WorldWideScience

Sample records for single nonlinear differential

  1. Single shot, double differential spectral measurements of inverse Compton scattering in the nonlinear regime

    Directory of Open Access Journals (Sweden)

    Y. Sakai

    2017-06-01

    Full Text Available Inverse Compton scattering (ICS is a unique mechanism for producing fast pulses—picosecond and below—of bright photons, ranging from x to γ rays. These nominally narrow spectral bandwidth electromagnetic radiation pulses are efficiently produced in the interaction between intense, well-focused electron and laser beams. The spectral characteristics of such sources are affected by many experimental parameters, with intense laser effects often dominant. A laser field capable of inducing relativistic oscillatory motion may give rise to harmonic generation and, importantly for the present work, nonlinear redshifting, both of which dilute the spectral brightness of the radiation. As the applications enabled by this source often depend sensitively on its spectra, it is critical to resolve the details of the wavelength and angular distribution obtained from ICS collisions. With this motivation, we present an experimental study that greatly improves on previous spectral measurement methods based on x-ray K-edge filters, by implementing a multilayer bent-crystal x-ray spectrometer. In tandem with a collimating slit, this method reveals a projection of the double differential angular-wavelength spectrum of the ICS radiation in a single shot. The measurements enabled by this diagnostic illustrate the combined off-axis and nonlinear-field-induced redshifting in the ICS emission process. The spectra obtained illustrate in detail the strength of the normalized laser vector potential, and provide a nondestructive measure of the temporal and spatial electron-laser beam overlap.

  2. Nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.

    1988-01-01

    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.

  3. Nonlinear elliptic differential equations with multivalued nonlinearities

    Indian Academy of Sciences (India)

    Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45

    Nonlinear elliptic differential equations with multivalued ... has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth .... A is upper semicontinuous (as a set-valued map) from every finite dimensional subspace of X into ...

  4. Negative Differential Resistance due to Nonlinearities in Single and Stacked Josephson Junctions

    DEFF Research Database (Denmark)

    Filatrella, Giovanni; Pierro, Vincenzo; Pedersen, Niels Falsig

    2014-01-01

    Josephson junction systems with a negative differential resistance (NDR) play an essential role for applications. As a well-known example, long Josephson junctions of the BSCCO type have been considered as a source of terahertz radiation in recent experiments. Numerical results for the dynamics o...

  5. Nonlinear differential equations

    CERN Document Server

    Struble, Raimond A

    2017-01-01

    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.

  6. Generalized solutions of nonlinear partial differential equations

    CERN Document Server

    Rosinger, EE

    1987-01-01

    During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin

  7. Single-ion nonlinear mechanical oscillator

    International Nuclear Information System (INIS)

    Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.

    2010-01-01

    We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.

  8. On implicit abstract neutral nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Hernández, Eduardo, E-mail: lalohm@ffclrp.usp.br [Universidade de São Paulo, Departamento de Computação e Matemática, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto (Brazil); O’Regan, Donal, E-mail: donal.oregan@nuigalway.ie [National University of Ireland, School of Mathematics, Statistics and Applied Mathematics (Ireland)

    2016-04-15

    In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.

  9. An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Moh’d Khier Al-Srihin

    2017-01-01

    Full Text Available In this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series expansion method to multiterm fractional differential equations, where we overcome the difficulty of computing iterated fractional derivatives, which are difficult to be computed in general. The terms of the series are obtained sequentially using a closed formula, where only integer derivatives have to be computed. Several examples are presented to illustrate the efficiency of the new approach and comparison with the Adomian decomposition method is performed.

  10. Nonlinear single-spin spectrum analyzer.

    Science.gov (United States)

    Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee

    2013-03-15

    Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.

  11. Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

    Directory of Open Access Journals (Sweden)

    Khaled A. Gepreel

    2013-01-01

    Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.

  12. Nonlinear partial differential equations and their applications

    CERN Document Server

    Lions, Jacques Louis

    2002-01-01

    This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, op

  13. Oscillation criteria for third order delay nonlinear differential equations

    Directory of Open Access Journals (Sweden)

    E. M. Elabbasy

    2012-01-01

    via comparison with some first differential equations whose oscillatory characters are known. Our results generalize and improve some known results for oscillation of third order nonlinear differential equations. Some examples are given to illustrate the main results.

  14. Exact solutions for some nonlinear systems of partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Darwish, A.A. [Department of Mathematics, Faculty of Science, Helwan University (Egypt)], E-mail: profdarwish@yahoo.com; Ramady, A. [Department of Mathematics, Faculty of Science, Beni-Suef University (Egypt)], E-mail: aramady@yahoo.com

    2009-04-30

    A direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear systems of partial differential equations (PDEs) is used and implemented in a computer algebraic system. New solutions for some nonlinear partial differential equations (NLPDEs) are obtained. Graphs of the solutions are displayed.

  15. Nonlinear and Nonsymmetric Single-Molecule Electronic Properties Towards Molecular Information Processing.

    Science.gov (United States)

    Tamaki, Takashi; Ogawa, Takuji

    2017-09-05

    This review highlights molecular design for nonlinear and nonsymmetric single-molecule electronic properties such as rectification, negative differential resistance, and switching, which are important components of future single-molecule information processing devices. Perspectives on integrated "molecular circuits" are also provided. Nonlinear and nonsymmetric single-molecule electronics can be designed by utilizing (1) asymmetric molecular cores, (2) asymmetric anchoring groups, (3) an asymmetric junction environment, and (4) asymmetric electrode materials. This review mainly focuses on the design of molecular cores.

  16. International Conference on Differential Equations and Nonlinear Mechanics

    CERN Document Server

    2001-01-01

    The International Conference on Differential Equations and Nonlinear Mechanics was hosted by the University of Central Florida in Orlando from March 17-19, 1999. One of the conference days was dedicated to Professor V. Lakshmikantham in th honor of his 75 birthday. 50 well established professionals (in differential equations, nonlinear analysis, numerical analysis, and nonlinear mechanics) attended the conference from 13 countries. Twelve of the attendees delivered hour long invited talks and remaining thirty-eight presented invited forty-five minute talks. In each of these talks, the focus was on the recent developments in differential equations and nonlinear mechanics and their applications. This book consists of 29 papers based on the invited lectures, and I believe that it provides a good selection of advanced topics of current interest in differential equations and nonlinear mechanics. I am indebted to the Department of Mathematics, College of Arts and Sciences, Department of Mechanical, Materials and Ae...

  17. High-order nonlinear differentiator and application to aircraft control

    Science.gov (United States)

    Wang, Xinhua; Shirinzadeh, Bijan

    2014-06-01

    In this paper, a high-order continuous nonlinear differentiator with lead compensation is presented based on finite-time stability. Not only the proposed high-order nonlinear differentiator can obtain the high-order derivatives of a signal, but also the chattering phenomenon can be reduced sufficiently. The parameters regulation is only required to be satisfied with Routh-Hurwitz Stability Criterion. The presented differentiator is a generalization of sliding mode differentiator and linear high-gain differentiator. The merits of the continuous differentiator include its simplicity, selecting parameters easily, restraining noises sufficiently, decreasing the phase shift and avoiding the chattering phenomenon. The theoretical results are confirmed by computer simulations and an experiment on a quadrotor aircraft: (i) the estimation of flying velocity and acceleration from the position measurement; (ii) a control law is designed based on the presented nonlinear differentiator to track a reference trajectory.

  18. Analytical solution of differential equation with cubic nonlinearity

    OpenAIRE

    Инхиреева, Т. А.; Козловских, Александр Владимирович

    2016-01-01

    This paper considers method of Cauchy problem solution for nonlinear differential equation. Source of solution error and way of eliminating it is studied. Solution obtained with suggestedmethod is compared with solution obtained with built-in MATLAB functions.

  19. Nonlinear ordinary differential equations analytical approximation and numerical methods

    CERN Document Server

    Hermann, Martin

    2016-01-01

    The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...

  20. Symmetries of nonlinear ordinary differential equations: The ...

    Indian Academy of Sciences (India)

    2015-10-21

    Oct 21, 2015 ... Lie point symmetries; -symmetries; Noether symmetries; contact symmetries; adjoint symmetries; nonlocal symmetries; hidden symmetries; ... 620 024, India; Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401, India ...

  1. GHM method for obtaining rationalsolutions of nonlinear differential equations.

    Science.gov (United States)

    Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo

    2015-01-01

    In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.

  2. Handbook of Nonlinear Partial Differential Equations

    CERN Document Server

    Polyanin, Andrei D

    2011-01-01

    New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with Maple(t), Mathematica(R), and MATLAB(R) Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They

  3. Linear differential equations to solve nonlinear mechanical problems: A novel approach

    OpenAIRE

    Nair, C. Radhakrishnan

    2004-01-01

    Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differe...

  4. Integral conditions for nonoscillation of second order nonlinear differential equations

    Czech Academy of Sciences Publication Activity Database

    Cecchi, M.; Došlá, Z.; Marini, M.; Vrkoč, Ivo

    2006-01-01

    Roč. 64, č. 6 (2006), s. 1278-1289 ISSN 0362-546X R&D Projects: GA AV ČR(CZ) IAA1163401 Institutional research plan: CEZ:AV0Z10190503 Keywords : change of integration * half-linear differential equation * nonlinear differential equation Subject RIV: BA - General Mathematics Impact factor: 0.677, year: 2006

  5. Nonlinear partial differential equations: Integrability, geometry and related topics

    Science.gov (United States)

    Krasil'shchik, Joseph; Rubtsov, Volodya

    2017-03-01

    Geometry and Differential Equations became inextricably entwined during the last one hundred fifty years after S. Lie and F. Klein's fundamental insights. The two subjects go hand in hand and they mutually enrich each other, especially after the "Soliton Revolution" and the glorious streak of Symplectic and Poisson Geometry methods in the context of Integrability and Solvability problems for Non-linear Differential Equations.

  6. Analytic solutions of nonlinear neutral and advanced differential equatios

    Directory of Open Access Journals (Sweden)

    Joseph Wiener

    1986-01-01

    Full Text Available A study is made of local existence and uniqueness theorems for analytic solutions of nonlinear differential equations of neutral and advanced types. These results are of special interest for advanced eauations whose solutions, in general, lose their margin of smoothness. Furthermore, existence of entire solutions is established for linear advanced differential systems with polynomial coefficients.

  7. Symmetries of nonlinear ordinary differential equations: The ...

    Indian Academy of Sciences (India)

    2015-10-21

    Oct 21, 2015 ... Abstract. Lie symmetry analysis is one of the powerful tools to analyse nonlinear ordinary dif- ferential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries, contact symmetries, hidden symmetries, nonlocal symmetries ...

  8. Symmetries of nonlinear ordinary differential equations: The ...

    Indian Academy of Sciences (India)

    2015-10-21

    Oct 21, 2015 ... equation and showed that it admits sl(3, R) algebra and constructed a linearizing trans- formation from ... ers of ˙x to zero, one obtains a set of linear partial differential equations for the unknown functions ξ and η. ...... [11] N H Ibragimov, Elementary Lie group analysis and ordinary differential equations (John.

  9. Backward stochastic differential equations from linear to fully nonlinear theory

    CERN Document Server

    Zhang, Jianfeng

    2017-01-01

    This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.

  10. Nonlinear partial differential equation in engineering

    CERN Document Server

    Ames, William F

    1972-01-01

    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

  11. Differential quadrature method of nonlinear bending of functionally graded beam

    Science.gov (United States)

    Gangnian, Xu; Liansheng, Ma; Wang, Youzhi; Quan, Yuan; Weijie, You

    2018-02-01

    Using the third-order shear deflection beam theory (TBT), nonlinear bending of functionally graded (FG) beams composed with various amounts of ceramic and metal is analyzed utilizing the differential quadrature method (DQM). The properties of beam material are supposed to accord with the power law index along to thickness. First, according to the principle of stationary potential energy, the partial differential control formulae of the FG beams subjected to a distributed lateral force are derived. To obtain numerical results of the nonlinear bending, non-dimensional boundary conditions and control formulae are dispersed by applying the DQM. To verify the present solution, several examples are analyzed for nonlinear bending of homogeneous beams with various edges. A minute parametric research is in progress about the effect of the law index, transverse shear deformation, distributed lateral force and boundary conditions.

  12. Analysis of solutions of a nonlinear scalar field differential equation

    Science.gov (United States)

    Muhamadiev, E. M.; Naimov, A. N.

    2017-10-01

    We consider a nonlinear differential equation arising in mathematical models of elementary particle theory. For this equation, we examine questions of the extendability of solutions, the boundedness of solutions at infinity, and the search for new conditions for the existence of a positive particle-like solution.

  13. Sturm-Picone type theorems for nonlinear differential systems

    Directory of Open Access Journals (Sweden)

    Aydin Tiryaki

    2015-06-01

    Full Text Available In this article, we establish a Picone-type inequality for a pair of first-order nonlinear differential systems. By using this inequality, we give Sturm-Picone type comparison theorems for these systems and a special class of second-order half-linear equations with damping term.

  14. Advances in nonlinear partial differential equations and stochastics

    CERN Document Server

    Kawashima, S

    1998-01-01

    In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.

  15. Exact solutions of some nonlinear partial differential equations using ...

    Indian Academy of Sciences (India)

    The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm ...

  16. Solving Nonlinear Partial Differential Equations with Maple and Mathematica

    CERN Document Server

    Shingareva, Inna K

    2011-01-01

    The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple an

  17. Positive Solutions for Coupled Nonlinear Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Wenning Liu

    2014-01-01

    Full Text Available We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones K1, K2 and computing the fixed point index in product cone K1×K2, we obtain that the system has a pair of positive solutions. It is remarkable that it is established on the Cartesian product of two cones, in which the feature of two equations can be opposite.

  18. Analysis of backward differentiation formula for nonlinear differential-algebraic equations with 2 delays.

    Science.gov (United States)

    Sun, Leping

    2016-01-01

    This paper is concerned with the backward differential formula or BDF methods for a class of nonlinear 2-delay differential algebraic equations. We obtain two sufficient conditions under which the methods are stable and asymptotically stable. At last, examples show that our methods are true.

  19. Numerical solution of two-dimensional non-linear partial differential ...

    African Journals Online (AJOL)

    linear partial differential equations using a hybrid method. The solution technique involves discritizing the non-linear system of partial differential equations (PDEs) to obtain a corresponding nonlinear system of algebraic difference equations to be ...

  20. Nonlinear partial differential equations for scientists and engineers

    CERN Document Server

    Debnath, Lokenath

    1997-01-01

    "An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. This reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel." ---Applied Mechanics Review (Review of First Edition) This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership. Topics and key features: * Thorough coverage of derivation and methods of soluti...

  1. Symposium on Nonlinear Semigroups, Partial Differential Equations and Attractors

    CERN Document Server

    Zachary, Woodford

    1987-01-01

    The original idea of the organizers of the Washington Symposium was to span a fairly narrow range of topics on some recent techniques developed for the investigation of nonlinear partial differential equations and discuss these in a forum of experts. It soon became clear, however, that the dynamical systems approach interfaced significantly with many important branches of applied mathematics. As a consequence, the scope of this resulting proceedings volume is an enlarged one with coverage of a wider range of research topics.

  2. Multiple Positive Solutions for Nonlinear Semipositone Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Wen-Xue Zhou

    2012-01-01

    Full Text Available We present some new multiplicity of positive solutions results for nonlinear semipositone fractional boundary value problem D0+αu(t=p(tf(t,u(t-q(t,0differentiation. One example is also given to illustrate the main result.

  3. Existence results for nonlinear implicit fractional differential equations

    Directory of Open Access Journals (Sweden)

    Mouffak Benchohra

    2014-09-01

    Full Text Available In this paper, we establish the existence and uniqueness of solution for a class of initial value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, Schauder' fixed point theorem and the nonlinear alternative of Leray-Schauder type. As applications, two examples are included to show the applicability of our results.

  4. 1/f Noise from nonlinear stochastic differential equations.

    Science.gov (United States)

    Ruseckas, J; Kaulakys, B

    2010-03-01

    We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/fbeta noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/fbeta noise, and provides further insights into the origin of 1/fbeta noise.

  5. Robust fast controller design via nonlinear fractional differential equations.

    Science.gov (United States)

    Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

    2017-07-01

    A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  6. Microhardness studies on nonlinear optical L-alanine single crystals

    Indian Academy of Sciences (India)

    Sci., Vol. 36, No. 3, June 2013, pp. 471–474. c Indian Academy of Sciences. Microhardness studies on nonlinear optical L-alanine single crystals. R HANUMANTHARAO† and S KALAINATHAN‡,∗ ... ter to the area of the impression left on the specimen. Both ... where P is the applied load in kg, d is in mm and Hv is in kg mm.

  7. High order analysis of nonlinear periodic differential equations

    International Nuclear Information System (INIS)

    Amore, Paolo; Lamas, Hector Montes

    2004-01-01

    In this Letter we apply a method recently devised in [Phys. Lett. A 316 (2003) 218] to find accurate approximate solutions to a certain class of nonlinear differential equations. The analysis carried out in [Phys. Lett. A 316 (2003) 218] is refined and results of much higher precision are obtained for the problems previously considered (Duffing equation, sextic oscillator). Fast convergence to the exact results is observed both for the frequency and for the Fourier coefficients. The method is also applied with success to more general polynomial potentials (the octic oscillator) and to the van der Pol equation

  8. Synthesis of robust nonlinear autopilots using differential game theory

    Science.gov (United States)

    Menon, P. K. A.

    1991-01-01

    A synthesis technique for handling unmodeled disturbances in nonlinear control law synthesis was advanced using differential game theory. Two types of modeling inaccuracies can be included in the formulation. The first is a bias-type error, while the second is the scale-factor-type error in the control variables. The disturbances were assumed to satisfy an integral inequality constraint. Additionally, it was assumed that they act in such a way as to maximize a quadratic performance index. Expressions for optimal control and worst-case disturbance were then obtained using optimal control theory.

  9. An efficient algorithm for solving nonlinear system of differential equations and applications

    Directory of Open Access Journals (Sweden)

    Mustafa GÜLSU

    2015-10-01

    Full Text Available In this article, we apply Chebyshev collocation method to obtain the numerical solutions of nonlinear systems of differential equations. This method transforms the nonlinear systems of differential equation to nonlinear systems of algebraic equations. The convergence of the numerical method are given and their applicability is illustrated with some examples.

  10. A Study of Impulsive Multiterm Fractional Differential Equations with Single and Multiple Base Points and Applications

    Directory of Open Access Journals (Sweden)

    Yuji Liu

    2014-01-01

    Full Text Available We discuss the existence and uniqueness of solutions for initial value problems of nonlinear singular multiterm impulsive Caputo type fractional differential equations on the half line. Our study includes the cases for a single base point fractional differential equation as well as multiple base points fractional differential equation. The asymptotic behavior of solutions for the problems is also investigated. We demonstrate the utility of our work by applying the main results to fractional-order logistic models.

  11. Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

    Directory of Open Access Journals (Sweden)

    Khaled A. Gepreel

    2012-01-01

    Full Text Available We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.

  12. Nonlinear evolution of single spike in Richtmyer-Meshkov instability

    International Nuclear Information System (INIS)

    Fukuda, Y.; Nishihara, K.; Wouchuk, J.G.

    2000-01-01

    Nonlinear evolution of single spike structure and vortex in the Richtmyer-Meshkov instability is investigated with the use of a two-dimensional hydrodynamic code. It is shown that singularity appears in the vorticity left by transmitted and reflected shocks at a corrugated interface. This singularity results in opposite sign of vorticity along the interface that causes double spiral structure of the spike. (authors)

  13. Hidden physics models: Machine learning of nonlinear partial differential equations

    Science.gov (United States)

    Raissi, Maziar; Karniadakis, George Em

    2018-03-01

    While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

  14. On the Ψ-Conditional Exponential Asymptotic Stability of Nonlinear Lyapunov Matrix Differential Equations

    Directory of Open Access Journals (Sweden)

    Diamandescu Aurel

    2016-07-01

    Full Text Available It is proved (necessary and sufficient conditions for Ψ– conditional exponential asymptotic stability of the trivial solution of nonlinear Lyapunov matrix differential equations

  15. On the Ψ-Conditional Asymptotic Stability of Nonlinear Lyapunov Matrix Differential Equations

    Directory of Open Access Journals (Sweden)

    Diamandescu Aurel

    2015-12-01

    Full Text Available It is proved (necessary and sufficient conditions for Ψ − conditional asymptotic stability of the trivial solution of linear or nonlinear Lyapunov matrix differential equations.

  16. Single-step digital backpropagation for nonlinearity mitigation

    DEFF Research Database (Denmark)

    Secondini, Marco; Rommel, Simon; Meloni, Gianluca

    2015-01-01

    Nonlinearity mitigation based on the enhanced split-step Fourier method (ESSFM) for the implementation of low-complexity digital backpropagation (DBP) is investigated and experimentally demonstrated. After reviewing the main computational aspects of DBP and of the conventional split-step Fourier...... is experimentally demonstrated by using a single-step DBP based on the ESSFM. The proposed DBP implementation requires only a single step of the ESSFM algorithm to achieve a transmission distance of 3200 km over a dispersion-unmanaged link. In comparison, a conventional DBP implementation requires 20 steps...

  17. Crystal growth and characterization of a semiorganic nonlinear optical single crystal of gamma glycine

    International Nuclear Information System (INIS)

    Prakash, J. Thomas Joseph; Kumararaman, S.

    2008-01-01

    Gamma glycine has been successfully synthesized by taking glycine and potassium chloride and single crystals have been grown by solvent evaporation method for the first time. The grown single crystals have been analyzed with XRD, Fourier transform infrared (FTIR), and thermo gravimetric and differential thermal analyses (TG/DTA) measurements. Its mechanical behavior has been assessed by Vickers microhardness measurements. Its nonlinear optical property has been tested by Kurtz powder technique. Its optical behavior was examined by UV-vis., and found that the crystal is transparent in the region between 240 and 1200 nm. Hence, it may be very much useful for the second harmonic generation (SHG) applications

  18. Nonlinear control and filtering using differential flatness approaches applications to electromechanical systems

    CERN Document Server

    Rigatos, Gerasimos G

    2015-01-01

    This monograph presents recent advances in differential flatness theory and analyzes its use for nonlinear control and estimation. It shows how differential flatness theory can provide solutions to complicated control problems, such as those appearing in highly nonlinear multivariable systems and distributed-parameter systems. Furthermore, it shows that differential flatness theory makes it possible to perform filtering and state estimation for a wide class of nonlinear dynamical systems and provides several descriptive test cases. The book focuses on the design of nonlinear adaptive controllers and nonlinear filters, using exact linearization based on differential flatness theory. The adaptive controllers obtained can be applied to a wide class of nonlinear systems with unknown dynamics, and assure reliable functioning of the control loop under uncertainty and varying operating conditions. The filters obtained outperform other nonlinear filters in terms of accuracy of estimation and computation speed. The bo...

  19. Approximate Solutions of Nonlinear Partial Differential Equations by Modified q-Homotopy Analysis Method

    Directory of Open Access Journals (Sweden)

    Shaheed N. Huseen

    2013-01-01

    Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.

  20. Nonlinear Schrödinger equations with single power nonlinearity and harmonic potential

    Science.gov (United States)

    Cipolatti, R.; de Macedo Lira, Y.; Trallero-Giner, C.

    2018-03-01

    We consider a generalized nonlinear Schrödinger equation (GNLS) with a single power nonlinearity of the form λ ≤ft\\vert \\varphi \\right\\vert p , with p  >  0 and λ\\in{R} , in the presence of a harmonic confinement. We report the conditions that p and λ must fulfill for the existence and uniqueness of ground states of the GNLS. We discuss the Cauchy problem and summarize which conditions are required for the nonlinear term λ ≤ft\\vert \\varphi \\right\\vert p to render the ground state solutions orbitally stable. Based on a new variational method we provide exact formulæ for the minimum energy for each index p and the changing range of values of the nonlinear parameter λ. Also, we report an approximate close analytical expression for the ground state energy, performing a comparative analysis of the present variational calculations with those obtained by a generalized Thomas-Fermi approach, and soliton solutions for the respective ranges of p and λ where these solutions can be implemented to describe the minimum energy.

  1. Single particle dynamics and nonlinear resonances in circular accelerators

    International Nuclear Information System (INIS)

    Ruth, R.D.

    1985-11-01

    The purpose of this paper is to introduce the reader to single particle dynamics in circular accelerators with an emphasis on nonlinear resonances. We begin with the Hamiltonian and the equations of motion in the neighborhood of the design orbit. In the linear theory this yields linear betatron oscillations about a closed orbit. It is useful then to introduce the action-angle variables of the linear problem. Next we discuss the nonlinear terms which are present in an actual accelerator, and in particular, we motivate the inclusion of sextupoles to cure chromatic effects. To study the effects of the nonlinear terms, we next discuss canonical perturbation theory which leads us to nonlinear resonances. After showing a few examples of perturbation theory, we abandon it when very close to a resonance. This leads to the study of an isolated resonance in one degree of freedom with a 'time'-dependent Hamiltonian. We see the familiar resonance structure in phase space which is simply closed islands when the nonlinear amplitude dependence of the frequency or 'tune' is included. To show the limits of the validity of the isolated resonance approximation, we discuss two criteria for the onset of chaotic motion. Finally, we study an isolated coupling resonance in two degrees of freedom with a 'time'-dependent Hamiltonian and calculate the two invariants in this case. This leads to a surface of section which is a 2-torus in 4-dimensional phase space. However, we show that it remains a 2-torus when projected into particular 3-dimensional subspaces, and thus can be viewed in perspective

  2. Exponential stability of nonlinear time-varying differential equations and applications

    Directory of Open Access Journals (Sweden)

    N. M. Linh

    2001-05-01

    Full Text Available In this paper, we give sufficient conditions for the exponential stability of a class of nonlinear time-varying differential equations. We use the Lyapunov method with functions that are not necessarily differentiable; hence we extend previous results. We also provide an application to exponential stability for nonlinear time-varying control systems.

  3. Non-linear partial differential equations an algebraic view of generalized solutions

    CERN Document Server

    Rosinger, Elemer E

    1990-01-01

    A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen

  4. Recent topics in non-linear partial differential equations 4

    CERN Document Server

    Mimura, M

    1989-01-01

    This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.

  5. Visual Aftereffects and Sensory Nonlinearities from a single Statistical Framework

    Directory of Open Access Journals (Sweden)

    Valero eLaparra

    2015-10-01

    Full Text Available When adapted to a particular scenery our senses may fool us: colors are misinterpreted, certain spatial patterns seem to fade out, and static objects appear to move in reverse. A mere empirical description of the mechanisms tuned to color, texture and motion may tell us where these visual illusions come from. However such empirical models of gain control do not explain why these mechanisms work in this apparently dysfunctional manner.Current normative explanations of aftereffects based on scene statistics derive gain changes by (1 invoking decorrelation and linear manifold matching/equalization, or (2 using nonlinear divisive normalization obtained from parametric scene models. These principled approaches have different drawbacks: the first is not compatible with the known saturation nonlinearities in the sensors and it cannot fully accomplish information maximization due to its linear nature. In the second, gain change is almost determined a priori by the assumed parametric image model linked to divisive normalization.In this study we show that both the response changes that lead to aftereffects and the nonlinear behavior can be simultaneously derived from a single statistical framework: the Sequential Principal Curves Analysis (SPCA. As opposed to mechanistic models, SPCA is not intended to describe how physiological sensors work, but it is focused on explaining why they behave as they do. Nonparametric SPCA has two key advantages as a normative model of adaptation: (i it is better than linear techniques as it is a flexible equalization that can be tuned for more sensible criteria other than plain decorrelation (either full information maximization or error minimization; and (ii it makes no a priori functional assumption regarding the nonlinearity, so the saturations emerge directly from the scene data and the goal (and not from the assumed function. It turns out that the optimal responses derived from these more sensible criteria and SPCA are

  6. Nonlinear dynamics of single-helicity neoclassical MHD tearing instabilities

    International Nuclear Information System (INIS)

    Spong, D.A.; Shaing, K.C.; Carreras, B.A.; Callen, J.D.; Garcia, L.

    1988-10-01

    Neoclassical magnetohydrodynamic (MHD) effects can significantly alter the nonlinear evolution of resistive tearing instabilities. This is studied numerically by using a flux-surface-averaged set of evolution equations that includes the lowest-order neoclassical MHD effects. The new terms in the equations are fluctuating bootstrap current, neoclassical modification of the resistivity, and neoclassical damping of the vorticity. Single-helicity tearing modes are studied in a cylindrical model over a range of neoclassical viscosities (μ/sub e//ν/sup e/) and values of the Δ' parameter of tearing mode theory. Increasing the neoclassical viscosity leads to increased growth rate and saturated island width as predicted analytically. The larger island width is caused by the fluctuating bootstrap current contribution in Ohm's law. The Δ' parameter no longer solely determines the island width, and finite-width saturated islands may be obtained even when Δ' is negative. The importance of the bootstrap current (/approximately/∂/rho///partial derivative/psi/) in the nonlinear dynamics leads us to examine the sensitivity of the results with respect to different models for the density evolution. 11 refs., 8 figs

  7. Non-linear friction in a single crystal of zirconium

    International Nuclear Information System (INIS)

    Ritchie, I.G.; Atrens, A.; Sprungmann, K.W.

    1980-04-01

    Non-linear internal friction phenomena in a single crystal of zirconium are investigated. Both the interactions between dislocations and immobile obstacles and between dislocations and mobile pinning points are involved. It is shown that vibration conditioning and programmed vibration annealing can be used to separate the time-dependent and strain-amplitude-dependent components of the internal friction. An impurity peaking effect has been generated by altering the effective concentration of obstacles by step changes in strain amplitude and vibration conditioning. Repeated thermal cycling at low strain amplitudes, through the terminal solid solubility boundary for hydrogen in zirconium, does not lead to the cumulative increase in dislocation density observed when polycrystalline samples are treated similarly. (auth)

  8. Exact solutions of some nonlinear partial differential equations using ...

    Indian Academy of Sciences (India)

    1Department of Mathematics, Islamic Azad University, Dezful Branch, Dezful, Iran ... such as physics, mechanics, chemistry, biology, mathematics and engineering. ... generates solitons. However, the balance between nonlinearity and genuinely nonlinear dispersion gives rise to the so-called compactons: solitons free of ...

  9. Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations

    International Nuclear Information System (INIS)

    Udaltsov, Vladimir S.; Goedgebuer, Jean-Pierre; Larger, Laurent; Cuenot, Jean-Baptiste; Levy, Pascal; Rhodes, William T.

    2003-01-01

    We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations

  10. Conservation laws for certain time fractional nonlinear systems of partial differential equations

    Science.gov (United States)

    Singla, Komal; Gupta, R. K.

    2017-12-01

    In this study, an extension of the concept of nonlinear self-adjointness and Noether operators is proposed for calculating conserved vectors of the time fractional nonlinear systems of partial differential equations. In our recent work (J Math Phys 2016; 57: 101504), by proposing the symmetry approach for time fractional systems, the Lie symmetries for some fractional nonlinear systems have been derived. In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems.

  11. Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory

    Directory of Open Access Journals (Sweden)

    Iman Eshraghi

    2016-09-01

    Full Text Available Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.

  12. Growth and characterization of nonlinear optical single crystals: bis ...

    Indian Academy of Sciences (India)

    Administrator

    Organic compound; growth from solution; characterization; nonlinear optical materials. 1. Introduction. Organic nonlinear optical (NLO) materials have attracted much attention due to their potential applications in telecommunication, optical switching, optical frequency conversion, THz generation, electro-optical and inte-.

  13. Applications of algebraic method to exactly solve some nonlinear partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Darwish, A.A. [Department of Mathematics, Faculty of Science, Helwan University (Egypt)]. E-mail: profdarwish@yahoo.com; Ramady, A. [Department of Mathematics, Faculty of Science, Beni-Suef University (Egypt)]. E-mail: aramady@yahoo.com

    2007-08-15

    A direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear evolution equations is used and implemented in a computer algebraic system. New solutions for some nonlinear partial differential equations (NLPDE's) are obtained. Graphs of the solutions are displayed.

  14. Positive Solutions for System of Nonlinear Fractional Differential Equations in Two Dimensions with Delay

    Directory of Open Access Journals (Sweden)

    Azizollah Babakhani

    2010-01-01

    Full Text Available We investigate the existence and uniqueness of positive solution for system of nonlinear fractional differential equations in two dimensions with delay. Our analysis relies on a nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorem in a cone.

  15. Method of the quasilinearization for nonlinear impulsive differential equations with linear boundary conditions

    Directory of Open Access Journals (Sweden)

    Paul Eloe

    2002-01-01

    Full Text Available The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved the convergence is quadratic.

  16. Stability and square integrability of solutions of nonlinear fourth order differential equations

    Directory of Open Access Journals (Sweden)

    Moussadek Remili

    2016-05-01

    Full Text Available The aim of the present paper is to establish a new result, which guarantees the asymptotic stability of zero solution and square integrability of solutions and their derivatives to nonlinear differential equations of fourth order.

  17. Existence and attractivity results for nonlinear first order random differential equations

    Directory of Open Access Journals (Sweden)

    Bapurao C. Dhage

    2010-01-01

    Full Text Available In this paper, the existence and attractivity results are proved for nonlinear first order ordinary random differential equations. Two examples are provided to demonstrate the realization of the abstract developed theory.

  18. An Existence Result for Nonlinear Fractional Differential Equations on Banach Spaces

    Directory of Open Access Journals (Sweden)

    Djamila Seba

    2009-01-01

    Full Text Available The aim of this paper is to investigate a class of boundary value problem for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of noncompactness.

  19. Some nonlinear integral inequalities arising in differential equations

    Directory of Open Access Journals (Sweden)

    Assia Guezane-Lakoud

    2008-05-01

    Full Text Available The aim of this paper is to obtain estimates for functions satisfying some nonlinear integral inequalities. Using ideas from Pachpatte [3], we generalize the estimates presented in [2,4].

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

    Directory of Open Access Journals (Sweden)

    Hassan A. Zedan

    2012-01-01

    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.

  1. Non-linear mixed-effects pharmacokinetic/pharmacodynamic modelling in NLME using differential equations

    DEFF Research Database (Denmark)

    Tornøe, Christoffer Wenzel; Agersø, Henrik; Madsen, Henrik

    2004-01-01

    equation (ODE) solver package odesolve and the non-Linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlme......The standard software for non-linear mixed-effect analysis of pharmacokinetic/phar-macodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as tong as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential...

  2. On the correct formulation of a nonlinear differential equations in Banach space

    Directory of Open Access Journals (Sweden)

    Mahmoud M. El-Borai

    2001-01-01

    Full Text Available We study, the existence and uniqueness of the initial value problems in a Banach space E for the abstract nonlinear differential equation (dn−1/dtn−1(du/dt+Au=B(tu+f(t,W(t, and consider the correct solution of this problem. We also give an application of the theory of partial differential equations.

  3. Analysis of an Nth-order nonlinear differential-delay equation

    Science.gov (United States)

    Vallée, Réal; Marriott, Christopher

    1989-01-01

    The problem of a nonlinear dynamical system with delay and an overall response time which is distributed among N individual components is analyzed. Such a system can generally be modeled by an Nth-order nonlinear differential delay equation. A linear-stability analysis as well as a numerical simulation of that equation are performed and a comparison is made with the experimental results. Finally, a parallel is established between the first-order differential equation with delay and the Nth-order differential equation without delay.

  4. From the hypergeometric differential equation to a non-linear Schrödinger one

    International Nuclear Information System (INIS)

    Plastino, A.; Rocca, M.C.

    2015-01-01

    We show that the q-exponential function is a hypergeometric function. Accordingly, it obeys the hypergeometric differential equation. We demonstrate that this differential equation can be transformed into a non-linear Schrödinger equation (NLSE). This NLSE exhibits both similarities and differences vis-a-vis the Nobre–Rego-Monteiro–Tsallis one. - Highlights: • We show that the q-exponential is a hypergeometric function. • It thus obeys the hypergeometric differential equation (HDE). • We show that the HDE can be cast as a non-linear Schrödinger equation. • This is different from the Nobre, Rego-Monteiro, Tsallis one.

  5. A Novel Differential Evolution Invasive Weed Optimization Algorithm for Solving Nonlinear Equations Systems

    Directory of Open Access Journals (Sweden)

    Yongquan Zhou

    2013-01-01

    Full Text Available In view of the traditional numerical method to solve the nonlinear equations exist is sensitive to initial value and the higher accuracy of defects. This paper presents an invasive weed optimization (IWO algorithm which has population diversity with the heuristic global search of differential evolution (DE algorithm. In the iterative process, the global exploration ability of invasive weed optimization algorithm provides effective search area for differential evolution; at the same time, the heuristic search ability of differential evolution algorithm provides a reliable guide for invasive weed optimization. Based on the test of several typical nonlinear equations and a circle packing problem, the results show that the differential evolution invasive weed optimization (DEIWO algorithm has a higher accuracy and speed of convergence, which is an efficient and feasible algorithm for solving nonlinear systems of equations.

  6. Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

    Directory of Open Access Journals (Sweden)

    Veyis Turut

    2013-01-01

    Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

  7. Synthesis, thermal and nonlinear optical characterization of L-arginine semi-oxalate single crystals

    Science.gov (United States)

    Vasudevan, P.; Gokulraj, S.; Sankar, S.

    2012-06-01

    Optically good quality L-arginine semi-oxalate, an organic nonlinear optical crystal, has been synthesized from aqueous solution by slow evaporation method. Single crystal X-ray diffraction (XRD) analysis reveals that the synthesized L-arginine semi-oxalate crystal possesses triclinic structure with unit cell dimensions as a=5.05Å, b=9.73Å, c=13.12Å, α=111.030, β=92.790 and γ=91.910. The Fourier transform infra-red (FTIR) spectroscopy was analyzed and the presence of functional groups of L-arginine semi-oxalate was confirmed. Thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) studies show that the material is thermally stable up to 1460C and the melting point is 1500C. Kurtz and Perry powder technique confirms that the second harmonic generation (SHG) efficiency is 0.32 times that of standard organic materials urea and KDP.

  8. An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

    Directory of Open Access Journals (Sweden)

    A. H. Bhrawy

    2014-01-01

    Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

  9. Differential reductions of the Kadomtsev-Petviashvili equation and associated higher dimensional nonlinear PDEs

    Science.gov (United States)

    Zenchuk, A. I.

    2009-11-01

    We represent an algorithm allowing one to construct new classes of partially integrable multidimensional nonlinear partial differential equations (PDEs) starting with the special type of solutions to the (1 + 1)-dimensional hierarchy of nonlinear PDEs linearizable by the matrix Hopf-Cole substitution (the Bürgers hierarchy). We derive examples of four-dimensional nonlinear matrix PDEs together with the scalar and three-dimensional reductions. Variants of the Kadomtsev-Petviashvili-type and Korteweg-de Vries-type equations are represented among them. Our algorithm is based on the combination of two Frobenius-type reductions and special differential reduction imposed on the matrix fields of integrable PDEs. It is shown that the derived four-dimensional nonlinear PDEs admit arbitrary functions of two variables in their solution spaces which clarifies the integrability degree of these PDEs.

  10. Thermal rectification and negative differential thermal conductance in harmonic chains with nonlinear system-bath coupling

    Science.gov (United States)

    Ming, Yi; Li, Hui-Min; Ding, Ze-Jun

    2016-03-01

    Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011), 10.1038/nnano.2011.71]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.

  11. Numerical approximations of nonlinear fractional differential difference equations by using modified He-Laplace method

    Directory of Open Access Journals (Sweden)

    J. Prakash

    2016-03-01

    Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.

  12. Singular and non-topological soliton solutions for nonlinear fractional differential equations

    Science.gov (United States)

    Ozkan, Guner

    2015-10-01

    In this article, the fractional derivatives are described in the modified Riemann-Liouville sense. We propose a new approach, namely an ansatz method, for solving fractional differential equations (FDEs) based on a fractional complex transform and apply it to solve nonlinear space-time fractional equations. As a result, the non-topological as well as the singular soliton solutions are obtained. This method can be suitable and more powerful for solving other kinds of nonlinear fractional FDEs arising in mathematical physics.

  13. Algorithmic Approximation of Optimal Value Differential Stability Bounds in Nonlinear Programming,

    Science.gov (United States)

    1981-08-01

    NCLASSIFIED RANO/PA6659 N IN *~4 112.0.0 ~11111,.. I32 111 IIIII 111111.25 MICROCOPY RESOLUTION TESI CHART NATIOt AL BJRLAU Of SIANDARD 1964 A * LEVEL 00 o pm...Sensitivity Analysis in Parametric Nonlinear Programming, Doctoral Dissertation, School of Engineering and Applied Science, The George Washington University...Differential Stability of the Optimal Value Function in Constrained Nonlinear Programing, Doctoral Disser- tation, School of Engineering and Applied

  14. Estimation of delays and other parameters in nonlinear functional differential equations

    Science.gov (United States)

    Banks, H. T.; Lamm, P. K. D.

    1983-01-01

    A spline-based approximation scheme for nonlinear nonautonomous delay differential equations is discussed. Convergence results (using dissipative type estimates on the underlying nonlinear operators) are given in the context of parameter estimation problems which include estimation of multiple delays and initial data as well as the usual coefficient-type parameters. A brief summary of some of the related numerical findings is also given.

  15. Analytical approximate solutions for a general class of nonlinear delay differential equations.

    Science.gov (United States)

    Căruntu, Bogdan; Bota, Constantin

    2014-01-01

    We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

  16. Existence and Uniqueness of Solutions for Coupled Systems of Higher-Order Nonlinear Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Ahmad Bashir

    2010-01-01

    Full Text Available We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.

  17. Identification Techniques for Nonlinear Differential Equations of Motion

    Science.gov (United States)

    1990-03-01

    using k/(27f n) . The value of the viscous damping is estimated on the basis of the magnitude of A1 at f=fn where JA1 j = 2nf c. 5.2.2 Puffing SDOF...Vibration, vol 81, 1982. 9. H.J. Rice , and J.A. Fitzpatrick. "A generalized technique for spectral analysis of nonlinear systems," Mechanical Systems...and Signal Processing, vol 2, 1988, pp 243-249. 40 10. H.J. Rice , H. Esmonde, and J.A. Fitzpatrick. "A spectral method for identifying quadratic

  18. Algorithms of estimation for nonlinear systems a differential and algebraic viewpoint

    CERN Document Server

    Martínez-Guerra, Rafael

    2017-01-01

    This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.

  19. 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: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)

    2013-09-02

    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.

  20. A single mode method for the analysis and identification of nonlinear MDOF systems

    Science.gov (United States)

    Huang, Liping; Iwan, W. D.

    In order to apply mode approach to describe a nonlinear system, the concept of modal response of nonlinear systems is examined, and an amplitude-dependent modal model is presented based on an analysis of a single mode of response. The effectiveness of this model is examined under different types and various levels of excitation. A corresponding identification procedure for cubic systems is proposed and applied to the analysis of a 3DOF soltening nonlinear system.

  1. The Dhage Iteration Principle for Coupled PBVPs of Nonlinear Second Order Differential Equations

    Directory of Open Access Journals (Sweden)

    Bapurao C. Dhage

    2015-05-01

    Full Text Available The present paper proposes a new monotone iteration principle for the existence as well as approximations of the coupled solutions for a coupled periodic boundary value problem of second order ordinary nonlinear differential equations. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper. We claim that the method as well as the results of this paper are new to literature on nonlinear analysis and applications.

  2. Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Jing Wu

    2012-01-01

    Full Text Available We study the eigenvalue interval for the existence of positive solutions to a semipositone higher order fractional differential equation = =   where ,  , , , satisfying , is the standard Riemann-Liouville derivative, , and is allowed to be changing-sign. By using reducing order method, the eigenvalue interval of existence for positive solutions is obtained.

  3. Calculation of Volterra kernels for solutions of nonlinear differential equations

    NARCIS (Netherlands)

    van Hemmen, JL; Kistler, WM; Thomas, EGF

    2000-01-01

    We consider vector-valued autonomous differential equations of the form x' = f(x) + phi with analytic f and investigate the nonanticipative solution operator phi bar right arrow A(phi) in terms of its Volterra series. We show that Volterra kernels of order > 1 occurring in the series expansion of

  4. Fault detection and diagnosis in nonlinear systems a differential and algebraic viewpoint

    CERN Document Server

    Martinez-Guerra, Rafael

    2014-01-01

    The high reliability required in industrial processes has created the necessity of detecting abnormal conditions, called faults, while processes are operating. The term fault generically refers to any type of process degradation, or degradation in equipment performance because of changes in the process's physical characteristics, process inputs or environmental conditions. This book is about the fundamentals of fault detection and diagnosis in a variety of nonlinear systems which are represented by ordinary differential equations. The fault detection problem is approached from a differential algebraic viewpoint, using residual generators based upon high-gain nonlinear auxiliary systems (‘observers’). A prominent role is played by the type of mathematical tools that will be used, requiring knowledge of differential algebra and differential equations. Specific theorems tailored to the needs of the problem-solving procedures are developed and proved. Applications to real-world problems, both with constant an...

  5. Microhardness studies on nonlinear optical L-alanine single crystals

    Indian Academy of Sciences (India)

    Keywords. Organic compounds; mechanical properties; hardness; anisotropy. 1. Introduction. Nonlinear optical applications find a variety of applica- tions such as frequency conversion, light modulation, opti- cal switching, optical memory storage and optical second harmonic generation (SHG) (Wang et al 1999; Chenthama ...

  6. Nonlinear digital out-of-plane waveguide coupler based on nonlinear scattering of a single graphene layer

    Science.gov (United States)

    Asadi, Reza; Ouyang, Zhengbiao

    2018-03-01

    A new mechanism for out-of-plane coupling into a waveguide is presented and numerically studied based on nonlinear scattering of a single nano-scale Graphene layer inside the waveguide. In this mechanism, the refractive index nonlinearity of Graphene and nonhomogeneous light intensity distribution occurred due to the interference between the out-of-plane incident pump light and the waveguide mode provide a virtual grating inside the waveguide, coupling the out-of-plane pump light into the waveguide. It has been shown that the coupling efficiency has two distinct values with high contrast around a threshold pump intensity, providing suitable condition for digital optical applications. The structure operates at a resonance mode due to band edge effect, which enhances the nonlinearity and decreases the required threshold intensity.

  7. Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method

    International Nuclear Information System (INIS)

    Lewandowski, Jerome L.V.

    2005-01-01

    A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details

  8. A semi-analytical approach for solving of nonlinear systems of functional differential equations with delay

    Science.gov (United States)

    Rebenda, Josef; Šmarda, Zdeněk

    2017-07-01

    In the paper, we propose a correct and efficient semi-analytical approach to solve initial value problem for systems of functional differential equations with delay. The idea is to combine the method of steps and differential transformation method (DTM). In the latter, formulas for proportional arguments and nonlinear terms are used. An example of using this technique for a system with constant and proportional delays is presented.

  9. GDTM-Padé technique for the non-linear differential-difference equation

    Directory of Open Access Journals (Sweden)

    Lu Jun-Feng

    2013-01-01

    Full Text Available This paper focuses on applying the GDTM-Padé technique to solve the non-linear differential-difference equation. The bell-shaped solitary wave solution of Belov-Chaltikian lattice equation is considered. Comparison between the approximate solutions and the exact ones shows that this technique is an efficient and attractive method for solving the differential-difference equations.

  10. Polarized dependence of nonlinear susceptibility in a single layer graphene system in infrared region

    Energy Technology Data Exchange (ETDEWEB)

    Solookinejad, G., E-mail: ghsolooki@gmail.com

    2016-09-15

    In this study, the linear and nonlinear susceptibility of a single-layer graphene nanostructure driven by a weak probe light and an elliptical polarized coupling field is discussed theoretically. The Landau levels of graphene can be separated in infrared or terahertz regions under the strong magnetic field. Therefore, by using the density matrix formalism in quantum optic, the linear and nonlinear susceptibility of the medium can be derived. It is demonstrated that by adjusting the elliptical parameter, one can manipulate the linear and nonlinear absorption as well as Kerr nonlinearity of the medium. It is realized that the enhanced Kerr nonlinearity can be possible with zero linear absorption and nonlinear amplification at some values of elliptical parameter. Our results may be having potential applications in quantum information science based on Nano scales devices.

  11. Direct application of Padé approximant for solving nonlinear differential equations.

    Science.gov (United States)

    Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

    2014-01-01

    This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

  12. Adaptive Neural Control of Nonaffine Nonlinear Systems without Differential Condition for Nonaffine Function

    Directory of Open Access Journals (Sweden)

    Chaojiao Sun

    2016-01-01

    Full Text Available An adaptive neural control scheme is proposed for nonaffine nonlinear system without using the implicit function theorem or mean value theorem. The differential conditions on nonaffine nonlinear functions are removed. The control-gain function is modeled with the nonaffine function probably being indifferentiable. Furthermore, only a semibounded condition for nonaffine nonlinear function is required in the proposed method, and the basic idea of invariant set theory is then constructively introduced to cope with the difficulty in the control design for nonaffine nonlinear systems. It is rigorously proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.

  13. Multipoint Singular Boundary-Value Problem for Systems of Nonlinear Differential Equations

    Directory of Open Access Journals (Sweden)

    Zdeněk Šmarda

    2009-01-01

    Full Text Available A singular Cauchy-Nicoletti problem for a system of nonlinear ordinary differential equations is considered. With the aid of combination of Ważewski's topological method and Schauder's principle, the theorem concerning the existence of a solution of this problem (having the graph in a prescribed domain is proved.

  14. Differential Polarization Nonlinear Optical Microscopy with Adaptive Optics Controlled Multiplexed Beams

    Directory of Open Access Journals (Sweden)

    Virginijus Barzda

    2013-09-01

    Full Text Available Differential polarization nonlinear optical microscopy has the potential to become an indispensable tool for structural investigations of ordered biological assemblies and microcrystalline aggregates. Their microscopic organization can be probed through fast and sensitive measurements of nonlinear optical signal anisotropy, which can be achieved with microscopic spatial resolution by using time-multiplexed pulsed laser beams with perpendicular polarization orientations and photon-counting detection electronics for signal demultiplexing. In addition, deformable membrane mirrors can be used to correct for optical aberrations in the microscope and simultaneously optimize beam overlap using a genetic algorithm. The beam overlap can be achieved with better accuracy than diffraction limited point-spread function, which allows to perform polarization-resolved measurements on the pixel-by-pixel basis. We describe a newly developed differential polarization microscope and present applications of the differential microscopy technique for structural studies of collagen and cellulose. Both, second harmonic generation, and fluorescence-detected nonlinear absorption anisotropy are used in these investigations. It is shown that the orientation and structural properties of the fibers in biological tissue can be deduced and that the orientation of fluorescent molecules (Congo Red, which label the fibers, can be determined. Differential polarization microscopy sidesteps common issues such as photobleaching and sample movement. Due to tens of megahertz alternating polarization of excitation pulses fast data acquisition can be conveniently applied to measure changes in the nonlinear signal anisotropy in dynamically changing in vivo structures.

  15. An approximation theory for nonlinear partial differential equations with applications to identification and control

    Science.gov (United States)

    Banks, H. T.; Kunisch, K.

    1982-01-01

    Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

  16. Detection of Differential Item Functioning with Nonlinear Regression: A Non-IRT Approach Accounting for Guessing

    Science.gov (United States)

    Drabinová, Adéla; Martinková, Patrícia

    2017-01-01

    In this article we present a general approach not relying on item response theory models (non-IRT) to detect differential item functioning (DIF) in dichotomous items with presence of guessing. The proposed nonlinear regression (NLR) procedure for DIF detection is an extension of method based on logistic regression. As a non-IRT approach, NLR can…

  17. Weak solutions for nonlinear fractional differential equations on reflexive Banach spaces

    Directory of Open Access Journals (Sweden)

    Mouffak Benchohra

    2010-09-01

    Full Text Available The aim of this paper is to investigate a class of boundary value problem for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.

  18. The focal boundary value problem for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Půža, B.

    2015-01-01

    Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1

  19. On periodic bounded and unbounded solutions of second order nonlinear ordinary differential equations

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, Alexander

    2017-01-01

    Roč. 24, č. 2 (2017), s. 241-263 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : nonlinear ordinary differential equations * periodic boundary value problem * solvability Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2017-0009/gmj-2017-0009. xml

  20. Existence results for boundary-value problems with nonlinear fractional differential inclusions and integral conditions

    Directory of Open Access Journals (Sweden)

    Samira Hamani

    2010-01-01

    Full Text Available In this article, the authors establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential inclusions involving the Caputo fractional derivative and nonlinear integral conditions. Both cases of convex and nonconvex valued right hand sides are considered. The topological structure of the set of solutions also examined.

  1. Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach spaces

    Directory of Open Access Journals (Sweden)

    Mouffak Benchohra

    2012-01-01

    Full Text Available The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.

  2. Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity

    Directory of Open Access Journals (Sweden)

    Leonid Berezansky

    2005-04-01

    Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.

  3. Stability of abstract nonlinear nonautonomous differential-delay equations with unbounded history-responsive operators

    Science.gov (United States)

    Gil', M. I.

    2005-08-01

    We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.

  4. Asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^n

    Directory of Open Access Journals (Sweden)

    Meng-Rong Li

    2013-11-01

    Full Text Available In this article we study properties of positive solutions of the ordinary differential equation $t^2u''=u^n$ for $1nonlinear terms are also considered.

  5. Differential polarization nonlinear optical microscopy with adaptive optics controlled multiplexed beams.

    Science.gov (United States)

    Samim, Masood; Sandkuijl, Daaf; Tretyakov, Ian; Cisek, Richard; Barzda, Virginijus

    2013-09-09

    Differential polarization nonlinear optical microscopy has the potential to become an indispensable tool for structural investigations of ordered biological assemblies and microcrystalline aggregates. Their microscopic organization can be probed through fast and sensitive measurements of nonlinear optical signal anisotropy, which can be achieved with microscopic spatial resolution by using time-multiplexed pulsed laser beams with perpendicular polarization orientations and photon-counting detection electronics for signal demultiplexing. In addition, deformable membrane mirrors can be used to correct for optical aberrations in the microscope and simultaneously optimize beam overlap using a genetic algorithm. The beam overlap can be achieved with better accuracy than diffraction limited point-spread function, which allows to perform polarization-resolved measurements on the pixel-by-pixel basis. We describe a newly developed differential polarization microscope and present applications of the differential microscopy technique for structural studies of collagen and cellulose. Both, second harmonic generation, and fluorescence-detected nonlinear absorption anisotropy are used in these investigations. It is shown that the orientation and structural properties of the fibers in biological tissue can be deduced and that the orientation of fluorescent molecules (Congo Red), which label the fibers, can be determined. Differential polarization microscopy sidesteps common issues such as photobleaching and sample movement. Due to tens of megahertz alternating polarization of excitation pulses fast data acquisition can be conveniently applied to measure changes in the nonlinear signal anisotropy in dynamically changing in vivo structures.

  6. Differential Polarization Nonlinear Optical Microscopy with Adaptive Optics Controlled Multiplexed Beams

    Science.gov (United States)

    Samim, Masood; Sandkuijl, Daaf; Tretyakov, Ian; Cisek, Richard; Barzda, Virginijus

    2013-01-01

    Differential polarization nonlinear optical microscopy has the potential to become an indispensable tool for structural investigations of ordered biological assemblies and microcrystalline aggregates. Their microscopic organization can be probed through fast and sensitive measurements of nonlinear optical signal anisotropy, which can be achieved with microscopic spatial resolution by using time-multiplexed pulsed laser beams with perpendicular polarization orientations and photon-counting detection electronics for signal demultiplexing. In addition, deformable membrane mirrors can be used to correct for optical aberrations in the microscope and simultaneously optimize beam overlap using a genetic algorithm. The beam overlap can be achieved with better accuracy than diffraction limited point-spread function, which allows to perform polarization-resolved measurements on the pixel-by-pixel basis. We describe a newly developed differential polarization microscope and present applications of the differential microscopy technique for structural studies of collagen and cellulose. Both, second harmonic generation, and fluorescence-detected nonlinear absorption anisotropy are used in these investigations. It is shown that the orientation and structural properties of the fibers in biological tissue can be deduced and that the orientation of fluorescent molecules (Congo Red), which label the fibers, can be determined. Differential polarization microscopy sidesteps common issues such as photobleaching and sample movement. Due to tens of megahertz alternating polarization of excitation pulses fast data acquisition can be conveniently applied to measure changes in the nonlinear signal anisotropy in dynamically changing in vivo structures. PMID:24022688

  7. Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro-Differential Equation

    Directory of Open Access Journals (Sweden)

    Berenguer MI

    2010-01-01

    Full Text Available This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of this type of equation, due to some properties of certain biorthogonal systems for the Banach spaces and .

  8. Partially solved differential systems with two-point non-linear boundary conditions

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rontó, M.; Varga, I.

    2017-01-01

    Roč. 18, č. 2 (2017), s. 1001-1014 ISSN 1787-2405 Institutional support: RVO:67985840 Keywords : implicit differential systems * non-linear two-point boundary conditions * parametrization technique Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.388, year: 2016 http://mat76.mat.uni-miskolc.hu/mnotes/article/2491

  9. Asymptotic Dichotomy in a Class of Odd-Order Nonlinear Differential Equations with Impulses

    Directory of Open Access Journals (Sweden)

    Kunwen Wen

    2013-01-01

    Full Text Available We investigate the oscillatory and asymptotic behavior of a class of odd-order nonlinear differential equations with impulses. We obtain criteria that ensure every solution is either oscillatory or (nonoscillatory and zero convergent. We provide several examples to show that impulses play an important role in the asymptotic behaviors of these equations.

  10. Existence and Multiplicity Results for Nonlinear Differential Equations Depending on a Parameter in Semipositone Case

    Directory of Open Access Journals (Sweden)

    Hailong Zhu

    2012-01-01

    Full Text Available The existence and multiplicity of solutions for second-order differential equations with a parameter are discussed in this paper. We are mainly concerned with the semipositone case. The analysis relies on the nonlinear alternative principle of Leray-Schauder and Krasnosel'skii's fixed point theorem in cones.

  11. Synthesis, growth, crystal structure, optical and third order nonlinear optical properties of quinolinium derivative single crystal: PNQI

    Science.gov (United States)

    Karthigha, S.; Krishnamoorthi, C.

    2018-03-01

    An organic quinolinium derivative nonlinear optical (NLO) crystal, 1-ethyl-2-[2-(4-nitro-phenyl)-vinyl]-quinolinium iodide (PNQI) was synthesized and successfully grown by slow evaporation solution growth technique. Formation of a crystalline compound was confirmed by single crystal X-ray diffraction. The quinolinium compound PNQI crystallizes in the triclinic crystal system with a centrosymmetric space group of P-1 symmetry. The molecular structure of PNQI was confirmed by 1H NMR and 13C NMR spectral studies. The thermal properties of the crystal have been investigated by thermogravimetric (TG) and differential scanning calorimetry (DSC) studies. The optical characteristics obtained from UV-Vis-NIR spectral data were described and the cut-off wavelength observed at 506 nm. The etching study was performed to analyse the growth features of PNQI single crystal. The third order NLO properties such as nonlinear refractive index (n2), nonlinear absorption coefficient (β) and nonlinear susceptibility (χ (3)) of the crystal were investigated using Z-scan technique at 632.8 nm of Hesbnd Ne laser.

  12. Growth and characterization of nonlinear optical single crystals: bis ...

    Indian Academy of Sciences (India)

    methoxy benzoate (C4MB) single crystals were successfully grown by the slow evaporation solution growth technique. The harvested crystals were subjected to single-crystal X-ray diffraction, spectral, optical, thermal and mechanical studies in ...

  13. Discontinuous Galerkin Methods for NonLinear Differential Systems

    Science.gov (United States)

    Barth, Timothy; Mansour, Nagi (Technical Monitor)

    2001-01-01

    This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

  14. Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

    KAUST Repository

    El-Beltagy, Mohamed A.

    2015-01-07

    Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

  15. Existence of Wave Front Solutions of an Integral Differential Equation in Nonlinear Nonlocal Neuronal Network

    Directory of Open Access Journals (Sweden)

    Lijun Zhang

    2014-01-01

    Full Text Available An integral-differential model equation arising from neuronal networks with very general kernel functions is considered in this paper. The kernel functions we study here include pure excitations, lateral inhibition, lateral excitations, and more general synaptic couplings (e.g., oscillating kernel functions. The main goal of this paper is to prove the existence and uniqueness of the traveling wave front solutions. The main idea we apply here is to reduce the nonlinear integral-differential equation into a solvable differential equation and test whether the solution we get is really a wave front solution of the model equation.

  16. Intermittently chaotic oscillations for a differential-delay equation with Gaussian nonlinearity

    Science.gov (United States)

    Hamilton, Ian

    1992-01-01

    For a differential-delay equation the time dependence of the variable is a function of the variable at a previous time. We consider a differential-delay equation with Gaussian nonlinearity that displays intermittent chaos. Although not the first example of a differential-delay equation that displays such behavior, for this example the intermittency is classified as type III, and the origin of the intermittent chaos may be qualitatively understood from the limiting forms of the equation for large and small variable magnitudes.

  17. 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

    2010-12-15

    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.)

  18. Equivalence transformations and differential invariants of a generalized nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Senthilvelan, M; Torrisi, M; Valenti, A

    2006-01-01

    By using Lie's invariance infinitesimal criterion, we obtain the continuous equivalence transformations of a class of nonlinear Schroedinger equations with variable coefficients. We construct the differential invariants of order 1 starting from a special equivalence subalgebra E χ o . We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schr?dinger equations which can be mapped, by means of an equivalence transformation of E χ o , to the well-known cubic Schroedinger equation. We also provide the explicit form of the transformation

  19. Spectral methods for a nonlinear initial value problem involving pseudo differential operators

    International Nuclear Information System (INIS)

    Pasciak, J.E.

    1982-01-01

    Spectral methods (Fourier methods) for approximating the solution of a nonlinear initial value problem involving pseudo differential operators are defined and analyzed. A semidiscrete approximation to the nonlinear equation based on an L 2 projection is described. The semidiscrete L 2 approximation is shown to be a priori stable and convergent under sufficient decay and smoothness assumptions on the initial data. It is shown that the semidiscrete method converges with infinite order, that is, higher order decay and smoothness assumptions imply higher order error bounds. Spectral schemes based on spacial collocation are also discussed

  20. Simple equation method for nonlinear partial differential equations and its applications

    Directory of Open Access Journals (Sweden)

    Taher A. Nofal

    2016-04-01

    Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.

  1. Dynamics of excited instantons in the system of forced Gursey nonlinear differential equations

    Science.gov (United States)

    Aydogmus, F.

    2015-02-01

    The Gursey model is a 4D conformally invariant pure fermionic model with a nonlinear spinor self-coupled term. Gursey proposed his model as a possible basis for a unitary description of elementary particles following the "Heisenberg dream." In this paper, we consider the system of Gursey nonlinear differential equations (GNDEs) formed by using the Heisenberg ansatz. We use it to understand how the behavior of spinor-type Gursey instantons can be affected by excitations. For this, the regular and chaotic numerical solutions of forced GNDEs are investigated by constructing their Poincaré sections in phase space. A hierarchical cluster analysis method for investigating the forced GNDEs is also presented.

  2. Highly efficient single-pass sum frequency generation by cascaded nonlinear crystals

    DEFF Research Database (Denmark)

    Hansen, Anders Kragh; Andersen, Peter E.; Jensen, Ole Bjarlin

    2015-01-01

    The cascading of nonlinear crystals has been established as a simple method to greatly increase the conversion efficiency of single-pass second-harmonic generation compared to a single-crystal scheme. Here, we show for the first time that the technique can be extended to sum frequency generation......, despite differences in the phase relations of the involved fields. An unprecedented 5.5 W of continuous-wave diffraction-limited green light is generated from the single-pass sum frequency mixing of two diode lasers in two periodically poled nonlinear crystals (conversion efficiency 50%). The technique...

  3. Nonlinear pulse propagation in a single-and a few-cycle regimes ...

    Indian Academy of Sciences (India)

    The propagation equation for a single- and a few-cycle pulses was derived in a cubic nonlinear medium including the Raman response. Using this equation, the propagation characteristics of a single- and a 4-cycle pulse, at 0.8 m wavelength, were studied numerically in one spatial dimension. It was shown that Raman ...

  4. A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

    Science.gov (United States)

    Benhammouda, Brahim; Vazquez-Leal, Hector

    2016-01-01

    This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

  5. Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

    Science.gov (United States)

    Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

    2014-01-01

    In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

  6. Lattice Boltzmann model for high-order nonlinear partial differential equations

    Science.gov (United States)

    Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

    2018-01-01

    In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

  7. Nonlinear growth of a single neoclassical MHD tearing mode in a tokamak

    International Nuclear Information System (INIS)

    Qu, W.X.; Callen, J.D.

    1985-10-01

    The nonlinear evolution equation for the growth of a single neoclassical MHD tearing mode is derived from the usual resistive MHD equations with neoclassical effects included. For the case Δ' > 0 where the usual resistive MHD modes are unstable, in nonlinear neoclassical MHD there is an intermediate time regime in which the island width w grows only as t/sup 1/2/. However, eventually the neoclassical MHD tearing modes are found to enter the usual resistive MHD Rutherford regime where w infinity t. Physically, the neoclassical MHD bootstrap current effects modify the linear and early nonlinear growth of tearing modes. However, eventually the magnetic islands flatten the pressure gradient within the island to remove these effects and return, at long times, to the usual quasilinear picture for the nonlinear evolution of a single resistive MHD tearing mode

  8. An ansatz for solving nonlinear partial differential equations in mathematical physics.

    Science.gov (United States)

    Akbar, M Ali; Ali, Norhashidah Hj Mohd

    2016-01-01

    In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

  9. Bright and dark soliton solutions for some nonlinear fractional differential equations

    Science.gov (United States)

    Ozkan, Guner; Ahmet, Bekir

    2016-03-01

    In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona-Mahoney (mBBM) equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions: amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional derivatives are described in the modified Riemann-Liouville sense.

  10. Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

    Science.gov (United States)

    Ma, Wen-Xiu; Zhou, Yuan

    2018-02-01

    Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u = 2(ln ⁡ f) x and u = 2(ln ⁡ f) xx, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations.

  11. Nonlinear single particle issues for the LHC at CERN

    CERN Document Server

    Schmidt, F

    1998-01-01

    One of the critical design issues of the LHC is the field quality of the super-conduting dipole and quadrupole magnets, in particular at injection energy. In close collaboration with the magnet designers the field quality is optimised with respect to required dynamic aperture and technological and financial limitations. The main tool is still brute force tracking simulations. The simulation codes are simple, easily adaptable to new requirements and highly optimised for the use on modern computer architectures. To perform the massive tracking studies needed to do this field quality optimisation, a cluster of 20 DEC alpha workstations has been purchased. On the other hand one has to analyse these tracking results with tools that can evaluate the highly nonlinear content of the accelerator structure. In the last decade the Normal Form Tool and more recently the Frequency Map Analysis have been introduced to our field which allow for such an analysis. A number of programs have been developed that are based on the...

  12. On periodic bounded and unbounded solutions of second order nonlinear ordinary differential equations

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, Alexander

    2017-01-01

    Roč. 24, č. 2 (2017), s. 241-263 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : nonlinear ordinary differential equations * periodic boundary value problem * solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2017-0009/gmj-2017-0009. xml

  13. Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method

    OpenAIRE

    Abuteen, Eman; Freihat, Asad; Al-Smadi, Mohammed; Khalil, Hammad; Khan, Rahmat Ali

    2017-01-01

    This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced Differential Transform Method (FRDTM). This technique provides the solutions very accurately and efficiently in convergent series formula with easily computable coefficients. The behavior of the approximate series solution for different values of fractional-order "a" ...

  14. Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method

    OpenAIRE

    Z. Pashazadeh Atabakan; A. Kazemi Nasab; A. Kılıçman; Zainidin K. Eshkuvatov

    2013-01-01

    Spectral homotopy analysis method (SHAM) as a modification of homotopy analysis method (HAM) is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange i...

  15. Approximating solutions of nonlinear PBVPs of second-order differential equations via hybrid fixed point theory

    Directory of Open Access Journals (Sweden)

    Bapurao C. Dhage

    2015-01-01

    Full Text Available In this article we prove the existence and approximations of solutions of periodic boundary-value problems of second-order ordinary nonlinear hybrid differential equations. We rely our results on Dhage iteration principle or method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. Our resutls are proved under weaker continuity and Lipschitz conditions. An example illustrates the theory developed in this article.

  16. Existence and Uniqueness Results for Nonlinear Implicit Fractional Differential Equations with Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Mouffak Benchohra

    2014-05-01

    Full Text Available In this paper, we establish the existence and uniqueness of solution for a class of boundary value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, Schauder's fixed point theorem and the nonlinear alterna- tive of Leray-Schauder type. As applications, two examples are included to show the applicability of our results.

  17. Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations

    Directory of Open Access Journals (Sweden)

    C. Ünlü

    2013-01-01

    Full Text Available A modification of the variational iteration method (VIM for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE obtained using the traditional variational iteration method give good approximations in the neighborhood of the initial position. The main advantage of the present method is that it can accelerate the convergence of the iterative approximate solutions relative to the approximate solutions obtained using the traditional variational iteration method. Illustrative examples are presented to show the validity of this modification.

  18. Approximating positive solutions of nonlinear first order ordinary quadratic differential equations

    Directory of Open Access Journals (Sweden)

    Bapurao C. Dhage

    2015-12-01

    Full Text Available In this paper, the authors prove the existence as well as approximations of the positive solutions for an initial value problem of first-order ordinary nonlinear quadratic differential equations. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations converges monotonically to the positive solution of related quadratic differential equations under some suitable mixed hybrid conditions. We base our results on the Dhage iteration method embodied in a recent hybrid fixed-point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.

  19. Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with Maxima

    Directory of Open Access Journals (Sweden)

    Shyam B. Dhage

    2016-03-01

    Full Text Available In this paper authors prove the existence as well as approximation of the positive solutions for a periodic boundary value problem of first order ordinary nonlinear quadratic differential equations with maxima. An algorithm for the solutions is developed and it is shown that certain sequence of successive approximations converges monotonically to the positive solution of considered quadratic differential equations under some suitable mixed hybrid conditions. Our results rely on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2014. A numerical example is also provided to illustrate the hypotheses and abstract theory developed in this paper.

  20. Oscillation criteria for third order nonlinear delay differential equations with damping

    Directory of Open Access Journals (Sweden)

    Said R. Grace

    2015-01-01

    Full Text Available This note is concerned with the oscillation of third order nonlinear delay differential equations of the form \\[\\label{*} \\left( r_{2}(t\\left( r_{1}(ty^{\\prime}(t\\right^{\\prime}\\right^{\\prime}+p(ty^{\\prime}(t+q(tf(y(g(t=0.\\tag{\\(\\ast\\}\\] In the papers [A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007, 54-68] and [M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Applied Math. Letters 23 (2010, 756-762], the authors established some sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates or converges to zero, provided that the second order equation \\[\\left( r_{2}(tz^{\\prime }(t\\right^{\\prime}+\\left(p(t/r_{1}(t\\right z(t=0\\tag{\\(\\ast\\ast\\}\\] is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates if equation (\\(\\ast\\ast\\ is nonoscillatory. We also establish results for the oscillation of equation (\\(\\ast\\ when equation (\\(\\ast\\ast\\ is oscillatory.

  1. Benzothiazolium Single Crystals: A New Class of Nonlinear Optical Crystals with Efficient THz Wave Generation.

    Science.gov (United States)

    Lee, Seung-Heon; Lu, Jian; Lee, Seung-Jun; Han, Jae-Hyun; Jeong, Chan-Uk; Lee, Seung-Chul; Li, Xian; Jazbinšek, Mojca; Yoon, Woojin; Yun, Hoseop; Kang, Bong Joo; Rotermund, Fabian; Nelson, Keith A; Kwon, O-Pil

    2017-08-01

    Highly efficient nonlinear optical organic crystals are very attractive for various photonic applications including terahertz (THz) wave generation. Up to now, only two classes of ionic crystals based on either pyridinium or quinolinium with extremely large macroscopic optical nonlinearity have been developed. This study reports on a new class of organic nonlinear optical crystals introducing electron-accepting benzothiazolium, which exhibit higher electron-withdrawing strength than pyridinium and quinolinium in benchmark crystals. The benzothiazolium crystals consisting of new acentric core HMB (2-(4-hydroxy-3-methoxystyryl)-3-methylbenzo[d]thiazol-3-ium) exhibit extremely large macroscopic optical nonlinearity with optimal molecular ordering for maximizing the diagonal second-order nonlinearity. HMB-based single crystals prepared by simple cleaving method satisfy all required crystal characteristics for intense THz wave generation such as large crystal size with parallel surfaces, moderate thickness and high optical quality with large optical transparency range (580-1620 nm). Optical rectification of 35 fs pulses at the technologically very important wavelength of 800 nm in 0.26 mm thick HMB crystal leads to one order of magnitude higher THz wave generation efficiency with remarkably broader bandwidth compared to standard inorganic 0.5 mm thick ZnTe crystal. Therefore, newly developed HMB crystals introducing benzothiazolium with extremely large macroscopic optical nonlinearity are very promising materials for intense broadband THz wave generation and other nonlinear optical applications. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  2. Single-nary philosophy for non-linear study of mechanics of materials

    International Nuclear Information System (INIS)

    Tran, C.

    2005-01-01

    Non-linear study of mechanics of materials is formulated in this paper as a problem of meta-intelligent system analysis. Non-linearity will be singled out as an important concept for understanding of high-order complex systems. Through single-nary thinking, which will be represented in this work, we introduce a modification of Aristotelian philosophy using modal logic and multi-valued logic (these logics we call 'high-order' logic). Next, non-linear cause - effect relations are expressed through non-additive measures and multiple-information aggregation principles based on fuzzy integration. The study of real time behaviors, required experiences and intuition, will be realized using truth measures (non-additive measures) and a procedure for information processing in intelligence levels. (author)

  3. A New Approximate Solution of Time-Fractional, Non-linear Schrodinger Equations Using Fractional Reduced Differential Transformation

    OpenAIRE

    Singh, Brajesh Kumar; Kumar, Pramod

    2016-01-01

    This paper is concerned with an alternative analytical solution of time-fractional nonlinear Schrodinger equation and nonlinear coupled Schrodinger equation obtained by employing fractional reduced differential transform method. The proposed solutions are obtained in series form, converges to the exact solution very rapidly. These results are agreed well with the results obtained by using differential transform method, homotopy perturbation method, homotopy analysis method and Adomian decompo...

  4. Semi-implicit spectral deferred correction methods for highly nonlinear partial differential equations

    Science.gov (United States)

    Guo, Ruihan; Xia, Yinhua; Xu, Yan

    2017-06-01

    The goal of this paper is to develop a novel semi-implicit spectral deferred correction (SDC) time marching method. The method can be used in a large class of problems, especially for highly nonlinear ordinary differential equations (ODEs) without easily separating of stiff and non-stiff components, which is more general and efficient comparing with traditional semi-implicit SDC methods. The proposed semi-implicit SDC method is based on low order time integration methods and corrected iteratively. The order of accuracy is increased for each additional iteration. And we also explore its local truncation error analytically. This SDC method is intended to be combined with the method of lines, which provides a flexible framework to develop high order semi-implicit time marching methods for nonlinear partial differential equations (PDEs). In this paper we mainly focus on the applications of the nonlinear PDEs with higher order spatial derivatives, e.g. convection diffusion equation, the surface diffusion and Willmore flow of graphs, the Cahn-Hilliard equation, the Cahn-Hilliard-Brinkman system and the phase field crystal equation. Coupled with the local discontinuous Galerkin (LDG) spatial discretization, the fully discrete schemes are all high order accurate in both space and time, and stable numerically with the time step proportional to the spatial mesh size. Numerical experiments are carried out to illustrate the accuracy and capability of the proposed semi-implicit SDC method.

  5. Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm.

    Science.gov (United States)

    Overgaard, Rune V; Jonsson, Niclas; Tornøe, Christoffer W; Madsen, Henrik

    2005-02-01

    Pharmacokinetic/pharmacodynamic modelling is most often performed using non-linear mixed-effects models based on ordinary differential equations with uncorrelated intra-individual residuals. More sophisticated residual error models as e.g. stochastic differential equations (SDEs) with measurement noise can in many cases provide a better description of the variations, which could be useful in various aspects of modelling. This general approach enables a decomposition of the intra-individual residual variation epsilon into system noise w and measurement noise e. The present work describes implementation of SDEs in a non-linear mixed-effects model, where parameter estimation was performed by a novel approximation of the likelihood function. This approximation is constructed by combining the First-Order Conditional Estimation (FOCE) method used in non-linear mixed-effects modelling with the Extended Kalman Filter used in models with SDEs. Fundamental issues concerning the proposed model and estimation algorithm are addressed by simulation studies, concluding that system noise can successfully be separated from measurement noise and inter-individual variability.

  6. Optimal Energy Measurement in Nonlinear Systems: An Application of Differential Geometry

    Science.gov (United States)

    Fixsen, Dale J.; Moseley, S. H.; Gerrits, T.; Lita, A.; Nam, S. W.

    2014-01-01

    Design of TES microcalorimeters requires a tradeoff between resolution and dynamic range. Often, experimenters will require linearity for the highest energy signals, which requires additional heat capacity be added to the detector. This results in a reduction of low energy resolution in the detector. We derive and demonstrate an algorithm that allows operation far into the nonlinear regime with little loss in spectral resolution. We use a least squares optimal filter that varies with photon energy to accommodate the nonlinearity of the detector and the non-stationarity of the noise. The fitting process we use can be seen as an application of differential geometry. This recognition provides a set of well-developed tools to extend our work to more complex situations. The proper calibration of a nonlinear microcalorimeter requires a source with densely spaced narrow lines. A pulsed laser multi-photon source is used here, and is seen to be a powerful tool for allowing us to develop practical systems with significant detector nonlinearity. The combination of our analysis techniques and the multi-photon laser source create a powerful tool for increasing the performance of future TES microcalorimeters.

  7. Summary report of the group on single-particle nonlinear dynamics

    International Nuclear Information System (INIS)

    Axinescu, S.; Bartolini, R.; Bazzani, A.

    1996-10-01

    This report summarizes the research on single-particle nonlinear beam dynamics. It discusses the following topics: analytical and semi-analytical tools; early prediction of the dynamic aperture; how the results are commonly presented; Is the mechanism of the dynamic aperture understand; ripple effects; and beam-beam effects

  8. A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Ji Juan-Juan

    2017-01-01

    Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

  9. A HAM-based wavelet approach for nonlinear ordinary differential equations

    Science.gov (United States)

    Yang, Zhaochen; Liao, Shijun

    2017-07-01

    Based on the homotopy analysis method (HAM) and the generalized Coiflet-type orthogonal wavelet, a new analytic approximation approach for solving nonlinear boundary value problems (governed by nonlinear ordinary differential equations), namely the wavelet homotopy analysis method (wHAM), is proposed. The basic ideas of the wHAM are described using the one-dimensional Bratu's equation as an example. This method not only keeps the main advantages of the normal HAM, but also possesses some new properties and advantages. First of all, the wHAM possesses high computational efficiency. Besides, based on multi-resolution analysis, it provides us a convenient way to balance the accuracy and efficiency by simply adjusting the resolution level. Furthermore, different from the normal HAM, the wHAM provides us much larger freedom to choose the auxiliary linear operator. In addition, just like the normal HAM, iteration can greatly accelerate the computational efficiency of the wHAM without loss of accuracy.

  10. Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces

    Directory of Open Access Journals (Sweden)

    Messaoud Bounkhel

    2013-01-01

    Full Text Available In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, ẋ(t∈F(t,x(t a.e. on I, x(t∈S, ∀t∈I, x(0=x0∈S, (*, where S is a closed subset in a Banach space , I=[0,T], (T>0, F:I×S→, is an upper semicontinuous set-valued mapping with convex values satisfying F(t,x⊂c(tx+xp, ∀(t,x∈I×S, where p∈ℝ, with p≠1, and c∈C([0,T],ℝ+. The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.

  11. Existence results for differential inclusions with nonlinear growth conditions in Banach spaces.

    Science.gov (United States)

    Bounkhel, Messaoud

    2013-01-01

    In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, x(·)(t) ∈ a.e. on I, x(t) ∈ S, ∀t ∈ I, x(0) = x₀ ∈ S, (∗), where S is a closed subset in a Banach space X, I = [0, T], (T > 0), F : I × S → X, is an upper semicontinuous set-valued mapping with convex values satisfying F(t, x) ⊂ c(t)(||x|| + ||x|| (p)K, ∀(t, x) ∈ I × S, where p ∈ ℝ, with p ≠ 1, and c ∈ C([0, T], ℝ(+)). The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.

  12. Dynamics of excited instantons in the system of forced Gursey nonlinear differential equations

    International Nuclear Information System (INIS)

    Aydogmus, F.

    2015-01-01

    The Gursey model is a 4D conformally invariant pure fermionic model with a nonlinear spinor self-coupled term. Gursey proposed his model as a possible basis for a unitary description of elementary particles following the “Heisenberg dream.” In this paper, we consider the system of Gursey nonlinear differential equations (GNDEs) formed by using the Heisenberg ansatz. We use it to understand how the behavior of spinor-type Gursey instantons can be affected by excitations. For this, the regular and chaotic numerical solutions of forced GNDEs are investigated by constructing their Poincaré sections in phase space. A hierarchical cluster analysis method for investigating the forced GNDEs is also presented

  13. Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

    Science.gov (United States)

    Hasegawa, Chihiro; Duffull, Stephen B

    2018-02-01

    Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

  14. Solution of Nonlinear Partial Differential Equations by New Laplace Variational Iteration Method

    Directory of Open Access Journals (Sweden)

    Eman M. A. Hilal

    2014-01-01

    Full Text Available The aim of this study is to give a good strategy for solving some linear and nonlinear partial differential equations in engineering and physics fields, by combining Laplace transform and the modified variational iteration method. This method is based on the variational iteration method, Laplace transforms, and convolution integral, introducing an alternative Laplace correction functional and expressing the integral as a convolution. Some examples in physical engineering are provided to illustrate the simplicity and reliability of this method. The solutions of these examples are contingent only on the initial conditions.

  15. Differential Evolution-Based PID Control of Nonlinear Full-Car Electrohydraulic Suspensions

    Directory of Open Access Journals (Sweden)

    Jimoh O. Pedro

    2013-01-01

    Full Text Available This paper presents a differential-evolution- (DE- optimized, independent multiloop proportional-integral-derivative (PID controller design for full-car nonlinear, electrohydraulic suspension systems. The multiloop PID control stabilises the actuator via force feedback and also improves the system performance. Controller gains are computed using manual tuning and through DE optimization to minimise a performance index, which addresses suspension travel, road holding, vehicle handling, ride comfort, and power consumption constraints. Simulation results showed superior performance of the DE-optimized PID-controlled active vehicle suspension system (AVSS over the manually tuned PID-controlled AVSS and the passive vehicle suspension system (PVSS.

  16. Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method

    Directory of Open Access Journals (Sweden)

    Z. Pashazadeh Atabakan

    2013-01-01

    Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.

  17. Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems

    Directory of Open Access Journals (Sweden)

    Qi Wang

    2012-01-01

    Full Text Available This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential θ-method is applied to p′(t=β0ωμp(t−τ/(ωμ+pμ(t−τ−γp(t and it is shown that the exponential θ-method has the same order of convergence as that of the classical θ-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.

  18. Global stability, periodic solutions, and optimal control in a nonlinear differential delay model

    Directory of Open Access Journals (Sweden)

    Anatoli F. Ivanov

    2010-09-01

    Full Text Available A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsey. An optimization problem for a maximal consumption is stated and solved for the latter.

  19. Asymptotic integration of some nonlinear differential equations with fractional time derivative

    International Nuclear Information System (INIS)

    Baleanu, Dumitru; Agarwal, Ravi P; Mustafa, Octavian G; Cosulschi, Mirel

    2011-01-01

    We establish that, under some simple integral conditions regarding the nonlinearity, the (1 + α)-order fractional differential equation 0 D α t (x') + f(t, x) = 0, t > 0, has a solution x element of C([0,+∞),R) intersection C 1 ((0,+∞),R), with lim t→0 [t 1-α x'(t)] element of R, which can be expanded asymptotically as a + bt α + O(t α-1 ) when t → +∞ for given real numbers a, b. Our arguments are based on fixed point theory. Here, 0 D α t designates the Riemann-Liouville derivative of order α in (0, 1).

  20. Tsallis distributions and 1/f noise from nonlinear stochastic differential equations.

    Science.gov (United States)

    Ruseckas, J; Kaulakys, B

    2011-11-01

    Probability distributions that emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this article we unite modeling of such distributions with the model of widespread 1/f noise. We propose a class of nonlinear stochastic differential equations giving both the q-exponential or q-Gaussian distributions of signal intensity, revealing long-range correlations and 1/f(β) behavior of the power spectral density. The superstatistical framework to get 1/f(β) noise with q-exponential and q-Gaussian distributions of the signal intensity is proposed, as well.

  1. Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Mourad Kerboua

    2014-12-01

    Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.

  2. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

    KAUST Repository

    Calatroni, Luca

    2013-08-01

    We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

  3. A topological approach to the existence of solutions for nonlinear differential equations with piecewise constant argument

    International Nuclear Information System (INIS)

    Huang Zhenkun; Wang Xinghua; Xia Yonghui

    2009-01-01

    In this paper, we investigate qualitative behavior of nonlinear differential equations with piecewise constant argument (PCA). A topological approach of Wazewski-type which gives sufficient conditions to guarantee that the graph of at least one solution stays in a given domain is formulated. Moreover, our results are also suitable for a class of general system of discrete equations. By using a regular polyfacial set, we apply our developed topological approach to cellular neural networks (CNNs) with PCA. Some new results are attained to reveal dynamic behavior of CNNs with PCA and discrete-time CNNs. Finally, an illustrative example of CNNs with PCA shows usefulness and effectiveness of our results.

  4. Single Image Super-Resolution by Non-Linear Sparse Representation and Support Vector Regression

    Directory of Open Access Journals (Sweden)

    Yungang Zhang

    2017-02-01

    Full Text Available Sparse representations are widely used tools in image super-resolution (SR tasks. In the sparsity-based SR methods, linear sparse representations are often used for image description. However, the non-linear data distributions in images might not be well represented by linear sparse models. Moreover, many sparsity-based SR methods require the image patch self-similarity assumption; however, the assumption may not always hold. In this paper, we propose a novel method for single image super-resolution (SISR. Unlike most prior sparsity-based SR methods, the proposed method uses non-linear sparse representation to enhance the description of the non-linear information in images, and the proposed framework does not need to assume the self-similarity of image patches. Based on the minimum reconstruction errors, support vector regression (SVR is applied for predicting the SR image. The proposed method was evaluated on various benchmark images, and promising results were obtained.

  5. Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System

    Directory of Open Access Journals (Sweden)

    Chen Yuming

    2011-01-01

    Full Text Available Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility.

  6. Computation of Value Functions in Nonlinear Differential Games with State Constraints

    KAUST Repository

    Botkin, Nikolai

    2013-01-01

    Finite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a generalized viscosity solution of the corresponding Hamilton-Jacobi-Bellman-Isaacs equation. Such a viscosity solution is defined as a function satisfying differential inequalities introduced by M. G. Crandall and P. L. Lions. The difference with the classical case is that these inequalities hold on an unknown in advance subset of the state space. The convergence rate of the numerical schemes is given. Numerical solution to a non-trivial three-dimensional example is presented. © 2013 IFIP International Federation for Information Processing.

  7. Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations

    KAUST Repository

    Cao, Jiguo

    2012-01-01

    Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.

  8. Convergent Power Series of sech⁡(x and Solutions to Nonlinear Differential Equations

    Directory of Open Access Journals (Sweden)

    U. Al Khawaja

    2018-01-01

    Full Text Available It is known that power series expansion of certain functions such as sech⁡(x diverges beyond a finite radius of convergence. We present here an iterative power series expansion (IPS to obtain a power series representation of sech⁡(x that is convergent for all x. The convergent series is a sum of the Taylor series of sech⁡(x and a complementary series that cancels the divergence of the Taylor series for x≥π/2. The method is general and can be applied to other functions known to have finite radius of convergence, such as 1/(1+x2. A straightforward application of this method is to solve analytically nonlinear differential equations, which we also illustrate here. The method provides also a robust and very efficient numerical algorithm for solving nonlinear differential equations numerically. A detailed comparison with the fourth-order Runge-Kutta method and extensive analysis of the behavior of the error and CPU time are performed.

  9. Progress Toward Single-Photon-Level Nonlinear Optics in Crystalline Microcavities

    Science.gov (United States)

    Kowligy, Abijith S.

    Over the last two decades, the emergence of quantum information science has uncovered many practical applications in areas such as communications, imaging, and sensing where harnessing quantum features of Nature provides tremendous benefits over existing methods exploiting classical physical phenomena. In this effort, one of the frontiers of research has been to identify and utilize quantum phenomena that are not susceptible to environmental and parasitic noise processes. Quantum photonics has been at the forefront of these studies because it allows room-temperature access to its inherently quantum-mechanical features, and allows leveraging the mature telecommunication industry. Accompanying the weak environmental influence, however, are also weak optical nonlinearities. Efficient nonlinear optical interactions are indispensible for many of the existing protocols for quantum optical computation and communication, e.g. high-fidelity entangling quantum logic gates rely on large nonlinear responses at the one- or few-photon-level. While this has been addressed to a great extent by interfacing photons with single quantum emitters and cold atomic gases, scalability has remained elusive. In this work, we identify the macroscopic second-order nonlinear polarization as a robust platform to address this challenge, and utilize the recent advances in the burgeoning field of optical microcavities to enhance this nonlinear response. In particular, we show theoretically that by using the quantum Zeno effect, low-noise, single-photon-level optical nonlinearities can be realized in lithium niobate whispering-gallery-mode microcavities, and present experimental progress toward this goal. Using the measured strength of the second-order nonlinear response in lithium niobate, we modeled the nonlinear system in the strong coupling regime using the Schrodinger picture framework and theoretically demonstrated that the single-photon-level operation can be observed for cavity lifetimes in

  10. Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

    Science.gov (United States)

    Gnoffo, Peter A.

    2015-01-01

    Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

  11. Fabrication of superconducting nanowire single-photon detectors by nonlinear femtosecond optical lithography

    Science.gov (United States)

    Minaev, N. V.; Tarkhov, M. A.; Dudova, D. S.; Timashev, P. S.; Chichkov, B. N.; Bagratashvili, V. N.

    2018-02-01

    This paper describes a new approach to the fabrication of superconducting nanowire single-photon detectors from ultrathin NbN films on SiO2 substrates. The technology is based on nonlinear femtosecond optical lithography and includes direct formation of the sensitive element of the detector (the meander) through femtosecond laser exposure of the polymethyl methacrylate resist at a wavelength of 525 nm and subsequent removal of NbN using plasma-chemical etching. The nonlinear femtosecond optical lithography method allows the formation of planar structures with a spatial resolution of ~50 nm. These structures were used to fabricate single-photon superconducting detectors with quantum efficiency no worse than 8% at a wavelength of 1310 nm and dark count rate of 10 s‑1 at liquid helium temperature.

  12. Graphical user interface for input output characterization of single variable and multivariable highly nonlinear systems

    Directory of Open Access Journals (Sweden)

    Shahrukh Adnan Khan M. D.

    2017-01-01

    Full Text Available This paper presents a Graphical User Interface (GUI software utility for the input/output characterization of single variable and multivariable nonlinear systems by obtaining the sinusoidal input describing function (SIDF of the plant. The software utility is developed on MATLAB R2011a environment. The developed GUI holds no restriction on the nonlinearity type, arrangement and system order; provided that output(s of the system is obtainable either though simulation or experiments. An insight to the GUI and its features are presented in this paper and example problems from both single variable and multivariable cases are demonstrated. The formulation of input/output behavior of the system is discussed and the nucleus of the MATLAB command underlying the user interface has been outlined. Some of the industries that would benefit from this software utility includes but not limited to aerospace, defense technology, robotics and automotive.

  13. A direct method for numerical solution of a class of nonlinear Volterra integro-differential equations and its application to the nonlinear fission and fusion reactor kinetics

    International Nuclear Information System (INIS)

    Nakahara, Yasuaki; Ise, Takeharu; Kobayashi, Kensuke; Itoh, Yasuyuki

    1975-12-01

    A new method has been developed for numerical solution of a class of nonlinear Volterra integro-differential equations with quadratic nonlinearity. After dividing the domain of the variable into subintervals, piecewise approximations are applied in the subintervals. The equation is first integrated over a subinterval to obtain the piecewise equation, to which six approximate treatments are applied, i.e. fully explicit, fully implicit, Crank-Nicolson, linear interpolation, quadratic and cubic spline. The numerical solution at each time step is obtained directly as a positive root of the resulting algebraic quadratic equation. The point reactor kinetics with a ramp reactivity insertion, linear temperature feedback and delayed neutrons can be described by one of this type of nonlinear Volterra integro-differential equations. The algorithm is applied to the Argonne benchmark problem and a model problem for a fast reactor without delayed neutrons. The fully implicit method has been found to be unconditionally stable in the sense that it always gives the positive real roots. The cubic spline method is divergent, and the other four methods are intermediate in between. From the estimation of the stability, convergency, accuracy and CPU time, it is concluded that the Crank-Nicolson method is best, then the linear interpolation method comes closely next to it. Discussions are also made on the possibility of applying the algorithm to the fusion reactor kinetics in the form of a nonlinear partial differential equation. (auth.)

  14. Nonlinear pulse propagation in a single- and a few-cycle regimes ...

    Indian Academy of Sciences (India)

    In this work, we study the effect of the delayed nonlinear response (intrapulse. Raman effect) on the propagation characteristics of a single- and a few-cycle pulse at 0.8 µm wavelength in a silica glass ..... 0.03923 fs2/µm, Tr = 3 fs and σ = 0.7. effect leads to a frequency shift toward higher frequencies, in the trailing edge and.

  15. NONLINEAR SYSTEM MODELING USING SINGLE NEURON CASCADED NEURAL NETWORK FOR REAL-TIME APPLICATIONS

    Directory of Open Access Journals (Sweden)

    S. Himavathi

    2012-04-01

    Full Text Available Neural Networks (NN have proved its efficacy for nonlinear system modeling. NN based controllers and estimators for nonlinear systems provide promising alternatives to the conventional counterpart. However, NN models have to meet the stringent requirements on execution time for its effective use in real time applications. This requires the NN model to be structurally compact and computationally less complex. In this paper a parametric method of analysis is adopted to determine the compact and faster NN model among various neural network architectures. This work proves through analysis and examples that the Single Neuron Cascaded (SNC architecture is distinct in providing compact and simpler models requiring lower execution time. The unique structural growth of SNC architecture enables automation in design. The SNC Network is shown to combine the advantages of both single and multilayer neural network architectures. Extensive analysis on selected architectures and their models for four benchmark nonlinear theoretical plants and a practical application are tested. A performance comparison of the NN models is presented to demonstrate the superiority of the single neuron cascaded architecture for online real time applications.

  16. Single-pulse CARS based multimodal nonlinear optical microscope for bioimaging.

    Science.gov (United States)

    Kumar, Sunil; Kamali, Tschackad; Levitte, Jonathan M; Katz, Ori; Hermann, Boris; Werkmeister, Rene; Považay, Boris; Drexler, Wolfgang; Unterhuber, Angelika; Silberberg, Yaron

    2015-05-18

    Noninvasive label-free imaging of biological systems raises demand not only for high-speed three-dimensional prescreening of morphology over a wide-field of view but also it seeks to extract the microscopic functional and molecular details within. Capitalizing on the unique advantages brought out by different nonlinear optical effects, a multimodal nonlinear optical microscope can be a powerful tool for bioimaging. Bringing together the intensity-dependent contrast mechanisms via second harmonic generation, third harmonic generation and four-wave mixing for structural-sensitive imaging, and single-beam/single-pulse coherent anti-Stokes Raman scattering technique for chemical sensitive imaging in the finger-print region, we have developed a simple and nearly alignment-free multimodal nonlinear optical microscope that is based on a single wide-band Ti:Sapphire femtosecond pulse laser source. Successful imaging tests have been realized on two exemplary biological samples, a canine femur bone and collagen fibrils harvested from a rat tail. Since the ultra-broad band-width femtosecond laser is a suitable source for performing high-resolution optical coherence tomography, a wide-field optical coherence tomography arm can be easily incorporated into the presented multimodal microscope making it a versatile optical imaging tool for noninvasive label-free bioimaging.

  17. The role of dendritic non-linearities in single neuron computation

    Directory of Open Access Journals (Sweden)

    Boris Gutkin

    2014-05-01

    Full Text Available Experiment has demonstrated that summation of excitatory post-synaptic protientials (EPSPs in dendrites is non-linear. The sum of multiple EPSPs can be larger than their arithmetic sum, a superlinear summation due to the opening of voltage-gated channels and similar to somatic spiking. The so-called dendritic spike. The sum of multiple of EPSPs can also be smaller than their arithmetic sum, because the synaptic current necessarily saturates at some point. While these observations are well-explained by biophysical models the impact of dendritic spikes on computation remains a matter of debate. One reason is that dendritic spikes may fail to make the neuron spike; similarly, dendritic saturations are sometime presented as a glitch which should be corrected by dendritic spikes. We will provide solid arguments against this claim and show that dendritic saturations as well as dendritic spikes enhance single neuron computation, even when they cannot directly make the neuron fire. To explore the computational impact of dendritic spikes and saturations, we are using a binary neuron model in conjunction with Boolean algebra. We demonstrate using these tools that a single dendritic non-linearity, either spiking or saturating, combined with somatic non-linearity, enables a neuron to compute linearly non-separable Boolean functions (lnBfs. These functions are impossible to compute when summation is linear and the exclusive OR is a famous example of lnBfs. Importantly, the implementation of these functions does not require the dendritic non-linearity to make the neuron spike. Next, We show that reduced and realistic biophysical models of the neuron are capable of computing lnBfs. Within these models and contrary to the binary model, the dendritic and somatic non-linearity are tightly coupled. Yet we show that these neuron models are capable of linearly non-separable computations.

  18. A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

    Science.gov (United States)

    Benhammouda, Brahim

    2016-01-01

    Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

  19. A three operator split-step method covering a larger set of non-linear partial differential equations

    Science.gov (United States)

    Zia, Haider

    2017-06-01

    This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

  20. A modified cubic B-spline differential quadrature method for three-dimensional non-linear diffusion equations

    Science.gov (United States)

    Dahiya, Sumita; Mittal, Ramesh Chandra

    2017-07-01

    This paper employs a differential quadrature scheme for solving non-linear partial differential equations. Differential quadrature method (DQM), along with modified cubic B-spline basis, has been adopted to deal with three-dimensional non-linear Brusselator system, enzyme kinetics of Michaelis-Menten type problem and Burgers' equation. The method has been tested efficiently to three-dimensional equations. Simple algorithm and minimal computational efforts are two of the major achievements of the scheme. Moreover, this methodology produces numerical solutions not only at the knot points but also at every point in the domain under consideration. Stability analysis has been done. The scheme provides convergent approximate solutions and handles different cases and is particularly beneficial to higher dimensional non-linear PDEs with irregularities in initial data or initial-boundary conditions that are discontinuous in nature, because of its capability of damping specious oscillations induced by high frequency components of solutions.

  1. Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation

    International Nuclear Information System (INIS)

    Zhang, Yu-Juan; Zhao, Dun; Luo, Hong-Gang

    2014-01-01

    We consider a wide class of integrable nonautonomous nonlinear integro-differential Schrödinger equation which contains the models for the soliton management in Bose–Einstein condensates, nonlinear optics, and inhomogeneous Heisenberg spin chain. With the help of the nonisospectral AKNS hierarchy, we obtain the N-fold Darboux transformation and the N-fold soliton-like solutions for the equation. The soliton management, especially the synchronized dispersive and nonlinear management in optical fibers is discussed. It is found that in the situation without external potential, the synchronized dispersive and nonlinear management can keep the integrability of the nonlinear Schrödinger equation; this suggests that in optical fibers, the synchronized dispersive and nonlinear management can control and maintain the propagation of a multi-soliton. - Highlights: • We consider a unified model for soliton management by an integrable integro-differential Schrödinger equation. • Using Lax pair, the N-fold Darboux transformation for the equation is presented. • The multi-soliton management is considered. • The synchronized dispersive and nonlinear management is suggested

  2. Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Yu-Juan [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China); Zhao, Dun, E-mail: zhaod@lzu.edu.cn [School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China); Center for Interdisciplinary Studies, Lanzhou University, Lanzhou 730000 (China); Luo, Hong-Gang [Center for Interdisciplinary Studies, Lanzhou University, Lanzhou 730000 (China); Beijing Computational Science Research Center, Beijing 100084 (China)

    2014-11-15

    We consider a wide class of integrable nonautonomous nonlinear integro-differential Schrödinger equation which contains the models for the soliton management in Bose–Einstein condensates, nonlinear optics, and inhomogeneous Heisenberg spin chain. With the help of the nonisospectral AKNS hierarchy, we obtain the N-fold Darboux transformation and the N-fold soliton-like solutions for the equation. The soliton management, especially the synchronized dispersive and nonlinear management in optical fibers is discussed. It is found that in the situation without external potential, the synchronized dispersive and nonlinear management can keep the integrability of the nonlinear Schrödinger equation; this suggests that in optical fibers, the synchronized dispersive and nonlinear management can control and maintain the propagation of a multi-soliton. - Highlights: • We consider a unified model for soliton management by an integrable integro-differential Schrödinger equation. • Using Lax pair, the N-fold Darboux transformation for the equation is presented. • The multi-soliton management is considered. • The synchronized dispersive and nonlinear management is suggested.

  3. A modified stochastic averaging method on single-degree-of-freedom strongly nonlinear stochastic vibrations

    International Nuclear Information System (INIS)

    Ge, Gen; Li, ZePeng

    2016-01-01

    A modified stochastic averaging method on single-degree-of-freedom (SDOF) oscillators under white noise excitations with strongly nonlinearity was proposed. Considering the existing approach dealing with strongly nonlinear SDOFs derived by Zhu and Huang [14, 15] is quite time consuming in calculating the drift coefficient and diffusion coefficients and the expressions of them are considerable long, the so-called He's energy balance method was applied to overcome the minor defect of the Zhu and Huang's method. The modified method can offer more concise approximate expressions of the drift and diffusion coefficients without weakening the accuracy of predicting the responses of the systems too much by giving an averaged frequency beforehand. Three examples, a cubic and quadratic nonlinearity coexisting oscillator, a quadratic nonlinear oscillator under external white noise excitations and an externally excited Duffing–Rayleigh oscillator, were given to illustrate the approach we proposed. The three examples were excited by the Gaussian white noise and the Gaussian colored noise separately. The stationary responses of probability density of amplitudes and energy, together with joint probability density of displacement and velocity are studied to verify the presented approach. The reliability of the systems were also investigated to offer further support. Digital simulations were carried out and the output of that are coincide with the theoretical approximations well.

  4. Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method.

    Science.gov (United States)

    Benhammouda, Brahim

    2015-01-01

    The solution of higher-index Hessenberg differential-algebraic equations (DAEs) is of great importance since this type of DAEs often arises in applications. Higher-index DAEs are known to be numerically and analytically difficult to solve. In this paper, we present a new analytical method for the solution of two classes of higher-index Hessenberg DAEs. The method is based on Adomian polynomials and the differential transform method (DTM). First, the DTM is applied to the DAE where the differential transforms of nonlinear terms are calculated using Adomian polynomials. Then, based on the index condition, the resulting recursion system is transformed into a nonsingular linear algebraic system. This system is then solved to obtain the coefficients of the power series solution. The main advantage of the proposed technique is that it does not require an index reduction nor a linearization. Two test problems are solved to demonstrate the effectiveness of the method. In addition, to extend the domain of convergence of the approximate series solution, we propose a post-treatment with Laplace-Padé resummation method.

  5. Modeling Laterally Loaded Single Piles Accounting for Nonlinear Soil-Pile Interactions

    Directory of Open Access Journals (Sweden)

    Maryam Mardfekri

    2013-01-01

    Full Text Available The nonlinear behavior of a laterally loaded monopile foundation is studied using the finite element method (FEM to account for soil-pile interactions. Three-dimensional (3D finite element modeling is a convenient and reliable approach to account for the continuity of the soil mass and the nonlinearity of the soil-pile interactions. Existing simple methods for predicting the deflection of laterally loaded single piles in sand and clay (e.g., beam on elastic foundation, p-y method, and SALLOP are assessed using linear and nonlinear finite element analyses. The results indicate that for the specific case considered here the p-y method provides a reasonable accuracy, in spite of its simplicity, in predicting the lateral deflection of single piles. A simplified linear finite element (FE analysis of piles, often used in the literature, is also investigated and the influence of accounting for the pile diameter in the simplified linear FE model is evaluated. It is shown that modeling the pile as a line with beam-column elements results in a reduced contribution of the surrounding soil to the lateral stiffness of the pile and an increase of up to 200% in the predicted maximum lateral displacement of the pile head.

  6. δ-expansion method for nonlinear stochastic differential equations describing wave propagation in a random medium.

    Science.gov (United States)

    Van Gorder, Robert A

    2010-11-01

    We apply the δ-expansion method to nonlinear stochastic differential equations describing wave propagation in a random medium. In particular, we focus our attention on a model describing a nonlinear wave propagating in a turbulent atmosphere which has random variations in the refractive index (we take these variations to be stochastic). The method allows us to construct much more reasonable perturbation solutions with relatively few terms (compared to standard "small-parameter" perturbation methods) due to more accurate linearization used in constructing the initial approximation. We demonstrate that the method allows one to compute effective wave numbers more precisely than other methods applied to the problem in the literature. The method also picks up on the stochastic damping of the solutions quickly, holding all of the relevant data in the initial term. These properties allow for both a qualitative and a quantitative construction of physically meaningful solutions. In particular, we show that the method allows one to retain higher-order harmonics which are hard to capture with standard perturbation methods based on small parameters.

  7. Existence Results for a Coupled System of Nonlinear Fractional Hybrid Differential Equations with Homogeneous Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Josefa Caballero

    2014-01-01

    Full Text Available We study an existence result for the following coupled system of nonlinear fractional hybrid differential equations with homogeneous boundary conditions D0+α[x(t/f(t,x(t,y(t]=g(t,x(t,y(t,D0+αy(t/f(t,y(t,x(t=g(t,y(t,x(t,  0

  8. Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem.

    Science.gov (United States)

    Lawson, Daniel J; Holtrop, Grietje; Flint, Harry

    2011-07-01

    Process models specified by non-linear dynamic differential equations contain many parameters, which often must be inferred from a limited amount of data. We discuss a hierarchical Bayesian approach combining data from multiple related experiments in a meaningful way, which permits more powerful inference than treating each experiment as independent. The approach is illustrated with a simulation study and example data from experiments replicating the aspects of the human gut microbial ecosystem. A predictive model is obtained that contains prediction uncertainty caused by uncertainty in the parameters, and we extend the model to capture situations of interest that cannot easily be studied experimentally. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  9. Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay

    Directory of Open Access Journals (Sweden)

    Zhonghai Guo

    2012-01-01

    Full Text Available We study the following second order mixed nonlinear impulsive differential equations with delay (r(tΦα(x′(t′+p0(tΦα(x(t+∑i=1npi(tΦβi(x(t-σ=e(t, t≥t0, t≠τk,x(τk+=akx(τk, x'(τk+=bkx'(τk, k=1,2,…, where Φ*(u=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence, and τk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.

  10. Linear program differentiation for single-channel speech separation

    DEFF Research Database (Denmark)

    Pearlmutter, Barak A.; Olsson, Rasmus Kongsgaard

    2006-01-01

    Many apparently difficult problems can be solved by reduction to linear programming. Such problems are often subproblems within larger systems. When gradient optimisation of the entire larger system is desired, it is necessary to propagate gradients through the internally-invoked LP solver....... For instance, when an intermediate quantity z is the solution to a linear program involving constraint matrix A, a vector of sensitivities dE/dz will induce sensitivities dE/dA. Here we show how these can be efficiently calculated, when they exist. This allows algorithmic differentiation to be applied...... to algorithms that invoke linear programming solvers as subroutines, as is common when using sparse representations in signal processing. Here we apply it to gradient optimisation of over complete dictionaries for maximally sparse representations of a speech corpus. The dictionaries are employed in a single...

  11. On nonlinearly-induced noise in single-channel optical links with digital backpropagation.

    Science.gov (United States)

    Beygi, Lotfollah; Irukulapati, Naga V; Agrell, Erik; Johannisson, Pontus; Karlsson, Magnus; Wymeersch, Henk; Serena, Paolo; Bononi, Alberto

    2013-11-04

    In this paper, we investigate the performance limits of electronic chromatic dispersion compensation (EDC) and digital backpropagation (DBP) for a single-channel non-dispersion-managed fiber-optical link. A known analytical method to derive the performance of the system with EDC is extended to derive a first-order approximation for the performance of the system with DBP. In contrast to the cubic growth of the variance of the nonlinear noise-like interference, often called nonlinear noise, with input power for EDC, a quadratic growth is observed with DBP using this approximation. Finally, we provide numerical results to verify the accuracy of the proposed approach and compare it with existing analytical models.

  12. Nonlinear evolution of single spike structure and vortex in Richtmeyer-Meshkov instability

    International Nuclear Information System (INIS)

    Fukuda, Yuko O.; Nishihara, Katsunobu; Okamoto, Masayo; Nagatomo, Hideo; Matsuoka, Chihiro; Ishizaki, Ryuichi; Sakagami, Hitoshi

    1999-01-01

    Nonlinear evolution of single spike structure and vortex in the Richtmyer-Meshkov instability is investigated for two dimensional case, and axial symmetric and non axial symmetric cases with the use of a three-dimensional hydrodynamic code. It is shown that singularity appears in the vorticity left by transmitted and reflected shocks at a corrugated interface. This singularity results in opposite sign of vorticity along the interface that causes double spiral structure of the spike. Difference of nonlinear growth rate and double spiral structure among three cases is also discussed by visualization of simulation data. In a case that there is no slip-off of initial spike axis, vorticity ring is relatively stable, but phase rotation occurs. (author)

  13. Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Dilna, N.; Rontó, András

    2010-01-01

    Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9

  14. Differential Transform Method with Complex Transforms to Some Nonlinear Fractional Problems in Mathematical Physics

    Directory of Open Access Journals (Sweden)

    Syed Tauseef Mohyud-Din

    2015-01-01

    Full Text Available This paper witnesses the coupling of an analytical series expansion method which is called reduced differential transform with fractional complex transform. The proposed technique is applied on three mathematical models, namely, fractional Kaup-Kupershmidt equation, generalized fractional Drinfeld-Sokolov equations, and system of coupled fractional Sine-Gordon equations subject to the appropriate initial conditions which arise frequently in mathematical physics. The derivatives are defined in Jumarie’s sense. The accuracy, efficiency, and convergence of the proposed technique are demonstrated through the numerical examples. It is observed that the presented coupling is an alternative approach to overcome the demerit of complex calculation of fractional differential equations. The proposed technique is independent of complexities arising in the calculation of Lagrange multipliers, Adomian’s polynomials, linearization, discretization, perturbation, and unrealistic assumptions and hence gives the solution in the form of convergent power series with elegantly computed components. All the examples show that the proposed combination is a powerful mathematical tool to solve other nonlinear equations also.

  15. A pertinent approach to solve nonlinear fuzzy integro-differential equations.

    Science.gov (United States)

    Narayanamoorthy, S; Sathiyapriya, S P

    2016-01-01

    Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations using homotopy perturbation method. A clear and detailed description of the proposed method is provided. Our main objective is to illustrate that the construction of appropriate convex homotopy in a proper way leads to highly accurate solutions with less computational work. The efficiency of the approximation technique is expressed via stability and convergence analysis so as to guarantee the efficiency and performance of the methodology. Numerical examples are demonstrated to verify the convergence and it reveals the validity of the presented numerical technique. Numerical results are tabulated and examined by comparing the obtained approximate solutions with the known exact solutions. Graphical representations of the exact and acquired approximate fuzzy solutions clarify the accuracy of the approach.

  16. Large Banks of Negative Differential Resistance Nonlinear Loads: A Hidden Threat to Power System Quality

    Directory of Open Access Journals (Sweden)

    Mahmood Ahmad

    2018-01-01

    Full Text Available DSM (Demand Side Management is a short term and comparatively low cost solution for energy starved countries. Replacement of IB (Incandescent Bulbs with CFL (Compact Fluorescent Lamps has proved its success throughout the world. The same solution, at larger scale, was proposed to Pakistan to mitigate power shortage on short term basis. Accordingly in year 2008, ADB (Asian Development Bank conducted a study and it was found that replacement of conventional IB with 30 million CFL will result into series of benefits for the stake holders and above all the Environment. The study, unfortunately didn’t take enough consideration of effect of CFLs on the power system being nonlinear device and so the power quality issues remained a secondary consideration. The focus of this paper remains on the effect of such non-linear load on consumers, it also envisages the erratic behaviour of such large penetration of CFLs on direct single phase, three phase, digital as well as electromechanical energy meters, under different loading conditions e.g. resistive load, SMPS (Switch Mode Power Supply, half and full-wave rectifiers. It also reflects harmonic pollution caused by CFLs, their effect on power system quality and the registration ability of electromechanical as well as digital energy meters. To this end Harmonic spectrum was recorded up to the 31st harmonic.

  17. Communication: atomic force detection of single-molecule nonlinear optical vibrational spectroscopy.

    Science.gov (United States)

    Saurabh, Prasoon; Mukamel, Shaul

    2014-04-28

    Atomic Force Microscopy (AFM) allows for a highly sensitive detection of spectroscopic signals. This has been first demonstrated for NMR of a single molecule and recently extended to stimulated Raman in the optical regime. We theoretically investigate the use of optical forces to detect time and frequency domain nonlinear optical signals. We show that, with proper phase matching, the AFM-detected signals closely resemble coherent heterodyne-detected signals. Applications are made to AFM-detected and heterodyne-detected vibrational resonances in Coherent Anti-Stokes Raman Spectroscopy (χ((3))) and sum or difference frequency generation (χ((2))).

  18. Dhage Iteration Method for Nonlinear First Order Hybrid Differential Equations with a Linear Perturbation of Second Type

    Directory of Open Access Journals (Sweden)

    B.C. Dhage

    2016-08-01

    Full Text Available In this paper the authors prove algorithms for the existence and approximation of the solutions for an initial and a periodic boundary value problem of nonlinear first order ordinary hybrid differential equations with a linear perturbation of second type via Dhage iteration method. Examples are furnished to illustrate the hypotheses and main abstract results of this paper.

  19. Dhage Iteration Method for Nonlinear First Order Hybrid Differential Equations with a Linear Perturbation of Second Type

    OpenAIRE

    B.C. Dhage

    2016-01-01

    In this paper the authors prove algorithms for the existence and approximation of the solutions for an initial and a periodic boundary value problem of nonlinear first order ordinary hybrid differential equations with a linear perturbation of second type via Dhage iteration method. Examples are furnished to illustrate the hypotheses and main abstract results of this paper.

  20. On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments

    Directory of Open Access Journals (Sweden)

    Youliang Fu

    2016-01-01

    Full Text Available This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included.

  1. A Study of Nonlinear Fractional Differential Equations of Arbitrary Order with Riemann-Liouville Type Multistrip Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Bashir Ahmad

    2013-01-01

    Full Text Available We develop the existence theory for nonlinear fractional differential equations of arbitrary order with Riemann-Liouville type boundary conditions involving nonintersecting finite many strips of arbitrary length. Our results are based on some standard tools of fixed point theory. For the illustration of the results, some examples are also discussed.

  2. Growth and physicochemical properties of second-order nonlinear optical 2-amino-5-chloropyridinium trichloroacetate single crystals

    Science.gov (United States)

    Renugadevi, R.; Kesavasamy, R.

    2015-09-01

    The growth of organic nonlinear optical (NLO) crystal 2-amino-5-chloropyridinium trichloroacetate (2A5CPTCA) has been synthesized and single crystals have been grown from methanol solvent by slow evaporation technique. The grown crystals were subjected to various characterization analyses in order to find out the suitability for device fabrication. Single crystal X-ray diffraction analysis reveals that 2A5CPTCA crystallizes in monoclinic system with the space group Cc. The grown crystal was further characterized by Fourier transform infrared spectral analysis to find out the functional groups. The nuclear magnetic resonance spectroscopy is a research technique that exploits the magnetic properties of certain atomic nuclei. The optical transparency window in the visible and near-IR (200--1100 nm) regions was found to be good for NLO applications. Thermogravimetric analysis and differential thermal analysis were used to study its thermal properties. The powder second harmonic generation efficiency measurement with Nd:YAG laser (1064 nm) radiation shows that the highest value when compared with the standard potassium dihydrogen phosphate crystal.

  3. Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method

    Science.gov (United States)

    Akbari, M. R.; Ganji, D. D.; Ahmadi, A. R.; Kachapi, Sayyid H. Hashemi

    2014-03-01

    In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.

  4. Nonlinear effects of a beam interacting with a single damped wave

    International Nuclear Information System (INIS)

    Stoltz, Peter H.; Cary, John R.

    2000-01-01

    A self-consistent nonlinear theory of the longitudinal dynamics of a low density beam interacting with a single damped wave is developed. In this paper, the model is applied to the coasting beam-cavity system of accelerator physics, but it also applies to beam-plasma systems and traveling wave tubes. Motivating the theory are numerical simulations showing different beam behaviors in the nonlinear regime depending on the amount of wave damping. For highly damped systems, breakoff and energy loss of a self-formed bunch from the beam is observed. This bunch breakoff and energy loss is the cause of the overshoot phenomenon of accelerator physics; furthermore this overshoot does not contradict the Keil-Schnell criterion, as the beam is far from a Gaussian distribution. An expression for the amount of cavity damping necessary for bunch breakoff is derived. Finally, using a single-particle model, an expression for the rate of energy loss of the bunch in terms of the cavity damping is derived. (c) 2000 American Institute of Physics

  5. Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

    Science.gov (United States)

    Bogdan, V. M.; Bond, V. B.

    1980-01-01

    The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

  6. Finger tapping movements of Parkinson's disease patients automatically rated using nonlinear delay differential equations.

    Science.gov (United States)

    Lainscsek, C; Rowat, P; Schettino, L; Lee, D; Song, D; Letellier, C; Poizner, H

    2012-03-01

    Parkinson's disease is a degenerative condition whose severity is assessed by clinical observations of motor behaviors. These are performed by a neurological specialist through subjective ratings of a variety of movements including 10-s bouts of repetitive finger-tapping movements. We present here an algorithmic rating of these movements which may be beneficial for uniformly assessing the progression of the disease. Finger-tapping movements were digitally recorded from Parkinson's patients and controls, obtaining one time series for every 10 s bout. A nonlinear delay differential equation, whose structure was selected using a genetic algorithm, was fitted to each time series and its coefficients were used as a six-dimensional numerical descriptor. The algorithm was applied to time-series from two different groups of Parkinson's patients and controls. The algorithmic scores compared favorably with the unified Parkinson's disease rating scale scores, at least when the latter adequately matched with ratings from the Hoehn and Yahr scale. Moreover, when the two sets of mean scores for all patients are compared, there is a strong (r = 0.785) and significant (p<0.0015) correlation between them.

  7. On the limits of probabilistic forecasting in nonlinear time series analysis II: Differential entropy.

    Science.gov (United States)

    Amigó, José M; Hirata, Yoshito; Aihara, Kazuyuki

    2017-08-01

    In a previous paper, the authors studied the limits of probabilistic prediction in nonlinear time series analysis in a perfect model scenario, i.e., in the ideal case that the uncertainty of an otherwise deterministic model is due to only the finite precision of the observations. The model consisted of the symbolic dynamics of a measure-preserving transformation with respect to a finite partition of the state space, and the quality of the predictions was measured by the so-called ignorance score, which is a conditional entropy. In practice, though, partitions are dispensed with by considering numerical and experimental data to be continuous, which prompts us to trade off in this paper the Shannon entropy for the differential entropy. Despite technical differences, we show that the core of the previous results also hold in this extended scenario for sufficiently high precision. The corresponding imperfect model scenario will be revisited too because it is relevant for the applications. The theoretical part and its application to probabilistic forecasting are illustrated with numerical simulations and a new prediction algorithm.

  8. Construction of a single/multiple wavelength RZ optical pulse source at 40 GHz by use of wavelength conversion in a high-nonlinearity DSF-NOLM

    DEFF Research Database (Denmark)

    Yu, Jianjun; Yujun, Qian; Jeppesen, Palle

    2001-01-01

    A single or multiple wavelength RZ optical pulse source at 40 GHz is successfully obtained by using wavelength conversion in a nonlinear optical loop mirror consisting of high nonlinearity-dispersion shifted fiber.......A single or multiple wavelength RZ optical pulse source at 40 GHz is successfully obtained by using wavelength conversion in a nonlinear optical loop mirror consisting of high nonlinearity-dispersion shifted fiber....

  9. Analysis and topology in nonlinear differential equations a tribute to Bernhard Ruf on the occasion of his 60th birthday

    CERN Document Server

    Ó, João; Tomei, Carlos

    2014-01-01

    This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in João Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60th birthday, is perceptible throughout the collection by the choice of themes and techniques. The many contributors consider modern topics in the calculus of variations, topological methods and regularity analysis, together with novel applications of partial differential equations. In keeping with the tradition of the workshop, emphasis is given to elliptic operators inserted in different contexts, both theoretical and applied. Topics include semi-linear and fully nonlinear equations and systems with different nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi type. Also treated are analytic aspects as well as applications such as diffusion problems in mathematical genetics and finance and evolution equations related to electromechanical ...

  10. Generalized Wronskian relations one dimensional Schroedinger equation and nonlinear partial differential equations solvable by the inverse scattering method

    International Nuclear Information System (INIS)

    Calogero, F.

    1976-01-01

    A generalized Wronskian type relation is used to obtain a number of expressions for the scattering and bound state parameters (reflection and transmission coefficients, bound state energies and normalization constants) in the context of the one dimensional Schroedinger equation. These expressions are in the form of integrals over the wave functions multiplied by appropriate (generally nonlinear) combinations of the potentials and their derivatives. Some of them provide the basis for deriving classes of nonlinear partial differential equations that are solvable by the inverse scattering method. The main interest of this approach rests in its simplicity and in its delivery of nonlinear evolution equations that may involve more than one (space) variable and contain coefficients that are not constant

  11. Single-photon blockade in a hybrid cavity-optomechanical system via third-order nonlinearity

    Science.gov (United States)

    Sarma, Bijita; Sarma, Amarendra K.

    2018-04-01

    Photon statistics in a weakly driven optomechanical cavity, with Kerr-type nonlinearity, are analyzed both analytically and numerically. The single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function g (2)(0). The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. A systematic study on the parameter regime for observing photon blockade in the weak coupling regime is reported. The parameter regime where the photon blockade is not realizable due to the combined effect of nonlinearities owing to the optomechanical coupling and the Kerr-effect is demonstrated. The experimental feasibility with state-of-the-art device parameters is discussed and it is observed that photon blockade could be generated at the telecommunication wavelength. An elaborate analysis of the thermal effects on photon antibunching is presented. The system is found to be robust against pure dephasing-induced decoherences and thermal phonon number fluctuations.

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

    CERN Document Server

    Tran Hy, J

    1998-01-01

    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 ...

  13. Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability

    International Nuclear Information System (INIS)

    Yan, R.; Aluie, H.; Betti, R.; Sanz, J.; Liu, B.; Frank, A.

    2016-01-01

    The nonlinear evolution of the single-mode ablative Rayleigh-Taylor instability is studied in three dimensions. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the three-dimensional (3D) terminal bubble velocity greatly exceeds both the two-dimensional (2D) value and the classical 3D bubble velocity. Unlike in 2D, the 3D short-wavelength bubble velocity does not saturate. The growing 3D bubble acceleration is driven by the unbounded accumulation of vorticity inside the bubble. The vorticity is transferred by mass ablation from the Rayleigh-Taylor spikes to the ablated plasma filling the bubble volume

  14. Probabilistically cloning two single-photon states using weak cross-Kerr nonlinearities

    International Nuclear Information System (INIS)

    Zhang, Wen; Rui, Pinshu; Zhang, Ziyun; Yang, Qun

    2014-01-01

    By using quantum nondemolition detectors (QNDs) based on weak cross-Kerr nonlinearities, we propose an experimental scheme for achieving 1→2 probabilistic quantum cloning (PQC) of a single-photon state, secretly choosing from a two-state set. In our scheme, after a QND is performed on the to-be-cloned photon and the assistant photon, a single-photon projection measurement is performed by a polarization beam splitter (PBS) and two single-photon trigger detectors (SPTDs). The measurement is to judge whether the PQC should be continued. If the cloning fails, a cutoff is carried out and some operations are omitted. This makes our scheme economical. If the PQC is continued according to the measurement result, two more QNDs and some unitary operations are performed on the to-be-cloned photon and the cloning photon to achieve the PQC in a nearly deterministic way. Our experimental scheme for PQC is feasible for future technology. Furthermore, the quantum logic network of our PQC scheme is presented. In comparison with similar networks, our PQC network is simpler and more economical. (paper)

  15. Investigation of gamma radiation effect on chemical properties and surface morphology of some nonlinear optical (NLO) single crystals

    Energy Technology Data Exchange (ETDEWEB)

    Ahlam, M.A., E-mail: omaymn771@yahoo.com [Department of Studies in Physics, University of Mysore, Manasagangotri, Mysore 570 006, Karnataka (India); Ravishankar, M.N. [Department of Studies in Physics, University of Mysore, Manasagangotri, Mysore 570 006, Karnataka (India); Vijayan, N. [Materials Characterization Division, National Physical Laboratory, New Delhi 110 012 (India); Govindaraj, G. [Department of Physics, Pondicherry University, Pondicherry 605 014 (India); Siddaramaiah [Department of Polymer and Technology, Sri Jayachamarajendra College of Engineering, Mysore 570 006 (India); Gnana Prakash, A.P., E-mail: gnanaprakash@physics.uni-mysore.ac.in [Department of Studies in Physics, University of Mysore, Manasagangotri, Mysore 570 006, Karnataka (India)

    2012-05-01

    The effect of Co-60 gamma irradiation on L-alanine cadmium chloride (LACC), L-alanine doped potassium dihydrogen orthophosphate (KDP) and L-arginine doped KDP nonlinear optical (NLO) single crystals were studied in doses ranging from 100 krad to 6 Mrad. The crystals were grown by slow evaporation method at room temperature. The effects of gamma irradiation on the chemical, surface morphology, DC electrical conductivity, thermal and mechanical properties of the grown crystals have been studied. The functional groups of unirradiated and irradiated crystals have been identified and confirmed by Fourier transform infrared (FTIR) studies. Scanning electron microscopy (SEM) of irradiated crystals shows some morphological changes in the crystals. The dc conductivity of LACC and L-alanine doped KDP crystals were found to increase with increase in radiation dose whereas in case of L-arginine doped KDP crystals, the dc conductivity was found to decrease with increase in radiation dose. Differential scanning calorimetry (DSC) thermograms reveals that there is no significant change in the melting point of the crystals after irradiation and the crystals does not decompose as a result of irradiation. The mechanical behavior of both unirradiated and irradiated crystals is explained with the indentation effects using Vicker's microhardness tester. The Vicker's hardness number H{sub V} and Mayer's index 'n' has been estimated and confirms that LACC belong to the hard materials.

  16. Existence and Analytic Approximation of Solutions of Duffing Type Nonlinear Integro-Differential Equation with Integral Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Alsaedi Ahmed

    2009-01-01

    Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.

  17. The Use of Iterative Methods to Solve Two-Dimensional Nonlinear Volterra-Fredholm Integro-Differential Equations

    OpenAIRE

    shadan sadigh behzadi

    2012-01-01

    In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integro-differential equation by using the following powerful, efficient but simple methods: (i) Modified Adomian decomposition method (MADM), (ii) Variational iteration method (VIM), (iii) Homotopy analysis method (HAM) and (iv) Modified homotopy perturbation method (MHPM). The uniqueness of the solution and the convergence of the proposed methods are proved in detail. Numerical examples are studied to demonstrate ...

  18. The Use of Iterative Methods to Solve Two-Dimensional Nonlinear Volterra-Fredholm Integro-Differential Equations

    Directory of Open Access Journals (Sweden)

    shadan sadigh behzadi

    2012-03-01

    Full Text Available In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integro-differential equation by using the following powerful, efficient but simple methods: (i Modified Adomian decomposition method (MADM, (ii Variational iteration method (VIM, (iii Homotopy analysis method (HAM and (iv Modified homotopy perturbation method (MHPM. The uniqueness of the solution and the convergence of the proposed methods are proved in detail. Numerical examples are studied to demonstrate the accuracy of the presented methods.

  19. State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities.

    Science.gov (United States)

    Korayem, M H; Nekoo, S R

    2015-07-01

    This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  20. Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

    Science.gov (United States)

    Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

    2016-01-01

    Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

  1. Single-step emulation of nonlinear fiber-optic link with gaussian mixture model

    DEFF Research Database (Denmark)

    Borkowski, Robert; Doberstein, Andy; Haisch, Hansjörg

    2015-01-01

    We use a fast and low-complexity statistical signal processing method to emulate nonlinear noise in fiber links. The proposed emulation technique stands in good agreement with the numerical NLSE simulation for 32 Gbaud DP-16QAM nonlinear transmission.......We use a fast and low-complexity statistical signal processing method to emulate nonlinear noise in fiber links. The proposed emulation technique stands in good agreement with the numerical NLSE simulation for 32 Gbaud DP-16QAM nonlinear transmission....

  2. Analytical study of nonlinear phase shift through stimulated Brillouin scattering in single mode fiber with the pump power recycling technique

    International Nuclear Information System (INIS)

    Al-Asadi, H A; Mahdi, M A; Bakar, A A A; Adikan, F R Mahamd

    2011-01-01

    We present a theoretical study of nonlinear phase shift through stimulated Brillouin scattering in single mode optical fiber. Analytical expressions describing the nonlinear phase shift for the pump and Stokes waves in the pump power recycling technique have been derived. The dependence of the nonlinear phase shift on the optical fiber length, the reflectivity of the optical mirror and the frequency detuning coefficient have been analyzed for different input pump power values. We found that with the recycling pump technique, the nonlinear phase shift due to stimulated Brillouin scattering reduced to less than 0.1 rad for 5 km optical fiber length and 0.65 reflectivity of the optical mirror, respectively, at an input pump power equal to 30 mW

  3. Attitude Control of a Single Tilt Tri-Rotor UAV System: Dynamic Modeling and Each Channel's Nonlinear Controllers Design

    Directory of Open Access Journals (Sweden)

    Juing-Shian Chiou

    2013-01-01

    Full Text Available This paper has implemented nonlinear control strategy for the single tilt tri-rotor aerial robot. Based on Newton-Euler’s laws, the linear and nonlinear mathematical models of tri-rotor UAVs are obtained. A numerical analysis using Newton-Raphson method is chosen for finding hovering equilibrium point. Back-stepping nonlinear controller design is based on constructing Lyapunov candidate function for closed-loop system. By imitating the linguistic logic of human thought, fuzzy logic controllers (FLCs are designed based on control rules and membership functions, which are much less rigid than the calculations computers generally perform. Effectiveness of the controllers design scheme is shown through nonlinear simulation model on each channel.

  4. Structural, thermal, optical and nonlinear optical properties of ethylenediaminium picrate single crystals

    Science.gov (United States)

    Indumathi, C.; T. C., Sabari Girisun; Anitha, K.; Alfred Cecil Raj, S.

    2017-07-01

    A new organic optical limiting material, ethylenediaminium picrate (EDAPA) was synthesized through acid base reaction and grown as single crystals by solvent evaporation method. Single crystal XRD analysis showed that EDAPA crystallizes in orthorhombic system with Cmca as space group. The formation of charge transfer complex during the reaction of ethylenediamine and picric acid was strongly evident through the recorded Fourier Transform Infra Red (FTIR), Raman and Nuclear Magnetic Resonance (NMR) spectrum. Thermal (TG-DTA and DSC) curves indicated that the material possesses high thermal stability with decomposition temperature at 243 °C. Optical (UV-Visible-NIR) analysis showed that the grown crystal was found to be transparent in the entire visible and NIR region. Z-scan studies with intense short pulse (532 nm, 5 ns, 100 μJ) excitations, revealed that EDAPA exhibited two photon absorption behaviour and the nonlinear absorption coefficient was found to be two orders of magnitude higher than some of the known optical limiter like Cu nano glasses. EDAPA exhibited a strong optical limiting action with low limiting threshold which make them a potential candidate for eye and photosensitive component protection against intense short pulse lasers.

  5. Coulomb effect and nonlinear optical properties of single-walled carbon nanotubes

    Science.gov (United States)

    Zhao, Hongbo; Mazumdar, Sumit

    2005-03-01

    We investigated theoretically nonlinear optical properties of ten single-walled carbon nanotubes (SWCNTs) with a wide range of diameters, within a semiempirical Pariser-Parr-Pople model with a long- range Coulomb interaction. The excited states are calculated within Single Configuration Interaction (SCI) scheme. In our previous work ootnotetextHongbo Zhao and Sumit Mazumdar, Phys. Rev. Lett. 93, 157402 (2004) we have shown that there occur dark exciton states below the first optically allowed exciton, and that this is the reason for low photoluminescence quantum efficiency. In the present work we report calculations of photoinduced absorption (PA) from both dark and optically allowed lowest excitons for a mixture of SWCNTs, and compare our result with experimental ultrafast PA spectra. As with π-conjugated polymers, the lowest PA energies give lower bounds to the exciton binding energies. Our SCI calculations do not take into account double excitations, and hence we are unable to describe the high energy PA in SWCNTs. We speculate that the origin of the high energy PA is the same as in PPV. ootnotetextA. Shukla, H. Ghosh and S. Mazumdar, Phys. Rev. B 67, 245203 (2003)

  6. Synthesis and characterization of nonlinear optical L-arginine semi-oxalate single crystal

    Science.gov (United States)

    Vasudevan, P.; Gokul Raj, S.; Sankar, S.

    2013-04-01

    L-arginine semi-oxalate single crystals have been synthesized by slow evaporation method at room temperature. Single crystal and powder X-ray diffraction analyses has been made to confirm the triclinic structure with non-centrosymmetric space group P1. The presence of functional groups of L-arginine semi-oxalate crystals was identified and confirmed by using the Fourier transform infrared spectroscopy. Molecular structure of the grown crystal was analyzed by 1H NMR and 13C NMR studies. Optical absorption studies carried out in wavelength range from 250 nm to 1200 nm have revealed that the material is completely transparent for the entire wavelength range studied. Thermal characterization using thermogravimetric analysis and differential scanning calorimetry studies show that the crystal is thermally stable up to 146 °C. The presence of second harmonic generation of the grown crystal was tested and its efficiency was determined by using Kurtz and Perry powder technique.

  7. Large negative differential conductance in single-molecule break junctions

    NARCIS (Netherlands)

    Perrin, Mickael L.; Frisenda, Riccardo; Koole, Max; Seldenthuis, Johannes S.; Gil, Jose A. Celis; Valkenier, Hennie; Hummelen, Jan C.; Renaud, Nicolas; Grozema, Ferdinand C.; Thijssen, Joseph M.; Dulic, Diana; van der Zant, Herre S. J.

    2014-01-01

    Molecular electronics aims at exploiting the internal structure and electronic orbitals of molecules to construct functional building blocks(1). To date, however, the overwhelming majority of experimentally realized single-molecule junctions can be described as single quantum dots, where transport

  8. Nonlinear analysis

    National Research Council Canada - National Science Library

    Rassias, Themistocles M

    1987-01-01

    ... known that nonlinear partial differential equations can not be treated in the same systematic way as linear ones and this volume provides, among other things, proofs of existence and uniqueness theorems for nonlinear differential equations of a global nature. However, the basic techniques which have proven to be efficient in dealing with li...

  9. Solar-Based Boost Differential Single Phase Inverter | Eya | Nigerian ...

    African Journals Online (AJOL)

    ... current concurrently and finally, it is portable. This research also shows the disparity between the simulated results of open loop and closed loop of boost differential inverter systems. The dc power source is photovoltaic cell. The maximum power point tracker is in-cooperated in capturing the maximum power from the sun.

  10. Contractivity properties of a class of linear multistep methods for nonlinear neutral delay differential equations

    International Nuclear Information System (INIS)

    Wang Wansheng; Li Shoufu; Wang Wenqiang

    2009-01-01

    In this paper, we show that under identical conditions which guarantee the contractivity of the theoretical solutions of general nonlinear NDDEs, the numerical solutions obtained by a class of linear multistep methods are also contractive.

  11. A Combined Experimental and Theoretical Investigations on N, N′- Diphenylguanidine Based Single Crystals For Nonlinear Optical Applications

    OpenAIRE

    Saravana Kumar, G; Roop Kumar, R; Murugakoothan, P

    2017-01-01

    International audience; Good quality N,N′-Diphenylguanidine based nonlinear optical single crystals were grown by slow evaporation technique. The cell parameters and space group were confirmed by single crystal X-ray diffraction analysis. The UV-vis study was carried out to assess the transmittance of the title crystals. The optical band gap was determined from the UV-vis analysis. The HOMO-LUMO analysis was carried out using DFT calculations. The presence of second harmonic generation (SHG) ...

  12. Fixed-point Theorem and the Nishida-Nirenberg Method in Solving Certain Nonlinear Singular Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Jose Ernie C. Lope

    2013-12-01

    Full Text Available In their 2012 work, Lope, Roque, and Tahara considered singular nonlinear partial differential equations of the form tut = F(t; x; u; ux, where the function F is assumed to be continuous in t and holomorphic in the other variables. They have shown that under some growth conditions on the coefficients of the partial Taylor expansion of F as t 0, the equation has a unique solution u(t; x with the same growth order as that of F(t; x; 0; 0. Koike considered systems of partial differential equations using the Banach fixed point theorem and the iterative method of Nishida and Nirenberg. In this paper, we prove the result obtained by Lope and others using the method of Koike, thereby avoiding the repetitive step of differentiating a recursive equation with respect to x as was done by the aforementioned authors.

  13. Three-Field Modelling of Nonlinear Nonsmooth Boundary Value Problems and Stability of Differential Mixed Variational Inequalities

    Directory of Open Access Journals (Sweden)

    J. Gwinner

    2013-01-01

    Full Text Available The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration. This approach leads to variational inequalities of mixed form for three coupled fields as unknowns and to related differential mixed variational inequalities in the time-dependent case. Secondly we are concerned with the stability of the solution set of a general class of differential mixed variational inequalities. Here we present a novel upper set convergence result with respect to perturbations in the data, including perturbations of the associated nonlinear maps, the nonsmooth convex functionals, and the convex constraint set. We employ epiconvergence for the convergence of the functionals and Mosco convergence for set convergence. We impose weak convergence assumptions on the perturbed maps using the monotonicity method of Browder and Minty.

  14. Active and Purely Dissipative Nambu Systems in General Thermostatistical Settings Described by Nonlinear Partial Differential Equations Involving Generalized Entropy Measures

    Directory of Open Access Journals (Sweden)

    T. D. Frank

    2016-12-01

    Full Text Available In physics, several attempts have been made to apply the concepts and tools of physics to the life sciences. In this context, a thermostatistic framework for active Nambu systems is proposed. The so-called free energy Fokker–Planck equation approach is used to describe stochastic aspects of active Nambu systems. Different thermostatistic settings are considered that are characterized by appropriately-defined entropy measures, such as the Boltzmann–Gibbs–Shannon entropy and the Tsallis entropy. In general, the free energy Fokker–Planck equations associated with these generalized entropy measures correspond to nonlinear partial differential equations. Irrespective of the entropy-related nonlinearities occurring in these nonlinear partial differential equations, it is shown that semi-analytical solutions for the stationary probability densities of the active Nambu systems can be obtained provided that the pumping mechanisms of the active systems assume the so-called canonical-dissipative form and depend explicitly only on Nambu invariants. Applications are presented both for purely-dissipative and for active systems illustrating that the proposed framework includes as a special case stochastic equilibrium systems.

  15. New 3D parallel GILD electromagnetic modeling and nonlinear inversion using global magnetic integral and local differential equation

    Energy Technology Data Exchange (ETDEWEB)

    Xie, G.; Li, J.; Majer, E.; Zuo, D.

    1998-07-01

    This paper describes a new 3D parallel GILD electromagnetic (EM) modeling and nonlinear inversion algorithm. The algorithm consists of: (a) a new magnetic integral equation instead of the electric integral equation to solve the electromagnetic forward modeling and inverse problem; (b) a collocation finite element method for solving the magnetic integral and a Galerkin finite element method for the magnetic differential equations; (c) a nonlinear regularizing optimization method to make the inversion stable and of high resolution; and (d) a new parallel 3D modeling and inversion using a global integral and local differential domain decomposition technique (GILD). The new 3D nonlinear electromagnetic inversion has been tested with synthetic data and field data. The authors obtained very good imaging for the synthetic data and reasonable subsurface EM imaging for the field data. The parallel algorithm has high parallel efficiency over 90% and can be a parallel solver for elliptic, parabolic, and hyperbolic modeling and inversion. The parallel GILD algorithm can be extended to develop a high resolution and large scale seismic and hydrology modeling and inversion in the massively parallel computer.

  16. Symbolic computation of exact solutions expressible in rational formal hyperbolic and elliptic functions for nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Wang Qi; Chen Yong

    2007-01-01

    With the aid of symbolic computation, some algorithms are presented for the rational expansion methods, which lead to closed-form solutions of nonlinear partial differential equations (PDEs). The new algorithms are given to find exact rational formal polynomial solutions of PDEs in terms of Jacobi elliptic functions, solutions of the Riccati equation and solutions of the generalized Riccati equation. They can be implemented in symbolic computation system Maple. As applications of the methods, we choose some nonlinear PDEs to illustrate the methods. As a result, we not only can successfully obtain the solutions found by most existing Jacobi elliptic function methods and Tanh-methods, but also find other new and more general solutions at the same time

  17. Nonlinear self-adjointness, conservation laws, and the construction of solutions of partial differential equations using conservation laws

    International Nuclear Information System (INIS)

    Ibragimov, N Kh; Avdonina, E D

    2013-01-01

    The method of nonlinear self-adjointness, which was recently developed by the first author, gives a generalization of Noether's theorem. This new method significantly extends approaches to constructing conservation laws associated with symmetries, since it does not require the existence of a Lagrangian. In particular, it can be applied to any linear equations and any nonlinear equations that possess at least one local conservation law. The present paper provides a brief survey of results on conservation laws which have been obtained by this method and published mostly in recent preprints of the authors, along with a method for constructing exact solutions of systems of partial differential equations with the use of conservation laws. In most cases the solutions obtained by the method of conservation laws cannot be found as invariant or partially invariant solutions. Bibliography: 23 titles

  18. Meloxicam pharmacokinetics using nonlinear mixed-effects modeling in ferrets after single subcutaneous administration.

    Science.gov (United States)

    Chinnadurai, S K; Messenger, K M; Papich, M G; Harms, C A

    2014-08-01

    This study was designed to investigate the pharmacokinetics of meloxicam, an oxicam class, nonsteroidal anti-inflammatory drug (NSAID), in ferrets. We determined the pharmacokinetic properties of a single subcutaneous dose of meloxicam (0.2 mg/kg) in nine male and nine female ferrets. Blood samples were collected by venipuncture of the cranial vena cava into heparinized syringes. Plasma meloxicam concentrations were determined by high-pressure liquid chromatography (HPLC). Pharmacokinetic variables were calculated using nonlinear mixed-effects modeling to take advantage of the population-based sampling scheme and to minimize sample volume collected per animal. Maximum plasma concentration, volume of distribution per absorption, and elimination half-life were 0.663 μg/mL, 0.21 L, and 11.4 h, respectively, for females and 0.920 μg/mL, 0.35 L, and 17.8 h, respectively, for males. Significant differences were found in each of the above parameters between male and female ferrets. Systemic clearance per absorption was not affected by gender and was 13.4 mL/h. Analgesic efficacy was not evaluated, but plasma meloxicam concentrations achieved in these animals are considered effective in other species. Sex differences in the pharmacokinetic behavior of meloxicam should be taken into consideration when treating ferrets. © 2014 John Wiley & Sons Ltd.

  19. A novel control framework for nonlinear time-delayed dual-master/single-slave teleoperation.

    Science.gov (United States)

    Ghorbanian, A; Rezaei, S M; Khoogar, A R; Zareinejad, M; Baghestan, K

    2013-03-01

    A novel trilateral control architecture for the Dual-master/Single-slave teleoperation is proposed in this paper. This framework has been used in surgical training and rehabilitation applications. In this structure, the slave motion has been controlled by weighted summation of signals transmitted by the operator referring to task control authority through the dominance factors. The nonlinear dynamics for telemanipulators are considered which were considered as disregarded issues in previous studies of this field. Bounded variable time-delay has been considered which affects the transmitted signals in the communication channels. Two types of controllers have been offered and an appropriate stability analysis for each controller has been demonstrated. The first controller includes Proportional with dissipative gains (P+d). The second one contains Proportional and Derivative with dissipative gains (PD+d). In both cases, the stability of the trilateral control framework is preserved by choosing appropriate controller's gains. It is shown that these controllers attempt to coordinate the positions of telemanipulators in the free motion condition. The stability of the Dual-master/Single-slave teleoperation has been proved by an appropriate Lyapunov like function and the stability conditions have been studied. In addition the proposed PD+d control architecture is modified for trilateral teleoperation with internet communication between telemanipulators that caused such communication complications as packet loss, data duplication and swapping. A number of experiments have been conducted with various levels of dominance factor to validate the effectiveness of the new control architecture. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

  20. A highly nonlinear differentially 4 uniform power mapping that permutes fields of even degree

    DEFF Research Database (Denmark)

    Leander, Gregor; Bracken, Carl

    2010-01-01

    Functions with low differential uniformity can be used as the s-boxes of symmetric cryptosystems as they have good resistance to differential attacks. The AES (Advanced Encryption Standard) uses a differentially 4 uniform function called the inverse function. Any function used in a symmetric cryp...

  1. On the Effect of Thermoelastic Damping in Nonlinear Micro Electro Mechanical Resonators using Differential Quadrature Method

    Directory of Open Access Journals (Sweden)

    A. Karami Mohammadi

    2015-07-01

    Full Text Available : In this paper, a nonlinear model of clamped-clamped microbeam actuated by electrostatic load with stretching and thermoelastic effects is presented. Free vibration frequency is calculated by discretization based on DQ method. Frequency is a complex value due to the thermoelastic effect that dissipates the energy. By separating the real and imaginary parts of frequency, quality factor of thermoelastic damping is calculated. Both stretching and thermoelastic effects are validated against the results of the reference papers. The variations of thermoelastic damping versus elasticity modulus, coefficient of thermal expansion and geometrical parameters such as thickness, gap distance, and length are investigated and these results are compared in the linear and nonlinear models for high values of voltage. Also, this paper shows that since for high values of electrostatic voltage the linear model reveals a large error for calculating the thermoelastic damping, the nonlinear model should be used for this purpose.

  2. Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field

    Science.gov (United States)

    Chen, J.; Palmadesso, P. J.

    1986-01-01

    The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.

  3. Nonlinear Phenomena in the Single-Mode Dynamics in an AFM Cantilever Beam

    KAUST Repository

    Ruzziconi, Laura

    2016-12-05

    This study deals with the nonlinear dynamics arising in an atomic force microscope cantilever beam. After analyzing the static behavior, a single degree of freedom Galerkin reduced order model is introduced, which describes the overall scenario of the structure response in a neighborhood of the primary resonance. Extensive numerical simulations are performed when both the forcing amplitude and frequency are varied, ranging from low up to elevated excitations. The coexistence of competing attractors with different characteristics is analyzed. Both the non-resonant and the resonant behavior are observed, as well as ranges of inevitable escape. Versatility of behavior is highlighted, which may be attractive in applications. Special attention is devoted to the effects of the tip-sample separation distance, since this aspect is of fundamental importance to understand the operation of an AFM. We explore the metamorphoses of the multistability region when the tip-sample separation distance is varied. To have a complete description of the AFM response, comprehensive behavior charts are introduced to detect the theoretical boundaries of appearance and disappearance of the main attractors. Also, extensive numerical simulations investigate the AFM response when both the forcing amplitude and the tip-sample separation distance are considered as control parameters. The main features are analyzed in detail and the obtained results are interpreted in terms of oscillations of the cantilever-tip ensemble. However, we note that all the aforementioned results represent the limit when disturbances are absent, which never occurs in practice. Here comes the importance of overcoming local investigations and exploring dynamics from a global perspective, by introducing dynamical integrity concepts. To extend the AFM results to the practical case where disturbances exist, we develop a dynamical integrity analysis. After performing a systematic basin of attraction analysis, integrity

  4. High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform.

    Science.gov (United States)

    Gui, Tao; Lu, Chao; Lau, Alan Pak Tao; Wai, P K A

    2017-08-21

    In this paper, we experimentally investigate high-order modulation over a single discrete eigenvalue under the nonlinear Fourier transform (NFT) framework and exploit all degrees of freedom for encoding information. For a fixed eigenvalue, we compare different 4 bit/symbol modulation formats on the spectral amplitude and show that a 2-ring 16-APSK constellation achieves optimal performance. We then study joint spectral phase, spectral magnitude and eigenvalue modulation and found that while modulation on the real part of the eigenvalue induces pulse timing drift and leads to neighboring pulse interactions and nonlinear inter-symbol interference (ISI), it is more bandwidth efficient than modulation on the imaginary part of the eigenvalue in practical settings. We propose a spectral amplitude scaling method to mitigate such nonlinear ISI and demonstrate a record 4 GBaud 16-APSK on the spectral amplitude plus 2-bit eigenvalue modulation (total 6 bit/symbol at 24 Gb/s) transmission over 1000 km.

  5. Power decoupling method for single phase differential buck converter

    DEFF Research Database (Denmark)

    Yao, Wenli; Tang, Yi; Zhang, Xiaobin

    2015-01-01

    inverter to improve the dc link power quality, and an improved active power decoupling method is proposed to achieve ripple power reduction for both AC-DC and DC-AC conversions. The ripple energy storage is realized by the filter capacitors, which are connected between the output terminal and the negative...... generation technique is proposed to provide accurate ripple power compensation, and closed-loop controllers are also designed based on small signal models. The effectiveness of this power decoupling method is verified by detailed simulation studies as well as laboratory prototype experimental results....... dc bus. By properly controlling the differential mode voltage of the capacitors, it is possible to transfer desired energy between the DC port and AC port. The common mode voltage is controlled in such a way that the ripple power on the dc side will be reduced. Furthermore, an autonomous reference...

  6. Application of the comparison principle to analysis of nonlinear systems. [using Lipschitz condition and differential equations

    Science.gov (United States)

    Gunderson, R. W.

    1975-01-01

    A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

  7. The mixed BVP for second order nonlinear ordinary differential equation at resonance

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan

    2017-01-01

    Roč. 290, 2-3 (2017), s. 393-400 ISSN 0025-584X Institutional support: RVO:67985840 Keywords : mixed problem at resonance * nonlinear ordinary differencial equation Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.742, year: 2016

  8. Boundary behavior of blow-up solutions to some weighted non-linear differential equations

    Directory of Open Access Journals (Sweden)

    Ahmed Mohammed

    2002-09-01

    Full Text Available We investigate, under appropriate conditions on the weight $g$ and the non-linearity $f$, the boundary behavior of solutions to $$(r^{alpha}(u'^{p-1}'=r^alpha g(rf(u, $$ $0

  9. Multiple single nucleotide polymorphism analysis using penalized regression in nonlinear mixed-effect pharmacokinetic models.

    Science.gov (United States)

    Bertrand, Julie; Balding, David J

    2013-03-01

    Studies on the influence of single nucleotide polymorphisms (SNPs) on drug pharmacokinetics (PK) have usually been limited to the analysis of observed drug concentration or area under the concentration versus time curve. Nonlinear mixed effects models enable analysis of the entire curve, even for sparse data, but until recently, there has been no systematic method to examine the effects of multiple SNPs on the model parameters. The aim of this study was to assess different penalized regression methods for including SNPs in PK analyses. A total of 200 data sets were simulated under both the null and an alternative hypothesis. In each data set for each of the 300 participants, a PK profile at six sampling times was simulated and 1227 genotypes were generated through haplotypes. After modelling the PK profiles using an expectation maximization algorithm, genetic association with individual parameters was investigated using the following approaches: (i) a classical stepwise approach, (ii) ridge regression modified to include a test, (iii) Lasso and (iv) a generalization of Lasso, the HyperLasso. Penalized regression approaches are often much faster than the stepwise approach. There are significantly fewer true positives for ridge regression than for the stepwise procedure and HyperLasso. The higher number of true positives in the stepwise procedure was accompanied by a higher count of false positives (not significant). We find that all approaches except ridge regression show similar power, but penalized regression can be much less computationally demanding. We conclude that penalized regression should be preferred over stepwise procedures for PK analyses with a large panel of genetic covariates.

  10. Crystal growth and characterization of semi-organic 2-amino-5-nitropyridinium bromide (2A5NPBr) single crystals for third-order nonlinear optical (NLO) applications

    Science.gov (United States)

    Vediyappan, Sivasubramani; Arumugam, Raja; Pichan, Karuppasamy; Kasthuri, Ramachandran; Muthu, Senthil Pandian; Perumal, Ramasamy

    2017-12-01

    Semi-organic nonlinear optical (NLO) 2-amino-5-nitropyridinium bromide (2A5NPBr) single crystals have been grown by slow evaporation solution technique (SEST) with the growth period of 60 days. The single-crystal XRD analysis confirms the unit cell parameters of the grown crystal. The crystallinity of grown 2A5NPBr was analyzed by powder X-ray diffraction (PXRD) measurement. The presence of functional groups of 2A5NPBr crystal was confirmed by Fourier transform infrared (FTIR) spectrum analysis. The optical transmittance of the grown crystal was analyzed by UV-Vis-NIR analysis. It shows good transparency in the visible and NIR region and it is favorable for nonlinear optical (NLO) device applications. The chemical etching study was carried out and it reveals that the grown crystal has less dislocation density. The photoconductivity study reveals that the grown crystal possesses positive photoconductive nature. The thermal stability of the crystal has been investigated by thermogravimetric (TG) and differential thermal analysis (DTA). The dielectric constant and dielectric loss as a function of frequency were measured. The electronic polarizability (α) of 2A5NPBr molecule has been calculated theoretically by different ways such as Penn analysis, Clausius-Mossotti relation, Lorentz-Lorenz equation, optical bandgap, and coupled dipole method (CDM). The obtained values of electronic polarizability (α) are in good agreement with each other. Laser damage threshold (LDT) of 2A5NPBr crystal has been measured using Nd:YAG laser with the wavelength of 1064 nm. Third-order nonlinear optical property of the grown crystal was studied by Z-scan technique using He-Ne laser of wavelength 632.8 nm.

  11. A multiple-scale power series method for solving nonlinear ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Chein-Shan Liu

    2016-02-01

    Full Text Available The power series solution is a cheap and effective method to solve nonlinear problems, like the Duffing-van der Pol oscillator, the Volterra population model and the nonlinear boundary value problems. A novel power series method by considering the multiple scales $R_k$ in the power term $(t/R_k^k$ is developed, which are derived explicitly to reduce the ill-conditioned behavior in the data interpolation. In the method a huge value times a tiny value is avoided, such that we can decrease the numerical instability and which is the main reason to cause the failure of the conventional power series method. The multiple scales derived from an integral can be used in the power series expansion, which provide very accurate numerical solutions of the problems considered in this paper.

  12. A New Monotone Iteration Principle in the Theory of Nonlinear Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Bapurao C. Dhage

    2015-08-01

    Full Text Available In this paper the author proves the algorithms for the existence as well as approximations of the solutions for the initial value problems of nonlinear fractional differential equations using the operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid fixed point theorems of Dhage (2014 in a partially ordered normed linear space and the existence and approximations of the solutions of the considered nonlinear fractional differential equations are obtained under weak mixed partial continuity and partial Lipschitz conditions. Our hypotheses and existence and approximation results are also well illustrated by some numerical examples.

  13. Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework

    KAUST Repository

    Cortes, Adriano Mauricio

    2014-01-01

    In this paper we present PetIGA, a high-performance implementation of Isogeometric Analysis built on top of PETSc. We show its use in solving nonlinear and time-dependent problems, such as phase-field models, by taking advantage of the high-continuity of the basis functions granted by the isogeometric framework. In this work, we focus on the Cahn-Hilliard equation and the phase-field crystal equation.

  14. Nonlinear Variation of Parameters Formula for Impulsive Differential Equations with Initial Time Difference and Application

    Directory of Open Access Journals (Sweden)

    Peiguang Wang

    2014-01-01

    Full Text Available This paper establishes variation of parameters formula for impulsive differential equations with initial time difference. As an application, one of the results is used to investigate stability properties of solutions.

  15. First order integro-differential equations in Banach algebras involving Caratheodory and discontinuous nonlinearities

    Directory of Open Access Journals (Sweden)

    Bapurao Dhage

    2005-11-01

    Full Text Available In this paper some existence theorems for the first order differential equations in Banach algebras is proved under the mixed generalized Lipschitz, Carathéodory and monotonicity conditions.

  16. Heteronuclear refocusing by nonlinear phase and amplitude modulation on a single transmitter channel.

    Science.gov (United States)

    Moore, Jay; Colón, Raul D; Tadanki, Sasidhar; Waddell, Kevin W

    2014-08-01

    The application of low magnetic fields to heteronuclear NMR has expanded recently alongside the emergence of methods for achieving near unity polarization of spin ensembles, independent of magnetic field strength. The parahydrogen induced hyperpolarization methods in particular, often use a hybrid arrangement where a high field spectrometer is used to detect or image polarized molecules that have been conjured on a separate, dedicated polarizer instrument operating at fields in the mT regime where yields are higher. For controlling polarizer chemistry, spare TTL channels of portable NMR spectrometers can be used to pulse program reaction timings in synchrony with heteronuclear RF transformations. The use of a spectrometer as a portable polarizer control module has the advantage of allowing detection in situ, simplifying the process of optimizing polarization yields prior to in vivo experimental trials. Suitable heteronuclear spectrometers compatible with this application are becoming more common, but are still sparsely available in comparison to a large existing infrastructure of single channel NMR consoles. With the goal of expanding the range of these systems to multinuclear applications, the feasibility of rotating a pair of heteronuclear spins ((13)C and (1)H) at 12mT was investigated in this study. Nonlinear phase and amplitude modulated waveforms designed to simultaneously refocus magnetization at 128kHz ((13)C) and 510kHz ((1)H) were generated numerically with optimal control. Although precise quantitative comparisons were not attempted due to limitations of the experimental setup, signals refocused at heteronuclear frequencies with this PANORAMIC approach (Precession And Nutation for Observing Rotation At Multiple Intervals about the Carrier) yielded amplitudes comparable to signals which were refocused using traditional block pulses on heteronuclear channels. Using this PANORAMIC approach to heteronuclear NMR at low field would reduce expense as well as

  17. Heteronuclear refocusing by nonlinear phase and amplitude modulation on a single transmitter channel

    Science.gov (United States)

    Moore, Jay; Colón, Raul D.; Tadanki, Sasidhar; Waddell, Kevin W.

    2014-08-01

    The application of low magnetic fields to heteronuclear NMR has expanded recently alongside the emergence of methods for achieving near unity polarization of spin ensembles, independent of magnetic field strength. The parahydrogen induced hyperpolarization methods in particular, often use a hybrid arrangement where a high field spectrometer is used to detect or image polarized molecules that have been conjured on a separate, dedicated polarizer instrument operating at fields in the mT regime where yields are higher. For controlling polarizer chemistry, spare TTL channels of portable NMR spectrometers can be used to pulse program reaction timings in synchrony with heteronuclear RF transformations. The use of a spectrometer as a portable polarizer control module has the advantage of allowing detection in situ, simplifying the process of optimizing polarization yields prior to in vivo experimental trials. Suitable heteronuclear spectrometers compatible with this application are becoming more common, but are still sparsely available in comparison to a large existing infrastructure of single channel NMR consoles. With the goal of expanding the range of these systems to multinuclear applications, the feasibility of rotating a pair of heteronuclear spins (13C and 1H) at 12 mT was investigated in this study. Nonlinear phase and amplitude modulated waveforms designed to simultaneously refocus magnetization at 128 kHz (13C) and 510 kHz (1H) were generated numerically with optimal control. Although precise quantitative comparisons were not attempted due to limitations of the experimental setup, signals refocused at heteronuclear frequencies with this PANORAMIC approach (Precession And Nutation for Observing Rotation At Multiple Intervals about the Carrier) yielded amplitudes comparable to signals which were refocused using traditional block pulses on heteronuclear channels. Using this PANORAMIC approach to heteronuclear NMR at low field would reduce expense as well as

  18. An efficient algorithm for computation of solitary wave solutions to nonlinear differential equations

    Science.gov (United States)

    Ayub, Kamran; Khan, M. Yaqub; Mahmood-Ul-Hassan, Qazi; Ahmad, Jamshad

    2017-09-01

    Nonlinear mathematical problems and their solutions attain much attention in solitary waves. In soliton theory, an efficient tool to attain various types of soliton solutions is the \\exp (-φ (ζ ))-expansion technique. This article is devoted to find exact travelling wave solutions of Drinfeld-Sokolov equation via a reliable mathematical technique. By using the proposed technique, we attain soliton wave solution of various types. It is observed that the technique under discussion is user friendly with minimum computational work, and can be extended for physical problems of different nature in mathematical physics.

  19. The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Yusuf Pandir

    2018-02-01

    Full Text Available In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.

  20. Single and Triple Differential Cross Sections for DoublePhotoionization of H-

    Energy Technology Data Exchange (ETDEWEB)

    Yip, Frank L.; Horner, Daniel A.; McCurdy, C. William; Rescigno,Thomas N.

    2007-02-15

    The hydride anion H- would not be bound in the absence ofelectron correlation. Electron correlation drives the doublephotoionization process and, thus should impact double photoionizationresults most strongly for H-. We present fully differential crosssections for the three-body breakup of H- by single photon absorption.The absolute triple-differential and single-differential cross sectionswere yielded by ab initio calculations making use of exterior complexscaling within a discrete variable representation partialwave basis.Results calculated at photon energies of 18eV and 30eV are compared withreported cross sections for helium calculated at 20eV above the doubleionization threshold. These comparisons show a clear signature of initialstate correlation that differentiate the He and H- cases.

  1. Estimation of Joule heating and its role in nonlinear electrical response of Tb0.5Sr0.5MnO3 single crystal

    Science.gov (United States)

    Nhalil, Hariharan; Elizabeth, Suja

    2016-12-01

    Highly non-linear I-V characteristics and apparent colossal electro-resistance were observed in non-charge ordered manganite Tb0.5Sr0.5MnO3 single crystal in low temperature transport measurements. Significant changes were noticed in top surface temperature of the sample as compared to its base while passing current at low temperature. By analyzing these variations, we realize that the change in surface temperature (ΔTsur) is too small to have caused by the strong negative differential resistance. A more accurate estimation of change in the sample temperature was made by back-calculating the sample temperature from the temperature variation of resistance (R-T) data (ΔTcal), which was found to be higher than ΔTsur. This result indicates that there are large thermal gradients across the sample. The experimentally derived ΔTcal is validated with the help of a simple theoretical model and estimation of Joule heating. Pulse measurements realize substantial reduction in Joule heating. With decrease in sample thickness, Joule heating effect is found to be reduced. Our studies reveal that Joule heating plays a major role in the nonlinear electrical response of Tb0.5Sr0.5MnO3. By careful management of the duty cycle and pulse current I-V measurements, Joule heating can be mitigated to a large extent.

  2. Growth and Characterization of Lithium Potassium Phthalate (LiKP) Single Crystals for Third Order Nonlinear Optical Applications

    Energy Technology Data Exchange (ETDEWEB)

    Sivakumar, B.; Mohan, R. [Preidency College, Bangalore (India); Raj, S. Gokul [RR and Dr. SR Technical Univ., Avadi (India); Kumar, G. Ramesh [Anna Univ., Arni (India)

    2012-11-15

    Single crystals of lithium potassium phthalate (LiKP) were successfully grown from aqueous solution by solvent evaporation technique. The grown crystals were characterized by single crystal X-ray diffraction. The lithium potassium phthalate C{sub 16} H{sub 12} K Li{sub 3} O{sub 11} belongs to triclinic system with the following unit-cell dimensions at 298(2) K; a = 7.405(5) A; b = 9.878(5) A; c = 13.396(5) A; α = 71.778(5) .deg.; β = 87.300(5) .deg.; γ = 85.405(5) .deg.; having a space group P1. Mass spectrometric analysis provides the molecular weight of the compound and possible ways of fragmentations occurs in the compound. Thermal stability of the crystal was also studied by both simultaneous TGA/DTA analyses. The UV-Vis-NIR spectrum shows a good transparency in the whole of Visible and as well as in the near IR range. Third order nonlinear optical studies have also been studied by Z-scan technique. Nonlinear absorption and nonlinear refractive index were found out and the third order bulk susceptibility of compound was also estimated.

  3. Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations.

    Science.gov (United States)

    Banks, H Thomas; Robbins, Danielle; Sutton, Karyn L

    2013-01-01

    In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and generalized sensitivity functions), especially in control and estimation problems. We summarize general existence and uniqueness results before turning to our main results on differentiation with respect to delays, etc. Finally we discuss use of our results in the context of estimation problems.

  4. Blow up of solutions to ordinary differential equations arising in nonlinear dispersive problems

    Directory of Open Access Journals (Sweden)

    Milena Dimova

    2018-03-01

    Full Text Available We study a new class of ordinary differential equations with blow up solutions. Necessary and sufficient conditions for finite blow up time are proved. Based on the new differential equation, a revised version of the concavity method of Levine is proposed. As an application we investigate the non-existence of global solutions to the Cauchy problem of Klein-Gordon, and to the double dispersive equations. We obtain necessary and sufficient condition for finite time blow up with arbitrary positive energy. A very general sufficient condition for blow up is also given.

  5. Detection of Differential Item Functioning with Nonlinear Regression: A Non-IRT Approach Accounting for Guessing

    Czech Academy of Sciences Publication Activity Database

    Drabinová, Adéla; Martinková, Patrícia

    2017-01-01

    Roč. 54, č. 4 (2017), s. 498-517 ISSN 0022-0655 R&D Projects: GA ČR GJ15-15856Y Institutional support: RVO:67985807 Keywords : differential item functioning * non- linear regression * logistic regression * item response theory Subject RIV: AM - Education OBOR OECD: Statistics and probability Impact factor: 0.979, year: 2016

  6. Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay

    Directory of Open Access Journals (Sweden)

    Erdal Korkmaz

    2017-06-01

    Full Text Available Abstract In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov’s second method. The results obtained essentially improve, include and complement the results in the literature.

  7. Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay.

    Science.gov (United States)

    Korkmaz, Erdal

    2017-01-01

    In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.

  8. New continual analogs of two-dimensional Toda lattices related with nonlinear integro-differential equations

    International Nuclear Information System (INIS)

    Savel'ev, M.V.

    1988-01-01

    Continual ''extensions'' of two-dimensional Toda lattices are proposed. They are described by integro-differential equations, generally speaking, with singular kernels, depending on new (third) variable. The problem of their integrability on the corresponding class of the initial discrete system solutions is discussed. The latter takes place, in particular, for the kernel coinciding with the causal function

  9. The nonlocal boundary value problems for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan

    -, č. 35 (2015), s. 23-50 ISSN 1126-8042 Institutional support: RVO:67985840 Keywords : higher order functional differential equations * Dirichlet boundary value problem * strong singularity Subject RIV: BA - General Mathematics http://ijpam.uniud.it/online_issue/201535/03-Mukhigulashvili.pdf

  10. Certain non-linear differential polynomials sharing a non zero polynomial

    Directory of Open Access Journals (Sweden)

    Majumder Sujoy

    2015-10-01

    functions sharing a nonzero polynomial and obtain two results which improves and generalizes the results due to L. Liu [Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 56 (2008, 3236-3245.] and P. Sahoo [Uniqueness and weighted value sharing of meromorphic functions, Applied. Math. E-Notes., 11 (2011, 23-32.].

  11. Comparison of nonlinearities in oscillation theory of half-linear differential equations

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel

    2008-01-01

    Roč. 121, č. 2 (2008), s. 93-105 ISSN 0236-5294 R&D Projects: GA AV ČR KJB100190701 Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear differential equation * comparison theorem * Riccati technique Subject RIV: BA - General Mathematics Impact factor: 0.317, year: 2008

  12. A HAM-based wavelet approach for nonlinear partial differential equations: Two dimensional Bratu problem as an application

    Science.gov (United States)

    Yang, Zhaochen; Liao, Shijun

    2017-12-01

    In this paper, a new analytic approach, namely the wavelet homotopy analysis method (wHAM), is developed for boundary value problems (BVPs) governed by nonlinear partial differential equations (PDEs), which successfully combines the homotopy analysis method (HAM) and the generalized Coiflet-type wavelet. To improve the computational efficiency and accuracy, a section-based wavelet approximation for partial derivatives is proposed. The two-dimensional Bratu equation is used as an example to illustrate its basic ideas of the wHAM. Numerical results verify the validity as well as great advantages of the wHAM. Compared with the normal HAM, the wHAM possesses not only larger freedom to choose the auxiliary linear operator, but also better convergence property and higher computational efficiency. In addition, the iteration approach can greatly accelerate convergence.

  13. Differential delay equations in chemical kinetics. Nonlinear models: The cross-shaped phase diagram and the Oregonator

    Science.gov (United States)

    Epstein, Irving R.; Luo, Yin

    1991-07-01

    Delayed feedback plays a key role in most, if not all chemical oscillators. We derive general results useful in the linear stability analysis of models that explicitly incorporate delay by using differential delay equations. Two models of nonlinear chemical oscillators, the cross-shaped phase diagram model of Boissonade and De Kepper and the Oregonator, are modified by deleting a feedback species and mimicking its effect by a delay in the kinetics of another variable. With an appropriate choice of the delay time, the reduced models behave very much like the full systems. It should be possible to carry out similar reductions on more complex mechanisms of oscillating reactions, thereby providing insight into the role of delayed feedback in these systems.

  14. Self-Similar Nanocavity Design with Ultrasmall Mode Volume for Single-Photon Nonlinearities

    DEFF Research Database (Denmark)

    Choi, Hyeongrak; Heuck, Mikkel; Englund, Dirk R.

    2017-01-01

    illustrate the design concept with a silicon-air one-dimensional photon crystal cavity that reaches an ultrasmall mode volume of V-eff similar to 7.01 x 10(-5)lambda(3) at lambda similar to 1550 nm. We show that the extreme light concentration in our design can enable ultrastrong Kerr nonlinearities, even...

  15. Positive Solutions for a Higher-Order Nonlinear Neutral Delay Differential Equation

    Directory of Open Access Journals (Sweden)

    Zeqing Liu

    2011-01-01

    pi,τi,βj,g∈C([to,+∞,ℝ, αj∈Cn−1([to,+∞,ℝ, f∈Cn−1([to,+∞×ℝk,ℝ, h∈C([to,+∞×ℝk,ℝ, and limt→+∞τi(t=limt→+∞αj(t=limt→+∞βj(t=+∞, i∈{1,2,…,m}, j∈{1,2,…,k}. By making use of the Leray-Schauder nonlinear alterative theorem, we establish the existence of uncountably many bounded positive solutions for the above equation. Our results improve and generalize some corresponding results in the field. Three examples are given which illustrate the advantages of the results presented in this paper.

  16. Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

    Science.gov (United States)

    Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

    2015-07-01

    Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

  17. Dynamics of a Bertrand duopoly with differentiated products and nonlinear costs: Analysis, comparisons and new evidences

    International Nuclear Information System (INIS)

    Brianzoni, Serena; Gori, Luca; Michetti, Elisabetta

    2015-01-01

    This paper studies mathematical properties and dynamics of a duopoly with price competition and horizontal product differentiation by introducing quadratic production costs (decreasing returns to scale), thus extending the model with linear costs (constant returns to scale) of Fanti et al. [11]. The economy is described by a two-dimensional non-invertible discrete time dynamic system. The paper first determines fixed points and other invariant sets, showing that synchronized dynamics can occur. Then, stability properties are compared in the cases of quadratic costs and linear costs by considering the degree of product differentiation and the speed of adjustment of prices as key parameters. It is also shown that synchronization takes place if products tend to be relatively complements and stressed similarities and differences between models with quadratic and linear costs. Finally, the paper focuses on the phenomenon of multistability thus underlying new evidences in comparison with the model with linear costs.

  18. The linkage of Zlib to Teapot for auto-differentiation map extraction and nonlinear analysis

    International Nuclear Information System (INIS)

    Sun, N.; Yan, Y.T.; Pilat, F.; Bourianoff, G.

    1993-05-01

    The differential Lie algebraic numerical library, Zlib has been linked to Teapot, the accelerator simulator code. This makes possible the use of the operational correction features of Teapot to produce a corrected lattice, and then choose either map or thin element-by-element tracking for tracking studies. Thin-element tracking is more accurate but slower than map tracking; therefore, the option of choosing one or the other is very desirable

  19. Differential Transform Method with Complex Transforms to Some Nonlinear Fractional Problems in Mathematical Physics

    OpenAIRE

    Mohyud-Din, Syed Tauseef; Awan, Farah Jabeen; Ahmad, Jamshad; Hassan, Saleh M.

    2015-01-01

    This paper witnesses the coupling of an analytical series expansion method which is called reduced differential transform with fractional complex transform. The proposed technique is applied on three mathematical models, namely, fractional Kaup-Kupershmidt equation, generalized fractional Drinfeld-Sokolov equations, and system of coupled fractional Sine-Gordon equations subject to the appropriate initial conditions which arise frequently in mathematical physics. The derivatives are defined in...

  20. Bulk crystal growth and their effective third order nonlinear optical properties of 2-(4-fluorobenzylidene) malononitrile (FBM) single crystal

    Science.gov (United States)

    Priyadharshini, A.; Kalainathan, S.

    2018-04-01

    2-(4-fluorobenzylidene) malononitrile (FBM), an organic third order nonlinear (TONLO) single crystal with the dimensions of 32 × 7 × 11 mm3, has been successfully grown in acetone solution by slow evaporation technique at 35 °C. The crystal system (triclinic), space group (P-1) and crystalline purity of the titular crystal were measured by single crystal and powder X-ray diffraction, respectively. The molecular weight and the multiple functional groups of the FBM material were confirmed through the mass and FT-IR spectral analysis. UV-Vis-NIR spectral study enroles that the FBM crystal exhibits excellent transparency (83%) in the entire visible and near infra-red region with a wide bandgap 2.90 eV. The low dielectric constant (εr) value of FBM crystal is appreciable for microelectronics industry applications. Thermal stability and melting point (130.09 °C) were ascertained by TGA-DSC analysis. The laser-induced surface damage threshold (LDT) value of FBM specimen is found to be 2.14 GW/cm2, it is fairly good compared to other reported NLO crystals. The third - order nonlinear optical character of the FBM crystal was confirmed through the typical single beam Z-scan technique. All these finding authorized that the organic crystal of FBM is favorably suitable for NLO applications.

  1. Control methods for localization of nonlinear waves.

    Science.gov (United States)

    Porubov, Alexey; Andrievsky, Boris

    2017-03-06

    A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

  2. Nonlinear optics at the single-photon level inside a hollow core fiber

    DEFF Research Database (Denmark)

    Hofferberth, Sebastian; Peyronel, Thibault; Liang, Qiyu

    2011-01-01

    Cold atoms inside a hollow core fiber provide an unique system for studying optical nonlinearities at the few-photon level. Confinement of both atoms and photons inside the fiber core to a diameter of just a few wavelengths results in high electric field intensity per photon and large optical...... depths with a relatively small number of atoms. We present our experimental apparatus and discuss results regarding all-optical switching at ultra-low light levels....

  3. Traveling wave solutions to some nonlinear fractional partial differential equations through the rational (G′/G-expansion method

    Directory of Open Access Journals (Sweden)

    Tarikul Islam

    2018-03-01

    Full Text Available In this article, the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regularized long wave (SRLW equation are successfully examined by the recently established rational (G′/G-expansion method. The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform. Consequently, the theories of the ordinary differential equations are implemented effectively. Three types closed form traveling wave solutions, such as hyperbolic function, trigonometric function and rational, are constructed by using the suggested method in the sense of conformable fractional derivative. The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel. It is observed that the performance of the rational (G′/G-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.

  4. Robust and adaptive techniques for numerical simulation of nonlinear partial differential equations of fractional order

    Science.gov (United States)

    Owolabi, Kolade M.

    2017-03-01

    In this paper, some nonlinear space-fractional order reaction-diffusion equations (SFORDE) on a finite but large spatial domain x ∈ [0, L], x = x(x , y , z) and t ∈ [0, T] are considered. Also in this work, the standard reaction-diffusion system with boundary conditions is generalized by replacing the second-order spatial derivatives with Riemann-Liouville space-fractional derivatives of order α, for 0 Fourier spectral method is introduced as a better alternative to existing low order schemes for the integration of fractional in space reaction-diffusion problems in conjunction with an adaptive exponential time differencing method, and solve a range of one-, two- and three-components SFORDE numerically to obtain patterns in one- and two-dimensions with a straight forward extension to three spatial dimensions in a sub-diffusive (0 reaction-diffusion case. With application to models in biology and physics, different spatiotemporal dynamics are observed and displayed.

  5. Growth and characterization of a single crystal of Urea Adipic acid (UAA) - A third order nonlinear optical material

    Science.gov (United States)

    Shanthi, A.; Krishnan, C.; Selvarajan, P.

    2014-03-01

    An organic single crystal of Urea Adipic acid (UAA) was successfully grown in methanol solvent by slow solvent evaporation technique at room temperature (30 °C). The structure of grown crystal was elucidated from the X-ray diffraction study and it belongs to monoclinic system with centrosymmetric space group P21/c. The optical transmission spectrum of UAA has been recorded and its theoretical calculations were carried out to determine the linear optical constants such as linear absorption coefficient, extinction coefficient, refractive index and reflectance etc. The third-order nonlinearities of UAA crystal have been investigated by Z-scan method. The values of nonlinear refractive index (n2), the absorption coefficient (β) and third-order nonlinear susceptibility (χ(3)) are found to be the order of 0.96 × 10-10 cm2/W, 1.248 × 10-4 cm/W and 6.44 × 10-8 esu respectively. Fourier Transform Infra Red and Raman spectroscopy studies reveal the intermolecular interactions present in the UAA sample. The dielectric and mechanical measurements of the title compound are also reported.

  6. Growth and characterization of a single crystal of Urea Adipic acid (UAA)--a third order nonlinear optical material.

    Science.gov (United States)

    Shanthi, A; Krishnan, C; Selvarajan, P

    2014-03-25

    An organic single crystal of Urea Adipic acid (UAA) was successfully grown in methanol solvent by slow solvent evaporation technique at room temperature (30 °C). The structure of grown crystal was elucidated from the X-ray diffraction study and it belongs to monoclinic system with centrosymmetric space group P21/c. The optical transmission spectrum of UAA has been recorded and its theoretical calculations were carried out to determine the linear optical constants such as linear absorption coefficient, extinction coefficient, refractive index and reflectance etc. The third-order nonlinearities of UAA crystal have been investigated by Z-scan method. The values of nonlinear refractive index (n2), the absorption coefficient (β) and third-order nonlinear susceptibility (χ((3))) are found to be the order of 0.96×10(-10) cm(2)/W, 1.248×10(-4) cm/W and 6.44×10(-8) esu respectively. Fourier Transform Infra Red and Raman spectroscopy studies reveal the intermolecular interactions present in the UAA sample. The dielectric and mechanical measurements of the title compound are also reported. Copyright © 2013 Elsevier B.V. All rights reserved.

  7. A unified active damping control for single-phase differential buck inverter with LCL-filter

    DEFF Research Database (Denmark)

    Yao, Wenli; Wang, Xiongfei; Zhang, Xiaobin

    2015-01-01

    and control of a grid-connected differential mode buck inverter with an LCL filter. A generalized small-signal model of the inverter is built first with the averaged switching model. It is shown that the LCL filter resonance merely occurs in the differential mode, while an LC filter resonance exists......The single-phase differential mode buck inverter is recently introduced with a differential mode for power transfer and a common mode for actively decoupling the second-order power oscillation. However, it is limited to islanded applications with an LC filter. This paper addresses the stability...... in the common mode, provided that the filter parameters of the two bridges are kept the same. A unified active damping control approach is then proposed for stabilizing the inverter and improving the transient performance under a wide range of grid impedance. Lastly, experimental tests are carried out...

  8. Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods

    International Nuclear Information System (INIS)

    Civalek, Oemer

    2005-01-01

    The nonlinear dynamic response of doubly curved shallow shells resting on Winkler-Pasternak elastic foundation has been studied for step and sinusoidal loadings. Dynamic analogues of Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by numerical examples. The shear parameter G of the Pasternak foundation and the stiffness parameter K of the Winkler foundation have been found to have a significant influence on the dynamic response of the shell. It is concluded from the present study that the HDQ-FD methodolgy is a simple, efficient, and accurate method for the nonlinear analysis of doubly curved shallow shells resting on two-parameter elastic foundation

  9. Single-cell entropy for accurate estimation of differentiation potency from a cell's transcriptome

    Science.gov (United States)

    Teschendorff, Andrew E.; Enver, Tariq

    2017-06-01

    The ability to quantify differentiation potential of single cells is a task of critical importance. Here we demonstrate, using over 7,000 single-cell RNA-Seq profiles, that differentiation potency of a single cell can be approximated by computing the signalling promiscuity, or entropy, of a cell's transcriptome in the context of an interaction network, without the need for feature selection. We show that signalling entropy provides a more accurate and robust potency estimate than other entropy-based measures, driven in part by a subtle positive correlation between the transcriptome and connectome. Signalling entropy identifies known cell subpopulations of varying potency and drug resistant cancer stem-cell phenotypes, including those derived from circulating tumour cells. It further reveals that expression heterogeneity within single-cell populations is regulated. In summary, signalling entropy allows in silico estimation of the differentiation potency and plasticity of single cells and bulk samples, providing a means to identify normal and cancer stem-cell phenotypes.

  10. Strongly increasing solutions of cyclic systems of second order differential equations with power-type nonlinearities

    Directory of Open Access Journals (Sweden)

    Jaroslav Jaroš

    2015-01-01

    Full Text Available We consider \\(n\\-dimensional cyclic systems of second order differential equations \\[(p_i(t|x_{i}'|^{\\alpha_i -1}x_{i}'' = q_{i}(t|x_{i+1}|^{\\beta_i-1}x_{i+1},\\] \\[\\quad i = 1,\\ldots,n, \\quad (x_{n+1} = x_1 \\tag{\\(\\ast\\}\\] under the assumption that the positive constants \\(\\alpha_i\\ and \\(\\beta_i\\ satisfy \\(\\alpha_1{\\ldots}\\alpha_n \\gt \\beta_1{\\ldots}\\beta_n\\ and \\(p_i(t\\ and \\(q_i(t\\ are regularly varying functions, and analyze positive strongly increasing solutions of system (\\(\\ast\\ in the framework of regular variation. We show that the situation for the existence of regularly varying solutions of positive indices for (\\(\\ast\\ can be characterized completely, and moreover that the asymptotic behavior of such solutions is governed by the unique formula describing their order of growth precisely. We give examples demonstrating that the main results for (\\(\\ast\\ can be applied to some classes of partial differential equations with radial symmetry to acquire accurate information about the existence and the asymptotic behavior of their radial positive strongly increasing solutions.

  11. Existence of entire solutions of some non-linear differential-difference equations

    Directory of Open Access Journals (Sweden)

    Minfeng Chen

    2017-04-01

    Full Text Available Abstract In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations ( f ′ ( z 2 + P 2 ( z f 2 ( z + c = Q ( z e α ( z $(f'(z^{2}+P^{2}(zf^{2}(z+c=Q(ze^{\\alpha(z}$ and ( f ′ ( z 2 + [ f ( z + c − f ( z ] 2 = Q ( z e α ( z $(f'(z^{2}+[f(z+c-f(z]^{2}=Q(ze^{\\alpha(z}$ , where P ( z $P(z$ , Q ( z $Q(z$ are two non-zero polynomials, α ( z $\\alpha(z$ is a polynomial and c ∈ C ∖ { 0 } $c\\in\\mathbb{C}\\backslash\\{0\\}$ . In addition, we investigate the non-existence of entire solutions of finite order of the differential-difference equation ( f ′ ( z n + P ( z f m ( z + c = Q ( z $(f'(z^{n}+P(zf^{m}(z+c=Q(z$ , where P ( z $P(z$ , Q ( z $Q(z$ are two non-constant polynomials, c ∈ C ∖ { 0 } $c\\in\\mathbb{C}\\backslash\\{0\\}$ , m, n are positive integers and satisfy 1 m + 1 n < 2 $\\frac{1}{m}+\\frac{1}{n}<2$ except for m = 1 $m=1$ , n = 2 $n=2$ .

  12. Synergistic combinations of five single drugs from Centella asiatica for neuronal differentiation.

    Science.gov (United States)

    Lin, Jinjin; Jiang, Hui; Ding, Xianting

    2017-01-01

    To identify alternatives of nerve growth factor, which could promote NF68 protein expression and contribute toward neuronal differentiation, five compounds namely: asiatic acid, madecassic, madecassoside, quercetin, and isoquercetin, obtained from Centella asiatica, were examined for their neuronal differentiation effects on PC12 cells. C. asiatica has been applied as an effective herbal medicine for the treatment of various diseases, including depression. According to a statistical design of experiments, both single compound and compound combinations were evaluated. A further statistical analysis indicated quantitative interactions between these five single compounds and led to the identification of the optimal drug combinations. Asiatic acid and madecassic appeared to show profound synergistic effects on neurofilaments expression in vitro. The optimized drug combinations were significantly more potent than single drugs and further investigation suggested that the optimal drug combination could be an analogue of nerve growth factor and could represent a potential treatment for neurodegenerative diseases.

  13. A new modification in the exponential rational function method for nonlinear fractional differential equations

    Science.gov (United States)

    Ahmed, Naveed; Bibi, Sadaf; Khan, Umar; Mohyud-Din, Syed Tauseef

    2018-02-01

    We have modified the traditional exponential rational function method (ERFM) and have used it to find the exact solutions of two different fractional partial differential equations, one is the time fractional Boussinesq equation and the other is the (2+1)-dimensional time fractional Zoomeron equation. In both the cases it is observed that the modified scheme provides more types of solutions than the traditional one. Moreover, a comparison of the recent solutions is made with some already existing solutions. We can confidently conclude that the modified scheme works better and provides more types of solutions with almost similar computational cost. Our generalized solutions include periodic, soliton-like, singular soliton and kink solutions. A graphical simulation of all types of solutions is provided and the correctness of the solution is verified by direct substitution. The extended version of the solutions is expected to provide more flexibility to scientists working in the relevant field to test their simulation data.

  14. Synthesis and characterization of γ-glycine – a nonlinear optical single crystal for optoelectronic and photonic applications

    Directory of Open Access Journals (Sweden)

    Latha A. Arputha

    2017-02-01

    Full Text Available A single crystal of gamma-glycine (GG, a polymorph of glycine, was synthesized by crystallization. The single crystal of GG was grown from an aqueous solution. The morphology of GG was studied in order to assess its growth facets. The good quality single crystals were subjected to X-ray diffraction studies to reveal their structure. The FT-IR spectral analysis was carried out to confirm the presence of expected functional groups. The UV-Vis analysis was done for GG single crystals to determine the optical transparency and band gap. Simultaneous TG-DTA analysis was employed to understand the thermal and physicochemical stability of the title compound. The mechanical stability and laser stability of GG single crystal were studied using Vickers microhardness test and laser induced damage threshold on different planes of the crystal to reveal its anisotropic nature. The dielectric measurement was carried out as a function of frequency and the results were discussed. The existence of second harmonic generation (SHG of the title compound was confirmed by Kurtz-Perry powder technique. The SHG effective nonlinearity and particle size dependence of GG powder sample were compared with a standard reference material: potassium dihydrogen phosphate (KDP.

  15. Nonlinear oscillations

    CERN Document Server

    Nayfeh, Ali Hasan

    1995-01-01

    Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim

  16. A NEW FRACTIONAL MODEL OF SINGLE DEGREE OF FREEDOM SYSTEM, BY USING GENERALIZED DIFFERENTIAL TRANSFORM METHOD

    Directory of Open Access Journals (Sweden)

    HASHEM SABERI NAJAFI

    2016-07-01

    Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.

  17. Finite time blow-up of solutions for a nonlinear system of fractional differential equations

    Directory of Open Access Journals (Sweden)

    Abdelaziz Mennouni

    2017-06-01

    Full Text Available In this article we study the blow-up in finite time of solutions for the Cauchy problem of fractional ordinary equations $$\\displaylines{ u_{t} +a_1\\,^{c}D_{0_{+}}^{\\alpha_1} u +a_2\\,^{c}D_{0_{+}}^{\\alpha_2} u+\\dots +a_{n}\\,^{c}D_{0_{+}}^{\\alpha_n} u =\\int_0^{t} \\frac{(t-s^{-\\gamma_1}}{ \\Gamma(1-\\gamma_1 }f(u(s,v(sds,\\cr v_{t} +b_1\\,^{c}D_{0_{+}}^{\\beta_1} v+ b_2\\,^{c}D_{0_{+}}^{\\beta_2} v+\\dots +b_{n}\\,^{c}D_{0_{+}}^{\\beta_n} v = \\int_0^{t} \\frac{(t-s^{-\\gamma_2}}{ \\Gamma(1-\\gamma_2 }g(u(s,v(sds, }$$ for t>0, where the derivatives are Caputo fractional derivatives of order $\\alpha_i, \\beta_i$, and f and g are two continuously differentiable functions with polynomial growth. First, we prove the existence and uniqueness of local solutions for the above system supplemented with initial conditions, then we establish that they blow-up in finite time.

  18. Solution of ODE u + p(u)(u')2 + q(u) = 0 and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations

    International Nuclear Information System (INIS)

    Liu Chengshi

    2008-01-01

    Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc, are reduced to an integrable ODE expressed by u + p(u)(u') 2 + q(u) = 0 whose general solution can be given. Furthermore, combining complete discrimination system for polynomial, the classifications of all single travelling wave solutions to these equations are obtained. The equation u + p(u)(u') 2 + q(u) = 0 includes the equation (u') 2 = f(u) as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.

  19. Differentiation of a bipotential glial progenitor cell in a single cell microculture.

    Science.gov (United States)

    Temple, S; Raff, M C

    Although it is known that most cells of the vertebrate central nervous system (CNS) are derived from the neuroepithelial cells of the neural tube, the factors determining whether an individual neuroepithelial cell develops into a particular type of neurone or glial cell remain unknown. A promising model for studying this problem is the bipotential glial progenitor cell in the developing rat optic nerve; this cell differentiates into a particular type of astrocyte (a type-2 astrocyte) if cultured in 10% fetal calf serum (FCS) and into an oligodendrocyte if cultured in serum-free medium. As the oligodendrocyte-type-2 astrocyte (0-2A) progenitor cell can differentiate along either glial pathway in neurone-free cultures, living axons clearly are not required for its differentiation, at least in vitro. However, the studies on 0-2A progenitor cells were carried out in bulk cultures of optic nerve, and so it was possible that other cell-cell interactions were required for differentiation in culture. We show here that 0-2A progenitor cells can differentiate into type-2 astrocytes or oligodendrocytes when grown as isolated cells in microculture, indicating that differentiation along either glial pathway in vitro does not require signals from other CNS cells, apart from the signals provided by components of the culture medium. We also show that single 0-2A progenitor cells can differentiate along either pathway without dividing, supporting our previous studies using 3H-thymidine and suggesting that DNA replication is not required for these cells to choose between the two differentiation programmes.

  20. Nonlinear least squares regression for single image scanning electron microscope signal-to-noise ratio estimation.

    Science.gov (United States)

    Sim, K S; Norhisham, S

    2016-11-01

    A new method based on nonlinear least squares regression (NLLSR) is formulated to estimate signal-to-noise ratio (SNR) of scanning electron microscope (SEM) images. The estimation of SNR value based on NLLSR method is compared with the three existing methods of nearest neighbourhood, first-order interpolation and the combination of both nearest neighbourhood and first-order interpolation. Samples of SEM images with different textures, contrasts and edges were used to test the performance of NLLSR method in estimating the SNR values of the SEM images. It is shown that the NLLSR method is able to produce better estimation accuracy as compared to the other three existing methods. According to the SNR results obtained from the experiment, the NLLSR method is able to produce approximately less than 1% of SNR error difference as compared to the other three existing methods. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.

  1. Signal Processing using Nonlinear Optical Eects in Single- and Few-Mode Fibers

    DEFF Research Database (Denmark)

    Friis, Søren Michael Mørk

    The stagnating increase in data transmission capacity in optical communication systems combined with the ever growing demand of transmission bandwidth is leading to an impending capacity crunch, referring to the point in time after which the available bandwidth of the individual user starts...... accounts for multiple effects present in nonlinear fibers such as four-wave mixing, Raman scattering, distributed loss, and dispersion, and it is valid in the depleted pump regime. After validating the model against well-known results of quantum models, the model is used to predict the impacts of Raman...... noise, loss, and pump depletion on the noise properties of parametric frequency conversion and phase-insensitive and phase-sensitive parametric amplification. An important part of realizing space-division multiplexing is the ability of optical signal processing so the second part of this thesis...

  2. A differential Michelson interferometer with orthogonal single frequency laser for nanometer displacement measurement

    International Nuclear Information System (INIS)

    Yan, Liping; Chen, Benyong; Wang, Bin

    2017-01-01

    A novel differential Michelson laser interferometer is proposed to eliminate the influence of environmental fluctuations for nanometer displacement measurement. This differential interferometer consists of two homodyne interferometers in which two orthogonal single frequency beams share common reference arm and partial measurement arm. By modulating the displacement of the common reference arm with a piezoelectric transducer, the common-mode displacement drift resulting from the environmental disturbances can be well suppressed and the measured displacement as differential-mode displacement signal is achieved. In addition, a phase difference compensation method is proposed for accurately determining the phase difference between interference signals by correcting the time interval according to the average speed in one cycle of interference signal. The nanometer displacement measurement experiments were performed to demonstrate the effectiveness and feasibility of the proposed interferometer and show that precision displacement measurement with standard deviation less than 1 nm has been achieved. (paper)

  3. Differential cross sections for single-electron capture in He{sup 2+}-D collisions

    Energy Technology Data Exchange (ETDEWEB)

    Bordenave-Montesquieu, D.; Dagnac, R. [Centre National de la Recherche Scientifique (CNRS), 31 - Toulouse (France)]|[Toulouse-3 Univ., 31 (France)

    1995-06-14

    A translational energy spectroscopy technique was used to study single-electron capture into the He{sup +} (n = 2) and He{sup +} (n 3) states in He{sup 2+}-D collisions. Differential cross sections were determined at 4, 6 and 8 keV in the angular range 5`-1{sup o}30` (laboratory frame). As expected, single-electron capture into the n = 2 state was found to be the dominant process; total cross sections for capture into the He{sup +} (n = 3) state were compared to other experimental and theoretical results. (author).

  4. Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC.

    Directory of Open Access Journals (Sweden)

    Zachary F Phillips

    Full Text Available We present a new technique for quantitative phase and amplitude microscopy from a single color image with coded illumination. Our system consists of a commercial brightfield microscope with one hardware modification-an inexpensive 3D printed condenser insert. The method, color-multiplexed Differential Phase Contrast (cDPC, is a single-shot variant of Differential Phase Contrast (DPC, which recovers the phase of a sample from images with asymmetric illumination. We employ partially coherent illumination to achieve resolution corresponding to 2× the objective NA. Quantitative phase can then be used to synthesize DIC and phase contrast images or extract shape and density. We demonstrate amplitude and phase recovery at camera-limited frame rates (50 fps for various in vitro cell samples and c. elegans in a micro-fluidic channel.

  5. Nonlinearly Additive Forces in Multivalent Ligand Binding to a Single Protein Revealed with Force Spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Ratto, T V; Rudd, R E; Langry, K C; Balhorn, R L; McElfresh, M W

    2005-07-15

    We present evidence of multivalent interactions between a single protein molecule and multiple carbohydrates at a pH where the protein can bind four ligands. The evidence is based not only on measurements of the force required to rupture the bonds formed between ConcanavalinA (ConA) and {alpha}-D-mannose, but also on an analysis of the polymer-extension force curves to infer the polymer architecture that binds the protein to the cantilever and the ligands to the substrate. We find that although the rupture forces for multiple carbohydrate connections to a single protein are larger than the rupture force for a single connection, they do not scale additively with increasing number. Specifically, the most common rupture forces are approximately 46, 66, and 85 pN, which we argue corresponds to 1, 2, and 3 ligands being pulled simultaneously from a single protein as corroborated by an analysis of the linkage architecture. As in our previous work polymer tethers allow us to discriminate between specific and non-specific binding. We analyze the binding configuration (i.e. serial versus parallel connections) through fitting the polymer stretching data with modified Worm-Like Chain (WLC) models that predict how the effective stiffness of the tethers is affected by multiple connections. This analysis establishes that the forces we measure are due to single proteins interacting with multiple ligands, the first force spectroscopy study that establishes single-molecule multivalent binding unambiguously.

  6. Nonlinear optical refraction of Al2O3 single crystal doping with nickel nanoparticles measured by the Kerr-lens autocorrelation technique

    International Nuclear Information System (INIS)

    Yu, Xiangxiang; Wang, Yuhua; Wang, Yumei

    2014-01-01

    The nonlinear refraction of a nickel doped α-Al 2 O 3 single crystal was measured with a 800 nm pulse using the Kerr-lens autocorrelation technique. The sample was fabricated by ion implantation using a metal vapor vacuum arc ion source. The value of the nonlinear refractive index, n 2 , of the sample was determined to be 7.9 × 10 −16 cm 2 W −1 . The mechanisms of nonlinear refraction of the bulk material and the nanoparticles have been discussed through the UV–vis spectrum and supercontinuum spectra. (paper)

  7. Differentiation of drug and non-drug Cannabis using a single nucleotide polymorphism (SNP) assay.

    Science.gov (United States)

    Rotherham, D; Harbison, S A

    2011-04-15

    Cannabis sativa is both an illegal drug and a legitimate crop. The differentiation of illegal drug Cannabis from non-drug forms of Cannabis is relevant in the context of the growth of fibre and seed oil varieties of Cannabis for commercial purposes. This differentiation is currently determined based on the levels of tetrahydrocannabinol (THC) in adult plants. DNA based methods have the potential to assay Cannabis material unsuitable for analysis using conventional means including seeds, pollen and severely degraded material. The purpose of this research was to develop a single nucleotide polymorphism (SNP) assay for the differentiation of "drug" and "non-drug"Cannabis plants. An assay was developed based on four polymorphisms within a 399 bp fragment of the tetrahydrocannabinolic acid (THCA) synthase gene, utilising the snapshot multiplex kit. This SNP assay was tested on 94 Cannabis plants, which included 10 blind samples, and was able to differentiate between "drug" and "non-drug"Cannabis in all cases, while also differentiating between Cannabis and other species. Non-drug plants were found to be homozygous at the four sites assayed while drug Cannabis plants were either homozygous or heterozygous. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

  8. Intensity-dependent nonlinear optical properties in a modulation-doped single quantum well

    International Nuclear Information System (INIS)

    Ungan, F.

    2011-01-01

    In the present work, the changes in the intersubband optical absorption coefficients and the refractive index in a modulation-doped quantum well have been investigated theoretically. Within the envelope function approach and the effective mass approximation, the electronic structure of the quantum well is calculated from the self-consistent numerical solution of the coupled Schroedinger-Poisson equations. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The numerical results GaAs/Al x Ga 1-x As are presented for typical modulation-doped quantum well system. The linear, third-order nonlinear and total absorption and refractive index changes depending on the doping concentration are investigated as a function of the incident optical intensity and structure parameters, such as quantum well width and stoichiometric ratio. The results show that the doping concentration, the structure parameters and the incident optical intensity have a great effect on the optical characteristics of these structures. - Highlights: → The doping concentration has a great effect on the optical characteristics of these structures. → The structure parameters have a great effect on the optical properties of these structures. → The total absorption coefficients reduced as the incident optical intensity increases. → The RICs reduced as the incident optical intensity increases.

  9. Coherent nonlinear optical response of single-layer black phosphorus: third-harmonic generation

    Science.gov (United States)

    Margulis, Vladimir A.; Muryumin, Evgeny E.; Gaiduk, Evgeny A.

    2017-10-01

    We theoretically calculate the nonlinear optical (NLO) response of phosphorene (a black phosphorus monolayer) to a normally incident and linearly polarized coherent laser radiation of frequency ω, resulting in the generation of radiation at frequency 3ω. We derive explicit analytic expressions for four independent nonvanishing elements of the third-order NLO susceptibility tensor, describing the third-harmonic generation (THG) from phosphorene. The final formulas are numerically evaluated for typical values of the system's parameters to explore how the efficiency of the THG varies with both the frequency and the polarization direction of the incident radiation. The results obtained show a resonant enhancement of the THG efficiency when the pump photon energy ℏω approaches a value of one third of the bandgap energy Eg (≈1.5 eV) of phosphorene. It is also shown that the THG efficiency exhibits a specific polarization dependence, allowing the THG to be used for determining the orientation of phosphorene's crystallographic axes. Our findings highlight the material's potential for practical application in nanoscale photonic devices such as frequency convertors operating in the near-infrared spectral range.

  10. Nonlinear magnetoelectric effect in paraelectric state of Co4Nb2O9 single crystal

    Czech Academy of Sciences Publication Activity Database

    Cao, Ym.; Deng, Gc.; Beran, Přemysl; Feng, Zj.; Kang, Bj.; Zhang, Jc.; Guiblin, N.; Dkhil, B.; Ren, W.; Cao, Sx.

    2017-01-01

    Roč. 7, č. 10 (2017), č. článku 14079. ISSN 2045-2322 Institutional support: RVO:61389005 Keywords : magnetoelectric * single crystal * neutron diffraction Subject RIV: BM - Solid Matter Physics ; Magnetism OBOR OECD: Condensed matter physics (including formerly solid state physics, supercond.) Impact factor: 4.259, year: 2016

  11. Observation of self-pulsing in singly resonant optical second-harmonic generation with competing nonlinearities

    DEFF Research Database (Denmark)

    Bache, Morten; Lodahl, Peter; Mamaev, Alexander V.

    2002-01-01

    We predict and experimentally observe temporal self-pulsing in singly resonant intracavity second-harmonic generation under conditions of simultaneous parametric oscillation. The threshold for self-pulsing as a function of cavity tuning and phase mismatch are found from analysis of a three-compon...

  12. Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation-Maximization (SAEM) Algorithm.

    Science.gov (United States)

    Chow, Sy-Miin; Lu, Zhaohua; Sherwood, Andrew; Zhu, Hongtu

    2016-03-01

    The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation-maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed.

  13. Growth, optical, electrical and photoconductivity studies of a novel nonlinear optical single crystal: Mercury cadmium chloride thiocyanate

    Science.gov (United States)

    Kumar, S. M. Ravi; Selvakumar, S.; Sagayaraj, P.; Anbarasi, A.

    2015-02-01

    SCN- ligand based organometallic non-linear optical mercury cadmium chloride thiocyanate (MCCTC) crystals are grown from water plus methanol mixed solvent by slow evaporation technique. The grown crystals are confirmed by single crystal X-ray diffraction analysis which reveals that the MCCTC belongs to rhombohedral system with R3c space group. MCCTC exhibits a SHG efficiency which is nearly 17 times more than that of KDP. The dielectric constant, dielectric loss measurements of the sample have been carried out for different frequencies (100 Hz to 5 MHz) and, temperatures (308 to 388 K) and the results are discussed. Photoconductivity study confirms that the title compound possesses negative photoconducting nature. The surface morphology of MCCTC was also investigated

  14. Quantitative single cell analysis of cell population dynamics during submandibular salivary gland development and differentiation

    Science.gov (United States)

    Nelson, Deirdre A.; Manhardt, Charles; Kamath, Vidya; Sui, Yunxia; Santamaria-Pang, Alberto; Can, Ali; Bello, Musodiq; Corwin, Alex; Dinn, Sean R.; Lazare, Michael; Gervais, Elise M.; Sequeira, Sharon J.; Peters, Sarah B.; Ginty, Fiona; Gerdes, Michael J.; Larsen, Melinda

    2013-01-01

    Summary Epithelial organ morphogenesis involves reciprocal interactions between epithelial and mesenchymal cell types to balance progenitor cell retention and expansion with cell differentiation for evolution of tissue architecture. Underlying submandibular salivary gland branching morphogenesis is the regulated proliferation and differentiation of perhaps several progenitor cell populations, which have not been characterized throughout development, and yet are critical for understanding organ development, regeneration, and disease. Here we applied a serial multiplexed fluorescent immunohistochemistry technology to map the progressive refinement of the epithelial and mesenchymal cell populations throughout development from embryonic day 14 through postnatal day 20. Using computational single cell analysis methods, we simultaneously mapped the evolving temporal and spatial location of epithelial cells expressing subsets of differentiation and progenitor markers throughout salivary gland development. We mapped epithelial cell differentiation markers, including aquaporin 5, PSP, SABPA, and mucin 10 (acinar cells); cytokeratin 7 (ductal cells); and smooth muscle α-actin (myoepithelial cells) and epithelial progenitor cell markers, cytokeratin 5 and c-kit. We used pairwise correlation and visual mapping of the cells in multiplexed images to quantify the number of single- and double-positive cells expressing these differentiation and progenitor markers at each developmental stage. We identified smooth muscle α-actin as a putative early myoepithelial progenitor marker that is expressed in cytokeratin 5-negative cells. Additionally, our results reveal dynamic expansion and redistributions of c-kit- and K5-positive progenitor cell populations throughout development and in postnatal glands. The data suggest that there are temporally and spatially discreet progenitor populations that contribute to salivary gland development and homeostasis. PMID:23789091

  15. Coherent non-linear optical response in SU(2) symmetry broken single and bilayer graphene

    Energy Technology Data Exchange (ETDEWEB)

    Kumar, Vipin, E-mail: k.vipin@iitg.ernet.in; Enamullah,; Kumar, Upendra; Setlur, Girish S.

    2014-03-01

    Anomalous Rabi oscillations in single and bilayer graphene, in the absence of time-reversal symmetry, are described. The main findings of this work are that intra-layer sublattice space asymmetry has a remarkable effect on anomalous Rabi frequency in single and bilayer graphene, namely it is offset by the asymmetry parameter. However, the conventional Rabi frequency is nearly independent of the asymmetry parameter. Inter-layer asymmetry in bilayer graphene has an even more significant effect on anomalous Rabi frequency. When inter-layer asymmetry is taken into account, the anomalous Rabi frequency versus the external field goes through a minimum. The induced current in the frequency domain in these systems shows a finite threshold behavior even for vanishingly small applied fields. These offset oscillations are attributable to the asymmetry parameter in these systems, and are observable only for weak applied fields. For stronger applied fields these phenomena tend towards those without asymmetry.

  16. On the existence of positive periodic solutions for totally nonlinear neutral differential equations of the second-order with functional delay

    Directory of Open Access Journals (Sweden)

    Emmanuel K. Essel

    2014-01-01

    Full Text Available We prove that the totally nonlinear second-order neutral differential equation \\[\\frac{d^2}{dt^2}x(t+p(t\\frac{d}{dt}x(t+q(th(x(t\\] \\[=\\frac{d}{dt}c(t,x(t-\\tau(t+f(t,\\rho(x(t,g(x(t-\\tau(t\\] has positive periodic solutions by employing the Krasnoselskii-Burton hybrid fixed point theorem.

  17. Classification of the centers, their cyclicity and isochronicity for a class of polynomial differential systems generalizing the linear systems with cubic homogeneous nonlinearities

    Science.gov (United States)

    Llibre, Jaume; Valls, Clàudia

    In this paper we classify the centers, the cyclicity of its Hopf bifurcation and their isochronicity for the polynomial differential systems in R of arbitrary degree d⩾3 odd that in complex notation z=x+iy can be written as z˙=(λ+i)z+((Az+Bzz¯+Czz+Dz), where λ∈R and A,B,C,D∈C. If d=3 we obtain the well-known class of all polynomial differential systems of the form a linear system with cubic homogeneous nonlinearities.

  18. Trilinear Higgs coupling determination via single-Higgs differential measurements at the LHC

    Science.gov (United States)

    Maltoni, Fabio; Pagani, Davide; Shivaji, Ambresh; Zhao, Xiaoran

    2017-12-01

    We study one-loop effects induced by an anomalous Higgs trilinear coupling on total and differential rates for the H→ 4ℓ decay and some of the main single-Higgs production channels at the LHC, namely, VBF, VH, t{\\bar{t}}H and tHj. Our results are based on a public code that calculates these effects by simply reweighting samples of Standard-Model-like events for a given production channel. For VH and t{\\bar{t}}H production, where differential effects are particularly relevant, we include Standard Model electroweak corrections, which have similar sizes but different kinematic dependences. Finally, we study the sensitivity of future LHC runs to determine the trilinear coupling via inclusive and differential measurements, considering also the case where the Higgs couplings to vector bosons and the top quark is affected by new physics. We find that the constraints on the couplings and the relevance of differential distributions critically depend on the expected experimental and theoretical uncertainties.

  19. Nonlinear Spectral Signatures and Spatiotemporal Behavior of Stimulated Raman Scattering from Single Laser Speckles

    International Nuclear Information System (INIS)

    Vu, H.X.; Yin, L.; DuBois, D.F.; Bezzerides, B.; Dodd, E.S.

    2005-01-01

    Simulations are reported of the Thomson scatter spectrum of electrostatic waves (ESWs) excited in single laser hot spots by backward stimulated Raman scattering (BSRS). Under conditions similar those in the recent experiments of Kline et al. [Phys. Rev. Lett. 94, 175003 (2005)], a spectral streak, resulting from the trapping-induced frequency shift of the ESW, is found for high wave-number ESWs, similar to the observations. This shift and parametric frequency matching lead to isolated BSRS pulses. Modes with acoustic dispersion, resulting from the trapping-modified electron velocity distribution, can enhance the frequency range of the streak

  20. Nonlinear beam mechanics

    NARCIS (Netherlands)

    Westra, H.J.R.

    2012-01-01

    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

  1. Accounting for technical noise in differential expression analysis of single-cell RNA sequencing data.

    Science.gov (United States)

    Jia, Cheng; Hu, Yu; Kelly, Derek; Kim, Junhyong; Li, Mingyao; Zhang, Nancy R

    2017-11-02

    Recent technological breakthroughs have made it possible to measure RNA expression at the single-cell level, thus paving the way for exploring expression heterogeneity among individual cells. Current single-cell RNA sequencing (scRNA-seq) protocols are complex and introduce technical biases that vary across cells, which can bias downstream analysis without proper adjustment. To account for cell-to-cell technical differences, we propose a statistical framework, TASC (Toolkit for Analysis of Single Cell RNA-seq), an empirical Bayes approach to reliably model the cell-specific dropout rates and amplification bias by use of external RNA spike-ins. TASC incorporates the technical parameters, which reflect cell-to-cell batch effects, into a hierarchical mixture model to estimate the biological variance of a gene and detect differentially expressed genes. More importantly, TASC is able to adjust for covariates to further eliminate confounding that may originate from cell size and cell cycle differences. In simulation and real scRNA-seq data, TASC achieves accurate Type I error control and displays competitive sensitivity and improved robustness to batch effects in differential expression analysis, compared to existing methods. TASC is programmed to be computationally efficient, taking advantage of multi-threaded parallelization. We believe that TASC will provide a robust platform for researchers to leverage the power of scRNA-seq. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.

  2. Synthesis, growth and characterization of L-Phenylalaninium methanesulfonate nonlinear optical single crystal

    Science.gov (United States)

    Mangaiyarkarasi, K.; Ravichandran, A. T.; Anitha, K.; Manivel, A.

    2018-03-01

    The titled compound, L-Phenylalaninium methanesulfonate (LPA-MS) was synthesized and grown into single crystals by slow solvent evaporation solution growth technique in aqueous solution containing equimolar concentrations of L-phenylalanine and methanesulfonic acid at room temperature. The grown crystals were subjected to single crystal X-ray diffraction studies. It crystallizes in the monoclinic crystal structure with P21 space group and the unit cell parameters are a = 5.312 (10) Å, b = 8.883 (2) Å and c = 25.830 (7) Å. The functional groups of the LPA-MS crystal were confirmed with FT-IR and FT-Raman analysis. The carbon-hydrogen skeleton was confirmed with 1H NMR and 13C NMR analysis. TG-DTG and DSC studies were carried out to determine the thermal stability of the crystals. The optical transparency ranges were studied through UV-vis-spectroscopy and the crystal was found to be transparent in the visible region. The second Harmonic generation (SHG) efficiency of the grown LPA-MS crystal was measured by the Kurtz-Perry powder technique. The dipolar nature of the L-phenylalaninium methanesulfonate and the presence of the intermolecular hydrogen bonding between the molecules are the vital factors responsible for the existence of SHG activity in the crystal.

  3. Stability analysis of nonlinear systems

    CERN Document Server

    Lakshmikantham, Vangipuram; Martynyuk, Anatoly A

    2015-01-01

    The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.

  4. Introduction to differential equations

    CERN Document Server

    Taylor, Michael E

    2011-01-01

    The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen

  5. Growth, spectral and optical characterization of a novel nonlinear optical organic material: D-Alanine DL-Mandelic acid single crystal

    Science.gov (United States)

    Jayaprakash, P.; Mohamed, M. Peer; Caroline, M. Lydia

    2017-04-01

    An organic nonlinear optical single crystal, D-alanine DL-mandelic acid was synthesized and successfully grown by slow evaporation solution growth technique at ambient temperature using solvent of aqueous solution. The unit cell parameters were assessed from single crystal X-ray diffraction analysis. The presence of diverse functional groups and vibrational modes were identified using Fourier Transform Infra Red and Fourier Transform Raman spectral analyses. The chemical structure of grown crystal has been identified by Nuclear Magnetic Resonance spectroscopic study. Ultraviolet-visible spectral analysis reveal that the crystal has lower cut-off wavelength down to 259 nm, is a key factor to exhibit second harmonic generation signal. The electronic optical band gap and Urbach energy is calculated as 5.31 eV and 0.2425 eV respectively from the UV absorption profile. The diverse optical properties such as, extinction coefficient, reflectance, linear refractive index, optical conductivity was calculated using UV-visible data. The relative second harmonic efficiency of the compound is found to be 0.81 times greater than that of KH2PO4 (KDP). The thermal stability of the grown crystal was studied by thermogravimetric analysis and differential thermal analysis techniques. The luminescence spectrum exhibited two peaks (520 nm, 564 nm) due to the donation of protons from carboxylic acid to amino group. The Vickers microhardness test was carried out employing one of the as-grown hard crystal and there by hardness number (Hv), Meyer's index (n), yield strength (σy), elastic stiffness constant (C11) and Knoop hardness number (HK) were assessed. The dielectric behaviour of the as-grown crystal was analyzed for different temperatures (313 K, 333 K, 353 K, and 373 K) at different frequencies.

  6. Investigation of inorganic nonlinear optical potassium penta borate tetra hydrate (PPBTH) single crystals grown by slow evaporation method

    Science.gov (United States)

    Arivuselvi, R.; Babu, P. Ramesh

    2018-03-01

    Borates family crystals were plays vital role in the field of non linear optics (NLO) due to needs of wide range of applications. In this report, NLO crystals (potassium penta borate tetra hydrate (KB5H8O12) are grown by slow evaporation method at room temperature (28° C) and studied their physical properties. The harvested single crystals are transparent with the dimension of 12 × 10 × 6 mm3 and colourless. X-ray diffraction of single crystals reveals that the grown crystal belongs to orthorhombic system with non-centrosymmetric space group Pba2. All the absorbed functional groups are present in the order of inorganic compounds expect 1688 cm-1 because of water (Osbnd H sbnd O blending) molecule present in the pristine. Crystals show transparent in the entire visible region with 5.9 eV optical band gap and also it shows excellence in both second and third order nonlinear optical properties. Crystals can withstand upto 154 °C without any phase changes which is observed using thermal (TGA/DTA) analysis.

  7. Growth and characterization of dichlorobis L-proline Zn(II): A semiorganic nonlinear optical single crystal

    Science.gov (United States)

    Lydia Caroline, M.; Kandasamy, A.; Mohan, R.; Vasudevan, S.

    2009-02-01

    A semiorganic nonlinear optical material dichlorobis L-proline Zn (II) (DBLPZ), with molecular formula [ZnCl 2(C 5H 9NO 2) 2], has been synthesized from mixed solvents of deionised water and methanol. Single crystals of DBLPZ were successfully grown by the slow evaporation method at an ambient temperature. Single-crystal X-ray diffractometer was utilized to measure unit cell parameters and to confirm the crystal structure. The powder X-ray diffraction pattern of the grown DBLPZ has been indexed. The modes of vibration of different molecular groups present in the sample were identified by the FTIR spectral analysis. The optical transmittance window and the lower cutoff wavelength of the DBLPZ have been identified by UV-vis-NIR studies. Thermal stability of the DBLPZ was determined from TG/DTA/DSC curves, which indicate that the material is stable up to 242.3 °C. The existence of second harmonic generation signals was observed using Nd:YAG laser with fundamental wavelength of 1064 nm possessing SHG efficiency of 0.5 times of KDP and hence it can be a potential material for the frequency-doubling process.

  8. Synthesis, crystal growth, optical, thermal, and mechanical properties of a nonlinear optical single crystal: ammonium sulfate hydrogen sulphamate (ASHS)

    Science.gov (United States)

    Sudhakar, K.; Nandhini, S.; Muniyappan, S.; Arumanayagam, T.; Vivek, P.; Murugakoothan, P.

    2018-04-01

    Ammonium sulfate hydrogen sulphamate (ASHS), an inorganic nonlinear optical crystal, was grown from the aqueous solution by slow evaporation solution growth technique. The single-crystal XRD confirms that the grown single crystal belongs to the orthorhombic system with the space group of Pna21. Powder XRD confirms the crystalline nature and the diffraction planes were indexed. Crystalline perfection of grown crystal was analysed by high-resolution X-ray diffraction rocking curve technique. UV-Vis-NIR studies revealed that ASHS crystal has optical transparency 65% and lower cut-off wavelength at 218 nm. The violet light emission of the crystal was identified by photoluminescence studies. The particle size-dependent second-harmonic generation efficiency for ASHS crystal was evaluated by Kurtz-Perry powder technique using Nd:YAG laser which established the existence of phase matching. Surface laser damage threshold value was evaluated using Nd:YAG laser. Optical homogeneity of the crystal was evaluated using modified channel spectrum method through birefringence study. Thermal analysis reveals that ASHS crystal is stable up to 213 °C. The mechanical behaviour of the ASHS crystal was analysed using Vickers microhardness study.

  9. Design of a Negative Differential Resistance Circuit Element Using Single-Electron Transistors

    Science.gov (United States)

    Dixon, D. C.; Heij, C. P.; Hadley, P.; Mooij, J. E.

    1998-03-01

    Electronic circuit elements displaying negative differential resistance (NDR), such as tunnel diodes, have a wide variety of device applications, including oscillators, amplifiers, logic, and memory. We present a two-terminal device using two single-electron transistors (SET's) that demonstrates an NDR profile tuneable with gate voltages. If the capacitive coupling between the SET's is sufficiently larger than the junction capacitances, the device exhibits multiply-peaked NDR, allowing its use as a multi-valued digital element. We will also report recent experimental progress in measurements of such a device, fabricated using standard Al tunnel junctions, but with an additional overlap capacitor to allow the required inter-SET coupling.

  10. Observation of negative differential resistance and single-electron tunneling in electromigrated break junctions

    International Nuclear Information System (INIS)

    Noguchi, Yutaka; Ueda, Rieko; Kubota, Tohru; Kamikado, Toshiya; Yokoyama, Shiyoshi; Nagase, Takashi

    2008-01-01

    We observed a negative differential resistance (NDR) along with single-electron tunneling (SET) in the electron transport of electromigrated break junctions with metal-free tetraphenylporphyrin (H 2 BSTBPP) at a temperature of 11 K. The NDR strongly depended on the applied gate voltages, and appeared only in the electron tunneling region of the Coulomb diamond. We could explain the mechanism of this new type of electron transport by a model assuming a molecular Coulomb island and local density of states of the source and the drain electrodes

  11. Single-band negative differential resistance in metallic armchair MoS2 nanoribbons

    International Nuclear Information System (INIS)

    Chen, Cheng; Wang, Xue-Feng; Li, Yao-Sheng; Cheng, Xue-Mei; Yao, A-Long

    2017-01-01

    Semiconductor armchair MoS 2 nanoribbons can be converted into conductors by edge functionalization of H atoms or OH groups. Those metallic nanoribbons exhibit I – V characteristics of a single half-filled band with strong negative differential resistance (NDR) under a voltage bias less than 1 V. This originates from the spatial separation between electrons in the conduction and valence bands. The NDR becomes spin dependent if the H atoms or OH groups are not uniformly adsorbed on the edge. Furthermore, the spin polarization can be greatly enhanced in heterojunctions of H- and OH-passivated nanoribbons. (paper)

  12. Identification of biomechanical nonlinearity in whole-body vibration using a reverse path multi-input-single-output method

    Science.gov (United States)

    Huang, Ya; Ferguson, Neil S.

    2018-04-01

    The study implements a classic signal analysis technique, typically applied to structural dynamics, to examine the nonlinear characteristics seen in the apparent mass of a recumbent person during whole-body horizontal random vibration. The nonlinearity in the present context refers to the amount of 'output' that is not correlated or coherent to the 'input', usually indicated by values of the coherence function that are less than unity. The analysis is based on the longitudinal horizontal inline and vertical cross-axis apparent mass of twelve human subjects exposed to 0.25-20 Hz random acceleration vibration at 0.125 and 1.0 ms-2 r.m.s. The conditioned reverse path frequency response functions (FRF) reveal that the uncorrelated 'linear' relationship between physical input (acceleration) and outputs (inline and cross-axis forces) has much greater variation around the primary resonance frequency between 0.5 and 5 Hz. By reversing the input and outputs of the physical system, it is possible to assemble additional mathematical inputs from the physical output forces and mathematical constructs (e.g. square root of inline force). Depending on the specific construct, this can improve the summed multiple coherence at frequencies where the response magnitude is low. In the present case this is between 6 and 20 Hz. The statistical measures of the response force time histories of each of the twelve subjects indicate that there are potential anatomical 'end-stops' for the sprung mass in the inline axis. No previous study has applied this reverse path multi-input-single-output approach to human vibration kinematic and kinetic data before. The implementation demonstrated in the present study will allow new and existing data to be examined using this different analytical tool.

  13. Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations

    CERN Document Server

    Aliyu, MDS

    2011-01-01

    A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter

  14. Power decoupling with autonomous reference generation for single-phase differential inverters

    DEFF Research Database (Denmark)

    Yao, Wenli; Zhang, Xiaobin; Wang, Xiongfei

    2015-01-01

    The second-harmonic power ripple in single-phase inverter may introduce the issue of low reliability and low power density. In order to replace the bulky dc-link capacitor, an alternative approach is to use active power decoupling so that the ripple power can be diverted into other energy storages...... are used for realizing an improved power decoupling control, capacitor voltage and inductor current regulation. By substituting the corresponding parameter into unified model, the proposed control loop can be applied to different inverter types (Buck, Buck-Boost and Boost). Finally, detailed laboratory....... However, the performance of existing active power decoupling methods depends heavily on certain control references, which unfortunately are parameter dependent. In this paper an autonomous reference generation technique is proposed for single phase differential inverter without relying on the system...

  15. Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. Part 2; Global Asymptotic Behavior of Time Discretizations

    Science.gov (United States)

    Yee, H. C.; Sweby, P. K.

    1995-01-01

    The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

  16. Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. 2; Global Asymptotic Behavior of Time Discretizations; 2. Global Asymptotic Behavior of time Discretizations

    Science.gov (United States)

    Yee, H. C.; Sweby, P. K.

    1995-01-01

    The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

  17. Parameter estimation in neuronal stochastic differential equation models from intracellular recordings of membrane potentials in single neurons

    DEFF Research Database (Denmark)

    Ditlevsen, Susanne; Samson, Adeline

    2016-01-01

    Dynamics of the membrane potential in a single neuron can be studied by estimating biophysical parameters from intracellular recordings. Diffusion processes, given as continuous solutions to stochastic differential equations, are widely applied as models for the neuronal membrane potential evolut...

  18. Two (multi point nonlinear Lyapunov systems associated with an n th order nonlinear system of differential equations – existence and uniqueness

    Directory of Open Access Journals (Sweden)

    Murty K. N.

    2000-01-01

    Full Text Available This paper presents a criterion for the existence and uniqueness of solutions to two and multipoint boundary value problems associated with an n th order nonlinear Lyapunov system. A variation of parameters formula is developed and used as a tool to obtain existence and uniqueness. We discuss solution of the second order problem by the ADI method and develop a fixed point method to find the general solution of the n th order Lyapunov system. The results of Barnett (SIAM J. Appl. Anal. 24(1, 1973 are a particular case.

  19. Estimating Young’s Modulus of Single-Walled Zirconia Nanotubes Using Nonlinear Finite Element Modeling

    Directory of Open Access Journals (Sweden)

    Ibrahim Dauda Muhammad

    2015-01-01

    Full Text Available The single-walled zirconia nanotube is structurally modeled and its Young’s modulus is valued by using the finite element approach. The nanotube was assumed to be a frame-like structure with bonds between atoms regarded as beam elements. The properties of the beam required for input into the finite element analysis were computed by connecting energy equivalence between molecular and continuum mechanics. Simulation was conducted by applying axial tensile strain on one end of the nanotube while the other end was fixed and the corresponding reaction force recorded to compute Young’s modulus. It was found out that Young’s modulus of zirconia nanotubes is significantly affected by some geometrical parameters such as chirality, diameter, thickness, and length. The obtained values of Young’s modulus for a certain range of diameters are in agreement with what was obtained in the few experiments that have been conducted so far. This study was conducted on the cubic phase of zirconia having armchair and zigzag configuration. The optimal diameter and thickness were obtained, which will assist in designing and fabricating bulk nanostructured components containing zirconia nanotubes for various applications.

  20. Single-component supported lipid bilayers probed using broadband nonlinear optics.

    Science.gov (United States)

    Olenick, Laura L; Chase, Hilary M; Fu, Li; Zhang, Yun; McGeachy, Alicia C; Dogangun, Merve; Walter, Stephanie R; Wang, Hong-Fei; Geiger, Franz M

    2018-01-31

    Broadband SFG spectroscopy is shown to offer considerable advantages over scanning systems in terms of signal-to-noise ratios when probing well-formed single-component supported lipid bilayers formed from zwitterionic lipids with PC headgroups. The SFG spectra obtained from bilayers formed from DOPC, POPC, DLPC, DMPC, DPPC and DSPC show a common peak at ∼2980 cm -1 , which is subject to interference between the C-H and the O-H stretches from the aqueous phase, while membranes having transition temperatures above the laboratory temperature produce SFG spectra with at least two additional peaks, one at ∼2920 cm -1 and another at ∼2880 cm -1 . The results validate spectroscopic and structural data from SFG experiments utilizing asymmetric bilayers in which one leaflet differs from the other in the extent of deuteration. Differences in H 2 O-D 2 O exchange experiments reveal that the lineshapes of the broadband SFG spectra are significantly influenced by interference from OH oscillators in the aqueous phase, even when those oscillators are not probed by the incident infrared light in our broadband setup. In the absence of spectral interference from the OH stretches of the solvent, the alkyl chain terminal methyl group of the bilayer is found to be tilted at an angle of 15° to 35° from the surface normal.

  1. On the existence and uniqueness problems of solutions for set-valued and single-valued nonlinear operator equations in probabilistic normed spaces

    Directory of Open Access Journals (Sweden)

    Shih-Sen Chang

    1994-01-01

    Full Text Available In this paper, we introduce the concept of more general probabilistic contractors in probabilistic normed spaces and show the existence and uniqueness of solutions for set-valued and single-valued nonlinear operator equations in Menger probabilistic normed spaces.

  2. Phase-Space Reconstruction: a Path Towards the Next Generation of Nonlinear Differential Equation Based Models and Its Implications Towards Non-Uniform Sampling Theory

    Energy Technology Data Exchange (ETDEWEB)

    Charles R. Tolle; Mark Pengitore

    2009-08-01

    This paper explores the overlaps between the Control community’s work on System Identification (SysID) and the Physics, Mathematics, Chaos, and Complexity communities’ work on phase-space reconstruction via time-delay embedding. There are numerous overlaps between the goals of each community. Nevertheless, the Controls community can gain new insight as well as some new very powerful tools for SysID from the latest developments within the Physics, Mathematics, Chaos, and Complexity communities. These insights are gained via the work on phase-space reconstruction of non-linear dynamics. New methods for discovering non-linear differential based equations that evolved from embedding operations can shed new light on hybrid-systems theory, Nyquest-Shannon’s Theories, and network based control theory. This paper strives to guide the Controls community towards a closer inspection of the tools and additional insights being developed within the Physics, Mathematics, Chaos, and Complexity communities for discovery of system dynamics, the first step in control system development. The paper introduces the concepts of phase-space reconstruction via time-delay embedding (made famous byWhitney, Takens, and Sauer’s Thoreoms), intergrate-and-fire embedding, and non-linear differential equation discovery based on Perona’s method.

  3. Toward multi-differential cross sections: measuring two angularities on a single jet

    Science.gov (United States)

    Larkoski, Andrew J.; Moult, Ian; Neill, Duff

    2014-09-01

    The analytic study of differential cross sections in QCD has typically focused on individual observables, such as mass or thrust, to great success. Here, we present a first study of double differential jet cross sections considering two recoil-free angularities measured on a single jet. By analyzing the phase space defined by the two angularities and using methods from soft-collinear effective theory, we prove that the double differential cross section factorizes at the boundaries of the phase space. We also show that the cross section in the bulk of the phase space cannot be factorized using only soft and collinear modes, excluding the possibility of a global factorization theorem in soft-collinear effective theory. Nevertheless, we are able to define a simple interpolation procedure that smoothly connects the factorization theorem at one boundary to the other. We present an explicit example of this at next-to-leading logarithmic accuracy and show that the interpolation is unique up to α {/s 4} order in the exponent of the cross section, under reasonable assumptions. This is evidence that the interpolation is sufficiently robust to account for all logarithms in the bulk of phase space to the accuracy of the boundary factorization theorem. We compare our analytic calculation of the double differential cross section to Monte Carlo simulation and find qualitative agreement. Because our arguments rely on general structures of the phase space, we expect that much of our analysis would be relevant for the study of phenomenologically well-motivated observables, such as N -subjettiness, energy correlation functions, and planar flow.

  4. Single-frequency pulsed Brillouin-thulium fiber laser at 2 µm with nonlinear polarization rotation and active phase modulation

    Science.gov (United States)

    Wang, Xiong; Lv, Haibin; Zhou, Pu; Wu, Weijun; Wang, Xiaolin; Xiao, Hu; Liu, Zejin

    2014-10-01

    We present a single-frequency (SF) pulsed fiber laser at 2 µm based on stimulated Brillouin scattering in a thulium-doped fiber laser. The effective feedback of the fiber laser is quite weak to induce pulse operation. Nonlinear polarization rotation and active phase modulation are employed to compress the pulse width and stabilize the pulse train. This SF pulsed Brillouin-thulium fiber laser (BTFL) can generate a stable pulse train with a repetition rate of ˜310 kHz and a pulse width of ˜200 ns. The repetition rate of the pulse train can be adjusted by controlling the cavity length, and the pulse width can be tuned between 200 and 500 ns. The central wavelength locates at 1971.58 nm with an optical signal-to-noise ratio of more than 40 dB, and the linewidth is about 6 MHz. This is the first demonstration of the SF pulsed BTFL as far as we know.

  5. Approximate non-linear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

    Science.gov (United States)

    Ouyang, Wei; Mao, Weijian

    2018-03-01

    An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-waves scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform (GRT). After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic non-linear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P-wave and S-wave information.

  6. Output-Feedback Nonlinear Adaptive Control Strategy of the Single-Phase Grid-Connected Photovoltaic System

    Directory of Open Access Journals (Sweden)

    Abdelmajid Abouloifa

    2018-01-01

    Full Text Available This paper addresses the problem of controlling the single-phase grid connected to the photovoltaic system through a full bridge inverter with LCL-filter. The control aims are threefold: (i imposing the voltage in the output of PV panel to track a reference provided by the MPPT block; (ii regulating the DC-link voltage to guarantee the power exchange between the source and AC grid; (iii ensuring a satisfactory power factor correction (PFC. The problem is dealt with using a cascade nonlinear adaptive controller that is developed making use of sliding-mode technique and observers in order to estimate the state variables and grid parameters, by measuring only the grid current, PV voltage, and the DC bus voltage. The control problem addressed by this work involves several difficulties, including the uncertainty of some parameters of the system and the numerous state variables are inaccessible to measurements. The results are confirmed by simulation under MATLAB∖Simulink∖SimPowerSystems, which show that the proposed regulator is robust with respect to climate changes.

  7. Single crystal growth and nonlinear optical properties of Nd3+ doped STGS crystal for self-frequency-doubling application

    Science.gov (United States)

    Chen, Feifei; Wang, Lijuan; Wang, Xinle; Cheng, Xiufeng; Yu, Fapeng; Wang, Zhengping; Zhao, Xian

    2017-11-01

    The self-frequency-doubling crystal is an important kind of multi-functional crystal materials. In this work, Nd3+ doped Sr3TaGa3Si2O14 (Nd:STGS) single crystals were successfully grown by using Czochralski pulling method, in addition, the nonlinear and laser-frequency-doubling properties of Nd:STGS crystals were studied. The continuous-wave laser at 1064 nm was demonstrated along different physical axes, where the maximum output power was obtained to be 295 mW for the Z-cut samples, much higher than the Y-cut (242 mW) and X-cut (217 mW) samples. Based on the measured refractive indexes, the phase matching directions were discussed and determined for type I (42.5°, 30°) and type II (69.5°, 0°) crystal cuts. As expected, self-frequency-doubling green laser at 529 nm was achieved with output powers being around 16 mW and 12 mW for type I and type II configurations, respectively.

  8. Nonlinear optical susceptibilities in the diffusion modified AlxGa1-xN/GaN single quantum well

    Science.gov (United States)

    Das, T.; Panda, S.; Panda, B. K.

    2018-05-01

    Under thermal treatment of the post growth AlGaN/GaN single quantum well, the diffusion of Al and Ga atoms across the interface is expected to form the diffusion modified quantum well with diffusion length as a quantitative parameter for diffusion. The modification of confining potential and position-dependent effective mass in the quantum well due to diffusion is calculated taking the Fick's law. The built-in electric field which arises from spontaneous and piezoelectric polarizations in the wurtzite structure is included in the effective mass equation. The electronic states are calculated from the effective mass equation using the finite difference method for several diffusion lengths. Since the effective well width decreases with increasing diffusion length, the energy levels increase with it. The intersubband energy spacing in the conduction band decreases with diffusion length due to built-in electric field and reduction of effective well width. The linear susceptibility for first-order and the nonlinear second-order and third-order susceptibilities are calculated using the compact density matrix approach taking only two levels. The calculated susceptibilities are red shifted with increase in diffusion lengths due to decrease in intersubband energy spacing.

  9. Imaging of single retinal ganglion cell with differential interference contrast microscopy (Conference Presentation)

    Science.gov (United States)

    Oh, Juyeong; Kim, Yu Jeong; Kim, Chul-Ki; Lee, Taik Jin; Seo, Mina; Lee, Seok; Woo, Deok Ha; Jun, Seong Chan; Park, Ki-Ho; Kim, Seok Hwan; Kim, Jae Hun

    2017-02-01

    Glaucoma is a progressive optic neuropathy, characterized by the selective loss of retinal ganglion cells (RGCs). Therefore, monitoring the change of number or morphology of RGC is essential for the early detection as well as investigation of pathophysiology of glaucoma. Since RGC layer is transparent and hyporeflective, the direct optical visualization of RGCs has not been successful so far. Therefore, glaucoma evaluation mostly depends on indirect diagnostic methods such as the evaluation of optic disc morphology or retinal nerve fiber layer thickness measurement by optical coherence tomography. We have previously demonstrated single photoreceptor cell imaging with differential interference contrast (DIC) microscopy. Herein, we successfully visualized single RGC using DIC microscopy. Since RGC layer is much less reflective than photoreceptor layer, various techniques including the control of light wavelength and bandwidth using a tunable band pass filter were adopted to reduce the chromatic aberration in z-axis for higher and clearer resolution. To verify that the imaged cells were the RGCs, the flat-mounted retina of Sprague-Dawley rat, in which the RGCs were retrogradely labeled with fluorescence, was observed by both fluorescence and DIC microscopies for direct comparison. We have confirmed that the cell images obtained by fluorescence microscopy were perfectly matched with cell images by DIC microscopy. As conclusion, we have visualized single RGC with DIC microscopy, and confirmed with fluorescence microscopy.

  10. Differentiation of Short Single-Stranded DNA Homopolymers in Solid-State Nanopores

    Science.gov (United States)

    Venta, Kimberly; Shemer, Gabriel; Puster, Matthew; Rodríguez-Manzo, Julio A.; Balan, Adrian; Rosenstein, Jacob K.; Shepard, Ken; Drndić, Marija

    2013-01-01

    In the last two decades, new techniques that monitor ionic current modulations as single molecules pass through a nanoscale pore have enabled numerous single-molecule studies. While biological nanopores have recently shown the ability to resolve single nucleotides within individual DNA molecules, similar developments with solid-state nanopores have lagged, due to challenges both in fabricating stable nanopores of similar dimensions as biological nanopores and in achieving sufficiently low-noise and high-bandwidth recordings. Here we show that small silicon nitride nanopores (0.8 to 2-nm-diameter in 5 to 8-nm-thick membranes) can resolve differences between ionic current signals produced by short (30 base) ssDNA homopolymers (poly(dA), poly(dC), poly(dT)), when combined with measurement electronics that allow a signal-to-noise ratio of better than 10 to be achieved at 1 MHz bandwidth. While identifying intramolecular DNA sequences with silicon nitride nanopores will require further improvements in nanopore sensitivity and noise levels, homopolymer differentiation represents an important milestone in the development of solid-state nanopores. PMID:23621759

  11. Nonlinear Localization due to a Double Negative Defect Layer in a One-Dimensional Photonic Crystal Containing Single Negative Material Layers

    International Nuclear Information System (INIS)

    Ali, Munazza Zulfiqar; Abdullah, Tariq

    2008-01-01

    We investigate the effects of introducing a defect layer in a one-dimensional photonic crystal containing single negative material layers on the transmission properties. The width of the defect layer is taken to be the same or smaller than the period of the structure. Different cases of the defect layer being linear or nonlinear and double positive or double negative are discussed. It is found that only a nonlinear double negative layer gives rises to a localized mode within the zero-φ eff gap in this kind of structure. It is also shown that the important characteristics of the nonlinear defect mode such as its frequency, its FWHM and the threshold of the associated bistability can be controlled by changing the widths of the defect layer and the host layers

  12. Capillary Electrophoresis Single-Strand Conformational Polymorphisms as a Method to Differentiate Algal Species

    Directory of Open Access Journals (Sweden)

    Alice Jernigan

    2015-01-01

    Full Text Available Capillary electrophoresis single-strand conformational polymorphism (CE-SSCP was explored as a fast and inexpensive method to differentiate both prokaryotic (blue-green and eukaryotic (green and brown algae. A selection of two blue-green algae (Nostoc muscorum and Anabaena inaequalis, five green algae (Chlorella vulgaris, Oedogonium foveolatum, Mougeotia sp., Scenedesmus quadricauda, and Ulothrix fimbriata, and one brown algae (Ectocarpus sp. were examined and CE-SSCP electropherogram “fingerprints” were compared to each other for two variable regions of either the 16S or 18S rDNA gene. The electropherogram patterns were remarkably stable and consistent for each particular species. The patterns were unique to each species, although some common features were observed between the different types of algae. CE-SSCP could be a useful method for monitoring changes in an algae species over time as potential shifts in species occurred.

  13. Analysis and differentiation of mineral dust by single particle laser mass spectrometry

    International Nuclear Information System (INIS)

    Gallavardin, S. J.; Lohmann, U.; Cziczo, Daniel J.

    2008-01-01

    This study evaluates the potential of single particle laser desorption/ionization mass spectrometry for the analysis of atmospherically relevant mineral dusts. Samples of hematite, goethite, calcium carbonate, calcium sulfate, silica, quartz, montmorrillonite, kaolinite, illite, hectorite, wollastonite and nephelinsyenit were investigated in positive and negative ion mode with a monopolar time-of-flight mass spectrometer where the desorption/ionization step was performed with a 193 nm excimer laser (∼10 9 W/cm 2 ). Particle size ranged from 500 nm to 3 (micro)m. Positive mass spectra mainly provide elemental composition whereas negative ion spectra provide information on element speciation and of a structural nature. The iron oxide, calcium-rich and aluminosilicate nature of particles is established in positive ion mode. The differentiation of calcium materials strongly relies on the calcium counter-ions in negative mass spectra. Aluminosilicates can be differentiated in both positive and negative ion mode using the relative abundance of various aluminum and silicon ions

  14. Antisolar differential rotation with surface lithium enrichment on the single K-giant V1192 Orionis

    Science.gov (United States)

    Kővári, Zs.; Strassmeier, K. G.; Carroll, T. A.; Oláh, K.; Kriskovics, L.; Kővári, E.; Kovács, O.; Vida, K.; Granzer, T.; Weber, M.

    2017-10-01

    Context. Stars with about 1-2 solar masses at the red giant branch (RGB) represent an intriguing period of stellar evolution, I.e. when the convective envelope interacts with the fast-rotating core. During these mixing episodes freshly synthesized lithium can come up to the stellar surface along with high angular momentum material. This high angular momentum may alter the surface rotation pattern. Aims: The single rapidly rotating K-giant V1192 Ori is revisited to determine its surface differential rotation, lithium abundance, and basic stellar properties such as a precise rotation period. The aim is to independently verify the antisolar differential rotation of the star and possibly find a connection to the surface lithium abundance. Methods: We applied time-series Doppler imaging to a new multi-epoch data set. Altogether we reconstructed 11 Doppler images from spectroscopic data collected with the STELLA robotic telescope between 2007-2016. We used our inversion code iMap to reconstruct all stellar surface maps. We extracted the differential rotation from these images by tracing systematic spot migration as a function of stellar latitude from consecutive image cross-correlations. Results: The position of V1192 Ori in the Hertzsprung-Russell diagram suggests that the star is in the helium core-burning phase just leaving the RGB bump. We measure A(Li)NLTE = 1.27, I.e. a value close to the anticipated transition value of 1.5 from Li-normal to Li-rich giants. Doppler images reveal extended dark areas arranged quasi-evenly along an equatorial belt. No cool polar spot is found during the investigated epoch. Spot displacements clearly suggest antisolar surface differential rotation with α = - 0.11 ± 0.02 shear coefficient. Conclusions: The surface Li enrichment and the peculiar surface rotation pattern may indicate a common origin. Based on data obtained with the STELLA robotic observatory in Tenerife, an AIP facility jointly operated by AIP and IAC.

  15. Bulk crystal growth and nonlinear optical characterization of semiorganic single crystal: Cadmium (II) dibromide L - Proline monohydrate

    Energy Technology Data Exchange (ETDEWEB)

    Balakrishnan, T., E-mail: balacrystalgrowth@gmail.com [Crystal Growth Laboratory, PG & Research Department of Physics, Periyar EVR College (Autonomous), Tiruchirappalli, 620 023, Tamil Nadu (India); Sathiskumar, S. [Crystal Growth Laboratory, PG & Research Department of Physics, Periyar EVR College (Autonomous), Tiruchirappalli, 620 023, Tamil Nadu (India); Ramamurthi, K. [Crystal Growth and Thin Film Laboratory, Department of Physics and Nanotechnology, SRM University, Kattankulathur, 603 203, Kancheepuram, Tamil Nadu (India); Thamotharan, S. [Department of Bioinformatics, School of Chemical and Biotechnology, SASTRA University, Thanjavur, 613 401 (India)

    2017-01-15

    Single crystal of a novel metal organic nonlinear optical (NLO) cadmium (II) dibromide L - proline monohydrate (CBLPM) of size 7 × 7 × 5 mm{sup 3} was grown from slow evaporation technique. Single crystal X – ray diffraction analysis reveals that the crystal belongs to orthorhombic system with lattice parameters a = 10.1891 (8) Å, b = 13.4961 (11) Å, c = 7.4491 (5) Å and space group P2{sub 1}2{sub 1}2{sub 1}. The powder X – ray diffraction pattern of CBLPM was recorded and the X – ray diffraction peaks were indexed. The various functional groups of CBLPM were identified by the FT – IR and FT – Raman spectral analyses. The optical transmittance window and lower cut off wavelength of CBLPM were identified from UV – Vis – NIR studies. The mechanical strength of the grown crystal was estimated using Vickers microhardness test. Dielectric constant and dielectric loss measurements were carried out at different temperatures in the frequency range of 50 Hz - 2 MHz. The photoluminescence spectrum was recorded in the wavelength range 200–400 nm and the estimated optical band gap was ∼4.1 eV. Etching studies were carried out for different etching time. Thermal stability of CBLPM was determined using thermogravimetric analysis. Laser induced damage threshold study was carried out for the grown crystal using Nd:YAG laser. Size dependent second harmonic generation efficiency of the grown crystal was determined by Kurtz and Perry powder technique with different particle size using Nd:YAG laser with wavelength 1064 nm. Second harmonic generation efficiency of the powdered CBLPM crystal was ∼2.3 times that of potassium dihydrogen orthophosphate. - Highlights: • CBLPM crystal belongs to orthorhombic crystal system with space group P2{sub 1}2{sub 1}2{sub 1.} • Transmittance of CBLPM is ∼80% in the 650–1100 nm range. • Powder SHG efficiency of CBLPM increases with increase in particle size. • SHG efficiency of 0.57 μm size powdered CBLPM is ∼2

  16. Terahertz semiconductor nonlinear optics

    DEFF Research Database (Denmark)

    Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias

    2013-01-01

    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...

  17. Distinct gene expression signatures in human embryonic stem cells differentiated towards definitive endoderm at single-cell level

    DEFF Research Database (Denmark)

    Norrman, Karin; Strömbeck, Anna; Semb, Henrik

    2013-01-01

    Characterization of directed differentiation of pluripotent stem cells towards therapeutically relevant cell types, including pancreatic beta-cells and hepatocytes, depends on molecular markers and assays that resolve the signature of individual cells. Pancreas and liver both have a common origin...... for the three activin A based protocols applied. Our data provide novel insights in DE gene expression at the cellular level of in vitro differentiated human embryonic stem cells, and illustrate the power of using single-cell gene expression profiling to study differentiation heterogeneity and to characterize...

  18. Overview study of the analytical analysis of the internal dynamics of nonlinear time heteronymous planetary differential systems

    Czech Academy of Sciences Publication Activity Database

    Hortel, Milan; Škuderová, Alena

    2016-01-01

    Roč. 821, č. 2016 (2016), s. 213-220 ISSN 1662-7482. [Engineering Mechanics 2015. Svratka, 11.05.2015-14.05.2015] R&D Projects: GA TA ČR(CZ) TA04011656 Institutional support: RVO:61388998 Keywords : nonlinear dynamics * time heteronymous systems * damping in gear mesh Subject RIV: JT - Propulsion, Motors ; Fuels http://www. scientific .net/AMM.821.213

  19. Plasticity of marrow mesenchymal stem cells from human first-trimester fetus: from single-cell clone to neuronal differentiation.

    Science.gov (United States)

    Zhang, Yihua; Shen, Wenzheng; Sun, Bingjie; Lv, Changrong; Dou, Zhongying

    2011-02-01

    Recent results have shown that bone marrow mesenchymal stem cells (BMSCs) from human first-trimester abortus (hfBMSCs) are closer to embryonic stem cells and perform greater telomerase activity and faster propagation than mid- and late-prophase fetal and adult BMSCs. However, no research has been done on the plasticity of hfBMSCs into neuronal cells using single-cell cloned strains without cell contamination. In this study, we isolated five single cells from hfBMSCs and obtained five single-cell cloned strains, and investigated their biological property and neuronal differentiation potential. We found that four of the five strains showed similar expression profile of surface antigen markers to hfBMSCs, and most of them differentiated into neuron-like cells expressing Nestin, Pax6, Sox1, β-III Tubulin, NF-L, and NSE under induction. One strain showed different expression profile of surface antigen markers from the four strains and hfBMSCs, and did not differentiate toward neuronal cells. We demonstrated for the first time that some of single-cell cloned strains from hfBMSCs can differentiate into nerve tissue-like cell clusters under induction in vitro, and that the plasticity of each single-cell cloned strain into neuronal cells is different.

  20. Investigation on the growth, spectral, lifetime, mechanical analysis and third-order nonlinear optical studies of L-methionine admixtured D-mandelic acid single crystal: A promising material for nonlinear optical applications

    Science.gov (United States)

    Jayaprakash, P.; Sangeetha, P.; Kumari, C. Rathika Thaya; Caroline, M. Lydia

    2017-08-01

    A nonlinear optical bulk single crystal of L-methionine admixtured D-mandelic acid (LMDMA) has been grown by slow solvent evaporation technique using water as solvent at ambient temperature. The crystallized LMDMA single crystal subjected to single crystal X-ray diffraction study confirmed monoclinic system with the acentric space group P21. The FTIR analysis gives information about the modes of vibration in the various functional groups present in LMDMA. The UV-visible spectral analysis assessed the optical quality and linear optical properties such as extinction coefficient, reflectance, refractive index and from which optical conductivity and electric susceptibility were also evaluated. The frequency doubling efficiency was observed using Kurtz Perry powder technique. A multiple shot laser was utilized to evaluate the laser damage threshold energy of the crystal. Discrete thermodynamic properties were carried out by TG-DTA studies. The hardness, Meyer's index, yield strength, elastic stiffness constant, Knoop hardness, fracture toughness and brittleness index were analyzed using Vickers microhardness tester. Layer growth pattern and the surface defect were examined by chemical etching studies using optical microscope. Fluorescence emission spectrum was recorded and lifetime was also studied. The electric field response of crystal was investigated from the dielectric studies at various temperatures at different frequencies. The third-order nonlinear optical response in LMDMA has been investigated using Z-scan technique with He-Ne laser at 632.8 nm and nonlinear parameters such as refractive index (n2), absorption coefficient (β) and susceptibility (χ3) investigated extensively for they are in optical phase conjucation, high-speed optical switches and optical dielectric devices.

  1. Nonlinear evolution equations

    CERN Document Server

    Uraltseva, N N

    1995-01-01

    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

  2. Total and single differential cross sections for the electron impact ionization of the ground state of helium

    International Nuclear Information System (INIS)

    Singh, T.S.C.; Choudhury, K.B.; Singh, M.B.; Deb, N.C.; Mukherjee, S.C.; Mazumdar, P.S.

    1997-01-01

    Total cross sections (TCS) and single differential cross sections (SDCS) have been computed for the single ionization of the ground state of helium by electron impact in a distorted wave formalism which takes into account the effects of the initial and final channel distortions. The present TCS and SDCS results are in fair agreement with the measured values and other theoretical predictions for the incident electron energy E i > 150 eV. (orig.)

  3. Nonlinear Boundary Value Problem for Concave Capillary Surfaces Occurring in Single Crystal Rod Growth from the Melt

    Directory of Open Access Journals (Sweden)

    Agneta Maria Balint

    2008-12-01

    Full Text Available The boundary value problem z″=((ρ⋅g⋅z−p/γ[1+(z′2]3/2−(1/r⋅[1+(z′2]⋅z′, r∈[r1, r0], z′(r1=−tan⁡(π/2−αg, z′(r0=−tan⁡αc, z(r0=0, and z(r is strictly decreasing on [r1,r0], is considered. Here, 0nonlinear boundary value problem (NLBVP. Numerical illustration is given. This kind of results is useful in the experiment planning and technology design of single crystal rod growth from the melt by edge-defined film-fed growth (EFG method. With this aim, this study was undertaken.

  4. Tunable magnetoresistance driven by magnetically sensitive negative differential resistance in an asymmetrically coupled single molecule junction

    Science.gov (United States)

    Warner, Ben; El Hallak, Fadi; Sharp, John; Persson, Mats; Fisher, Andrew J.; Hirjibehedin, Cyrus F.

    2014-03-01

    Using scanning tunneling microscopy, we study the effects of interactions between individual magnetic molecules that are separated from an underlying copper surface by a thin-insulating layer of copper nitride (Cu2N). For electrical transport through a junction containing an individual iron phthalocyanine (FePc) molecule on Cu2N, we observe two novel magnetoresistance behaviors that arise from negative differential resistance (NDR) that shifts by unexpectedly large amounts in a magnetic field. Because voltage is dropped asymmetrically in this double barrier junction, the FePc can become transiently charged when its states are aligned with the Fermi energy of the Cu, resulting in the observed NDR effect. Furthermore, the asymmetric coupling magnifies the observed voltage sensitivity of the magnetic field dependence of the NDR - which inherently is on the scale of the Zeeman energy - by almost two orders of magnitude. These findings represent a new basis for making magnetoresistance devices at the single molecule scale. Furthermore, the enhancement of the energy scales created by asymmetric coupling of the junction can be combined with other multi-step tunneling processes to allow for the investigation of other phenomena that normally would be difficult to observe.

  5. Fully differential single-photon double ionization of neon and argon

    Science.gov (United States)

    Yip, Frank; Martin, Fernando; Rescigno, Thomas; McCurdy, C.

    2013-05-01

    Double photoionization of neon and argon differ significantly from helium in that three different final state couplings of the residual double ion (1 S , 1 D , and 3 P) are possible and greatly impact the observed angular distributions, but the multi-electron nature of such targets makes ab initio theoretical treatments of this correlated process a challenge. Triply differential cross sections (TDCS) have been calculated for single photon double ionization of these heavier rare gases at various photon energies by utilizing an expanded frozen-core treatment to represent the remaining N - 2 target electrons of the residual ion. The resulting angular distributions are compared with and show significant agreement with existing experimental data. Work supported by U. S. Dept. of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences Contract DE-AC02-05CH11231, by the MICINN Projects No. FIS2010-15127, No. ACI2008-0777,No. CSD 2007-00010, and ERC Advanced Grant 290853.

  6. Single-cell qPCR facilitates the optimization of hematopoietic differentiation in hPSCs/OP9 coculture system.

    Science.gov (United States)

    Chen, Haide; Jiang, Mengmeng; Xiao, Lei; Huang, He

    2018-03-15

    Human pluripotent stem cells (hPSCs)/OP9 coculture system is a widely used hematopoietic differentiation approach. The limited understanding of this process leads to its low efficiency. Thus, we used single-cell qPCR to reveal the gene expression profiles of individual CD34+ cells from different stages of differentiation. According to the dynamic gene expression of hematopoietic transcription factors, we overexpressed specific hematopoietic transcription factors (Gata2, Lmo2, Etv2, ERG, and SCL) at an early stage of hematopoietic differentiation. After overexpression, we generated more CD34+ cells with normal expression level of CD43 and CD31, which are used to define various hematopoietic progenitors. Furthermore, these CD34+ cells possessed normal differentiation potency in colony-forming unit assays and normal gene expression profiles. In this study, we demonstrated that single-cell qPCR can provide guidance for optimization of hematopoietic differentiation and transient overexpression of selected hematopoietic transcription factors can enhance hematopoietic differentiation.

  7. Kramers-Moyal expansion for stochastic differential equations with single and multiple delays: Applications to financial physics and neurophysics

    International Nuclear Information System (INIS)

    Frank, T.D.

    2007-01-01

    We present a generalized Kramers-Moyal expansion for stochastic differential equations with single and multiple delays. In particular, we show that the delay Fokker-Planck equation derived earlier in the literature is a special case of the proposed Kramers-Moyal expansion. Applications for bond pricing and a self-inhibitory neuron model are discussed

  8. Single-Wire Electric-Field Coupling Power Transmission Using Nonlinear Parity-Time-Symmetric Model with Coupled-Mode Theory

    Directory of Open Access Journals (Sweden)

    Xujian Shu

    2018-03-01

    Full Text Available The output power and transmission efficiency of the traditional single-wire electric-field coupling power transmission (ECPT system will drop sharply with the increase of the distance between transmitter and receiver, thus, in order to solve the above problem, in this paper, a new nonlinear parity-time (PT-symmetric model for single-wire ECPT system based on coupled-mode theory (CMT is proposed. The proposed model for single-wire ECPT system not only achieves constant output power but also obtains a high constant transmission efficiency against variable distance, and the steady-state characteristics of the single-wire ECPT system are analyzed. Based on the theoretical analysis and circuit simulation, it shows that the transmission efficiency with constant output power remains 60% over a transmission distance of approximately 34 m without the need for any tuning. Furthermore, the application of a nonlinear PT-symmetric circuit based on CMT enables robust electric power transfer to moving devices or vehicles.

  9. Multifunctional Bi{sub 2}ZnOB{sub 2}O{sub 6} single crystals for second and third order nonlinear optical applications

    Energy Technology Data Exchange (ETDEWEB)

    Iliopoulos, K. [LUNAM Université, Université d' Angers, CNRS UMR 6200, Laboratoire MOLTECH-Anjou, 2 Bd Lavoisier, 49045 Angers Cedex (France); Institute of Chemical Engineering Sciences, Foundation for Research and Technology Hellas (FORTH/ICE-HT), 26504 Patras (Greece); Kasprowicz, D. [Faculty of Technical Physics, Poznan University of Technology, Nieszawska 13 A, 60-965 Poznan (Poland); Majchrowski, A. [Institute of Applied Physics, Military University of Technology, Kaliskiego 2, 00-908 Warszawa (Poland); Michalski, E. [Institute of Optoelectronics, Military University of Technology, Kaliskiego 2, 00-908 Warszawa (Poland); Gindre, D.; Sahraoui, B., E-mail: bouchta.sahraoui@univ-angers.fr [LUNAM Université, Université d' Angers, CNRS UMR 6200, Laboratoire MOLTECH-Anjou, 2 Bd Lavoisier, 49045 Angers Cedex (France)

    2013-12-02

    Bi{sub 2}ZnOB{sub 2}O{sub 6} nonlinear optical single crystals were grown by means of the Kyropoulos method from stoichiometric melt. The second and third harmonic generation (SHG/THG) of Bi{sub 2}ZnOB{sub 2}O{sub 6} crystals were investigated by the SHG/THG Maker fringes technique. Moreover, SHG microscopy studies were carried out providing two-dimensional SHG images as a function of the incident laser polarization. The high nonlinear optical efficiency combined with the possibility to grow high quality crystals make Bi{sub 2}ZnOB{sub 2}O{sub 6} an excellent candidate for photonic applications.

  10. Preparation, characterization and non-linear optical properties of pristine m-nitroaniline ( m-NA) and its recycled polystyrene (Re-PS) coated single crystals

    Science.gov (United States)

    Adhyapak, P. V.; Islam, M.; Aiyer, R. C.; Mulik, U. P.; Negi, Y. S.; Amalnerkar, D. P.

    2008-05-01

    Meta-nitroaniline ( m-NA) is one of the organic single crystals extensively studied due to its high non-linear effect. m-NA is also known to exhibit comparable or even better non-linear optical (NLO) properties than known inorganic materials. In this paper, we report development of m-NA single crystals by solution growth technique using different solvent systems. The size of the single crystal varies depending on solvent. The highest average crystal size acquired was 10 mm×5 mm×5 mm using methyl ethyl ketone and acetone as solvent. These single crystals were characterized using various physico-chemical techniques such as XRD and scanning electron microscopy (SEM). The developed crystals were subsequently coated with recycled polystyrene (Re-PS) (1, 2, 5 and 10 wt% concentrations) to study the effect of polymer coating on the second harmonic generation (SHG) properties of the single crystals. The purpose of polymer coating on m-NA single crystal is to improve surface morphology of crystal (i.e. it makes surface smooth) and to enhance power handling capacity for pulse laser of a crystal which, in turn, improves the SHG intensity. The optimum percentage of coating was determined for the m-NA single crystals obtained from different solvent systems. Furthermore, the polymer coating also plays key role in preventing the degradation of the m-NA crystal (well-known as highly sublime material) and ultimately increasing the shelf life of the crystal for its device application.

  11. On finfing solutions of two-point boundary value problems for a class of non-linear functional differential systems

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rontó, M.; Shchobak, N.

    2012-01-01

    Roč. 13, May 04 (2012), s. 1-17 ISSN 1417-3875. [Colloquium on the Qualitative Theory of Differential Equations /9./. Szeged, 28.06.2011-01.07.2011] Institutional research plan: CEZ:AV0Z10190503 Keywords : functional differential equation * two-point conditions * successive approximations Subject RIV: BA - General Math ematics Impact factor: 0.740, year: 2012 http://www. math .u-szeged.hu/ejqtde/periodica.html?periodica=3¶mtipus_ertek=publications¶m_ertek=-1

  12. 10 ps resolution, 160 ns full scale range and less than 1.5% differential non-linearity time-to-digital converter module for high performance timing measurements

    Energy Technology Data Exchange (ETDEWEB)

    Markovic, B.; Tamborini, D.; Villa, F.; Tisa, S.; Tosi, A.; Zappa, F. [Politecnico di Milano, Dipartimento di Elettronica e Informazione, Piazza Leonardo da Vinci 32, 20133 Milano (Italy)

    2012-07-15

    We present a compact high performance time-to-digital converter (TDC) module that provides 10 ps timing resolution, 160 ns dynamic range and a differential non-linearity better than 1.5% LSB{sub rms}. The TDC can be operated either as a general-purpose time-interval measurement device, when receiving external START and STOP pulses, or in photon-timing mode, when employing the on-chip SPAD (single photon avalanche diode) detector for detecting photons and time-tagging them. The instrument precision is 15 ps{sub rms} (i.e., 36 ps{sub FWHM}) and in photon timing mode it is still better than 70 ps{sub FWHM}. The USB link to the remote PC allows the easy setting of measurement parameters, the fast download of acquired data, and their visualization and storing via an user-friendly software interface. The module proves to be the best candidate for a wide variety of applications such as: fluorescence lifetime imaging, time-of-flight ranging measurements, time-resolved positron emission tomography, single-molecule spectroscopy, fluorescence correlation spectroscopy, diffuse optical tomography, optical time-domain reflectometry, quantum optics, etc.

  13. Dynamics of Nonlinear Excitation of the High-Order Mode in a Single-Mode Step-Index Optical Fiber

    Science.gov (United States)

    Burdin, V.; Bourdine, A.

    2018-04-01

    This work is concerned with approximate model of higher-order mode nonlinear excitation in a singlemode silica optical fiber. We present some results of simulation for step-index optical fiber under femtosecond optical pulse launching, which confirm ability of relatively stable higher-order mode excitation in such singlemode optical fiber over sufficiently narrow range of launched optical power variation.

  14. Existence of solutions of the Dirichlet problem for an infinite system of nonlinear differential-functional equations of elliptic type

    Directory of Open Access Journals (Sweden)

    Tomasz S. Zabawa

    2005-01-01

    Full Text Available The Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem. The result is based on Chaplygin's method of lower and upper functions.

  15. A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm.

    Science.gov (United States)

    El-Qulity, Said Ali; Mohamed, Ali Wagdy

    2016-01-01

    This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness.

  16. Nonlinear elliptic differential equations with multivalued nonlinearities

    Indian Academy of Sciences (India)

    Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45

    locally Lipschitz functionals we prove the existence of at least two nontrivial solutions. (multiplicity theorem). Keywords. Upper solution; lower solution; order interval; truncation function; pseudomonotone operator; coercive operator; extremal solution; Yosida approxima- tion; nonsmooth Palais–Smale condition; critical point; ...

  17. A New Nonlinear Regression Approach That Allows Detection of Inter-Individual Differences in Single-Point Radioligand Binding Studies

    Science.gov (United States)

    2000-08-01

    Georgetown U. Med. Ctr., 3900 Reservoir Rd., Washington, DC 20007; 2Applied Mathematics Program, Johns Hopkins University, 9601 Medical Center Dr., Rockville...TERMS Nonlinear regresion , Monte-Carlo 15. NUMBER OF PAGES randomization, Scheffe’s test, radioligand binding 16. PRICE CODE 24 17. SECURITY 18...appropriate for this situation. Indeed, here it is necessary to formulate this problem as a multiple linear regression model expressed with the aid of

  18. SPP propagation in nonlinear glass-metal interface

    KAUST Repository

    Sagor, Rakibul Hasan

    2011-12-01

    The non-linear propagation of Surface-Plasmon-Polaritons (SPP) in single interface of metal and chalcogenide glass (ChG) is considered. A time domain simulation algorithm is developed using the Finite Difference Time Domain (FDTD) method. The general polarization algorithm incorporated in the auxiliary differential equation (ADE) is used to model frequency-dependent dispersion relation and third-order nonlinearity of ChG. The main objective is to observe the nonlinear behavior of SPP propagation and study the dynamics of the whole structure. © 2011 IEEE.

  19. Terahertz Nonlinear Optics in Semiconductors

    DEFF Research Database (Denmark)

    Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.

    2013-01-01

    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...... breathing of a single-cycle THz pulse in a semiconductor....

  20. Nonlinear Differential Equations and Feedback Control Design for the Urban-Rural Resident Pension Insurance in China

    Science.gov (United States)

    Wang, Lijian

    2015-12-01

    Facing many problems of the urban-rural resident pension insurance system in China, one should firstly make sure that this system can be optimized. This paper, based on the modern control theory, sets up differential equations as models to describe the urban-rural resident pension insurance system, and discusses the globally asymptotic stability in the sense of Liapunov for the urban-rural resident pension insurance system in the new equilibrium point. This research sets the stage for our further discussion, and it is theoretically important and convenient for optimizing the urban-rural resident pension insurance system.

  1. Early transcriptional and epigenetic regulation of CD8+ T cell differentiation revealed by single-cell RNA-seq

    Science.gov (United States)

    Kakaradov, Boyko; Arsenio, Janilyn; Widjaja, Christella E.; He, Zhaoren; Aigner, Stefan; Metz, Patrick J.; Yu, Bingfei; Wehrens, Ellen J.; Lopez, Justine; Kim, Stephanie H.; Zuniga, Elina I.; Goldrath, Ananda W.; Chang, John T.; Yeo, Gene W.

    2017-01-01

    SUMMARY During microbial infection, responding CD8+ T lymphocytes differentiate into heterogeneous subsets that together provide immediate and durable protection. To elucidate the dynamic transcriptional changes that underlie this process, we applied a single-cell RNA sequencing approach and analyzed individual CD8+ T lymphocytes sequentially throughout the course of a viral infection in vivo. Our analyses revealed a striking transcriptional divergence among cells that had undergone their first division and identified previously unknown molecular determinants controlling CD8+ T lymphocyte fate specification. These findings suggest a model of terminal effector cell differentiation initiated by an early burst of transcriptional activity and subsequently refined by epigenetic silencing of transcripts associated with memory lymphocytes, highlighting the power and necessity of single-cell approaches. PMID:28218746

  2. A comparative analysis of particle swarm optimization and differential evolution algorithms for parameter estimation in nonlinear dynamic systems

    International Nuclear Information System (INIS)

    Banerjee, Amit; Abu-Mahfouz, Issam

    2014-01-01

    The use of evolutionary algorithms has been popular in recent years for solving the inverse problem of identifying system parameters given the chaotic response of a dynamical system. The inverse problem is reformulated as a minimization problem and population-based optimizers such as evolutionary algorithms have been shown to be efficient solvers of the minimization problem. However, to the best of our knowledge, there has been no published work that evaluates the efficacy of using the two most popular evolutionary techniques – particle swarm optimization and differential evolution algorithm, on a wide range of parameter estimation problems. In this paper, the two methods along with their variants (for a total of seven algorithms) are applied to fifteen different parameter estimation problems of varying degrees of complexity. Estimation results are analyzed using nonparametric statistical methods to identify if an algorithm is statistically superior to others over the class of problems analyzed. Results based on parameter estimation quality suggest that there are significant differences between the algorithms with the newer, more sophisticated algorithms performing better than their canonical versions. More importantly, significant differences were also found among variants of the particle swarm optimizer and the best performing differential evolution algorithm

  3. Fast and quantitative differentiation of single-base mismatched DNA by initial reaction rate of catalytic hairpin assembly.

    Science.gov (United States)

    Li, Chenxi; Li, Yixin; Xu, Xiao; Wang, Xinyi; Chen, Yang; Yang, Xiaoda; Liu, Feng; Li, Na

    2014-10-15

    The widely used catalytic hairpin assembly (CHA) amplification strategy generally needs several hours to accomplish one measurement based on the prevailingly used maximum intensity detection mode, making it less practical for assays where high throughput or speed is desired. To make the best use of the kinetic specificity of toehold domain for circuit reaction initiation, we developed a mathematical model and proposed an initial reaction rate detection mode to quantitatively differentiate the single-base mismatch. Using the kinetic mode, assay time can be reduced substantially to 10 min for one measurement with the comparable sensitivity and single-base mismatch differentiating ability as were obtained by the maximum intensity detection mode. This initial reaction rate based approach not only provided a fast and quantitative differentiation of single-base mismatch, but also helped in-depth understanding of the CHA system, which will be beneficial to the design of highly sensitive and specific toehold-mediated hybridization reactions. Copyright © 2014 Elsevier B.V. All rights reserved.

  4. Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

    Science.gov (United States)

    Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; D'Incerti, Ludovico; Jovicich, Jorge

    2015-03-01

    In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D2), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.

  5. Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

    International Nuclear Information System (INIS)

    Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; Jovicich, Jorge; D'Incerti, Ludovico

    2015-01-01

    In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D 2 ), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes

  6. Studies on 2-amino-5-nitropyridinium nitrate (2A5NPN): A semi-organic third order nonlinear optical single crystal

    Energy Technology Data Exchange (ETDEWEB)

    Sivasubramani, V.; Pandian, Muthu Senthil, E-mail: senthilpandianm@ssn.edu.in; Ramasamy, P. [SSN Research Centre, SSN College of Engineering, Kalavakkam-603 110, Chennai, Tamilnadu (India)

    2016-05-23

    2-amino-5-nitropyridinium nitrate (2A5NPN) is a semi-organic nonlinear optical crystal and optically good quality 2A5NPN single crystals were successfully grown by slow evaporation solution growth technique (SEST) at ambient temperature. The crystallographic structure of the grown crystal was determined by single crystal X-Ray diffraction analysis and it belongs to Monoclinic crystal system with centro symmetric crystalline nature. The crystallinity of the grown crystal was confirmed by powder X-ray diffraction analysis. The other physical properties of grown crystals are also characterized using TG-DTA, UV-Visible NIR, chemical etching, photoconductivity and Z-scan measurements. The Z-scan method reveals that the 2A5NPN crystal possesses multi photon absorption behaviour and the significantly higher third order susceptibility and it is a promising potential NLO material.

  7. Development of a scientific torsional system experiment containing controlled single or dual-clearance non-linearities: Examination of step-responses

    Science.gov (United States)

    Krak, Michael D.; Singh, Rajendra

    2017-02-01

    The chief goal of this paper is to propose a new laboratory experiment that exhibits the step-response of a torsional system containing one or two controlled clearances. This work is motivated by the disadvantages of prior large-scale experiments which utilize production vehicle drivelines and their components with significant real-life complexities. The conceptual and physical design features, which include sizing, modal properties, excitation, and instrumentation, are discussed with the goal of creating a controlled experiment. Like prior literature, a step-down torque excitation is selected and all analyses are performed on the acceleration signals to observe vibro-impact in the time domain. Typical measurements (for both the single and dual-clearance configurations) exhibit rich non-linear behavior, including the double-sided impact regime and a time-varying oscillatory period. Additionally, new measurements are compared to predictions from simple reduced order non-linear models to verify the feasibility of the proposed experiment. Finally, the utility of this experiment is demonstrated by comparing its measurements to a prior large-scale experiment that accommodates a production vehicle clutch damper with multiple stages. The hardening and softening effects in both experiments are discussed in the context of double and single-sided impacts as well as the oscillatory periods that vary with time.

  8. 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.

  9. Single- and Multiple-Objective Optimization with Differential Evolution and Neural Networks

    Science.gov (United States)

    Rai, Man Mohan

    2006-01-01

    Genetic and evolutionary algorithms have been applied to solve numerous problems in engineering design where they have been used primarily as optimization procedures. These methods have an advantage over conventional gradient-based search procedures became they are capable of finding global optima of multi-modal functions and searching design spaces with disjoint feasible regions. They are also robust in the presence of noisy data. Another desirable feature of these methods is that they can efficiently use distributed and parallel computing resources since multiple function evaluations (flow simulations in aerodynamics design) can be performed simultaneously and independently on ultiple processors. For these reasons genetic and evolutionary algorithms are being used more frequently in design optimization. Examples include airfoil and wing design and compressor and turbine airfoil design. They are also finding increasing use in multiple-objective and multidisciplinary optimization. This lecture will focus on an evolutionary method that is a relatively new member to the general class of evolutionary methods called differential evolution (DE). This method is easy to use and program and it requires relatively few user-specified constants. These constants are easily determined for a wide class of problems. Fine-tuning the constants will off course yield the solution to the optimization problem at hand more rapidly. DE can be efficiently implemented on parallel computers and can be used for continuous, discrete and mixed discrete/continuous optimization problems. It does not require the objective function to be continuous and is noise tolerant. DE and applications to single and multiple-objective optimization will be included in the presentation and lecture notes. A method for aerodynamic design optimization that is based on neural networks will also be included as a part of this lecture. The method offers advantages over traditional optimization methods. It is more

  10. Soliton trapping and comb self-referencing in a single microresonator with χ(2) and χ(3) nonlinearities.

    Science.gov (United States)

    Xue, Xiaoxiao; Zheng, Xiaoping; Weiner, Andrew M

    2017-10-15

    A shaped doublet pump pulse is proposed for a simultaneous octave-spanning soliton Kerr frequency comb generation and second-harmonic conversion in a single microresonator. The temporal soliton in the cavity is trapped atop a doublet-pulse pedestal, resulting in a greatly expanded soliton region compared to that with a general Gaussian pulse pump. The possibility of single-microresonator comb self-referencing in a single silicon nitride microring that can facilitate compact on-chip optical clocks is demonstrated via simulation.

  11. MORE: mixed optimization for reverse engineering--an application to modeling biological networks response via sparse systems of nonlinear differential equations.

    Science.gov (United States)

    Sambo, Francesco; de Oca, Marco A Montes; Di Camillo, Barbara; Toffolo, Gianna; Stützle, Thomas

    2012-01-01

    Reverse engineering is the problem of inferring the structure of a network of interactions between biological variables from a set of observations. In this paper, we propose an optimization algorithm, called MORE, for the reverse engineering of biological networks from time series data. The model inferred by MORE is a sparse system of nonlinear differential equations, complex enough to realistically describe the dynamics of a biological system. MORE tackles separately the discrete component of the problem, the determination of the biological network topology, and the continuous component of the problem, the strength of the interactions. This approach allows us both to enforce system sparsity, by globally constraining the number of edges, and to integrate a priori information about the structure of the underlying interaction network. Experimental results on simulated and real-world networks show that the mixed discrete/continuous optimization approach of MORE significantly outperforms standard continuous optimization and that MORE is competitive with the state of the art in terms of accuracy of the inferred networks.

  12. A Novel Scheme for Optimal Control of a Nonlinear Delay Differential Equations Model to Determine Effective and Optimal Administrating Chemotherapy Agents in Breast Cancer.

    Science.gov (United States)

    Ramezanpour, H R; Setayeshi, S; Akbari, M E

    2011-01-01

    Determining the optimal and effective scheme for administrating the chemotherapy agents in breast cancer is the main goal of this scientific research. The most important issue here is the amount of drug or radiation administrated in chemotherapy and radiotherapy for increasing patient's survival. This is because in these cases, the therapy not only kills the tumor cells, but also kills some of the healthy tissues and causes serious damages. In this paper we investigate optimal drug scheduling effect for breast cancer model which consist of nonlinear ordinary differential time-delay equations. In this paper, a mathematical model of breast cancer tumors is discussed and then optimal control theory is applied to find out the optimal drug adjustment as an input control of system. Finally we use Sensitivity Approach (SA) to solve the optimal control problem. The goal of this paper is to determine optimal and effective scheme for administering the chemotherapy agent, so that the tumor is eradicated, while the immune systems remains above a suitable level. Simulation results confirm the effectiveness of our proposed procedure. In this paper a new scheme is proposed to design a therapy protocol for chemotherapy in Breast Cancer. In contrast to traditional pulse drug delivery, a continuous process is offered and optimized, according to the optimal control theory for time-delay systems.

  13. Investigations of a compartmental model for leucine kinetics using non-linear mixed effects models with ordinary and stochastic differential equations.

    Science.gov (United States)

    Berglund, Martin; Sunnåker, Mikael; Adiels, Martin; Jirstrand, Mats; Wennberg, Bernt

    2012-12-01

    Non-linear mixed effects (NLME) models represent a powerful tool to simultaneously analyse data from several individuals. In this study, a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady-state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analysed. We find that the interindividual variation of the model parameters is much smaller for the NLME models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual, the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion, NLME models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies.

  14. Visualization of multivalent histone modification in a single cell reveals highly concerted epigenetic changes on differentiation of embryonic stem cells

    DEFF Research Database (Denmark)

    Hattori, Naoko; Niwa, Tohru; Kimura, Kana

    2013-01-01

    . Bivalent modification was clearly visualized by iChmo in wild-type embryonic stem cells (ESCs) known to have it, whereas rarely in Suz12 knockout ESCs and mouse embryonic fibroblasts known to have little of it. iChmo was applied to analysis of epigenetic and phenotypic changes of heterogeneous cell......Combinations of histone modifications have significant biological roles, such as maintenance of pluripotency and cancer development, but cannot be analyzed at the single cell level. Here, we visualized a combination of histone modifications by applying the in situ proximity ligation assay, which...... population, namely, ESCs at an early stage of differentiation, and this revealed that the bivalent modification disappeared in a highly concerted manner, whereas phenotypic differentiation proceeded with large variations among cells. Also, using this method, we were able to visualize a combination...

  15. Linear and nonlinear optical properties of a single dopant in strained AlAs/GaAs spherical core/shell quantum dots

    Science.gov (United States)

    El Haouari, M.; Talbi, A.; Feddi, E.; El Ghazi, H.; Oukerroum, A.; Dujardin, F.

    2017-01-01

    The hydrostatic pressure influence on the binding energy and on the optical properties (linear and third nonlinear) associated to the 1 s - 1 p intersubband transition of single dopant in a AlAs / GaAs spherical core/shell structure is investigated. The combined effects of the problem variables such as the core and shell sizes, the donor position in the structure and the pressure dependence of the physical parameters of the material have been analyzed. Our calculations are performed in the framework of the effective mass approximation and the energies are obtained by using a variational method. The results show that the linear and nonlinear parts of the absorption coefficient and the refractive index associated to the intersubband 1 s - 1 p transition undergo important changes. There are several interesting results to point out such as the shift of the absorption coefficients and refractive index to high values of photon energy. Another significant result is that the donor position considerably affects the optical properties and their corresponding amplitude.

  16. Determination of nanogram quantities of osmium-labeled single stranded DNA by differential pulse stripping voltammetry

    Czech Academy of Sciences Publication Activity Database

    Kizek, René; Havran, Luděk; Fojta, Miroslav; Paleček, Emil

    2002-01-01

    Roč. 55, 1/2 (2002), s. 199-121 ISSN 1567-5394 R&D Projects: GA ČR GV204/97/K084; GA ČR GA204/00/D049; GA AV ČR IAA4004108 Institutional research plan: CEZ:AV0Z5004920 Keywords : differential pulse stripping voltammetry * microdetermination of DNA * chemical modification of DNA Subject RIV: BO - Biophysics Impact factor: 1.463, year: 2002

  17. Growth and PhysioChemical Properties of Second-Order Nonlinear Optical L-Threonine Single Crystals

    Directory of Open Access Journals (Sweden)

    G. Ramesh Kumar

    2009-01-01

    Full Text Available The present aim of the paper is to grow and to study the various properties of L-threonine amino acid single crystal in various aspects. Crystal growth of L-threonine single crystals has been carried out with the help of crystallization kinetics. pH and deuteration effects on the properties of the grown crystals have been studied and the results presented in a lucid manner. The various second-order NLO parameters were evaluated using anharmonic oscillator model. Particle and ion irradiation effects on structural, optical, and surface properties of the crystals have also been studied in detail.

  18. Nonlinear dynamics of two-phase flow

    International Nuclear Information System (INIS)

    Rizwan-uddin

    1986-01-01

    Unstable flow conditions can occur in a wide variety of laboratory and industry equipment that involve two-phase flow. Instabilities in industrial equipment, which include boiling water reactor (BWR) cores, steam generators, heated channels, cryogenic fluid heaters, heat exchangers, etc., are related to their nonlinear dynamics. These instabilities can be of static (Ledinegg instability) or dynamic (density wave oscillations) type. Determination of regions in parameters space where these instabilities can occur and knowledge of system dynamics in or near these regions is essential for the safe operation of such equipment. Many two-phase flow engineering components can be modeled as heated channels. The set of partial differential equations that describes the dynamics of single- and two-phase flow, for the special case of uniform heat flux along the length of the channel, can be reduced to a set of two coupled ordinary differential equations [in inlet velocity v/sub i/(t) and two-phase residence time tau(t)] involving history integrals: a nonlinear ordinary functional differential equation and an integral equation. Hence, to solve these equations, the dependent variables must be specified for -(nu + tau) ≤ t ≤ 0, where nu is the single-phase residence time. This system of nonlinear equations has been solved analytically using asymptotic expansion series for finite but small perturbations and numerically using finite difference techniques

  19. Nonlinear drift tearing mode

    International Nuclear Information System (INIS)

    Zelenyj, L.M.; Kuznetsova, M.M.

    1989-01-01

    Nonlinear study of magnetic perturbation development under single-mode conditions in collision-free plasma in configurations with the magnetic field shear is investigated. Results are obtained with regard of transverse component of electrical field and its effect on ion dynamics within wide range of ion Larmor radius value and values of magnetic field shear. Increments of nonlinear drift tearing mode are obtained and it is shown that excitation drastic conditions of even linearly stable modes are possible. Mechanism of instability nonlinear stabilization is considered and the value of magnetic island at the saturation threshold is estimeted. Energy of nonlinear drift tearing mode is discussed

  20. Self-phase modulation of a single-cycle terahertz pulse by nonlinear free-carrier response in a semiconductor

    DEFF Research Database (Denmark)

    Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.

    2012-01-01

    We investigate the self-phase modulation (SPM) of a single-cycle terahertz pulse in a semiconductor, using bulk n-GaAs as a model system. The SPM arises from the heating of free electrons in the electric field of the terahertz pulse, leading to an ultrafast reduction of the plasma frequency...

  1. Studies on the growth aspects, structural, thermal, dielectric and third order nonlinear optical properties of solution grown 4-methylpyridinium p-nitrophenolate single crystal

    Science.gov (United States)

    Devi, S. Reena; Kalaiyarasi, S.; Zahid, I. MD.; Kumar, R. Mohan

    2016-11-01

    An ionic organic optical crystal of 4-methylpyridinium p-nitrophenolate was grown from methanol by slow evaporation method at ambient temperature. Powder and single crystal X-ray diffraction studies revealed the crystal system and its crystalline perfection. The rocking curve recorded from HRXRD study confirmed the crystal quality. FTIR spectral analysis confirmed the functional groups present in the title compound. UV-visible spectral study revealed the optical window and band gap of grown crystal. The thermal, electrical and surface laser damage threshold properties of harvested crystal were examined by using TGA/DTA, LCR/Impedance Analyzer and Nd:YAG laser system respectively. The third order nonlinear optical property of grown crystal was elucidated by Z-scan technique.

  2. Motor impulsivity differentiates between psychiatric inpatients with multiple versus single lifetime suicide attempts.

    Science.gov (United States)

    Colborn, Victoria A; LaCroix, Jessica M; Neely, Laura L; Tucker, Jennifer; Perera, Kanchana; Daruwala, Samantha E; Grammer, Geoffrey; Weaver, Jennifer; Ghahramanlou-Holloway, Marjan

    2017-07-01

    A history of multiple suicide attempts conveys greater risk for suicide than a single attempt. Impulsivity may partially explain the association between multiple attempts and increased risk. We examined trait impulsivity, ability to engage in goal-directed behaviors, and impulse control among psychiatrically hospitalized United States military personnel and their dependents. Individuals with a history of multiple versus single attempts had significantly higher motor impulsivity, indicating spur of the moment action. Providers are encouraged to directly assess and treat motor impulsivity among suicidal individuals. Further research should explore whether motor impulsivity is a mechanism of change in psychosocial suicide prevention interventions. Copyright © 2017. Published by Elsevier B.V.

  3. Bulk crystal growth, optical, mechanical and ferroelectric properties of new semiorganic nonlinear optical and piezoelectric Lithium nitrate monohydrate oxalate single crystal

    Science.gov (United States)

    Dalal, Jyoti; Kumar, Binay

    2016-01-01

    New semiorganic nonlinear optical single crystals of Lithium nitrate oxalate monohydrate (LNO) were grown by slow evaporation solution technique. Single crystal X-ray diffraction study indicated that LNO crystal belongs to the triclinic system with space group P1. Various functional groups present in the material were identified by FTIR and Raman analysis. UV-vis study showed the high transparency of crystals with a wide band gap 5.01 eV. Various Optical constants i.e. Urbach energy (Eu), extinction coefficient (K), refractive index, optical conductivity, electric susceptibility with real and imaginary parts of dielectric constant were calculated using the transmittance data which have applications in optoelectronic devices. A sharp emission peak was found at 438 nm in photoluminescence measurement, which revealed suitability of crystal for fabricating violet lasers. In dielectric studies, a peak has been observed at 33 °C which is due to ferroelectric to paraelectric phase transition. Piezoelectric charge coefficients (d33 = 9.2 pC/N and g33) have been calculated, which make it a suitable for piezoelectric devices applications. In ferroelectric studies, a saturated loop was found in which the values of coercive field and remnant polarization were found to be 2.18 kV/cm and 0.39 μC/cm2, respectively. Thermal behavior was studied by TGA and DSC studies. The relative SHG efficiency of LNO was found to be 1.2 times that of KDP crystal. In microhardness study, Meyer's index value was found to be 1.78 which revealed its soft nature. These optical, dielectric, piezoelectric, ferroelectric, mechanical and non-linear optical properties of grown crystal establish the usefulness of this material for optoelectronics, non-volatile memory and piezoelectric devices applications.

  4. Synthesis, optical, experimental and theoretical investigation of third order nonlinear optical properties of 8-hydroxyquinolinium 2-carboxy-6-nitrophthalate monohydrate single crystal

    Science.gov (United States)

    Bharathi, M. Divya; Bhuvaneswari, R.; Srividya, J.; Vinitha, G.; Prithiviraajan, R. N.; Anbalagan, G.

    2018-02-01

    Single crystals of 8-hydroxyquinolinium 2-carboxy-6-nitrophthalate monohydrate (8HQNP) were obtained from slow evaporation solution growth method using methanol-water (1:1) as a solvent. Powder X-ray diffraction was utilized to compute the unit cell parameters and dislocation density of 8HQNP crystal. The crystalline perfection of the as-grown crystal was investigated by high-resolution X-ray diffraction at room temperature. The molecular structure was analyzed by identifying the functional groups from FT-IR and FT-Raman spectra. The cut-off wavelength and the corresponding optical band gap obtained from an optical spectrum were 376 nm and 3.29 eV respectively. The dispersion nature of refractive index was investigated by the single-oscillator Wemple and Di-Domenico model. Red emission was observed in the photoluminescence spectrum when excited with 376 nm. The low birefringence and high laser damage threshold (8.538 GW/cm2) values dictate the suitability of the crystal for optical devices. Z-scan studies revealed the third order nonlinear absorption coefficient (β) and refractive index (n2) of the 8HQNP crystal. The theoretical value of third order nonlinear susceptibility obtained from density function theory is good accordance with the experimental value. The frontier molecular orbital energy gap decreases with increasing external electric field in different directions which attributed to the enhancement of the second hyperpolarizability. The grown title crystal is thermally stable up to 102 °C which was identified using thermal analysis. Mechanical strength of 8HQNP was estimated by using Vicker's microhardness studies.

  5. Dynamics of lineage commitment revealed by single-cell transcriptomics of differentiating embryonic stem cells

    NARCIS (Netherlands)

    Semrau, Stefan; Goldmann, Johanna E; Soumillon, Magali; Mikkelsen, Tarjei S; Jaenisch, Rudolf; van Oudenaarden, Alexander

    2017-01-01

    Gene expression heterogeneity in the pluripotent state of mouse embryonic stem cells (mESCs) has been increasingly well-characterized. In contrast, exit from pluripotency and lineage commitment have not been studied systematically at the single-cell level. Here we measure the gene expression

  6. SINGLE VERSUS MULTIPLE TRIAL VECTORS IN CLASSICAL DIFFERENTIAL EVOLUTION FOR OPTIMIZING THE QUANTIZATION TABLE IN JPEG BASELINE ALGORITHM

    Directory of Open Access Journals (Sweden)

    B Vinoth Kumar

    2017-07-01

    Full Text Available Quantization Table is responsible for compression / quality trade-off in baseline Joint Photographic Experts Group (JPEG algorithm and therefore it is viewed as an optimization problem. In the literature, it has been found that Classical Differential Evolution (CDE is a promising algorithm to generate the optimal quantization table. However, the searching capability of CDE could be limited due to generation of single trial vector in an iteration which in turn reduces the convergence speed. This paper studies the performance of CDE by employing multiple trial vectors in a single iteration. An extensive performance analysis has been made between CDE and CDE with multiple trial vectors in terms of Optimization process, accuracy, convergence speed and reliability. The analysis report reveals that CDE with multiple trial vectors improves the convergence speed of CDE and the same is confirmed using a statistical hypothesis test (t-test.

  7. Single-strand-conformation polymorphism of ribosomal DNA for rapid species differentiation in genus Phytophthora.

    Science.gov (United States)

    Kong, Ping; Hong, Chuanxue; Richardson, Patricia A; Gallegly, Mannon E

    2003-08-01

    Single-strand-conformation polymorphism (SSCP) of ribosomal DNA of 29 species (282 isolates) of Phytophthora was characterized in this study. Phytophthora boehmeriae, Phytophthora botryosa, Phytophthora cactorum, Phytophthora cambivora, Phytophthora capsici, Phytophthora cinnamomi, Phytophthora colocasiae, Phytophthora fragariae, Phytophthora heveae, Phytophthora hibernalis, Phytophthora ilicis, Phytophthora infestans, Phytophthora katsurae, Phytophthora lateralis, Phytophthora meadii, Phytophthora medicaginis, Phytophthora megakarya, Phytophthora nicotianae, Phytophthora palmivora, Phytophthora phaseoli, Phytophthora pseudotsugae, Phytophthora sojae, Phytophthora syringae, and Phytophthora tropicalis each showed a unique SSCP pattern. Phytophthora citricola, Phytophthora citrophthora, Phytophthora cryptogea, Phytophthora drechsleri, and Phytophthora megasperma each had more than one distinct pattern. A single-stranded DNA ladder also was developed, which facilitates comparison of SSCP patterns within and between gels. With a single DNA fingerprint, 277 isolates of Phytophthora recovered from irrigation water and plant tissues in Virginia were all correctly identified into eight species at substantially reduced time, labor, and cost. The SSCP analysis presented in this work will aid in studies on taxonomy, genetics, and ecology of the genus Phytophthora.

  8. EFFECTOR OF TRANSCRIPTION2 is involved in xylem differentiation and includes a functional DNA single strand cutting domain.

    Science.gov (United States)

    Ivanov, Rumen; Tiedemann, Jens; Czihal, Andreas; Schallau, Anna; Diep, Le Hong; Mock, Hans-Peter; Claus, Bernhard; Tewes, Annegret; Bäumlein, Helmut

    2008-01-01

    EFFECTORS OF TRANSCRIPTION2 (ET) are plant-specific regulatory proteins characterized by the presence of two to five C-terminal DNA- and Zn-binding repeats, and a highly conserved cysteine pattern. We describe the structural characterization of the three member Arabidopsis thaliana ET gene family and reveal some allelic sequence polymorphisms. A mutation analysis showed that AtET2 affects the expression of various KNAT genes involved in the maintenance of the undifferentiated state of cambial meristem cells. It also plays a role in the regulation of GA5 (gibberellin 3-beta-dioxygenase) and the cell-cycle-related GASA4. A correlation was established between AtET2 expression and the cellular differentiation state. AtET-GFP fusion proteins shuttle between the cytoplasm and nucleus, with the AtET2 product prevented from entering the nucleus in non-differentiating cells. Within the nucleus, AtET2 probably acts via a single strand cutting domain. A more general regulatory role for ET factors is proposed, governing cell differentiation in cambial meristems, a crucial process for the development of plant vascular tissues.

  9. Single-cell RNA-seq reveals changes in cell cycle and differentiation programs upon aging of hematopoietic stem cells

    Science.gov (United States)

    Kowalczyk, Monika S.; Tirosh, Itay; Heckl, Dirk; Rao, Tata Nageswara; Dixit, Atray; Haas, Brian J.; Schneider, Rebekka K.; Wagers, Amy J.; Ebert, Benjamin L.; Regev, Aviv

    2015-01-01

    Both intrinsic cell state changes and variations in the composition of stem cell populations have been implicated as contributors to aging. We used single-cell RNA-seq to dissect variability in hematopoietic stem cell (HSC) and hematopoietic progenitor cell populations from young and old mice from two strains. We found that cell cycle dominates the variability within each population and that there is a lower frequency of cells in the G1 phase among old compared with young long-term HSCs, suggesting that they traverse through G1 faster. Moreover, transcriptional changes in HSCs during aging are inversely related to those upon HSC differentiation, such that old short-term (ST) HSCs resemble young long-term (LT-HSCs), suggesting that they exist in a less differentiated state. Our results indicate both compositional changes and intrinsic, population-wide changes with age and are consistent with a model where a relationship between cell cycle progression and self-renewal versus differentiation of HSCs is affected by aging and may contribute to the functional decline of old HSCs. PMID:26430063

  10. Simple Adaptive Single Differential Coherence Detection of BPSK Signals in IEEE 802.15.4 Wireless Sensor Networks.

    Science.gov (United States)

    Zhang, Gaoyuan; Wen, Hong; Wang, Longye; Xie, Ping; Song, Liang; Tang, Jie; Liao, Runfa

    2017-12-26

    In this paper, we propose an adaptive single differential coherent detection (SDCD) scheme for the binary phase shift keying (BPSK) signals in IEEE 802.15.4 Wireless Sensor Networks (WSNs). In particular, the residual carrier frequency offset effect (CFOE) for differential detection is adaptively estimated, with only linear operation, according to the changing channel conditions. It was found that the carrier frequency offset (CFO) and chip signal-to-noise ratio (SNR) conditions do not need a priori knowledge. This partly benefits from that the combination of the trigonometric approximation sin - 1 ( x ) ≈ x and a useful assumption, namely, the asymptotic or high chip SNR, is considered for simplification of the full estimation scheme. Simulation results demonstrate that the proposed algorithm can achieve an accurate estimation and the detection performance can completely meet the requirement of the IEEE 802.15.4 standard, although with a little loss of reliability and robustness as compared with the conventional optimal single-symbol detector.

  11. Proximity-Based Differential Single-Cell Analysis of the Niche to Identify Stem/Progenitor Cell Regulators.

    Science.gov (United States)

    Silberstein, Lev; Goncalves, Kevin A; Kharchenko, Peter V; Turcotte, Raphael; Kfoury, Youmna; Mercier, Francois; Baryawno, Ninib; Severe, Nicolas; Bachand, Jacqueline; Spencer, Joel A; Papazian, Ani; Lee, Dongjun; Chitteti, Brahmananda Reddy; Srour, Edward F; Hoggatt, Jonathan; Tate, Tiffany; Lo Celso, Cristina; Ono, Noriaki; Nutt, Stephen; Heino, Jyrki; Sipilä, Kalle; Shioda, Toshihiro; Osawa, Masatake; Lin, Charles P; Hu, Guo-Fu; Scadden, David T

    2016-10-06

    Physiological stem cell function is regulated by secreted factors produced by niche cells. In this study, we describe an unbiased approach based on the differential single-cell gene expression analysis of mesenchymal osteolineage cells close to, and further removed from, hematopoietic stem/progenitor cells (HSPCs) to identify candidate niche factors. Mesenchymal cells displayed distinct molecular profiles based on their relative location. We functionally examined, among the genes that were preferentially expressed in proximal cells, three secreted or cell-surface molecules not previously connected to HSPC biology-the secreted RNase angiogenin, the cytokine IL18, and the adhesion molecule Embigin-and discovered that all of these factors are HSPC quiescence regulators. Therefore, our proximity-based differential single-cell approach reveals molecular heterogeneity within niche cells and can be used to identify novel extrinsic stem/progenitor cell regulators. Similar approaches could also be applied to other stem cell/niche pairs to advance the understanding of microenvironmental regulation of stem cell function. Copyright © 2016 Elsevier Inc. All rights reserved.

  12. Proximity-based differential single cell analysis of the niche to identify stem/progenitor cell regulators

    Science.gov (United States)

    Silberstein, Lev; Goncalves, Kevin A; Kharchenko, Peter V; Turcotte, Raphael; Kfoury, Youmna; Mercier, Francois; Baryawno, Ninib; Severe, Nicolas; Bachand, Jacqueline; Spencer, Joel; Papazian, Ani; Lee, Dongjun; Chitteti, Brahmananda Reddy; Srour, Edward F; Hoggatt, Jonathan; Tate, Tiffany; Celso, Cristina Lo; Ono, Noriaki; Nutt, Stephen; Heino, Jyrki; Sipilä, Kalle; Shioda, Toshihiro; Osawa, Masatake; Lin, Charles P; Hu, Guo-fu; Scadden, David T

    2016-01-01

    SUMMARY Physiological stem cell function is regulated by secreted factors produced by niche cells. In this study, we describe an unbiased approach based on differential single-cell gene expression analysis of mesenchymal osteolineage cells close to and further removed from hematopoietic stem/progenitor cells to identify candidate niche factors. Mesenchymal cells displayed distinct molecular profiles based on their relative location. Amongst the genes which were preferentially expressed in proximal cells, we functionally examined three secreted or cell surface molecules not previously connected to HSPC biology: the secreted RNase Angiogenin, the cytokine IL18 and the adhesion molecule Embigin and discovered that all of these factors are HSPC quiescence regulators. Our proximity-based differential single cell approach therefore reveals molecular heterogeneity within niche cells and can be used to identify novel extrinsic stem/progenitor cell regulators. Similar approaches could also be applied to other stem cell/niche pairs to advance understanding of microenvironmental regulation of stem cell function. PMID:27524439

  13. A single-shot nonlinear autocorrelation approach for time-resolved physics in the vacuum ultraviolet spectral range

    International Nuclear Information System (INIS)

    Rompotis, Dimitrios

    2016-02-01

    In this work, a single-shot temporal metrology scheme operating in the vacuum-extreme ultraviolet spectral range has been designed and experimentally implemented. Utilizing an anti-collinear geometry, a second-order intensity autocorrelation measurement of a vacuum ultraviolet pulse can be performed by encoding temporal delay information on the beam propagation coordinate. An ion-imaging time-of-flight spectrometer, offering micrometer resolution has been set-up for this purpose. This instrument enables the detection of a magnified image of the spatial distribution of ions exclusively generated by direct two-photon absorption in the combined counter-propagating pulse focus and thus obtain the second-order intensity autocorrelation measurement on a single-shot basis. Additionally, an intense VUV light source based on high-harmonic generation has been experimentally realized. It delivers intense sub-20 fs Ti:Sa fifth-harmonic pulses utilizing a loose-focusing geometry in a long Ar gas cell. The VUV pulses centered at 161.8 nm reach pulse energies of 1.1 μJ per pulse, while the corresponding pulse duration is measured with a second-order, fringe-resolved autocorrelation scheme to be 18 ± 1 fs on average. Non-resonant, two-photon ionization of Kr and Xe and three-photon ionization of Ne verify the fifth-harmonic pulse intensity and indicate the feasibility of multi-photon VUV pump/VUV probe studies of ultrafast atomic and molecular dynamics. Finally, the extended functionally of the counter-propagating pulse metrology approach is demonstrated by a single-shot VUV pump/VUV probe experiment aiming at the investigation of ultrafast dissociation dynamics of O 2 excited in the Schumann-Runge continuum at 162 nm.

  14. Differential activation behavior of dermal dendritic cells underlies the strain-specific Th1 responses to single epicutaneous immunization.

    Science.gov (United States)

    Lee, Chih-Hung; Chen, Jau-Shiuh; Chiu, Hsien-Ching; Hong, Chien-Hui; Liu, Ching-Yi; Ta, Yng-Cun; Wang, Li-Fang

    2016-12-01

    Epicutaneous immunization with allergens is an important sensitization route for atopic dermatitis. We recently showed in addition to the Th2 response following single epicutaneous immunization, a remarkable Th1 response is induced in B6 mice, but not in BALB/c mice, mimicking the immune response to allergens in human non-atopics and atopics. We investigated the underlying mechanisms driving this differential Th1 response between BALB/c and B6 mice. We characterized dermal dendritic cells by flow cytometric analysis. We measured the induced Th1/Th2 responses by measuring the IFN-γ/IL-13 contents of supernatants of antigen reactivation cultures of lymph node cells. We demonstrate that more dermal dendritic cells with higher activation status migrate into draining lymph nodes of B6 mice compared to BALB/c mice. Dermal dendritic cells of B6 mice have a greater ability to capture protein antigen than those of BALB/c mice. Moreover, increasing the activation status or amount of captured antigen in dermal dendritic cells induced a Th1 response in BALB/c mice. Further, differential activation behavior, but not antigen-capturing ability of dermal dendritic cells between BALB/c and B6 mice is dendritic cell-intrinsic. These results show that the differential activation behavior of dermal dendritic cells underlies the strain-specific Th1 responses following single epicutaneous immunization. Furthermore, our findings highlight the potential differences between human atopics and non-atopics and provide useful information for the prediction and prevention of atopic diseases. Copyright © 2016 Japanese Society for Investigative Dermatology. Published by Elsevier Ireland Ltd. All rights reserved.

  15. Nonlinear Least-Squares Based Method for Identifying and Quantifying Single and Mixed Contaminants in Air with an Electronic Nose

    Directory of Open Access Journals (Sweden)

    Margaret A. Ryan

    2005-12-01

    Full Text Available The Jet Propulsion Laboratory has recently developed and built an electronic nose(ENose using a polymer-carbon composite sensing array. This ENose is designed to be usedfor air quality monitoring in an enclosed space, and is designed to detect, identify andquantify common contaminants at concentrations in the parts-per-million range. Itscapabilities were demonstrated in an experiment aboard the National Aeronautics and SpaceAdministration’s Space Shuttle Flight STS-95. This paper describes a modified nonlinearleast-squares based algorithm developed to analyze data taken by the ENose, and itsperformance for the identification and quantification of single gases and binary mixtures oftwelve target analytes in clean air. Results from laboratory-controlled events demonstrate theeffectiveness of the algorithm to identify and quantify a gas event if concentration exceedsthe ENose detection threshold. Results from the flight test demonstrate that the algorithmcorrectly identifies and quantifies all registered events (planned or unplanned, as singles ormixtures with no false positives and no inconsistencies with the logged events and theindependent analysis of air samples.

  16. Non-linear oscillations

    CERN Document Server

    Hagedorn, Peter

    1982-01-01

    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.

  17. Crystal growth, morphology, thermal and spectral studies of an organosulfur nonlinear optical bis(guanidinium) 5-sulfosalicylate (BG5SS) single crystals

    Science.gov (United States)

    Dhavamurthy, M.; Peramaiyan, G.; Babu, K. Syed Suresh; Mohan, R.

    2015-04-01

    Organosulfur nonlinear optical single crystals of orthorhombic bis(guanidinium) 5-sulfosalicylate (2CH6N3 +·C7H4O6S2-·H2O) with dimension 14 mm × 4 mm × 5 mm have been grown from methanol and water solvents in 1:1 ratio by the slow evaporation growth technique. The crystal structure and morphology of the crystals have been studied by single-crystal X-ray diffraction. FTIR spectroscopic studies were carried out to identify the functional groups and vibrational modes present in the grown crystals. The UV-Vis spectrum was studied to analyze the linear optical properties of the grown crystals. The thermal gravimetric analysis was conducted on the grown crystals, and the result revealed that the grown crystal is thermally stable up to 65 °C. The dielectric tensor components ɛ 11, ɛ 22 and ɛ 33 of BG5SS crystal were evaluated as a function of frequency at 40 °C. The surface laser damage threshold for the grown crystal was measured using Nd:YAG laser. Further, Vickers micro-hardness study was carried out to analyze the mechanical strength of the grown crystals for various loads.

  18. Growth, Optical, Dielectric and Ferroelectric Properties of Non-Linear Optical Single Crystal: Glycine-Phthalic Acid

    Science.gov (United States)

    Suresh, Sagadevan

    2016-11-01

    Single crystals of glycine-phthalic acid (GPA) were grown by slow evaporation process using aqueous solution. X-ray diffraction analysis was used to examine its cell structure and it was found that the GPA crystal corresponded to the orthorhombic system. To identify absorption range and cut-off wavelength for the GPA crystal, UV-visible spectrum was recorded. UV-visible spectroscopy was used to study the optical constants such as the refractive index, the extinction coefficient, electrical susceptibility, and optical conductivity. As a function of different frequencies and temperatures, the dielectric constant and the dielectric loss were examined. The electrical properties like plasma energy, Penn gap, Fermi energy, and polarizability were determined for the analysis of the second harmonic generation (SHG). Using the Kurtz powder technique, the SHG of the GPA crystal was studied. Investigations relating to hysteresis were carried out to ascertain the ferroelectric nature of the material.

  19. Inflation threshold: A nonlinear trapping-induced threshold for the rapid onset of stimulated Raman scattering from a single laser speckle

    International Nuclear Information System (INIS)

    Vu, H. X.; DuBois, D. F.; Bezzerides, B.

    2007-01-01

    The rapid onset, with increasing laser intensity, of levels of backward stimulated Raman scattering (BSRS) exceeding linear convective predictions, from single laser hot spots was predicted by simulations [Vu et al., Phys. Plasmas 9, 1745 (2002)], and has been observed [Montgomery et al., Phys. Plasmas 9, 2311 (2002)] in nonlinear regimes dominated by electron trapping. A theory for this inflation threshold is given here. The threshold is the result of competition between velocity diffusion and trapping, and is exceeded when the convectively amplified SRS Langmuir wave (LW) achieves an amplitude for which the coherent trapping velocity increment of electrons in the LW (the half-width of the trapping separatrix) exceeds the rms diffusion velocity (resulting from background plasma fluctuations), accumulated in one bounce time, for electrons with mean velocities near the phase velocity of the LW. The results of this theory, when the kinetic theory of the one-dimensional (1D) reduced-description particle-in-cell (RPIC) simulation is used, are in good agreement with a series of 1D RPIC simulations. The theory is naturally generalized to three dimensions, and is compatible with macroscopic laser interaction codes such as pF3d [Berger et al., Phys. Plasmas 5, 4337 (1998)]. Comparison of the LW trapping-induced inflation threshold to the LW threshold for the Langmuir decay instability provides an estimate for the transition between nonlinear saturation regimes. In an independent hot spot model of many hot spots, statistics suggests that the inflation threshold intensity will control the rapid onset of strong BSRS in laser beams smoothed by random phase plates

  20. Single and Double differential Drell-Yan cross section measurements using the CMS detector

    CERN Document Server

    Walia, Genius

    2017-01-01

    The neutral current Drell-Yan (DY) process, q$\\overline{q}$$\\to$Z/$\\gamma$$^*$$\\to$$\\mu^{+}$$\\mu^{-}$, is one of the best-studied benchmark physics processes at the LHC. The large production cross section and the experimentally clean final state allows excellent tests for perturbative Quantum Chromodynamics (QCD). A thorough understanding of the transverse momentum(qT) spectra of the vector bosons at hadron colliders is essential for a future high precision measurement of the mass of the W boson. However the measurements at LHC are limited due to the resolution in the measurement of momenta of the daughter leptons, electron and muon, in particular. The phistar ($\\phi^{*}$) variable, which uses the angular correlation of the lepton pairs from Z decay to probe the transverse momenta the vector boson, has intrinsically better resolution and less sensitivity to experimental systematic uncertainties compared to qT. Results from differential cross-measurements as function of the phi* variable will be presented in ...

  1. Structural Differentiation between Layered Single (Ni) and Double Metal Hydroxides (Ni–Al LDHs) Using Wavelet Transformation

    Energy Technology Data Exchange (ETDEWEB)

    Siebecker, Matthew G. [University of Delaware, Delaware Environmental Institute; Sparks, Donald L. [University of Delaware, Delaware Environmental Institute

    2017-09-07

    Layered double hydroxides (LDHs) are anionic clays important in disciplines such as environmental chemistry, geochemistry, and materials science. Developments in signal processing of extended X-ray absorption fine structure (EXAFS) data, such as wavelet transformation (WT), have been used to identify transition metals and Al present in the hydroxide sheets of LDHs. The WT plots of LDHs should be distinct from those of isostructural single metal hydroxides. However, no direct comparison of these minerals appears in the literature using WT. This work systematically analyzes a suite of Ni-rich mineral standards, including Ni–Al LDHs, single metal Ni hydroxides, and Ni-rich silicates using WT. The results illustrate that the WT plots for α-Ni(OH)2 and Ni–Al LDHs are often indistinguishable from each other, with similar two-component plots for the different mineral types. This demonstrates that the WT of the first metal shell often cannot be used to differentiate an LDH from a single metal hydroxide. Interlayer anions adsorbed to the hydroxide sheet of α-Ni(OH)2 affect the EXAFS spectra and are not visible in the FT but are clearly resolved and discrete in the WT.

  2. Synthesis, growth, optical and anisotropic mechanical behaviour of organic nonlinear optical imidazolium 2-chloro-4-nitrobenzoate single crystals

    Science.gov (United States)

    Krishnakumar, Varadharajan; Jayaprakash, Jeyaram; Boobas, Singaram; Komathi, Muniraj

    2016-10-01

    The title compound, imidazolium 2-chloro-4-nitrobenzoate (I2C4NB), has been synthesized and optical quality single crystals were grown with a dimension of 4 × 2 × 1 mm3 using an ethanol and acetone (1:1) mixed solvent by slow evaporation solution growth technique. The powder XRD analysis confirmed the crystal structure and found that it is crystallized in the non-centrosymmetric space group P21 with the monoclinic system. The symmetries of molecular vibrations were confirmed by FT-IR spectrum. The CHN(S) analysis confirmed the stoichiometric composition of the grown crystal. It also exhibits a good transparency in the entire visible region (300-800nm) and it was thermally stable up to 131.1 °C. The microhardness measurement shows the anisotropic nature of I2C4NB and also that it belongs to a soft material category. Photoconductivity studies reveal a linear increase of the photocurrent with respect to the applied electric field. HOMO LUMO studies were carried out for the crystal. The second harmonic generation test by the Kurtz powder method shows that the crystal exhibits phase matching and a conversion efficiency which is 2 times that of KDP.

  3. Growth and characterization of organic second order nonlinear optical (NLO) 4-chloroanilinium-L-tartrate monohydrate single crystals

    Science.gov (United States)

    Jeyaram, Jayaprakash; Varadharajan, Krishnakumar; Singaram, Boobas; Rajendhran, Ranjith

    2018-03-01

    The protonated organic single crystal of 4-chloroanilinium-L-tartrate monohydrate (4CALTM) was successfully grown by slow evaporation solution technique at room temperature. Powder X-ray diffraction confirmed the crystal system of the grown crystal and its lattice parameters were calculated. Microanalysis confirms the elemental compositions and the vibrations of the functional groups were confirmed by Fourier transform infrared (FTIR) spectroscopy technique. The grown crystal exhibits 65% of optical transparency in the 289-800 nm range and the optical bandgap was calculated. The dielectric constant and loss were studied as a function of frequency at different temperatures. The TG-DSC analysis shows the thermal stability of the grown crystal. Vickers hardness measurement reveals the mechanically soft nature of the crystal, and it obeys the reverse indentation size effect (RISE). The positive photoconductivity of the crystal was supported by a linear increase of photocurrent on illumination. Kurtz - Perry powder technique shows the second harmonic generation efficiency of a range of particles (25-300 μm) and the phasematching ability of the crystal.

  4. Differential pulse amplitude modulation for multiple-input single-output OWVLC

    Science.gov (United States)

    Yang, S. H.; Kwon, D. H.; Kim, S. J.; Son, Y. H.; Han, S. K.

    2015-01-01

    White light-emitting diodes (LEDs) are widely used for lighting due to their energy efficiency, eco-friendly, and small size than previously light sources such as incandescent, fluorescent bulbs and so on. Optical wireless visible light communication (OWVLC) based on LED merges lighting and communications in applications such as indoor lighting, traffic signals, vehicles, and underwater communications because LED can be easily modulated. However, physical bandwidth of LED is limited about several MHz by slow time constant of the phosphor and characteristics of device. Therefore, using the simplest modulation format which is non-return-zero on-off-keying (NRZ-OOK), the data rate reaches only to dozens Mbit/s. Thus, to improve the transmission capacity, optical filtering and pre-, post-equalizer are adapted. Also, high-speed wireless connectivity is implemented using spectrally efficient modulation methods: orthogonal frequency division multiplexing (OFDM) or discrete multi-tone (DMT). However, these modulation methods need additional digital signal processing such as FFT and IFFT, thus complexity of transmitter and receiver is increasing. To reduce the complexity of transmitter and receiver, we proposed a novel modulation scheme which is named differential pulse amplitude modulation. The proposed modulation scheme transmits different NRZ-OOK signals with same amplitude and unit time delay using each LED chip, respectively. The `N' parallel signals from LEDs are overlapped and directly detected at optical receiver. Received signal is demodulated by power difference between unit time slots. The proposed scheme can overcome the bandwidth limitation of LEDs and data rate can be improved according to number of LEDs without complex digital signal processing.

  5. Single Particle Laser Mass Spectrometry Applied to Differential Ice Nucleation Experiments at the AIDA Chamber

    International Nuclear Information System (INIS)

    Gallavardin, S. J.; Froyd, Karl D.; Lohmann, U.; Moehler, Ottmar; Murphy, Daniel M.; Cziczo, Dan

    2008-01-01

    Experiments conducted at the Aerosol Interactions and Dynamics in the Atmosphere (AIDA) chamber located in Karlsruhe, Germany permit investigation of particle properties that affect the nucleation of ice at temperature and water vapor conditions relevant to cloud microphysics and climate issues. Ice clouds were generated by heterogeneous nucleation of Arizona test dust (ATD), illite, and hematite and homogeneous nucleation of sulfuric acid. Ice crystals formed in the chamber were inertially separated from unactivated, or 'interstitial' aerosol particles with a pumped counterflow virtual impactor (PCVI), then evaporated. The ice residue (i.e., the aerosol which initiated ice nucleation plus any material which was scavenged from the gas- and/or particle-phase), was chemically characterized at the single particle level using a laser ionization mass spectrometer. In this manner the species that first nucleated ice could be identified out of a mixed aerosol population in the chamber. Bare mineral dust particles were more effective ice nuclei (IN) than similar particles with a coating. Metallic particles from contamination in the chamber initiated ice nucleation before other species but there were few enough that they did not compromise the experiments. Nitrate, sulfate, and organics were often detected on particles and ice residue, evidently from scavenging of trace gas-phase species in the chamber. Hematite was a more effective ice nucleus than illite. Ice residue was frequently larger than unactivated test aerosol due to the formation of aggregates due to scavenging, condensation of contaminant gases, and the predominance of larger aerosol in nucleation

  6. New Method for Differentiation of Granuloviruses (Betabaculoviruses Based on Multitemperature Single Stranded Conformational Polymorphism

    Directory of Open Access Journals (Sweden)

    Martyna Krejmer-Rabalska

    2017-12-01

    Full Text Available Baculoviruses have been used as biopesticides for decades. Recently, due to the excessive use of chemical pesticides there is a need for finding new agents that may be useful in biological protection. Sometimes few isolates or species are discovered in one host. In the past few years, many new baculovirus species have been isolated from environmental samples, thoroughly characterized and thanks to next generation sequencing methods their genomes are being deposited in the GenBank database. Next generation sequencing (NGS methodology is the most certain way of detection, but it has many disadvantages. During our studies, we have developed a method based on Polymerase chain reaction (PCR followed by Multitemperature Single Stranded Conformational Polymorphism (MSSCP which allows for distinguishing new granulovirus isolates in only a few hours and at low-cost. On the basis of phylogenetic analysis of betabaculoviruses, representative species have been chosen. The alignment of highly conserved genes—granulin and late expression factor-9, was performed and the degenerate primers were designed to amplify the most variable, short DNA fragments flanked with the most conserved sequences. Afterwards, products of PCR reaction were analysed by MSSCP technique. In our opinion, the proposed method may be used for screening of new isolates derived from environmental samples.

  7. A Simple Differential Mode EMI Suppressor for the LLCL-Filter-Based Single-Phase Grid-Tied Transformerless Inverter

    DEFF Research Database (Denmark)

    Ji, Junhao; Wu, Weimin; He, Yuanbin

    2015-01-01

    The single-phase power converter topologies evolving of photovoltaic applications are still including passive filters, like the LCLor LLCL-filter. Compared with the LCL-filter, the total inductance of the LLCL-filter can be reduced a lot. However, due to the resonant inductor in series...... with the bypass capacitor, the differential mode (DM) electromagnetic interference (EMI) noise attenuation of an LLCL-filter-based grid-tied inverter declines. Conventionally, a capacitor was inserted in parallel with the LC resonant circuit branch of the LLCL-filter to suppress the DM EMI noise. In order...... to achieve a small value of capacitor as well as to minimize the additional reactive power, a novel simple DM EMI suppressor for the LLCL-filter-based system is proposed. The characters of two kinds of DM EMI suppressor are analyzed and compared in detail. Simulations and experiments on a 0.5-kW 110-V/50-Hz...

  8. The singly averaged differential equations of satellite motion for e greater than or equal to 0 and less than 1

    Science.gov (United States)

    Dallas, S. S.; Khan, I.

    1976-01-01

    The singly-averaged differential equations of motion of a satellite are developed in terms of parameters valid for all eccentricities less than one. The perturbations included in the acceleration model are due to an aspherical central planet (zonal harmonics up to degree 20 and resonant harmonics up to degree and order 20), atmospheric drag for a time-varying atmosphere, third-body gravity (the sun and moon for an earth satellite), solar radiation pressure with shadowing, and impulsive maneuvers. Analytic averaging is used to remove short-period terms due to the aspherical central planet and third-body gravity. Numerical averaging is used to remove short-period terms due to atmospheric drag and solar radiation pressure.

  9. Single assay for simultaneous detection and differential identification of human and avian influenza virus types, subtypes, and emergent variants.

    Directory of Open Access Journals (Sweden)

    David Metzgar

    Full Text Available For more than four decades the cause of most type A influenza virus infections of humans has been attributed to only two viral subtypes, A/H1N1 or A/H3N2. In contrast, avian and other vertebrate species are a reservoir of type A influenza virus genome diversity, hosting strains representing at least 120 of 144 combinations of 16 viral hemagglutinin and 9 viral neuraminidase subtypes. Viral genome segment reassortments and mutations emerging within this reservoir may spawn new influenza virus strains as imminent epidemic or pandemic threats to human health and poultry production. Traditional methods to detect and differentiate influenza virus subtypes are either time-consuming and labor-intensive (culture-based or remarkably insensitive (antibody-based. Molecular diagnostic assays based upon reverse transcriptase-polymerase chain reaction (RT-PCR have short assay cycle time, and high analytical sensitivity and specificity. However, none of these diagnostic tests determine viral gene nucleotide sequences to distinguish strains and variants of a detected pathogen from one specimen to the next. Decision-quality, strain- and variant-specific pathogen gene sequence information may be critical for public health, infection control, surveillance, epidemiology, or medical/veterinary treatment planning. The Resequencing Pathogen Microarray (RPM-Flu is a robust, highly multiplexed and target gene sequencing-based alternative to both traditional culture- or biomarker-based diagnostic tests. RPM-Flu is a single, simultaneous differential diagnostic assay for all subtype combinations of type A influenza viruses and for 30 other viral and bacterial pathogens that may cause influenza-like illness. These other pathogen targets of RPM-Flu may co-infect and compound the morbidity and/or mortality of patients with influenza. The informative specificity of a single RPM-Flu test represents specimen-specific viral gene sequences as determinants of virus type, A

  10. On the design of experiments for determining ternary mixture free energies from static light scattering data using a nonlinear partial differential equation.

    Science.gov (United States)

    Wahle, Chris W; Ross, David S; Thurston, George M

    2012-07-21

    We mathematically design sets of static light scattering experiments to provide for model-independent measurements of ternary liquid mixing free energies to a desired level of accuracy. A parabolic partial differential equation (PDE), linearized from the full nonlinear PDE [D. Ross, G. Thurston, and C. Lutzer, J. Chem. Phys. 129, 064106 (2008)], describes how data noise affects the free energies to be inferred. The linearized PDE creates a net of spacelike characteristic curves and orthogonal, timelike curves in the composition triangle, and this net governs diffusion of information coming from light scattering measurements to the free energy. Free energy perturbations induced by a light scattering perturbation diffuse along the characteristic curves and towards their concave sides, with a diffusivity that is proportional to the local characteristic curvature radius. Consequently, static light scattering can determine mixing free energies in regions with convex characteristic curve boundaries, given suitable boundary data. The dielectric coefficient is a Lyapunov function for the dynamical system whose trajectories are PDE characteristics. Information diffusion is heterogeneous and system-dependent in the composition triangle, since the characteristics depend on molecular interactions and are tangent to liquid-liquid phase separation coexistence loci at critical points. We find scaling relations that link free energy accuracy, total measurement time, the number of samples, and the interpolation method, and identify the key quantitative tradeoffs between devoting time to measuring more samples, or fewer samples more accurately. For each total measurement time there are optimal sample numbers beyond which more will not improve free energy accuracy. We estimate the degree to which many-point interpolation and optimized measurement concentrations can improve accuracy and save time. For a modest light scattering setup, a sample calculation shows that less than two

  11. Single Particle Differentiation through 2D Optical Fiber Trapping and Back-Scattered Signal Statistical Analysis: An Exploratory Approach.

    Science.gov (United States)

    Paiva, Joana S; Ribeiro, Rita S R; Cunha, João P S; Rosa, Carla C; Jorge, Pedro A S

    2018-02-27

    Recent trends on microbiology point out the urge to develop optical micro-tools with multifunctionalities such as simultaneous manipulation and sensing. Considering that miniaturization has been recognized as one of the most important paradigms of emerging sensing biotechnologies, optical fiber tools, including Optical Fiber Tweezers (OFTs), are suitable candidates for developing multifunctional small sensors for Medicine and Biology. OFTs are flexible and versatile optotools based on fibers with one extremity patterned to form a micro-lens. These are able to focus laser beams and exert forces onto microparticles strong enough (piconewtons) to trap and manipulate them. In this paper, through an exploratory analysis of a 45 features set, including time and frequency-domain parameters of the back-scattered signal of particles trapped by a polymeric lens, we created a novel single feature able to differentiate synthetic particles (PMMA and Polystyrene) from living yeasts cells. This single statistical feature can be useful for the development of label-free hybrid optical fiber sensors with applications in infectious diseases detection or cells sorting. It can also contribute, by revealing the most significant information that can be extracted from the scattered signal, to the development of a simpler method for particles characterization (in terms of composition, heterogeneity degree) than existent technologies.

  12. Differential-interference-contrast digital in-line holography microscopy based on a single-optical-element.

    Science.gov (United States)

    Zhang, Yuchao; Xie, Changqing

    2015-11-01

    Both digital in-line holography (DIH) and zone plate-based microscopy have received considerable interest as powerful imaging tools. However, the former suffers from a twin-image noise problem. The latter suffers from low efficiency and difficulty in fabrication. Here, we present an effective and efficient phase-contrast imaging approach, named differential-interference-contrast digital in-line holography (DIC-DIH), by using a single optical element to split the incident light into a plane wave and a converging spherical wave and generate a two-dimensional (2D) DIC effect simultaneously. Specifically, to improve image contrast, we present a new single optical element, termed 2D DIC compound photon sieves, by combining two overlaid binary gratings and a compound photon sieve through two logical XOR operations. The proof-of-concept experiments demonstrate that the proposed technique can eliminate the twin-image noise problem and improve image contrast with high efficiency. Additionally, we present an example of the phase-contrast imaging nonuniform thick photoresist development process.

  13. Nonlinear optics

    CERN Document Server

    Bloembergen, Nicolaas

    1996-01-01

    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

  14. [Nonlinear magnetohydrodynamics

    International Nuclear Information System (INIS)

    1994-01-01

    Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile

  15. Statistical measures approximations for the Gaussian part of the stochastic nonlinear damped Duffing oscillator solution process under the application of Wiener Hermite expansion linked by the multi-step differential transformed method

    Directory of Open Access Journals (Sweden)

    R.A. Zait

    2016-07-01

    Full Text Available In this paper, the stochastic Wiener Hermite expansion (WHE is used to find the statistical measures (mean and variance of the first order stochastic approximation (Gaussian part of the stochastic solution processes related to the nonlinear damped Duffing oscillator model which is excited randomly by white noise process. Under the application of WHE, a deterministic model is generated to simulate the statistical measures. In next stages, smi-analytical treatments are performed under applying multi-step differential transformed method (Ms-DTM and some cases study are illustrated related to the statistical properties using Mathematica10 software.

  16. Image Quality of a Novel Frequency Selective Nonlinear Blending Algorithm: An Ex Vivo Phantom Study in Comparison to Single-Energy Acquisitions and Dual-Energy Acquisitions With Monoenergetic Reconstructions.

    Science.gov (United States)

    Bongers, Malte N; Bier, Georg; Marcus, Roy; Ditt, Hendrik; Kloth, Christopher; Schabel, Christoph; Nikolaou, Konstantin; Horger, Marius

    2016-10-01

    Aim of this ex vivo phantom study was to evaluate the contrast enhancement applying a new frequency split nonlinear blending algorithm (best contrast [BC]) and to compare it with standard 120-kV single-energy computed tomography (SECT) images, as well as with low-kiloelectron volt monoenergetic extrapolations (Mono+40-100keV) from dual-energy CT (DECT) and with low-kilovolt (70-100 kV) SECT acquisitions. A dilution series of iodinated contrast material-filled syringes was centered in an attenuation phantom and was scanned with SECT70-120kV and DECT80-100/Sn150. Monoenergetic images (40-100 keV) were reconstructed, and a new manual frequency split nonlinear blending algorithm (BC) was applied to SECT70kV and SECT120kV images. Manual BC settings were set to simulate a reading situation with fixed overall best values (FVBC120kV) as well as to achieve best possible values for each syringe (BVBC120kV) for maximum contrast enhancement. Contrast-to-noise ratios (CNRs) were used as an objective region of interest-based image analysis parameter. Two radiologists evaluated the detectability of hyperdense and hypodense syringes (Likert). Results were compared between SECT70-100kV, Mono+40-100keV, and DECT80-100/Sn150kV, as well as FVBC120kV, BVBC120kV, and BC70kV. Highest CNR without BC was detected at SECT70kV (5.04 ± 0.12) and Mono+40keV (4.40 ± 0.11). FVBC and BVBC images allow a significant increase of CNR compared with SECT120kV (CNRBVBC, 5.21 ± 0.15; CNRFVBC, 5.12 ± 0.16; CNRSECT120kV, 2.5 ± 0.08; all P ≤ 0.01). There was no significant difference in CNR between BVBC and FVBC. Averaged CNR in BVBC and FVBC was significantly higher compared with Mono+40-100keV (all P ≤ 0.01). Compared with SECT70kV, averaged CNR in BVBC and FVBC show no significant differences. BVBC70kV (7.67 ± 0.17) significantly increases CNR in SECT70kV up to 213%.Subjective image analysis showed an interobserver agreement of 0.63 to 0.83 (κ), confirming the superiority of BC in detecting

  17. FRF decoupling of nonlinear systems

    Science.gov (United States)

    Kalaycıoğlu, Taner; Özgüven, H. Nevzat

    2018-03-01

    Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.

  18. Length distribution of single-walled carbon nanotubes in aqueous suspension measured by electrospray differential mobility analysis.

    Science.gov (United States)

    Pease, Leonard F; Tsai, De-Hao; Fagan, Jeffery A; Bauer, Barry J; Zangmeister, Rebecca A; Tarlov, Michael J; Zachariah, Michael R

    2009-12-01

    The first characterization of the length distribution of single-walled carbon nanotubes (SWCNT) dispersed in a liquid by electrospray differential mobility analysis (ES-DMA) is presented. Although an understanding of geometric properties of SWCNTs, including length, diameter, aspect ratio, and chirality, is essential for commercial applications, rapid characterization of nanotube length distributions remains challenging. Here the use of ES-DMA to obtain length distributions of DNA-wrapped SWCNTs dispersed in aqueous solutions is demonstrated. Lengths measured by ES-DMA compare favorably with those obtained from multiangle light scattering, dynamic light scattering, field flow fractionation with UV/vis detection, and atomic force microscopy, validating ES-DMA as a technique to measure SWCNTs of <250 nm in length. The nanotubes are previously purified and dispersed by wrapping with oligomeric DNA in aqueous solution and centrifuging to remove bundles and amorphous carbon. These dispersions are particularly attractive due to their amenability to bulk processing, ease of storage, high concentration, compatibility with biological and high-throughput manufacturing environments, and for their potential applications ranging from electronics and hydrogen-storage vessels to anticancer agents.

  19. Improved Power Decoupling Scheme for Single-Phase Grid-Connected Differential Inverter with Realistic Mismatch in Storage Capacitances

    DEFF Research Database (Denmark)

    Yao, Wenli; Wang, Xiongfei; Loh, Poh Chiang

    2017-01-01

    the intention of this paper to quantify ac and dc imperfections experienced by the differential inverter when storage mismatch occurs. A simple improved scheme is then proposed for raising performance of the differential inverter (or the differential rectifier where desired). Simulation and experimental results...

  20. Automatic differentiation bibliography

    Energy Technology Data Exchange (ETDEWEB)

    Corliss, G.F. (comp.)

    1992-07-01

    This is a bibliography of work related to automatic differentiation. Automatic differentiation is a technique for the fast, accurate propagation of derivative values using the chain rule. It is neither symbolic nor numeric. Automatic differentiation is a fundamental tool for scientific computation, with applications in optimization, nonlinear equations, nonlinear least squares approximation, stiff ordinary differential equation, partial differential equations, continuation methods, and sensitivity analysis. This report is an updated version of the bibliography which originally appeared in Automatic Differentiation of Algorithms: Theory, Implementation, and Application.

  1. Fully nonlinear elliptic equations

    CERN Document Server

    Caffarelli, Luis A

    1995-01-01

    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

  2. Nonlinear Science

    CERN Document Server

    Yoshida, Zensho

    2010-01-01

    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

  3. Growth and characterization of organic nonlinear optical material: Benzilic acid

    Science.gov (United States)

    Baraniraj, T.; Philominathan, P.

    2009-07-01

    The organic nonlinear optical crystals of benzilic acid were grown by the slow evaporation method using ethanol as a solvent. Single-crystal X-ray diffraction (XRD), powder XRD studies and Fourier transform infrared (FTIR) spectral analysis were carried out to confirm the benzilic acid crystal. The optical transparency was studied by ultra violet (UV)-visible spectral analysis. Thermal properties of the grown crystals were studied by thermogravimetric and differential thermal analyses. The melting point of the grown crystal was confirmed by differential scanning calorimetry (DSC) analysis. The second harmonic generation (SHG) efficiency was found to be 2 times that of KDP.

  4. Proteomic signatures and aberrations of mouse embryonic stem cells containing a single human chromosome 21 in neuronal differentiation: an in vitro model of Down syndrome.

    Science.gov (United States)

    Kadota, M; Nishigaki, R; Wang, C C; Toda, T; Shirayoshi, Y; Inoue, T; Gojobori, T; Ikeo, K; Rogers, M S; Oshimura, M

    2004-01-01

    Neurodegeneration in fetal development of Down syndrome (DS) patients is proposed to result in apparent neuropathological abnormalities and to contribute to the phenotypic characteristics of mental retardation and premature development of Alzheimer disease. In order to identify the aberrant and specific genes involved in the early differentiation of DS neurons, we have utilized an in vitro neuronal differentiation system of mouse ES cells containing a single human chromosome 21 (TT2F/hChr21) with TT2F parental ES cells as a control. The paired protein extracts from TT2F and TT2F/hChr21 cells at several stages of neuronal differentiation were subjected to two-dimensional polyacrylamide gel electrophoresis protein separation followed by matrix-assisted laser desorption/ionization-time of flight mass spectrometry to identify the proteins differentially expressed between TT2F and TT2F/hChr21 cells. We provide here a novel set of specific gene products altered in early differentiating DS neuronal cells, which differs from that identified in adult or fetal brain with DS. The aberrant protein expression in early differentiating neurons, due to the hChr21 gene dosage effects or chromosomal imbalance, may affect neuronal outgrowth, proliferation and differentiation, producing developmental abnormalities in neural patterning, which eventually leads to formation of a suboptimal functioning neuronal network in DS.

  5. Measurements of Single Diffraction at $\\sqrt{s}$ = 630 GeV Evidence for a Non-Linear $\\alpha(t)$ of the Pomeron

    CERN Document Server

    Brandt, A.; Kuzucu, A.; Lynn, D.; Medinnis, M.; Ozdes, N.; Schlein, P.E.; Zeyrek, M.T.; Zweizig, J.G.; Cheze, J.B.; Zsembery, J.

    1998-01-01

    We report measurements of the inclusive differential cross section for the single-diffractive reactions: p + pbar --> p + X and p + pbar --> X + pbar at sqrt(s) = 630 GeV, in the momentum transfer range, t = 0.8--2.0 GeV^2 and final state Feynman-x > 0.90. Based on the assumption of factorization, several new features of the Pomeron Flux Factor are determined from simultaneous fits to our UA8 data and lower energy data from the CHLM collaboration at the CERN-Intersecting Storage Rings. Prominent among these is that the effective Pomeron Regge trajectory requires a term quadratic in t, with coefficient, a'' = 0.079 +- 0.012 GeV^-2. We also show that the data require a Pomeron-proton cross section that first decreases with increasing diffractive mass (corresponding to the PPR term in the triple-Regge expansion) and then increases at larger mass (the PPP term), similar to real particle total cross sections. We measure the product, (K x sigma0) = 0.72 +- 0.10 mb/GeV^2, where K is the normalization constant of the...

  6. Stability of non-linear constitutive formulations for viscoelastic fluids

    CERN Document Server

    Siginer, Dennis A

    2014-01-01

    Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids provides a complete and up-to-date view of the field of constitutive equations for flowing viscoelastic fluids, in particular on their non-linear behavior, the stability of these constitutive equations that is their predictive power, and the impact of these constitutive equations on the dynamics of viscoelastic fluid flow in tubes. This book gives an overall view of the theories and attendant methodologies developed independently of thermodynamic considerations as well as those set within a thermodynamic framework to derive non-linear rheological constitutive equations for viscoelastic fluids. Developments in formulating Maxwell-like constitutive differential equations as well as single integral constitutive formulations are discussed in the light of Hadamard and dissipative type of instabilities.

  7. Nonlinear systems

    CERN Document Server

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

    2018-01-01

    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...

  8. Application of "parallel" moiré deflectometry and the single beam Z-scan technique in the measurement of the nonlinear refractive index.

    Science.gov (United States)

    Rasouli, Saifollah; Ghasemi, H; Tavassoly, M T; Khalesifard, H R

    2011-06-01

    In this paper, the application of "parallel" moiré deflectometry in measuring the nonlinear refractive index of materials is reported. In "parallel" moiré deflectometry the grating vectors are parallel, and the resulting moiré fringes are also parallel to the grating lines. Compared to "rotational" moiré deflectometry and the Z-scan technique, which cannot easily determine the moiré fringe's angle of rotation and is sensitive to power fluctuations, respectively, "parallel" moiré deflectometry is more reliable, which allows one to measure the radius of curvature of the light beam by measuring the moiré fringe spacing. The nonlinear refractive index of the sample, including the sense of the change, is obtained from the moiré fringe spacing curve. The method is applied for measuring the nonlinear refractive index of ferrofluids.

  9. The classification of single travelling wave solutions to the Camassa ...

    Indian Academy of Sciences (India)

    Introduction. Classifications of single travelling wave solutions to some nonlinear differential equations have been obtained extensively by the complete discrimination system for polynomial method proposed by Liu [1–7]. Furthermore, Wang and Li [8] used Liu's method and factorization method proposed by Cornejo-Pérez ...

  10. Cerebral peritumoral oedema study: Does a single dynamic MR sequence assessing perfusion and permeability can help to differentiate glioblastoma from metastasis?

    International Nuclear Information System (INIS)

    Lehmann, Pierre; Saliou, Guillaume; Marco, Giovanni de; Monet, Pauline; Souraya, Stoquart-Elsankari; Bruniau, Alexis; Vallée, Jean Noel; Ducreux, Denis

    2012-01-01

    Our purpose was to differentiate glioblastoma from metastasis using a single dynamic MR sequence to assess perfusion and permeability parameters. 24 patients with glioblastoma or cerebral metastasis with peritumoral oedema were recruited and explored with a 3 T MR unit. Post processing used DPTools software. Regions of interest were drawn around contrast enhancement to assess relative cerebral blood volume and permeability parameters. Around the contrast enhancement Glioblastoma present high rCBV with modification of the permeability, metastasis present slight modified rCBV without modification of permeability. In conclusion, peritumoral T2 hypersignal exploration associating morphological MR and functional MR parameters can help to differentiate cerebral metastasis from glioblastoma.

  11. Nonlinear optics

    CERN Document Server

    Boyd, Robert W

    2013-01-01

    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

  12. Image charge effects in single-molecule junctions: Breaking of symmetries and negative-differential resistance in a benzene single-electron transistor

    DEFF Research Database (Denmark)

    Kaasbjerg, Kristen; Flensberg, K.

    2011-01-01

    blockade regime. This results in the appearance of a so-called blocking state, which gives rise to negative-differential resistance (NDR). We show that the appearance of NDR and its magnitude in the symmetry-broken benzene SET depends in a complicated way on the interplay between the many-body matrix...

  13. No effect of traction in patients with low back pain: a single centre, single blind, randomized controlled trial of Intervertebral Differential Dynamics Therapy.

    NARCIS (Netherlands)

    Schimmel, J.J.; Kleuver, M. de; Horsting, P.P.; Spruit-van Eijk, M.; Jacobs, W.C.; Limbeek, J. van

    2009-01-01

    Low back pain (LBP) poses a significant problem to society. Although initial conservative therapy may be beneficial, persisting chronic LBP still frequently leads to expensive invasive intervention. A novel non-invasive therapy that focuses on discogenic LBP is Intervertebral Differential Dynamics

  14. On the weakly nonlinear, transversal vibrations of a conveyor belt with a low and time-varying velocity

    NARCIS (Netherlands)

    Suweken, G.; van Horssen, W.T.

    2002-01-01

    In this paper the weakly nonlinear, transversal vibrations of a conveyor belt will be considered. The belt is assumed to move with a low and time-varying speed. Using Kirchhoff's approach a single equation of motion will be derived from a coupled system of partial differential equations describing

  15. Partial Differential Equations

    CERN Document Server

    1988-01-01

    The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

  16. Nonlinear reconstruction

    Science.gov (United States)

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

    2017-12-01

    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.

  17. Nonlinear analysis

    CERN Document Server

    Gasinski, Leszek

    2005-01-01

    Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.

  18. Practical Nonlinearities

    Science.gov (United States)

    2016-07-01

    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

  19. Classification of biological signals using linear and nonlinear features.

    Science.gov (United States)

    Balli, T; Palaniappan, R

    2010-07-01

    This paper investigates the characterization ability of linear and nonlinear features and proposes combining such features in order to improve the classification of biological signals, in particular single-trial electroencephalogram (EEG) and electrocardiogram (ECG) data. For this purpose, three data sets composed of ECG, epileptic EEG and finger-movement EEG were utilized. The characterization ability of seven nonlinear features namely the approximate entropy, largest Lyapunov exponents, correlation dimension, nonlinear prediction error, Hurst exponent, higher order autocovariance and asymmetry due to time reversal are compared with two linear features namely the autoregressive (AR) reflection coefficients and AR model coefficients. The features were tested by their ability to differentiate between different classes of data using a linear discriminant analysis (LDA) method with tenfold cross-validation. The class separability of combined linear and nonlinear features was assessed using sequential floating forward search with linear discriminant analysis method (SFFS-LDA). The results demonstrated that linear and nonlinear features on their own provided comparable results for the ECG data set and the finger-movement EEG data set whilst the linear features provided a better class separability compared to nonlinear features for the epileptic EEG data set. Combining linear and nonlinear features demonstrated a significant improvement in the class separability for all of the data sets where an average improvement of 20.56% was obtained with the ECG data set, 7.45% with finger-movement data set and 6.62% with the epileptic EEG data set. Overall results suggest that the use of combined linear and nonlinear feature sets would be a better approach for the characterization and classification of biological signals such as EEG and ECG.

  20. Development of an embryoid body-based screening strategy for assessing the hepatocyte differentiation potential of human embryonic stem cells following single-cell dissociation.

    Science.gov (United States)

    Greenhough, Sebastian; Bradburn, Helen; Gardner, John; Hay, David C

    2013-02-01

    We have devised an embryoid body-based screening method for the selection of human embryonic stem cell (hESC) lines capable of forming functional hepatocyte-like cells (HLCs) after single-cell dissociation. The screening method highlighted one cell line from a panel of five that produced albumin-positive cells during embryoid body (EB) formation. Cell lines that did not produce albumin-positive cells during EB formation were shown to respond less well to directed differentiation following single-cell replating. Additionally, the seeding density of the pluripotent populations prior to differentiation was shown to exert a significant effect on the hepatic function of the final population of cells. In summary, we have developed a simple procedure that facilitates the identification of human hESC lines that tolerate single-cell replating and are capable of differentiating to HLCs. Although the hepatic function of cells produced by this method is ∼10-fold lower than our current gold standard stem cell-derived models, we believe that these findings represent an incremental step toward producing HLCs at scale.

  1. Application Of Waterloo Maple 9.5 And Wolfram Mathematica 5.1 Software For Analytic Solving Of Certain Nonlinear Partial Differential Equations Of Physics

    Directory of Open Access Journals (Sweden)

    Łukasz T. Stępień

    2008-01-01

    Full Text Available In the current paper some applications of the packet MAPLE (v. 9.5 for analytic solving ofcertain nonline partial differential equations have been presented. Additionally, for graphicpresentation of the found solutions packet MATHEMATICA (v. 5.1 has been applied.

  2. The scaled boundary FEM for nonlinear problems

    Science.gov (United States)

    Lin, Zhiliang; Liao, Shijun

    2011-01-01

    The traditional scaled boundary finite-element method (SBFEM) is a rather efficient semi-analytical technique widely applied in engineering, which is however valid mostly for linear differential equations. In this paper, the traditional SBFEM is combined with the homotopy analysis method (HAM), an analytic technique for strongly nonlinear problems: a nonlinear equation is first transformed into a series of linear equations by means of the HAM, and then solved by the traditional SBFEM. In this way, the traditional SBFEM is extended to nonlinear differential equations. A nonlinear heat transfer problem is used as an example to show the validity and computational efficiency of this new SBFEM.

  3. Absolute non-linear optical coefficients measurements of CsLiB 6O 10 single crystals by second harmonic generation

    Science.gov (United States)

    Sifi, A.; Klein, R. S.; Maillard, A.; Kugel, G. E.; Péter, A.; Polgár, K.

    2003-10-01

    We present absolute measurements of the effective non-linear optical coefficients deff of cesium lithium borate crystals (CsLiB 6O 10, CLBO) by second harmonic generation using a continuous Nd-YAG laser source. The experiments were carried out at room temperature, on crystals cut perpendicular to type I or type II phase matching directions, with two different crystal lengths along the propagation direction. The d36 and d14 non-linear coefficients involved in deff developments are deduced and are shown to be equal as it is predicted by the Kleinman symmetry. Two different compositions prepared by the Czochralski technique from melt with compositions of 1:1:6 and 1:1:5.5 molar ratios of Cs 2O, Li 2O and B 2O 3 are comparatively studied.

  4. Performance of the tariffs of a single-phase electric energy meter, type electronic, operating with non-linear loads; Desempenho tarifario do medidor monofasico de energia eletrica do tipo eletronico operando com cargas nao-lineares

    Energy Technology Data Exchange (ETDEWEB)

    Santos, G.B.; Pinheiro Neto, D.; Lisita, L.R.; Machado, P.C.M.; Oliveira, J.V.M. [Universidade Federal de Goias (UFG), Goiania, GO (Brazil). Escola de Engenharia Eletrica e de Computacao], Emails: guilhermebsantos@gmail.com, daywes@gmail.com, lrlisi-ta@gmail.com, pcesar@eee.ufg.br, joao.eee@gmail.com

    2009-07-01

    This paper analyzes the behavior of a electronic meter of single-phase in the laboratory when it is subjected to a environment with linear loads and nonlinear loads kind residential and commercial. It differs from correlated studies mainly for making use of real loads encountered in day-to-day, rather than as sources of electronic loads how has been observed in the state of the art. The comparison of results is made based on high precision energy pattern developed by virtual instrumentation means.

  5. Types of work-related behavior and experiences and stress coping strategies among single mothers and mothers in relationships differentiating role of work satisfaction.

    Science.gov (United States)

    Napora, Elżbieta; Andruszkiewicz, Anna; Basińska, Małgorzata Anna

    2018-01-01

    The purpose of the study has been to describe functioning of single and mothers in relationships (married or in informal relationships) at work and verify if the declared degree of work satisfaction differentiates types of behavior at work and stress coping strategies in both groups of mothers. The study was conducted on equal samples of single mothers (N = 186) and mothers from 2-parent families (N = 186) using Latack Coping Scale that measures work-related stress coping strategies, the AVEM (Arbeitsbezogenes Verhaltens- und Erlebensmuster - Work-Related Behavior and Experience Pattern) questionnaire, and a survey. It showed similarity between the studied groups in terms of the measured variables. There were considerable differences between single and married mothers in terms of support seeking strategies. The interaction of work satisfaction and the type of motherhood significantly differentiates (p = 0.03) the avoidance strategy of resignation. That strategy of resignation was more frequently used by single mothers with lower work satisfaction, who were distinctly different from those whose work satisfaction was higher, and from the mothers in relationships (married or in informal relationships) (regardless of the level of their work satisfaction). Int J Occup Med Environ Health 2018;31(1):55-69. This work is available in Open Access model and licensed under a CC BY-NC 3.0 PL license.

  6. The Impact of Electronic Medical Records on Hospital-Acquired Adverse Safety Events: Differential Effects Between Single-Source and Multiple-Source Systems.

    Science.gov (United States)

    Bae, Jaeyong; Rask, Kimberly J; Becker, Edmund R

    The objective was to examine differential impacts between single-source and multiple-source electronic medical record (EMR) systems, as measured by number of vendor products, on hospital-acquired patient safety events. The data source was the 2009-2010 State Inpatient Databases of the Healthcare Cost and Utilization Project for California, New York, and Florida, and the Information Technology Supplement to the American Hospital Association's Annual Survey. Multivariable regression analyses were conducted to estimate the differential impacts of EMRs between single-source and multiple-source EMR systems on hospital-acquired patient safety events. In all, 1.98% of adult surgery hospitalizations had at least 1 hospital-acquired patient safety event. Basic EMRs with a single vendor or self-developed EMR systems were associated with a significant decrease in patient safety events by 0.38 percentage point, or 19.2%, whereas basic EMRs with multiple vendors had an insignificant association. A single-source EMR system enhances the impact of EMRs on reducing patient safety events.

  7. In vivo single-voxel proton MR spectroscopy in the differentiation of high-grade gliomas and solitary metastases

    International Nuclear Information System (INIS)

    Fan, G.; Sun, B.; Wu, Z.; Guo, Q.; Guo, Y.

    2004-01-01

    AIM: To determine whether single-voxel proton magnetic resonance spectroscopy (1HMRS) could be used to differentiate gliomas from metastases on the basis of differences in metabolite levels in the different involved regions. MATERIALS AND METHODS: Twenty-two patients (age range from 32 to 62 years, with a median age of 46.7 years) with a solitary brain tumour (14 gliomas, eight metastases) underwent conventional, gadolinium-DTPA enhanced T1-weighted images, and 1HMRS before surgical resection. Spectra from the enhancing tumour, the peritumoural region, and normal brain were obtained from 1HMRS. A point resolved spectroscopy sequence was required for 1HMRS. The metabolites in the spectra include: N-acetylaspartate (NAA), choline (CHO), creatine compounds (CR), myo-inositol (MI), lactate (LAC), glutamate and glutamine (Glu-n). Relative concentrations of metabolites were related to the peak area, and expressed with reference to CR. Student's t-test was used to determine whether there was a statistically significant difference in relative metabolic ratios between high-grade gliomas and metastases. Meanwhile, 16 of all 22 patients were re-examined using magnetic resonance imaging (MRI) within 6 months of surgical resection. Recurrence was present in three patients (two gliomas, one metastasis). RESULTS: Of the 14 patients with gliomas, the peaks of NAA were reduced in three cases; the peaks of LAC, which were elevated, appeared as typical double-peaks in the peritumoural region in nine cases; the peaks of Glu-n, which were also elevated, had a zigzag appearance in seven cases. The peaks of MI were increased in the tumoural region in eight cases, and CHO levels were elevated in all 14 cases. Of the eight patients with metastases, Glu-n peaks in the tumoural region in three cases and CHO peaks in the tumoural region in four cases were elevated, respectively, while the peaks of CR were reduced in three cases, and the peaks of NAA were markedly reduced in four cases within

  8. Nonlinear optimization

    CERN Document Server

    Ruszczynski, Andrzej

    2011-01-01

    Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...

  9. Single-Cell Gene Expression Analysis of a Human ESC Model of Pancreatic Endocrine Development Reveals Different Paths to β-Cell Differentiation.

    Science.gov (United States)

    Petersen, Maja Borup Kjær; Azad, Ajuna; Ingvorsen, Camilla; Hess, Katja; Hansson, Mattias; Grapin-Botton, Anne; Honoré, Christian

    2017-10-10

    The production of insulin-producing β cells from human embryonic stem cells (hESCs) in vitro represents a promising strategy for a cell-based therapy for type 1 diabetes mellitus. To explore the cellular heterogeneity and temporal progression of endocrine progenitors and their progeny, we performed single-cell qPCR on more than 500 cells across several stages of in vitro differentiation of hESCs and compared them with human islets. We reveal distinct subpopulations along the endocrine differentiation path and an early lineage bifurcation toward either polyhormonal cells or β-like cells. We uncover several similarities and differences with mouse development and reveal that cells can take multiple paths to the same differentiation state, a principle that could be relevant to other systems. Notably, activation of the key β-cell transcription factor NKX6.1 can be initiated before or after endocrine commitment. The single-cell temporal resolution we provide can be used to improve the production of functional β cells. Copyright © 2017 The Author(s). Published by Elsevier Inc. All rights reserved.

  10. Mathematical modeling and applications in nonlinear dynamics

    CERN Document Server

    Merdan, Hüseyin

    2016-01-01

    The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

  11. Frequency-dependent linear and non-linear response properties of single carrier quantum dots: Role of effective mass and anharmonicity in the confinement potential

    Energy Technology Data Exchange (ETDEWEB)

    Mandal, Parikshit [Department of Chemistry, Physical Chemistry Section, Visva Bharati University, Santiniketan, Birbhum 731 235, West Bengal (India); Ghosh, Manas [Department of Chemistry, Physical Chemistry Section, Visva Bharati University, Santiniketan, Birbhum 731 235, West Bengal (India)], E-mail: pcmg77@rediffmail.com

    2008-09-01

    We explore the pattern of frequency-dependent linear and non-linear optical (NLO) response of one electron quantum dots harmonically confined in two dimensions. For some fixed values of transverse magnetic field strength ({omega}{sub c}), and harmonic confinement potential ({omega}{sub 0}), the influence of effective mass (m*) of the system and the symmetry breaking anharmonic interaction on the frequency-dependent linear ({alpha}), and the first ({beta}), and second ({gamma}) NLO responses of the dot is computed through linear variational route. The investigation reveals interesting roles played by the anharmonic interaction and effective mass in modulating the response properties.

  12. The density functional study of electronic structure, electronic charge density, linear and nonlinear optical properties of single crystal alpha-LiAlTe{sub 2}

    Energy Technology Data Exchange (ETDEWEB)

    Reshak, A.H. [New Technologies-Research Center, University of West Bohemia, Univerzitni 8, 306 14 Pilsen (Czech Republic); Center of Excellence Geopolymer and Green Technology, School of Material Engineering, University Malaysia Perlis, 01007 Kangar, Perlis (Malaysia); Khan, Wilayat, E-mail: walayat76@gmail.com [New Technologies-Research Center, University of West Bohemia, Univerzitni 8, 306 14 Pilsen (Czech Republic)

    2014-04-01

    Highlights: • FP-LAPW technique is used for calculating the electronic structure. • The band structure shows that the calculated compound is semiconductor. • The complex dielectric function has been calculated. • Nonlinear optical properties has also been calculated. • This compound can be used for molecular engineering of the crystals. - Abstract: Self-consistent calculations is performed using the full potential linear augmented plane wave (FP-LAPW) technique based on density functional theory (DFT) to investigate the electronic band structure, density of states, electronic charge density, linear and non-linear optical properties of α-LiAlTe{sub 2} compound having tetragonal symmetry with space group I4{sup ¯}2d. The electronic structure are calculated using the Ceperley Alder local density approach (CA-LDA), Perdew Burke and Ernzerhof generalize gradient approach (PBE-GGA), Engel–Vosko generalize gradient approach (EVGGA) and modified Becke Johnson approach (mBJ). Band structure calculations of (α-LiAlTe{sub 2}) depict semiconducting nature with direct band gap of 2.35 eV (LDA), 2.48 eV (GGA), 3.05 eV (EVGGA) and 3.13 eV (mBJ), which is comparable to experimental value. The calculated electronic charge density show ionic interaction between Te and Li atoms and polar covalent interaction between Al and Te atoms. Some optical susceptibilities like dielectric constants, refractive index, extension co-efficient, reflectivity and energy loss function have been calculated and analyzed on the basis of electronic structure. The compound α-LiAlTe{sub 2} provides a considerable negative value of birefringence of −0.01. Any anisotropy observed in the linear optical properties which are in favor to enhance the nonlinear optical properties. The symbol χ{sub abc}{sup (2)}(ω) represents the second order nonlinear optical susceptibilities, possess six non-zero components in this symmetry (tetragonal), called: 1 2 3, 2 1 3, 2 3 1, 1 3 2, 3 1 2 and 3 2 1

  13. Nonlinear free vibration control of beams using acceleration delayed-feedback control

    International Nuclear Information System (INIS)

    Alhazza, Khaled A; Alajmi, Mohammed; Masoud, Ziyad N

    2008-01-01

    A single-mode delayed-feedback control strategy is developed to reduce the free vibrations of a flexible beam using a piezoelectric actuator. A nonlinear variational model of the beam based on the von Kàrmàn nonlinear type deformations is considered. Using Galerkin's method, the resulting governing partial differential equations of motion are reduced to a system of nonlinear ordinary differential equations. A linear model using the first mode is derived and is used to characterize the damping produced by the controller as a function of the controller's gain and delay. Three-dimensional figures showing the damping magnitude as a function of the controller gain and delay are presented. The characteristic damping of the controller as predicted by the linear model is compared to that calculated using direct long-time integration of a three-mode nonlinear model. Optimal values of the controller gain and delay using both methods are obtained, simulated and compared. To validate the single-mode approximation, numerical simulations are performed using a three-mode full nonlinear model. Results of the simulations demonstrate an excellent controller performance in mitigating the first-mode vibration

  14. MHD flow and nonlinear radiative heat transfer of Sisko nanofluid over a nonlinear stretching sheet

    Directory of Open Access Journals (Sweden)

    B.C. Prasannakumara

    2017-01-01

    Full Text Available The problem of heat and mass transfer of Siskonanofluid flow over a nonlinear stretching sheet under the influence of nonlinear thermal radiation and chemical reaction is considered. suitable set of similarity transformations are implemented to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. An efficient Runge–Kutta–Fehlberg fourth–fifth order method along with shooting technique is employed to solve the reduced equations. The influence of several emerging physical parameters on velocity, temperature and concentration profiles for both linear and nonlinear stretching sheet in the presence of linear and nonlinear thermal radiation has been studied and analyzed through plotted graphs and tables in detail. It is found that the Nusselt and Sherwood number are high in case of nonlinear stretching sheet than linear. Further, it is observed that the nonlinear thermal radiation has more influence on temperature profiles than linear.

  15. Numerical treatment of a nonlinear hyperbolic equation

    Directory of Open Access Journals (Sweden)

    Nabiha Brik

    2017-03-01

    Full Text Available In this work we consider a nonlinear elliptic partial differential equation, which is derived from an application of a nonlinear Schrödinger equation. Using a variational approach on this problem leads to an optimization problem with a nonlinear constraint. A numerical solution based on finite-element method is used. We propose a new iterative algorithm to relax this problem to a quadratic version.

  16. Differential manifolds

    CERN Document Server

    Kosinski, Antoni A

    2007-01-01

    The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.""How useful it is,"" noted the Bulletin of the American Mathematical Society, ""to have a single, sho

  17. Nonlinear integral inequality in two independent variables

    Directory of Open Access Journals (Sweden)

    P. T. Vaz

    1988-01-01

    Full Text Available In this note, the authors obtain a generalization of the integral inequality of Bihari [1] to a nonlinear inequality in two independent variables. With the aid of this inequality a bound for the solution of a nonlinear partial differential equation is established.

  18. Nonlinear Dynamics: Maps, Integrators and Solitons

    Energy Technology Data Exchange (ETDEWEB)

    Parsa, Z.

    1998-10-01

    For many physical systems of interest in various disciplines, the solution to nonlinear differential equations describing the physical systems can be generated using maps, symplectic integrators and solitons. We discuss these methods and apply them for various examples.

  19. Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

    Directory of Open Access Journals (Sweden)

    Ahmed HamdyM

    2010-01-01

    Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.

  20. Nonlinearity management and diffraction management for the ...

    Indian Academy of Sciences (India)

    Variational equations and partial differential equation have been simulated numerically. Analytical and numerical studies have shown that nonlinearity management and diffraction management stabilize the pulse against decay or collapse providing undisturbed propagation even for larger energies of the incident beam.