Salomon S [Departamento de Fisica, Universidade Federal de Sao Carlos, Caixa Postal 676, Sao Carlos, 13565-905 Sao Paulo (Brazil)], E-mail:


    Here I show that a classical or quantum bit state plus one simple operation, an action, are sufficient ingredients to derive a quantum dynamical equation that rules the sequential changes of the state. Then, by assuming that a freely moving massive particle is the qubit carrier, it is found that both, the particle position in physical space and the qubit state, change in time according to the Pauli-Schroedinger equation. So, this approach suggests the following conjecture: because it carries one qubit of information the particle motion has its description enslaved by the very existence of the internal degree of freedom. It is compelled to be described no more classically but by a wavefunction. I also briefly discuss the Dirac equation in terms of qubits.

  9. The Schroedinger functional for Gross-Neveu models

    Energy Technology Data Exchange (ETDEWEB)

    Leder, B.


    Gross-Neveu type models with a finite number of fermion flavours are studied on a two-dimensional Euclidean space-time lattice. The models are asymptotically free and are invariant under a chiral symmetry. These similarities to QCD make them perfect benchmark systems for fermion actions used in large scale lattice QCD computations. The Schroedinger functional for the Gross-Neveu models is defined for both, Wilson and Ginsparg-Wilson fermions, and shown to be renormalisable in 1-loop lattice perturbation theory. In two dimensions four fermion interactions of the Gross-Neveu models have dimensionless coupling constants. The symmetry properties of the four fermion interaction terms and the relations among them are discussed. For Wilson fermions chiral symmetry is explicitly broken and additional terms must be included in the action. Chiral symmetry is restored up to cut-off effects by tuning the bare mass and one of the couplings. The critical mass and the symmetry restoring coupling are computed to second order in lattice perturbation theory. This result is used in the 1-loop computation of the renormalised couplings and the associated beta-functions. The renormalised couplings are defined in terms of suitable boundary-to-boundary correlation functions. In the computation the known first order coefficients of the beta-functions are reproduced. One of the couplings is found to have a vanishing betafunction. The calculation is repeated for the recently proposed Schroedinger functional with exact chiral symmetry, i.e. Ginsparg-Wilson fermions. The renormalisation pattern is found to be the same as in the Wilson case. Using the regularisation dependent finite part of the renormalised couplings, the ratio of the Lambda-parameters is computed. (orig.)

  10. Nonlinear scattering: The states which are close to a soliton

    Energy Technology Data Exchange (ETDEWEB)

    Buslaev, V.S.; Perelman, G.S.


    We assume that the nonlinear Schroedinger equation with sufficiently general nonlinearity admits solutions of the soliton type. The Cauchy problem with initial data close to a soliton is considered. We also assume that the linearization of the equation in the vicinity of the soliton possesses only a real spectrum. The main result claims that the asymptotic behavior of the solution as t {yields} + {infinity} is given by the sum of a soliton with deformed parameters and a dispersive tail, i.e., a solution of the linear Schroedinger equation. The case of the minimal spectrum has been considered in the previous paper.

  11. Accurate calculation of the complex eigenvalues of the Schroedinger equation with an exponential potential

    Energy Technology Data Exchange (ETDEWEB)

    Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima (Mexico)], E-mail:; Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Division Quimica Teorica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail:


    We show that the Riccati-Pade method is suitable for the calculation of the complex eigenvalues of the Schroedinger equation with a repulsive exponential potential. The accuracy of the results is remarkable for realistic potential parameters.

  12. Star points on cubic surfaces

    NARCIS (Netherlands)

    Nguyen, T.C.


    A cubic surface in P 3 is given by a non-zero cubic homogeneous polynomial in 4 variables. Fixing an ordering of monomials of degree 3 in the polynomial ring k[x0; x1; x2; x3 ], each cubic surface denes a point in P 19 . The locus P 19 of singular cubic surfaces is a closed subset of

  13. Occurrence of stable periodic modes in a pendulum with cubic ...

    Indian Academy of Sciences (India)

    Abstract. Dynamical systems with nonlinear damping show interesting behavior in the periodic and chaotic phases. The Froude pendulum with cubical and linear damping is a paradigm for such a system. In this work the driven Froude pendulum is studied by the harmonic balancing method; the resulting nonlinear response ...

  14. Occurrence of stable periodic modes in a pendulum with cubic ...

    Indian Academy of Sciences (India)

    Dynamical systems with nonlinear damping show interesting behavior in the periodic and chaotic phases. The Froude pendulum with cubical and linear damping is a paradigm for such a system. In this work the driven Froude pendulum is studied by the harmonic balancing method; the resulting nonlinear response curves ...

  15. Solution of the Cubic

    Indian Academy of Sciences (India)

    to solving a cubic equation. Thus Cardano's formula filled the essential gap in our understanding of the so- lu tions of polynomial equations. The purpose of this .... great influence on Euler. Finally, it was Euler who uti- lized these symbols throughout his writings and made them the language of mathematics. Thus the mathe-.

  16. Connected Cubic Network Graph

    Directory of Open Access Journals (Sweden)

    Burhan Selçuk


    Full Text Available Hypercube is a popular interconnection network. Due to the popularity of hypercube, more researchers pay a great effort to develop the different variants of hypercube. In this paper, we have proposed a variant of hypercube which is called as “Connected Cubic Network Graphs”, and have investigated the Hamilton-like properties of Connected Cubic Network Graphs (CCNG. Firstly, we defined CCNG and showed the characteristic analyses of CCNG. Then, we showed that the CCNG has the properties of Hamilton graph, and can be labeled using a Gray coding based recursive algorithm. Finally, we gave the comparison results, a routing algorithm and a bitonic sort algorithm for CCNG. In case of sparsity and cost, CCNG is better than Hypercube.

  17. Guarded Cubical Type Theory

    DEFF Research Database (Denmark)

    Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald


    terms. CTT provides a computational interpretation of functional extensionality, enjoys canonicity for the natural numbers type, and is conjectured to support decidable type-checking. Our new type theory, guarded cubical type theory (GCTT), provides a computational interpretation of extensionality......This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning...... with coinductive types. We wish to implement GDTT with decidable type checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\\"of type theory in which the identity type is replaced by abstract paths between...

  18. On the chirally rotated Schroedinger functional with Wilson fermions

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez Lopez, Jenifer


    There are many phenomena in nature, which are closely linked to the low energy regime of QCD. From a theoretical point of view, these low energy phenomena can be dealt with only by means of non-perturbative methods. It is the central goal of this thesis to provide a framework for such a nonperturbative renormalization. For that purpose, we employ a 4-dimensional lattice as a regulator of QCD. As a renormalization scheme, we propose a finite volume Schroedinger functional scheme and here in particular, the chirally rotated Schroedinger functional ({chi}SF). We first perform analytical studies of the {chi}SF at tree-level of perturbation theory, in the continuum and on the lattice. We study the eigenvalue spectrum of the continuum Dirac operator, equipped with chirally rotated SF boundary conditions, and derive the corresponding quark propagator. We then determine the tree-level quark propagator on the lattice, employing massless Wilson fermions as a regulator of the theory. Beyond tree-level, all studies are performed in the quenched approximation of QCD, as a first, computationally much simpler step to understand the properties of the newly proposed {chi}SF scheme. One of the main targets of the present work, has been to perform the non-perturbative tuning of the two required coefficients of the {chi}SF scheme, such that a well defined continuum limit can be reached. We demonstrate, as the first main result of this thesis, that the tuning is feasible and that, moreover, physical quantities are insensitive to the particular tuning condition. As in any lattice regularization with SF-like boundary conditions, there are also in the {chi}SF a couple of counterterms at the boundaries, whose coefficients need to be tuned in order to remove the O(a) discretization effects originated at the boundaries. However, besides these boundary O(a) effects, the {chi}SF is expected to be compatible with bulk automatic O(a)-improvement. We show here that, indeed, the scaling behavior

  19. Nonlinear electrorheological instability of two Rivlin-Ericksen elastico-viscous fluids

    Energy Technology Data Exchange (ETDEWEB)

    El-Dib, Yusry O [Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo (Egypt)


    The behaviour of surface waves propagating between two Rivlin-Ericksen elastico-viscous fluids is examined. The investigation is made in the presence of a vertical electric field and a relative horizontal constant velocity. The influence of both surface tension and gravity force is taken into account. Due to the inclusion of streaming flow a mathematical simplification is considered. The viscoelastic contribution is demonstrated in the boundary conditions. From this point of view the approximation equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion under nonlinear boundary conditions lead to derivation of a nonlinear equation governing the interfacial displacement and having damping terms with complex coefficients. This equation is accomplished by utilizing the cubic nonlinearity. The use of the Gardner-Morikawa transformation yields a simplified linear dispersion relation so that the periodic solution for the linear form is utilized. The perturbation analysis, in the light of the multiple scales in both space and time, leads to imposing the well-known nonlinear Schroedinger equation having complex coefficients. The stability criteria are discussed theoretically and illustrated graphically in which stability diagrams are obtained. Regions of stability and instability are identified for the electric fields versus the wavenumber for the wavetrain of the disturbance. Numerical calculations showed that the ratio of the dielectric constant plays a dual role in the stability criteria. The damping role for the viscosity coefficient is observed. The viscoelasticity coefficient plays two different roles. A stabilizing influence is observed through the linear scope and a destabilizing role in the nonlinear stability picture is seen.

  20. Guarded Cubical Type Theory

    DEFF Research Database (Denmark)

    Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald


    types. This further expands the foundations of CTT as a basis for formalisation in mathematics and computer science. We present examples to demonstrate the expressivity of our type theory, all of which have been checked using a prototype type-checker implementation, and present semantics in a presheaf......This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning...... with coinductive types. We wish to implement GDTT with decidable type-checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\\"of type theory in which the identity type is replaced by abstract paths between...

  1. Higher-Order Approximation of Cubic-Quintic Duffing Model

    DEFF Research Database (Denmark)

    Ganji, S. S.; Barari, Amin; Babazadeh, H.


    We apply an Artificial Parameter Lindstedt-Poincaré Method (APL-PM) to find improved approximate solutions for strongly nonlinear Duffing oscillations with cubic-quintic nonlinear restoring force. This approach yields simple linear algebraic equations instead of nonlinear algebraic equations...... without analytical solution which makes it a unique solution. It is demonstrated that this method works very well for the whole range of parameters in the case of the cubic-quintic oscillator, and excellent agreement of the approximate frequencies with the exact one has been observed and discussed...... this analytical solution with the Newton-Harmonic Balancing Approach. Results indicate that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems. Utter simplicity of the solution procedure confirms that this method can be easily extended to other kinds...

  2. Solutions of type IIB and D=11 supergravity with Schroedinger(z) symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Donos, Aristomenis [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gauntlett, Jerome P. [Imperial College, London (United Kingdom). Theoretical Physics Group; Imperial College, London (United Kingdom). Inst. for Mathematical Sciences


    We construct families of supersymmetric solutions of type IIB and D=11 supergravity that are invariant under the non-relativistic Schroedinger(z) algebra for various values of the dynamical exponent z. The new solutions are based on five- and seven-dimensional Sasaki-Einstein manifolds, respectively, and include supersymmetric solutions with z=2. (orig.)

  3. The solution of the Schroedinger equation for complex Hamiltonian systems in two dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Chand, Fakir [Department of Physics, Kurukshetra University, Kurukshetra-136 119, Haryana (India); Singh, Ram Mehar [Department of Physics, Haryana College of Technology and Management, Kaithal-136 027, Haryana (India); Kumar, Narender [Department of Physics, Kurukshetra University, Kurukshetra-136 119, Haryana (India); Mishra, S C [Department of Physics, Kurukshetra University, Kurukshetra-136 119, Haryana (India)


    We investigate the ground state solutions of the Schroedinger equation for complex (non-Hermitian) Hamiltonian systems in two dimensions within the framework of an extended complex phase-space approach. The eigenvalues and eigenfunctions of some two-dimensional complex potentials are found.

  4. Nonlinear Hamiltonian systems

    DEFF Research Database (Denmark)

    Jørgensen, Michael Finn


    It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two......-dimensional defocusing Nonlinear Schroedinger (NLS) equation are studied analytically and numerically. It is found that no bound states exist. When the initial condition is a dark ring on a background of finite amplitude, the ring initially shrinks until the curvature effects become dominant, forcing the ring to expand...... particular configurations of the Discrete Self-Trapping (DST) system are shown to be completely solvable. One of these systems includes the Toda lattice in a certain limit. An explicit integration is carried through for this Near-Toda lattice. The Near-Toda lattice is then generalized to include singular...

  5. Obtention of Schroedinger-Cat-Like-States through canonical transformations in the quantum phase space; Obtencion de estados tipo gato de Schroedinger mediante transformaciones canonicas en el espacio fase cuantico

    Energy Technology Data Exchange (ETDEWEB)

    Zuniga S, A. [Instituto Politecnico Nacional, Departamento de Fisica, Escuela Superior de Fisica y Matematicas, Edificio 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico D.F. (Mexico)


    Employing canonical transformations defined in the coherent-state representation of quantum mechanics, we introduce Schroedinger-Cat- Like-States. The squeezed displaced number states with real squeezing parameter are contained in these states. (Author)

  6. On the dynamic buckling of a lightly damped elastic cubic model ...

    African Journals Online (AJOL)

    In this paper, we employ a generalization of Lindsted-Poincare technique to determine the dynamic buckling load of a lightly and viscously damped elastic cubic model structure modulated by a sinusoidally slowly varying dynamic load. The imperfect elastic cubic (nonlinear) structure is itself a generalization of most elastic ...

  7. Solitons in quadratic nonlinear photonic crystals

    DEFF Research Database (Denmark)

    Corney, Joel Frederick; Bang, Ole


    We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....

  8. Octanuclear cubic coordination cages. (United States)

    Tidmarsh, Ian S; Faust, Thomas B; Adams, Harry; Harding, Lindsay P; Russo, Luca; Clegg, William; Ward, Michael D


    Two new bis-bidentate bridging ligands have been prepared, L (naph) and L (anth), which contain two chelating pyrazolyl-pyridine units connected to an aromatic spacer (naphthalene-1,5-diyl and anthracene-9,10-diyl respectively) via methylene connectors. Each of these reacts with transition metal dications having a preference for octahedral coordination geometry to afford {M 8L 12} (16+) cages (for L (anth), M = Cu, Zn; for L (naph), M = Co, Ni, Cd) which have an approximately cubic arrangement of metal ions with a bridging ligand spanning each of the twelve edges, and a large central cavity containing a mixture of anions and/or solvent molecules. The cages based on L (anth) have two cyclic helical {M 4L 4} faces, of opposite chirality, connected by four additional L (anth) ligands as "pillars"; all metal centers have a meridional tris-chelate configuration. In contrast the cages based on L (naph) have (noncrystallographic) S 6 symmetry, with a diagonally opposite pair of corners having a facial tris-chelate configuration with the other six being meridional. An additional significant difference between the two types of structure is that the cubes containing L (anth) do not show significant interligand aromatic stacking interactions. However, in the cages based on L (naph), there are six five-membered stacks of aromatic ligand fragments around the periphery, each based on an alternating array of electron-rich (naphthyl) and electron-deficient (pyrazolyl-pyridine, coordinated to M (2+)) aromatic units. A consequence of this is that the cages {M 8(L (naph)) 12} (16+) retain their structural integrity in polar solvents, in contrast to the cages {M 8(L (anth)) 12} (16+) which dissociate in polar solvents. Consequently, the cages {M 8(L (naph)) 12} (16+) give NMR spectra in agreement with the symmetry observed in the solid state, and their fluorescence spectra (for M = Cd) display (in addition to the normal naphthalene-based pi-pi* fluorescence) a lower-energy exciplex


    Directory of Open Access Journals (Sweden)



    applications in digital image processing and in the study of dynamical systems, but in the actual literature there is not an extension of their properties using fuzzy sets. In this paper is proposed a generalization of the concept of cubical complex and of some of their properties, such as connectedness, polyhedral realization, connected component and holes, using fuzzy sets. The upper and lower trees of a fuzzy cubical complex are defined, which give information about the way in which its regional extrema are related. The homology groups of a fuzzy cubical complex are defined and it is shown that the rank of the 0-homology group of a given level is equal with the number of regional maxima of that level. Finally, it is shown how to associate a fuzzy cubical complex with a bidimensional digital grayscale image in order to study somo of its topological properties.

  10. NLO anomalous dimension of multiplicatively renormalizable four-fermion operators in Schroedinger Functional schemes

    Energy Technology Data Exchange (ETDEWEB)

    Palombi, Filippo [' E. Fermi' Research Center, c/o Compendio Viminale - pal. F, I-00184 Rome (Italy); Pena, Carlos [DESY, Theory Group, Notkestrasse 85, D-22603 Hamburg (Germany); Sint, Stefan [Departamento de Fisica Teorica C-XI and Instituto de Fisica Teorica C-XVI, Universidad Autonoma de Madrid, Cantoblanco, E-28049 Madrid (Spain)


    Renormalization constants for multiplicatively renormalizable parity-odd four-fermion operators are computed in various different Schroedinger Functional (SF) schemes and lattice regularizations with Wilson quarks at one-loop order in perturbation theory. Our results are used in the calculation of their NLO anomalous dimensions, through matching to continuum schemes. They also enable a comparison of the two-loop perturbative RG running to the previously obtained nonperturbative one in the region of small renormalized coupling.

  11. Cryptographic Analysis in Cubic Time

    DEFF Research Database (Denmark)

    Nielson, Flemming; Nielson, Hanne Riis; Seidl, H.


    The spi-calculus is a variant of the polyadic pi-calculus that admits symmetric cryptography and that admits expressing communication protocols in a precise though still abstract way. This paper shows that context-independent control flow analysis can be calculated in cubic time despite the fact...... that the spi-calculus operates over an infinite universe of values. Our approach is based on Horn Clauses with Sharing and we develop transformations to pass from the infinite to the finite and to deal with the polyadic nature of input and output. We prove that this suffices for obtaining a cubic time...

  12. A quenched study of the Schroedinger functional with chirally rotated boundary conditions. Applications

    Energy Technology Data Exchange (ETDEWEB)

    Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik


    In a previous paper (J. G. Lopez et al.,2012) we have discussed the non-perturbative tuning of the chirally rotated Schroedinger functional ({chi}SF). This tuning is required to eliminate bulk O(a) cutoff effects in physical correlation functions. Using our tuning results obtained in this paper we perform scaling and universality tests analyzing the residual O(a) cutoff effects of several step-scaling functions and we compute renormalization factors at the matching scale. As an example of possible application of the {chi}SF we compute the renormalized strange quark mass using large volume data obtained from Wilson twisted mass fermions at maximal twist. (orig.)

  13. Some Exact Results for the Schroedinger Wave Equation with a Time Dependent Potential (United States)

    Campbell, Joel


    The time dependent Schroedinger equation with a time dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wave function at the origin, one may derive the wave function everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the p otential lead to conservation of the normalization of the probability density.

  14. Some exact results for the Schroedinger wave equation with a time-dependent potential

    Energy Technology Data Exchange (ETDEWEB)

    Campbell, Joel [NASA Langley Research Center, MS 488, Hampton, VA 23681 (United States)], E-mail:


    The time-dependent Schroedinger equation with a time-dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wavefunction at the origin, one may derive the wavefunction everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the potential lead to the conservation of the normalization of the probability density.

  15. A quenched study of the Schroedinger functional with chirally rotated boundary conditions. Non-preturbative tuning

    Energy Technology Data Exchange (ETDEWEB)

    Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik


    The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)

  16. Quaternionic factorization of the Schroedinger operator and its applications to some first-order systems of mathematical physics

    Energy Technology Data Exchange (ETDEWEB)

    Kravchenko, Viktor G [Faculdade de Ciencias y Tecnologia, Universidade do Algarve, Campus de Gambelas, 8000 Faro (Portugal); Kravchenko, Vladislav V [Depto de Telecomunicaciones, SEPI ESIME Zacatenco, Instituto Politecnico Nacional, Av. IPN S/N, Edif. 1 CP 07738, DF (Mexico)


    We show that an ample class of physically meaningful partial differential systems of first order such as the Dirac equation with different one-component potentials, static Maxwell's system and the system describing the force-free magnetic fields are equivalent to a single quaternionic equation which in its turn reduces in general to a Schroedinger equation with quaternionic potential, and in some situations this last can be diagonalized. The rich variety of methods developed for different problems corresponding to the Schroedinger equation can be applied to the systems considered in the present work.

  17. Numbers for reducible cubic scrolls

    Directory of Open Access Journals (Sweden)

    Israel Vainsencher


    Full Text Available We show how to compute the number of reducible cubic scrolls of codimension 2 in (math blackboard symbol Pn incident to the appropriate number of linear spaces.Mostramos como calcular o número de rolos cúbicos redutíveis de codimensão 2 em (math blackboard symbol Pn incidentes a espaços lineares apropriados.

  18. Randomized Block Cubic Newton Method

    KAUST Repository

    Doikov, Nikita


    We study the problem of minimizing the sum of three convex functions: a differentiable, twice-differentiable and a non-smooth term in a high dimensional setting. To this effect we propose and analyze a randomized block cubic Newton (RBCN) method, which in each iteration builds a model of the objective function formed as the sum of the natural models of its three components: a linear model with a quadratic regularizer for the differentiable term, a quadratic model with a cubic regularizer for the twice differentiable term, and perfect (proximal) model for the nonsmooth term. Our method in each iteration minimizes the model over a random subset of blocks of the search variable. RBCN is the first algorithm with these properties, generalizing several existing methods, matching the best known bounds in all special cases. We establish ${\\\\cal O}(1/\\\\epsilon)$, ${\\\\cal O}(1/\\\\sqrt{\\\\epsilon})$ and ${\\\\cal O}(\\\\log (1/\\\\epsilon))$ rates under different assumptions on the component functions. Lastly, we show numerically that our method outperforms the state-of-the-art on a variety of machine learning problems, including cubically regularized least-squares, logistic regression with constraints, and Poisson regression.

  19. Automated lattice perturbation theory in the Schroedinger functional. Implementation and applications in HQET

    Energy Technology Data Exchange (ETDEWEB)

    Hesse, Dirk


    The author developed the pastor software package for automated lattice perturbation theory calculations in the Schroedinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schroedinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.

  20. Bell's theorem and quantum realism. Reassessment in light of the Schroedinger paradox

    Energy Technology Data Exchange (ETDEWEB)

    Shakur, Asif M. [Salisbury Univ., MD (United States). Dept. of Physics; Hemmick, Douglas L.


    Quantum theory presents a strange picture of the world, offering no real account of physical properties apart from observation. Neils Bohr felt that this reflected a core truth of nature: ''There is no quantum world. There is only an abstract mathematical description.'' Among the most significant developments since Bohr's day has been the theorem of John S. Bell. It is important to consider whether Bell's analysis supports such a denial of microrealism. In this book, we evaluate the situation in terms of an early work of Erwin Schroedinger. Doing so, we see how Bell's theorem is conceptually related to the Conway and Kochen Free Will theorem and also to all the major anti-realism efforts. It is easy to show that none of these analyses imply the impossibility of objective realism. We find that Schroedinger's work leads to the derivation of a new series of theoretical proofs and potential experiments, each involving ''entanglement,'' the link between particles in some quantum systems. (orig.)

  1. Cubic Matrix, Nambu Mechanics and Beyond


    Yoshiharu, KAWAMURA; Department of Physics, Shinshu University


    We propose a generalization of cubic matrix mechanics by introducing a canonical triplet and study its relation to Nambu mechanics. The generalized cubic matrix mechanics we consider can be interpreted as a 'quantum' generalization of Nambu mechanics.

  2. Cubic Matrix, Nambu Mechanics and Beyond


    Kawamura, Y.


    We propose a generalization of cubic matrix mechanics by introducing a canonical triplet and study its relation to Nambu mechanics. The generalized cubic matrix mechanics we consider can be interpreted as a “quantum” generalization of Nambu mechanics.

  3. Solving Cubic Equations by Polynomial Decomposition (United States)

    Kulkarni, Raghavendra G.


    Several mathematicians struggled to solve cubic equations, and in 1515 Scipione del Ferro reportedly solved the cubic while participating in a local mathematical contest, but did not bother to publish his method. Then it was Cardano (1539) who first published the solution to the general cubic equation in his book "The Great Art, or, The Rules of…

  4. Cubic colloids : Synthesis, functionalization and applications

    NARCIS (Netherlands)

    Castillo, S.I.R.


    This thesis is a study on cubic colloids: micron-sized cubic particles with rounded corners (cubic superballs). Owing to their shape, particle packing for cubes is more efficient than for spheres and results in fascinating phase and packing behavior. For our cubes, the particle volume fraction when

  5. A generalized cubic Volterra lattice hierarchy and its integrable couplings system

    Energy Technology Data Exchange (ETDEWEB)

    Xia Tiecheng [Department of Mathematics, Shanghai University, Shanghai 200444 (China); Department of Mathematics, Bohai University, Jinzhou of Liaoning Province 121000 (China); Department of Mathematics, Tianjin University, Tianjin 300072 (China); E-mail:; You Fucai [Department of Mathematics, Bohai University, Jinzhou of Liaoning Province 121000 (China); Chen Dengyuan [Department of Mathematics, Shanghai University, Shanghai 200444 (China)


    In terms of properties of the known loop algebra A{approx}{sub 1} and difference operators, a new algebraic system {chi} is constructed. By using the algebraic system {chi}, a discrete matrix spectral problem is introduced and a hierarchy of nonlinear lattice equations is derived. From the hierarchy the celebrated cubic Volterra lattice equation is engendered. We call the hierarchy a generalized cubic Volterra hierarchy. Then an extended algebraic system {chi}-bar of {chi} is presented, from which the integrable couplings system of the generalized cubic Volterra lattice are obtained.

  6. Time-dependent Schroedinger equations with effective mass in (2 + 1) dimensions: intertwining relations and Darboux operators

    Energy Technology Data Exchange (ETDEWEB)

    Cobian, Hector [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, 28045 Colima, Colima (Mexico); Schulze-Halberg, Axel, E-mail:, E-mail:, E-mail: [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, IN 46408 (United States)


    We construct Darboux transformations for time-dependent Schroedinger equations with position-dependent mass in (2 + 1) dimensions. Several examples illustrate our results, which complement and generalize former findings for the constant mass case in two spatial variables (Schulze-Halberg 2010 J. Math. Phys. 51 033521).

  7. Spinning solitons in cubic-quintic nonlinear media

    Indian Academy of Sciences (India)

    Author Affiliations. Lucian-Cornel Crasovan1 Boris A Malomed2 Dumitru Mihalache1. Department of Theoretical Physics, Institute of Atomic Physics, P.O. Box MG-6, Bucharest, Romania; Department of Interdisciplinary Sciences, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel ...

  8. Schroedinger Eigenmaps with nondiagonal potentials for spatial-spectral clustering of hyperspectral imagery (United States)

    Cahill, Nathan D.; Czaja, Wojciech; Messinger, David W.


    Schroedinger Eigenmaps (SE) has recently emerged as a powerful graph-based technique for semi-supervised manifold learning and recovery. By extending the Laplacian of a graph constructed from hyperspectral imagery to incorporate barrier or cluster potentials, SE enables machine learning techniques that employ expert/labeled information provided at a subset of pixels. In this paper, we show how different types of nondiagonal potentials can be used within the SE framework in a way that allows for the integration of spatial and spectral information in unsupervised manifold learning and recovery. The nondiagonal potentials encode spatial proximity, which when combined with the spectral proximity information in the original graph, yields a framework that is competitive with state-of-the-art spectral/spatial fusion approaches for clustering and subsequent classification of hyperspectral image data.

  9. Application of a new functional expansion to the cubic anharmonic oscillator (United States)

    Fliess, Michel; Lamnabhi-Lagarrigue, Françoise


    A new representation of causal functionals is introduced which makes use of noncommutative generating power series and iterated integrals. This technique allows the solutions of nonlinear differential equations with forcing terms to be obtained in a simple and natural way. It generalizes some properties of Fourier and Laplace transforms to nonlinear systems and leads to effective computations of various perturbative expansions. Illustrations by means of the cubic anharmonic oscillator are given in both the deterministic and the stochastic cases.

  10. Cubic AlGaN/GaN structures for device application

    Energy Technology Data Exchange (ETDEWEB)

    Schoermann, Joerg


    The aim of this work was the growth and the characterization of cubic GaN, cubic AlGaN/GaN heterostructures and cubic AlN/GaN superlattice structures. Reduction of the surface and interface roughness was the key issue to show the potential for the use of cubic nitrides in futur devices. All structures were grown by plasma assisted molecular beam epitaxy on free standing 3C-SiC (001) substrates. In situ reflection high energy electron diffraction was first investigated to determine the Ga coverage of c-GaN during growth. Using the intensity of the electron beam as a probe, optimum growth conditions were found when a 1 monolayer coverage is formed at the surface. GaN samples grown under these conditions reveal excellent structural properties. On top of the c-GaN buffer c-AlGaN/GaN single and multiple quantum wells were deposited. The well widths ranged from 2.5 to 7.5 nm. During growth of Al{sub 0.15}Ga{sub 0.85}N/GaN quantum wells clear reflection high energy electron diffraction oscillations were observed indicating a two dimensional growth mode. We observed strong room-temperature, ultraviolet photoluminescence at about 3.3 eV with a minimum linewidth of 90 meV. The peak energy of the emission versus well width is reproduced by a square-well Poisson- Schroedinger model calculation. We found that piezoelectric effects are absent in c-III nitrides with a (001) growth direction. Intersubband transition in the wavelength range from 1.6 {mu}m to 2.1 {mu}m was systematically investigated in AlN/GaN superlattices (SL), grown on 100 nm thick c-GaN buffer layers. The SLs consisted of 20 periods of GaN wells with a thickness between 1.5 nm and 2.1 nm and AlN barriers with a thickness of 1.35 nm. The first intersubband transitions were observed in metastable cubic III nitride structures in the range between 1.6 {mu}m and 2.1 {mu}m. (orig.)

  11. Numerical treatment of Hunter Saxton equation using cubic trigonometric B-spline collocation method (United States)

    Hashmi, M. S.; Awais, Muhammad; Waheed, Ammarah; Ali, Qutab


    In this article, authors proposed a computational model based on cubic trigonometric B-spline collocation method to solve Hunter Saxton equation. The nonlinear second order partial differential equation arises in modeling of nematic liquid crystals and describes some aspects of orientation wave. The problem is decomposed into system of linear equations using cubic trigonometric B-spline collocation method with quasilinearization. To show the efficiency of the proposed method, two numerical examples have been tested for different values of t. The results are described using error tables and graphs and compared with the results existed in literature. It is evident that results are in good agreement with analytical solution and better than Arbabi, Nazari, and Davishi, Optik 127, 5255-5258 (2016). In current problem, it is also observed that the cubic trigonometric B-spline gives better results as compared to cubic B-spline.

  12. A general formula for Rayleigh-Schroedinger perturbation energy utilizing a power series expansion of the quantum mechanical Hamiltonian

    Energy Technology Data Exchange (ETDEWEB)

    Herbert, J.M.


    Perturbation theory has long been utilized by quantum chemists as a method for approximating solutions to the Schroedinger equation. Perturbation treatments represent a system`s energy as a power series in which each additional term further corrects the total energy; it is therefore convenient to have an explicit formula for the nth-order energy correction term. If all perturbations are collected into a single Hamiltonian operator, such a closed-form expression for the nth-order energy correction is well known; however, use of a single perturbed Hamiltonian often leads to divergent energy series, while superior convergence behavior is obtained by expanding the perturbed Hamiltonian in a power series. This report presents a closed-form expression for the nth-order energy correction obtained using Rayleigh-Schroedinger perturbation theory and a power series expansion of the Hamiltonian.

  13. Solution of the Schroedinger equation for time-dependent 1D harmonic oscillators using the orthogonal functions invariant

    Energy Technology Data Exchange (ETDEWEB)

    Guasti, M Fernandez [Depto de Fisica, CBI, Universidad A Metropolitana - Iztapalapa, 09340 Mexico, DF, Apdo Postal 55-534 (Mexico); Moya-Cessa, H [INAOE, Coordinacion de Optica, Apdo Postal 51 y 216, 72000 Puebla, Pue. (Mexico)


    An extension of the classical orthogonal functions invariant to the quantum domain is presented. This invariant is expressed in terms of the Hamiltonian. Unitary transformations which involve the auxiliary function of this quantum invariant are used to solve the time-dependent Schroedinger equation for a harmonic oscillator with time-dependent parameter. The solution thus obtained is in agreement with the results derived using other methods which invoke the Lewis invariant in their procedures.

  14. Cubical local partial orders on cubically subdivided spaces - existence and construction

    DEFF Research Database (Denmark)

    Fajstrup, Lisbeth

    The geometric models of Higher Dimensional Automata and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes, such ...

  15. Topics in Cubic Special Geometry

    CERN Document Server

    Bellucci, Stefano; Roychowdhury, Raju


    We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbit...

  16. (real and complex) of the general cubic

    African Journals Online (AJOL)

    ES Obe

    + cx + d = 0 have been formulated and presented. The explicit hyperbolic expressions for the complex roots have been developed for the first time in history thereby enabling the establishment of harmony in the solution of cubic equations. Also, four alternative expressions for the only real root of the cubic have also been ...

  17. Nonlinear hydromagnetic Rayleigh-Taylor instability for strong viscous fluids in porous media

    CERN Document Server

    El-Dib, Y O


    In the present work a weakly nonlinear stability for magnetic fluid is discussed. The research of an interface between two strong viscous homogeneous incompressible fluids through porous medium is investigated theoretically and graphically. The effect of the vertical magnetic field has been demonstrated in this study. The linear form of equation of motion is solved in the light of the nonlinear boundary conditions. The boundary value problem leads to construct nonlinear characteristic equation having complex coefficients in elevation function. The nonlinearity is kept to third-order expansion. The nonlinear characteristic equation leads to derive the well-known nonlinear Schroedinger equation. This equation having complex coefficients of the disturbance amplitude varies in both space and time. Stability criteria have been performed for nonlinear Chanderasekhar dispersion relation including the porous effects. Stability conditions are discussed through the assumption of equal kinematic viscosity. The calculati...

  18. Nonlinear Dispersive Instabilities in Kelvin-Helmholtz Magnetohydrodynamic Flows

    Energy Technology Data Exchange (ETDEWEB)

    Khater, A.H.; Seadawy, A.R. [Cairo Univ., Beni-Suef (Egypt). Mathematics Dept.; Callebaut, D.K. [Univ. Antwerpen (Belgium). Dept. Natuurkunde


    In this paper a weakly nonlinear theory of wave propagation in superposed fluids in the presence of magnetic fields is presented. The equations governing the evolution of the amplitude of the progressive waves are reported. The nonlinear evolution of Kelvin-Helmholtz instability (KHI) is examined in 2 + 1 dimensions in the context of magnetohydrodynamics (MHD). We study the envelope properties of the 2 + 1 dimensional wave packet. We converted the resulting nonlinear equation for the evolution of the wave packets in a 2 + 1 dimensional nonlinear Schroedinger (NLS) equation by using the function transformation method into a sine-Gordon equation, which depends only on one function, {zeta}. We obtained rather general classes of solutions of the equation in {zeta} which leads to rather general soliton solutions of the 2 + 1 dimensional NLS equation. This result contains interesting specific solutions such as N multiple solitons, propagational breathers and quadratic solitons.

  19. A formal derivation of the Gibbs entropy for classical systems following the Schroedinger quantum mechanical approach

    Energy Technology Data Exchange (ETDEWEB)

    Santillan, M [Cinvestav-IPN, Unidad Monterrey, Parque de Investigacion e Innovacion Tecnologica, Autopista Monterrey-Aeropuerto Km 10, 66600 Apodaca NL (Mexico); Zeron, E S [Departamento de Matematicas, Cinvestav-IPN, 07000 Mexico DF (Mexico); Rio-Correa, J L del [Departamento de Fisica, Universidad Autonoma Metropolitana Iztapalapa, 09340 Mexico DF (Mexico)], E-mail:, E-mail:, E-mail:


    In the traditional statistical mechanics textbooks, the entropy concept is first introduced for the microcanonical ensemble and then extended to the canonical and grand-canonical cases. However, in the authors' experience, this procedure makes it difficult for the student to see the bigger picture and, although quite ingenuous, the subtleness of the demonstrations to pass from the microcanonical to the canonical and grand-canonical ensembles is hard to grasp. In the present work, we adapt the approach used by Schroedinger to introduce the entropy definition for quantum mechanical systems to derive a classical mechanical entropy definition, which is valid for all ensembles and is in complete agreement with the Gibbs entropy. Afterwards, we show how the specific probability densities for the microcanonical and canonical ensembles can be obtained from the system macrostate, the entropy definition and the second law of thermodynamics. After teaching the approach introduced in this paper for several years, we have found that it allows a better understanding of the statistical mechanics foundations. On the other hand, since it demands previous knowledge of thermodynamics and mathematical analysis, in our experience this approach is more adequate for final-year undergraduate and graduate physics students.

  20. Plasmons and Coulomb drag in Dirac/Schroedinger hybrid electron systems (United States)

    Principi, Alessandro; Carrega, Matteo; Asgari, Reza; Pellegrini, Vittorio; Polini, Marco


    We show that the plasmon spectrum of an ordinary two-dimensional electron gas (2DEG) hosted in a GaAs heterostructure is significantly modified when a graphene sheet is placed on the surface of the semiconductor in close proximity to the 2DEG. Long-range Coulomb interactions between massive electrons and massless Dirac fermions lead to a new set of optical and acoustic intra-subband plasmons. Here we compute the dispersion of these coupled modes within the Random Phase Approximation, providing analytical expressions in the long-wavelength limit that shed light on their dependence on the Dirac velocity and Dirac-fermion density. We also evaluate the resistivity in a Coulomb-drag transport setup. These Dirac/Schroedinger hybrid electron systems are experimentally feasible and open new research opportunities for fundamental studies of electron-electron interaction effects in two spatial dimensions. Work in Pisa was supported by MIUR through the program ``FIRB - Futuro in Ricerca 2010.'' Grant no. RBFR10M5BT (``Plasmons and terahertz devices in graphene'').

  1. An asymptotic solution of the Schroedinger equation for the elliptic wire in the magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Bejenari, I; Kantser, V [Institute of Electronic Engineering and Industrial Technologies, Academiei str., 3/3, MD2028 Chisinau (Moldova, Republic of)], E-mail:


    An asymptotic solution of the Schroedinger equation with non-separable variables is obtained for a particle confined to an infinite elliptic cylinder potential well under an applied uniform longitudinal magnetic field. Using the standard-problem method, dimension-quantized eigenvalues have been calculated when the magnetic length is large enough in comparison with the half of the distance between the boundary ellipse focuses. In semi-classical approximation, the confined electron (hole) states are divided into the boundary states (BS), ring states (RS), hyperbolic caustic states (HCS) and harmonic oscillator states (HOS). For large angular momentum quantum numbers and small radial quantum numbers, the BS and RS are grouped into the 'whispering gallery' mode. They associate with particles moving along the wire cross section boundary. The motion is limited from the wire core by the elliptic caustic. Consisting of the HCS and HOS, the 'jumping ball' modes correspond to the states of particle moving along a wire diameter when the angular momentum quantum number is much less than the radial quantum number. In this case, the motion is restricted by the hyperbolic caustics and two boundary ellipse arcs. For excited hole states in a Bi wire, the energy spectrum and space probability distribution are analyzed.

  2. Generalized quantum isotonic nonlinear oscillator in d dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Hall, Richard L [Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec H3G 1M8 (Canada); Saad, Nasser [Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Avenue, Charlottetown, PEI C1A 4P3 (Canada); Yesiltas, Oezlem, E-mail: rhall@mathstat.concordia.c, E-mail: nsaad@upei.c, E-mail: [Department of Physics, Faculty of Arts and Sciences, Gazi University, 06500 Ankara (Turkey)


    We present a supersymmetric analysis for the d-dimensional Schroedinger equation with the generalized isotonic nonlinear-oscillator potential V(r) = B{sup 2}/r{sup 2} + {omega}{sup 2}r{sup 2} + 2g(r{sup 2} - a{sup 2})/(r{sup 2} + a{sup 2}){sup 2}, B {>=} 0. We show that the eigenequation for this potential is exactly solvable provided g = 2 and ({omega}a{sup 2}){sup 2} = B{sup 2} + (l + (d - 2)/2){sup 2}. Under these conditions, we obtain explicit formulae for all the energies and normalized bound-state wavefunctions.

  3. Quadratic-like dynamics of cubic polynomials


    Blokh, Alexander; Oversteegen, Lex; Ptacek, Ross; Timorin, Vladlen


    A small perturbation of a quadratic polynomial with a non-repelling fixed point gives a polynomial with an attracting fixed point and a Jordan curve Julia set, on which the perturbed polynomial acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of thei...

  4. Heisenberg antiferromagnets with exchange and cubic anisotropies

    Energy Technology Data Exchange (ETDEWEB)

    Bannasch, G [MPI fuer Physik komplexer Systeme, 01187 Dresden (Germany); Selke, W, E-mail: selke@physik.rwth-aachen.d [Institut fuer Theoretische Physik, RWTH Aachen University and JARA-SIM, 52056 Aachen (Germany)


    We study classical Heisenberg antiferromagnets with uniaxial exchange anisotropy and a cubic anisotropy term on simple cubic lattices in an external magnetic field using ground state considerations and extensive Monte Carlo simulations. In addition to the antiferromagnetic phase field-induced spin-flop and non-collinear, biconical phases may occur. Phase diagrams and critical as well as multicritical phenomena are discussed. Results are compared to previous findings.

  5. An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method

    Energy Technology Data Exchange (ETDEWEB)

    Belendez, A., E-mail: a.belendez@ua.e [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Mendez, D.I. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Marini, S. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)


    The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.

  6. Exploring the performance of a nonlinear tuned mass damper

    DEFF Research Database (Denmark)

    Alexander, Nicholas A.; Schilder, Frank


    We explore the performance of a nonlinear tuned mass damper (NTMD), which is modeled as a two degree of freedom system with a cubic nonlinearity. This nonlinearity is physically derived from a geometric configuration of two pairs of springs. The springs in one pair rotate as they extend, which re...

  7. Time-dependent probability density function in cubic stochastic processes (United States)

    Kim, Eun-jin; Hollerbach, Rainer


    We report time-dependent probability density functions (PDFs) for a nonlinear stochastic process with a cubic force using analytical and computational studies. Analytically, a transition probability is formulated by using a path integral and is computed by the saddle-point solution (instanton method) and a new nonlinear transformation of time. The predicted PDF p (x ,t ) in general involves a time integral, and useful PDFs with explicit dependence on x and t are presented in certain limits (e.g., in the short and long time limits). Numerical simulations of the Fokker-Planck equation provide exact time evolution of the PDFs and confirm analytical predictions in the limit of weak noise. In particular, we show that transient PDFs behave drastically differently from the stationary PDFs in regard to the asymmetry (skewness) and kurtosis. Specifically, while stationary PDFs are symmetric with the kurtosis smaller than 3, transient PDFs are skewed with the kurtosis larger than 3; transient PDFs are much broader than stationary PDFs. We elucidate the effect of nonlinear interaction on the strong fluctuations and intermittency in the relaxation process.

  8. Charge capture and impact excitation processes in H{sup +} on He{sup +} collisions: a case study by the time-dependent Schroedinger equation method

    Energy Technology Data Exchange (ETDEWEB)

    Tong Xiaomin [Cold Trapped Ions Project, ICORP, Japan Science and Technology Corporation (JST), Axis 3F, 1-40-2 Fuda Chofu, Tokyo 182-0024 (Japan)]. E-mail:; Kato, Daiji; Watanabe, Tsutomu [Cold Trapped Ions Project, ICORP, Japan Science and Technology Corporation (JST), Axis 3F, 1-40-2 Fuda Chofu, Tokyo 182-0024 (Japan); Ohtani, Shunsuke [Cold Trapped Ions Project, ICORP, Japan Science and Technology Corporation (JST), Axis 3F, 1-40-2 Fuda Chofu, Tokyo 182-0024 (Japan); University of Electro-Communication, Chofu, Tokyo 182-0021 (Japan)


    We have studied the charge capture and impact excitation processes in H{sup +} on He{sup +} collisions over a wide range of collision energies by solving the time-dependent Schroedinger equation with the classical trajectory approximation for the projectile. The time-dependent Schroedinger equation is solved by the split-operator method with a generalized pseudospectral (non-uniform grid) method in the energy representation. The calculated charge capture cross sections are in good agreement with the available experimental measurements. Our calculated charge capture and impact excitation cross sections are also in reasonable agreement with various close-coupling calculations. Combined with time-dependent density functional theory, our Schroedinger equation method (time propagation) holds significant promise for studying many-electron processes in atom-ion collisions. (author)

  9. Nonlinear oscillation system of mass with serial linear and nonlinear springs

    DEFF Research Database (Denmark)

    Seyedalizadeh Ganji,, S.R; Barari, Amin; Karimpour, S


    In this paper, two powerful methods called Max–Min and parameter expansion have been applied for the determination of the periodic solutions of the nonlinear free vibration of a conservative oscillator with inertia and static type cubic nonlinearities. It is found that these methods introduce two...

  10. Dise\\~no de una Arquitectura para la Solucion de la Ecuacion de Schroedinger usando el Metodo de Numerov

    CERN Document Server

    Rodriguez-Toro, Victor A; Velasco-Medina, Jaime


    This paper presents a first approach in order to design an optimal architecture to implement the Numerov method, which solves the time-independent Schroedinger equation (TISE) for one dimension. The design and simulation have been performed by using 64-bits floating-point megafunctions available in Quartus II (Version 9.0). The verification of these results was done by using Matlab. According to these results, it is possible to extend this design to parallel structures, which would be able to calculate several TISE solutions.

  11. Extension of the homotopy pertubation method for solving nonlinear differential-difference equations

    Energy Technology Data Exchange (ETDEWEB)

    Mousa, Mohamed Medhat [Benha Univ. (Egypt). Benha High Inst. of Technology; Al-Farabi Kazakh National Univ., Almaty (Kazakhstan); Kaltayev, Aidarkan [Al-Farabi Kazakh National Univ., Almaty (Kazakhstan); Bulut, Hasan [Firat Univ., Elazig (Turkey). Dept. of Mathematics


    In this paper, we have extended the homotopy perturbation method (HPM) to find approximate analytical solutions for some nonlinear differential-difference equations (NDDEs). The discretized modified Korteweg-de Vries (mKdV) lattice equation and the discretized nonlinear Schroedinger equation are taken as examples to demonstrate the validity and the great potential of the HPM in solving such NDDEs. Comparisons are made between the results of the presented method and exact solutions. The obtained results reveal that the HPM is a very effective and convenient tool for solving such kind of equations. (orig.)

  12. Four-dimensional black holes in Einsteinian cubic gravity (United States)

    Bueno, Pablo; Cano, Pablo A.


    We construct static and spherically symmetric generalizations of the Schwarzschild- and Reissner-Nordström-(anti-)de Sitter [RN-(A)dS] black-hole solutions in four-dimensional Einsteinian cubic gravity (ECG). The solutions are characterized by a single function which satisfies a nonlinear second-order differential equation. Interestingly, we are able to compute independently the Hawking temperature T , the Wald entropy S and the Abbott-Deser mass M of the solutions analytically as functions of the horizon radius and the ECG coupling constant λ . Using these we show that the first law of black-hole mechanics is exactly satisfied. Some of the solutions have positive specific heat, which makes them thermodynamically stable, even in the uncharged and asymptotically flat case. Further, we claim that, up to cubic order in curvature, ECG is the most general four-dimensional theory of gravity which allows for nontrivial generalizations of Schwarzschild- and RN-(A)dS characterized by a single function which reduce to the usual Einstein gravity solutions when the corresponding higher-order couplings are set to zero.

  13. Experimental investigation on water flow in cubic arrays of spheres (United States)

    Huang, K.; Wan, J. W.; Chen, C. X.; He, L. Q.; Mei, W. B.; Zhang, M. Y.


    One-dimensional uniform flow in homogeneous porous media was experimentally investigated. Head drop experiments were conducted in four test tubes with cubic arrays of spheres in diameter 3 mm, 5 mm, 8 mm and 10 mm. The experimental results indicate that Darcy’s law should be an approximate expression by neglecting the inertial term for flow at low velocity. Nonlinearity is attributed to inertial term in porous medium before the turbulent flow emerges. Forchheimer equation with constant coefficients can well predict the flow in porous medium. The relationship between the diameter of the particles and the coefficients a and b in the equations were verified. Different Ergun type equations were used to predict the head drop and compared to the experimental data. It shows that the Irmay equation could well predict the fluid flow in cubic arrays of spheres, while the prediction of head drop by Ergun equation was much higher than observed data. It indicates that the coefficients α and β in the Ergun type equations have certain relations with porosity or the pore structure and would vary for different medium. The discontinuity observed was interpreted by transition from steady flow to weakly turbulence and compared with previous studies.

  14. Quantum corrections for the cubic Galileon in the covariant language (United States)

    Saltas, Ippocratis D.; Vitagliano, Vincenzo


    We present for the first time an explicit exposition of quantum corrections within the cubic Galileon theory including the effect of quantum gravity, in a background- and gauge-invariant manner, employing the field-reparametrisation approach of the covariant effective action at 1-loop. We show that the consideration of gravitational effects in combination with the non-linear derivative structure of the theory reveals new interactions at the perturbative level, which manifest themselves as higher-operators in the associated effective action, which' relevance is controlled by appropriate ratios of the cosmological vacuum and the Galileon mass scale. The significance and concept of the covariant approach in this context is discussed, while all calculations are explicitly presented.

  15. On the reduction of the multidimensional stationary Schroedinger equation to a first-order equation and its relation to the pseudoanalytic function theory

    Energy Technology Data Exchange (ETDEWEB)

    Kravchenko, Vladislav V [Departmento de Telecomunicaciones, SEPI, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, CP 07738 Mexico DF (Mexico)


    Given a particular solution of a one-dimensional stationary Schroedinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schroedinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schroedinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schroedinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schroedinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schroedinger equation. Moreover, for an ample

  16. Nonlinear integrable systems related to arbitrary space-time dependence of the spectral transform

    CERN Document Server

    León, J


    Abstract: We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the spectral transform (in general nonlinear and with non-analytic dispersion relations). The main theorem is that the compatibility conditions gives always a true nonlinear evolution because it can always be written as an identity between polynomials in the spectral variable $k$. This general result is then used to obtain first a method to generate a new class of solutions to the nonlinear Schroedinger equation, and second to construct the spectral transform theory for solving initial-boundary value problems for resonant wave-coupling processes (like self-induced transparency in two-level media, or stimulated Brillouin scattering of plasma waves or else stimulated Raman scattering in nonlinear optics etc...).

  17. The Exact Limit of Some Cubic Towers

    DEFF Research Database (Denmark)

    Anbar Meidl, Nurdagül; Beelen, Peter; Nguyen, Nhut


    Recently, a new explicit tower of function fields was introduced by Bassa, Beelen, Garcia and Stichtenoth (BBGS). This resulted in currently the best known lower bound for Ihara’s constant in the case of non-prime finite fields. In particular over cubic fields, the tower’s limit is at least as good...

  18. A look through 'lens' cubic mitochondria. (United States)

    Almsherqi, Zakaria; Margadant, Felix; Deng, Yuru


    Cell membranes may fold up into three-dimensional nanoperiodic cubic structures in biological systems. Similar geometries are well studied in other disciplines such as mathematics, physics and polymer chemistry. The fundamental function of cubic membranes in biological systems has not been uncovered yet; however, their appearance in specialized cell types indicates a role as structural templates or perhaps direct physical entities with specialized biophysical properties. The mitochondria located at the inner segment of the retinal cones of tree shrew (Tupaia glis and Tupaia belangeri) contain unique patterns of concentric cristae with a highly ordered membrane arrangement in three dimensions similar to the photonic nanostructures observed in butterfly wing scales. Using a direct template matching method, we show that the inner mitochondrial membrane folds into multi-layered (8 to 12 layers) gyroid cubic membrane arrangements in the photoreceptor cells. Three-dimensional simulation data demonstrate that such multi-layer gyroid membrane arrangements in the retinal cones of a tree shrew's eye can potentially function as: (i) multi-focal lens; (ii) angle-independent interference filters to block UV light; and (iii) a waveguide photonic crystal. These theoretical results highlight for the first time the significance of multi-layer cubic membrane arrangements to achieve near-quasi-photonic crystal properties through the simple and reversible biological process of continuous membrane folding.

  19. A monotonicity conjecture for real cubic maps

    Energy Technology Data Exchange (ETDEWEB)

    Dawson, S.P. [Los Alamos National Lab., NM (United States); Galeeva, R. [Northwestern Univ., Evanston, IL (United States); Milnor, J. [State Univ. of New York, Stony Brook, NY (United States); Tresser, C. [International Business Machines Corp., Yorktown Heights, NY (United States)


    This will be an outline of work in progress. We study the conjecture that the topological entropy of a real cubic map depends ``monotonely`` on its parameters, in the sense that each locus of constant entropy in parameter space is a connected set. This material will be presented in more detail in a later paper.

  20. Cubical version of combinatorial differential forms

    DEFF Research Database (Denmark)

    Kock, Anders


    The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry....

  1. Modified semi-classical methods for nonlinear quantum oscillations problems

    Energy Technology Data Exchange (ETDEWEB)

    Moncrief, Vincent [Department of Physics and Department of Mathematics, Yale University, P.O. Box 208120, New Haven, Connecticut 06520 (United States); Marini, Antonella [Department of Mathematics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA and Department of Mathematics, University of L' Aquila, Via Vetoio, 67010 L' Aquila, AQ (Italy); Maitra, Rachel [Department of Physics, Albion College, 611 E. Porter Street, Albion, Michigan 49224 (United States)


    We develop a modified semi-classical approach to the approximate solution of Schroedinger's equation for certain nonlinear quantum oscillations problems. In our approach, at lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. With suitable smoothness, convexity and coercivity properties imposed on its potential energy function, we prove, using methods drawn from the calculus of variations together with the (Banach space) implicit function theorem, the existence of a global, smooth 'fundamental solution' to this equation. Higher order quantum corrections thereto, for both ground and excited states, can then be computed through the integration of associated systems of linear transport equations, derived from Schroedinger's equation, and formal expansions for the corresponding energy eigenvalues obtained therefrom by imposing the natural demand for smoothness on the (successively computed) quantum corrections to the eigenfunctions. For the special case of linear oscillators our expansions naturally truncate, reproducing the well-known exact solutions for the energy eigenfunctions and eigenvalues. As an explicit application of our methods to computable nonlinear problems, we calculate a number of terms in the corresponding expansions for the one-dimensional anharmonic oscillators of quartic, sectic, octic, and dectic types and compare the results obtained with those of conventional Rayleigh/Schroedinger perturbation theory. To the orders considered (and, conjecturally, to all orders) our eigenvalue expansions agree with those of Rayleigh/Schroedinger theory whereas our wave functions more accurately capture the more-rapid-than-gaussian decay known to hold for the exact solutions to these problems. For the quartic oscillator in particular our results strongly suggest that both the ground state energy eigenvalue expansion and its associated wave

  2. Effective nonlinearities and multi-wavelength second-harmonic generation in modulated quasi-phase-matching gratings

    DEFF Research Database (Denmark)

    Bang, Ole; Graversen, T. W.; Clausen, Carl A. Balslev


    Quasi-phase-matching gratings induces Kerr effects in quadratic nonlinear materials. We show analytically and confirm numerically how modulating the grating changes the effective quadratic and cubic nonlinearities and allows for multi-wavelength second-harmonic generation.......Quasi-phase-matching gratings induces Kerr effects in quadratic nonlinear materials. We show analytically and confirm numerically how modulating the grating changes the effective quadratic and cubic nonlinearities and allows for multi-wavelength second-harmonic generation....

  3. Linearizability conditions of quasi-cubic systems

    Directory of Open Access Journals (Sweden)

    Wentao Huang


    Full Text Available In this paper we study the linearizability problem of the two-dimensional complex quasi-cubic system $\\dot{z}=z+(zw^{d}(a_{30}z^{3}+a_{21}z^{2}w+a_{12}zw^2+a_{03}w^{3},~\\dot{w}=-w-(zw^{d}(b_{30}w^{3}+b_{21}w^{2}z+b_{12}wz^2+b_{03}z^{3}$, where $z, w, a_{ij}, b_{ij}\\in \\mathbb{C}$ and $d$ is a real number. We find a transformation to change the quasi-cubic system into an equivalent quintic system and then obtain the necessary and sufficient linearizability conditions by the Darboux linearization method or by proving the existence of linearizing transformations.

  4. Analytical solutions of the Schroedinger equation for a two-dimensional exciton in magnetic field of arbitrary strength

    Energy Technology Data Exchange (ETDEWEB)

    Hoang-Do, Ngoc-Tram; Hoang, Van-Hung; Le, Van-Hoang [Department of Physics, Ho Chi Minh City University of Pedagogy, 280 An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)


    The Feranchuk-Komarov operator method is developed by combining with the Levi-Civita transformation in order to construct analytical solutions of the Schroedinger equation for a two-dimensional exciton in a uniform magnetic field of arbitrary strength. As a result, analytical expressions for the energy of the ground and excited states are obtained with a very high precision of up to four decimal places. Especially, the precision is uniformly stable for the whole range of the magnetic field. This advantage appears due to the consideration of the asymptotic behaviour of the wave-functions in strong magnetic field. The results could be used for various physical analyses and the method used here could also be applied to other atomic systems.

  5. Nonlinear q-Generalizations of Quantum Equations: Homogeneous and Nonhomogeneous Cases—An Overview

    Directory of Open Access Journals (Sweden)

    Fernando D. Nobre


    Full Text Available Recent developments on the generalizations of two important equations of quantum physics, namely the Schroedinger and Klein–Gordon equations, are reviewed. These generalizations present nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard linear equations are recovered in the limit q → 1 . Interestingly, these equations present a common, soliton-like, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In both cases, the corresponding well-known Einstein energy-momentum relations, as well as the Planck and the de Broglie ones, are preserved for arbitrary values of q. In order to deal appropriately with the continuity equation, a classical field theory has been developed, where besides the usual Ψ ( x → , t , a new field Φ ( x → , t must be introduced; this latter field becomes Ψ * ( x → , t only when q → 1 . A class of linear nonhomogeneous Schroedinger equations, characterized by position-dependent masses, for which the extra field Φ ( x → , t becomes necessary, is also investigated. In this case, an appropriate transformation connecting Ψ ( x → , t and Φ ( x → , t is proposed, opening the possibility for finding a connection between these fields in the nonlinear cases. The solutions presented herein are potential candidates for applications to nonlinear excitations in plasma physics, nonlinear optics, in structures, such as those of graphene, as well as in shallow and deep water waves.

  6. Neutrosophic Cubic MCGDM Method Based on Similarity Measure

    Directory of Open Access Journals (Sweden)

    Surapati Pramanik


    Full Text Available The notion of neutrosophic cubic set is originated from the hybridization of the concept of neutrosophic set and interval valued neutrosophic set. We define similarity measure for neutrosophic cubic sets and prove some of its basic properties.

  7. Spherical model provides visual aid for cubic crystal study (United States)

    Bacigalupi, R. J.; Spakowski, A. E.


    Transparent sphere of polymethylmethacrylate with major zones and poles of cubic crystals is used to make crystallographic visualizations and to interpret Laue X ray diffraction of single cubic crystals.



    Lambert, F.; Musette, M.


    Soliton instabilities in atomic nonlinear chains with competitive first and second neighbour interactions of cubic type are discussed on the basis of the nonlinear string equation. The puzzling one-way character of the observed resonance processes is explained in terms of the analytic behaviour of two-soliton solutions near resonance. The importance of s.c. "intermediate solitary waves" is underlined.

  9. Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

    DEFF Research Database (Denmark)

    Guo, Hairun; Zeng, Xianglong; Zhou, Binbin


    We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...

  10. The special symplectic structure of binary cubics


    Slupinski, Marcus J.; Stanton, Robert


    Let $k$ be a field of characteristic not $2$ or $3$. Let $V$ be the $k$-space of binary cubic polynomials. The natural symplectic structure on $k^2$ promotes to a symplectic structure $\\omega$ on $V$ and from the natural symplectic action of $\\textrm{Sl}(2,k)$ one obtains the symplectic module $(V,\\omega)$. We give a complete analysis of this symplectic module from the point of view of the associated moment map, its norm square $Q$ (essentially the classical discriminant) and the symplectic g...

  11. Ionization of atoms by strong infrared fields: Solution of the time-dependent Schroedinger equation in momentum space for a model based on separable potentials

    Energy Technology Data Exchange (ETDEWEB)

    Tetchou Nganso, Hugues [Universite Catholique de Louvain (Belgium); University of Douala (Cameroon); Popov, Yuri [Moscow State University (Russian Federation); Piraux, Bernard [Universite Catholique de Louvain (Belgium); Madronero, Javier [Technische Universitaet Muenchen (Germany); Kwato Njock, Moise Godfroy [University of Douala (Cameroon)


    We consider the ionization of atomic hydrogen by a strong infrared field. By starting from the corresponding time-dependent Schroedinger equation in momentum space, we develop a model in which the kernel of the non-local Coulomb potential is replaced by a finite sum of separable potentials. Each separable potential supports one bound state of atomic hydrogen. Here, we consider only the 1s, 2s and 2p states. In this way, the full 3-dimensional Schroedinger equation reduces to a system of a few coupled 1-dimensional linear Volterra integral equations. This model is a theoretical tool to understand the actual role of the atomic potential in the intensity regime where tunnel ionization is supposed to take place and where the experimental data for the first ATI peaks are in contradiction with the theoretical predictions based on the strong field approximation model.

  12. Statistical mechanics of a discrete Schrödinger equation with saturable nonlinearity

    DEFF Research Database (Denmark)

    Samuelsen, Mogens R.; Khare, Avinash; Saxena, Avadh


    We study the statistical mechanics of the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work regarding the statistical mechanics of the one-dimensional DNLS equation with a cubic nonlinearity...

  13. About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

    Energy Technology Data Exchange (ETDEWEB)

    Dubrovsky, V. G.; Topovsky, A. V. [Novosibirsk State Technical University, Karl Marx prosp. 20, Novosibirsk 630092 (Russian Federation)


    New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

  14. Magnetoelastic oscillations in ferromagnets with cubic symmetry (United States)

    Baryakhtar, V. G.; Danilevich, A. G.


    This is a study of the influence of magnetoelastic interactions on the properties of ferromagnets with cubic symmetry. The dispersion relations for coupled magnetoelastic waves are calculated for all the ground states of a ferromagnet with cubic symmetry. It is shown that the magnetoelastic interaction coefficient depends on the directions of the magnetic moment of the ferromagnet and the external magnetic field, as well as on the direction of the wave vector of the collective oscillations. These results are used as the basis for quantitative calculations of the dispersion relations for an NiMnGa alloy with shape memory. The features of the magnetoelastic interaction owing to martensite phase transitions in which one of the elastic moduli becomes anomalously small are discussed. These calculations show that a reduction in the elastic moduli of the crystal causes a substantial increase in the magnetoelastic interaction. It is also shown that the existence of a magnetoelastic interaction leads to a decrease in the experimentally determined elastic moduli.

  15. Bose-Einstein condensation under the cubic-quintic Gross-Pitaevskii equation in radial domains (United States)

    Luckins, Ellen K.; Van Gorder, Robert A.


    We study stationary and quasi-stationary solutions for the cubic-quintic Gross-Pitaevskii equation modeling Bose-Einstein condensates (BECs) in one, two, and three spatial dimensions under the assumption of radial symmetry with the BEC dynamics influenced by a confining potential. We consider both repulsive and attractive cubic interactions - corresponding respectively to repulsive and attractive two-body interactions - under similar frameworks in order to deduce the effects of the potentials in each case. We also carefully consider the role played by the quintic nonlinearity (modeling the strength of inter-atomic coupling) in modifying the solutions arising due to a purely cubic interaction term. In one spatial dimension, we obtain a variety of exact solutions in the zero-potential limit (including new periodic solutions which generalize known soliton solutions) as well as perturbation solutions for small amplitude confining potentials. For more general forms of the confining potential, we rely on numerical simulations, but these agree with the analytical results when the latter are valid. We also consider the limit where the quintic term dominates the cubic term (with such a limit relevant in the study of a Tonks-Girardeau gas). Under the assumption of radial symmetry, we also consider cylindrical (or, cigar-shaped) and spherical BECs. We consider the nonperturbative regime where either the potential or the amplitude of the solutions is large, obtaining various qualitative analytical results. When the kinetic energy term is small (relative to the nonlinearity and the confining potential), we recover the expected Thomas-Fermi approximation for the stationary solutions. Numerical simulations, under a variety of external confining potentials, are then used to understand the role these potentials play on the BEC solution structure for both the attractive and repulsive regimes. This assortment of analytical and numerical results allows us to better understand the

  16. Collapse arrest and soliton stabilization in nonlocal nonlinear media

    DEFF Research Database (Denmark)

    Bang, Ole; Krolikowski, Wieslaw; Wyller, John


    We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian...... that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric and have a positive definite Fourier spectrum, but can otherwise be of completely arbitrary shape and degree of nonlocality...

  17. Nonlinear optics

    CERN Document Server

    Bloembergen, Nicolaas


    Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe

  18. Cathodoluminescence of cubic GaN epilayers

    Energy Technology Data Exchange (ETDEWEB)

    Wang, C.; As, D.J.; Schikora, D.; Schoettker, B.; Lischka, K. [Paderborn Univ. (Gesamthochschule) (Germany). Fachbereich 6 - Physik


    Cathodoluminescence (CL) of MBE grown cubic GaN epilayers has been studied as a function of the e-beam excitation intensity. The room temperature CL-spectrum is dominated by a near edge band with a FWHM as narrow as 55 meV at high excitation. It consists of an excitonic and a band-acceptor transition. A broad emission band peaked at 2.4 eV is observed at low excitation. Using a simple model based on bimolecular rate equations the concentration of defects involved in this transition is estimated to be about 10{sup 15} cm{sup -3}. CL-measurements with varying excitation intensity reveal that these recombination levels have only minor influence on the performance of high injection optoelectronic devices like laser diodes. Our CL-measurements show also that the deep centres are homogeneously distributed within the epilayer. (orig.) 11 refs.

  19. Triangulation of cubic panorama for view synthesis. (United States)

    Zhang, Chunxiao; Zhao, Yan; Wu, Falin


    An unstructured triangulation approach, new to our knowledge, is proposed to apply triangular meshes for representing and rendering a scene on a cubic panorama (CP). It sophisticatedly converts a complicated three-dimensional triangulation into a simple three-step triangulation. First, a two-dimensional Delaunay triangulation is individually carried out on each face. Second, an improved polygonal triangulation is implemented in the intermediate regions of each of two faces. Third, a cobweblike triangulation is designed for the remaining intermediate regions after unfolding four faces to the top/bottom face. Since the last two steps well solve the boundary problem arising from cube edges, the triangulation with irregular-distribution feature points is implemented in a CP as a whole. The triangular meshes can be warped from multiple reference CPs onto an arbitrary viewpoint by face-to-face homography transformations. The experiments indicate that the proposed triangulation approach provides a good modeling for the scene with photorealistic rendered CPs.

  20. Robustness of Multiple High Speed TCP CUBIC Connections Under Severe Operating Conditions

    DEFF Research Database (Denmark)

    Pilimon, Artur; Ruepp, Sarah Renée; Berger, Michael Stübert


    on and supported by packet-level simulations. The results show that the aggressive nature of CUBIC’s nonlinear congestion window control principle causes a degradation of the time-average throughput at the moderate level of random packet loss even under increasing Round-Trip-Time of the flow. However......We study the adaptation capabilities and robustness of the high-speed TCP CUBIC algorithm. For this purpose we consider a network environment with variable and high random packet loss and a large Bandwidth-Delay product, shared by multiple heterogeneous TCP connections. The analysis is based...

  1. Fusion arrest and collapse phenomena due to Kerr-nonlinearity in quadratic media

    DEFF Research Database (Denmark)

    Johansen, Steffen Kjær; Bang, Ole; Sørensen, Mads Peter


    Emphasizing collapse phenomena it is investigated to what extend the always present cubic nonlinearity affects the properties of soliton interaction in quadratic bulk media. An effective particle approach is applied and verified by numerical simulations....

  2. Multi-shocks generation and collapsing instabilities induced by competing nonlinearities

    KAUST Repository

    Crosta, Matteo


    We investigate dispersive shock dynamics in materials with competing cubic-quintic nonlinearities. Whitham theory of modulation, hydrodynamic analysis and numerics demonstrate a rich physical scenario, ranging from multi-shock generation to collapse.

  3. Shape preserving rational cubic spline for positive and convex data

    Directory of Open Access Journals (Sweden)

    Malik Zawwar Hussain


    Full Text Available In this paper, the problem of shape preserving C2 rational cubic spline has been proposed. The shapes of the positive and convex data are under discussion of the proposed spline solutions. A C2 rational cubic function with two families of free parameters has been introduced to attain the C2 positive curves from positive data and C2 convex curves from convex data. Simple data dependent constraints are derived on free parameters in the description of rational cubic function to obtain the desired shape of the data. The rational cubic schemes have unique representations.

  4. Solving Buckmaster equation using cubic B-spline and cubic trigonometric B-spline collocation methods (United States)

    Chanthrasuwan, Maveeka; Asri, Nur Asreenawaty Mohd; Hamid, Nur Nadiah Abd; Majid, Ahmad Abd.; Azmi, Amirah


    The cubic B-spline and cubic trigonometric B-spline functions are used to set up the collocation in finding solutions for the Buckmaster equation. These splines are applied as interpolating functions in the spatial dimension while the finite difference method (FDM) is used to discretize the time derivative. The Buckmaster equation is linearized using Taylor's expansion and solved using two schemes, namely Crank-Nicolson and fully implicit. The von Neumann stability analysis is carried out on the two schemes and they are shown to be conditionally stable. In order to demonstrate the capability of the schemes, some problems are solved and compared with analytical and FDM solutions. The proposed methods are found to generate more accurate results than the FDM.

  5. Nonlinear analysis

    CERN Document Server

    Nanda, Sudarsan


    "Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.

  6. Nonlinear Science

    CERN Document Server

    Yoshida, Zensho


    This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl

  7. Design of a nonlinear torsional vibration absorber (United States)

    Tahir, Ammaar Bin

    Tuned mass dampers (TMD) utilizing linear spring mechanisms to mitigate destructive vibrations are commonly used in practice. A TMD is usually tuned for a specific resonant frequency or an operating frequency of a system. Recently, nonlinear vibration absorbers attracted attention of researchers due to some potential advantages they possess over the TMDs. The nonlinear vibration absorber, or the nonlinear energy sink (NES), has an advantage of being effective over a broad range of excitation frequencies, which makes it more suitable for systems with several resonant frequencies, or for a system with varying excitation frequency. Vibration dissipation mechanism in an NES is passive and ensures that there is no energy backflow to the primary system. In this study, an experimental setup of a rotational system has been designed for validation of the concept of nonlinear torsional vibration absorber with geometrically induced cubic stiffness nonlinearity. Dimensions of the primary system have been optimized so as to get the first natural frequency of the system to be fairly low. This was done in order to excite the dynamic system for torsional vibration response by the available motor. Experiments have been performed to obtain the modal parameters of the system. Based on the obtained modal parameters, the design optimization of the nonlinear torsional vibration absorber was carried out using an equivalent 2-DOF modal model. The optimality criterion was chosen to be maximization of energy dissipation in the nonlinear absorber attached to the equivalent 2-DOF system. The optimized design parameters of the nonlinear absorber were tested on the original 5-DOF system numerically. A comparison was made between the performance of linear and nonlinear absorbers using the numerical models. The comparison showed the superiority of the nonlinear absorber over its linear counterpart for the given set of primary system parameters as the vibration energy dissipation in the former is

  8. Topological Oxide Insulator in Cubic Perovskite Structure (United States)

    Jin, Hosub; Rhim, Sonny H.; Im, Jino; Freeman, Arthur J.


    The emergence of topologically protected conducting states with the chiral spin texture is the most prominent feature at the surface of topological insulators. On the application side, large band gap and high resistivity to distinguish surface from bulk degrees of freedom should be guaranteed for the full usage of the surface states. Here, we suggest that the oxide cubic perovskite YBiO3, more than just an oxide, defines itself as a new three-dimensional topological insulator exhibiting both a large bulk band gap and a high resistivity. Based on first-principles calculations varying the spin-orbit coupling strength, the non-trivial band topology of YBiO3 is investigated, where the spin-orbit coupling of the Bi 6p orbital plays a crucial role. Taking the exquisite synthesis techniques in oxide electronics into account, YBiO3 can also be used to provide various interface configurations hosting exotic topological phenomena combined with other quantum phases. PMID:23575973

  9. The square of a planar cubic graph is 7-colorable

    DEFF Research Database (Denmark)

    Thomassen, Carsten


    We prove the conjecture made by G. Wegner in 1977 that the square of every planar, cubic graph is 7-colorable. Here, 7 cannot be replaced by 6.......We prove the conjecture made by G. Wegner in 1977 that the square of every planar, cubic graph is 7-colorable. Here, 7 cannot be replaced by 6....

  10. Nonlinear systems

    CERN Document Server

    Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús


    This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many  new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...

  11. The anisotropic Kerr nonlinear refractive index of the beta-barium borate (β-BaB2O4) nonlinear crystal

    DEFF Research Database (Denmark)

    Bache, Morten; Guo, Hairun; Zhou, Binbin


    We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (β-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant χ(3) cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments in the literat...

  12. Experimental Identification of Concentrated Nonlinearity in Aeroelastic System

    Directory of Open Access Journals (Sweden)

    Nayfeh Ali H


    Full Text Available Identification of concentrated nonlinearity in the torsional spring of an aeroelastic system is performed. This system consists of a rigid airfoil that is supported by a linear spring in the plunge motion and a nonlinear spring in the pitch motion. Quadratic and cubic nonlinearities in the pitch moment are introduced to model the concentrated nonlinearity. The representation of the aerodynamic loads by the Duhamel formulation yielded accurate values for the flutter speed and frequency. The results show that the use of the Duhamel formulation to represent the aerodynamic loads yields excellent agreement between the experimental data and the numerical predictions.

  13. Polyimide nanocomposites based on cubic zirconium tungstate (United States)

    Ramasubramanian Sharma, Gayathri


    In this research, cubic zirconium tungstate (ZrW2O8) was used as a filler to reduce the CTE of polyimides (PI), and the effect of ZrW2O8 nanoparticles on the bulk polymer properties was studied. Polyimides are high performance polymers with exceptional thermal stability, and there is a need for PIs with low CTEs for high temperature applications. The nanofiller, cubic ZrW2O8, is well known for its isotropic negative thermal expansion (NTE) over a wide temperature range from -272.7 to 777°C. The preparation of nanocomposites involved the synthesis of ZrW 2O8 nanofiller, engineering the polymer-filler interface using linker groups and optimization of processing strategies to prepare free-standing PI nanocomposite films. A hydrothermal method was used to synthesize ZrW 2O8 nanoparticles. Polyimide-ZrW2O8 interface interaction was enhanced by covalently bonding linker moieties to the surface of ZrW2O8 nanoparticles. Specifically, ZrW 2O8 nanoparticles were functionalized with two different linker groups: (1) a short aliphatic silane, and (2) low molecular weight PI. The surface functionalization was confirmed using X-ray photoelectron spectroscopy and thermal gravimetric analysis (TGA). Reprecipitation blending was used to prepare the freestanding PI-ZrW2O8 nanocomposite films with up to 15 volume% filler loading. SEM images showed the improvements in polymer-filler wetting behavior achieved using interface engineering. SEM images indicated that there was better filler dispersion in the PI matrix using reprecipitation blending, compared to the filler dispersion achieved in the nanocomposites prepared using conventional blending technique. The structure-property relationships in PI-ZrW2O8 nanocomposites were investigated by studying the thermal degradation, glass transition, tensile and thermal expansion properties of the nanocomposites. The properties were studied as a function of filler loading and interface linker groups. Addition of ZrW2O8 nanoparticles did not

  14. Generalized nonlinear Proca equation and its free-particle solutions

    Energy Technology Data Exchange (ETDEWEB)

    Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)


    We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)

  15. The compressibility of cubic white and orthorhombic, rhombohedral, and simple cubic black phosphorus

    Energy Technology Data Exchange (ETDEWEB)

    Clark, Simon M; Zaug, Joseph


    The effect of pressure on the crystal structure of white phosphorus has been studied up to 22.4 GPa. The ?alpha phase was found to transform into the alpha' phase at 0.87 +- 0.04 GPa with a volume change of 0.1 +- 0.3 cc/mol. A fit of a second order Birch- Murnaghan equation to the data gave Vo = 16.94 ? 0.08 cc/mol and Ko = 6.7 +- 0.5 GPa for the alpha phase and Vo = 16.4 +- 0.1 cc/mol and Ko = 9.1 +- 0.3 GPa for the alpha' phase. The alpha' phase was found to transform to the A17 phase of black phosphorus at 2.68 +- 0.34 GPa and then with increasing pressure to the A7 and then simple cubic phase of black phosphorus. A fit of a second order Birch-Murnaghan equation to our data combined with previous measurements gave Vo = 11.43 +- 0.05 cc/mol and Ko = 34.7 +- 0.5 GPa for the A17 phase, Vo = 9.62 +- 0.01 cc/mol and Ko = 65.0 +- 0.6 GPa for the A7 phase and , Vo = 9.23 +- 0.01 cc/mol and Ko = 72.5 +- 0.3 GPa for the simple cubic phase.

  16. Nonlinear optics

    CERN Document Server

    Boyd, Robert W


    Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q

  17. Hardness and thermal stability of cubic silicon nitride

    DEFF Research Database (Denmark)

    Jiang, Jianzhong; Kragh, Flemming; Frost, D. J.


    The hardness and thermal stability of cubic spinel silicon nitride (c-Si3N4), synthesized under high-pressure and high-temperature conditions, have been studied by microindentation measurements, and x-ray powder diffraction and scanning electron microscopy, respectively The phase at ambient...... temperature has an average hardness of 35.31 GPa, slightly larger than SiO2 stishovite, which is often referred to as the third hardest material after diamond and cubic boron nitride. The cubic phase is stable up to 1673 K in air. At 1873 K, alpha -and beta -Si3N4 phases are observed, indicating a phase...

  18. On q-power cycles in cubic graphs

    DEFF Research Database (Denmark)

    Bensmail, Julien


    In the context of a conjecture of Erdos and Gyárfás, we consider, for any q ≥ 2, the existence of q-power cycles (i.e. with length a power of q) in cubic graphs. We exhibit constructions showing that, for every q ≥ 3, there exist arbitrarily large cubic graphs with no q-power cycles. Concerning...... the remaining case q = 2 (which corresponds to the conjecture of Erdos and Gyárfás), we show that there exist arbitrarily large cubic graphs whose only 2-power cycles have length 4 only, or 8 only....

  19. On q-Power Cycles in Cubic Graphs


    Bensmail Julien


    International audience; In the context of a conjecture of Erdős and Gyárfás, we consider, for any $q ≥ 2$, the existence of q-power cycles (i.e. with length a power of q) in cubic graphs. We exhibit constructions showing that, for every $q ≥ 3$, there exist arbitrarily large cubic graphs with no q-power cycles. Concerning the remaining case $q = 2$ (which corresponds to the conjecture of Erdős and Gyárfás), we show that there exist arbitrarily large cubic graphs whose only 2-power cycles have...

  20. Nonlinear Waves in the Terrestrial Quasiparallel Foreshock (United States)

    Hnat, B.; Kolotkov, D. Y.; O'Connell, D.; Nakariakov, V. M.; Rowlands, G.


    We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.

  1. Nonlinear reconstruction (United States)

    Zhu, Hong-Ming; Yu, Yu; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran


    We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to the nonlinear scale (rδrδL>0.5 for k ≲1 h /Mpc ) with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully nonlinear fields, potentially substantially expanding the baryon acoustic oscillations and redshift space distortions information content of dense large scale structure surveys, including for example SDSS main sample and 21 cm intensity mapping initiatives.

  2. Stationary nonlinear Schrödinger equation on simplest graphs (United States)

    Sabirov, K. K.; Sobirov, Z. A.; Babajanov, D.; Matrasulov, D. U.


    We treat the stationary (cubic) nonlinear Schrödinger equation (NLSE) on simplest graphs. The solutions are obtained for primary star graph with the boundary conditions providing vertex matching and flux conservation. Both, repulsive and attractive nonlinearities are considered. It is shown that the method can be extended to the case of arbitrary number of bonds in star graphs and for other simplest topologies.

  3. Practical Nonlinearities (United States)


    architectures , practical nonlinearities, nonlinear dynamics 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT: SAR 8. NUMBER OF PAGES...performers from Mesodynamic Architectures (MESO) and uPNT all to include devices in these runs. This cost-sharing was planned, and is necessary for...contributions to the performance of MEMS gyroscopes. In particular, we have demonstrated for the first time that Parametric Amplification can improve the

  4. Numerically exact dynamics of the interacting many-body Schroedinger equation for Bose-Einstein condensates. Comparison to Bose-Hubbard and Gross-Pitaevskii theory

    Energy Technology Data Exchange (ETDEWEB)

    Sakmann, Kaspar


    In this thesis, the physics of trapped, interacting Bose-Einstein condensates is analyzed by solving the many-body Schroedinger equation. Particular emphasis is put on coherence, fragmentation and reduced density matrices. First, the ground state of a trapped Bose-Einstein condensate and its correlation functions are obtained. Then the dynamics of a bosonic Josephson junction is investigated by solving the time-dependent many-body Schroedinger equation numerically exactly. These are the first exact results in literature in this context. It is shown that the standard approximations of the field, Gross-Pitaevskii theory and the Bose-Hubbard model fail at weak interaction strength and within their range of expected validity. For stronger interactions the dynamics becomes strongly correlated and a new equilibration phenomenon is discovered. By comparison with exact results it is shown that a symmetry of the Bose- Hubbard model between attractive and repulsive interactions must be considered an artefact of the model. A conceptual innovation of this thesis are time-dependent Wannier functions. Equations of motion for time-dependent Wannier functions are derived from the variational principle. By comparison with exact results it is shown that lattice models can be greatly improved at little computational cost by letting the Wannier functions of a lattice model become time-dependent. (orig.)

  5. The Schroedinger-Poisson equations as the large-N limit of the Newtonian N-body system. Applications to the large scale dark matter dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Briscese, Fabio [Northumbria University, Department of Mathematics, Physics and Electrical Engineering, Newcastle upon Tyne (United Kingdom); Citta Universitaria, Istituto Nazionale di Alta Matematica Francesco Severi, Gruppo Nazionale di Fisica Matematica, Rome (Italy)


    In this paper it is argued how the dynamics of the classical Newtonian N-body system can be described in terms of the Schroedinger-Poisson equations in the large N limit. This result is based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. According to the Calogero conjecture, the emerging effective Planck constant is computed in terms of the parameters of the N-body system as ℎ ∝ M{sup 5/3}G{sup 1/2}(N/ left angle ρ right angle){sup 1/6}, where is G the gravitational constant, N and M are the number and the mass of the bodies, and left angle ρ right angle is their average density. The relevance of this result in the context of large scale structure formation is discussed. In particular, this finding gives a further argument in support of the validity of the Schroedinger method as numerical double of the N-body simulations of dark matter dynamics at large cosmological scales. (orig.)

  6. Symbolic derivation of high-order Rayleigh-Schroedinger perturbation energies using computer algebra: Application to vibrational-rotational analysis of diatomic molecules

    Energy Technology Data Exchange (ETDEWEB)

    Herbert, John M. [Kansas State Univ., Manhattan, KS (United States). Dept. of Chemistry


    Rayleigh-Schroedinger perturbation theory is an effective and popular tool for describing low-lying vibrational and rotational states of molecules. This method, in conjunction with ab initio techniques for computation of electronic potential energy surfaces, can be used to calculate first-principles molecular vibrational-rotational energies to successive orders of approximation. Because of mathematical complexities, however, such perturbation calculations are rarely extended beyond the second order of approximation, although recent work by Herbert has provided a formula for the nth-order energy correction. This report extends that work and furnishes the remaining theoretical details (including a general formula for the Rayleigh-Schroedinger expansion coefficients) necessary for calculation of energy corrections to arbitrary order. The commercial computer algebra software Mathematica is employed to perform the prohibitively tedious symbolic manipulations necessary for derivation of generalized energy formulae in terms of universal constants, molecular constants, and quantum numbers. As a pedagogical example, a Hamiltonian operator tailored specifically to diatomic molecules is derived, and the perturbation formulae obtained from this Hamiltonian are evaluated for a number of such molecules. This work provides a foundation for future analyses of polyatomic molecules, since it demonstrates that arbitrary-order perturbation theory can successfully be applied with the aid of commercially available computer algebra software.

  7. Monotonicity preserving splines using rational cubic Timmer interpolation (United States)

    Zakaria, Wan Zafira Ezza Wan; Alimin, Nur Safiyah; Ali, Jamaludin Md


    In scientific application and Computer Aided Design (CAD), users usually need to generate a spline passing through a given set of data, which preserves certain shape properties of the data such as positivity, monotonicity or convexity. The required curve has to be a smooth shape-preserving interpolant. In this paper a rational cubic spline in Timmer representation is developed to generate interpolant that preserves monotonicity with visually pleasing curve. To control the shape of the interpolant three parameters are introduced. The shape parameters in the description of the rational cubic interpolant are subjected to monotonicity constrained. The necessary and sufficient conditions of the rational cubic interpolant are derived and visually the proposed rational cubic Timmer interpolant gives very pleasing results.

  8. Bicontinuous cubic liquid crystalline nanoparticles for oral delivery of Doxorubicin

    DEFF Research Database (Denmark)

    Swarnakar, Nitin K; Thanki, Kaushik; Jain, Sanyog


    PURPOSE: The present study explores the potential of bicontinous cubic liquid crystalline nanoparticles (LCNPs) for improving therapeutic potential of doxorubicin. METHODS: Phytantriol based Dox-LCNPs were prepared using hydrotrope method, optimized for various formulation components, process var...

  9. The First Derivative of Ramanujans Cubic Continued Fraction


    Bagis, Nikos


    We give the complete evaluation of the first derivative of the Ramanujans cubic continued fraction using Elliptic functions. The Elliptic functions are easy to handle and give the results in terms of Gamma functions and radicals from tables.

  10. On the exact solutions of nonlinear diffusion-reaction equations with ...

    Indian Academy of Sciences (India)

    Attempts have been made to look for the soliton content in the solutions of the recently studied nonlinear diffusion-reaction equations [R S Kaushal, J. Phys. 38, 3897 (2005)] involving quadratic or cubic nonlinearities in addition to the convective flux term which renders the system nonconservative and the corresponding ...

  11. Elastic properties of cubic crystals: Every's versus Blackman's diagram


    Paszkiewicz, T.; Wolski, S.


    Blackman's diagram of two dimensionless ratios of elastic constants is frequently used to correlate elastic properties of cubic crystals with interatomic bondings. Every's diagram of a different set of two dimensionless variables was used by us for classification of various properties of such crystals. We compare these two ways of characterization of elastic properties of cubic materials and consider the description of various groups of materials, e.g. simple metals, oxides, and alkali halide...

  12. On the Rank of Elliptic Curves in Elementary Cubic Extensions

    Directory of Open Access Journals (Sweden)

    Rintaro Kozuma


    Full Text Available We give a method for explicitly constructing an elementary cubic extension L over which an elliptic curve ED:y2+Dy=x3  (D∈Q∗ has Mordell-Weil rank of at least a given positive integer by finding a close connection between a 3-isogeny of ED and a generic polynomial for cyclic cubic extensions. In our method, the extension degree [L:Q] often becomes small.

  13. Recurrence phase shift in Fermi-Pasta-Ulam nonlinear dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Devine, N., E-mail: [Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia); Ankiewicz, A. [Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia); Genty, G. [Tampere University of Technology, Optics Laboratory, FI-33101 Tampere (Finland); Dudley, J.M. [Institut FEMTO-ST UMR 6174 CNRS/Universite de Franche-Comte, Besancon (France); Akhmediev, N. [Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200 (Australia)


    We show that the dynamics of Fermi-Pasta-Ulam recurrence is associated with a nonlinear phase shift between initial and final states that are otherwise identical, after a full growth-return cycle. The properties of this phase shift are studied for the particular case of the self-focussing nonlinear Schroedinger equation, and we describe the magnitude of the phase shift in terms of the system parameters. This phase shift, accumulated during the nonlinear recurrence cycle, is a previously-unremarked feature of the Fermi-Pasta-Ulam problem, and we anticipate its wide significance as an essential feature of related dynamics in other systems. -- Highlights: → The dynamics of FPU recurrence is associated with a phase shift between initial and final states. → The properties of this phase shift are studied for the self-focussing NLS equation. → This phase shift is a previously-unremarked feature of the FPU growth-return cycle. → We anticipate its wide significance as an essential feature of related dynamics in other systems.

  14. Spline solutions for nonlinear two point boundary value problems

    Directory of Open Access Journals (Sweden)

    Riaz A. Usmani


    Full Text Available Necessary formulas are developed for obtaining cubic, quartic, quintic, and sextic spline solutions of nonlinear boundary value problems. These methods enable us to approximate the solution of the boundary value problems, as well as their successive derivatives smoothly. Numerical evidence is included to demonstrate the relative performance of these four techniques.

  15. Energy harvesting of nonlinear damping system under time delayed feedback gain

    Directory of Open Access Journals (Sweden)

    Bichri A.


    Full Text Available This paper presents the application of delayed feedback velocity for optimizing the harvested power in cubic nonlinear damper system. We consider a harvester consisting of a nonlinear single degree of freedom system (spring-masse-damper subjected to a base excitation near the primary resonance. Analytical investigation using the multiple scales method is performed to obtain approximation of the amplitude response. This amplitude can be used to extract the average power. Results show that for appropriate values of the feedback gain, energy harvesting is more efficient at resonance compared to the cubic nonlinear damper system without time delay.

  16. Numerical simulation of two dimensional sine-Gordon solitons using modified cubic B-spline differential quadrature method

    Directory of Open Access Journals (Sweden)

    H. S. Shukla


    Full Text Available In this paper, a modified cubic B-spline differential quadrature method (MCB-DQM is employed for the numerical simulation of two-space dimensional nonlinear sine-Gordon equation with appropriate initial and boundary conditions. The modified cubic B-spline works as a basis function in the differential quadrature method to compute the weighting coefficients. Accordingly, two dimensional sine-Gordon equation is transformed into a system of second order ordinary differential equations (ODEs. The resultant system of ODEs is solved by employing an optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme (SSP-RK54. Numerical simulation is discussed for both damped and undamped cases. Computational results are found to be in good agreement with the exact solution and other numerical results available in the literature.

  17. Non-linear Schrödinger Dynamics of Matrix D-branes

    CERN Document Server

    Mavromatos, Nikolaos E; Mavromatos, Nick E.; Szabo, Richard J.


    We formulate an effective Schroedinger wave equation describing the quantum dynamics of a system of D0-branes by applying the Wilson renormalization group equation to the worldsheet partition function of a deformed sigma-model describing the system, which includes the quantum recoil due to the exchange of string states between the individual D-particles. We arrive at an effective Fokker-Planck equation for the probability density with diffusion coefficient determined by the total kinetic energy of the recoiling system. We use Galilean invariance of the system to show that there are three possible solutions of the associated non-linear Schroedinger equation depending on the strength of the open string interactions among the D-particles. When the open string energies are small compared to the total kinetic energy of the system, the solutions are governed by freely-propagating solitary waves. When the string coupling constant reaches a dynamically determined critical value, the system is described by minimal unc...

  18. Stabilities of Cubic Mappings in Various Normed Spaces: Direct and Fixed Point Methods

    Directory of Open Access Journals (Sweden)

    H. Azadi Kenary


    Full Text Available In 1940 and 1964, Ulam proposed the general problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”. In 1941, Hyers solved this stability problem for linear mappings. According to Gruber (1978 this kind of stability problems are of the particular interest in probability theory and in the case of functional equations of different types. In 1981, Skof was the first author to solve the Ulam problem for quadratic mappings. In 1982–2011, J. M. Rassias solved the above Ulam problem for linear and nonlinear mappings and established analogous stability problems even on restricted domains. The purpose of this paper is the generalized Hyers-Ulam stability for the following cubic functional equation: (++(−=(++(−+2(3−(,≥2 in various normed spaces.

  19. Local optimality of cubic lattices for interaction energies (United States)

    Bétermin, Laurent


    We study the local optimality of simple cubic, body-centred-cubic and face-centred-cubic lattices among Bravais lattices of fixed density for some finite energy per point. Following the work of Ennola (Math Proc Camb 60:855-875, 1964), we prove that these lattices are critical points of all the energies, we write the second derivatives in a simple way and we investigate the local optimality of these lattices for the theta function and the Lennard-Jones-type energies. In particular, we prove the local minimality of the FCC lattice (resp. BCC lattice) for large enough (resp. small enough) values of its scaling parameter and we also prove the fact that the simple cubic lattice is a saddle point of the energy. Furthermore, we prove the local minimality of the FCC and the BCC lattices at high density (with an optimal explicit bound) and its local maximality at low density in the Lennard-Jones-type potential case. We then show the local minimality of FCC and BCC lattices among all the Bravais lattices (without a density constraint). The largest possible open interval of density's values where the simple cubic lattice is a local minimizer is also computed.

  20. N-soliton interactions: Effects of linear and nonlinear gain and loss (United States)

    Carretero-González, R.; Gerdjikov, V. S.; Todorov, M. D.


    We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the nonlinear Schrödinger equation perturbed simultaneously by linear and nonlinear gain/loss terms. We derive the corresponding perturbed complex Toda chain in the case of a combination of linear, cubic, and/or quintic terms. We show that the soliton interactions dynamics for this reduced PCTC model compares favorably to full numerical results of the original perturbed nonlinear Schrödinger equation.

  1. Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities

    DEFF Research Database (Denmark)

    Bergé, L.; Bang, O.; Juul Rasmussen, J.


    , mutually trapped waves can self-focus until collapse whenever their respective powers exceed some thresholds. On the contrary, coupled waves diffracting in a one-dimensional plane never collapse and may evolve towards stable solitonlike structures. For higher transverse dimension numbers, we investigate...

  2. Numerical study of solitary wave stability in cubic nonlinear Dirac equations in 1D (United States)

    Lakoba, T. I.


    Recently there has occurred a controversy between the semi-analytical prediction of linear stability of the soliton of the massive Gross-Neveu model and direct numerical observations of its instability for small values of the frequency. We revisit the problem of numerical computation of this soliton, find a mechanism behind the numerical instability observed in earlier studies, and propose methods to stably compute the soliton over long times. Thus, we confirm the semi-analytical prediction of the soliton's being linearly stable.

  3. Engineering of effective quadratic and cubic nonlinearities in two-period QPM gratings

    DEFF Research Database (Denmark)

    Bang, Ole; Clausen, Carl A. Balslev; Torner, L.


    Summary form only given. Quasi-phase-matching (QPM) by electric-field poling in ferro-electric materials, such as LiNbO3 , is promising due to the possibilities of engineering the photolithographic mask, and thus the QPM grating, without also generating a linear grating. A proper design of the lo......Summary form only given. Quasi-phase-matching (QPM) by electric-field poling in ferro-electric materials, such as LiNbO3 , is promising due to the possibilities of engineering the photolithographic mask, and thus the QPM grating, without also generating a linear grating. A proper design...... of the longitudinal grating structure allows for distortion free temporal pulse compression, soliton shaping, broad-band phase matching, multiwavelength second-harmonic generation (SHG), and an enhanced cascaded phase shift. Transverse patterning can be used for beam-tailoring, broad-band SHG and soliton steering....

  4. Soliton interaction in quadratic and cubic bulk media

    DEFF Research Database (Denmark)

    Johansen, Steffen Kjær; Bang, Ole


    in lossless bulk second order nonlinear optical materials with a nonvanishing third order nonlinearity. It is known that in pure second order systems a single soliton can never collapse whereas in systems with both nonlinearities and that stable single soliton propagation can only in some circumstances...

  5. Comparison of electron bands of hexagonal and cubic diamond (United States)

    Salehpour, M. R.; Satpathy, S.


    Using the local-density-theory and the linear-muffin-tin-orbitals method, we calculate the electron band structures of hexagonal (lonsdaleite) and cubic diamond. Even though the arrangement of atoms is very similar between the two crystal structures, we find significant differences in the electron bands, especially in the conduction bands. In particular, including estimated corrections on top of the local-density results, we find the lowest theoretical gap of hexagonal diamond to be 4.5 eV, i.e., a remarkable 1.1-eV drop as compared to that of cubic diamond. The lowest gap in the hexagonal structure is still indirect as in the cubic structure, but the gap is now from Γ to K. The reduction of the band gap should be observable in optical-absorption or reflectivity experiments.

  6. Mechanisms of optical gain in cubic gallium nitrite (United States)

    Holst, J.; Eckey, L.; Hoffmann, A.; Broser, I.; Schöttker, B.; As, D. J.; Schikora, D.; Lischka, K.


    We report on the mechanisms of optical gain in cubic GaN. Intensity-dependent gain spectra allow a distinction of the processes involved in providing optical amplification. For moderate excitation levels, the biexciton decay is responsible for a gain structure at 3.265 eV. With increasing excitation densities, gain is observed on the high energy side of the cubic band gap due to band filling processes. For the highest pump intensities, the electron-hole plasma is the dominant gain process. Gain values up to 210 cm-1 were obtained, indicating the high potential of cubic GaN for device applications. The observed gain mechanisms are similar to those of hexagonal GaN.

  7. Deformation of the cubic open string field theory

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Taejin, E-mail:


    We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.

  8. Deformation of the cubic open string field theory

    Directory of Open Access Journals (Sweden)

    Taejin Lee


    Full Text Available We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.

  9. Tetragonal and cubic zirconia multilayered ceramic constructs created by EPD. (United States)

    Mochales, Carolina; Frank, Stefan; Zehbe, Rolf; Traykova, Tania; Fleckenstein, Christine; Maerten, Anke; Fleck, Claudia; Mueller, Wolf-Dieter


    The interest in electrophoretic deposition (EPD) for nanomaterials and ceramics production has widely increased due to the versatility of this technique to effectively combine different materials in unique shapes and structures. We successfully established an EPD layering process with submicrometer sized powders of Y-TZP with different mol percentages of yttrium oxide (3 and 8%) and produced multilayers of alternating tetragonal and cubic phases with a clearly defined interface. The rationale behind the design of these multilayer constructs was to optimize the properties of the final ceramic by combining the high mechanical toughness of the tetragonal phase of zirconia together with the high ionic conductivity of its cubic phase. In this work, a preliminary study of the mechanical properties of these constructs proved the good mechanical integrity of the multilayered constructs obtained as well as crack deflection in the interface between tetragonal and cubic zirconia layers.

  10. On Compatible Normal Odd Partitions in Cubic Graphs

    CERN Document Server

    Fouquet, Jean-Luc


    A normal odd partition T of the edges of a cubic graph is a partition into trails of odd length (no repeated edge) such that each vertex is the end vertex of exactly one trail of the partition and internal in some trail. For each vertex v, we can distinguish the edge for which this vertex is pending. Three normal odd partitions are compatible whenever these distinguished edges are distinct for each vertex. We examine this notion and show that a cubic 3 edge-colorable graph can always be provided with three compatible normal odd partitions. The Petersen graph has this property and we can construct other cubic graphs with chromatic index four with the same property. Finally, we propose a new conjecture which, if true, would imply the well known Fan and Raspaud Conjecture

  11. Simple nonlinear interferometer-based all-optical thresholder and its applications for optical CDMA. (United States)

    Kravtsov, Konstantin; Prucnal, Paul R; Bubnov, Mikhail M


    We present an experimental demonstration of an ultrafast all-optical thresholder based on a nonlinear Sagnac interferometer. The proposed design is intended for operation at very small nonlinear phase shifts. Therefore, it requires an in-loop nonlinearity lower than for the classical nonlinear loop mirror scheme. Only 15 meters of conventional (non-holey) silica-based fiber is used as a nonlinear element. The proposed thresholder is polarization insensitive and is good for multi-wavelength operation, meeting all the requirements for autocorrelation detection in various optical CDMA communication systems. The observed cubic transfer function is superior to the quadratic transfer function of second harmonic generation-based thresholders.

  12. 3D confocal imaging in CUBIC-cleared mouse heart

    Energy Technology Data Exchange (ETDEWEB)

    Nehrhoff, I.; Bocancea, D.; Vaquero, J.; Vaquero, J.J.; Lorrio, M.T.; Ripoll, J.; Desco, M.; Gomez-Gaviro, M.V.


    Acquiring high resolution 3D images of the heart enables the ability to study heart diseases more in detail. Here, the CUBIC (clear, unobstructed brain imaging cocktails and computational analysis) clearing protocol was adapted for thick mouse heart sections to increase the penetration depth of the confocal microscope lasers into the tissue. The adapted CUBIC clearing of the heart lets the antibody penetrate deeper into the tissue by a factor of five. The here shown protocol enables deep 3D highresolution image acquisition in the heart. This allows a much more accurate assessment of the cellular and structural changes that underlie heart diseases. (Author)

  13. Trace spaces in a pre-cubical complex

    DEFF Research Database (Denmark)

    Raussen, Martin

    arc length which moreover is shown to be invariant under directed homotopies. D-paths up to reparametrization (called traces) can thus be represented by arc length parametrized d-paths. Under weak additional conditions,it is shown that trace spaces in a pre-cubical complex are separable metric spaces......In directed algebraic topology, (spaces of) directed irreversible (d)-paths are studied from a topological and from a categorical point of view. Motivated by models for concurrent computation, we study in this paper spaces of d-paths in a pre-cubical complex. Such paths are equipped with a natural...

  14. Trapping of cubic ZnO nanocrystallites at ambient conditions

    DEFF Research Database (Denmark)

    Decremps, F.; Pellicer-Porres, J.; Datchi, F.


    Dense powder of nanocrystalline ZnO has been recovered at ambient conditions in the metastable cubic structure after a heat treatment at high pressure (15 GPa and 550 K). Combined x-ray diffraction (XRD) and x-ray absorption spectroscopy (XAS) experiments have been performed to probe both long...

  15. Aspects on mediated glucose oxidation at a supported cubic phase. (United States)

    Aghbolagh, Mahdi Shahmohammadi; Khani Meynaq, Mohammad Yaser; Shimizu, Kenichi; Lindholm-Sethson, Britta


    A supported liquid crystalline cubic phase housing glucose oxidase on an electrode surface has been suggested as bio-anode in a biofuel. The purpose of this investigation is to clarify some aspect on the mediated enzymatic oxidation of glucose in such a bio-anode where the mediator ferrocene-carboxylic acid and glucose were dissolved in the solution. The enzyme glucose oxidase was housed in the water channels of the mono-olein cubic phase. The system was investigated with cyclic voltammetry at different scan rates and the temperature was varied between 15°C and 30°C. The diffusion coefficient of the mediator and also the film resistance was estimated showing a large decrease in the mass-transport properties as the temperature was decreased. The current from mediated oxidation of glucose at the electrode surface increased with decreasing film thickness. The transport of the mediator in the cubic phase was the rate-limiting step in the overall reaction, where the oxidation of glucose took place at the outer surface of the cubic phase. Copyright © 2017 Elsevier B.V. All rights reserved.

  16. Computation of conjugate depths in cubic-shape open channels ...

    African Journals Online (AJOL)

    For rectangular channels, an explicit equation for obtaining the conjugate depth has been derived and is available in any standard hydraulics text. This paper is to develop a procedure for computing the conjugate depth in cubic-shaped open channels, given an initial depth. This procedure involves the use of a table or a ...

  17. A Unified Approach to Teaching Quadratic and Cubic Equations. (United States)

    Ward, A. J. B.


    Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

  18. computation of conjugate depths in cubic-shaped open channels

    African Journals Online (AJOL)

    channels, an explicit equation for obtaining the conjugate depth has been derived and is available in any standard hydraulics text. This paper is to develop a procedure for computing the conjugate depth in cubic-shaped open channels, given an initial depth. This procedure involves the use of a table or a chart and avoids ...

  19. A look through ‘lens’ cubic mitochondria (United States)

    Almsherqi, Zakaria; Margadant, Felix; Deng, Yuru


    Cell membranes may fold up into three-dimensional nanoperiodic cubic structures in biological systems. Similar geometries are well studied in other disciplines such as mathematics, physics and polymer chemistry. The fundamental function of cubic membranes in biological systems has not been uncovered yet; however, their appearance in specialized cell types indicates a role as structural templates or perhaps direct physical entities with specialized biophysical properties. The mitochondria located at the inner segment of the retinal cones of tree shrew (Tupaia glis and Tupaia belangeri) contain unique patterns of concentric cristae with a highly ordered membrane arrangement in three dimensions similar to the photonic nanostructures observed in butterfly wing scales. Using a direct template matching method, we show that the inner mitochondrial membrane folds into multi-layered (8 to 12 layers) gyroid cubic membrane arrangements in the photoreceptor cells. Three-dimensional simulation data demonstrate that such multi-layer gyroid membrane arrangements in the retinal cones of a tree shrew's eye can potentially function as: (i) multi-focal lens; (ii) angle-independent interference filters to block UV light; and (iii) a waveguide photonic crystal. These theoretical results highlight for the first time the significance of multi-layer cubic membrane arrangements to achieve near-quasi-photonic crystal properties through the simple and reversible biological process of continuous membrane folding. PMID:24098837

  20. A simple method for indexing powder diffraction patterns of cubic ...

    African Journals Online (AJOL)

    A simple method for indexing powder diffraction patterns of cubic materials:(1) using the θ-values of reference. ... Tanzania Journal of Science ... Alternatively, you can download the PDF file directly to your computer, from where it can be ...

  1. Influence of strontium on the cubic to ordered hexagonal phase ...

    Indian Academy of Sciences (India)

    ... Lecture Workshops · Refresher Courses · Symposia. Home; Journals; Bulletin of Materials Science; Volume 23; Issue 6. Influence of strontium on the cubic to ordered hexagonal phase transformation in barium magnesium niobate. M Thirumal A K Ganguli. Phase Transitions Volume 23 Issue 6 December 2000 pp 495-498 ...

  2. Interaction of dispersed cubic phases with blood components

    DEFF Research Database (Denmark)

    Bode, J C; Kuntsche, Judith; Funari, S S


    The interaction of aqueous nanoparticle dispersions, e.g. based on monoolein/poloxamer 407, with blood components is an important topic concerning especially the parenteral way of administration. Therefore, the influence of human and porcine plasma on dispersed cubic phases was investigated. Part...

  3. Tangent Lines without Derivatives for Quadratic and Cubic Equations (United States)

    Carroll, William J.


    In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

  4. Specific heat of the simple-cubic Ising model

    NARCIS (Netherlands)

    Feng, X.; Blöte, H.W.J.


    We provide an expression quantitatively describing the specific heat of the Ising model on the simple-cubic lattice in the critical region. This expression is based on finite-size scaling of numerical results obtained by means of a Monte Carlo method. It agrees satisfactorily with series expansions

  5. C2-rational cubic spline involving tension parameters

    Indian Academy of Sciences (India) Keywords. Interpolation; rational; spline; tension parameter; monotonicity; convexity; continuity. Abstract. In the present paper, 1-piecewise rational cubic spline function involving tension parameters is considered which produces a monotonic interpolant to a given ...

  6. The traveling salesman problem on cubic and subcubic graphs

    NARCIS (Netherlands)

    S. Boyd; R.A. Sitters (René); S.L. van der Ster; L. Stougie (Leen)


    htmlabstractWe study the traveling salesman problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3-conjecture for metric TSP, which says that the integrality gap, i.e., the worst case

  7. A New Method to Solve Numeric Solution of Nonlinear Dynamic System

    Directory of Open Access Journals (Sweden)

    Min Hu


    Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.

  8. Waveguide quantum electrodynamics - nonlinear physics at the few-photon level

    Energy Technology Data Exchange (ETDEWEB)

    Schneider, Michael; Sproll, Tobias; Martens, Christoph [Max-Born-Institut, Max-Born-Str. 2A, 12489 Berlin (Germany); Schmitteckert, Peter [Institut fuer Nanotechnologie, Karlsruher Institut fuer Technologie (KIT), 76344 Eggenstein-Leopoldshafen (Germany); Busch, Kurt [Max-Born-Institut, Max-Born-Str. 2A, 12489 Berlin (Germany); Humboldt-Universitaet zu Berlin, Institut fuer Physik, AG Theoretische Optik und Photonik, Newtonstr. 15, 12489 Berlin (Germany)


    The transport of few photons in 1D structures coupled to a fermionic impurity gives rise to a set of non-linear effects, induced by an effective interaction due to Pauli blocking such as photon bunching and the formation of atom-photon bound states. We analyze a specific example of such systems, namely a 1-D waveguide coupled to a 2-level system, for the case of one and two-photon transport. Therefore we have developed a general theoretical framework, which contains analytic approaches originating in methods of quantum field theory, like path integrals and Feynman diagrams as well as powerful numerical tools based on solving the time-dependent Schroedinger equation. Owing its generality, our approach is also applicable to more involved setups, including disorder and dissipation as well as more complicated impurities such as driven and undriven 3-level systems.

  9. Ground states of nonlinear Schrödinger systems with saturable nonlinearity in R{sup 2} for two counterpropagating beams

    Energy Technology Data Exchange (ETDEWEB)

    Lin, Tai-Chia, E-mail: [Institute of Applied Mathematical Sciences and Mathematics Division, National Center for Theoretical Sciences (NCTS) at Taipei, National Taiwan University, Taipei 10617, Taiwan (China); Belić, Milivoj R. [Texas A and M University at Qatar, P.O. Box 23874, Doha (Qatar); Petrović, Milan S. [Institute of Physics, P.O. Box 57, 11001 Belgrade (Serbia); Chen, Goong [Texas A and M University at Qatar, P.O. Box 23874, Doha (Qatar); Department of Mathematics and Institute for Quantum Science and Engineering, Texas A and M University, College Station, Texas 77843 (United States)


    Counterpropagating optical beams in nonlinear media give rise to a host of interesting nonlinear phenomena such as the formation of spatial solitons, spatiotemporal instabilities, self-focusing and self-trapping, etc. Here we study the existence of ground state (the energy minimizer under the L{sup 2}-normalization condition) in two-dimensional (2D) nonlinear Schrödinger (NLS) systems with saturable nonlinearity, which describes paraxial counterpropagating beams in isotropic local media. The nonlinear coefficient of saturable nonlinearity exhibits a threshold which is crucial in determining whether the ground state exists. The threshold can be estimated by the Gagliardo-Nirenberg inequality and the ground state existence can be proved by the energy method, but not the concentration-compactness method. Our results also show the essential difference between 2D NLS equations with cubic and saturable nonlinearities.

  10. Solitary waves on nonlinear elastic rods. I

    DEFF Research Database (Denmark)

    Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.


    Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...... the solitary waves numerically. It is demonstrated that the waves behave almost like solitons in agreement with the fact that the improved Boussinesq equations are nearly integrable. Thus three conservation theorems can be derived from the equations. A new subsonic quasibreather is found in the case of a cubic...

  11. Affine equivalence of cubic homogeneous rotation symmetric Boolean functions

    CERN Document Server

    Cusick, Thomas W


    Homogeneous rotation symmetric Boolean functions have been extensively studied in recent years because of their applications in cryptography. Little is known about the basic question of when two such functions are affine equivalent. The simplest case of quadratic rotation symmetric functions which are generated by cyclic permutations of the variables in a single monomial was only settled in 2009. This paper studies the much more complicated cubic case for such functions. A new concept of \\emph{patterns} is introduced, by means of which the structure of the smallest group G_n, whose action on the set of all such cubic functions in $n$ variables gives the affine equivalence classes for these functions under permutation of the variables, is determined. We conjecture that the equivalence classes are the same if all nonsingular affine transformations, not just permutations, are allowed. This conjecture is verified if n < 22. Our method gives much more information about the equivalence classes; for example, in t...

  12. The Piecewise Cubic Method (PCM) for computational fluid dynamics (United States)

    Lee, Dongwook; Faller, Hugues; Reyes, Adam


    We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed solutions are evolved in time with a fourth-order accuracy by tracing the characteristics of the cubic polynomials. As a result, our temporal update scheme provides a significantly simpler and computationally more efficient approach in achieving fourth order accuracy in time, relative to the comparable fourth-order Runge-Kutta method. We demonstrate that the solutions of PCM converges at fifth-order in solving 1D smooth flows described by hyperbolic conservation laws. We test the new scheme on a range of numerical experiments, including both gas dynamics and magnetohydrodynamics applications in multiple spatial dimensions.

  13. Negative thermal expansion materials related to cubic zirconium tungstate (United States)

    Lind, Cora


    A non-hydrolytic sol-gel method for the preparation of ZrW2O 8 was developed. A new trigonal polymorph was discovered, which is structurally related to trigonal ZrMO2O8 and MnRe2O 8 as evidenced by powder x-ray diffraction and EXAFS studies. Seeding of the starting mixtures with cubic ZrW2O8 promoted crystallization of the cubic phase instead of trigonal material. Dehydration of ZrW2O7(OH)2·2H 2O gave cubic ZrW2O8 at 650°C, and a modification of this route led to the discovery of the new NTE materials cubic ZrMo 2O8 and HfMo2O8. These compounds crystallize in the same temperature range as the more stable trigonal AMo2O 8 polymorphs. To facilitate preparation of phase pure cubic molybdates, the influence of precursor chemistry on the crystallization behavior was investigated. The synthesis was extended to the solid solution system ZrxHf 1-xMoyW2-yO8 (0 ≤ x ≤ 1, 0 ≤ y ≤ 2). All compounds showed negative thermal expansion between 77 and 573 K. High-pressure in situ diffraction experiments were conducted on several AM2O8 polymorphs. With the exception of monoclinic ZrMo2O8, all materials underwent at least one pressure induced phase transition. Quasi-hydrostatic experiments on cubic AMo 2O8 led to a reversible transition to a new high-pressure structure, while low-pressure amorphization was observed under non-hydrostatic conditions. Isothermal kinetic studies of the cubic to trigonal transformation for ZrMo2O8 were carried out on four samples. Apparent activation energies of 170--290 kJ/mol were obtained using an Avrami model in combination with an Arrhenius analysis. This corresponds to 5% conversion levels after one year at temperatures between 220 and 315°C. Ex situ studies showed that the conversion at lower temperatures was considerably slower than what would be expected from extrapolation of the kinetic data. Drop solution calorimetry was carried out on several polymorphs of ZrMo 2O8, HfMo2O8 and ZrW2O 8. Only monoclinic ZrMo2O8 was enthalpically

  14. Plasma simulation with the Differential Algebraic Cubic Interpolated Propagation scheme

    Energy Technology Data Exchange (ETDEWEB)

    Utsumi, Takayuki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment


    A computer code based on the Differential Algebraic Cubic Interpolated Propagation scheme has been developed for the numerical solution of the Boltzmann equation for a one-dimensional plasma with immobile ions. The scheme advects the distribution function and its first derivatives in the phase space for one time step by using a numerical integration method for ordinary differential equations, and reconstructs the profile in phase space by using a cubic polynomial within a grid cell. The method gives stable and accurate results, and is efficient. It is successfully applied to a number of equations; the Vlasov equation, the Boltzmann equation with the Fokker-Planck or the Bhatnagar-Gross-Krook (BGK) collision term and the relativistic Vlasov equation. The method can be generalized in a straightforward way to treat cases such as problems with nonperiodic boundary conditions and higher dimensional problems. (author)

  15. Structural and magnetic transitions in cubic Mn3Ga. (United States)

    Kharel, P; Huh, Y; Al-Aqtash, N; Shah, V R; Sabirianov, R F; Skomski, R; Sellmyer, D J


    The structural, magnetic and electron-transport properties of cubic Mn3Ga have been investigated. The alloys prepared by arc melting and melt-spinning show an antiferromagnetic spin order at room temperature but undergo coupled structural and magnetic phase transitions at 600 and 800 K. First-principles calculations show that the observed magnetic properties are consistent with that of a cubic Mn3Ga crystallizing in the disordered Cu3Au-type structure. The samples exhibit metallic electron transport with a resistance minimum near 30 K, followed by a logarithmic upturn below the minimum. The observed anomaly in the low-temperature resistivity has been discussed as a consequence of electron scattering at the low-lying excitations of the structurally disordered Mn3Ga lattice.

  16. Experimental core electron density of cubic boron nitride

    DEFF Research Database (Denmark)

    Wahlberg, Nanna; Bindzus, Niels; Bjerg, Lasse

    candidate because of its many similarities with diamond: bonding pattern in the extended network structure, hardness, and the quality of the crystallites.3 However, some degree ionic interaction is a part of the bonding in boron nitride, which is not present in diamond. By investigating the core density...... beyond multipolar modeling of the valence density. As was recently shown in a benchmark study of diamond by Bindzus et al.1 The next step is to investigate more complicated chemical bonding motives, to determine the effect of bonding on the core density. Cubic boron nitride2 lends itself as a perfect...... in boron nitride we may obtain a deeper understanding of the effect of bonding on the total density. We report here a thorough investigation of the charge density of cubic boron nitride with a detailed modelling of the inner atom charge density. By combining high resolution powder X-ray diffraction data...

  17. Highly Aminated Mesoporous Silica Nanoparticles with Cubic Pore Structure

    KAUST Repository

    Suteewong, Teeraporn


    Mesoporous silica with cubic symmetry has attracted interest from researchers for some time. Here, we present the room temperature synthesis of mesoporous silica nanoparticles possessing cubic Pm3n symmetry with very high molar ratios (>50%) of 3-aminopropyl triethoxysilane. The synthesis is robust allowing, for example, co-condensation of organic dyes without loss of structure. By means of pore expander molecules, the pore size can be enlarged from 2.7 to 5 nm, while particle size decreases. Adding pore expander and co-condensing fluorescent dyes in the same synthesis reduces average particle size further down to 100 nm. After PEGylation, such fluorescent aminated mesoporous silica nanoparticles are spontaneously taken up by cells as demonstrated by fluorescence microscopy.

  18. Dislocations in hexagonal and cubic GaN (United States)

    Blumenau, A. T.; Elsner, J.; Jones, R.; Heggie, M. I.; Öberg, S.; Frauenheim, T.; Briddon, P. R.


    The structure and electronic activity of several types of dislocations in both hexagonal and cubic GaN are calculated using first-principles methods. Most of the stoichiometric dislocations investigated in hexagonal GaN do not induce deep acceptor states and thus cannot be responsible for the yellow luminescence. However, it is shown that electrically active point defects, in particular gallium vacancies and oxygen-related defect complexes, can be trapped at the stress field of the dislocations and may be responsible for this luminescence. For cubic GaN, we find the ideal stoichiometric 60° dislocation to be electrically active and the glide set to be more stable than the shuffle. The dissociation of the latter is considered.

  19. Cubic-phase GaN light-emitting diodes (United States)

    Yang, Hui; Zheng, L. X.; Li, J. B.; Wang, X. J.; Xu, D. P.; Wang, Y. T.; Hu, X. W.; Han, P. D.


    The feasibility of growing device-quality cubic GaN/GaAs(001) films by metal organic chemical vapor deposition has been demonstrated. The optical quality of the GaN films was characterized by room-temperature photoluminescence measurements, which shows a full width at half maximum of 46 meV. The structural quality of the films was investigated by transmission electron microscopy. There are submicron-size grains free from threading dislocations and stacking faults. More importantly, a cubic-phase GaN blue light-emitting diode has been fabricated. The device process, which is very simple and compatible with current GaAs technology, indicates a promising future for the blue light-emitting diode.

  20. Nonlinear Elasticity (United States)

    Fu, Y. B.; Ogden, R. W.


    This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.

  1. Nonlinear resonances

    CERN Document Server

    Rajasekar, Shanmuganathan


    This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...

  2. Anodic etching of p-type cubic silicon carbide (United States)

    Harris, G. L.; Fekade, K.; Wongchotigul, K.


    p-Type cubic silicon carbide was anodically etched using an electrolyte of HF:HCl:H2O. The etching depth was determined versus time with a fixed current density of 96.4 mA/sq cm. It was found that the etching was very smooth and very uniform. An etch rate of 22.7 nm/s was obtained in a 1:1:50 HF:HCl:H2O electrolyte.

  3. Large scale structures and the cubic galileon model

    CERN Document Server

    Bhattacharya, Sourav; Tomaras, Theodore N


    The maximum size of a bound cosmic structure is computed perturbatively as a function of its mass in the framework of the cubic galileon, proposed recently to model the dark energy of our Universe. Comparison of our results with observations constrains the matter-galileon coupling of the model to $0.03\\lesssim \\alpha \\lesssim 0.17$, thus improving previous bounds based solely on solar system physics.

  4. Influence of strontium on the cubic to ordered hexagonal phase ...

    Indian Academy of Sciences (India)


    Abstract. Oxides of the type Ba3–xSrxMgNb2O9 were synthesized by the solid state route. The x = 0 compo- sition (Ba3MgNb2O9) was found to crystallize in a disordered (cubic) perovskite structure when sintered at. 1000C. For higher Sr doping (x ≥ 0⋅5), there was clearly the presence of an ordered hexagonal phase ...

  5. Dry Powder Precursors of Cubic Liquid Crystalline Nanoparticles (cubosomes) (United States)

    Spicer, Patrick T.; Small, William B.; Small, William B.; Lynch, Matthew L.; Burns, Janet L.


    Cubosomes are dispersed nanostructured particles of cubic phase liquid crystal that have stimulated significant research interest because of their potential for application in controlled-release and drug delivery. Despite the interest, cubosomes can be difficult to fabricate and stabilize with current methods. Most of the current work is limited to liquid phase processes involving high shear dispersion of bulk cubic liquid crystalline material into sub-micron particles, limiting application flexibility. In this work, two types of dry powder cubosome precursors are produced by spray-drying: (1) starch-encapsulated monoolein is produced by spray-drying a dispersion of cubic liquid crystalline particles in an aqueous starch solution and (2) dextran-encapsulated monoolein is produced by spray-drying an emulsion formed by the ethanol-dextran-monoolein-water system. The encapsulants are used to decrease powder cohesion during drying and to act as a soluble colloidal stabilizer upon hydration of the powders. Both powders are shown to form (on average) 0.6 μm colloidally-stable cubosomes upon addition to water. However, the starch powders have a broader particle size distribution than the dextran powders because of the relative ease of spraying emulsions versus dispersions. The developed processes enable the production of nanostructured cubosomes by end-users rather than just specialized researchers and allow tailoring of the surface state of the cubosomes for broader application.

  6. Packing of nonoverlapping cubic particles: Computational algorithms and microstructural characteristics (United States)

    Malmir, Hessam; Sahimi, Muhammad; Tabar, M. Reza Rahimi


    Packing of cubic particles arises in a variety of problems, ranging from biological materials to colloids and the fabrication of new types of porous materials with controlled morphology. The properties of such packings may also be relevant to problems involving suspensions of cubic zeolites, precipitation of salt crystals during CO2 sequestration in rock, and intrusion of fresh water in aquifers by saline water. Not much is known, however, about the structure and statistical descriptors of such packings. We present a detailed simulation and microstructural characterization of packings of nonoverlapping monodisperse cubic particles, following up on our preliminary results [H. Malmir et al., Sci. Rep. 6, 35024 (2016), 10.1038/srep35024]. A modification of the random sequential addition (RSA) algorithm has been developed to generate such packings, and a variety of microstructural descriptors, including the radial distribution function, the face-normal correlation function, two-point probability and cluster functions, the lineal-path function, the pore-size distribution function, and surface-surface and surface-void correlation functions, have been computed, along with the specific surface and mean chord length of the packings. The results indicate the existence of both spatial and orientational long-range order as the the packing density increases. The maximum packing fraction achievable with the RSA method is about 0.57, which represents the limit for a structure similar to liquid crystals.

  7. Trace spaces in a pre-cubical complex

    DEFF Research Database (Denmark)

    Raussen, Martin


    In directed algebraic topology, directed irreversible (d)-paths and spaces consisting of d-paths are studied from a topological and from a categorical point of view. Motivated by models for concurrent computation, we study in this paper spaces of d-paths in a pre-cubical complex. Such paths are e...... are separable metric spaces which are locally contractible and locally compact. Moreover, they have the homotopy type of a CW-complex.......In directed algebraic topology, directed irreversible (d)-paths and spaces consisting of d-paths are studied from a topological and from a categorical point of view. Motivated by models for concurrent computation, we study in this paper spaces of d-paths in a pre-cubical complex. Such paths...... are equipped with a natural arc length which moreover is shown to be invariant under directed homotopies. D-paths up to reparametrization (called traces) can thus be represented by arc length parametrized d-paths. Under weak additional conditions, it is shown that trace spaces in a pre-cubical complex...

  8. Iron-substituted cubic silsesquioxane pillared clays : Synthesis, characterization and acid catalytic activity

    NARCIS (Netherlands)

    Potsi, Georgia; Ladavos, Athanasios K.; Petrakis, Dimitrios; Douvalis, Alexios P.; Sanakis, Yiannis; Katsiotis, Marios S.; Papavassiliou, Georgios; Alhassan, Saeed; Gournis, Dimitrios; Rudolf, Petra


    Novel pillared structures were developed from the intercalation of iron-substituted cubic silsesquioxanes in a sodium and an acid-activated montmorillonite nanoclay and evaluated as acid catalysts. Octameric cubic oligosiloxanes were formed upon controlled hydrolytic polycondensation of the

  9. Generation and Nonlinear Dynamical Analyses of Fractional-Order Memristor-Based Lorenz Systems

    Directory of Open Access Journals (Sweden)

    Huiling Xi


    Full Text Available In this paper, four fractional-order memristor-based Lorenz systems with the flux-controlled memristor characterized by a monotone-increasing piecewise linear function, a quadratic nonlinearity, a smooth continuous cubic nonlinearity and a quartic nonlinearity are presented, respectively. The nonlinear dynamics are analyzed by using numerical simulation methods, including phase portraits, bifurcation diagrams, the largest Lyapunov exponent and power spectrum diagrams. Some interesting phenomena, such as inverse period-doubling bifurcation and intermittent chaos, are found to exist in the proposed systems.

  10. The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities

    KAUST Repository

    Crosta, M


    By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose–Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.


    Directory of Open Access Journals (Sweden)

    Hanna Bordyuh


    Full Text Available In the present work we analyze the characteristics of holographic grating recording and consider a mechanism of optical nonlinearity in the lyotropic liquid crystal (LLC — viologen samples. Taking into account structural and electrooptical properties of the admixture molecules it is possible to suggest that the recording is realized due to the change of polarizability of π-electron system of coloured viologen derivatives under the action of laser radiation. The main nonlinear optical parameters such as nonlinear refraction coefficient n2, cubic nonlinear susceptibility χ(3, and hyperpolarizability γ were calculated.

  12. Key parameters governing the densification of cubic-Li7La3Zr2O12 Li+ conductors (United States)

    Yi, Eongyu; Wang, Weimin; Kieffer, John; Laine, Richard M.


    Cubic-Li7La3Zr2O12 (LLZO) is regarded as one of the most promising solid electrolytes for the construction of inherently safe, next generation all-solid-state Li batteries. Unfortunately, sintering these materials to full density with controlled grain sizes, mechanical and electrochemical properties relies on energy and equipment intensive processes. In this work, we elucidate key parameters dictating LLZO densification by tracing the compositional and structural changes during processing calcined and ball-milled Al3+ doped LLZO powders. We find that the powders undergo ion (Li+/H+) exchange during room temperature processing, such that on heating, the protonated LLZO lattice collapses and crystallizes to its constituent oxides, leading to reaction driven densification at ionic conductivity (1.3 ± 0.1 mS cm-1) and record low ionic area specific resistance (2 Ω cm2).

  13. Nonlinear Materials Characterization Facility (United States)

    Federal Laboratory Consortium — The Nonlinear Materials Characterization Facility conducts photophysical research and development of nonlinear materials operating in the visible spectrum to protect...

  14. Quantum Electromagnetic Nonlinearity Affecting Charges and Dipole Moments (United States)

    Adorno, T. C.; Gitman, D. M.; Shabad, A. E.; Shishmarev, A. A.


    Due to the nonlinearity of QED, a static charge becomes a magnetic dipole if placed in a magnetic field, and a magnetic monopole on the background is a combination of constant electric and magnetic fields. Already without external field, the cubic Maxwell equation for the field of a point charge has a soliton solution with a finite field energy and finite potential, the energy-momentum vector of a moving soliton being the same as that of a point massive particle. Equations are given for self-coupling dipole moments. Any theoretically found value for a multipole moment of a baryon or a meson should be subjected to nonlinear renormalization.

  15. Multiphase Weakly Nonlinear Geometric Optics for Schrödinger Equations

    KAUST Repository

    Carles, Rémi


    We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrödinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading order amplitude of the solution, but does not alter the rapid oscillations. We consider initial states which are superpositions of slowly modulated plane waves, and use the framework of Wiener algebras. A detailed analysis of the corresponding nonlinear wave mixing phenomena is given, including a geometric interpretation of the resonance structure for cubic nonlinearities. As an application, we recover and extend some instability results for the nonlinear Schrödinger equation on the torus in negative order Sobolev spaces. © 2010 Society for Industrial and Applied Mathematics.

  16. Flow and dispersion in an urban cubical cavity (United States)

    Ryu, Young-Hee; Baik, Jong-Jin

    Flow and dispersion in an urban cubical cavity are numerically investigated using a Reynolds-averaged Navier-Stokes equations (RANS) model with the renormalization group (RNG) k- ɛ turbulence closure model. The urban cubical cavity is surrounded by flank walls that are parallel to the streamwise direction, called end-walls, as well as upstream and downstream walls. A primary vortex and secondary vortices including end-wall vortices are formed in the cavity. Because of the end-wall drag effect, the averaged mean-flow kinetic energy in the cavity is smaller than that in an urban street canyon that is open in the along-canyon direction. A trajectory analysis shows that the end-wall vortices cause fluid particles to move in the spanwise direction, indicating that flow in the cavity is essentially three-dimensional. The iso-surfaces of the Okubo-Weiss criterion capture cavity vortices well. The pollutant concentration is high near the bottom of the upstream side in the case of continuous pollutant emission, whereas it is high near the center of the primary vortex in the case of instantaneous pollutant emission. To get some insight into the degree of pollutant escape from the cavity according to various meteorological factors, extensive numerical experiments with different ambient wind speeds and directions, inflow turbulence intensities, and cavity-bottom heating intensities are performed. For each experiment, we calculate the time constant, which is defined as the time taken for the pollutant concentration to decrease to e-1 of its initial value. The time constant decreases substantially with increasing ambient wind speed, and tends to decrease with increasing inflow turbulence intensity and cavity-bottom heating intensity. The time constant increases as the ambient wind direction becomes oblique. High ambient wind speed is found to be the most crucial factor for ventilating the cavity, thus improving air quality in an urban cubical cavity.

  17. Stress reduction of cubic boron nitride films by oxygen addition

    Energy Technology Data Exchange (ETDEWEB)

    Ye, J. [Forschungszentrum Karlsruhe, IMF I, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany)], E-mail:; Ulrich, S.; Ziebert, C.; Stueber, M. [Forschungszentrum Karlsruhe, IMF I, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany)


    Cubic boron nitride (c-BN) films with significantly reduced residual stresses were successfully grown onto silicon substrates by means of controlled oxygen addition into the films. The deposition was based on radio-frequency magnetron sputtering of a hexagonal boron nitride (h-BN) target, and was accomplished in a reactive mode using gas mixtures of argon, nitrogen, and oxygen at 0.3 Pa pressure, 400 deg. C growth temperature, and - 250 V substrate bias. Results of systematic investigations are shown in this article with respect to the critical influences of oxygen concentration during deposition upon the stress, cubic phase fraction, as well as nanohardness of the deposited films. Under the specified growth conditions, the formation of c-BN was generally completely hindered for oxygen concentrations above 1.5 vol.% in the gas mixture. At concentrations below approximately 1 vol.%, the added oxygen exhibits however marginal influences on the c-BN fraction, but on the other side a strong impact on the stress of the deposited films. Cubic-phase dominated films (containing 70-80 vol.% c-BN) with their compressive stress three times reduced were thus produced through careful control of oxygen fraction in the gas mixture, showing an excellent nanohardness of almost 60 GPa. For such films, a post-deposition thermal treatment at 900 deg. C led to an additional drastic stress reduction resulting in a final residual stress that is almost 10 times lower than that of as-deposited c-BN films without intentional oxygen addition.

  18. Cubic Phases, Cubosomes and Ethosomes for Cutaneous Application. (United States)

    Esposito, Elisabetta; Drechsler, Markus; Nastruzzi, Claudio; Cortesi, Rita


    Cutaneous administration represents a good strategy to treat skin diseases, avoiding side effects related to systemic administration. Apart from conventional therapy, based on the use of semi-solid formulation such as gel, ointments and creams, recently the use of specialized delivery systems based on lipid has been taken hold. This review provides an overview about the use of cubic phases, cubosomes and ethosomes, as lipid systems recently proposed to treat skin pathologies. In addition in the final part of the review cubic phases, cubosomes and ethosomes are compared to solid lipid nanoparticles and lecithin organogel with respect to their potential as delivery systems for cutaneous application. It has been reported that lipid nanosystems are able to dissolve and deliver active molecules in a controlled fashion, thereby improving their bioavailability and reducing side-effects. Particularly lipid matrixes are characterized by skin affinity and biocompatibility allowing their application on skin. Indeed, after cutaneous administration, the lipid matrix of cubic phases and cubosomes coalesces with the lipids of the stratum comeum and leads to the formation of a lipid depot from which the drug associated to the nanosystem can be released in the deeper skin strata in a controlled manner. Ethosomes are characterized by a malleable structure that promotes their interaction with skin, improving their potential as skin delivery systems with respect to liposomes. Also in the case of solid lipid nanoparticles it has been suggested a deep interaction between lipid matrix and skin strata that endorses sustained and prolonged drug release. Concerning lecithin organogel, the peculiar structure of this system, where lecithin exerts a penetration enhancer role, allows a deep interaction with skin strata, promoting the transdermal absorption of the encapsulated drugs.

  19. Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices. (United States)

    Cramer, M; Eisert, J; Illuminati, F


    We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices and parabolic confining potentials. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimension within mean-field and perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose-Fermi mixtures in optical lattices.

  20. Compressibility and thermal expansion of cubic silicon nitride

    DEFF Research Database (Denmark)

    Jiang, Jianzhong; Lindelov, H.; Gerward, Leif


    The compressibility and thermal expansion of the cubic silicon nitride (c-Si3N4) phase have been investigated by performing in situ x-ray powder-diffraction measurements using synchrotron radiation, complemented with computer simulations by means of first-principles calculations. The bulk...... compressibility of the c-Si3N4 phase originates from the average of both Si-N tetrahedral and octahedral compressibilities where the octahedral polyhedra are less compressible than the tetrahedral ones. The origin of the unit cell expansion is revealed to be due to the increase of the octahedral Si-N and N-N bond...

  1. C2-rational cubic spline involving tension parameters

    Indian Academy of Sciences (India)

    iИ1 ИfЕ122Y 128Ж; Е122Y 156Ж; Е150Y 184Ж; Е178Y 184Ж;. Е206Y 156Ж; Е206Y 128Ж; Е178Y 100Ж; Е150Y 100Ж;. Е122Y 72Ж; Е122Y 44Ж; Е150Y 16Ж; Е178Y 16Ж;. Е206Y 44Ж; Е206Y 72ЖgY we obtain the C2-rational cubic spline interpolant. Thus for different values of the tension parameters r and t, ...

  2. Evidence for cubic phase in deposited germanium nanocrystals

    CERN Document Server

    Bostedt, C; Plitzko, J M; Möller, T; Terminello, L J


    Germanium nanocrystals with sizes ranging from 1 to 5 nm are condensed out of the gas phase in helium or argon buffer-gas atmospheres and subsequently deposited. The generated particle sizes are found to depend on the buffer gas, with helium yielding a narrower size distribution than argon and argon exhibiting a stronger pressure dependence of the produced particle sizes. Structural analysis of nanoparticles with average sizes around 5 nm reveals the bulklike cubic (diamond) phase - in contrast to recent experiments which suggest the tetragonal phase for similar-sized particles. These results are explained in terms of particle formation dynamics.

  3. Tensor tomography of stresses in cubic single crystals

    Directory of Open Access Journals (Sweden)

    Dmitry D. Karov


    Full Text Available The possibility of optical tomography applying to investigation of a two-dimensional and a three-dimensional stressed state in single cubic crystals has been studied. Stresses are determined within the framework of the Maxwell piezo-optic law (linear dependence of the permittivity tensor on stresses and weak optical anisotropy. It is shown that a complete reconstruction of stresses in a sample is impossible both by translucence it in the parallel planes system and by using of the elasticity theory equations. For overcoming these difficulties, it is offered to use a method of magnetophotoelasticity.

  4. Rotary Ultrasonic Machining of Poly-Crystalline Cubic Boron Nitride

    Directory of Open Access Journals (Sweden)

    Kuruc Marcel


    Full Text Available Poly-crystalline cubic boron nitride (PCBN is one of the hardest material. Generally, so hard materials could not be machined by conventional machining methods. Therefore, for this purpose, advanced machining methods have been designed. Rotary ultrasonic machining (RUM is included among them. RUM is based on abrasive removing mechanism of ultrasonic vibrating diamond particles, which are bonded on active part of rotating tool. It is suitable especially for machining hard and brittle materials (such as glass and ceramics. This contribution investigates this advanced machining method during machining of PCBN.

  5. Nonlinear beam mechanics

    NARCIS (Netherlands)

    Westra, H.J.R.


    In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like

  6. Identifiability of nonlinear systems

    Energy Technology Data Exchange (ETDEWEB)

    Tunali, E.T.


    The parameter identifiability problem of deterministic, nonlinear dynamical control systems is studied in the framework of differential geometric systems theory. The relations between nonlinear observability, nonlinear functional expansions and identifiability are investigated and necessary and sufficient conditions are obtained for a class of nonlinear systems. In a different approach, by using the uniqueness theorem of nonlinear system realization theory, necessary and sufficient conditions are obtained for another class of nonlinear systems. These results provide an insight to the identifiability problem of nonlinear systems. The results are illustrated by examples that also show the effectiveness of the conditions obtained. Finally, some possible research topics in this area are suggested.

  7. Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations

    Energy Technology Data Exchange (ETDEWEB)

    Mikaelian, K O


    We extend our earlier model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities to the more general class of hydrodynamic instabilities driven by a time-dependent acceleration g(t) . Explicit analytic solutions for linear as well as nonlinear amplitudes are obtained for several g(t)'s by solving a Schroedinger-like equation d{sup 2}{eta}/dt{sup 2} - g(t)kA{eta} = 0 where A is the Atwood number and k is the wavenumber of the perturbation amplitude {eta}(t). In our model a simple transformation k {yields} k{sub L} and A {yields} A{sub L} connects the linear to the nonlinear amplitudes: {eta}{sup nonlinear} (k,A) {approx} (1/k{sub L})ln{eta}{sup linear} (k{sub L}, A{sub L}). The model is found to be in very good agreement with direct numerical simulations. Bubble amplitudes for a variety of accelerations are seen to scale with s defined by s = {integral} {radical}g(t)dt, while spike amplitudes prefer scaling with displacement {Delta}x = {integral}[{integral}g(t)dt]dt.

  8. Cathodoluminescence of homogeneous cubic GaN/GaAs(001) layers (United States)

    Wang, C.; As, D. J.; Schöttker, B.; Schikora, D.; Lischka, K.


    The cathodoluminescence (CL) of cubic (c-) GaN epitaxial layers is investigated at temperatures between 50 K and 300 K. The low temperature CL spectra show three well resolved emission lines (3.26 eV, 3.17 eV and 3.08 eV) which are due to excitonic, donor-acceptor and free to acceptor transitions. Spatially resolved measurements of the intensity of the excitonic emission demonstrate the homogeneity of the layers which are free of microcrystalline inclusions. The room temperature CL of the layers has a full width at half maximum of 56 meV and is due to excitonic recombination as is concluded from the zero-shift of the line position when the excitation intensity is varied over some orders of magnitude. The intensity of a broad emission band at 2.4 eV shows a strong nonlinear variation of the intensity at high excitation levels. Using a rate equation model for the near band edge and the deep 2.4 eV emission we are able to describe the intensity variation of these radiative transitions as a function of the excitation intensity. Depth resolved CL measurements reveal a homogeneous depth distribution of deep recombination centres responsible for the deep 2.4 eV luminescence band.

  9. Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition metals (United States)

    Derlet, P. M.; Nguyen-Manh, D.; Dudarev, S. L.


    We investigate the structure and mobility of single self-interstitial atom and vacancy defects in body-centered-cubic transition metals forming groups 5B (vanadium, niobium, and tantalum) and 6B (chromium, molybdenum, and tungsten) of the Periodic Table. Density-functional calculations show that in all these metals the axially symmetric ⟨111⟩ self-interstitial atom configuration has the lowest formation energy. In chromium, the difference between the energies of the ⟨111⟩ and the ⟨110⟩ self-interstitial configurations is very small, making the two structures almost degenerate. Local densities of states for the atoms forming the core of crowdion configurations exhibit systematic widening of the “local” d band and an upward shift of the antibonding peak. Using the information provided by electronic structure calculations, we derive a family of Finnis-Sinclair-type interatomic potentials for vanadium, niobium, tantalum, molybdenum, and tungsten. Using these potentials, we investigate the thermally activated migration of self-interstitial atom defects in tungsten. We rationalize the results of simulations using analytical solutions of the multistring Frenkel-Kontorova model describing nonlinear elastic interactions between a defect and phonon excitations. We find that the discreteness of the crystal lattice plays a dominant part in the picture of mobility of defects. We are also able to explain the origin of the non-Arrhenius diffusion of crowdions and to show that at elevated temperatures the diffusion coefficient varies linearly as a function of absolute temperature.

  10. Stationary states of the two-dimensional nonlinear Schrödinger model with disorder

    DEFF Research Database (Denmark)

    Gaididei, Yuri Borisovich; Hendriksen, D.; Christiansen, Peter Leth


    Solitonlike excitations in the presence of disorder in the two-dimensional cubic nonlinear Schrodinger equation are analyzed. The continuum as well as the discrete problem are analyzed. In the continuum model, otherwise unstable excitations are stabilized in the presence of disorder. In the discr...

  11. Collapse arresting in an inhomogeneous two-dimensional nonlinear Schrodinger model

    DEFF Research Database (Denmark)

    Schjødt-Eriksen, Jens; Gaididei, Yuri Borisovich; Christiansen, Peter Leth


    Collapse of (2 + 1)-dimensional beams in the inhomogeneous two-dimensional cubic nonlinear Schrodinger equation is analyzed numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams that in a homogeneous medium would collapse may be...

  12. String scattering amplitudes and deformed cubic string field theory (United States)

    Lai, Sheng-Hong; Lee, Jen-Chi; Lee, Taejin; Yang, Yi


    We study string scattering amplitudes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. The four-string scattering amplitudes with three tachyons and an arbitrary string state are calculated. The string field theory yields the string scattering amplitudes evaluated on the world sheet of string scattering whereas the conventional method, based on the first quantized theory brings us the string scattering amplitudes defined on the upper half plane. For the highest spin states, generated by the primary operators, both calculations are in perfect agreement. In this case, the string scattering amplitudes are invariant under the conformal transformation, which maps the string world sheet onto the upper half plane. If the external string states are general massive states, generated by non-primary field operators, we need to take into account carefully the conformal transformation between the world sheet and the upper half plane. We show by an explicit calculation that the string scattering amplitudes calculated by using the deformed cubic string field theory transform into those of the first quantized theory on the upper half plane by the conformal transformation, generated by the Schwarz-Christoffel mapping.

  13. Elastic properties of cubic crystals: Every's versus Blackman's diagram (United States)

    Paszkiewicz, T.; Wolski, S.


    Blackman's diagram of two dimensionless ratios of elastic constants is frequently used to correlate elastic properties of cubic crystals with interatomic bondings. Every's diagram of a different set of two dimensionless variables was used by us for classification of various properties of such crystals. We compare these two ways of characterization of elastic properties of cubic materials and consider the description of various groups of materials, e.g. simple metals, oxides, and alkali halides. With exception of intermediate valent compounds, the correlation coefficients for Every's diagrams of various groups of materials are greater than for Blackaman's diagrams, revealing the existence of a linear relationship between two dimensionless Every's variables. Alignment of elements and compounds along lines of constant Poisson's ratio v(lang100rang, m), (m arbitrary perpendicular to lang100rang) is observed. Division of the stability region in Blackman's diagram into region of complete auxetics, auxetics and non-auxetics is introduced. Correlations of a scaling and an acoustic anisotropy parameter are considered.

  14. Mixed convection in a double lid-driven cubic cavity

    Energy Technology Data Exchange (ETDEWEB)

    Nasreddine, Ouertatania; Nader, Ben Cheikha; Brahim, Ben Beyaa; Taieb, Lilia [Faculte des Sciences de Tunis, Dept. de Physique (Tunisia); Campo, A. [University of Texas at San Antonio, Dept. of Mechanical Engineering, San Antonio, TX (United States)


    To study the intricate three-dimensional flow structures and the companion heat transfer rates in double lid-driven cubic cavity heated from the top and cooled from below, a numerical methodology based on the finite volume method and a full multigrid acceleration is utilized in this paper. The four remaining walls forming the cubic cavity are adiabatic. The working fluid is air so that the Prandtl number equates to 0.71. Numerical solutions are generated for representative combinations of the controlling Reynolds number inside 100 {<=} Re {<=} 1000 and the Richardson numbers inside 0.001 {<=} Ri {<=} 10. Typical sets of streamlines and isotherms are presented to analyze the tortuous circulatory flow patterns set up by the competition between the forced flow created by the double driven walls and the buoyancy force of the fluid. For extreme combinations of high Ri and low Re, the heat transfer is essentially dominated by conduction. On the other hand, for extreme combinations of small Ri and high Re, the heat transfer becomes convective dominating. Numerical values of the overall Nusselt number in harmony with the Re- and Ri-intervals are presented and they are compared afterward against the standard case of a single lid driven cavity. It is discovered that a remarkable heat transfer improvement of up to 76% can be reached for the particular combination of Re=400 and Ri=1. (authors)

  15. On a family of cubic graphs containing the flower snarks

    CERN Document Server

    Fouquet, Jean-Luc; Vanherpe, Jean-Marie


    We consider cubic graphs formed with $k \\geq 2$ disjoint claws $C_i \\sim K_{1, 3}$ ($0 \\leq i \\leq k-1$) such that for every integer $i$ modulo $k$ the three vertices of degree 1 of $\\ C_i$ are joined to the three vertices of degree 1 of $C_{i-1}$ and joined to the three vertices of degree 1 of $C_{i+1}$. Denote by $t_i$ the vertex of degree 3 of $C_i$ and by $T$ the set $\\{t_1, t_2,..., t_{k-1}\\}$. In such a way we construct three distinct graphs, namely $FS(1,k)$, $FS(2,k)$ and $FS(3,k)$. The graph $FS(j,k)$ ($j \\in \\{1, 2, 3\\}$) is the graph where the set of vertices $\\cup_{i=0}^{i=k-1}V(C_i) \\setminus T$ induce $j$ cycles (note that the graphs $FS(2,2p+1)$, $p\\geq2$, are the flower snarks defined by Isaacs \\cite{Isa75}). We determine the number of perfect matchings of every $FS(j,k)$. A cubic graph $G$ is said to be {\\em 2-factor hamiltonian} if every 2-factor of $G$ is a hamiltonian cycle. We characterize the graphs $FS(j,k)$ that are 2-factor hamiltonian (note that FS(1,3) is the "Triplex Graph" of Robe...

  16. Symmetry group of an impenetrable cubic well potential (United States)

    Hernández-Castillo, A. O.; Lemus, R.


    When the symmetry group of a quantum particle in an impenetrable cubic well potential is considered to be the O_h group, systematic accidental degeneracy appears. This degeneracy becomes natural when a new symmetry group, embedding the O_h group, is proposed. This new group turns out to be the semidirect product G=T \\wedge O_h, where T is a two-dimensional compact continuous group whose generators correspond to linear combinations of the one-dimensional Hamiltonians. The systematic degeneracy is studied in detail, the new group is identified and its irreducible representations are constructed by means of induction, an approach that allows the irreducibility and completeness to be assured. Similar to the hydrogen atom, we establish a one-to-one reciprocation between the energy and the new group irreducible representations. The impenetrable rectangular and square boxes are also analyzed as a reduction of symmetry from the cubic system. Pythagorean degeneracy as well as that due to commensurable sides is not considered.

  17. New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis (United States)

    van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, G.; Hogeweij, G. M. D.; Tanaka, K.; Tamura, N.; Zwart, H. J.; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M. R.; The LHD Experiment Group


    A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by two gyrotrons has been used to directly quantify the amplitude of the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions and also the absence of cubic and higher order components. The non-linear component is analyzed using the Volterra series, which is the non-linear generalization of transfer functions. This allows us to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles where the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles, demonstrating the significant impact that non-linearity can have.

  18. PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena (United States)

    Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo


    derivative nonlinear Schroedinger (DNLS) equation. Ragnisco and Zullo [18] construct Backlund transformations for the trigonometric classical Gaudin magnet in the partially anisotropic (xxz) case, identifying the subcase of transformations that preserve the real character of the variables. The recently discovered exceptional polynomials are complete polynomial systems that satisfy Sturm-Liouville problems but differ from the classical families of Hermite, Laguerre and Jacobi. Gomez-Ullate et al [19] prove that the families of exceptional orthogonal polynomials known to date can be obtained from the classical ones via a Darboux transformation, which becomes a useful tool to derive some of their properties. Integrability in the context of classical mechanics is associated to the existence of a sufficient number of conserved quantities, which allows sometimes an explicit integration of the equations of motion. This is the case for the motion of the Chaplygin sleigh, a rigid body motion on a fluid with nonholonomic constraints studied in the paper by Fedorov and Garcia-Naranjo [20], who derive explicit solutions and study their asymptotic behaviour. In connection with classical mechanics, some techniques of KAM theory have been used by Procesi [21] to derive normal forms for the NLS equation in its Hamiltonian formulation and prove existence and stability of quasi-periodic solutions in the case of periodic boundary conditions. Algebraic and group theoretic aspects of integrability are covered in a number of papers in the issue. The quest for symmetries of a system of differential equations usually allows us to reduce the order or the number of equations or to find special solutions possesing that symmetry, but algebraic aspects of integrable systems encompass a wide and rich spectrum of techniques, as evidenced by the following contributions. Muriel and Romero [22] perform a systematic study of all second order nonlinear ODEs that are linearizable by generalized Sundman and

  19. The band structures of three-dimensional nonlinear plasma photonic crystals (United States)

    Zhang, Hai-Feng


    In this paper, the properties of the photonic band gaps (PBGs) for three-dimensional (3D) nonlinear plasma photonic crystals (PPCs) are theoretically investigated by the plane wave expansion method, whose equations for calculations also are deduced. The configuration of 3D nonlinear PPCs is the Kerr nonlinear dielectric spheres (Kerr effect is considered) inserted in the plasma background with simple-cubic lattices. The inserted dielectric spheres are Kerr nonlinear dielectrics whose relative permittivities are the functions of the external light intensity. Three different Kerr nonlinear dielectrics are considered, which can be expressed as the functions of space coordinates. The influences of the parameters for the Kerr nonlinear dielectrics on the PBGs also are discussed. The calculated results demonstrate that the locations, bandwidths and number of PBGs can be manipulated with the different Kerr nonlinear dielectrics. Compared with the conventional 3D dielectric PCs and PPCs with simple-cubic lattices, the more PBGs or larger PBG can be achieved in the 3D nonlinear PPCs. Those results provide a new way to design the novel devices based on the PPCs.

  20. A novel nonlinear damage resonance intermodulation effect for structural health monitoring (United States)

    Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele


    This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

  1. Initial post dynamic buckling of a quadratic-cubic column ...

    African Journals Online (AJOL)

    The imperfection is assumed in the shape of the mth term in the Fourier sine series expansion with small (in absolute value) Fourier coefficients. A generalization of Lindsted-Poincare procedure is used and the structure under investigation is, on the main, a nonlinear oscillatory system with small perturbations. The results ...

  2. Más allá del laboratorio: las dimensiones sociológicas de la ecuación de Schroedinger Más allá del laboratorio: las dimensiones sociológicas de la ecuación de Schroedinger

    Directory of Open Access Journals (Sweden)

    Miguel A.V. Ferreira


    Full Text Available In the present work it is exposed synthetically part of an empirical investigation in the field of the sociology of scientific knowledge. From the sociological perspective that assumes the (social activity producing scientific knowledge as one of the epistemological components of this knowledge, it is exposed as, from an autobservational methodology, it has been possible to state the constituently reflexive nature of this activity. A reflexivity in which the formal and formalizeable it is intermingled very indisociably with the existential and informalizable. We present, from these methodologic foundations a (sociological vision of Schroedinger equation that reveals it in its social nataure: beyond its neutral appearance, formal and mathematical, it shows one agencial and active potentiality, shows all the dimensions of an authentic social subject.En el presente trabajo se expone sintéticamente parte de lo que ha sido una investigación empírica en el campo de la sociología del conocimiento científico. Desde la perspectiva sociológica que asume la actividad (social productora de conocimiento científico como uno de los constituyentes epistemológicos de dicho conocimiento, se expone cómo a partir de una metodología autobservacional se ha podido constatar la naturaleza constitutivamente reflexiva de dicha actividad. Una reflexividad en la que lo formal y formalizable se entremezcla indisociablemente con lo informal y vivencial. Presentamos, a partir de estos fundamentos metodológicos, una visión (sociológica de la ecuación de Schroedinger que la revela en su naturaleza social: más allá de su apariencia neutra, formal y matemática, muestra una virtualidad agencial y activa, muestra todas las dimensiones de un auténtico sujeto social. Proponemos, para culminar, que el tipo de reflexividad que entendemos constitutivo de la práctica científica y, por extensión, de cualquier práctica social, se distancia de lo que ha venido defini

  3. Inter- and intraband transitions in cubic nitride quantum wells

    Energy Technology Data Exchange (ETDEWEB)

    Rodrigues, S.C.P. [Sao Paulo Univ. (Brazil). Inst. de Fisica de Sao Carlos; Sao Paulo Univ. (Brazil). Inst. de Fisica; Sipahi, G.M. [Sao Paulo Univ. (Brazil). Inst. de Fisica de Sao Carlos; Scolfaro, L.M.R.; Noriega, O.C.; Leite, J.R. [Sao Paulo Univ. (Brazil). Inst. de Fisica; Frey, T.; As, D.J.; Schikora, D.; Lischka, K. [Paderborn Univ. (Gesamthochschule) (Germany). Fachbereich 6 - Physik


    In this work we analyze the luminescence emissions from selected isolated GaN/InGaN quantum wells comparing measured and theoretical photoluminescence (PL) spectra. The calculations are performed within the k.p method by means of an 8 x 8 Kane Hamiltonian, generalized to treat different materials. Strain effects due to the large lattice mismatch between InN and GaN are taken into account. From the direct comparison with experimental results, we found evidence for transitions involving confined levels which, besides those related to quantum dots, may be ascribed to the first electron-heavy-hole transition in the quantum wells. Since the studies of optical properties of quantum wells based on cubic nitrides are at an early stage, the results reported here will provide guidelines for the interpretation of forthcoming experiments. (orig.)

  4. Surface irregularities of MBE grown cubic GaN layers (United States)

    Lima, A. P.; Frey, T.; Köhler, U.; Wang, C.; As, D. J.; Schöttker, B.; Lischka, K.; Schikora, D.


    Cubic GaN layers are grown by molecular beam epitaxy on (0 0 1)GaAs substrates. The influence of intentional deviations from stoichiometric growth conditions on the structural homogeneity of the epitaxial layers and the GaN/GaAs interface was studied. Optical micrographs and AFM-images of the epilayers grown in a Ga-stabilised regime reveal the existence of different types of surface irregularities. We conclude that the irregularities observed are the result of successively melt-back etching in GaN and GaAs and solution growth within Ga-droplets due to the change of the saturation conditions of the liquid Ga-phase on the surface of the growing film.

  5. Linear electro-optic effect in cubic silicon carbide (United States)

    Tang, Xiao; Irvine, Kenneth G.; Zhang, Dongping; Spencer, Michael G.


    The first observation is reported of the electrooptic effect of cubic silicon carbide (beta-SiC) grown by a low-pressure chemical vapor deposition reactor using the hydrogen, silane, and propane gas system. At a wavelength of 633 nm, the value of the electrooptic coefficient r41 in beta-SiC is determined to be 2.7 +/- 0.5 x 10 (exp-12) m/V, which is 1.7 times larger than that in gallium arsenide measured at 10.6 microns. Also, a half-wave voltage of 6.4 kV for beta-SiC is obtained. Because of this favorable value of electrooptic coefficient, it is believed that silicon carbide may be a promising candidate in electrooptic applications for high optical intensity in the visible region.

  6. A cubic autocatalytic reaction in a continuous stirred tank reactor

    Energy Technology Data Exchange (ETDEWEB)

    Yakubu, Aisha Aliyu; Yatim, Yazariah Mohd [School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang Malaysia (Malaysia)


    In the present study, the dynamics of the cubic autocatalytic reaction model in a continuous stirred tank reactor with linear autocatalyst decay is studied. This model describes the behavior of two chemicals (reactant and autocatalyst) flowing into the tank reactor. The behavior of the model is studied analytically and numerically. The steady state solutions are obtained for two cases, i.e. with the presence of an autocatalyst and its absence in the inflow. In the case with an autocatalyst, the model has a stable steady state. While in the case without an autocatalyst, the model exhibits three steady states, where one of the steady state is stable, the second is a saddle point while the last is spiral node. The last steady state losses stability through Hopf bifurcation and the location is determined. The physical interpretations of the results are also presented.

  7. The electric field of a uniformly charged cubic shell (United States)

    McCreery, Kaitlin; Greenside, Henry


    As an integrative and insightful example for undergraduates learning about electrostatics, we discuss how to use symmetry, Coulomb's law, superposition, Gauss's law, and visualization to understand the electric field E (x ,y ,z ) produced by a uniformly charged cubic shell. We first discuss how to deduce qualitatively, using freshman-level physics, the perhaps surprising fact that the interior electric field is nonzero and has a complex structure, pointing inwards from the middle of each face of the shell and pointing outwards towards each edge and corner. We then discuss how to understand the quantitative features of the electric field by plotting an analytical expression for E along symmetry lines and on symmetry surfaces of the shell.

  8. Photonic band gaps in body-centered-cubic structures (United States)

    Hornreich, R. M.; Shtrikman, S.; Sommers, C.


    Photonic energy bands in body-centered-cubic bcc materials are analyzed by considering structures having O8 (I4132) space-group symmetry. Such structures can be realized physically by interlacing cylindrical elements oriented along crystallographic axes. In addition to heterogeneous systems composed entirely of dielectric materials, the possibility of using conducting materials (particularly at microwave frequencies) is studied. We find that (a) band gaps occur in heterogeneous dielectric systems when materials having a dielectric constant of 100 or more are properly placed in the O8 unit cell, and (b) utilizing conducting materials can significantly widen the excluded frequency band, the result being that band gaps of more than 20% should be attainable with O8 structures at microwave frequencies. Experimental verification of these results should be possible in this spectral region.

  9. Spatial 't Hooft loop to cubic order in hot QCD

    CERN Document Server

    Giovannangeli, P.


    Spatial 't Hooft loops of strength k measure the qualitative change in the behaviour of electric colour flux in confined and deconfined phase of SU (N) gauge theory. They show an area law in the deconfined phase, known analytica lly to two loop order with a ``k-scaling'' law k(N-k). In this paper we comput e the O(g^3) correction to the tension. It is due to neutral gluon fields that get their mass through interaction with the wall. The simple k-scaling is lost in cubic order. The generic problem of non-convexity shows up in this order an d the cure is provided. The result for large N is explicitely given. We show tha t nonperturbative effects appear at O(g^5).

  10. Bounce universe and black holes from critical Einsteinian cubic gravity (United States)

    Feng, Xing-Hui; Huang, Hyat; Mai, Zhan-Feng; Lü, Hong


    We show that there exists a critical point for the coupling constants in Einsteinian cubic gravity in which the linearized equations on the maximally symmetric vacuum vanish identically. We construct an exact isotropic bounce universe in the critical theory in four dimensions. The comoving time runs from minus infinity to plus infinity, yielding a smooth universe bouncing between two de Sitter vacua. In five dimensions, we adopt a numerical approach to construct a bounce solution, in which a singularity occurs before the bounce takes place. We then construct exact anisotropic bounces that connect two isotropic de Sitter spacetimes with flat spatial sections. We further construct exact anti-de Sitter black holes in the critical theory in four and five dimensions and obtain an exact anti-de Sitter worm brane in four dimensions.

  11. Perbaikan Metode Penghitungan Debit Sungai Menggunakan Cubic Spline Interpolation

    Directory of Open Access Journals (Sweden)

    Budi I. Setiawan


    Full Text Available Makalah ini menyajikan perbaikan metode pengukuran debit sungai menggunakan fungsi cubic spline interpolation. Fungi ini digunakan untuk menggambarkan profil sungai secara kontinyu yang terbentuk atas hasil pengukuran jarak dan kedalaman sungai. Dengan metoda baru ini, luas dan perimeter sungai lebih mudah, cepat dan tepat dihitung. Demikian pula, fungsi kebalikannnya (inverse function tersedia menggunakan metode. Newton-Raphson sehingga memudahkan dalam perhitungan luas dan perimeter bila tinggi air sungai diketahui. Metode baru ini dapat langsung menghitung debit sungaimenggunakan formula Manning, dan menghasilkan kurva debit (rating curve. Dalam makalah ini dikemukaan satu canton pengukuran debit sungai Rudeng Aceh. Sungai ini mempunyai lebar sekitar 120 m dan kedalaman 7 m, dan pada saat pengukuran mempunyai debit 41 .3 m3/s, serta kurva debitnya mengikuti formula: Q= 0.1649 x H 2.884 , dimana Q debit (m3/s dan H tinggi air dari dasar sungai (m.

  12. Diamond and Cubic Boron Nitride: Properties, Growth and Applications (United States)

    Soltani, A.; Talbi, A.; Mortet, V.; BenMoussa, A.; Zhang, W. J.; Gerbedoen, J.-C.; De Jaeger, J.-C.; Gokarna, A.; Haenen, K.; Wagner, P.


    Since their first synthesis, cubic boron nitride (c-BN) and diamond thin films have triggered a vivid interest in these wide band gap materials for many different applications. Because of superior properties, c-BN and diamond can be applied in optic, electronic and acoustic for high performances devices. In this discussion, we first describe briefly the properties of c-BN and diamond and we review both the growth techniques and the progresses achieved in the synthesis of c-BN and diamond, and in a second part, characteristics of new c-BN and diamond UV detectors for solar observation are reported. These photo-detectors present extremely low dark current, high breakdown voltage, high responsivity and stability under UV irradiation. Finally, diamond based acoustic devices and sensors are presented. High frequency acoustic wave devices can be design for high frequency filtering or sensing applications. Diamond/AlN micro-cantilevers are excellent platform for sensor applications.

  13. Modelling gravity on a hyper-cubic lattice

    CERN Document Server

    Tate, Kyle


    We present an elegant and simple dynamical model of symmetric, non-degenerate (n x n) matrices of fixed signature defined on a n-dimensional hyper-cubic lattice with nearest-neighbor interactions. We show how this model is related to General Relativity, and discuss multiple ways in which it can be useful for studying gravity, both classical and quantum. In particular, we show that the dynamics of the model when all matrices are close to the identity corresponds exactly to a finite-difference discretization of weak-field gravity in harmonic gauge. We also show that the action which defines the full dynamics of the model corresponds to the Einstein-Hilbert action to leading order in the lattice spacing, and use this observation to define a lattice analogue of the Ricci scalar and Einstein tensor. Finally, we perform a mean-field analysis of the statistical mechanics of this model.

  14. Topologically correct cortical segmentation using Khalimsky's cubic complex framework (United States)

    Cardoso, Manuel J.; Clarkson, Matthew J.; Modat, Marc; Talbot, Hugues; Couprie, Michel; Ourselin, Sébastien


    Automatic segmentation of the cerebral cortex from magnetic resonance brain images is a valuable tool for neuroscience research. Due to the presence of noise, intensity non-uniformity, partial volume effects, the limited resolution of MRI and the highly convoluted shape of the cerebral cortex, segmenting the brain in a robust, accurate and topologically correct way still poses a challenge. In this paper we describe a topologically correct Expectation Maximisation based Maximum a Posteriori segmentation algorithm formulated within the Khalimsky cubic complex framework, where both the solution of the EM algorithm and the information derived from a geodesic distance function are used to locally modify the weighting of a Markov Random Field and drive the topology correction operations. Experiments performed on 20 Brainweb datasets show that the proposed method obtains a topologically correct segmentation without significant loss in accuracy when compared to two well established techniques.

  15. Lipidic cubic phase serial millisecond crystallography using synchrotron radiation

    Directory of Open Access Journals (Sweden)

    Przemyslaw Nogly


    Full Text Available Lipidic cubic phases (LCPs have emerged as successful matrixes for the crystallization of membrane proteins. Moreover, the viscous LCP also provides a highly effective delivery medium for serial femtosecond crystallography (SFX at X-ray free-electron lasers (XFELs. Here, the adaptation of this technology to perform serial millisecond crystallography (SMX at more widely available synchrotron microfocus beamlines is described. Compared with conventional microcrystallography, LCP-SMX eliminates the need for difficult handling of individual crystals and allows for data collection at room temperature. The technology is demonstrated by solving a structure of the light-driven proton-pump bacteriorhodopsin (bR at a resolution of 2.4 Å. The room-temperature structure of bR is very similar to previous cryogenic structures but shows small yet distinct differences in the retinal ligand and proton-transfer pathway.

  16. Computation of L ⊕ for several cubic Pisot numbers

    Directory of Open Access Journals (Sweden)

    Julien Bernat


    Full Text Available In this article, we are dealing with β-numeration, which is a generalization of numeration in a non-integer base. We consider the class of simple Parry numbers such that d β (1 = 0.k 1 d-1  k d with d ∈ ℕ, d ≥ 2 and k 1  ≥ k d  ≥ 1. We prove that these elements define Rauzy fractals that are stable under a central symmetry. We use this result to compute, for several cases of cubic Pisot units, the maximal length among the lengths of the finite β-fractional parts of sums of two β-integers, denoted by L ⊕. In particular, we prove that L ⊕  = 5 in the Tribonacci case.

  17. Electron spin dynamics in cubic GaN (United States)

    Buß, J. H.; Schupp, T.; As, D. J.; Brandt, O.; Hägele, D.; Rudolph, J.


    The electron spin dynamics in cubic GaN is comprehensively investigated by time-resolved magneto-optical Kerr-rotation spectroscopy over a wide range of temperatures, magnetic fields, and doping densities. The spin dynamics is found to be governed by the interplay of spin relaxation of localized electrons and Dyakonov-Perel relaxation of delocalized electrons. Localized electrons significantly contribute to spin relaxation up to room temperature at moderate doping levels, while Dyakonov-Perel relaxation dominates for high temperatures or degenerate doping levels. Quantitative agreement to Dyakonov-Perel theory requires a larger value of the spin-splitting constant than theoretically predicted. Possible reasons for this discrepancy are discussed, including the role of charged dislocations.

  18. Preparation and pharmacokinetic study of fenofibrate cubic liquid crystalline

    Directory of Open Access Journals (Sweden)

    Shijie Wei


    Full Text Available An LCC delivery system for Fenofibrate (Fen was developed to improve its poorly oral bioavailability. Fen-LCC preparation methods were screened, and the prepared Fen-LCC was then characterized by a polarizing microscope and transmission electron microscopy (TEM. The spray drying technique was selected to dry and solidify particles into powder. The in vitro release of Fen-LCC was measured and in vivo pharmacokinetic experiments were carried out on rats after oral administration. Particles prepared through the high-temperature input method exhibited structural characteristics of LCC, and re-dissolved particles maintained the same features. The LCC delivery system can significantly improve in vitro release outcomes. After oral administration, AUCs of the suspension and LCC systems were measured at 131.6853 µg⋅h/ml and 1435.72893 µg⋅h/ml, respectively. The spray drying process presented here better maintains cubic structures, and the LCC system significantly improves bioavailability levels.

  19. Modified wave operators for nonlinear Schrodinger equations in one and two dimensions

    Directory of Open Access Journals (Sweden)

    Nakao Hayashi


    Full Text Available We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schr"{o}dinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13

  20. Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

    Energy Technology Data Exchange (ETDEWEB)

    Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)


    We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.

  1. On Poisson Nonlinear Transformations

    Directory of Open Access Journals (Sweden)

    Nasir Ganikhodjaev


    Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.

  2. Nonlinear Hysteretic Torsional Waves. (United States)

    Cabaret, J; Béquin, P; Theocharis, G; Andreev, V; Gusev, V E; Tournat, V


    We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

  3. Flutter analysis of an airfoil with nonlinear damping using equivalent linearization

    Directory of Open Access Journals (Sweden)

    Chen Feixin


    Full Text Available The equivalent linearization method (ELM is modified to investigate the nonlinear flutter system of an airfoil with a cubic damping. After obtaining the linearization quantity of the cubic nonlinearity by the ELM, an equivalent system can be deduced and then investigated by linear flutter analysis methods. Different from the routine procedures of the ELM, the frequency rather than the amplitude of limit cycle oscillation (LCO is chosen as an active increment to produce bifurcation charts. Numerical examples show that this modification makes the ELM much more efficient. Meanwhile, the LCOs obtained by the ELM are in good agreement with numerical solutions. The nonlinear damping can delay the occurrence of secondary bifurcation. On the other hand, it has marginal influence on bifurcation characteristics or LCOs.

  4. Epitaxial growth and optical transitions of cubic GaN films (United States)

    Schikora, D.; Hankeln, M.; As, D. J.; Lischka, K.; Litz, T.; Waag, A.; Buhrow, T.; Henneberger, F.


    Single-phase cubic GaN layers are grown by plasma-assisted molecular-beam epitaxy. The temperature dependence of the surface reconstruction is elaborated. The structural stability of the cubic growth in dependence of the growth stoichiometry is studied by RHEED measurements and numerical simulations of the experimental RHEED patterns. Growth oscillations on cubic GaN are recorded at higher substrate temperatures and nearly stoichiometric adatom coverage. Photoluminescence reveals the dominant optical transitions of cubic GaN and, by applying an external magnetic field, their characteristic g factors are determined.

  5. Subalgebras of BCK/BCI-Algebras Based on Cubic Soft Sets

    Directory of Open Access Journals (Sweden)

    G. Muhiuddin


    Full Text Available Operations of cubic soft sets including “AND” operation and “OR” operation based on P-orders and R-orders are introduced and some related properties are investigated. An example is presented to show that the R-union of two internal cubic soft sets might not be internal. A sufficient condition is provided, which ensure that the R-union of two internal cubic soft sets is also internal. Moreover, some properties of cubic soft subalgebras of BCK/BCI-algebras based on a given parameter are discussed.

  6. Cubic liquid crystalline nanoparticles: optimization and evaluation for ocular delivery of tropicamide. (United States)

    Verma, Purnima; Ahuja, Munish


    The purpose of this study was to investigate the potential of cubic liquid crystalline nanoparticles for ocular delivery of tropicamide. Ultrasound-assisted fragmentation of cubic liquid crystalline bulk phases resulted in cubic liquid crystalline nanoparticles employing Pluronic F127 as dispersant. The effects of process variables such as sonication time, sonication amplitude, sonication depth, and pre-mixing time on particle size and polydispersity index was investigated using central composite design. The morphology of tropicamide-loaded nanoparticles was found to be nearly cubical in shape by transmission electron microscopy observation. Further, small angle X-ray scattering experiment confirmed the presence of D and P phase cubic structures in coexistence. The optimized tropicamide-loaded cubic nanoparticles showed in vitro corneal permeation of tropicamide across isolated porcine cornea comparable to its commercial preparation, Tropicacyl®. Ocular tolerance was evaluated by Hen's egg-chorioallantoic membrane test and histological studies. The results of in vivo mydriatic response study demonstrated a remarkably higher area under mydriatic response curve (AUC0→1440 min) values of cubic nanoparticles over Tropicacyl® indicating better therapeutic value of cubic nanoparticles. Furthermore, tropicamide-loaded cubic nanoparticles exhibited prolonged mydriatic effect on rabbits as compared to commercial conventional aqueous ophthalmic solution.

  7. Non-spherical micelles in an oil-in-water cubic phase

    DEFF Research Database (Denmark)

    Leaver, M.; Rajagopalan, V.; Ulf, O.


    The cubic phase formed between the microemulsion and hexagonal phases of the ternary pentaethylene glycol dodecyl ether (C12E5)-decane-water system and that doped with small amounts of sodium dodecylsulfate (SDS) have been investigated. The presence of discrete oil-swollen micelles in the cubic...... scattering experiments indicate that the lattice parameter for the cubic phase is inconsistent with a simple packing of micelles. Whilst insufficient reflections were observed to establish the space group of the cubic phase uniquely, those that were are consistent with two commonly observed space groups...

  8. Prediction of Gas Injection Effect on Asphaltene Precipitation Onset Using the Cubic and Cubic-Plus-Association Equations of State

    DEFF Research Database (Denmark)

    Arya, Alay; Liang, Xiaodong; von Solms, Nicolas


    precipitation onset condition during gas injection. The modeling approach is used with the Soave Redlich Kwong, Soave Redlich Kwong-Plus-Huron Vidal mixing rule and cubic-plus-association (CPA) equations of state (EoS). Six different reservoir fluids are studied with respect to asphaltene onset precipitation...... during nitrogen, hydrocarbon gas mixture, and carbon dioxide injection. It is also shown how to extend the modeling approach when the reservoir fluid is split into multiple pseudocomponents. It is observed that the modeling approach using any of the three models can predict the gas injection effect......Gas injection is a proven enhanced oil recovery technique. The gas injection changes the reservoir oil composition, temperature, and pressure conditions, which may result in asphaltene precipitation. In this work, we have used a modeling approach from the literature in order to predict asphaltene...

  9. Noncommutative Nonlinear Supersymmetry


    Nishino, Hitoshi; Rajpoot, Subhash


    We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4, 6 and 10.

  10. Nonlinear fractional relaxation

    Indian Academy of Sciences (India)

    Nonlinear fractional equation; nonlinear fractional relaxation; -expansion. Abstract. We define a nonlinear model for fractional relaxation phenomena. We use -expansion method to analyse this model. By studying the fundamental solutions of this model we find that when → 0 the model exhibits a fast decay rate and ...

  11. Advances in nonlinear optics

    CERN Document Server

    Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong


    This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.

  12. Nonlinear Microwave Optomechanics

    NARCIS (Netherlands)

    Shevchuk, O.


    The nonlinearity is essential for creation of non-classical states of the cavity or mechanical resonator such as squeezed or cat states. A microwave cavity can be made nonlinear by, for instance, adding Josephson junctions. The mechanical resonator is inherently nonlinear. The radiation pressure

  13. Nonlinear Dynamics of Electrostatically Actuated MEMS Arches

    KAUST Repository

    Al Hennawi, Qais M.


    In this thesis, we present theoretical and experimental investigation into the nonlinear statics and dynamics of clamped-clamped in-plane MEMS arches when excited by an electrostatic force. Theoretically, we first solve the equation of motion using a multi- mode Galarkin Reduced Order Model (ROM). We investigate the static response of the arch experimentally where we show several jumps due to the snap-through instability. Experimentally, a case study of in-plane silicon micromachined arch is studied and its mechanical behavior is measured using optical techniques. We develop an algorithm to extract various parameters that are needed to model the arch, such as the induced axial force, the modulus of elasticity, and the initially induced initial rise. After that, we excite the arch by a DC electrostatic force superimposed to an AC harmonic load. A softening spring behavior is observed when the excitation is close to the first resonance frequency due to the quadratic nonlinearity coming from the arch geometry and the electrostatic force. Also, a hardening spring behavior is observed when the excitation is close to the third (second symmetric) resonance frequency due to the cubic nonlinearity coming from mid-plane stretching. Then, we excite the arch by an electric load of two AC frequency components, where we report a combination resonance of the summed type. Agreement is reported among the theoretical and experimental work.

  14. Nonreciprocal wave transmission through an extended discrete nonlinear Schrödinger dimer (United States)

    Wasay, Muhammad Abdul


    We analyze a one-dimensional extended discrete nonlinear Schrödinger (DNLS) dimer model for nonreciprocal wave transmission. The extension corresponds to the addition of a nonlocal or intersite nonlinear response in addition to a purely cubic local (on-site) nonlinear response, which refines the purely cubic model and aligns to more realistic situations. We observe that a diodelike action persists in the extended case; however, the inclusion of nonlocal response tends to reduce the diode action. We show that this extension results in achieving the diode effect at lower incoming intensities as compared to the purely cubic case. We also report that a nearly perfect diode action is possible in the extended case for a higher level of asymmetry between on-site potentials than its cubic counterpart. Moreover, we vary different site-dependent parameters to probe for regimes of a better diode effect within this extended model. We also present the corresponding stability analysis for the exact stationary solutions to the extended DNLS equation, we discuss the bifurcation behavior in detail, and we explicitly give the regions of stability.

  15. Lagrange interpolation and modified cubic B-spline differential quadrature methods for solving hyperbolic partial differential equations with Dirichlet and Neumann boundary conditions (United States)

    Jiwari, Ram


    In this article, the author proposed two differential quadrature methods to find the approximate solution of one and two dimensional hyperbolic partial differential equations with Dirichlet and Neumann's boundary conditions. The methods are based on Lagrange interpolation and modified cubic B-splines respectively. The proposed methods reduced the hyperbolic problem into a system of second order ordinary differential equations in time variable. Then, the obtained system is changed into a system of first order ordinary differential equations and finally, SSP-RK3 scheme is used to solve the obtained system. The well known hyperbolic equations such as telegraph, Klein-Gordon, sine-Gordon, Dissipative non-linear wave, and Vander Pol type non-linear wave equations are solved to check the accuracy and efficiency of the proposed methods. The numerical results are shown in L∞ , RMS andL2 errors form.

  16. Supra-transmission and bistability in nonlinear media with a photonic and electronic forbidden band gap; Supratransmission et bistabilite nonlineaire dans les milieux a bandes interdites photoniques et electroniques

    Energy Technology Data Exchange (ETDEWEB)

    Chevriaux, D


    We study wave scattering in different nonlinear media possessing a natural forbidden band gap. In particular, we show the existence of a bistable behavior in media governed by the sine-Gordon equation (short pendular chain, Josephson junction array, quantum Hall bilayer), or the nonlinear Schroedinger equation (Kerr and Bragg media), in discrete and continuous models. These different media are submitted to periodic boundary conditions with a frequency in the forbidden band gap and an amplitude that determines their stability states. Indeed, for a sufficient amplitude (supra-transmission), the medium switches from reflector to transmitter, hence allowing the output signal to jump from evanescent to large values. We give a complete analytical description of the bistability that allows to understand the different stationary states observed and to predict the switch of one state to the other. (author)

  17. Nonlinear dynamics and complexity

    CERN Document Server

    Luo, Albert; Fu, Xilin


    This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

  18. Characterization, Microstructure, and Dielectric properties of cubic pyrochlore structural ceramics

    KAUST Repository

    Li, Yangyang


    The (BMN) bulk materials were sintered at 1050°C, 1100°C, 1150°C, 1200°C by the conventional ceramic process, and their microstructure and dielectric properties were investigated by Scanning electron microscopy (SEM), X-ray diffraction (XRD), Raman spectroscopy, Transmission electron microscopy (TEM) (including the X-ray energy dispersive spectrometry EDS and high resolution transmission electron microscopy HRTEM) and dielectric impedance analyzer. We systematically investigated the structure, dielectric properties and voltage tunable property of the ceramics prepared at different sintering temperatures. The XRD patterns demonstrated that the synthesized BMN solid solutions had cubic phase pyrochlore-type structure when sintered at 1050°C or higher, and the lattice parameter (a) of the unit cell in BMN solid solution was calculated to be about 10.56Å. The vibrational peaks observed in the Raman spectra of BMN solid solutions also confirmed the cubic phase pyrochlore-type structure of the synthesized BMN. According to the Scanning Electron Microscope (SEM) images, the grain size increased with increasing sintering temperature. Additionally, it was shown that the densities of the BMN ceramic tablets vary with sintering temperature. The calculated theoretical density for the BMN ceramic tablets sintered at different temperatures is about 6.7521 . The density of the respective measured tablets is usually amounting more than 91% and 5 approaching a maximum value of 96.5% for sintering temperature of 1150°C. The microstructure was investigated by using Scanning Transmission Electron Microscope (STEM), X-ray diffraction (XRD). Combined with the results obtained from the STEM and XRD, the impact of sintering temperature on the macroscopic and microscopic structure was discussed. The relative dielectric constant ( ) and dielectric loss ( ) of the BMN solid solutions were measured to be 161-200 and (at room temperature and 100Hz-1MHz), respectively. The BMN solid

  19. Electroluminescence of cubic boron nitride single crystal flakes with color-zoning (United States)

    Liu, Xiuhuan; Wang, Shuang; Chen, Zhanguo; Jia, Gang; Bian, Tianliang; Hou, Lixin; Wang, Qi; Liu, Nian


    The current-voltage (I-V) characteristics and phenomena of electroluminescence of cubic boron nitride (cBN) single crystal flakes with color-zoning under extremely non-uniform electric fields (ENUEFs) induced by needle-plate electrodes were observed. When a cBN flake with sizes of 0.3×0.3×0.1 mm3 was tightly fixed between the tungsten needle and brass plate electrodes in the atmosphere, the I-V relationship exhibited nonlinearity, and peculiar phenomena of electroluminescence with bright blue-violet light appeared at the bias voltage in a range of 700-1200 V. The current-controlled differential negative resistance was synchronously observed. The electroluminescent phenomena were somewhat different for cases of the needle electrode respectively contacting to the amber and transparent zones. The electroluminescent radiations of cBN flakes biased at voltages with a range of 600-1550 V were also investigated in vacuum. In a vacuum chamber, the green emitting phosphor spread around the cBN flake might be excited by the vacuum ultraviolet (VUV) emission from the cBN crystal, and the green fluorescence was observed by naked eyes. The VUV radiation spectrum with a peak wavelength of 149 nm was measured. In the atmosphere, the blue-violet light emission may be the gas discharge resulted from the air ionization induced by the VUV emission from the cBN crystal under the ENUEF, and the ENUEF subsequently keeps the air discharging. The VUV emission from the cBN crystal under the ENUEF can be caused by the original interband transition and the subsequent intraband transfer for electrons, and the final electron-hole direct recombination.

  20. Nonlinear dynamic susceptibilities of interacting and noninteracting magnetic nanoparticles

    CERN Document Server

    Joensson, P; García-Palacios, J L; Svedlindh, P


    The linear and cubic dynamic susceptibilities of solid dispersions of nanosized maghemite gamma-Fe sub 2 O sub 3 particles have been measured for three samples with a volume concentration of magnetic particles ranging from 0.3% to 17%, in order to study the effect of dipole-dipole interactions. Significant differences between the dynamic response of the samples are observed. While the linear and cubic dynamic susceptibilities of the most dilute sample compare reasonably well with the corresponding expressions proposed by Raikher and Stepanov for noninteracting particles, the nonlinear dynamic response of the most concentrated sample exhibits at low temperatures similar features as observed in a Ag(11 at% Mn) spin glass.

  1. Liquid water in the domain of cubic crystalline ice Ic (United States)

    Jenniskens, P.; Banham, S. F.; Blake, D. F.; McCoustra, M. R.


    Vapor-deposited amorphous water ice when warmed above the glass transition temperature (120-140 K), is a viscous liquid which exhibits a viscosity vs temperature relationship different from that of liquid water at room temperature. New studies of thin water ice films now demonstrate that viscous liquid water persists in the temperature range 140-210 K. where it coexists with cubic crystalline ice. The liquid character of amorphous water above the glass transition is demonstrated by (1) changes in the morphology of water ice films on a nonwetting surface observed in transmission electron microscopy (TEM) at around 175 K during slow warming, (2) changes in the binding energy of water molecules measured in temperature programmed desorption (TPD) studies, and (3) changes in the shape of the 3.07 micrometers absorption band observed in grazing angle reflection-absorption infrared spectroscopy (RAIRS) during annealing at high temperature. whereby the decreased roughness of the water surface is thought to cause changes in the selection rules for the excitation of O-H stretch vibrations. Because it is present over such a wide range of temperatures, we propose that this form of liquid water is a common material in nature. where it is expected to exist in the subsurface layers of comets and on the surfaces of some planets and satellites.


    Directory of Open Access Journals (Sweden)

    STACHEL Hellmuth


    On each strophoid there is a symmetric relation of points, so-called ‘associated’ points, with a series of properties: The lines connecting associated points P and P’ are tangent of the negative pedal curve. Tangents at associated points intersect at a point which again lies on the cubic. For all pairs (P, P’ of associated points, the midpoints lie on a line through the node N. For any two pairs (P, P’ and (Q, Q’ of associated points, the points of intersection between the lines PQ and P’Q’ as well as between PQ’ and P’Q are again placed on the strophoid and mutually associated. The lines PQ and PQ’ are symmetric with respect to the line connecting P with the node. Thus, strophoids generalize Apollonian circles: For given non-collinear points A, A’ and N the locus of points X such that one angle bisector of the lines XA and XA’ passes through N is a strophoid.

  3. Cubic Phase Formation in Phospholipid and PEG-Lipid Mixtures (United States)

    Murley, Kimberly; Cunningham, Beth; Wolfe, David; Williams, Patrick


    Lipid systems modeling cell membranes are capable of self-assembling into various liquid crystal mesophases with varying geometry and dimensions. We have suggested that it is possible to engineer the lipid systems through the incorporation of covalently attached polymer lipids to produce unique effects. The results of this engineering process include both the stabilization of lipid phases that normally exist over very limited temperature ranges and the induction of novel phases that are not normally present in the parent lipid. In this study, we used x-ray diffraction and NMR to investigate the phase behavior of the DOPE:PEG:MO and MO:PEG:D2O systems with varying molar ratios and PEG sizes. The phase diagram which we have generated indicates the conditions necessary to induce specific phase structures and sizes into three-dimensional cubic lipid systems. This information may be useful to create nanostructures which will be valuable in applications such as protein crystallization and protein biochip development.

  4. Research of Cubic Bezier Curve NC Interpolation Signal Generator

    Directory of Open Access Journals (Sweden)

    Shijun Ji


    Full Text Available Interpolation technology is the core of the computer numerical control (CNC system, and the precision and stability of the interpolation algorithm directly affect the machining precision and speed of CNC system. Most of the existing numerical control interpolation technology can only achieve circular arc interpolation, linear interpolation or parabola interpolation, but for the numerical control (NC machining of parts with complicated surface, it needs to establish the mathematical model and generate the curved line and curved surface outline of parts and then discrete the generated parts outline into a large amount of straight line or arc to carry on the processing, which creates the complex program and a large amount of code, so it inevitably introduce into the approximation error. All these factors affect the machining accuracy, surface roughness and machining efficiency. The stepless interpolation of cubic Bezier curve controlled by analog signal is studied in this paper, the tool motion trajectory of Bezier curve can be directly planned out in CNC system by adjusting control points, and then these data were put into the control motor which can complete the precise feeding of Bezier curve. This method realized the improvement of CNC trajectory controlled ability from the simple linear and circular arc to the complex project curve, and it provides a new way for economy realizing the curve surface parts with high quality and high efficiency machining.

  5. Cubic mesoporous Ag@CN: a high performance humidity sensor. (United States)

    Tomer, Vijay K; Thangaraj, Nishanthi; Gahlot, Sweta; Kailasam, Kamalakannan


    The fabrication of highly responsive, rapid response/recovery and durable relative humidity (%RH) sensors that can precisely monitor humidity levels still remains a considerable challenge for realizing the next generation humidity sensing applications. Herein, we report a remarkably sensitive and rapid %RH sensor having a reversible response using a nanocasting route for synthesizing mesoporous g-CN (commonly known as g-C3N4). The 3D replicated cubic mesostructure provides a high surface area thereby increasing the adsorption, transmission of charge carriers and desorption of water molecules across the sensor surfaces. Owing to its unique structure, the mesoporous g-CN functionalized with well dispersed catalytic Ag nanoparticles exhibits excellent sensitivity in the 11-98% RH range while retaining high stability, negligible hysteresis and superior real time %RH detection performances. Compared to conventional resistive sensors based on metal oxides, a rapid response time (3 s) and recovery time (1.4 s) were observed in the 11-98% RH range. Such impressive features originate from the planar morphology of g-CN as well as unique physical affinity and favourable electronic band positions of this material that facilitate water adsorption and charge transportation. Mesoporous g-CN with Ag nanoparticles is demonstrated to provide an effective strategy in designing high performance %RH sensors and show great promise for utilization of mesoporous 2D layered materials in the Internet of Things and next generation humidity sensing applications.

  6. Serial femtosecond crystallography of soluble proteins in lipidic cubic phase

    Energy Technology Data Exchange (ETDEWEB)

    Fromme, Raimund; Ishchenko, Andrii; Metz, Markus; Chowdhury, Shatabdi Roy; Basu, Shibom; Boutet, Sébastien; Fromme, Petra; White, Thomas A.; Barty, Anton; Spence, John C. H.; Weierstall, Uwe; Liu, Wei; Cherezov, Vadim


    Serial femtosecond crystallography (SFX) at X-ray free-electron lasers (XFELs) enables high-resolution protein structure determination using micrometre-sized crystals at room temperature with minimal effects from radiation damage. SFX requires a steady supply of microcrystals intersecting the XFEL beam at random orientations. An LCP–SFX method has recently been introduced in which microcrystals of membrane proteins are grown and delivered for SFX data collection inside a gel-like membrane-mimetic matrix, known as lipidic cubic phase (LCP), using a special LCP microextrusion injector. Here, it is demonstrated that LCP can also be used as a suitable carrier medium for microcrystals of soluble proteins, enabling a dramatic reduction in the amount of crystallized protein required for data collection compared with crystals delivered by liquid injectors. High-quality LCP–SFX data sets were collected for two soluble proteins, lysozyme and phycocyanin, using less than 0.1 mg of each protein.

  7. Anti-phase domains in cubic GaN

    Energy Technology Data Exchange (ETDEWEB)

    Maria Kemper, Ricarda; Schupp, Thorsten; Haeberlen, Maik; Lindner, Joerg; Josef As, Donat [University of Paderborn, Department of Physics, Warburger Str. 100, D-33098 Paderborn (Germany); Niendorf, Thomas; Maier, Hans-Juergen [University of Paderborn, Lehrstuhl fuer Werkstoffkunde, Pohlweg 47-49, D-33098 Paderborn (Germany); Dempewolf, Anja; Bertram, Frank; Christen, Juergen [University of Magdeburg, Institut fuer Festkoerperphysik, P.O. Box 4120, D-39016 Magdeburg (Germany); Kirste, Ronny; Hoffmann, Axel [Technische Universitaet Berlin, Institute of Solid State Physics, Hardenbergstr. 36, D-10623 Berlin (Germany)


    The existence of anti-phase domains in cubic GaN grown on 3C-SiC/Si (001) substrates by plasma-assisted molecular beam epitaxy is reported. The influence of the 3C-SiC/Si (001) substrate morphology is studied with emphasis on the anti-phase domains (APDs). The GaN nucleation is governed by the APDs of the substrate, resulting in equal plane orientation and the same anti-phase boundaries. The presence of the APDs is independent of the GaN layer thickness. Atomic force microscopy surface analysis indicates lateral growth anisotropy of GaN facets in dependence of the APD orientation. This anisotropy can be linked to Ga and N face types of the {l_brace}111{r_brace} planes, similar to observations of anisotropic growth in 3C-SiC. In contrast to 3C-SiC, however, a difference in GaN phase composition for the two types of APDs can be measured by electron backscatter diffraction, {mu}-Raman and cathodoluminescence spectroscopy.

  8. Double-valued representations of the four-dimensional cubic lattice rotation group

    Energy Technology Data Exchange (ETDEWEB)

    Mandula, J.E.; Shpiz, E. (Washington Univ., St. Louis, MO (USA). Dept. of Physics)


    The double-valued representations of the rotation symmetry group of the four-dimensional cubic lattice are described. Their connections with double-valued representations of the three-dimensional cubic lattice rotation group and of the continuous O(3) and O(4) groups are given in detail.

  9. Double-valued representations of the four-dimensional cubic lattice rotation group (United States)

    Mandula, Jeffrey E.; Shpiz, Edward


    The double-valued representations of the rotation symmetry group of the four-dimensional cubic lattice are described. Their connections with double-valued representations of the three-dimensional cubic lattice rotation group and of the continuous O(3) and O(4) groups are given in detail.

  10. Extending a Property of Cubic Polynomials to Higher-Degree Polynomials (United States)

    Miller, David A.; Moseley, James


    In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

  11. The double-end-pumped cubic Nd: YVO4 laser: Temperature ...

    Indian Academy of Sciences (India)


    Nov 27, 2015 ... Thermal effects of a double-end-pumped cubic Nd:YVO4 laser crystal are investigated in this paper. A detailed analysis of temperature distribution and thermal stress in cubic crystal with circular shape pumping is discussed. It has been shown that by considering the total input powers as constant, the ...

  12. Cubic Invariant Spherical Surface Harmonics in Conjunction With Diffraction Strain Pole-Figures

    NARCIS (Netherlands)

    Brakman, C.M.


    Four kinds of cubic invariant spherical surface harmonics are introduced. It has been shown previously that these harmonics occur in the equations relating measured diffraction (line-shift) elastic strain and macro-stresses generating these strains for the case of textured cubic materials. As a

  13. Defect structure of cubic solid solutions of alkaline earth and rare earth fluorides

    NARCIS (Netherlands)

    DenHartog, HW


    In this paper we will consider the disorder in some cubic solid solutions consisting of one of the alkaline earth fluorides and one of the rare earth fluorides. This is an attractive group of model materials, because these materials have a rather simple overall cubic structure. We will discuss the

  14. Nonlinear standing waves, resonance phenomena, and frequency characteristics of distributed systems (United States)

    Rudenko, O. V.


    This review is dedicated to resonator oscillations under conditions of a strongly expressed nonlinearity under which steep shock fronts emerge in the wave profiles. Models and approximated methods for their analysis for quadratic and cubic nonlinear media are examined, as well as for nonlinearity when taking into account the mobility of boundaries. The forms of the profiles are calculated both for a steady-state oscillation regime and during the establishment of the profiles. Dissipative losses and selective losses at specially chosen frequencies are considered. An analysis of nonlinear Q-factor is given. The possibility of increasing the acoustic energy accumulated in the cavity of the resonator is discussed. Special attention is given to various physical phenomena that are exhibited only in nonlinear acoustic fields.

  15. Modulation stability and optical soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms and its applications (United States)

    Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen


    In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.

  16. Nonlinear graphene plasmonics (United States)

    Ooi, Kelvin J. A.; Tan, Dawn T. H.


    The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.

  17. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng


    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  18. Hidden Statistics of Schroedinger Equation (United States)

    Zak, Michail


    Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.

  19. Quantum effective potential, electron transport and conformons in biopolymers

    Energy Technology Data Exchange (ETDEWEB)

    Dandoloff, Rossen [Laboratoire de Physique Theorique et Modelisation, Universite de Cergy-Pontoise, F-95302 Cergy-Pontoise (France); Balakrishnan, Radha [The Institute of Mathematical Sciences, Chennai 600113 (India)


    In the Kirchhoff model of a biopolymer, conformation dynamics can be described in terms of solitary waves, for certain special cross-section asymmetries. Applying this to the problem of electron transport, we show that the quantum effective potential arising due to the bends and twists of the polymer enables us to formalize and quantify the concept of a conformon that has been hypothesized in biology. Its connection to the soliton solution of the cubic nonlinear Schroedinger equation emerges in a natural fashion.

  20. Nonlinear evolution equations

    CERN Document Server

    Uraltseva, N N


    This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

  1. Organic nonlinear optical materials (United States)

    Umegaki, S.


    Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.

  2. Ultrafast Nonlinear Optical Spectroscopy

    National Research Council Canada - National Science Library

    Wagner, Kelvin


    We have developed an Ultrafast optical nonlinear spectroscopy facility with the motivation of studying spatio-temporal soliton interactions for all-optical switching application and several associated...

  3. NC-TODIM-Based MAGDM under a Neutrosophic Cubic Set Environment

    Directory of Open Access Journals (Sweden)

    Surapati Pramanik


    Full Text Available A neutrosophic cubic set is the hybridization of the concept of a neutrosophic set and an interval neutrosophic set. A neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets has been reported in the current literature. In the present paper, we propose the score and accuracy functions for neutrosophic cubic sets and prove their basic properties. We also develop a strategy for ranking of neutrosophic cubic numbers based on the score and accuracy functions. We firstly develop a TODIM (Tomada de decisao interativa e multicritévio in the neutrosophic cubic set (NC environment, which we call the NC-TODIM. We establish a new NC-TODIM strategy for solving multi attribute group decision making (MAGDM in neutrosophic cubic set environment. We illustrate the proposed NC-TODIM strategy for solving a multi attribute group decision making problem to show the applicability and effectiveness of the developed strategy. We also conduct sensitivity analysis to show the impact of ranking order of the alternatives for different values of the attenuation factor of losses for multi-attribute group decision making strategies.

  4. Sustained small oscillations in nonlinear control systems. [launch vehicle dynamics (United States)

    George, J. H.; Gunderson, R. W.; Hahn, H.


    Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.

  5. Human middle-ear nonlinearity measurements using laser Doppler vibrometry (United States)

    Gladiné, Kilian; Muyshondt, Pieter G. G.; Dirckx, Joris J. J.


    It has long been supposed that the middle-ear has near to perfect linear characteristics, and several attempts have been made to investigate this hypothesis. In conclusion, the middle-ear was regarded as a linear system at least up till sound pressure levels of 120 dB. Because of the linear relationship between Doppler shift of light and the vibration velocity of the object on which the light is reflected, laser Doppler vibrometry (LDV) is an intrinsically highly linear measurement technique. Therefore it allows straightforward detection of very small nonlinearities in a vibration response. In this paper, laser Doppler vibrometry and multisine stimulation are used to detect nonlinear distortions in the vibration response at the umbo of the tympanic membrane of seven human cadaver temporal bones. Nonlinear distortions were detected starting from sound pressure levels of 99 dB and measurements were performed up to 120 dB. These distortions can be subdivided into even degree (e.g. quadratic distortion tones) and odd degree nonlinear distortions (e.g. cubic distortion tones). We illustrate that with odd multisine stimulation the level of even and odd degree nonlinear distortions can be investigated separately. In conclusion, laser Doppler vibrometry is an adequate tool to detect nonlinear distortions in the middle-ear system and to quantify the level of such distortions even at 57 dB below the vibration response. The possibility to analyze even degree and odd degree nonlinear distortion levels separately can help in future work to pinpoint the source of the nonlinearity.

  6. Chiral Surface Twists and Skyrmion Stability in Nanolayers of Cubic Helimagnets. (United States)

    Leonov, A O; Togawa, Y; Monchesky, T L; Bogdanov, A N; Kishine, J; Kousaka, Y; Miyagawa, M; Koyama, T; Akimitsu, J; Koyama, Ts; Harada, K; Mori, S; McGrouther, D; Lamb, R; Krajnak, M; McVitie, S; Stamps, R L; Inoue, K


    Theoretical analysis and Lorentz transmission electron microscopy (LTEM) investigations in an FeGe wedge demonstrate that chiral twists arising near the surfaces of noncentrosymmetric ferromagnets [Meynell et al., Phys. Rev. B 90, 014406 (2014)] provide a stabilization mechanism for magnetic Skyrmion lattices and helicoids in cubic helimagnet nanolayers. The magnetic phase diagram obtained for freestanding cubic helimagnet nanolayers shows that magnetization processes differ fundamentally from those in bulk cubic helimagnets and are characterized by the first-order transitions between modulated phases. LTEM investigations exhibit a series of hysteretic transformation processes among the modulated phases, which results in the formation of the multidomain patterns.

  7. Dislocation Velocities and Dislocation Structure in Cubic Zirconia and Sapphire (United States)

    Farber, Boris Yarovlevick

    The dislocation structure around elevated temperature indentations in 9.4 and 21 mol% rm Y_2O _3 fully-stabilized cubic ZrO_2 (c-ZrO_2) was investigated using selective etching and transmission electron microscopy (TEM). Cracking arising from interaction between slip bands was observed in the 21 mol% rm Y_2O _3 material, and direct evidence of the formation of Lomer type dislocation pile-ups leading to crack nucleation was obtained by TEM. Stress and temperature dependencies of the edge and screw dislocation velocities in c-ZrO_2 were measured. The activation energy for motion of the edge dislocations (5.0 +/- 0.4 eV) is slightly lower than that for screw dislocations (5.6 +/- 0.6 eV). The stress exponent (m) is close to 1 at low temperatures (stress relaxation in the vicinity of room temperature Knoop indents in c-ZrO_2 was investigated using photoelasticity method. A rapid low temperature stress relaxation was observed, and a mechanism was proposed. The temperature dependence of the Vickers hardness was measured on the basal (0001} and pyramidal {11|23} planes of single crystal alpha -Al_2O_3 (sapphire) from room temperature to 1273 K. The plastic zone surrounding the indents was investigated using selective etching and TEM. Indentation was accompanied by three competitive damage processes: fracture, twinning and dislocation plasticity. At room temperature, cracking predominated. At intermediate temperatures, extensive rhombohedral twinning was observed, while at higher temperatures, prismatic slip bands on {11|20} dominated the microstructure. The dislocation substructure at the vicinity of the indents consists of fairly straight dislocations lying on basal and/or prism planes and aligned along crystallographic directions. The details of the glide dissociation of perfect screw dislocations into three collinear partials, the mechanism of the microplasticity of sapphire single crystals, and details of the Peierls potential are discussed. An anomalously high low

  8. Lasers for nonlinear microscopy. (United States)

    Wise, Frank


    Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.

  9. Friction and nonlinear dynamics


    Manini, N.; Braun, O. M.; Tosatti, E.; Guerra, R.; Vanossi, A.


    The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.

  10. Nonlinear Maneuver Autopilot (United States)

    Menon, P. K. A.; Badgett, M. E.; Walker, R. A.


    Trajectory-control laws based on singular-perturbation theory and nonlinear dynamical modeling. Nonlinear maneuver autopilot commands flight-test trajectories of F-15 airplane. Underlying theory of controller enables separation of variables processed in fast and slow control loops, reducing amount of computation required.

  11. Nonlinear Optics and Applications (United States)

    Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)


    Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.

  12. Use of the Primitive Unit Cell in Understanding Subtle Features of the Cubic Closest-Packed Structure (United States)

    Hawkins, John A.; Rittenhouse, Jeffrey L.; Soper, Linda M.; Rittenhouse, Robert C.


    One of the most important crystal structures adopted by metals is characterized by the "abcabc"...stacking of close-packed layers. This structure is commonly referred to in textbooks as the cubic close-packed (ccp) or face-centered cubic (fcc) structure, since the entire lattice can be generated by replication of a face-centered cubic unit cell…

  13. Nonlinear optics and photonics

    CERN Document Server

    He, Guang S


    This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...

  14. Fourier-mode dynamics for the nonlinear Schrödinger equation in one-dimensional bounded domains. (United States)

    Caputo, J G; Efremidis, N K; Hang, Chao


    We analyze the 1D focusing nonlinear Schrödinger equation in a finite interval with homogeneous Dirichlet or Neumann boundary conditions. There are two main dynamics, the collapse which is very fast and a slow cascade of Fourier modes. For the cubic nonlinearity the calculations show no long-term energy exchange between Fourier modes as opposed to higher nonlinearities. This slow dynamics is explained by fairly simple amplitude equations for the resonant Fourier modes. Their solutions are well behaved so filtering high frequencies prevents collapse. Finally, these equations elucidate the unique role of the zero mode for the Neumann boundary conditions.

  15. Epitaxial growth and properties of cubic group III-nitride layers (United States)

    Schikora, D.; Schoettger, B.; As, Donat J.; Lischka, K.


    Single-phase cubic GaN and InN layers are grown by plasma assisted MBE. The temperature-dependence of the surface reconstruction is elaborated. The structural stability of the cubic growth in dependence of the growth stoichiometry is studied by RHEED measurements and numerical simulations of the experimental RHEED patterns. Growth oscillations on cubic GaN and during the growth of GaN-InN single quantum wells are recorded at nearly stoichiometric adatom coverage. Photoluminescence reveals the dominant optical transitions of cubic GaN and InN. Using in-situ RHEED to control the surface stoichiometry it is possible to grow N-stabilized layers resulting in intrinsic p-type GaN epilayers with hole concentrations of about p equals 1 X 1013 cm-3 and mobilities of about (mu) p equals 320 cm2/Vs, respectively.


    Energy Technology Data Exchange (ETDEWEB)

    Jiang, Weilin; Spurgeon, Steven R.; Liu, Jia; Edwards, Danny J.; Schreiber, Daniel K.; Henager, Charles H.; Kurtz, Richard J.; Wang, Yongqiang


    The aim of this study is to characterize precipitates in Mg+ ion implanted and high-temperature annealed cubic silicon carbide using scanning transmission electron microscopy, electron energy loss spectroscopy and atom probe tomography.

  17. Unified treatment of coupled optical and acoustic phonons in piezoelectric cubic materials

    DEFF Research Database (Denmark)

    Willatzen, Morten; Wang, Zhong Lin


    A unified treatment of coupled optical and acoustic phonons in piezoelectric cubic materials is presented whereby the lattice displacement vector and the internal ionic displacement vector are found simultaneously. It is shown that phonon couplings exist in pairs only; either between the electric...... potential and the lattice displacement coordinate perpendicular to the phonon wave vector or between the two other lattice displacement components. The former leads to coupled acousto-optical phonons by virtue of the piezoelectric effect. We then establish three new conjectures that entirely stem from...... piezoelectricity in a cubic structured material slab. First, it is shown that isolated optical phonon modes generally cannot exist in piezoelectric cubic slabs. Second, we prove that confined acousto-optical phonon modes only exist for a discrete set of in-plane wave numbers in piezoelectric cubic slabs. Third...

  18. Three-dimensional unsteady natural convection and entropy generation in an inclined cubical trapezoidal cavity with

    National Research Council Canada - National Science Library

    Ahmed Kadhim Hussein; Kolsi Lioua; Ramesh Chand; S. Sivasankaran; Rasoul Nikbakhti; Dong Li; Borjini Mohamed Naceur; Ben Aïssia Habib


    Numerical computation of unsteady laminar three-dimensional natural convection and entropy generation in an inclined cubical trapezoidal air-filled cavity is performed for the first time in this work...

  19. Cubic membranes: a legend beyond the Flatland* of cell membrane organization. (United States)

    Almsherqi, Zakaria A; Kohlwein, Sepp D; Deng, Yuru


    Cubic membranes represent highly curved, three-dimensional nanoperiodic structures that correspond to mathematically well defined triply periodic minimal surfaces. Although they have been observed in numerous cell types and under different conditions, particularly in stressed, diseased, or virally infected cells, knowledge about the formation and function of nonlamellar, cubic structures in biological systems is scarce, and research so far is restricted to the descriptive level. We show that the "organized smooth endoplasmic reticulum" (OSER; Snapp, E.L., R.S. Hegde, M. Francolini, F. Lombardo, S. Colombo, E. Pedrazzini, N. Borgese, and J. Lippincott-Schwartz. 2003. J. Cell Biol. 163:257-269), which is formed in response to elevated levels of specific membrane-resident proteins, is actually the two-dimensional representation of two subtypes of cubic membrane morphology. Controlled OSER induction may thus provide, for the first time, a valuable tool to study cubic membrane formation and function at the molecular level.

  20. Vibration mitigation of a bridge cable using a nonlinear energy sink: design and experiment

    Directory of Open Access Journals (Sweden)

    Weiss Mathieu


    Full Text Available This work deals with the design and experiment of a cubic nonlinear energy sink (NES for horizontal vibration mitigation of a bridge cable. Modal analysis of horizontal linear modes of the cable is experimentally performed using accelerometers and displacement sensors. A theoretical simplified 2-dof model of the coupled cable-NES system is used to analytically design the NES by mean of multi-time scale systems behaviours and detection its invariant manifold, equilibrium and singular points which stand for periodic and strongly modulated regimes, respectively. Numerical integration is used to confirm the efficiency of the designed NES for the system under step release excitation. Then, the prototype system is built using geometrical cubic nonlinearity as the potential of the NES. Efficiency of the prototype system for mitigation of horizontal vibrations of the cable under for step release and forced excitations is experimentally demonstrated.

  1. Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models. (United States)

    Low, Ian; Yin, Zhewei


    We present a Ward identity for nonlinear sigma models using generalized nonlinear shift symmetries, without introducing current algebra or coset space. The Ward identity constrains correlation functions of the sigma model such that the Adler's zero is guaranteed for S-matrix elements, and gives rise to a subleading single soft theorem that is valid at the quantum level and to all orders in the Goldstone decay constant. For tree amplitudes, the Ward identity leads to a novel Berends-Giele recursion relation as well as an explicit form of the subleading single soft factor. Furthermore, interactions of the cubic biadjoint scalar theory associated with the single soft limit, which was previously discovered using the Cachazo-He-Yuan representation of tree amplitudes, can be seen to emerge from matrix elements of conserved currents corresponding to the generalized shift symmetry.

  2. Quantitative determination of hexagonal minority phase in cubic GaN using Raman spectroscopy (United States)

    Siegle, H.; Eckey, L.; Hoffmann, A.; Thomsen, C.; Meyer, B. K.; Schikora, D.; Hankeln, M.; Lischka, K.


    We show that Raman scattering is a very sensitive and straightforward tool for the quantitative determination of a structural minority phase in GaN. In- and on-plane excitations, as well as polarization dependent measurements on predominantly cubic and hexagonal GaN samples, were performed and forward scattering effects were found. We were able to verify as an example the phase purity of a cubic GaN sample down to the 1% level.

  3. Cubic and quartic planar differential systems with exact algebraic limit cycles

    Directory of Open Access Journals (Sweden)

    Ahmed Bendjeddou


    Full Text Available We construct cubic and quartic polynomial planar differential systems with exact limit cycles that are ovals of algebraic real curves of degree four. The result obtained for the cubic case generalizes a proposition of [9]. For the quartic case, we deduce for the first time a class of systems with four algebraic limit cycles and another for which nested configurations of limit cycles occur.

  4. Selective Chemical Vapor Deposition Growth of Cubic FeGe Nanowires That Support Stabilized Magnetic Skyrmions. (United States)

    Stolt, Matthew J; Li, Zi-An; Phillips, Brandon; Song, Dongsheng; Mathur, Nitish; Dunin-Borkowski, Rafal E; Jin, Song


    Magnetic skyrmions are topologically stable vortex-like spin structures that are promising for next generation information storage applications. Materials that host magnetic skyrmions, such as MnSi and FeGe with the noncentrosymmetric cubic B20 crystal structure, have been shown to stabilize skyrmions upon nanostructuring. Here, we report a chemical vapor deposition method to selectively grow nanowires (NWs) of cubic FeGe out of three possible FeGe polymorphs for the first time using finely ground particles of cubic FeGe as seeds. X-ray diffraction and transmission electron microscopy (TEM) confirm that these micron-length NWs with ∼100 nm to 1 μm diameters have the cubic B20 crystal structure. Although Fe 13 Ge 8 NWs are also formed, the two types of NWs can be readily differentiated by their faceting. Lorentz TEM imaging of the cubic FeGe NWs reveals a skyrmion lattice phase under small applied magnetic fields (∼0.1 T) at 233 K, a skyrmion chain state at lower temperatures (95 K) and under high magnetic fields (∼0.4 T), and a larger skyrmion stability window than bulk FeGe. This synthetic approach to cubic FeGe NWs that support stabilized skyrmions opens a route toward the exploration of new skyrmion physics and devices based on similar nanostructures.

  5. Nonlinear Geometric and Material Behavior of Composite Shells with Large Strains (United States)


    B.S., M.S. Captain, USAF Approved: /A4. N. P la tto, Ch r n 7 Profesor , Depart en of Aeronautics & Astronautics P J. Torvik DATE Professor...complexities. For composite shells, some studies use a first-order transverse shear theory with bi-linear elas- tic -plastic material behavior [6, 10, 13, 16...the classical thin shell. Investigations of the limitations of elastic-plas- tic cubic-nonlinear HTSD theory were based on the shallow isotropic shell

  6. On the theory of weak turbulence for the nonlinear Schrödinger equation

    CERN Document Server

    Escobedo, M


    The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.

  7. Non-linear oscillations

    CERN Document Server

    Hagedorn, Peter


    Thoroughly revised and updated, the second edition of this concise text provides an engineer's view of non-linear oscillations, explaining the most important phenomena and solution methods. Non-linear descriptions are important because under certain conditions there occur large deviations from the behaviors predicted by linear differential equations. In some cases, completely new phenomena arise that are not possible in purely linear systems. The theory of non-linear oscillations thus has important applications in classical mechanics, electronics, communications, biology, and many other branches of science. In addition to many other changes, this edition has a new section on bifurcation theory, including Hopf's theorem.

  8. Nonlinear fiber optics

    CERN Document Server

    Agrawal, Govind P


    The Optical Society of America (OSA) and SPIE - The International Society for Optical Engineering have awarded Govind Agrawal with an honorable mention for the Joseph W. Goodman Book Writing Award for his work on Nonlinear Fiber Optics, 3rd edition.Nonlinear Fiber Optics, 3rd Edition, provides a comprehensive and up-to-date account of the nonlinear phenomena occurring inside optical fibers. It retains most of the material that appeared in the first edition, with the exception of Chapter 6, which is now devoted to the polarization effects relevant for light propagation in optical

  9. Nonlinear wave equations

    CERN Document Server

    Li, Tatsien


    This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

  10. Nonlinear Source Emulator

    DEFF Research Database (Denmark)

    Nguyen-Duy, Khiem

    and remains the prime source of energy in non-terrestrial applications such as those in sky-explorers. However, a renewable energy source is expensive, bulky, and its performance is weather dependent, which make testing of downstream converters very difficult. As a result, a nonlinear source emulator (NSE...... generator unit. Because nonlinear energy sources come in different sizes and power rating, a single NSE may not be sufficient to simulate a wide selection of nonlinear sources. For this reason, the proposed NSE system is realized as modules. Stacking or connecting multiple modules in parallel will allow...

  11. Determining Parameters of Fractional-Exponential Heredity Kernels of Nonlinear Viscoelastic Materials (United States)

    Golub, V. P.; Pavlyuk, Ya. V.; Fernati, P. V.


    The problem of determining the parameters of fractional-exponential heredity kernels of nonlinear viscoelastic materials is solved. The methods for determining the parameters that are used in the cubic theory of viscoelasticity and the nonlinear theories based on the conditions of similarity of primary creep curves and isochronous creep diagrams are analyzed. The parameters of fractional-exponential heredity kernels are determined and experimentally validated for the oriented polypropylene, FM3001 and FM10001 nylon fibers, microplastics, TC 8/3-250 glass-reinforced plastic, SWAM glass-reinforced plastic, and contact molding glass-reinforced plastic.

  12. The Equivalent Linearization Method with a Weighted Averaging for Analyzing of Nonlinear Vibrating Systems

    Directory of Open Access Journals (Sweden)

    N. D. Anh

    Full Text Available Abstract In this paper, the Equivalent Linearization Method (ELM with a weighted averaging, which is proposed by Anh (Anh, 2015, is applied to analyze some vibrating systems with nonlinearities. The strongly nonlinear Duffing oscillator with third, fifth, and seventh powers of the amplitude, the other strongly nonlinear oscillators and the cubic Duffing with discontinuity are considered. The results obtained via this method are compared with the ones achieved by the Min-Max Approach (MMA, the Modified Lindstedt - Poincare Method (MLPM, the Parameter - Expansion Method (PEM, the Homotopy Perturbation Method (HPM and 4th order Runge-Kutta method. The obtained results demonstrate that this method is very convenient for solving nonlinear equations and also can be successfully exerted to a lot of practical engineering and physical problems.

  13. Introduction to nonlinear science

    CERN Document Server

    Nicolis, G


    One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...

  14. Crossing a Nonlinear Resonance

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 9. Crossing a Nonlinear Resonance: Adiabatic Invariants and the Melnikov-Arnold Integral. Sudhir R Jain. General Article Volume 19 Issue 9 September 2014 pp 797-813 ...

  15. Nonlinearity in nanomechanical cantilevers

    DEFF Research Database (Denmark)

    Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.


    Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development....... In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its...... predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory...

  16. Nonlinear differential equations

    CERN Document Server

    Struble, Raimond A


    Detailed treatment covers existence and uniqueness of a solution of the initial value problem, properties of solutions, properties of linear systems, stability of nonlinear systems, and two-dimensional systems. 1962 edition.

  17. Nonlinear Correlation Spectroscopy (NLCS)


    Geissbuehler, Matthias; Bonacina, Luigi; Shcheslavskiy, Vladislav; Bocchio, Noelia L.; Geissbuehler, Stefan; Leutenegger, Marcel; Maerki, Iwan; Wolf, Jean-Pierre; Lasser, Theo


    We present a novel concept for optical spectroscopy called nonlinear correlation spectroscopy (NLCS). NLCS analyses coherent field fluctuations of the second and third harmonic light generated by diffusing nanoparticles. Particles based on noncentrosymmetric nonlinear materials such as KNbO(3) show a strong second as well as third harmonic response. The method and the theory are introduced and experimental NLCS results in fetal calf serum are presented showing the promising selectivity of thi...

  18. Terahertz semiconductor nonlinear optics

    DEFF Research Database (Denmark)

    Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias


    In this proceedings we describe our recent results on semiconductor nonlinear optics, investigated using single-cycle THz pulses. We demonstrate the nonlinear absorption and self-phase modulation of strong-field THz pulses in doped semiconductors, using n-GaAs as a model system. The THz nonlinear......In this proceedings we describe our recent results on semiconductor nonlinear optics, investigated using single-cycle THz pulses. We demonstrate the nonlinear absorption and self-phase modulation of strong-field THz pulses in doped semiconductors, using n-GaAs as a model system. The THz...... is determined by (but not equal to) the electron momentum relaxation rate. Single cycle pulses of light, irrespective of the frequency range to which they belong, inherently have an ultrabroadband spectrum covering many octaves of frequencies. Unlike the single-cycle pulses in optical domain, the THz pulses can...... be easily sampled with sub-cycle resolution using conventional femtosecond lasers. This makes the THz pulses accessible model tools for direct observation of general nonlinear optical phenomena occurring in the single-cycle regime....

  19. Nonlinear Multiantenna Detection Methods

    Directory of Open Access Journals (Sweden)

    Chen Sheng


    Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.

  20. Handbook of nonlinear optical crystals

    CERN Document Server

    Dmitriev, Valentin G; Nikogosyan, David N


    This Handbook of Nonlinear Optical Crystals provides a complete description of the properties and applications of nonlinear crystals In addition, it presents the most important equations for calculating the main parameters of nonlinear frequency converters This comprehensive reference work will be of great value to all scientists and engineers working in nonlinear optics, quantum electronics and laser physics

  1. Nonlinear Analysis in Counseling Research (United States)

    Balkin, Richard S.; Richey Gosnell, Katelyn M.; Holmgren, Andrew; Osborne, Jason W.


    Nonlinear effects are both underreported and underrepresented in counseling research. We provide a rationale for evaluating nonlinear effects and steps to evaluate nonlinear relationships in counseling research. Two heuristic examples are provided along with discussion of the results and advantages to evaluating nonlinear effects.

  2. Nonlinear reflection of shock shear waves in soft elastic media. (United States)

    Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël


    For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.

  3. Detecting accelerometric nonlinearities in the international space station (United States)

    Sáez, N.; Gavaldà, Jna.; Ruiz, X.; Shevtsova, V.


    The present work aims to study mechanical nonlinearities detected in the accelerometric records during a thermodiffusion experiment performed at the International Space Station, ISS. In that experiment the test cell was subjected to harmonic vibrations of different frequencies and amplitudes. Accelerometric data associated to the runs were downloaded from NASA PIMS website. Second order spectral analysis shows that the shaker modifies the normality of the data and introduces nonlinearities in the distribution of energy. High Order Spectral Analysis, HOSA, based on the bispectrum, bicoherence, trispectrum and tricoherence functions enabled us to study the kind of these nonlinearities. Additionally, a new method using the biphase and triphase histograms helps us to assess if quadratic and/or cubic phase coupling mechanisms are responsible for the anomalous nonlinear energy transfer detected. Finally, the RMS acceleration values are investigated to check if the vibratory limit requirements of the ISS are exceeded. This methodology is important not only in generic research of aerospace engineering but also in space sciences in order to help space researchers to characterize more globally their experiments. It is mentioned finally that HOSA techniques are not new, but never have been used in the analysis of accelerometric data coming from the ISS.

  4. Nonlinear Approaches in Engineering Applications

    CERN Document Server

    Jazar, Reza


    Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...

  5. Soliton compression to few-cycle pulses with a high quality factor by engineering cascaded quadratic nonlinearities

    DEFF Research Database (Denmark)

    Zeng, Xianglong; Guo, Hairun; Zhou, Binbin


    We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression...... with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest...... soliton order, which is kept larger than unity to ensure further compression. This is done by increasing the cascaded quadratic nonlinearity in the new section with an engineered reduced residual phase mismatch. The low soliton orders in each section ensure excellent pulse quality and high efficiency...

  6. Nonlinear Dynamics of a Magnetically Driven Duffing-Type Spring-Magnet Oscillator in the Static Magnetic Field of a Coil (United States)

    Donoso, Guillermo; Ladera, Celso L.


    We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the…

  7. Zone-Center Raman Active Modes In Cubic And Hexagonal Diamond (United States)

    Mehl, Michael J.; Pickard, Warren E.


    The recent interest in the growth of thin diamond films has led us to consider the differences between the hexagonal (lonsdaleite) and cubic structures. Both phases have very similar properties, and empirical and theoretical considerations indicate that their structural energies are nearly identical. When thin films are grown the hexagonal phase may compete with the cubic phase, making characterization of the film difficult. Cubic diamond has one Raman active mode, while hexagonal diamond has three. The opportunity thus exists for Raman spectroscopy to differentiate between the two tetrahedrally bonded phases (as well as "amorphous" or graphitic phases). Electronic structure calculations can be used to obtain theoretical Q=0 frequencies of the Raman active modes in both structures. We have used the first principles Linearized Augmented Plane Wave method within the local density approximation to calculate the zone center phonon frequencies. The calculated frequency of the cubic diamond Raman mode is 1336 cm-1, very close to the experimental value of 1333 cm-1. Our calculations indicate that the hexagonal structure A t has a zone-center frequency of 1269 cm-1, the Elg mode is at 1215 cm-1, and the E1g mode is at 430 cm-1. Anharmonic corrections are rather large (2-3%) in the cubic diamond Raman mode and in the hexagonal Al mode, but are not important in the E2g and Elg modes. We will compare our results with the available experimental information.

  8. Development of Technology Parameter Towards Shipbuilding Productivity Predictor Using Cubic Spline Approach

    Directory of Open Access Journals (Sweden)

    Bagiyo Suwasono


    Full Text Available Ability of production processes associated with state-of-the-art technology, which allows the shipbuilding, is customized with modern equipment. It will give impact to level of productivity and competitiveness. This study proposes a nonparametric regression cubic spline approach with 1 knot, 2 knots, and 3 knots. The application programs Tibco Spotfire S+ showed that a cubic spline with 2 knots (4.25 and 4.50 gave the best result with the value of GCV = 56.21556, and R2 = 94.03%.Estimation result of cubic spline with 2 knots for the PT. Batamec shipyard = 35.61 MH/CGT, PT. Dok & Perkapalan Surabaya = 27.49 MH/CGT, PT. Karimun Sembawang Shipyard = 27.49 MH/CGT, and PT. PAL Indonesia = 19.89 MH/CGT.

  9. Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Method

    Directory of Open Access Journals (Sweden)

    Jun Ye


    Full Text Available To describe both certain linguistic neutrosophic information and uncertain linguistic neutrosophic information simultaneously in the real world, this paper originally proposes the concept of a linguistic neutrosophic cubic number (LNCN, including an internal LNCN and external LNCN. In LNCN, its uncertain linguistic neutrosophic number consists of the truth, indeterminacy, and falsity uncertain linguistic variables, and its linguistic neutrosophic number consists of the truth, indeterminacy, and falsity linguistic variables to express their hybrid information. Then, we present the operational laws of LNCNs and the score, accuracy, and certain functions of LNCN for comparing/ranking LNCNs. Next, we propose a LNCN weighted arithmetic averaging (LNCNWAA operator and a LNCN weighted geometric averaging (LNCNWGA operator to aggregate linguistic neutrosophic cubic information and discuss their properties. Further, a multiple attribute decision-making method based on the LNCNWAA or LNCNWGA operator is developed under a linguistic neutrosophic cubic environment. Finally, an illustrative example is provided to indicate the application of the developed method.

  10. Cubic Copper Hexacyanoferrates Nanoparticles: Facile Template-Free Deposition and Electrocatalytic Sensing Towards Hydrazine

    Directory of Open Access Journals (Sweden)

    Xingxing Wang


    Full Text Available Cubic copper hexacyanoferrate (CuHCF nanoparticles prepared via electrolytic deposition are presented with their morphology and crystalline structure characterized with SEM and XRD. The advantage of this methodology is that it allows the fabrication of uniform cubic nanoparticles with permeable structures onto the desired underlying electrode substrate. It was observed that the CuHCF film acts as a permeable membrane for cations such as K+, Na+, Li+, and NH4+ with a selection order of K+> Li+>NH4+> Na+. Furthermore, the analytical utility of these cubic-like CuHCF morphologies supported on a glassy carbon electrode was evaluated towards the electrochemical oxidation of hydrazine which was found to exhibit a linear response over the range 66 M to 17 mM with a detection limit corresponding to 16.5 M.

  11. Nonlinear dynamics of structures

    CERN Document Server

    Oller, Sergio


    This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics.   This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects.   Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution  are studied, and the theoretical concepts and its programming algorithms are presented.  

  12. Multidimensional nonlinear descriptive analysis

    CERN Document Server

    Nishisato, Shizuhiko


    Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for futu...

  13. Nonlinear elastic waves in materials

    CERN Document Server

    Rushchitsky, Jeremiah J


    The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...

  14. Nonlinear Optical Properties of Materials

    CERN Document Server

    Ganeev, Rashid A


    This book is mostly concerned on the experimental research of the nonlinear optical characteristics of various media, low- and high-order harmonic generation in different materials, and formation, and nonlinear optical characterization of clusters. We also demonstrate the inter-connection between these areas of nonlinear optics.   Nonlinear optical properties of media such as optical limiting can be applied in various areas of science and technology. To define suitable materials for these applications, one has to carefully analyse the nonlinear optical characteristics of various media, such as the nonlinear refractive indices, coefficients of nonlinear absorption, saturation absorption intensities, etc. Knowing the nonlinear optical parameters of materials is also important for describing the propagation effects, self-interaction of intense laser pulses, and optimisation of various nonlinear optical processes. Among those processes one can admit the importance of the studies of the frequency conversion of c...

  15. On the scenario of reconnection in non-twist cubic maps

    Energy Technology Data Exchange (ETDEWEB)

    Tigan, Gheorghe [Department of Mathematics, ' Politehnica' University of Timisoara, Pta Victoriei, No. 2, 300006 Timisoara, Timis (Romania)]. E-mail:


    In this paper, we study the reconnection process in the dynamics of cubic non-twist maps, introduced in [Howard JE, Humpherys J. Nonmonotonic twist maps. Physica D 1995; 256-76]. In order to describe the route to reconnection of the involved Poincare-Birkhoff chains we investigate an approximate interpolating Hamiltonian of the map under study. Our study reveals that the scenario of reconnection of cubic non-twist maps is different from that occurring in the dynamics of quadratic non-twist maps.

  16. Analysis of moderately thin-walled beam cross-sections by cubic isoparametric elements

    DEFF Research Database (Denmark)

    Høgsberg, Jan Becker; Krenk, Steen


    In technical beam theory the six equilibrium states associated with homogeneous tension, bending, shear and torsion are treated as individual load cases. This enables the formulation of weak form equations governing the warping from shear and torsion. These weak form equations are solved...... numerically by introducing a cubic-linear two-dimensional isoparametric element. The cubic interpolation of this element accurately represents quadratic shear stress variations along cross-section walls, and thus moderately thin-walled cross-sections are effectively discretized by these elements. The ability...

  17. Cubic systems with invariant affine straight lines of total parallel multiplicity seven

    Directory of Open Access Journals (Sweden)

    Alexandru Suba


    Full Text Available In this article, we study the planar cubic differential systems with invariant affine straight lines of total parallel multiplicity seven. We classify these system according to their geometric properties encoded in the configurations of invariant straight lines. We show that there are only 17 different topological phase portraits in the Poincar\\'e disc associated to this family of cubic systems up to a reversal of the sense of their orbits, and we provide representatives of every class modulo an affine change of variables and rescaling of the time variable.

  18. Preconditioning cubic spline collocation method by FEM and FDM for elliptic equations

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Sang Dong [KyungPook National Univ., Taegu (Korea, Republic of)


    In this talk we discuss the finite element and finite difference technique for the cubic spline collocation method. For this purpose, we consider the uniformly elliptic operator A defined by Au := -{Delta}u + a{sub 1}u{sub x} + a{sub 2}u{sub y} + a{sub 0}u in {Omega} (the unit square) with Dirichlet or Neumann boundary conditions and its discretization based on Hermite cubic spline spaces and collocation at the Gauss points. Using an interpolatory basis with support on the Gauss points one obtains the matrix A{sub N} (h = 1/N).

  19. GA Based Rational cubic B-Spline Representation for Still Image Interpolation

    Directory of Open Access Journals (Sweden)

    Samreen Abbas


    Full Text Available In this paper, an image interpolation scheme is designed for 2D natural images. A local support rational cubic spline with control parameters, as interpolatory function, is being optimized using Genetic Algorithm (GA. GA is applied to determine the appropriate values of control parameter used in the description of rational cubic spline. Three state-of-the-art Image Quality Assessment (IQA models with traditional one are hired for comparison with existing image interpolation schemes and perceptual quality check of resulting images. The results show that the proposed scheme is better than the existing ones in comparison.

  20. Effect of shear on cubic phases in gels of a diblock copolymer

    DEFF Research Database (Denmark)

    Hamley, I.W.; Pople, J.A.; Fairclough, J.P.A.


    The effect of shear on the orientation of cubic micellar phases formed by a poly(oxyethylene)poly(oxybutylene) diblock copolymer in aqueous solution has been investigated using small-angle x-ray scattering (SAXS) and small-angle neutron scattering (SANS). SAXS was performed on samples oriented...... in a Couette cell using steady shear, and SANS was performed on samples subject to oscillatory shear in situ in a rheometer with a shear sandwich configuration. A body-centered-cubic (bcc) phase observed for gels with concentrations greater than 30 wt % copolymer was found to orient into a polydomain structure...

  1. Secure optical generalized filter bank multi-carrier system based on cubic constellation masked method. (United States)

    Zhang, Lijia; Liu, Bo; Xin, Xiangjun


    A secure optical generalized filter bank multi-carrier (GFBMC) system with carrier-less amplitude-phase (CAP) modulation is proposed in this Letter. The security is realized through cubic constellation-masked method. Large key space and more flexibility masking can be obtained by cubic constellation masking aligning with the filter bank. An experiment of 18 Gb/s encrypted GFBMC/CAP system with 25-km single-mode fiber transmission is performed to demonstrate the feasibility of the proposed method.

  2. Nonlinear aerodynamic wing design (United States)

    Bonner, Ellwood


    The applicability of new nonlinear theoretical techniques is demonstrated for supersonic wing design. The new technology was utilized to define outboard panels for an existing advanced tactical fighter model. Mach 1.6 maneuver point design and multi-operating point compromise surfaces were developed and tested. High aerodynamic efficiency was achieved at the design conditions. A corollary result was that only modest supersonic penalties were incurred to meet multiple aerodynamic requirements. The nonlinear potential analysis of a practical configuration arrangement correlated well with experimental data.

  3. Engineered nonlinear lattices

    DEFF Research Database (Denmark)

    Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.


    We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...... discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term...

  4. Nonlinear fiber optics

    CERN Document Server

    Agrawal, Govind


    Since the 4e appeared, a fast evolution of the field has occurred. The 5e of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers, the basis of all our telecommunications infastructure as well as being used in the medical field. Reflecting the big developments in research, this new edition includes major new content: slow light effects, which offers a reduction in noise and power consumption and more ordered network traffic-stimulated Brillouin scattering; vectorial treatment of highly nonlinear fibers; and a brand new chapter o

  5. Tunable nonlinear graphene metasurfaces (United States)

    Smirnova, Daria A.; Miroshnichenko, Andrey E.; Kivshar, Yuri S.; Khanikaev, Alexander B.


    We introduce an important approach for enhancing the nonlinear response of graphene through its resonant coupling to a plasmonic metasurface via cascaded Fano resonances. Such a hybrid metasurface supports two types of subradiant resonant modes, i.e., asymmetric modes of structured metamaterial elements ("metamolecules") and graphene plasmons exhibiting strong mutual coupling and avoided dispersion crossing. We demonstrate that the tunability of graphene plasmons facilitates the strong interaction between the subradiant modes, modifying the spectral position and lifetime of the Fano resonances. We reveal that a strong resonant interaction, combined with the subwavelength localization of plasmons, leads to an enhanced nonlinear response and high efficiency of the second-harmonic generation.

  6. Fully nonlinear elliptic equations

    CERN Document Server

    Caffarelli, Luis A


    The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equa

  7. Oscillations in nonlinear systems

    CERN Document Server

    Hale, Jack K


    By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa

  8. Vibration reduction of beams under successive traveling loads by means of linear and nonlinear dynamic absorbers (United States)

    Samani, Farhad S.; Pellicano, Francesco


    The goal of the present work is to assess the performances of dynamic vibration absorbers (DVA) in suppressing the vibrations of a simply supported beam subjected to an infinite sequence of regularly spaced concentrated moving loads. In particular, several types of DVA are considered: linear, cubic, higher odd-order monomials and piecewise linear stiffness; linear, cubic and linear-quadratic viscous damping. The purpose is to clarify if nonlinear DVAs show improvements with respect to the classical linear devices. The dynamic scenario is deeply investigated in a wide range of operating conditions, spanning the parameter space of the DVA (damping, stiffness). Nonlinear stiffness can lead to complex dynamics such as quasi-periodic, chaotic and sub-harmonic responses; moreover, acting on the stiffness nonlinearity no improvement is found with respect to the linear DVA. A nonlinear non-symmetric dissipation in the DVA leads to a great reduction of the beam response, the reduction is larger with respect to the linear DVA.

  9. Metal nanospheres under intense continuous-wave illumination: A unique case of nonperturbative nonlinear nanophotonics (United States)

    Gurwich, I.; Sivan, Y.


    We show that the standard perturbative (i.e., cubic) description of the thermal nonlinear response of a single metal nanosphere to intense continuous-wave (CW) illumination is sufficient only for a temperature rise of up to 100 degrees above room temperature. Beyond this regime, the slowing down of the temperature rise requires a nonperturbative description of the nonlinear response, even though the permittivity is linearly dependent on the temperature and despite the deep subwavelength effective propagation distances involved. Using experimental data, we show that, generically, the increase of the imaginary part of the metal permittivity dominates the increase of the host permittivity as well as the resonance shift due to the joint changes to the real parts of the metal and host. Thus, the main nonlinear effect is a decrease of the quality factor of the resonance. We further analyze the relative importance of the various contributions to the temperature rise and thermal nonlinearity, compare the nonlinearity of Au and Ag, demonstrate the potential effect of the nanoparticle morphology, and show that although the thermo-optical nonlinearity of the host typically plays a minor role, its thermal conductivity and its temperature dependence is important. Finally, we discuss the differences between CW and ultrafast thermal nonlinearities.

  10. Chirped soliton solutions for the generalized nonlinear Schrödinger equation with polynomial nonlinearity and non-Kerr terms of arbitrary order (United States)

    Triki, Houria; Porsezian, K.; Grelu, Philippe


    A generalized nonlinear Schrödinger equation with polynomial Kerr nonlinearity and non-Kerr terms of an arbitrarily higher order is investigated. This model can be applied to the femtosecond pulse propagation in highly-nonlinear optical media. We introduce a new chirping ansatz given as an expansion in powers of intensity of the light pulse and obtain both linear and nonlinear chirp contributions associated with propagating optical pulses. By taking the cubic-quintic-septic-nonic nonlinear Schrödinger (NLS) equation with seventh-order non-Kerr terms as an example for the generalized equation with Kerr and non-Kerr nonlinearity of arbitrary order, we derive families of chirped soliton solutions under certain parametric conditions. The solutions comprise bright, kink, anti-kink, and fractional-transform soliton solutions. In addition, we found the exact soliton solution for the model under consideration using a new ansatz. The parametric conditions for the existence of chirped solitons are also reported.

  11. Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

    DEFF Research Database (Denmark)

    Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole


    We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types...... of nonlinear impurity modes, one- and two-hump symmetric localized modes and asymmetric localized modes, for both focusing and defocusing nonlinearity and two different (attractive or repulsive) types of impurity. We obtain an analytical stability criterion for the nonlinear localized modes and consider...... the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site....

  12. Nonlinear elliptic systems with exponential nonlinearities

    Directory of Open Access Journals (Sweden)

    Said El Manouni


    Full Text Available In this paper we investigate the existence of solutions for {gather*} -mathop{m div}( a(| abla u | ^N| abla u |^{N-2}u = f(x,u,v quad mbox{in } Omega -mathop{m div}(a(| abla v| ^N| abla v |^{N-2}v = g(x,u,v quad mbox{in } Omega u(x = v(x = 0 quad mbox{on }partial Omega. end{gather*} Where $Omega$ is a bounded domain in ${mathbb{R}}^N$, $Ngeq 2$, $f$ and $g$ are nonlinearities having an exponential growth on $Omega$ and $a$ is a continuous function satisfying some conditions which ensure the existence of solutions.

  13. Nonlinear silicon photonics (United States)

    Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.


    Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.

  14. Intramolecular and nonlinear dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Davis, M.J. [Argonne National Laboratory, IL (United States)


    Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.

  15. Nonlinear Regression with R

    CERN Document Server

    Ritz, Christian; Parmigiani, Giovanni


    R is a rapidly evolving lingua franca of graphical display and statistical analysis of experiments from the applied sciences. This book provides a coherent treatment of nonlinear regression with R by means of examples from a diversity of applied sciences such as biology, chemistry, engineering, medicine and toxicology.

  16. Nonlinearities in Microwave Superconductivity


    Ledenyov, Dimitri O.; Ledenyov, Viktor O.


    The research is focused on the modeling of nonlinear properties of High Temperature Superconducting (HTS) thin films, using Bardeen, Cooper, Schrieffer and Lumped Element Circuit theories, with purpose to enhance microwave power handling capabilities of microwave filters and optimize design of microwave circuits in micro- and nano- electronics.

  17. Topics in Nonlinear Dynamics

    DEFF Research Database (Denmark)

    Mosekilde, Erik

    Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...

  18. Limits to Nonlinear Inversion

    DEFF Research Database (Denmark)

    Mosegaard, Klaus


    For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on ou...

  19. Nonlinear Control System

    Directory of Open Access Journals (Sweden)

    Jaydeep Jesur


    and features are added such a way that it can be also used for design of nonlinear control systems to achieve desired performance. It is very simple to learn this tool. One can easily use it with preliminary knowledge of DF and PPT methods.

  20. Generalized Nonlinear Yule Models (United States)

    Lansky, Petr; Polito, Federico; Sacerdote, Laura


    With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.

  1. Nonlinear dynamics: Challenges and perspectives

    Indian Academy of Sciences (India)

    . Nonlinear .... engineering problems as well as population dynamics, economics, social dynamics, etc. [11]. 2.1 Nonlinear ordinary ..... niques such as dispersion management method have been developed. Multina- tional organizations have ...

  2. Nonlinear Optical Terahertz Technology Project (United States)

    National Aeronautics and Space Administration — Our approach is based on high-Q optical WGM resonators made with a nonlinear crystal. Such resonators have been demonstrated to dramatically enhance nonlinear...

  3. Nonlinear spectral imaging of fungi

    NARCIS (Netherlands)

    Knaus, H.


    Nonlinear microscopy combined with fluorescence spectroscopy is known as nonlinear spectral imaging microscopy (NLSM). This method provides simultaneously specimen morphology – distinguishing different parts in a tissue – and (auto)fluorescence spectra, thus their biochemical composition. A novel

  4. Strong nonlinear oscillators analytical solutions

    CERN Document Server

    Cveticanin, Livija


    This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.

  5. Representations of the rotation reflection symmetry group of the four-dimensional cubic lattice (United States)

    Mandula, Jeffrey E.; Zweig, George; Govaerts, Jan


    The structure and representations of the rotation reflection symmetry group of the four-dimensional cubic lattice are described. Their connections with the representations of the three-dimensional lattice rotation reflection group, and with the representations of the continuous O(3) and O(4) groups are given.

  6. Representations of the rotation reflection symmetry group of the four-dimensional cubic lattice

    Energy Technology Data Exchange (ETDEWEB)

    Mandula, J.E. (Washington Univ., St. Louis, MO (USA). Dept. of Physics); Zweig, G. (Los Alamos National Lab., NM (USA)); Govaerts, J. (Louvain Univ. (Belgium). Inst. for Theoretical Physics)


    The structure and representations of the rotation reflection symmetry group of the four-dimensional cubic lattice are described. Their connections with the representations of the three-dimensional lattice rotation reflection group, and with the representations of the continuous O(3) and O(4) groups are given.

  7. Electron correlation in a three dimensional cluster of the cubic lattice ...

    African Journals Online (AJOL)

    We study the one-band Hubbard model in a three dimensional simple cubic lattice, with periodic boundary conditions, by means of a variational analytic approach. Ground state energies and pairing correlations depend implicitly on the interaction strength (U/41). It is shown that for two electrons, the interaction is always ...

  8. Motion of a Rigid Rod Rocking Back and Forth Cubic-Quintic Duffing Oscillators

    DEFF Research Database (Denmark)

    Ganji, S. S.; Barari, Amin; Karimpour, S.


    In this work, we implemented the first-order approximation of the Iteration Perturbation Method (IPM) for approximating the behavior of a rigid rod rocking back and forth on a circular surface without slipping as well as Cubic-Quintic Duffing Oscillators. Comparing the results with the exact...

  9. Surface relaxation and surface energy of face –centered Cubic ...

    African Journals Online (AJOL)


    Surface relaxation and surface energy of face –centered Cubic metals. 1AGHEMENLO H E; *2IYAYI, S E; 3AVWIRI ,G O. 1, 3 Department of Physics, Ambrose Alli University, Ekpoma, Nigeria. 2 Department of Physics, University of Benin, Benin City, Nigeria. 3 Department of Physics, University of Port Harcourt, PH, Nigeria.

  10. Semisymmetric cubic graphs of order 16p2 16p2 16p2

    Indian Academy of Sciences (India)

    An undirected graph without isolated vertices is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. In this paper, we inquire the existence of connected semisymmetric cubic graphs of order 162. It is shown that for every odd prime , there exists a semisymmetric ...

  11. The influence of a cubic building on a roof mounted wind turbine

    NARCIS (Netherlands)

    Micallef, D.; Sant, Tonio; Simao Ferreira, C.


    The performance of a wind turbine located above a cubic building is not well understood. This issue is of fundamental importance for the design of small scale wind turbines. One variable which is of particular importance in this respect is the turbine height above roof level. In this work, the

  12. Estimating cubic volume of small diameter tree-length logs from ponderosa and lodgepole pine. (United States)

    Marlin E. Plank; James M. Cahill


    A sample of 351 ponderosa pine (Pinus ponderosa Dougl. ex Laws.) and 509 lodgepole pine (Pinus contorta Dougl. ex Loud.) logs were used to evaluate the performance of three commonly used formulas for estimating cubic volume. Smalian's formula, Bruce's formula, and Huber's formula were tested to determine which...

  13. Lactoferrin-derived antimicrobial peptide induces a micellar cubic phase in a model membrane system

    NARCIS (Netherlands)

    Bastos, M.; Silva, T.; Teixeira, V.; Nazmi, K.; Bolscher, J.G.M.; Funari, S.S.; Uhríková, D.


    The observation of a micellar cubic phase is reported for a mixture of an antimicrobial peptide from the Lactoferrin family, LFampin 265-284, and a model membrane system of dimyristoylphosphatidylcholine/dimyristoylphosphatidylglycerol (3:1), as derived from small-angle x-ray diffraction (SAXD)

  14. Estimating load weights with Huber's Cubic Volume formula: a field trial. (United States)

    Dale R. Waddell


    Log weights were estimated from the product of Huber's cubic volume formula and green density. Tags showing estimated log weights were attached to logs in the field, and the weights were tallied into a single load weight as logs were assembled for aerial yarding. Accuracy of the estimated load weights was evaluated by comparing the predicted with the actual load...

  15. Towards high-resolution 3D flow field measurements at cubic meter scales

    NARCIS (Netherlands)

    Schanz, Daniel; Huhn, Florian; Gesemann, Sebastian; Dierksheide, Uwe; van de Meerendonk, R.; Manovski, P.; Schröder, A.

    We present results from two large-volume volumetric flow experiments. The first of these, investigating a thermal plume at low velocities (up to 0.35 m/s) demonstrates the abilities and requirements to reach volume sizes up to and probably beyond one cubic meter. It is shown that the use of Helium

  16. Localized Pd Overgrowth on Cubic Pt Nanocrystals for Enhanced Electrocatalytic Oxidation of Formic Acid

    Energy Technology Data Exchange (ETDEWEB)

    Lee, H.; Habas, S.E.; Somorjai, G.A.; Yang, P.


    Binary Pt/Pd nanoparticles were synthesized by localized overgrowth of Pd on cubic Pt seeds for the investigation of electrocatalytic formic acid oxidation. The binary particles exhibited much less self-poisoning and a lower activation energy relative to Pt nanocubes, consistent with the single crystal study.

  17. Maximal independent set graph partitions for representations of body-centered cubic lattices

    DEFF Research Database (Denmark)

    Erleben, Kenny


    A maximal independent set graph data structure for a body-centered cubic lattice is presented. Refinement and coarsening operations are defined in terms of set-operations resulting in robust and easy implementation compared to a quad-tree-based implementation. The graph only stores information...

  18. On the dynamic Stability of a quadratic-cubic elastic model structure ...

    African Journals Online (AJOL)

    The main substance of this investigation is the determination of the dynamic buckling load of an imperfect quadratic-cubic elastic model structure , which ,in itself, is a Mathematical generalization of some of the many physical structures normally encountered in engineering practice and allied fields. The load function in ...

  19. A Comparison of Low Performing Students' Achievements in Factoring Cubic Polynomials Using Three Different Strategies (United States)

    Ogbonnaya, Ugorji I.; Mogari, David L.; Machisi, Eric


    In this study, repeated measures design was employed to compare low performing students' achievements in factoring cubic polynomials using three strategies. Twenty-five low-performing Grade 12 students from a secondary school in Limpopo province took part in the study. Data was collected using achievement test and was analysed using repeated…

  20. Non--Cubic Symmetry of the Electronic Response in AFM Late Transition--Metal Oxides. (United States)

    Posternak, M.; Baldereschi, A.; Massidda, S.; Resta, R.


    The late transition--metal monoxides (MnO, FeO, CoO, NiO) have the rocksalt structure in their paramagnetic phase, while below the Neel temperature a weak structural distortion accompanies an AFM ordering of type II. Therefore, it is generally assumed that most nonmagnetic (i.e. spin--integrated) crystalline properties are essentially cubic: we give here convincing evidence of the contrary. We focus on the half--filled d shell oxide MnO as the most suitable case study, on which we perform accurate ab--initio, all--electron calculations, within different one--particle schemes. In order to study the symmetry lowering due to AFM ordering, we assume an ideal cubic geometry throughout. The calculated TO frequencies and Born effective charge tensor do not have cubic symmetry. The standard LSD severely exaggerates the deviations from cubic symmetry, confirming its unreliability for calculating properties of insulating AFM oxides, while a model self--energy correction scheme(S. Massidda et al.), Phys. Rev. B 55, 13494 (1997). reduces considerably the anisotropy. We also explain the origin and the magnitude of this effect in terms of the mixed charge--transfer/Mott--Hubbard character of MnO.


    Ferčec, Brigita; Mahdi, Adam


    Using methods of computational algebra we obtain an upper bound for the cyclicity of a family of cubic systems. We overcame the problem of nonradicality of the associated Bautin ideal by moving from the ring of polynomials to a coordinate ring. Finally, we determine the number of limit cycles bifurcating from each component of the center variety.

  2. Polarized infrared reflectance study of free standing cubic GaN grown by molecular beam epitaxy

    Energy Technology Data Exchange (ETDEWEB)

    Lee, S.C., E-mail: [Nano-Optoelectronics Research Laboratory, School of Physics, Universiti Sains Malaysia, 11800 Penang (Malaysia); Department of Physics, Faculty of Science, University of Malaya, 50603 Kuala Lumpur (Malaysia); Ng, S.S.; Hassan, H. Abu; Hassan, Z.; Zainal, N. [Nano-Optoelectronics Research Laboratory, School of Physics, Universiti Sains Malaysia, 11800 Penang (Malaysia); Novikov, S.V.; Foxon, C.T.; Kent, A.J. [School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD (United Kingdom)


    Optical properties of free standing cubic gallium nitride grown by molecular beam epitaxy system are investigated by a polarized infrared (IR) reflectance technique. A strong reststrahlen band, which reveals the bulk-like optical phonon frequencies, is observed. Meanwhile, continuous oscillation fringes, which indicate the sample consists of two homogeneous layers with different dielectric constants, are observed in the non-reststrahlen region. By obtaining the first derivative of polarized IR reflectance spectra measured at higher angles of incidence, extra phonon resonances are identified at the edges of the reststrahlen band. The observations are verified with the theoretical results simulated based on a multi-oscillator model. - Highlights: • First time experimental studies of IR optical phonons in bulk like, cubic GaN layer. • Detection of extra phonon modes of cubic GaN by polarized IR reflectance technique. • Revelation of IR multiphonon modes of cubic GaN by first derivative numerical method. • Observation of multiphonon modes requires very high angle of incidence. • Resonance splitting effect induced by third phonon mode is a qualitative indicator.

  3. The breakdown of the weakly-nonlinear regime for kinetic instabilities (United States)

    Sanz-Orozco, David; Berk, Herbert; Wang, Ge


    The evolution of marginally-unstable waves that interact resonantly with populations of energetic particles is governed by a well-known cubic integro-differential equation for the mode amplitude. One of the outcomes predicted by the equation is the so-called ``explosive'' regime, where the amplitude grows indefinitely, eventually taking the equation outside of its domain of validity. Beyond this point, only full Vlasov simulations will accurately describe the evolution of the mode amplitude. In this work, we study the breakdown of the cubic equation in detail. We find that, while the cubic equation is still valid, the distribution function of the energetic particles locally flattens or ``folds'' in phase space. This feature is unexpected in view of the assumptions of the theory that are given in. We also derive fifth-order terms in the wave equation, which not only give us a more accurate description of the marginally-unstable modes, but they also allow us to predict the breakdown of the cubic equation. Our findings allow us to better understand the transition between weakly-nonlinear modes and the long-term chirping modes that ultimately emerge.

  4. Nonlinear electrorheological instability of two Rivlin-Ericksen elastico-viscous fluids

    CERN Document Server

    El-Dib, Y O


    The behaviour of surface waves propagating between two Rivlin-Ericksen elastico-viscous fluids is examined. The investigation is made in the presence of a vertical electric field and a relative horizontal constant velocity. The influence of both surface tension and gravity force is taken into account. Due to the inclusion of streaming flow a mathematical simplification is considered. The viscoelastic contribution is demonstrated in the boundary conditions. From this point of view the approximation equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion under nonlinear boundary conditions lead to derivation of a nonlinear equation governing the interfacial displacement and having damping terms with complex coefficients. This equation is accomplished by utilizing the cubic nonlinearity. The use of the Gardner-Morikawa transformation yields a simplified linear dispersion relation so that the periodic solution for the linear form is utilized. The ...

  5. Unifying different interpretations of the nonlinear response in glass-forming liquids (United States)

    Gadige, P.; Albert, S.; Michl, M.; Bauer, Th.; Lunkenheimer, P.; Loidl, A.; Tourbot, R.; Wiertel-Gasquet, C.; Biroli, G.; Bouchaud, J.-P.; Ladieu, F.


    This work aims at reconsidering several interpretations coexisting in the recent literature concerning nonlinear susceptibilities in supercooled liquids. We present experimental results on glycerol and propylene carbonate, showing that the three independent cubic susceptibilities have very similar frequency and temperature dependences, for both their amplitudes and phases. This strongly suggests a unique physical mechanism responsible for the growth of these nonlinear susceptibilities. We show that the framework proposed by two of us [J.-P. Bouchaud and G. Biroli, Phys. Rev. B 72, 064204 (2005), 10.1103/PhysRevB.72.064204], where the growth of nonlinear susceptibilities is intimately related to the growth of glassy domains, accounts for all the salient experimental features. We then review several complementary and/or alternative models and show that the notion of cooperatively rearranging glassy domains is a key (implicit or explicit) ingredient to all of them. This paves the way for future experiments, which should deepen our understanding of glasses.

  6. Investigation of the nonlinear static and dynamic behaviour of rectangular microplates under electrostatic actuation

    KAUST Repository

    Saghir, Shahid


    We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary resonance. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased.

  7. Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures. (United States)

    Gnutzmann, Sven; Waltner, Daniel


    We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phys. Rev. E 93, 032204 (2016)2470-004510.1103/PhysRevE.93.032204]. For closed example graphs (interval, ring, star graph, tadpole graph), we calculate spectral curves and show how the description of spectra reduces to known characteristic functions of linear quantum graphs in the low-intensity limit. Analogously for open examples, we show how nonlinear scattering of stationary waves arises and how it reduces to known linear scattering amplitudes at low intensities. In the short-wavelength asymptotics we discuss how genuine nonlinear effects may be described using the leading order of canonical perturbation theory: bifurcation of spectral curves (and the corresponding solutions) in closed graphs and multistability in open graphs.

  8. Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems (United States)

    Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Grelu, Philippe; Mihalache, Dumitru


    This review is dedicated to recent progress in the active field of rogue waves, with an emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector, and multidimensional integrable nonlinear systems. We first give a brief outline of the historical background of the rogue wave research, including referring to relevant up-to-date experimental results. Then we present an in-depth discussion of the scalar rogue waves within two different integrable frameworks—the infinite nonlinear Schrödinger (NLS) hierarchy and the general cubic-quintic NLS equation, considering both the self-focusing and self-defocusing Kerr nonlinearities. We highlight the concept of chirped Peregrine solitons, the baseband modulation instability as an origin of rogue waves, and the relation between integrable turbulence and rogue waves, each with illuminating examples confirmed by numerical simulations. Later, we recur to the vector rogue waves in diverse coupled multicomponent systems such as the long-wave short-wave equations, the three-wave resonant interaction equations, and the vector NLS equations (alias Manakov system). In addition to their intriguing bright–dark dynamics, a series of other peculiar structures, such as coexisting rogue waves, watch-hand-like rogue waves, complementary rogue waves, and vector dark three sisters, are reviewed. Finally, for practical considerations, we also remark on higher-dimensional rogue waves occurring in three closely-related (2  +  1)D nonlinear systems, namely, the Davey–Stewartson equation, the composite (2  +  1)D NLS equation, and the Kadomtsev–Petviashvili I equation. As an interesting contrast to the peculiar X-shaped light bullets, a concept of rogue wave bullets intended for high-dimensional systems is particularly put forward by combining contexts in nonlinear optics.

  9. Terahertz Nonlinear Optics in Semiconductors

    DEFF Research Database (Denmark)

    Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.


    We demonstrate the nonlinear optical effects – selfphase modulation and saturable absorption of a single-cycle THz pulse in a semiconductor. Resulting from THz-induced modulation of Drude plasma, these nonlinear optical effects, in particular, lead to self-shortening and nonlinear spectral...

  10. Fault Detection for Nonlinear Systems

    DEFF Research Database (Denmark)

    Stoustrup, Jakob; Niemann, H.H.


    The paper describes a general method for designing fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension of methods based...

  11. Nonlinearity, Conservation Law and Shocks

    Indian Academy of Sciences (India)

    Nonlinearity, Conservation Law and Shocks. Part I : Genuine Nonlinearity and Discontinuous Solutions. Phoolan Prasad is with the. Department of. Mathematics, Indian. Institute of Science and has been working in the area of nonlinear waves and hyperbolic partial differential equations. He is deeply interested in.

  12. Evaluation of Two New Smoothing Methods in Equating: The Cubic B-Spline Presmoothing Method and the Direct Presmoothing Method (United States)

    Cui, Zhongmin; Kolen, Michael J.


    This article considers two new smoothing methods in equipercentile equating, the cubic B-spline presmoothing method and the direct presmoothing method. Using a simulation study, these two methods are compared with established methods, the beta-4 method, the polynomial loglinear method, and the cubic spline postsmoothing method, under three sample…

  13. Nonlinear (Anharmonic Casimir Oscillator

    Directory of Open Access Journals (Sweden)

    Habibollah Razmi


    Full Text Available We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an nonlinear (anharmonic Casimir oscillator. Generally, the equation of motion of this nonlinear micromechanical Casimir oscillator has no exact solvable (analytical solution and the turning point(s of the system has (have no fixed position(s; however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are approximately sinusoidal solution(s for the problem (the variable turning points are collected in a very small interval of positions. This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.

  14. Essentials of nonlinear optics

    CERN Document Server

    Murti, Y V G S


    Current literature on Nonlinear Optics varies widely in terms of content, style, and coverage of specific topics, relative emphasis of areas and the depth of treatment. While most of these books are excellent resources for the researchers, there is a strong need for books appropriate for presenting the subject at the undergraduate or postgraduate levels in Universities. The need for such a book to serve as a textbook at the level of the bachelors and masters courses was felt by the authors while teaching courses on nonlinear optics to students of both science and engineering during the past two decades. This book has emerged from an attempt to address the requirement of presenting the subject at college level. A one-semester course covering the essentials can effectively be designed based on this.

  15. Augmented nonlinear differentiator design (United States)

    Shao, Xingling; Liu, Jun; Yang, Wei; Tang, Jun; Li, Jie


    This paper presents a sigmoid function based augmented nonlinear differentiator (AND) for calculating the noise-less time derivative from a noisy measurement. The prominent advantages of the present differentiation technique are: (i) compared to the existing tracking differentiators, better noise suppression ability can be achieved without appreciable delay; (ii) the enhanced noise-filtering mechanism not only can be applied to the designed differentiator, but also can be extended for improving noise-tolerance capability of the available differentiators. In addition, the convergence property and robustness performance against noises are investigated via singular perturbation theory and describing function method, respectively. Also, comparison with several classical differentiators is given to illustrate the superiority of AND in noise suppression. Finally, applications on autopilot design and displacement following for nonlinear mass spring mechanical system are given to demonstrate the effectiveness and applicability of the proposed AND technique.

  16. Monte Carlo and nonlinearities

    CERN Document Server

    Dauchet, Jérémi; Blanco, Stéphane; Caliot, Cyril; Charon, Julien; Coustet, Christophe; Hafi, Mouna El; Eymet, Vincent; Farges, Olivier; Forest, Vincent; Fournier, Richard; Galtier, Mathieu; Gautrais, Jacques; Khuong, Anaïs; Pelissier, Lionel; Piaud, Benjamin; Roger, Maxime; Terrée, Guillaume; Weitz, Sebastian


    The Monte Carlo method is widely used to numerically predict systems behaviour. However, its powerful incremental design assumes a strong premise which has severely limited application so far: the estimation process must combine linearly over dimensions. Here we show that this premise can be alleviated by projecting nonlinearities on a polynomial basis and increasing the configuration-space dimension. Considering phytoplankton growth in light-limited environments, radiative transfer in planetary atmospheres, electromagnetic scattering by particles and concentrated-solar-power-plant productions, we prove the real world usability of this advance on four test-cases that were so far regarded as impracticable by Monte Carlo approaches. We also illustrate an outstanding feature of our method when applied to sharp problems with interacting particles: handling rare events is now straightforward. Overall, our extension preserves the features that made the method popular: addressing nonlinearities does not compromise o...

  17. Nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.


    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  18. Nonlinear data assimilation

    CERN Document Server

    Van Leeuwen, Peter Jan; Reich, Sebastian


    This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.

  19. Optothermal nonlinearity of silica aerogel

    CERN Document Server

    Braidotti, Maria Chiara; Fleming, Adam; Samuels, Michiel C; Di Falco, Andrea; Conti, Claudio


    We report on the characterization of silica aerogel thermal optical nonlinearity, obtained by z-scan technique. The results show that typical silica aerogels have nonlinear optical coefficient similar to that of glass $(\\simeq 10^{-12} $m$^2/$W), with negligible optical nonlinear absorption. The non\\-li\\-near coefficient can be increased to values in the range of $10^{-10} $m$^2/$W by embedding an absorbing dye in the aerogel. This value is one order of magnitude higher than that observed in the pure dye and in typical highly nonlinear materials like liquid crystals.

  20. Elastic nonlinearity imaging. (United States)

    Hall, Timothy J; Oberait, Assad A; Barbone, Paul E; Sommer, Amy M; Gokhale, Nachiket H; Goenezent, Sevan; Jiang, Jingfeng


    Previous work has demonstrated improved diagnostic performance of highly trained breast radiologists when provided with B-mode plus elastography images over B-mode images alone. In those studies we have observed that elasticity imaging can be difficult to perform if there is substantial motion of tissue out of the image plane. So we are extending our methods to 3D/4D elasticity imaging with 2D arrays. Further, we have also documented the fact that some breast tumors change contrast with increasing deformation and those observations are consistent with in vitro tissue measurements. Hence, we are investigating imaging tissue stress-strain nonlinearity. These studies will require relatively large tissue deformations (e.g., > 20%) which will induce out of plane motion further justifying 3D/4D motion tracking. To further enhance our efforts, we have begun testing the ability to perform modulus reconstructions (absolute elastic parameter) imaging of in vivo breast tissues. The reconstructions are based on high quality 2D displacement estimates from strain imaging. Piecewise linear (secant) modulus reconstructions demonstrate the changes in elasticity image contrast seen in strain images but, unlike the strain images, the contrast in the modulus images approximates the absolute modulus contrast. Nonlinear reconstructions assume a reasonable approximation to the underlying constitutive relations for the tissue and provide images of the (near) zero-strain shear modulus and a nonlinearity parameter that describes the rate of tissue stiffening with increased deformation. Limited data from clinical trials are consistent with in vitro measurements of elastic properties of tissue samples and suggest that the nonlinearity of invasive ductal carcinoma exceeds that of fibroadenoma and might be useful for improving diagnostic specificity. This work is being extended to 3D.