Can a Chaotic Solution in the QCD Evolution Equation Restrain High-Energy Collider Physics?
ZHU Wei; SHEN Zhen-Qi; RUAN Jian-Hong
2008-01-01
We indicate that the random aperiodic oscillation of the gluon distributions in a modified Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation has positive Lyapunov exponents. This first example of chaos in QCD evolution equations raises the sudden disappearance of the gluon distributions at a critical small value of the Bjorken variable x and may stop the increase of the new particle events in an ultra high energy hadron collider.
On restraining convective subgrid-scale production in Burgers’ equation
Helder, Joop; Verstappen, Roel
2008-01-01
Since most turbulent flows cannot be computed directly from the (incompressible) Navier–Stokes equations, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider nonlinear approximations of the convective term that preserve the symmetry and con
On restraining convective subgrid-scale production in Burgers' equation
Helder, Joop; Verstappen, Roel
2008-01-01
Since most turbulent flows cannot be computed directly from the (incompressible) Navier-Stokes equations, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider nonlinear approximations of the convective term that preserve the symmetry and con
Boussinesq evolution equations
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
Discovering evolution equations with applications
McKibben, Mark
2011-01-01
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochast
Mode decomposition evolution equations.
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2012-03-01
Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be
Nonlinear evolution equations in QCD
Stasto, A. M.
2004-01-01
The following lectures are an introduction to the phenomena of partonic saturation and nonlinear evolution equations in Quantum Chromodynamics. After a short introduction to the linear evolution, the problems of unitarity bound and parton saturation are discussed. The nonlinear Balitsky-Kovchegov evolution equation in the high energy limit is introduced, and the progress towards the understanding of the properties of its solution is reviewed. We discuss the concepts of the saturation scale, g...
A New Unified Evolution Equation
1998-01-01
WE propose a new unified evolution equation for parton distribution functions appropriate for both large and small Bjorken x. Compared with the Ciafaloni- Catani-Fiorani-Marchesini equation, the cancellation of soft poles between virtual and real gluon emissions is made explicitly without introducing infrared cutoffs, next-to-leading contributions to the Sudakov resummation can be included systematically, and the scales of the running coupling constants are determined unambiguously.
Nonlocal higher order evolution equations
Rossi, Julio D.
2010-06-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
Stochastic Evolution Equations with Adapted Drift
Pronk, M.
2013-01-01
In this thesis we study stochastic evolution equations in Banach spaces. We restrict ourselves to the two following cases. First, we consider equations in which the drift is a closed linear operator that depends on time and is random. Such equations occur as mathematical models in for instance
Balitsky-JIMWLK evolution equation at NLO
Chirilli Giovanni Antonio
2014-01-01
Full Text Available Wilson line operators are infinite gauge factors ordered along the straight lines of the fast moving particles. Scattering amplitudes of proton-Nucleus or Nucleus-Nucleus collisions at high-energy are written in terms of matrix elements of these operators and the energy dependence of such amplitudes is obtained by the evolution equation with respect to the rapidity parameter: the Balitsky-JIMWLK evolution equation. A brief description of the derivation of the Balitsky-JIMWLK evolution equation at leading order and nextto-leading order will be presented.
Infrared Evolution Equations: Method and Applications
Ermolaev, B. I.; Greco, M; Troyan, S. I.
2007-01-01
It is a brief review on composing and solving Infrared Evolution Equations. They can be used in order to calculate amplitudes of high-energy reactions in different kinematic regions in the double-logarithmic approximation.
Quasilinear evolution equations of the third order
Andrei V. Faminskii
2007-11-01
Full Text Available The present paper is a survey concerned with certain aspects of solvability and well-posedness of initial and initial-boundary value problems for various quasilinear evolution equations of the third order. This class includes, for example, Korteweg-de Vries (KdV and Zakharov-Kuznetsov (ZK equations.
Stochastic equations of evolution of channeled particles
Koshcheev, V P
2001-01-01
The stochastic equations of evolution of lateral energy of the fast charged channeled particles is obtained from the condition of nonpreservation of the adiabatic invariant. The electric potential of the crystal is presented in form of the sum of its average value and the potential fluctuation, caused by the thermal oscillations of the atomic nuclei and the quantum fluctuations of the atomic electrons. The problem is solved for the cases of the planar and axial channeling of the fast charged particles. The Fokker-Planck equation may easily plotted on the basis of the stochastic equation for evolution of the lateral energy
Advanced functional evolution equations and inclusions
Benchohra, Mouffak
2015-01-01
This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.
QCD evolution equations from conformal symmetry
Braun, V M
2014-01-01
QCD evolution equations in $\\text{MS}$-like schemes can be recovered from the same equations in a modified theory, QCD in non-integer $d=4-2\\epsilon$ dimensions, which enjoys exact scale and conformal invariance at the critical point. Restrictions imposed by the conformal symmetry of the modified theory allow one to obtain complete evolution kernels in integer (physical) dimensions at the given order of perturbation theory from the spectrum of anomalous dimensions added by the calculation of the special conformal anomaly at one order less. We use this technique to derive two-loop evolution equations for flavor-nonsinglet quark-antiquark light-ray operators that encode the scale dependence of generalized hadron parton distributions.
Antiperiodic Problems for Nonautonomous Parabolic Evolution Equations
R. N. Wang
2014-01-01
Full Text Available This work focuses on the antiperiodic problem of nonautonomous semilinear parabolic evolution equation in the form u′(t=A(tu(t+f(t,u(t, t∈R, u(t+T=-u(t, t∈R, where (Att∈R (possibly unbounded, depending on time, is a family of closed and densely defined linear operators on a Banach space X. Upon making some suitable assumptions such as the Acquistapace and Terreni conditions and exponential dichotomy on (Att∈R, we obtain the existence results of antiperiodic mild solutions to such problem. The antiperiodic problem of nonautonomous semilinear parabolic evolution equation of neutral type is also considered. As sample of application, these results are applied to, at the end of the paper, an antiperiodic problem for partial differential equation, whose operators in the linear part generate an evolution family of exponential stability.
Moving interfaces and quasilinear parabolic evolution equations
Prüss, Jan
2016-01-01
In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions...
Emmy Noether and Linear Evolution Equations
P. G. L. Leach
2013-01-01
Full Text Available Noether’s Theorem relates the Action Integral of a Lagrangian with symmetries which leave it invariant and the first integrals consequent upon the variational principle and the existence of the symmetries. These each have an equivalent in the Schrödinger Equation corresponding to the Lagrangian and by extension to linear evolution equations in general. The implications of these connections are investigated.
Evolution equations of von Karman type
Cherrier, Pascal
2015-01-01
In these notes we consider two kinds of nonlinear evolution problems of von Karman type on Euclidean spaces of arbitrary even dimension. Each of these problems consists of a system that results from the coupling of two highly nonlinear partial differential equations, one hyperbolic or parabolic and the other elliptic. These systems take their name from a formal analogy with the von Karman equations in the theory of elasticity in two dimensional space. We establish local (respectively global) results for strong (resp., weak) solutions of these problems and corresponding well-posedness results in the Hadamard sense. Results are found by obtaining regularity estimates on solutions which are limits of a suitable Galerkin approximation scheme. The book is intended as a pedagogical introduction to a number of meaningful application of classical methods in nonlinear Partial Differential Equations of Evolution. The material is self-contained and most proofs are given in full detail. The interested reader will gain a ...
Spatial evolution equation of wind wave growth
王伟; 孙孚; 戴德君
2003-01-01
Based on the dynamic essence of air-sea interactions, a feedback type of spatial evolution equation is suggested to match reasonably the growing process of wind waves. This simple equation involving the dominant factors of wind wave growth is able to explain the transfer of energy from high to low frequencies without introducing the concept of nonlinear wave-wave interactions, and the results agree well with observations. The rate of wave height growth derived in this dissertation is applicable to both laboratory and open sea, which solidifies the physical basis of using laboratory experiments to investigate the generation of wind waves. Thus the proposed spatial evolution equation provides a new approach for the research on dynamic mechanism of air-sea interactions and wind wave prediction.
Unpolarized coupled DGLAP evolution equation at small-
Saurav Bhattacharjee; Ranjit Baishya; Jayanata Kumar Sarma
2013-01-01
In this paper, we have obtained the solution of the unpolarized coupled Dokshitzer–Gribove–Lipatov–Alterelli–Parisi (DGLAP) evolution equation in leading order at the small- limit. Here, we have used a Taylor series expansion, separation of functions and then the method of characteristics to solve the evolution equations. We have also calculated -evolution of singlet and gluon distribution functions and the results are compared with E665 and NNPDF data for singlet structure function and GRV1998 and MRST2004 gluon parametrizations. It is shown that our results are in good agreement with the parametrizations especially at small-x and high-2 region. From global parametrizations and our results, we have seen that the singlet and gluon distribution functions increase when 2 increases for fixed values of .
Semigroup methods for evolution equations on networks
Mugnolo, Delio
2014-01-01
This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations. Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations. This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to ellip...
E. M. E. Zayed
2014-01-01
Full Text Available We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
TAYLOR EXPANSION METHOD FOR NONLINEAR EVOLUTION EQUATIONS
HE Yin-nian
2005-01-01
A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0-th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1-st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example,namely, the two-dimensional Navier-Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.
Nonsmooth analysis of doubly nonlinear evolution equations
Mielke, Alexander; Savare', Giuseppe
2011-01-01
In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy functional,for existence of solutions to the related Cauchy problem. We prove our main existence result by passing to the limit in a time-discretization scheme with variational techniques. Finally, we discuss an application to a material model in finite-strain elasticity.
Effective evolution equations from quantum dynamics
Benedikter, Niels; Schlein, Benjamin
2016-01-01
These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems and their time evolution. Section 2 introduces the mean-field regime for bosonic systems and explains how the many-body dynamics can be approximated in this limit using the Hartree equation. Section 3 presents a method, based on the use of coherent states, for rigorously proving the convergence towards the Hartree dynamics, while the fluctuations around the Hartree equation are considered in Section 4. Section 5 focuses on a discussion of a more subtle regime, in which the many-body evolution can be approximated by means of t...
Integral solutions of fractional evolution equations with nondense domain
Haibo Gu
2017-06-01
Full Text Available In this article, we study the existence of integral solutions for two classes of fractional order evolution equations with nondensely defined linear operators. First, we consider the nonhomogeneous fractional order evolution equation and obtain its integral solution by Laplace transform and probability density function. Subsequently, based on the form of integral solution for nonhomogeneous fractional order evolution equation, we investigate the existence of integral solution for nonlinear fractional order evolution equation by noncompact measure method.
DYNAMIC BIFURCATION OF NONLINEAR EVOLUTION EQUATIONS
MA TIAN; WANG SHOUHONG
2005-01-01
The authors introduce a notion of dynamic bifurcation for nonlinear evolution equations, which can be called attractor bifurcation. It is proved that as the control parameter crosses certain critical value, the system bifurcates from a trivial steady state solution to an attractor with dimension between m and m + 1, where m + 1 is the number of eigenvalues crossing the imaginary axis. The attractor bifurcation theory presented in this article generalizes the existing steady state bifurcations and the Hopf bifurcations. It provides a unified point of view on dynamic bifurcation and can be applied to many problems in physics and mechanics.
Existence families, functional calculi and evolution equations
deLaubenfels, Ralph
1994-01-01
This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, ...
Dynamic Evolution Equations for Isolated Smoke Vortexes in Rational Mechanics
Jianhua, Xiao
2011-01-01
Smoke circle vortexes are a typical dynamic phenomenon in nature. The similar circle vortexes phenomenon appears in hurricane, turbulence, and many others. A semi-empirical method is constructed to get some intrinsic understanding about such circle vortex structures. Firstly, the geometrical motion equations for smoke circle is formulated based on empirical observations. Based on them, the mechanic dynamic motion equations are established. Finally, the general dynamic evolution equations for smoke vortex are formulated. They are dynamic evolution equations for exact stress field and dynamic evolution equations for average stress field. For industrial application and experimental data processing, their corresponding approximation equations for viscous fluid are given. Some simple discussions are made.
ANALYTICAL SOLUTIONS FOR SOME NONLINEAR EVOLUTION EQUATIONS
胡建兰; 张汉林
2003-01-01
The following partial differential equations are studied: generaliz ed fifth-orderKdV equation, water wave equation, Kupershmidt equation, couples KdV equation. Theanalytical solutions to these problems via using various ansaiz es by introducing a second-order ordinary differential equation are found out.
无
2006-01-01
A trial equation method to nonlinear evolution equation with rank inhomogeneous is given. As applications, the exact traveling wave solutions to some higher-order nonlinear equations such as generalized Boussinesq equation,generalized Pochhammer-Chree equation, KdV-Burgers equation, and KS equation and so on, are obtained. Among these, some results are new. The proposed method is based on the idea of reduction of the order of ODE. Some mathematical details of the proposed method are discussed.
Some new solutions of nonlinear evolution equations with variable coefficients
Virdi, Jasvinder Singh
2016-05-01
We construct the traveling wave solutions of nonlinear evolution equations (NLEEs) with variable coefficients arising in physics. Some interesting nonlinear evolution equations are investigated by traveling wave solutions which are expressed by the hyperbolic functions, the trigonometric functions and rational functions. The applied method will be used in further works to establish more entirely new solutions for other kinds of such nonlinear evolution equations with variable coefficients arising in physics.
Approximate Generalized Conditional Symmetries for Perturbed Evolution Equations
ZHANG Shun-Li; WANG Yong; LOU Sen-Yue
2007-01-01
The concept of approximate generalized conditional symmetry (AGCS) for the perturbed evolution equations is introduced, and how to derive approximate conditional invariant solutions to the perturbed equations via their AGCSs is illustrated with examples.
Controllability of quasilinear stochastic evolution equations in Hilbert spaces
P. Balasubramaniam
2001-01-01
Full Text Available Controllability of the quasilinear stochastic evolution equation is studied using semigroup theory and a stochastic version of the well known fixed point theorem. An application to stochastic partial differential equations is given.
Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations
Ren, Jiagang; Zhang, Xicheng
2008-01-01
We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result can be used to deal with a large class of quasi linear stochastic partial differential equations, such as stochastic porous medium equations and stochastic reaction diffusion equations with polynomial growth zero order term and $p$-Laplacian second order term.
The chaotic effects in a nonlinear QCD evolution equation
Zhu, Wei; Shen, Zhenqi; Ruan, Jianhong
2016-10-01
The corrections of gluon fusion to the DGLAP and BFKL equations are discussed in a united partonic framework. The resulting nonlinear evolution equations are the well-known GLR-MQ-ZRS equation and a new evolution equation. Using the available saturation models as input, we find that the new evolution equation has the chaos solution with positive Lyapunov exponents in the perturbative range. We predict a new kind of shadowing caused by chaos, which blocks the QCD evolution in a critical small x range. The blocking effect in the evolution equation may explain the Abelian gluon assumption and even influence our expectations to the projected Large Hadron Electron Collider (LHeC), Very Large Hadron Collider (VLHC) and the upgrade (CppC) in a circular e+e- collider (SppC).
Yusuf Gurefe; Abdullah Sonmezoglu; Emine Misirli
2011-12-01
In this paper some exact solutions including soliton solutions for the KdV equation with dual power law nonlinearity and the (, ) equation with generalized evolution are obtained using the trial equation method. Also a more general trial equation method is proposed.
Travelling wave solutions for ( + 1)-dimensional nonlinear evolution equations
Jonu Lee; Rathinasamy Sakthivel
2010-10-01
In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of ( + 1)-dimensional nonlinear evolution equations. Four models, the ( + 1)-dimensional generalized Boussinesq equation, ( + 1)-dimensional sine-cosine-Gordon equation, ( + 1)-double sinh-Gordon equation and ( + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.
Existence of solutions of abstract fractional impulsive semilinear evolution equations
K. Balachandran
2010-01-01
Full Text Available In this paper we prove the existence of solutions of fractional impulsive semilinear evolution equations in Banach spaces. A nonlocal Cauchy problem is discussed for the evolution equations. The results are obtained using fractional calculus and fixed point theorems. An example is provided to illustrate the theory.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
EXACT SOLITARY WAVE SOLUTIONS OF THETWO NONLINEAR EVOLUTION EQUATIONS
ZhuYanjuan; ZhangChunhua
2005-01-01
The solitary wave solutions of the combined KdV-mKdV-Burgers equation and the Kolmogorov-Petrovskii-Piskunov equation are obtained by means of the direct algebra method, which can be generalized to deal with high dimensional nonlinear evolution equations.
Extension of Variable Separable Solutions for Nonlinear Evolution Equations
JIA Hua-Bing; ZHANG Shun-Li; XU Wei; ZHU Xiao-Ning; WANG Yong-Mao; LOU Sen-Yue
2008-01-01
We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separablecation, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.
The fundamental solutions for fractional evolution equations of parabolic type
Mahmoud M. El-Borai
2004-01-01
Full Text Available The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.
A new application of Riccati equation to some nonlinear evolution equations
Geng Tao [School of Science, PO Box 122, Beijing University of Posts and Telecommunications, Beijing 100876 (China)], E-mail: taogeng@yahoo.com.cn; Shan Wenrui [School of Science, PO Box 122, Beijing University of Posts and Telecommunications, Beijing 100876 (China)
2008-03-03
By means of symbolic computation, a new application of Riccati equation is presented to obtain novel exact solutions of some nonlinear evolution equations, such as nonlinear Klein-Gordon equation, generalized Pochhammer-Chree equation and nonlinear Schroedinger equation. Comparing with the existing tanh methods and the proposed modifications, we obtain the exact solutions in the form as a non-integer power polynomial of tanh (or tan) functions by using this method, and the availability of symbolic computation is demonstrated.
WANG Mei-Jiao; WANG Qi
2006-01-01
In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions' soliton-like solutions and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.
Preliminary group classification of quasilinear third-order evolution equations
Ding-jiang HUANG; Hong-qing ZHANG
2009-01-01
Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transfor-mations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non-equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.
QCD evolution equations for high energy partons in nuclear matter
Kinder-Geiger, Klaus; Geiger, Klaus; Mueller, Berndt
1994-01-01
We derive a generalized form of Altarelli-Parisi equations to decribe the time evolution of parton distributions in a nuclear medium. In the framework of the leading logarithmic approximation, we obtain a set of coupled integro- differential equations for the parton distribution functions and equations for the virtuality (``age'') distribution of partons. In addition to parton branching processes, we take into account fusion and scattering processes that are specific to QCD in medium. Detailed balance between gain and loss terms in the resulting evolution equations correctly accounts for both real and virtual contributions which yields a natural cancellation of infrared divergences.
CAUCHY PROBLEM OF ONE TYPE OF ATMOSPHERE EVOLUTION EQUATIONS
HE Juan-xiong; HE You-hua
2006-01-01
One type of evolution atmosphere equations was discussed. It is found that according to the stratification theory, (i) the inertial force has no influence on the criterion of the well-posed Cauchy problem; (ii) the compressibility plays no role on the well-posed condition of the Cauchy problem of the viscid atmosphere equations, but changes the well-posed condition of the viscid atmosphere equations; (iii) this type of atmosphere evolution equations is ill-posed on the hyperplane t = 0 in spite of its compressibility and viscosity; (iv) the Cauchy problem of compressible viscosity atmosphere with still initial motion is ill-posed.
Long term dynamics of stochastic evolution equations
Bierkens, Gregorius Nicolaas Johannes Cornelis
2010-01-01
Stochastic differential equations with delay are the inspiration for this thesis. Examples of such equations arise in population models, control systems with delay and noise, lasers, economical models, neural networks, environmental pollution and in many other situations. In such models we are often
Long term dynamics of stochastic evolution equations
Bierkens, Gregorius Nicolaas Johannes Cornelis
2010-01-01
Stochastic differential equations with delay are the inspiration for this thesis. Examples of such equations arise in population models, control systems with delay and noise, lasers, economical models, neural networks, environmental pollution and in many other situations. In such models we are often
Lectures on nonlinear evolution equations initial value problems
Racke, Reinhard
2015-01-01
This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...
Physical entropy, information entropy and their evolution equations
无
2001-01-01
Inspired by the evolution equation of nonequilibrium statistical physics entropy and the concise statistical formula of the entropy production rate, we develop a theory of the dynamic information entropy and build a nonlinear evolution equation of the information entropy density changing in time and state variable space. Its mathematical form and physical meaning are similar to the evolution equation of the physical entropy: The time rate of change of information entropy density originates together from drift, diffusion and production. The concise statistical formula of information entropy production rate is similar to that of physical entropy also. Furthermore, we study the similarity and difference between physical entropy and information entropy and the possible unification of the two statistical entropies, and discuss the relationship among the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy as well as the connection between them and the entropy evolution equation.
Some remarks on a second order evolution equation
Mohammed Aassila
1998-07-01
Full Text Available We prove the strong asymptotic stability of solutions to a second order evolution equation when the LaSalle's invariance principle cannot be applied due to the lack of monotonicity and compactness.
Linearizing neutrino evolution equations including neutrino-antineutrino pairing correlations
Väänänen, D
2013-01-01
We linearize the neutrino mean-field evolution equations describing the neutrino propagation in a background of matter and of neutrinos, using techniques from many-body microscopic approaches. The procedure leads to an eigenvalue equation that allows to identify instabilities in the evolution, associated with a change of the curvature of the neutrino energy-density surface. Our result includes all contributions from the neutrino Hamiltonian and is generalizable to linearize the equations of motion at an arbitrary point of the evolution. We then consider the extended equations that comprise the normal mean field as well as the abnormal mean field that is associated with neutrino-antineutrino pairing correlations. We first re-derive the extended neutrino Hamiltonian and show that such a Hamiltonian can be diagonalized by introducing a generalized Bogoliubov transformation with quasi-particle operators that mix neutrinos and antineutrinos. We give the eigenvalue equations that determine the energies of the quasi...
Modelling of nonlinear shoaling based on stochastic evolution equations
Kofoed-Hansen, Henrik; Rasmussen, Jørgen Hvenekær
1998-01-01
A one-dimensional stochastic model is derived to simulate the transformation of wave spectra in shallow water including generation of bound sub- and super-harmonics, near-resonant triad wave interaction and wave breaking. Boussinesq type equations with improved linear dispersion characteristics...... are recast into evolution equations for the complex amplitudes, and serve as the underlying deterministic model. Next, a set of evolution equations for the cumulants is derived. By formally introducing the well-known Gaussian closure hypothesis, nonlinear evolution equations for the power spectrum...... and bispectrum are derived. A simple description of depth-induced wave breaking is incorporated in the model equations, assuming that the total rate of dissipation may be distributed in proportion to the spectral energy density on each discrete frequency. The proposed phase-averaged model is compared...
Symmetries and (Related Recursion Operators of Linear Evolution Equations
Giampaolo Cicogna
2010-02-01
Full Text Available Significant cases of time-evolution equations, the linear Schr¨odinger and the Fokker–Planck equation are considered. It is known that equations of this type can be transformed, in some cases, into a highly simplified form. The properties of these equations in their initial and their simplified form are compared, showing in particular that this transformation partially prevents a clear understanding and a full application of the (physically relevant notion of the so-called step up/down operators. These operators are shown to be recursion operators, related to the Lie point symmetries of the equations, which are also carefully discussed.
NEW EXACT TRAVELLING WAVE SOLUTIONS TO THREE NONLINEAR EVOLUTION EQUATIONS
Sirendaoreji
2004-01-01
Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation.
THE NONLOCAL INITIAL PROBLEMS OF A SEMILINEAR EVOLUTION EQUATION
王远弟; 冉启康
2004-01-01
The purpose of this paper is to investigate the existence of solutions to a nonlocal Cauchy problem for an evolution equation. The methods used here include the abstract semigroup methods in proper spaces and Schauder's theorem.And the abstract results are applied to a system of nonlinear partial differential equations with nonlinear boundary conditions.
Heat polynomial analogs for higher order evolution equations
G. N. Hile
2001-05-01
Full Text Available Polynomial solutions analogous to the heat polynomials are demonstrated for higher order linear homogeneous evolution equations with coefficients depending on the time variable. Further parallels with the heat polynomials are established when the equation is parabolic with constant coefficients and only highest order terms.
A variational approach to nonlinear evolution equations in optics
D Anderson; M Lisak; A Berntson
2001-11-01
A tutorial review is presented of the use of direct variational methods based on RayleighRitz optimization for ﬁnding approximate solutions to various nonlinear evolution equations. The practical application of the approach is demonstrated by some illustrative examples in connection with the nonlinear Schrödinger equation.
Exact null controllability of degenerate evolution equations with scalar control
Fedorov, Vladimir E; Shklyar, Benzion
2012-12-31
Necessary and sufficient conditions for the exact null controllability of a degenerate linear evolution equation with scalar control are obtained. These general results are used to examine the exact null controllability of the Dzektser equation in the theory of seepage. Bibliography: 13 titles.
Prolongation Structure of Semi-discrete Nonlinear Evolution Equations
无
2007-01-01
Based on noncommutative differential calculus, we present a theory of prolongation structure for semi-discrete nonlinear evolution equations. As an illustrative example, a semi-discrete model of the nonlinear Schr(o)dinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.
Invariant Measures for a Random Evolution Equation with Small Perturbations
Fu Bao XI
2001-01-01
In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equation. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.
Evolution equations for higher moments of angular momentum distributions
Hägler, P
1998-01-01
Based on a sumrule for the nucleon spin we expand quark and gluon orbital angular momentum operators and derive an evolution matrix for higher moments of the corresponding distributions. In combination with the spin-dependent DGLAP-matrix we find a complete set of spin and orbital angular momentum evolution equations.
Construction of Solution for the Third Order Dispersion Evolution Equation
ZHANG Li-xun; LIU Yong-zhi; WANG Kang-ning
2004-01-01
The Golstein's strong solution formula of the second order evolution equation expands to that of the third dispersion equation by the analogy method. The semigroup expressions of its generating operator of the third order dispersion equation are obtained, and the expression to satisfy the semigroup conditions in the three orthogonal Hilbert space of the construction is also proved. Furthermore, the necessary and sufficient conditions of the generating operator's unitary semigroup are given.
Dynamic Evolution Equations for Isolated Smoke Vortexes in Rational Mechanics
2011-01-01
Smoke circle vortexes are a typical dynamic phenomenon in nature. The similar circle vortexes phenomenon appears in hurricane, turbulence, and many others. A semi-empirical method is constructed to get some intrinsic understanding about such circle vortex structures. Firstly, the geometrical motion equations for smoke circle is formulated based on empirical observations. Based on them, the mechanic dynamic motion equations are established. Finally, the general dynamic evolution equations for ...
New travelling wave solutions for nonlinear stochastic evolution equations
Hyunsoo Kim; Rathinasamy Sakthivel
2013-06-01
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic Broer–Kaup equation and stochastic coupled Korteweg–de Vries (KdV) equation. The study highlights the significant features of the method employed and its capability of handling nonlinear stochastic problems.
Landscape evolution models: A review of their fundamental equations
Chen, Alex; Darbon, Jérôme; Morel, Jean-Michel
2014-08-01
This paper reviews the main physical laws proposed in landscape evolution models (LEMs). It discusses first the main partial differential equations involved in these models and their variants. These equations govern water runoff, stream incision, regolith-bedrock interaction, hillslope evolution, and sedimentation. A synthesis of existing LEMs is proposed. It proposes three models with growing complexity and with a growing number of components: two-equation models with only two components, governing water and bedrock evolution; three-equation models with three components where water, bedrock, and sediment interact; and finally models with four equations and four interacting components, namely water, bedrock, suspended sediment, and regolith. This analysis is not a mere compilation of existing LEMs. It attempts at giving the simplest and most general physically consistent set of equations, coping with all requirements stated in LEMs and LEM software. Three issues are in particular addressed and hopefully resolved. The first one is a correct formulation of the water transport equation down slopes. A general formulation for this equation is proposed, coping not only with the simplest form computing the drainage area but also with a sound energy dissipation argument associated with the Saint-Venant shallow water equations. The second issue arises from the coexistence of two competing modes, namely the detachment-limited erosion mode on hillslopes, and the transport-limited sediment transport on river beds. The third issue (linked to the second) is the fact that no conservation law is available for material in these two modes. A simple solution proposed to resolve these issues is the introduction, as suggested by several authors, of an additional variable for suspended sediment load in water. With only three variables and three equations, the above-mentioned contradictions seem to be eliminated. Several numerical experiments on real digital elevation models (DEMs
Approximate Controllability of Fractional Integrodifferential Evolution Equations
R. Ganesh
2013-01-01
Full Text Available This paper addresses the issue of approximate controllability for a class of control system which is represented by nonlinear fractional integrodifferential equations with nonlocal conditions. By using semigroup theory, p-mean continuity and fractional calculations, a set of sufficient conditions, are formulated and proved for the nonlinear fractional control systems. More precisely, the results are established under the assumption that the corresponding linear system is approximately controllable and functions satisfy non-Lipschitz conditions. The results generalize and improve some known results.
On the solution of fractional evolution equations
Kilbas, Anatoly A [Department of Mathematics and Mechanics, Belarusian State University, 220050 Minsk (Belarus); Pierantozzi, Teresa [Departamento de Matematica Aplicada, Facultad de Informatica, Universidad Complutense, E-28040 Madrid (Spain); Trujillo, Juan J [Departamento de Analisis Matematico, Universidad de la Laguna, 38271 La Laguna-Tenerife (Spain); Vazquez, Luis [Departamento de Matematica Aplicada, Facultad de Informatica, Universidad Complutense, E-28040 Madrid (Spain)
2004-03-05
This paper is devoted to the solution of the bi-fractional differential equation ({sup C}D{sup {alpha}}{sub t}u)(t, x) = {lambda}({sup L}D{sup {beta}}{sub x}u)(t, x) (t>0, -{infinity}
Second order evolution equations which describe pseudospherical surfaces
Catalano Ferraioli, D.; de Oliveira Silva, L. A.
2016-06-01
Second order evolution differential equations that describe pseudospherical surfaces are considered. These equations are equivalent to the structure equations of a metric with Gaussian curvature K = - 1, and can be seen as the compatibility condition of an associated sl (2 , R) -valued linear problem, also referred to as a zero curvature representation. Under the assumption that the linear problem is defined by 1-forms ωi =fi1 dx +fi2 dt, i = 1 , 2 , 3, with fij depending on (x , t , z ,z1 ,z2) and such that f21 = η, η ∈ R, we give a complete and explicit classification of equations of the form zt = A (x , t , z) z2 + B (x , t , z ,z1) . According to the classification, these equations are subdivided in three main classes (referred to as Types I-III) together with the corresponding linear problems. Explicit examples of differential equations of each type are determined by choosing certain arbitrary differentiable functions. Svinolupov-Sokolov equations admitting higher weakly nonlinear symmetries, Boltzmann equation and reaction-diffusion equations like Murray equation are some known examples of such equations. Other explicit examples are presented, as well.
Numerical solution of $Q^2$ evolution equations for fragmentation functions
Hirai, M
2011-01-01
Semi-inclusive hadron-production processes are becoming important in high-energy hadron reactions. They are used for investigating properties of quark-hadron matters in heavy-ion collisions, for finding the origin of nucleon spin in polarized lepton-nucleon and nucleon-nucleon reactions, and possibly for finding exotic hadrons. In describing the hadron-production cross sections in high-energy reactions, fragmentation functions are essential quantities. A fragmentation function indicates the probability of producing a hadron from a parton. Its $Q^2$ dependence is described by the standard DGLAP (Dokshitzer-Gribov-Lipatov-Altarelli-Parisi) evolution equations, which are often used in theoretical and experimental analyses of the fragmentation functions and in calculating semi-inclusive cross sections. The DGLAP equations are complicated integro-differential equations, which cannot be solved in an analytical method. In this work, a simple method is employed for solving the evolution equations by using Gauss-Legen...
Periodic feedback stabilization for linear periodic evolution equations
Wang, Gengsheng
2016-01-01
This book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.
New traveling wave solutions for nonlinear evolution equations
El-Wakil, S.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Madkour, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-06-11
The generalized Jacobi elliptic function expansion method is used with a computerized symbolic computation for constructing the new exact traveling wave solutions. The validity and reliability of the method is tested by its applications on a class of nonlinear evolution equations of special interest in mathematical physics. As a result, many exact traveling wave solutions are obtained which include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
Soft-gluon resolution scale in QCD evolution equations
Hautmann, F.; Jung, H.; Lelek, A.; Radescu, V.; Žlebčík, R.
2017-09-01
QCD evolution equations can be recast in terms of parton branching processes. We present a new numerical solution of the equations. We show that this parton-branching solution can be applied to analyze infrared contributions to evolution, order-by-order in the strong coupling αs, as a function of the soft-gluon resolution scale parameter. We examine the cases of transverse-momentum ordering and angular ordering. We illustrate that this approach can be used to treat distributions which depend both on longitudinal and on transverse momenta.
Solitons and periodic solutions to a couple of fractional nonlinear evolution equations
M Mirzazadeh; M Eslami; Anjan Biswas
2014-03-01
This paper studies a couple of fractional nonlinear evolution equations using first integral method. These evolution equations are foam drainage equation and Klein–Gordon equation (KGE), the latter of which is considered in (2 + 1) dimensions. For the fractional evolution, the Jumarie’s modified Riemann–Liouville derivative is considered. Exact solutions to these equations are obtained.
Hierarchically Organized Iterative Solutions of the Evolution Equations in QCD
Jadach, S; Was, Z
2007-01-01
The task of Monte Carlo simulation of the evolution of the parton distributions in QCD and of constructing new parton shower Monte Carlo algorithms requires new way of organizing solutions of the QCD evolution equations, in which quark-gluon transitions on one hand and quark-quark or gluon-gluon transitions (pure gluonstrahlung) on the other hand, are treated separately and differently. This requires certain reorganization of the iterative solutions of the QCD evolution equations and leads to what we refer to as a hierarchic iterative solutions of the evolution equations. We present three formal derivations of such a solution. Results presented here are already used in the other recent works to formulate new MC algorithms for the parton-shower-like implementations of the QCD evolution equations. They are primarily of the non-Markovian type. However, such a solution can be used for the Markovian-type MCs as well. We also comment briefly on the relation of the presented formalism to similar methods used in othe...
Almost Periodic Solutions for Impulsive Fractional Stochastic Evolution Equations
Toufik Guendouzi
2014-08-01
Full Text Available In this paper, we consider the existence of square-mean piecewise almost periodic solutions for impulsive fractional stochastic evolution equations involving Caputo fractional derivative. The main results are obtained by means of the theory of operators semi-group, fractional calculus, fixed point technique and stochastic analysis theory and methods adopted directly from deterministic fractional equations. Some known results are improved and generalized.
Beyer, Horst Reinhard
2007-01-01
The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis. Only some examples require more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Particular stress is on equations of the hyperbolic type since considerably less often treated in the literature. Also, evolution equations from fundamental physics need to be compatible with the theory of special relativity and therefore are of hyperbolic type. Throughout, detailed applications are given to hyperbolic partial differential equations occurring in problems of current theoretical physics, in particular to Hermitian hyperbolic systems. This volume is thus also of interest to readers from theoretical physics.
BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS
彭艳
2014-01-01
In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameterαgoes to zero.
The Peridic Wave Solutions for Two Nonlinear Evolution Equations
ZHANG Jin-Liang; WANG Ming-Liang; CHENG Dong-Ming; FANG Zong-De
2003-01-01
By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobielliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions andthe other type of traveling wave solutions for the system are obtained.
Fractional evolution equation nonlocal problems with noncompact semigroups
Xuping Zhang
2016-01-01
Full Text Available This paper is concerned with the existence results of mild solutions to the nonlocal problem of fractional semilinear integro-differential evolution equations. New existence theorems are obtained by means of the fixed point theorem for condensing maps. The results extend and improve some related results in this direction.
Approximating solutions of neutral stochastic evolution equations with jumps
2009-01-01
In this paper, we establish existence and uniqueness of the mild solutions to a class of neutral stochastic evolution equations driven by Poisson random measures in some Hilbert space. Moreover, we adopt the Faedo-Galerkin scheme to approximate the solutions.
Evolutions of Wave Patterns in Whitham-Broer-Kaup Equation
ZHANG Zheng-Di; BI Qin-Sheng
2009-01-01
Upon investigation of the parameter influence on the structure of WBK equation, transition boundaries are derived. All possible bounded waves as well as the existence conditions are obtained. The evolution of waves with variation of the parameters is discussed in detail, which reveals the bifurcation mechanism between different wave patterns.
Economic Analysis of Traffic Flow with an Evolution Equation
冯苏苇
2005-01-01
Based on two main hypotheses of traffic economical equilibrium and the relationship between traffic density and the demand, an evolution equation of traffic cost was proposed to describe the change of cost under decreasing toll. Economical explanation of the model and a numerical case were given to demonstrate the constraint between the marginal traffic demand and the flow velocity.
Admissible and Restrained Revision
Booth, R; 10.1613/jair.1874
2011-01-01
As partial justification of their framework for iterated belief revision Darwiche and Pearl convincingly argued against Boutiliers natural revision and provided a prototypical revision operator that fits into their scheme. We show that the Darwiche-Pearl arguments lead naturally to the acceptance of a smaller class of operators which we refer to as admissible. Admissible revision ensures that the penultimate input is not ignored completely, thereby eliminating natural revision, but includes the Darwiche-Pearl operator, Nayaks lexicographic revision operator, and a newly introduced operator called restrained revision. We demonstrate that restrained revision is the most conservative of admissible revision operators, effecting as few changes as possible, while lexicographic revision is the least conservative, and point out that restrained revision can also be viewed as a composite operator, consisting of natural revision preceded by an application of a "backwards revision" operator previously studied by Papini. ...
An evolution equation modeling inversion of tulip flames
Dold, J.W. [Univ. of Bristol (United Kingdom). School of Mathematics; Joulin, G. [E.N.S.M.A., Poitiers (France). Lab. d`Energetique et de Detonique
1995-02-01
The authors attempt to reduce the number of physical ingredients needed to model the phenomenon of tulip-flame inversion to a bare minimum. This is achieved by synthesizing the nonlinear, first-order Michelson-Sivashinsky (MS) equation with the second order linear dispersion relation of Landau and Darrieus, which adds only one extra term to the MS equation without changing any of its stationary behavior and without changing its dynamics in the limit of small density change when the MS equation is asymptotically valid. However, as demonstrated by spectral numerical solutions, the resulting second-order nonlinear evolution equation is found to describe the inversion of tulip flames in good qualitative agreement with classical experiments on the phenomenon. This shows that the combined influences of front curvature, geometric nonlinearity and hydrodynamic instability (including its second-order, or inertial effects, which are an essential result of vorticity production at the flame front) are sufficient to reproduce the inversion process.
On the solutions of fractional order of evolution equations
Morales-Delgado, V. F.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.
2017-01-01
In this paper we present a discussion of generalized Cauchy problems in a diffusion wave process, we consider bi-fractional-order evolution equations in the Riemann-Liouville, Liouville-Caputo, and Caputo-Fabrizio sense. Through Fourier transforms and Laplace transform we derive closed-form solutions to the Cauchy problems mentioned above. Similarly, we establish fundamental solutions. Finally, we give an application of the above results to the determination of decompositions of Dirac type for bi-fractional-order equations and write a formula for the moments for the fractional vibration of a beam equation. This type of decomposition allows us to speak of internal degrees of freedom in the vibration of a beam equation.
Multi-soliton rational solutions for some nonlinear evolution equations
Osman Mohamed S.
2016-01-01
Full Text Available The Korteweg-de Vries equation (KdV and the (2+ 1-dimensional Nizhnik-Novikov-Veselov system (NNV are presented. Multi-soliton rational solutions of these equations are obtained via the generalized unified method. The analysis emphasizes the power of this method and its capability of handling completely (or partially integrable equations. Compared with Hirota’s method and the inverse scattering method, the proposed method gives more general exact multi-wave solutions without much additional effort. The results show that, by virtue of symbolic computation, the generalized unified method may provide us with a straightforward and effective mathematical tool for seeking multi-soliton rational solutions for solving many nonlinear evolution equations arising in different branches of sciences.
Parametrization of the QCD coupling in the evolution equations
Ermolaev, B.I. [H. Niewodniczanski Nuclear Physics Institute PAN, 31-342 Krakow (Poland); Ioffe Physico-Technical Institute, 194021 St. Petersburg (Russian Federation)], E-mail: boris.ermolaev@cern.ch; Troyan, S.I. [St. Petersburg Institute of Nuclear Physics, 188300 Gatchina (Russian Federation)
2008-08-21
We examine the parametrization of the QCD coupling in the evolution equations, including DGLAP. Our conclusion is that the well-known parametrization, where the argument of the coupling is k{sub perpendicular}{sup 2}/{beta} or just k{sub perpendicular}{sup 2}, stands only if the lowest integration limit in the transverse momentum space (the starting point {mu}{sup 2} of the Q{sup 2}-evolution) obeys the relation {mu}>>{lambda}{sub QCD}exp({pi}/2), otherwise the coupling should be replaced by the more complicated expression presented in Eq. (29)
Parametrization of the QCD coupling in the Evolution Equations
Ermolaev, B I
2008-01-01
We examine the parametrization of the QCD coupling in the Evolution Equations, including DGLAP. Our conclusion is that the well-known parametrization, where the argument of the coupling is k^2_{\\perp}/\\beta or just k^2_{\\perp}, stands only if the lowest integration limit in the transverse momentum space (the starting point mu^2 of the Q^2 -evolution) obeys the relation mu >> Lambda_{QCD} \\exp {(\\pi/2)}, otherwise the coupling should be replaced by the more complicated expression presented in Eq. (37).
Analytic treatment of nonlinear evolution equations using ﬁrst integral method
Ahmet Bekir; Ömer Ünsal
2012-07-01
In this paper, we show the applicability of the ﬁrst integral method to combined KdV-mKdV equation, Pochhammer–Chree equation and coupled nonlinear evolution equations. The power of this manageable method is conﬁrmed by applying it for three selected nonlinear evolution equations. This approach can also be applied to other nonlinear differential equations.
Phase and precession evolution in the Burgers equation
Buzzicotti, Michele; Biferale, Luca; Bustamante, Miguel D
2015-01-01
We present a phenomenological study of the phase dynamics of the one-dimensional stochastically forced Burgers equation. We propose a way to link coherent structures in real space with the evolution of triads in Fourier space. The method is based on the idea that the real space structures can be associated with entangled correlations amongst the phase precession frequencies and the amplitude evolution of triads in Fourier space. As a result, triad precession frequencies show a non-Gaussian distribution with multiple peaks and fat tails, and there is a significant correlation between triad precession frequencies and amplitude growth. Links with dynamical systems approach are briefly discussed, such as the role of unstable critical points in state space. This analysis has been further developed for Burgers equation evolved on a fractal Fourier set. In this latter case, we observe a depletion of intermittency as a function of the fractal dimension $D$, and the simultaneous reduction of the correlation between th...
Solitary wave solutions to nonlinear evolution equations in mathematical physics
Anwar Ja’afar Mohamad Jawad; M Mirzazadeh; Anjan Biswas
2014-10-01
This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.
On an evolution equation in a cell motility model
Mizuhara, Matthew S.; Berlyand, Leonid; Rybalko, Volodymyr; Zhang, Lei
2016-04-01
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells on a substrate. The key issue is the evolution of the cell membrane (interface curve) which involves shape change and net motion. This issue can be addressed both qualitatively and quantitatively by studying the evolution equation of the sharp interface limit for this system. However, this equation is non-linear and non-local and existence of solutions presents a significant analytical challenge. We establish existence of solutions for a wide class of initial data in the so-called subcritical regime. Existence is proved in a two step procedure. First, for smooth (H2) initial data we use a regularization technique. Second, we consider non-smooth initial data that are more relevant from the application point of view. Here, uniform estimates on the time when solutions exist rely on a maximum principle type argument. We also explore the long time behavior of the model using both analytical and numerical tools. We prove the nonexistence of traveling wave solutions with nonzero velocity. Numerical experiments show that presence of non-linearity and asymmetry of the initial curve results in a net motion which distinguishes it from classical volume preserving curvature motion. This is done by developing an algorithm for efficient numerical resolution of the non-local term in the evolution equation.
Relaxation in control systems of fractional semilinear evolution equations
Xiaoyou Liu
2014-01-01
Full Text Available We consider a control system described by fractional semilinear evolution equations with a mixed multivalued control constraint whose values are nonconvex closed sets. Along with the original system, we consider the system in which the constraint on the control is the closed convex hull of the original constraint. We obtain existence results for the control systems and study relations between the solution sets of the two systems. An example is given to illustrate the abstract results.
Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations
Alghamdi, Moataz
2017-06-18
We introduce a symbolic computational approach to detecting all permutation and parity symmetries in any general evolution equation, and to generating associated invariant polynomials, from given monomials, under the action of these symmetries. Traditionally, discrete point symmetries of differential equations are systemically found by solving complicated nonlinear systems of partial differential equations; in the presence of Lie symmetries, the process can be simplified further. Here, we show how to find parity- and permutation-type discrete symmetries purely based on algebraic calculations. Furthermore, we show that such symmetries always form groups, thereby allowing for the generation of new group-invariant conserved quantities from known conserved quantities. This work also contains an implementation of the said results in Mathematica. In addition, it includes, as a motivation for this work, an investigation of the connection between variational symmetries, described by local Lie groups, and conserved quantities in Hamiltonian systems.
Studying on Opinion Evolution by Hamilton-Jacobi Equation
Feng, Chen-Jie; Huo, Jie; Hao, Rui; Wang, Xu-Ming
2016-01-01
A physical description of an opinion evolution is conducted based on the Hamilton-Jacobi equation derived from a generalized potential and the corresponding Langevin equation. The investigation mainly focuses on the heterogeneities such as age, connection circle and overall quality of the participants involved in the opinion exchange process. The evolutionary patterns of opinion can be described by solution of the Hamilton-Jacobi equation, information entropy. The results show that the overall qualities of the participants play critical roles in forming an opinion. The higher the overall quality is, the easier the consensus can reach. The solution also demonstrates that the age and the connection circle of the agents play equally important roles in forming an opinion. The essence of the age, overall quality, and connection circle corresponds to the maturity of thought (opinion inertia), reason and intelligence, influence strength of the environment, respectively. So the information entropy distributes in the ...
A Hierarchy of New Nonlinear Evolution Equations Associated with a 3 × 3 Matrix Spectral Problem
GENG Xian-Guo; LI Fang
2009-01-01
A 3 × 3 matrix spectral problem with three potentials and the corresponding hierarchy of new nonlinear evolution equations are proposed. Generalized Hamiltonian structures for the hierarchy of nonlinear evolution equations are derived with the aid of trace identity.
A Direct Algebraic Method in Finding Particular Solutions to Some Nonlinear Evolution Equations
LIUChun-Ping; CHENJian-Kang; CAIFan
2004-01-01
Firstly, a direct algebraic method and a routine way in finding traveling wave solutions to nonlinear evolution equations are explained. And then some new exact solutions for some evolution equations are obtained by using the method.
Total Restrained Bondage in Graphs
Nader JAFARI RAD; Roslan HASNI; Joanna RACZEK; Lutz VOLKMANN
2013-01-01
A subset S of vertices of a graph G with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V(G)-S is also adjacent to a vertex in V(G)-S.The total restrained domination number of G is the minimum cardinality of a total restrained dominating set of G.In this paper we initiate the study of total restrained bondage in graphs.The total restrained bondage number in a graph G with no isolated vertex,is the minimum cardinality of a subset of edges E such that G-E has no isolated vertex and the total restrained domination number of G-E is greater than the total restrained domination number of G.We obtain several properties,exact values and bounds for the total restrained bondage number of a graph.
Korennoy, Ya. A.; Man'ko, V. I.
2017-04-01
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time). The general formalism of quantizers and dequantizers determining the star product quantization scheme in these representations is given. Taking the Gaussian functions as the distributions of the tomographic parameters the correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators in the form of singular and regular generalized functions are derived. Evolution equations and stationary states equations for symplectic and optical joint probability distributions are obtained.
Time evolution of the wave equation using rapid expansion method
Pestana, Reynam C.
2010-07-01
Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.
Structure scalars and evolution equations in f( G) cosmology
Sharif, M.; Fatima, H. Ismat
2017-01-01
In this paper, we study the dynamics of self-gravitating fluid using structure scalars for spherical geometry in the context of f( G) cosmology. We construct structure scalars through orthogonal splitting of the Riemann tensor and deduce a complete set of equations governing the evolution of dissipative anisotropic fluid in terms of these scalars. We explore different causes of density inhomogeneity which turns out to be a necessary condition for viable models. It is explicitly shown that anisotropic inhomogeneous static spherically symmetric solutions can be expressed in terms of these scalar functions.
Evolution equation for soft physics at high energy
Brogueira, P.; Dias de Deus, J.
2010-07-01
Based on the nonlinear logistic equation we study, in a qualitative and semi-quantitative way, the evolution with energy and saturation of the elastic differential cross-section in pp(\\bar{p}p) collisions at high energy. Geometrical scaling occurs at the black disc limit, and scaling develops first for small values of the scaling variable |t|σtot.. Our prediction for dσ/dt at LHC, with two zeros and a minimum at large |t| differs, as far as we know, from all existing ones.
Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation
V. O. Vakhnenko
2016-01-01
Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.
An extended functional transformation method and its application in some evolution equations
Ding Hai-Yong; Xu Xi-Xiang; Yang Hong-Xiang
2005-01-01
In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact, is a solution of the famous KdV equation, so this transformation gives a transformation between KdV equation and other soliton equations. Then many new exact solutions can be given by virtue of the solutions of KdV equation.
Solving Partial Differential Equations Using a New Differential Evolution Algorithm
Natee Panagant
2014-01-01
Full Text Available This paper proposes an alternative meshless approach to solve partial differential equations (PDEs. With a global approximate function being defined, a partial differential equation problem is converted into an optimisation problem with equality constraints from PDE boundary conditions. An evolutionary algorithm (EA is employed to search for the optimum solution. For this approach, the most difficult task is the low convergence rate of EA which consequently results in poor PDE solution approximation. However, its attractiveness remains due to the nature of a soft computing technique in EA. The algorithm can be used to tackle almost any kind of optimisation problem with simple evolutionary operation, which means it is mathematically simpler to use. A new efficient differential evolution (DE is presented and used to solve a number of the partial differential equations. The results obtained are illustrated and compared with exact solutions. It is shown that the proposed method has a potential to be a future meshless tool provided that the search performance of EA is greatly enhanced.
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan
2016-05-01
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations
S.A. El-Wakil
2016-02-01
Full Text Available A method for solving three types of nonlinear evolution equations namely KdV, modified KdV and Burgers equations, with self-similar solutions is presented. The method employs ideas from symmetry reduction to space and time variables and similarity reductions for nonlinear evolution equations are performed. The obtained self-similar solutions of KdV and mKdV equations are related to Bessel and Airy functions whereas those of Burgers equation are related to the error and Hermite functions. These solutions appear as new types of solitary, shock and periodic waves. Also, the method can be applied to other nonlinear evolution equations in mathematical physics.
Multiple scales analysis and travelling wave solutions for KdV type nonlinear evolution equations
Ayhan, Burcu; Ozer, M. Naci; Bekir, Ahmet
2017-01-01
Nonlinear evolution equations are the mathematical models of problems that arise in many field of science. These equations has become an important field of study in applied mathematics in recent years. We apply exact solution methods and multiple scale method which is known as a perturbation method to nonlinear evolution equations. Using exact solution methods we get travelling wave solutions expressed by hyperbolic functions, trigonometric functions and rational functions. Also we derive Nonlinear Schrödinger (NLS) type equations from Korteweg-de Vries (KdV) type nonlinear evolution equations and we get approximate solutions for KdV type equations using multiple scale method. The proposed methods are direct and effective and can be used for many nonlinear evolution equations. It is shown that these methods provide a powerful mathematical tool to solve nonlinear evolution equations in mathematical physics.
Nonlinear evolution operators and semigroups applications to partial differential equations
Pavel, Nicolae H
1987-01-01
This research monograph deals with nonlinear evolution operators and semigroups generated by dissipative (accretive), possibly multivalued operators, as well as with the application of this theory to partial differential equations. It shows that a large class of PDE's can be studied via the semigroup approach. This theory is not available otherwise in the self-contained form provided by these Notes and moreover a considerable part of the results, proofs and methods are not to be found in other books. The exponential formula of Crandall and Liggett, some simple estimates due to Kobayashi and others, the characterization of compact semigroups due to Brézis, the proof of a fundamental property due to Ursescu and the author and some applications to PDE are of particular interest. Assuming only basic knowledge of functional analysis, the book will be of interest to researchers and graduate students in nonlinear analysis and PDE, and to mathematical physicists.
Central equation of state in spherical characteristic evolutions
Barreto, W; Barrios, E
2009-01-01
We study the evolution of a perfect--fluid sphere coupled to a scalar radiation field. By ensuring a Ricci invariant regularity as a conformally flat spacetime at the central world line we find that the fluid coupled to the scalar field satisfies the equation of state $\\rho_c+3p_c=$ constant at the center of the sphere, where the energy $\\rho_c$ density and the pressure $p_c$ do not necessarily contain the scalar field contribution. The fluid can be interpreted as anisotropic and radiant because of the scalar field, but it becomes perfect and non radiative at the center of the sphere. These results are being currently considered to build up a numerical relativistic hydrodynamic solver.
Entropy production and the geometry of dissipative evolution equations
Reina, Celia; Zimmer, Johannes
2015-11-01
Purely dissipative evolution equations are often cast as gradient flow structures, z ˙=K (z ) D S (z ) , where the variable z of interest evolves towards the maximum of a functional S according to a metric defined by an operator K . While the functional often follows immediately from physical considerations (e.g., the thermodynamic entropy), the operator K and the associated geometry does not necessarily do so (e.g., Wasserstein geometry for diffusion). In this paper, we present a variational statement in the sense of maximum entropy production that directly delivers a relationship between the operator K and the constraints of the system. In particular, the Wasserstein metric naturally arises here from the conservation of mass or energy, and depends on the Onsager resistivity tensor, which, itself, may be understood as another metric, as in the steepest entropy ascent formalism. This variational principle is exemplified here for the simultaneous evolution of conserved and nonconserved quantities in open systems. It thus extends the classical Onsager flux-force relationships and the associated variational statement to variables that do not have a flux associated to them. We further show that the metric structure K is intimately linked to the celebrated Freidlin-Wentzell theory of stochastically perturbed gradient flows, and that the proposed variational principle encloses an infinite-dimensional fluctuation-dissipation statement.
Evolution Equations on Gabor Transforms and their Applications
Duits, Remco; Janssen, Bart; Bruurmijn, Mark; Florack, Luc; van Assen, Hans
2011-01-01
We introduce a systematic approach to the design, implementation and analysis of left-invariant evolution schemes acting on Gabor transform, primarily for applications in signal and image analysis. Within this approach we relate operators on signals to operators on Gabor transforms. In order to obtain a translation and modulation invariant operator on the space of signals, the corresponding operator on the reproducing kernel space of Gabor transforms must be left invariant, i.e. it should commute with the left regular action of the reduced Heisenberg group H_r. By using the left-invariant vector fields on H_r in the generators of our evolution equations on Gabor transforms, we naturally employ the essential group structure on the domain of a Gabor transform. Here we distinguish between two tasks. Firstly, we consider non-linear adaptive left-invariant convection (reassignment) to sharpen Gabor transforms, while maintaining the original signal. Secondly, we consider signal enhancement via left-invariant diffus...
Alvarez-Estrada, R.F.
1979-08-01
A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly.
Generalized Dromion Structures of New (2 + 1)-Dimensional Nonlinear EvolutionEquation
ZHANG Jie-Fang
2001-01-01
We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released.
Propagation of Gluons From a Non-Perturbative Evolution Equation in Axial Gauges
Kinder-Geiger, Klaus
1999-01-01
We derive a non-perturbative evolution equation for the gluon propagator in axial gauges based on the framework of Wetterich's formulation of the exact renormalization group. We obtain asymptotic solutions to this equation in the ultraviolet and infrared limits.
Yao Yuqin [College of Sciences, Shanghai University, Shanghai 200436 (China)] e-mail: yyqinw@126.com
2005-11-01
In this paper, based on the well-known Sine-Poisson equation, a new Sine-Poisson equation expansion method with constant coefficients or variable coefficients is presented, which can be used to construct more new exact solutions of nonlinear evolution equations in mathematical physics. The KdV-mKdV equation and the typical breaking soliton equation are chosen to illustrate our method such that many types of new exact solutions are obtained, which include exponential solutions, kink-shaped solutions, singular solutions and soliton-like solutions.
Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio
2014-10-01
The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.
Yusuf Pandir
2012-01-01
Full Text Available We obtain the classification of exact solutions, including soliton, rational, and elliptic solutions, to the one-dimensional general improved Camassa Holm KP equation and KdV equation by the complete discrimination system for polynomial method. In discussion, we propose a more general trial equation method for nonlinear partial differential equations with generalized evolution.
MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES
王良龙; 王志成
2004-01-01
This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.
Explicit Traveling Wave Solutions to Nonlinear Evolution Equations
Linghai ZHANG
2011-01-01
First of all,some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations,nonlinear dissipative dispersive wave equations,nonlinear convection equations,nonlinear reaction diffusion equations and nonlinear hyperbolic equations,respectively.
Extended evolution equations for neutrino propagation in astrophysical and cosmological environments
Volpe, Cristina; Espinoza, Catalina
2013-01-01
We derive the evolution equations for a system of neutrinos interacting among themselves and with a matter background, based upon the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. This theoretical framework gives an (unclosed) set of first-order coupled integro-differential equations governing the evolution of the reduced density matrices. By employing the hierarchy, we first rederive the mean-field evolution equations for the neutrino one-body density matrix associated with a system of neutrinos and anti-neutrinosinteracting with matter and with an anisotropic neutrino background. Then, we derive extended evolution equations to determine neutrino flavour conversion beyond the commonly used mean-field approximation. To this aim we include neutrino-antineutrino pairing correlations to the two-body density matrix. The inclusion of these new contributions leads to an extended evolution equation for the normal neutrino density and to an equation for the abnormal one involving the pairing mean-field. We d...
Single and multi-solitary wave solutions to a class of nonlinear evolution equations
Wang, Deng-Shan; Li, Hongbo
2008-07-01
In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations. Many examples are given to illustrate the algorithm. At the same time, some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations, such as Camassa-Holm equation, Kolmogorov-Petrovskii-Piskunov equation, and so on. Then a direct constructive method called multi-auxiliary equations expansion method is described to derive the multi-solitary wave solutions of nonlinear evolution equations. Finally, a class of novel multi-solitary wave solutions of the (2+1)-dimensional asymmetric version of the Nizhnik-Novikov-Veselov equation are given by three direct methods. The algorithm proposed in this paper can be steadily applied to some other nonlinear problems.
Renormalization of the unitary evolution equation for coined quantum walks
Boettcher, Stefan; Li, Shanshan; Portugal, Renato
2017-03-01
We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential for attaining the Grover limit for quantum search algorithms in physically realizable, low-dimensional geometries. In particular, we analyze the exact real-space renormalization group (RG) procedure recently introduced to study the scaling of quantum walks on fractal networks. While this procedure, when implemented numerically, was able to provide some deep insights into the relation between classical and quantum walks, its analytic basis has remained obscure. Our discussion here is laying the groundwork for a rigorous implementation of the RG for this important class of transport and algorithmic problems, although some instances remain unresolved. Specifically, we find that the RG fixed-point analysis of the classical walk, which typically focuses on the dominant Jacobian eigenvalue {λ1} , with walk dimension dw\\text{RW}={{log}2}{λ1} , needs to be extended to include the subdominant eigenvalue {λ2} , such that the dimension of the quantum walk obtains dw\\text{QW}={{log}2}\\sqrt{{λ1}{λ2}} . With that extension, we obtain analytically previously conjectured results for dw\\text{QW} of Grover walks on all but one of the fractal networks that have been considered.
无
2010-01-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or
Symmetry Reduction and Cauchy Problems for a Class of Fourth-Order Evolution Equations
LI Ji-Na; ZHANG Shun-Li
2008-01-01
We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations to Cauehy problems for systems of ordinary differential equations (ODEs).We classify a class of fourth-order evolution equations which admit certain higher-order generalized conditional symmetries (GCSs) and give some examples to show the main reduction procedure.These reductions cannot be derived within the framework of the standard Lie approach,which hints that the technique presented here is something essential for the dimensional reduction of evolution equations.
ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES
WEI Wei; XIANG Xiaoling
2004-01-01
In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presentedThe equations con-tain nonlinear monotone operators and a nonmonotone perturbationMoreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of second-order nonlinear evolution equations is verifiedOur abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.
CHEN Jiang; HE Hong-Sheng; YANG Kong-Qing
2005-01-01
A generalized F-expansion method is introduced and applied to (3+ 1)-dimensional Kadomstev-Petviashvili(KP) equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the trigonometric function solutions and the solitary wave solutions can be obtained. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.
Stochastic integration in Banach spaces and applications to parabolic evolution equations
Veraar, M.C.
2006-01-01
Stochastic partial differential equations (SPDEs) of evolution type are usually modelled as ordinary stochastic differential equations (SDEs) in an infinite-dimensional state space. In many examples such as the stochastic heat and wave equation, this viewpoint may lead to existence and uniqueness re
Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves
Eldeberky, Y.; Madsen, Per A.
1999-01-01
This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary c...
Stochastic integration in Banach spaces and applications to parabolic evolution equations
Veraar, M.C.
2006-01-01
Stochastic partial differential equations (SPDEs) of evolution type are usually modelled as ordinary stochastic differential equations (SDEs) in an infinite-dimensional state space. In many examples such as the stochastic heat and wave equation, this viewpoint may lead to existence and uniqueness
Equations of State: Gateway to Planetary Origin and Evolution (Invited)
Melosh, J.
2013-12-01
Research over the past decades has shown that collisions between solid bodies govern many crucial phases of planetary origin and evolution. The accretion of the terrestrial planets was punctuated by planetary-scale impacts that generated deep magma oceans, ejected primary atmospheres and probably created the moons of Earth and Pluto. Several extrasolar planetary systems are filled with silicate vapor and condensed 'tektites', probably attesting to recent giant collisions. Even now, long after the solar system settled down from its violent birth, a large asteroid impact wiped out the dinosaurs, while other impacts may have played a role in the origin of life on Earth and perhaps Mars, while maintaining a steady exchange of small meteorites between the terrestrial planets and our moon. Most of these events are beyond the scale at which experiments are possible, so that our main research tool is computer simulation, constrained by the laws of physics and the behavior of materials during high-speed impact. Typical solar system impact velocities range from a few km/s in the outer solar system to 10s of km/s in the inner system. Extrasolar planetary systems expand that range to 100s of km/sec typical of the tightly clustered planetary systems now observed. Although computer codes themselves are currently reaching a high degree of sophistication, we still rely on experimental studies to determine the Equations of State (EoS) of materials critical for the correct simulation of impact processes. The recent expansion of the range of pressures available for study, from a few 100 GPa accessible with light gas guns up to a few TPa from current high energy accelerators now opens experimental access to the full velocity range of interest in our solar system. The results are a surprise: several groups in both the USA and Japan have found that silicates and even iron melt and vaporize much more easily in an impact than previously anticipated. The importance of these findings is
2008-01-01
Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
WANG Shundin; ZHANG Hua
2008-01-01
Using functional derivative technique In quantum field theory,the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations.The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by Introducing the time translation operator.The functional partial differential evolution equations were solved by algebraic dynam-ics.The algebraic dynamics solutions are analytical In Taylor series In terms of both initial functions and time.Based on the exact analytical solutions,a new nu-merical algorithm-algebraic dynamics algorithm was proposed for partial differ-ential evolution equations.The difficulty of and the way out for the algorithm were discussed.The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
Junchao Chen; Biao Li
2012-03-01
In this paper, an extended multiple (′/)-expansion method is proposed to seek exact solutions of nonlinear evolution equations. The validity and advantages of the proposed method is illustrated by its applications to the Sharma–Tasso–Olver equation, the sixth-order Ramani equation, the generalized shallow water wave equation, the Caudrey–Dodd–Gibbon–Sawada–Kotera equation, the sixth-order Boussinesq equation and the Hirota–Satsuma equations. As a result, various complexiton solutions consisting of hyperbolic functions, trigonometric functions, rational functions and their mixture with parameters are obtained. When some parameters are taken as special values, the known double solitary-like wave solutions are derived from the double hyperbolic function solution. In addition, this method can also be used to deal with some high-dimensional and variable coefﬁcients’ nonlinear evolution equations.
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Restrained roman domination in graphs
Roushini Leely Pushpam
2015-03-01
Full Text Available A Roman dominating function (RDF on a graph G = (V,E is defined to be a function satisfying the condition that every vertex u for which f(u = 0 is adjacent to at least one vertex v for which f(v = 2. A set S V is a Restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in . We define a Restrained Roman dominating function on a graph G = (V,E to be a function satisfying the condition that every vertex u for which f(u = 0 is adjacent to at least one vertex v for which f(v = 2 and at least one vertex w for which f(w = 0. The weight of a Restrained Roman dominating function is the value . The minimum weight of a Restrained Roman dominating function on a graph G is called the Restrained Roman domination number of G and denoted by . In this paper, we initiate a study of this parameter.
TRAVELLING WAVE SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS BY USING SYMBOLIC COMPUTATION
FanEngui
2001-01-01
Abstract. A Riccati equation involving a parameter and symbolic computation are used to uni-formly construct the different forms of travelling wave solutions for nonlinear evolution equa-tions. It is shown that the sign of the parameter can be applied in judging the existence of vari-ous forms of travelling wave solutions. An efficiency of this method is demonstrated on some e-quations,which include Burgers-Huxley equation,Caudrey-Dodd-Gibbon-Kawada equation,gen-eralized Benjamin-Bona-Mahony equation and generalized Fisher equation.
Nonlinear evolution equations and Painlevé test
Steeb, Willi-Hans
1988-01-01
This book is an edited version of lectures given by the authors at a seminar at the Rand Afrikaans University. It gives a survey on the Painlevé test, Painlevé property and integrability. Both ordinary differential equations and partial differential equations are considered.
A procedure to construct exact solutions of nonlinear evolution equations
Adem Cengiz Çevikel; Ahmet Bekir; Mutlu Akar; Sait San
2012-09-01
In this paper, we implemented the functional variable method for the exact solutions of the Zakharov-Kuznetsov-modified equal-width (ZK-MEW), the modified Benjamin-Bona-Mohany (mBBM) and the modified kdV-Kadomtsev-Petviashvili (kdV-KP) equation. By using this scheme, we found some exact solutions of the above-mentioned equation. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. The functional variable method presents a wider-applicability for handling nonlinear wave equations.
Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations
无
2005-01-01
By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
SIMILARITY REDUCTIONS FOR THE NONLINEAR EVOLUTION EQUATION ARISING IN THE FERMI-PASTA-ULAM PROBLEM
谢福鼎; 闫振亚; 张鸿庆
2002-01-01
Four families of similarity reductions are obtained for the nonlinear evolution equation arising in the Fermi-Pasta-Ulam problem via using both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou.
The Liouville equation for flavour evolution of neutrinos and neutrino wave packets
Hansen, Rasmus Sloth Lundkvist
2016-01-01
We consider several aspects related to the form, derivation and applications of the Liouville equation (LE) for flavour evolution of neutrinos. To take into account the quantum nature of neutrinos we derive the evolution equation for the matrix of densities using wave packets instead of Wigner functions. The obtained equation differs from the standard LE by an additional term which is proportional to the difference of group velocities. We show that this term describes loss of the propagation coherence in the system. In absence of inelastic collisions, the LE can be reduced to a single derivative equation over a trajectory coordinate. Additional time and spacial dependence may steam from initial (production) conditions. The transition from single neutrino evolution to the evolution of a neutrino gas is considered.
New exact solutions to the generalized KdV equation with generalized evolution
Yongan Xie; Shengqiang Tang; Dahe Feng
2012-04-01
In this paper, by using a transformation and an application of Fan subequation, we study a class of generalized Korteweg–de Vries (KdV) equation with generalized evolution. As a result, more types of exact solutions to the generalized KdV equation with generalized evolution are obtained, which include more general single-hump solitons, multihump solitons, kink solutions and Jacobian elliptic function solutions with double periods.
Nonpoint Symmetry and Reduction of Nonlinear Evolution and Wave Type Equations
Ivan Tsyfra
2015-01-01
Full Text Available We study the symmetry reduction of nonlinear partial differential equations with two independent variables. We propose new ansätze reducing nonlinear evolution equations to system of ordinary differential equations. The ansätze are constructed by using operators of nonpoint classical and conditional symmetry. Then we find solution to nonlinear heat equation which cannot be obtained in the framework of the classical Lie approach. By using operators of Lie-Bäcklund symmetries we construct the solutions of nonlinear hyperbolic equations depending on arbitrary smooth function of one variable too.
Nonlinear evolution equations associated with the chiral-field spectral problem
Bruschi, M.; Ragnisco, O. (Istituto Nazionale di Fisica Nucleare, Roma (Italy); Dipt. di Fisica, Univ. Rome (Italy))
1985-08-11
In this paper we derive and investigate the class of nonlinear evolution equations (NEEs) associated with the linear problem psisub(x) = lambdaApsi. It turns out that many physically interesting NEEs pertain to this class: for instance, the chiral-field equation, the nonlinear Klein-Gordon equations, the Heisenberg and Papanicolau spin chain models, the modified Boussinesq equation, the Wadati-Konno-Ichikawa equations, etc. We display also the Baecklund transformations for such a class and exploit them to derive in a special case the one-soliton solution.
Kröger, Tim; Lukáčová-Medvid'ová, Mária
2005-06-01
In this paper we propose a new finite volume evolution Galerkin (FVEG) scheme for the shallow water magnetohydrodynamic (SMHD) equations. We apply the exact integral equations already used in our earlier publications to the SMHD system. Then, we approximate these integral equation in a general way which does not exploit any particular property of the SMHD equations and should thus be applicable to arbitrary systems of hyperbolic conservation laws in two space dimensions. In particular, we investigate more deeply the approximation of the spatial derivatives which appear in the integral equations. The divergence free condition is satisfied discretely, i.e. at each vertex. First numerical results confirm reliability of the numerical scheme.
Complex Modified Korteweg--DeVries equation, a non-integrable evolution equation
Karney, C.F.F.; Sen, A.; Chu, F.Y.F.
1978-06-01
The two-dimensional steady-state propagation of electrostatic waves is governed by delta v/delta tau + delta/sup 3/v/delta xi/sup 3/ + delta((absolute value of v)/sup 2/v)/delta xi = 0, the Complex Modified Korteweg-DeVries equation. The properties of this equation are studied.
Integrable nonlinear evolution partial differential equations in 4 + 2 and 3 + 1 dimensions.
Fokas, A S
2006-05-19
The derivation and solution of integrable nonlinear evolution partial differential equations in three spatial dimensions has been the holy grail in the field of integrability since the late 1970s. The celebrated Korteweg-de Vries and nonlinear Schrödinger equations, as well as the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations, are prototypical examples of integrable evolution equations in one and two spatial dimensions, respectively. Do there exist integrable analogs of these equations in three spatial dimensions? In what follows, I present a positive answer to this question. In particular, I first present integrable generalizations of the KP and DS equations, which are formulated in four spatial dimensions and which have the novelty that they involve complex time. I then impose the requirement of real time, which implies a reduction to three spatial dimensions. I also present a method of solution.
Transport equations for a general class of evolution equations with random perturbations
Guo, Maozheng; Wang, Xiao-Ping
1999-10-01
We derive transport equations from a general class of equations of form iut=H(X,D)u+V(X,D)u where H(X,D) and V(X,D) are pseudodifferential operators (Weyl operator) with symbols H(x,k) and V(x,k), where H(x,k) being polynomial in k and smooth in x,V(x,k) is a mean zero random function and is stationary in space variable. We also consider system of equations in the above form. Such equations cover many of the equations that arise in wave propagations, such as those considered in a paper by Ryzhik, Papanicolaou, and Keller [Wave Motion 24, 327-370 (1996)]. Our results generalize those by Ryzhik, Papanicolau, and Keller.
The derivative-dependent functional variable separation for the evolution equations
Zhang Shun-Li; Lou Sen-Yue; Qu Chang-Zheng
2006-01-01
This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A(u,ux)uxx+B(u,ux,ut) which admits the derivativedependent functional separable solutions (DDFSSs). We also extend the concept of the DDFSS to cover other variable separation approaches.
WANG Peng-Zhou; ZHANG Shun-Li
2008-01-01
We present basic theory of variable separation for (1 + 1)-dimensional nonlinear evolution equations with mixed partial derivatives. As an application, we classify equations uxt = A(u, ux)uxxx + B(u, ux) that admits derivative-dependent functional separable solutions (DDFSSs) and illustrate how to construct those DDFSSs with some examples.
Real-space renormalization-group approach to field evolution equations.
Degenhard, Andreas; Rodríguez-Laguna, Javier
2002-03-01
An operator formalism for the reduction of degrees of freedom in the evolution of discrete partial differential equations (PDE) via real-space renormalization group is introduced, in which cell overlapping is the key concept. Applications to (1+1)-dimensional PDEs are presented for linear and quadratic equations that are first order in time.
EXISTENCE RESULTS FOR IMPULSIVE NEUTRAL EVOLUTION DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY
无
2011-01-01
This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theories of evolution systems,we prove some existence theorems. As an application,an example is also given to illustrate the obtained results.
Bi-Hamiltonian Structure of a Third-Order Nonlinear Evolution Equation on Plane Curve Motions
无
2007-01-01
In the present paper, we identify the integrability of the third-order nonlinear evolution equation ut = (1/2)((uxx + u)-2)x in a Hamiltonian viewpoint. We prove that the recursion operator obtained by S. Yu. Sakovich is hereditary, and then deduce a bi-Hamiltonian structure of the equation by using some decomposition of the hereditary operator. A hierarchy associated to the equation is also shown.
Lie Symmetries of (1+2 Nonautonomous Evolution Equations in Financial Mathematics
Andronikos Paliathanasis
2016-05-01
Full Text Available We analyse two classes of ( 1 + 2 evolution equations which are of special interest in Financial Mathematics, namely the Two-dimensional Black-Scholes Equation and the equation for the Two-factor Commodities Problem. Our approach is that of Lie Symmetry Analysis. We study these equations for the case in which they are autonomous and for the case in which the parameters of the equations are unspecified functions of time. For the autonomous Black-Scholes Equation we find that the symmetry is maximal and so the equation is reducible to the ( 1 + 2 Classical Heat Equation. This is not the case for the nonautonomous equation for which the number of symmetries is submaximal. In the case of the two-factor equation the number of symmetries is submaximal in both autonomous and nonautonomous cases. When the solution symmetries are used to reduce each equation to a ( 1 + 1 equation, the resulting equation is of maximal symmetry and so equivalent to the ( 1 + 1 Classical Heat Equation.
Travelling Wave Solutions to a Special Type of Nonlinear Evolution Equation
XU Gui-Qiong; LI Zhi-Bin
2003-01-01
A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of "rank". The key idea of this method is to make use of the arbitrariness of the manifold in Painleve analysis. We selected a new expansion variable and thus obtained a rich variety of travelling wave solutions to nonlinear evolution equation, which covered solitary wave solutions, periodic wave solutions, Weierstrass elliptic function solutions, and rational solutions. Three illustrative equations are investigated by this means, and abundant travelling wave solutions are obtained in a systematic way. In addition, some new solutions are firstly reported here.
Two Kinds of Square-Conservative Integrators for Nonlinear Evolution Equations
CHEN Jing-Bo; LIU Hong
2008-01-01
@@ Based on the Lie-group and Gauss-Legendre methods, two kinds of square-conservative integrators for squareconservative nonlinear evolution equations are presented. Lie-group based square-conservative integrators are linearly implicit, while Gauss-Legendre based square-conservative integrators are nonlinearly implicit and iterarive schemes are needed to solve the corresponding integrators. These two kinds of integrators provide natural candidates for simulating square-conservative nonlinear evolution equations in the sense that these integrators not only preserve the square-conservative properties of the continuous equations but also are nonlinearly stable.Numerical experiments are performed to test the presented integrators.
Gluon distributions from Oliveira-Martin-Ryskin combined BFKL+DGLAP evolution equations
Toton, Dawid
2014-01-01
Kwiecinski, Martin, Stasto [13] argue for inclusion of DGLAP terms into BFKL evolution of unintegrated gluon density. The equation was reformulated by Oliveira, Martin, Ryskin [6] employing the opening angle {\\theta} = k/xp as the evolution variable. It leads to a description of a {\\theta}-integrated gluon density. This paper is a numerical study of these two similar combined BFKL+DGLAP formulations. It is a demonstration of feasibility of the new approach. The different ways of subtracting the contribution common for BFKL and DGLAP proposed in [13] and [6] are compared. The numerical tests confirm that the {\\theta} variable is a more natural evolution variable for this kind of equation.
Evolution equation for classical and quantum light in turbulence
Roux, FS
2015-06-01
Full Text Available angular momentum (OAM) basis. As such, the IPE consists of an infinite set of coupled first order differential equations. To solve this IPE one needs to truncate the set, which introduces errors that render the solutions inaccurate [4]. So far the IPE...
Evolution equation for the shape function in the parton model approach to inclusive B decays
Baek, Seungwon [University of Montreal, Montreal, QC (Canada); Lee, Kangyoung [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of)
2005-08-15
We derive an evolution equation for the shape function of the b quark in an analogous way to the Altarelli-Parisi equation by incorporating the perturbative QCD correction to the inclusive semileptonic decays of the B meson. Since the parton picture works well for inclusive B decays due to the heavy mass of the b quark, the scaling feature manifests and the decay rate may be expressed by a single structure function describing the light-cone distribution of the b quark apart from the kinematic factor. The evolution equation introduces a q{sup 2} dependence of the shape function and violates the scaling properties. We solve the evolution equation and discuss the phenomenological implication.
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.
Spectral approach to axisymmetric evolution of Einstein's equations
Schell, Christian
2014-01-01
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the occurrence of coordinate singularities on the axis of symmetry and at the origin. Spherical harmonics are manifestly regular on the axis and hence take care of that issue automatically. In addition a spectral approach has computational advantages when the equations are implemented. Therefore we spectrally decompose all the variables in the appropriate harmonics. A central point in the formulation is the gauge choice. One of our results is that the commonly used maximal-isothermal gauge turns out to be incompatible with tensor harmonic expansions, and we introduce a new gauge that is better suited. We also address the regularisation of the coordinate singularity at the origin.
An almost symmetric Strang splitting scheme for nonlinear evolution equations.
Einkemmer, Lukas; Ostermann, Alexander
2014-07-01
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.
Stability of planar diffusion wave for nonlinear evolution equation
无
2012-01-01
It is known that the one-dimensional nonlinear heat equation ut = f(u)x1x1,f'(u) 0,u(±∞,t) = u±,u+ = u_ has a unique self-similar solution u(x1/1+t).In multi-dimensional space,u(x1/1+t) is called a planar diffusion wave.In the first part of the present paper,it is shown that under some smallness conditions,such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation:ut-△f(u) = 0,x ∈ Rn.The optimal time decay rate is obtained.In the second part of this paper,it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping:utt + utt+ △f(u) = 0,x ∈ Rn.The time decay rate is also obtained.The proofs are given by an elementary energy method.
A convective-advective balance approach for solving some nonlinear evolution equations analytically
Abdel Hamid, B. [United Arab Emirates Univ. (United Arab Emirates). Dept. of Mathematics and Computer Science
1999-09-01
A symbolic computation-based approach of balancing the convective and advective effects in a nonlinear evolution equation leads to a transformation that maps the nonlinear equation onto either a linear one or to a system of linear and homogeneous equations. The method is demonstrated by mapping Burgers' equation and nonlinear heat equation onto the linear heat equation. It is shown that the transformation obtained by balancing the convective-advective effects are reducible to those obtained by the Cole and Hopf through Backlund transformation. The method is also used to transform the modified KdV equation into a system of linear and homogeneous functions in the partial derivatives which leads to an exact solution. Computations in the presented approach are carried out in a straightforward way.
Loewner Theory in annulus I: evolution families and differential equations
Contreras, Manuel D; Gumenyuk, Pavel
2010-01-01
Loewner Theory, based on dynamical viewpoint, is a powerful tool in Complex Analysis, which plays a crucial role in such important achievements as the proof of famous Bieberbach's conjecture and well-celebrated Schramm's Stochastic Loewner Evolution (SLE). Recently Bracci et al [Bracci et al, to appear in J. Reine Angew. Math. Available on ArXiv 0807.1594; Bracci et al, Math. Ann. 344(2009), 947--962; Contreras et al, Revista Matematica Iberoamericana 26(2010), 975--1012] have proposed a new approach bringing together all the variants of the (deterministic) Loewner Evolution in a simply connected reference domain. We construct an analogue of this theory for the annulus. In this paper, the first of two articles, we introduce a general notion of an evolution family over a system of annuli and prove that there is a 1-to-1 correspondence between such families and semicomplete weak holomorphic vector fields. Moreover, in the non-degenerate case, we establish a constructive characterization of these vector fields a...
Hasibun Naher
2014-10-01
Full Text Available In this article, new extension of the generalized and improved (G′/G-expansion method is proposed for constructing more general and a rich class of new exact traveling wave solutions of nonlinear evolution equations. To demonstrate the novelty and motivation of the proposed method, we implement it to the Korteweg-de Vries (KdV equation. The new method is oriented toward the ease of utilize and capability of computer algebraic system and provides a more systematic, convenient handling of the solution process of nonlinear equations. Further, obtained solutions disclose a wider range of applicability for handling a large variety of nonlinear partial differential equations.
YAN Zhen-Ya
2004-01-01
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the correspondingsystem of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2+1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.
YANZhen-Ya
2004-01-01
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the corresponding system of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2+1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.
Canonical structure of evolution equations with non-linear dispersive terms
B Talukdar; J Shamanna; S Ghosh
2003-07-01
The inverse problem of the variational calculus for evolution equations characterized by non-linear dispersive terms is analysed with a view to clarify why such a system does not follow from Lagrangians. Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac’s theory of constraints. The speciﬁc results presented refer to the third- and ﬁfth-order equations of the so-called distinguished subclass.
Finitely approximable random sets and their evolution via differential equations
Ananyev, B. I.
2016-12-01
In this paper, random closed sets (RCS) in Euclidean space are considered along with their distributions and approximation. Distributions of RCS may be used for the calculation of expectation and other characteristics. Reachable sets on initial data and some ways of their approximate evolutionary description are investigated for stochastic differential equations (SDE) with initial state in some RCS. Markov property of random reachable sets is proved in the space of closed sets. For approximate calculus, the initial RCS is replaced by a finite set on the integer multidimensional grid and the multistage Markov chain is substituted for SDE. The Markov chain is constructed by methods of SDE numerical integration. Some examples are also given.
Gibbon, John
2007-06-01
More than 160 years after their invention by Hamilton, quaternions are now widely used in the aerospace and computer animation industries to track the orientation and paths of moving objects undergoing three-axis rotations. Here it is shown that they provide a natural way of selecting an appropriate orthonormal frame—designated the quaternion-frame—for a particle in a Lagrangian flow, and of obtaining the equations for its dynamics. How these ideas can be applied to the three-dimensional Euler fluid equations is then considered. This work has some bearing on the issue of whether the Euler equations develop a singularity in a finite time. Some of the literature on this topic is reviewed, which includes both the Beale-Kato-Majda theorem and associated work on the direction of vorticity by Constantin, Fefferman, and Majda and by Deng, Hou, and Yu. It is then shown how the quaternion formalism provides an alternative formulation in terms of the Hessian of the pressure.
Rubin, M. B.; Cardiff, P.
2017-06-01
Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.
Three-quark interaction: The driving force in the inhomogeneous evolution equations
Bartnik, E.A.; Namyslowski, J.M.
1984-09-01
Using perturbative QCD on the light cone (A/sub +/ = 0 gauge), and the Brodsky-Lepage collinear projection, we make a partial-wave projection (in the l/sub z/ component) of the Weinberg equation, and find a set of evolution equations for distribution amplitudes. For l/sub z/not =0 our equations are inhomogeneous, and their solutions show an increasing QCD perturbative effect for the currently available momentum transfers. The driving force of the inhomogenous evolution equations is a three-quark irreducible interaction, which gives terms approx.(1-x)/sup 3/ in the proton's deep-inelastic structure function, breaks the SU(6) symmetry, and contributes to the deviation of the d/u ratio for proton from the value 1/2. That force couples a qq-bar pair to one transverse gluon and one Coulomb gluon.
Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation
Zhaqilao,, E-mail: zhaqilao@imnu.edu.cn
2013-12-06
A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed.
Existence of solutions for non-autonomous functional evolution equations with nonlocal conditions
Xianlong Fu
2012-07-01
Full Text Available In this work, we study the existence of mild solutions and strict solutions of semilinear functional evolution equations with nonlocal conditions, where the linear part is non-autonomous and generates a linear evolution system. The fraction power theory and alpha-norm are used to discuss the problems so that the obtained results can be applied to the equations in which the nonlinear terms involve spatial derivatives. In particular, the compactness condition or Lipschitz condition for the function g in the nonlocal conditions appearing in various literatures is not required here. An example is presented to show the applications of the obtained results
New prospects in direct, inverse and control problems for evolution equations
Fragnelli, Genni; Mininni, Rosa
2014-01-01
This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.
STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS
闫振亚; 张鸿庆
2001-01-01
The homogeneous balance method was improved and applied to two systems of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions contain Wang's and Zhang's results and other new types of analytical solutions, such as rational fraction solutions and periodic solutions. The way can also be applied to solve more nonlinear partial differential equations.
Integrable Equations and Their Evolutions Based on Intrinsic Geometry of Riemann Spaces
Paul Bracken
2009-01-01
Full Text Available The intrinsic geometry of surfaces and Riemannian spaces will be investigated. It is shown that many nonlinear partial differential equations with physical applications and soliton solutions can be determined from the components of the relevant metric for the space. The manifolds of interest are surfaces and higher-dimensional Riemannian spaces. Methods for specifying integrable evolutions of surfaces by means of these equations will also be presented.
Application of Exp-function method for nonlinear evolution equations with variable coefficients
El-Wakil, S.A.; Madkour, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Faculty of Education for Girls, Physics Department, King Kahlid University, Bisha, Kingdom Saudi Arabia (Saudi Arabia)], E-mail: m_abdou_eg@yahoo.com
2007-09-10
In this Letter, the Exp-function method with the aid of symbolic computational system Maple is used to obtain generalized solitary solutions and periodic solutions of a generalized Zakharov-Kuznetsov equation with variable coefficients. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics.
A new approach to investigation of evolution differential equations in Banach spaces
Alber, Y I
1993-01-01
and that $B$ is dense in $H$. The stabilization of solutions of evolution equations has been proven either in the sense of weak convergence in $B$ or in the norm of $H$ space, and only asymptotic estimates of stabilization rate have been obtained [15]. In the present paper we consider equations of type (0.1) without conditions (0.2) and establish stabilization with both
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Medvidová, Maria Lukáčová -; Noelle, Sebastian; Kraft, Marcus
2015-01-01
We present a new well-balanced finite volume method within the framework of the finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for the shallow water equations with source terms modelling the bottom topography and Coriolis forces. Results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensio...
Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system
Lukácová-Medvid'ová, Maria; Warnecke, Gerald; Zahaykah, Yousef
2003-01-01
The subject of the paper is the derivation and analysis of third order finite volume evolution Galerkin schemes for the two-dimensional wave equation system. To achieve this the first order approximate evolution operator is considered. A recovery stage is carried out at each level to generate a piecewise polynomial approximation from the piecewise constants, to feed into the calculation of the fluxes. We estimate the truncation error and give numerical examples to demonstrate the higher order...
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Lukácová-Medvid'ová, Maria; Kraft, Marcus
2005-01-01
We present a new well-balanced finite volume method within the framework of the finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for the shallow water equations with source terms modelling the bottom topography and Coriolis forces. Results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of the multidime...
Infinitely-many conservation laws for two (2+1)-dimensional nonlinear evolution equations in fluids
Yan Jiang; Bo Tian; Pan Wang; Kun Su
2014-07-01
In this paper, a method that can be used to construct the infinitely-many conservation laws with the Lax pair is generalized from the (1+1)-dimensional nonlinear evolution equations (NLEEs) to the (2+1)-dimensional ones. Besides, we apply that method to the Kadomtsev– Petviashvili (KP) and Davey–Stewartson equations in fluids, and respectively obtain their infinitelymany conservation laws with symbolic computation. Based on that method, we can also construct the infinitely-many conservation laws for other multidimensional NLEEs possessing the Lax pairs, including the cylindrical KP, modified KP and (2+1)-dimensional Gardner equations, in fluids, plasmas, optical fibres and Bose–Einstein condensates.
A Higher Dimensional Loop Algebra and Integrable Couplings System of Evolution Equations Hierarchy
夏铁成; 于发军; 陈登远
2005-01-01
An extension of the Lie algebra An-1 has been proposed [ Phys. Lett. A, 2003, 310 : 19-24 ]. In this paper, the new Lie algebra was used to construct a new higher dimensional loop algebra G～. Based on the loop algebra G～, the integrable couplings system of the NLS-MKdV equations hierarchy was obtained. As its reduction case, generalized nonlinear NLS-MKdV equations were obtained. The method proposed in this letter can be applied to other hierarchies of evolution equations.
ZHOU Zhen-Jiang; LI Zhi-Bin
2003-01-01
An explicit N-fold Darboux transformation for evolution equations determined by general 2×2 AKNS system is constructed. By using the Darboux transformation, the solutions of the evolution equations are reduced to solving alinear algebraic system, from which a unified and explicit formulation of 2N-soliton solutions for the evolution equation are given. Furthermore, a reduction technique for MKdV equation is presented, and an N-fold Darboux transformation of MKdV hierarchy is constructed through the reduction technique. A Maple package which can entirely automatically output the exact N-soliton solutions of the MKdV equation is developed.
2PI Effective Action and Evolution Equations of N = 4 super Yang-Mills
Smolic, Jelena
2011-01-01
We employ nPI effective action techniques to study N = 4 super Yang-Mills, and write down the 2PI effective action of the theory. We also supply the evolution equations of two-point correlators within the theory.
Exact Solutions of Some (1+1)-Dimensional Nonlinear Evolution Equations
无
2006-01-01
By means of the variable separation method, new exact solutions of some (1+1)-dimensional nonlinear evolution equations are obtained. Abundant localized excitations can be found by selecting corresponding arbitrary functions appropriately. Namely, the new soliton-like localized excitations and instanton-like localized excitations are presented.
Localized Excitations in a Sixth-Order (1+1)-Dimensional Nonlinear Evolution Equation
SHEN Shou-Feng
2005-01-01
In this letter, by means of the Lax pair, Darboux transformation, and variable separation approach, a new exact solution of a sixth-order (1+ 1)-dimensional nonlinear evolution equation, which includes some arbitrary functions,is obtained. Abundant new localized excitations can be found by selecting appropriate functions and they are illustrated both analytically and graphically.
Archana Chauhan
2011-08-01
Full Text Available In this work we consider a class of impulsive fractional-order semilinear evolution equations with a nonlocal initial condition. By means of solution operator and application of fixed point theorems we established the existence and uniqueness of a mild solution.
V. Vijayakumar
2014-09-01
Full Text Available In this article, we study the existence of mild solutions for nonlocal Cauchy problem for fractional neutral evolution equations with infinite delay. The results are obtained by using the Banach contraction principle. Finally, an application is given to illustrate the theory.
On a Class of Multitime Evolution Equations with Nonlocal Initial Conditions
F. Zouyed
2007-01-01
Full Text Available The existence and uniqueness of the strong solution for a multitime evolution equation with nonlocal initial conditions are proved. The proof is essentially based on a priori estimates and on the density of the range of the operator generated by the considered problem.
The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation
Mo Jia-Qi; Lin Su-Rong
2009-01-01
This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method,it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homotopic mapping,it obtains an approximate solution with an arbitrary degree of accuracy for the solitary wave. From the approximate solution obtained by using the homotopic mapping method,it possesses a good accuracy.
2PI effective action and evolution equations of N=4 super Yang-Mills
Smolic, Jelena; Smolic, Milena [University of Amsterdam, Institute for Theoretical Physics, Amsterdam (Netherlands)
2012-08-15
We employ nPI effective action techniques to study N=4 super Yang-Mills, and write down the 2PI effective action of the theory to two-loop order in the symmetric phase. We also supply the evolution equations of two-point correlators within the theory. (orig.)
The evolution of galaxies in the mirror of the coagulation equation
Kontorovich, V. M.
2017-01-01
Smoluchowski equation and its generalizations, describing the merger of the particles, allow us to understand the main stages of the formation of galaxy mass functions, established as a result of mergers, and their evolution and thus provides an explanation for the results of long-term observations with the Hubble Space Telescope and large ground-based telescopes.
An Exact Evolution Equation of the Curvature Perturbation for Closed Universe
章德海; 孙成一
2004-01-01
As is well known, the exact evolution equation of the curvature perturbation plays a very important role in investigation of the inflation power spectrum of the flat universe. However, the corresponding exact extension for the non-flat universes has not yet been given clearly. Interest in the non-flat, specially closed, universes has been aroused recently. The need for this extension is pressing. We start with the most elementary physical consideration and obtain finally this exact evolution equation of the curvature perturbation for the non-flat universes, as well as the evolutionary controlling parameter and the exact expression of the variable mass in this equation. We approximately perform a primitive and immature analysis on the power spectrum of non-flat universes. This analysis shows that the exact evolution equation of the curvature perturbation for the non-flat universes is very complicated, and we need to carry out many numerical and analytic works for this new equation in the future to judge whether the universe is flat or closed by comparison of theories with observations.
Evolution Equation for a Joint Tomographic Probability Distribution of Spin-1 Particles
Korennoy, Ya. A.; Man'ko, V. I.
2016-11-01
The nine-component positive vector optical tomographic probability portrait of quantum state of spin-1 particles containing full spatial and spin information about the state without redundancy is constructed. Also the suggested approach is expanded to symplectic tomography representation and to representations with quasidistributions like Wigner function, Husimi Q-function, and Glauber-Sudarshan P-function. The evolution equations for constructed vector optical and symplectic tomograms and vector quasidistributions for arbitrary Hamiltonian are found. The evolution equations are also obtained in special case of the quantum system of charged spin-1 particle in arbitrary electro-magnetic field, which are analogs of non-relativistic Proca equation in appropriate representations. The generalization of proposed approach to the cases of arbitrary spin is discussed. The possibility of formulation of quantum mechanics of the systems with spins in terms of joint probability distributions without the use of wave functions or density matrices is explicitly demonstrated.
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new application of the homotopy analysis method (HAM for solving evolution equations described in terms of nonlinear partial differential equations (PDEs. The new approach, termed bivariate spectral homotopy analysis method (BISHAM, is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. The applicability of the new approach has been demonstrated by application on several examples of nonlinear evolution PDEs, namely, Fisher’s, Burgers-Fisher’s, Burger-Huxley’s, and Fitzhugh-Nagumo’s equations. Comparison with known exact results from literature has been used to confirm accuracy and effectiveness of the proposed method.
Ayhan, Burcu; Özer, M. Naci; Bekir, Ahmet
2016-08-01
In this article, we applied the method of multiple scales for Korteweg-de Vries (KdV) type equations and we derived nonlinear Schrödinger (NLS) type equations. So we get a relation between KdV type equations and NLS type equations. In addition, exact solutions were found for KdV type equations. The ( G'} over G )-expansion methods and the ( {G'} over G, {1 over G}} )-expansion methods were proposed to establish new exact solutions for KdV type differential equations. We obtained periodic and hyperbolic function solutions for these equations. These methods are very effective for getting travelling wave solutions of nonlinear evolution equations (NEEs).
Music for untying restrained patients.
Janelli, L M; Kanski, G
1998-03-01
The purpose of this descriptive pilot study was two-fold: (a) to test psychometrically an observational instrument designed to measure patient behaviors displayed while unrestrained and receiving a musical intervention; and (b) to determine the effect of a musical intervention on the behavioral reactions of physically restrained patients. The Restraint-Music Response Instrument (RMRI) is a 40-item observational checklist consisting of 22 positive and 18 negative responses developed by the researchers. Content validity was assessed by a panel of experts. The RMRI was tested for interrater reliability using three simulated and 10 actual patients. Results suggest that the RMRI is a valid and reliable measure of patients' responses to music but requires additional study with a control group not receiving the intervention.
Kirsch, Andreas; Rieder, Andreas
2016-08-01
It is common knowledge—mainly based on experience—that parameter identification problems in partial differential equations are ill-posed. Yet, a mathematical sound argumentation is missing, except for some special cases. We present a general theory for inverse problems related to abstract evolution equations which explains not only their local ill-posedness but also provides the Fréchet derivative and its adjoint of the corresponding parameter-to-solution map which are needed, e.g., in Newton-like solvers. Our abstract results are applied to inverse problems related to the following first order hyperbolic systems: Maxwell’s equation (electromagnetic scattering in conducting media) and elastic wave equation (seismic imaging).
Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions
Maccari, A. [Technical Institute G. Cardano, Piazza della Resistenza 1, 00015 Monterotondo, Rome (Italy)
1997-08-01
Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio{endash}temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a {open_quotes}universal{close_quotes} character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part. {copyright} {ital 1997 American Institute of Physics.}
A New Generalization of Extended Tanh-Function Method for Solving Nonlinear Evolution Equations
ZHENG Xue-Dong; CHEN Yong; LI Biao; ZHANG Hong-Qing
2003-01-01
Making use of a new generalized ansatze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations.As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extendedtanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain othernew and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profilesolitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.
Traveling wave solutions of nonlinear evolution equations via the enhanced (G′/G-expansion method
Kamruzzaman Khan
2014-07-01
Full Text Available In this article, an enhanced (G′/G-expansion method is suggested to find the traveling wave solutions for the modified Korteweg de-Vries (mKDV equation. Abundant traveling wave solutions are derived, which are expressed by the hyperbolic and trigonometric functions involving several parameters. The efficiency of this method for finding these exact solutions has been demonstrated. It is shown that the proposed method is effective and can be used for many other nonlinear evolution equations (NLEEs in mathematical physics.
Approximated Lax pairs for the reduced order integration of nonlinear evolution equations
Gerbeau, Jean-Frédéric; Lombardi, Damiano
2014-05-01
A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the basis on which the solution is searched for evolves in time according to a dynamics specific to the problem. It is therefore well-suited to solving problems with progressive front or wave propagation. Another difference with other reduced-order methods is that it is not based on an off-line/on-line strategy. Numerical examples are shown for the linear advection, KdV and FKPP equations, in one and two dimensions.
Liu Chunping
2003-06-02
Using a direct algebraic method, more new exact solutions of the Kolmogorov-Petrovskii-Piskunov equation are presented by formula form. Then a theorem concerning the relation between the kink-type solution and the kink-bell-type solution of nonlinear evolution equations is given. Finally, the applications of the theorem to several well-known equations in physics are also discussed.
Existence results for a class of parabolic evolution equations in Banach spaces
WangJing; XueXingmei
2003-01-01
We discuss the existence results of the parabolic evolution equation d(x(t) + g(t,x(t)))/dt + A(t)x(t) =f( t ,x(t)) in Banach spaces, where A (t) generates an evolution system and functions f, g are continuous. We get the theorem of existence of a mild solution, the theorem of existence and uniqueness of a mild solution and the theorem of existence and uniqueness of an S-classieal (semi-classical) solution. We extend the cases when g(t) = 0 or A(t) = A.
On the evolution equations for a self-gravitating charged scalar field
Pugliese, Daniela
2013-01-01
We consider a complex scalar field minimally coupled to gravity and to a U(1) gauge symmetry and we construct of a first order symmetric hyperbolic evolution system for the Einstein-Maxwell-Klein-Gordon system. Our analysis is based on a 1+3 tetrad formalism which makes use of the components of the Weyl tensor as one of the unknowns. In order to ensure the symmetric hyperbolicity of the evolution equations, implied by the Bianchi identity, we introduce a tensor of rank 3 corresponding to the covariant derivative of the Faraday tensor, and two tensors of rank 2 for the covariant derivative of the vector potential and the scalar field.
Atmospheric neutrinos, nu_e-nu_s oscillations, and a novel neutrino evolution equation
Akhmedov, Evgeny
2016-01-01
If a sterile neutrino nu_s with an eV-scale mass and a sizeable mixing to the electron neutrino exists, as indicated by the reactor and gallium neutrino anomalies, a strong resonance enhancement of nu_e-nu_s oscillations of atmospheric neutrinos should occur in the TeV energy range. At these energies neutrino flavour transitions in the 3+1 scheme depend on just one neutrino mass squared difference and are fully described within a 3-flavour oscillation framework. We demonstrate that the flavour transitions of atmospheric nu_e can actually be very accurately described in a 2-flavour framework, with neutrino flavour evolution governed by an inhomogeneous Schroedinger-like equation. Evolution equations of this type have not been previously considered in the theory of neutrino oscillations.
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Lukáčová-Medvid'ová, M.; Noelle, S.; Kraft, M.
2007-01-01
We present a new well-balanced finite volume method within the framework of the finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for the shallow water equations with source terms modelling the bottom topography and Coriolis forces. Results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are taken into account explicitly. We derive a well-balanced approximation of the integral equations and prove that the FVEG scheme is well-balanced for the stationary steady states as well as for the steady jets in the rotational frame. Several numerical experiments for stationary and quasi-stationary states as well as for steady jets confirm the reliability of the well-balanced FVEG scheme.
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Implicit Euler approximation of stochastic evolution equations with fractional Brownian motion
Kamrani, Minoo; Jamshidi, Nahid
2017-03-01
This work was intended as an attempt to motivate the approximation of quasi linear evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter H >1/2 . The spatial approximation method is based on Galerkin and the temporal approximation is based on implicit Euler scheme. An error bound and the convergence of the numerical method are given. The numerical results show usefulness and accuracy of the method.
Finite volume evolution Galerkin (FVEG) methods for three-dimensional wave equation system
Lukácová-Medvid'ová, Maria; Warnecke, Gerald; Zahaykah, Yousef
2004-01-01
The subject of the paper is the derivation of finite volume evolution Galerkin schemes for three-dimensional wave equation system. The aim is to construct methods which take into account all of the infinitely many directions of propagation of bicharacteristics. The idea is to evolve the initial function using the characteristic cone and then to project onto a finite element space. Numerical experiments are presented to demonstrate the accuracy and the multidimensional behaviour of the solutio...
Schüler, D.; Alonso, S.; Bär, M. [Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, 10587 Berlin (Germany); Torcini, A. [CNR-Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi - Via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); INFN Sez. Firenze, via Sansone 1, I-50019 Sesto Fiorentino (Italy)
2014-12-15
Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.
Mean-Field Backward Stochastic Evolution Equations in Hilbert Spaces and Optimal Control for BSPDEs
Ruimin Xu
2014-01-01
Full Text Available We obtain the existence and uniqueness result of the mild solutions to mean-field backward stochastic evolution equations (BSEEs in Hilbert spaces under a weaker condition than the Lipschitz one. As an intermediate step, the existence and uniqueness result for the mild solutions of mean-field BSEEs under Lipschitz condition is also established. And then a maximum principle for optimal control problems governed by backward stochastic partial differential equations (BSPDEs of mean-field type is presented. In this control system, the control domain need not to be convex and the coefficients, both in the state equation and in the cost functional, depend on the law of the BSPDE as well as the state and the control. Finally, a linear-quadratic optimal control problem is given to explain our theoretical results.
arXiv GeV-scale hot sterile neutrino oscillations: a derivation of evolution equations
Ghiglieri, J.
2017-05-23
Starting from operator equations of motion and making arguments based on a separation of time scales, a set of equations is derived which govern the non-equilibrium time evolution of a GeV-scale sterile neutrino density matrix and active lepton number densities at temperatures T > 130 GeV. The density matrix possesses generation and helicity indices; we demonstrate how helicity permits for a classification of various sources for leptogenesis. The coefficients parametrizing the equations are determined to leading order in Standard Model couplings, accounting for the LPM resummation of 1+n 2+n scatterings and for all 2 2 scatterings. The regime in which sphaleron processes gradually decouple so that baryon plus lepton number becomes a separate non-equilibrium variable is also considered.
Kranc: a Mathematica application to generate numerical codes for tensorial evolution equations
Husa, S; Lechner, C; Husa, Sascha; Hinder, Ian; Lechner, Christiane
2004-01-01
We present a suite of Mathematica-based computer-algebra packages, termed "Kranc", which comprise a toolbox to convert (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code. Kranc can be used as a "rapid prototyping" system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations.
Population Thinking, Price’s Equation and the Analysis of Economic Evolution
Andersen, Esben Sloth
2004-01-01
well as a means of accounting for evolution and as a starting point for the explanation of evolution. The applications of Price’s equation cover the partitioning and analysis of relatively short-term evolutionary change within individual industries as well as the study of more complexly structured...... applicable to economic evolution due to the development of what may be called a general evometrics. Central to this evometrics is a method for partitioning evolutionary change developed by George Price into the selection effect and what may be called the innovation effect. This method serves surprisingly...... populations of firms. By extrapolating these applications of Price’s evometrics, the paper suggests that his approach may play a central role in the emerging evolutionary econometrics....
史定华; 徐洪; 等
2002-01-01
For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution,the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations,called density evolution equations.It was proved that the time-dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi-group method.In this proof,it is not necessary to suppose that the repair rate function is bounded.The technique of the proof is valuable for many density evolution equatons.
Operational Solution of Non-Integer Ordinary and Evolution-Type Partial Differential Equations
Konstantin V. Zhukovsky
2016-12-01
Full Text Available A method for the solution of linear differential equations (DE of non-integer order and of partial differential equations (PDE by means of inverse differential operators is proposed. The solutions of non-integer order ordinary differential equations are obtained with recourse to the integral transforms and the exponent operators. The generalized forms of Laguerre and Hermite orthogonal polynomials as members of more general Appèl polynomial family are used to find the solutions. Operational definitions of these polynomials are used in the context of the operational approach. Special functions are employed to write solutions of DE in convolution form. Some linear partial differential equations (PDE are also explored by the operational method. The Schrödinger and the Black–Scholes-like evolution equations and solved with the help of the operational technique. Examples of the solution of DE of non-integer order and of PDE are considered with various initial functions, such as polynomial, exponential, and their combinations.
Rice Sean H
2008-09-01
Full Text Available Abstract Background Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly. The Price equation is thus poorly equipped to study an important class of evolutionary processes. Results I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation, but it is derived independently and contains terms with no analog in Price's formulation. This equation shows that the effects of selection are actually amplified by random variation in fitness. It also generalizes the known tendency of populations to be pulled towards phenotypes with minimum variance in fitness, and shows that this is matched by a tendency to be pulled towards phenotypes with maximum positive asymmetry in fitness. This equation also contains a term, having no analog in the Price equation, that captures cases in which the fitness of parents has a direct effect on the phenotype of their offspring. Conclusion Directional evolution is influenced by the entire distribution of individual fitness, not just the mean and variance. Though all moments of individuals' fitness distributions contribute to evolutionary change, the ways that they do so follow some general rules. These rules are invisible to the Price equation because it describes evolution retrospectively. An equally general
Rice, Sean H
2008-09-25
Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly. The Price equation is thus poorly equipped to study an important class of evolutionary processes. I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation, but it is derived independently and contains terms with no analog in Price's formulation. This equation shows that the effects of selection are actually amplified by random variation in fitness. It also generalizes the known tendency of populations to be pulled towards phenotypes with minimum variance in fitness, and shows that this is matched by a tendency to be pulled towards phenotypes with maximum positive asymmetry in fitness. This equation also contains a term, having no analog in the Price equation, that captures cases in which the fitness of parents has a direct effect on the phenotype of their offspring. Directional evolution is influenced by the entire distribution of individual fitness, not just the mean and variance. Though all moments of individuals' fitness distributions contribute to evolutionary change, the ways that they do so follow some general rules. These rules are invisible to the Price equation because it describes evolution retrospectively. An equally general prospective evolution equation compliments the Price equation
Bessaih, Hakima
2015-04-01
The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the obstacles. We represent the solid obstacles by holes in the fluid domain. The macroscopic (homogenized) equation is derived as another stochastic partial differential equation, defined in the whole non perforated domain. Here, the initial stochastic perturbation on the boundary becomes part of the homogenized equation as another stochastic force. We use the twoscale convergence method after extending the solution with 0 in the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. In order to pass to the limit on the boundary integrals, we rewrite them in terms of integrals in the whole domain. In particular, for the stochastic integral on the boundary, we combine the previous idea of rewriting it on the whole domain with the assumption that the Brownian motion is of trace class. Due to the particular boundary condition dealt with, we get that the solution of the stochastic homogenized equation is not divergence free. However, it is coupled with the cell problem that has a divergence free solution. This paper represents an extension of the results of Duan and Wang (Comm. Math. Phys. 275:1508-1527, 2007), where a reaction diffusion equation with a dynamical boundary condition with a noise source term on both the interior of the domain and on the boundary was studied, and through a tightness argument and a pointwise two scale convergence method the homogenized equation was derived. © American Institute of Mathematical Sciences.
Successful restrained eating and trait impulsiveness.
van Koningsbruggen, Guido M; Stroebe, Wolfgang; Aarts, Henk
2013-01-01
Restrained eaters with high scores on the Perceived Self-Regulatory Success in Dieting Scale (PSRS) are more successful than low scorers in regulating their food intake. According to the theory of temptation-elicited goal activation (Fishbach, Friedman, & Kruglanski, 2003), they have become successful because, due to earlier repeated instances of successful self-control, they formed an associative link between temptations and thoughts of dieting. It is unclear, however, why they should have been more successful in earlier attempts at self-control than their unsuccessful counterparts. We examined whether trait impulsiveness plays a role by investigating the associations between dietary restraint, trait impulsiveness, and PSRS. Results showed that the interaction between dietary restraint and impulsiveness predicted dieting success: A lower level of impulsiveness was associated with greater dieting success among restrained eaters. These results suggest that restrained eaters who are less impulsive are more likely to become successful restrained eaters as identified with the PSRS.
N. N. Romanova
1998-01-01
Full Text Available The dynamics of weakly nonlinear wave trains in unstable media is studied. This dynamics is investigated in the framework of a broad class of dynamical systems having a Hamiltonian structure. Two different types of instability are considered. The first one is the instability in a weakly supercritical media. The simplest example of instability of this type is the Kelvin-Helmholtz instability. The second one is the instability due to a weak linear coupling of modes of different nature. The simplest example of a geophysical system where the instability of this and only of this type takes place is the three-layer model of a stratified shear flow with a continuous velocity profile. For both types of instability we obtain nonlinear evolution equations describing the dynamics of wave trains having an unstable spectral interval of wavenumbers. The transformation to appropriate canonical variables turns out to be different for each case, and equations we obtained are different for the two types of instability we considered. Also obtained are evolution equations governing the dynamics of wave trains in weakly subcritical media and in media where modes are coupled in a stable way. Presented results do not depend on a specific physical nature of a medium and refer to a broad class of dynamical systems having the Hamiltonian structure of a special form.
Bashir Ahmad
2015-09-01
Full Text Available This article presents necessary conditions for the existence of weak solutions of the following space-nonlocal evolution equations on $\\mathbb{H}\\times(0, +\\infty$, where $\\mathbb{H}$ is the Heisenberg group: $$\\displaylines{ \\frac{\\partial^2 u }{\\partial t^2} + (- \\Delta_{\\mathbb{H}}^{\\alpha/2}|u|^m = |u|^{p},\\cr \\frac{\\partial u}{\\partial t} + (- \\Delta_{\\mathbb{H}}^{\\alpha/2} |u|^m = |u|^{p},\\cr \\frac{\\partial^2 u }{\\partial t^2} + (- \\Delta_{\\mathbb{H}}^{\\alpha/2} |u|^m + \\frac{\\partial u }{\\partial t} = |u|^p, }$$ $p \\in \\mathbb{R}, p>1, m \\in \\mathbb{N}$. Moreover, the life span for each equation is estimated under some suitable conditions. Our method of proof is based on the test function method.
Evolution equations of the probabilistic generalization of the Voigt profile function
Pagnini, Gianni
2007-01-01
The spectrum profile that emerges in molecular spectroscopy and atmospheric radiative transfer as the combined effect of Doppler and pressure broadenings is known as the Voigt profile function. Because of its convolution integral representation, the Voigt profile can be interpreted as the probability density function of the sum of two independent random variables with Gaussian density (due to the Doppler effect) and Lorentzian density (due to the pressure effect). Since these densities belong to the class of symmetric L\\'evy stable distributions, a probabilistic generalization is proposed as the convolution of two arbitrary symmetric L\\'evy densities. We study the case when the widths of the considered distributions depend on a scale-factor $\\tau$ that is representative of spatial inhomogeneity or temporal non-stationarity. The evolution equations for this probabilistic generalization of the Voigt function are here introduced and interpreted as generalized diffusion equations containing two Riesz space-fracti...
Multivector Fields and Jet Fields Setting Evolution Equations in Field Theories
Echeverría-Enríquez, A; Román-Roy, N
1997-01-01
The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle $J^1E\\to E\\to M$, it is shown that integrable multivector fields in $E$ are equivalent to integrable jet fields in $J^1E$ (connections in $E$). This result is applied to the particular case of multivector fields in the manifold $J^1E$ and jet fields in the repeated jet bundle $J^1J^1E$, in order to characterize integrable multivector fields and jet fields whose integral manifolds are canonical liftings of sections. These results allow us to set the lagrangian evolution equations for first-order classical field theories in three equivalent geometrical ways (in a form similar to that in which the lagrangian dynamical equations of non-autonomous mechanical systems are usually given).
Unified QCD evolution equations and the dominant behaviour of structure functions at low x
Peschanski, R; Peschanski, R; Wallon, S
1994-01-01
We consider a system of evolution equations for quark and gluon structure functions satisfying the leading-logarithmic behaviour due to both QCD collinear \\left(LLQ^2 \\right) and infrared (LL1/x) singularities. We show that these equations leave undetermined an arbitrary regular function of j in the Mellin-transformed weights. We consider the constraints resulting from energy-momentum conservation and from the decoupling of quark loops in the leading j -plane singularity. These constraints can be fulfilled without influencing the leading-log terms. As a particular consequence of the second constraint, the location of the leading singularity is determined in terms of the (LL1/x) and \\left(LLQ^2 \\right) kernels. It leads to a value significantly lower than the LL1/x evaluation, while remaining at j > 1, and compatible with the behaviour of structure functions observed at HERA.
A Matrix Approach to Numerical Solution of the DGLAP Evolution Equations
Ratcliffe, P G
2001-01-01
A matrix-based approach to numerical integration of the DGLAP evolution equations is presented. The method arises naturally on discretisation of the Bjorken x variable, a necessary procedure for numerical integration. Owing to peculiar properties of the matrices involved, the resulting equations take on a particularly simple form and may be solved in closed analytical form in the variable t=ln(alpha_0/alpha). Such an approach affords parametrisation via data x bins, rather than fixed functional forms. Thus, with the aid of the full correlation matrix, appraisal of the behaviour in different x regions is rendered more transparent and free of pollution from unphysical cross-correlations inherent to functional parametrisations. Computationally, the entire programme results in greater speed and stability; the matrix representation developed is extremely compact. Moreover, since the parameter dependence is linear, fitting is very stable and may be performed analytically in a single pass over the data values.
Mottaghizadeh, Marzieh; Taghavi-Shahri, Fatemeh
2016-01-01
We analytically solved the QED $\\otimes$ QCD coupled DGLAP evolution equations at leading order (LO) quantum electrodynamics (QED) and next to leading order (NLO) quantum chromodynamics (QCD) approximations, using the Laplace transform method and then computed the proton structure function in terms of the unpolarized parton distributions functions. Our analyitical solutions for parton densities are in good agreement with those from APFEL (A PDF Evolution Library) (Computer Physics Communications 185, 1647-1668 (2014)) and CT14QED (Phys. Rev. D 93, 114015 (2016)) global parameterizations. We also compared the proton structure function, $F_{2}^{p}(x,Q^{2})$, with experimental data released by the ZEUS and H1 collaborations at HERA. There is a nice agreement between them in the range of low and high x and $Q^{2}$.
Evolution of superoscillations for Schrödinger equation in a uniform magnetic field
Colombo, F.; Gantner, J.; Struppa, D. C.
2017-09-01
Aharonov-Berry superoscillations are band-limited functions that oscillate faster than their fastest Fourier component. Superoscillations appear in several fields of science and technology, such as Aharonov's weak measurement in quantum mechanics, in optics, and in signal processing. An important issue is the study of the evolution of superoscillations using the Schrödinger equation when the initial datum is a weak value. Some superoscillatory functions are not square integrable, but they are real analytic functions that can be extended to entire holomorphic functions. This fact leads to the study of the continuity of a class of convolution operators acting on suitable spaces of entire functions with growth conditions. In this paper, we study the evolution of a superoscillatory initial datum in a uniform magnetic field. Moreover, we collect some results on convolution operators that appear in the theory of superoscillatory functions using a direct approach that allows the convolution operators to have non-constant coefficients of polynomial type.
Hilditch, David; Bugner, Marcus; Rueter, Hannes; Bruegmann, Bernd
2016-01-01
A long-standing problem in numerical relativity is the satisfactory treatment of future null-infinity. We propose an approach for the evolution of hyperboloidal initial data in which the outer boundary of the computational domain is placed at infinity. The main idea is to apply the `dual foliation' formalism in combination with hyperboloidal coordinates and the generalized harmonic gauge formulation. The strength of the present approach is that, following the ideas of Zenginoglu, a hyperboloidal layer can be naturally attached to a central region using standard coordinates of numerical relativity applications. Employing a generalization of the standard hyperboloidal slices, developed by Calabrese et. al., we find that all formally singular terms take a trivial limit as we head to null-infinity. A byproduct is a numerical approach for hyperboloidal evolution of nonlinear wave equations violating the null-condition. The height-function method, used often for fixed background spacetimes, is generalized in such a...
On an abstract evolution equation with a spectral operator of scalar type
Marat V. Markin
2002-01-01
Full Text Available It is shown that the weak solutions of the evolution equation y′(t=Ay(t, t∈[0,T (0
Time-evolution of quantum systems via a complex nonlinear Riccati equation. II. Dissipative systems
Cruz, Hans; Schuch, Dieter; Castaños, Octavio; Rosas-Ortiz, Oscar
2016-10-01
In our former contribution (Cruz et al., 2015), we have shown the sensitivity to the choice of initial conditions in the evolution of Gaussian wave packets via the nonlinear Riccati equation. The formalism developed in the previous work is extended to effective approaches for the description of dissipative quantum systems. By means of simple examples we show the effects of the environment on the quantum uncertainties, correlation function, quantum energy contribution and tunnelling currents. We prove that the environmental parameter γ is strongly related with the sensitivity to the choice of initial conditions.
SELF-SIMILAR SINGULAR SOLUTION OF A P-LAPLACIAN EVOLUTION EQUATION WITH GRADIENT ABSORPTION TERM
Shi Peihu
2004-01-01
In this paper we deal with the self-similar singular solution of the p-Laplacian evolution equation ut = div(|△u|p-2△u) - |△u|q for p ＞ 2 and q ＞ 1 in Rn × (0,∞). We prove that when p ＞ q + n/(n + 1) there exist self-similar singular solutions, while p (≤) q+n/(n+ 1) there is no any self-similar singular solution. In case of existence, the self-similar singular solutions are the self-similar very singular solutions,which have compact support. Moreover, the interface relation is obtained.
Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds
Bollermann, Andreas; Noelle, Sebastian; Medvidová, Maria Lukáčová -
2015-01-01
We present a new Finite Volume Evolution Galerkin (FVEG) scheme for the solution of the shallow water equations (SWE) with the bottom topography as a source term. Our new scheme will be based on the FVEG methods presented in (Luk\\'a\\v{c}ov\\'a, Noelle and Kraft, J. Comp. Phys. 221, 2007), but adds the possibility to handle dry boundaries. The most important aspect is to preserve the positivity of the water height. We present a general approach to ensure this for arbitrary finite volume schemes...
Li Wenting [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)], E-mail: lwt.wentinglee@yahoo.com.cn; Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)
2009-03-15
Based on symbolic computation and the idea of rational expansion method, a new generalized compound Riccati equations rational expansion method (GCRERE) is suggested to construct a series of exact complexiton solutions for nonlinear evolution equations. Compared with most existing rational expansion methods and other sophisticated methods, the proposed method not only recover some known solutions, but also find some new and general complexiton solutions. The validity and reliability of the method is tested by its application to the (2+1)-dimensional Burgers equation. It is shown that more complexiton solutions can be found by this new method.
无
2010-01-01
We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.
Liu, Chengshi
2010-08-01
We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.
Evolution equation for B-meson distribution amplitude in HQET in the coordinate space
Kawamura, Hiroyuki
2010-01-01
The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the "quasilocal" kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate-space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation $t$ in terms of the DA at a lower renormalization scale $\\mu$ with smaller interquark separations $zt$ ($z \\leq 1$). This formula allows us to present rigorous calculat...
On the classification of scalar evolution equations with non-constant separant
Hümeyra Bilge, Ayşe; Mizrahi, Eti
2017-01-01
The ‘separant’ of the evolution equation u t = F, where F is some differentiable function of the derivatives of u up to order m, is the partial derivative \\partial F/\\partial {{u}m}, where {{u}m}={{\\partial}m}u/\\partial {{x}m} . As an integrability test, we use the formal symmetry method of Mikhailov-Shabat-Sokolov, which is based on the existence of a recursion operator as a formal series. The solvability of its coefficients in the class of local functions gives a sequence of conservation laws, called the ‘conserved densities’ {ρ(i)}, i=-1,1,2,3,\\ldots . We apply this method to the classification of scalar evolution equations of orders 3≤slant m≤slant 15 , for which {ρ(-1)}={≤ft[\\partial F/\\partial {{u}m}\\right]}-1/m} and {{ρ(1)} are non-trivial, i.e. they are not total derivatives and {ρ(-1)} is not linear in its highest order derivative. We obtain the ‘top level’ parts of these equations and their ‘top dependencies’ with respect to the ‘level grading’, that we defined in a previous paper, as a grading on the algebra of polynomials generated by the derivatives u b+i , over the ring of {{C}∞} functions of u,{{u}1},\\ldots,{{u}b} . In this setting b and i are called ‘base’ and ‘level’, respectively. We solve the conserved density conditions to show that if {ρ(-1)} depends on u,{{u}1},\\ldots,{{u}b}, then, these equations are level homogeneous polynomials in {{u}b+i},\\ldots,{{u}m} , i≥slant 1 . Furthermore, we prove that if {ρ(3)} is non-trivial, then {ρ(-1)}={≤ft(α ub2+β {{u}b}+γ \\right)}1/2} , with b≤slant 3 while if {{ρ(3)} is trivial, then {ρ(-1)}={≤ft(λ {{u}b}+μ \\right)}1/3} , where b≤slant 5 and α, β, γ, λ and μ are functions of u,\\ldots,{{u}b-1} . We show that the equations that we obtain form commuting flows and we construct their recursion operators that are respectively of orders 2 and 6 for non-trivial and trivial {{ρ(3)} respectively. Omitting lower order
Destrade, M.
2010-12-08
We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.
Evolution equations for the joint probability of several compositions in turbulent combustion
Bakosi, Jozsef [Los Alamos National Laboratory
2010-01-01
One-point statistical simulations of turbulent combustion require models to represent the molecular mixing of species mass fractions, which then determine the reaction rates. For multi-species mixing the Dirichlet distribution has been used to characterize the assumed joint probability density function (PDF) of several scalars, parametrized by solving modeled evolution equations for their means and the sum of their variances. The PDF is then used to represent the mixing state and to obtain the chemical reactions source terms in moment closures or large eddy simulation. We extend the Dirichlet PDF approach to transported PDF methods by developing its governing stochastic differential equation (SDE). The transport equation, as opposed to parametrizing the assumed PDF, enables (1) the direct numerical computation of the joint PDF (and therefore the mixing model to directly account for the flow dynamics (e.g. reaction) on the shape of the evolving PDF), and (2) the individual specification of the mixing timescales of each species. From the SDE, systems of equations are derived that govern the first two moments, based on which constraints are established that provide consistency conditions for material mixing. A SDE whose solution is the generalized Dirichlet PDF is also developed and some of its properties from the viewpoint of material mixing are investigated. The generalized Dirichlet distribution has the following advantages over the standard Dirichlet distribution due to its more general covariance structure: (1) its ability to represent differential diffusion (i.e. skewness) without affecting the scalar means, and (2) it can represent both negatively and positively correlated scalars. The resulting development is a useful representation of the joint PDF of inert or reactive scalars in turbulent flows: (1) In moment closures, the mixing physics can be consistently represented by one underlying modeling principle, the Dirichlet or the generalized Dirichlet PDF, and
发展方程xttt+iCx=f的解结构%CONSTRUCTION OF SOLUTION FOR EVOLUTION EQUATION xttt+iCx=f
张利勋; 刘永智; 王康宁
2006-01-01
The construction of solution for three-order evolution equation xttt=A3x is skillfully obtained and the semigroup of equation operator is theoretically proved,then the solution for three-order evolution equation xttt+iCx=f is constructed from the appropriate transformation,and the necessary and sufficient conditions of its unitary semigroup are presented.
Hasibun Naher
2012-01-01
Full Text Available The generalized Riccati equation mapping is extended with the basic (G′/G-expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the (2+1-dimensional modified Zakharov-Kuznetsov equation by applying this method. Further, the auxiliary equation G′(η=w+uG(η+vG2(η is executed with arbitrary constant coefficients and called the generalized Riccati equation. The obtained solutions including solitons and periodic solutions are illustrated through the hyperbolic functions, the trigonometric functions, and the rational functions. In addition, it is worth declaring that one of our solutions is identical for special case with already established result which verifies our other solutions. Moreover, some of obtained solutions are depicted in the figures with the aid of Maple.
Description of the evolution of inhomogeneities on a dark matter halo with the Vlasov equation
Domínguez-Fernández, Paola; Jiménez-Vázquez, Erik; Alcubierre, Miguel; Montoya, Edison; Núñez, Darío
2017-09-01
We use a direct numerical integration of the Vlasov equation in spherical symmetry with a background gravitational potential to determine the evolution of a collection of particles in different models of a galactic halo in order to test its stability against perturbations. Such collection is assumed to represent a dark matter inhomogeneity which is represented by a distribution function defined in phase-space. Non-trivial stationary states are obtained and determined by the virialization of the system. We describe some features of these stationary states by means of the properties of the final distribution function and final density profile. We compare our results using the different halo models and find that the NFW halo model is the most stable of them, in the sense that an inhomogeneity in this halo model requires a shorter time to virialize.
On polynomial solutions to Fokker-Planck and sinked density evolution equations
Zuparic, Mathew
2015-04-01
We analytically solve for the time dependent solutions of various density evolution models. With specific forms of the diffusion, drift and sink coefficients, the eigenfunctions can be expressed in terms of hypergeometric functions. We obtain the relevant discrete and continuous spectra for the eigenfunctions. With non-zero sink terms the discrete spectra eigenfunctions are generalizations of well known orthogonal polynomials: the so-called associated-Laguerre, Bessel, Fisher-Snedecor and Romanovski functions. We use MacRobert’s proof to obtain closed form expressions for the continuous normalization of the Romanovski density function. Finally, we apply our results to obtain the analytical solutions associated with the Bertalanffy-Richards-Langevin equation.
L2-stability of traveling wave solutions to nonlocal evolution equations
Lang, Eva; Stannat, Wilhelm
2016-10-01
Stability of the traveling wave solution to a general class of one-dimensional nonlocal evolution equations is studied in L2-spaces, thereby providing an alternative approach to the usual spectral analysis with respect to the supremum norm. We prove that the linearization around the traveling wave solution satisfies a Lyapunov-type stability condition in a weighted space L2 (ρ) for a naturally associated density ρ. The result can be applied to obtain stability of the traveling wave solution under stochastic perturbations of additive or multiplicative type. For small wave speeds, we also prove an alternative Lyapunov-type stability condition in L2 (m), where m is the symmetrizing density for the traveling wave operator, which allows to derive a long-term stochastic stability result.
Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation
Villois, Alberto; Krstulovic, Giorgio
2016-01-01
The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using a recently-developed accurate and robust tracking algorithm, all quantised vortices are extracted from the fields. The Vinen's decay law for the total vortex length with a coefficient that is in quantitative agreement with the values measured in Helium II is observed. The topology of the tangle is then studied showing that linked rings may appear during the decay. The tracking also allows for determining the statistics of small-scales quantities of vortex lines, exhibiting large fluctuations of curvature and torsion. Finally, the temporal evolution of the Kelvin wave spectrum is obtained providing evidence of the development of a weak-wave turbulence cascade.
Domínguez-González, Leomaris; Andreani, Louis; Stanek, Klaus P.; Gloaguen, Richard
2016-06-01
We reply to the comments of Mitchell et al. on our paper entitled "Geomorpho-tectonic evolution of the Jamaican restraining bend". The comments contain statements about the methods that need to be balanced. We agree that the interpretation of the modeled drainage network in some karstified parts of the Jamaican island is difficult, but this does not affect the validity of our analysis elsewhere. We consider that our geomorphic analyses (which also include topographic profiles and morphometric maps) are still valid. The view expressed by Mitchell et al. that we used serially developed landscapes to 'date' progressive uplift is an oversimplification of our discussion. We highlighted the differences between the geomorpho-tectonic provinces of Jamaica, and we proposed to explain these differences by a model which involves (1) a westward propagation of the restraining bend and (2) a difference in tectonic styles between the different provinces of Jamaica. Our interpretation does not contradict existing models based on seismotectonic data, provenance analysis or on the origin of Jamaican bauxite. There is a disagreement between James-Williamson et al. (2014), which suggested that central Jamaica was already being uplifted by the end of the Late Miocene, and Domínguez-González et al. (2015), which proposed a Pliocene to present onset of the NE-trending compression toward the SW. However, the timing of the deformation in central and western Jamaica is still poorly constrained and, at this time, any interpretation of the uplift history of central Jamaica should be considered as hypothetical.
Successful restrained eating and trait impulsiveness
van koningsbruggen, G.M.; Stroebe, Wolfgang; Aarts, H.
2013-01-01
Restrained eaters with high scores on the Perceived Self-Regulatory Success in Dieting Scale (PSRS) are more successful than low scorers in regulating their food intake. According to the theory of temptation-elicited goal activation (Fishbach, Friedman, & Kruglanski, 2003), they have become successf
dos Santos, B Coutinho; Tsallis, C
2010-12-01
We consider a class of single-particle one-dimensional stochastic equations which include external field, additive, and multiplicative noises. We use a parameter θ ∊ [0,1] which enables the unification of the traditional Itô and Stratonovich approaches, now recovered, respectively, as the θ=0 and θ=1/2 particular cases to derive the associated Fokker-Planck equation (FPE). These FPE is a linear one, and its stationary state is given by a q-Gaussian distribution with q=(τ+2M(2-θ))/(τ+2M(1-θ)<3), where τ ≥ 0 characterizes the strength of the confining external field and M ≥ 0 is the (normalized) amplitude of the multiplicative noise. We also calculate the standard kurtosis κ(₁) and the q-generalized kurtosis κ(q) (i.e., the standard kurtosis but using the escort distribution instead of the direct one). Through these two quantities we numerically follow the time evolution of the distributions. Finally, we exhibit how these quantities can be used as convenient calibrations for determining the index q from numerical data obtained through experiments, observations, or numerical computations.
Cosmological constraints on the dark energy equation of state and its evolution
Hannestad, S
2004-01-01
We have calculated constraints on the evolution of the equation of state of the dark energy, w(z), from a joint analysis of data from the cosmic microwave background, large scale structure and type-Ia supernovae. In order to probe the time-evolution of w we propose a new, simple parametrization of w, which has the advantage of being transparent and simple to extend to more parameters as better data becomes available. Furthermore it is well behaved in all asymptotic limits. Based on this parametrization we find that w(z=0)=-1.43^{+0.16}_{-0.38} and dw/dz(z=0) = 1.0^{+1.0}_{-0.8}. For a constant w we find that -1.34 < w < -0.79 at 95% C.L. Thus, allowing for a time-varying w shifts the best fit present day value of w down. However, even though models with time variation in w yield a lower chi^2 than pure LambdaCDM models, they do not have a better goodness-of-fit. Rank correlation tests on SNI-a data also do not show any need for a time-varying w.
El Mouden, C; André, J-B; Morin, O; Nettle, D
2014-02-01
Transmitted culture can be viewed as an inheritance system somewhat independent of genes that is subject to processes of descent with modification in its own right. Although many authors have conceptualized cultural change as a Darwinian process, there is no generally agreed formal framework for defining key concepts such as natural selection, fitness, relatedness and altruism for the cultural case. Here, we present and explore such a framework using the Price equation. Assuming an isolated, independently measurable culturally transmitted trait, we show that cultural natural selection maximizes cultural fitness, a distinct quantity from genetic fitness, and also that cultural relatedness and cultural altruism are not reducible to or necessarily related to their genetic counterparts. We show that antagonistic coevolution will occur between genes and culture whenever cultural fitness is not perfectly aligned with genetic fitness, as genetic selection will shape psychological mechanisms to avoid susceptibility to cultural traits that bear a genetic fitness cost. We discuss the difficulties with conceptualizing cultural change using the framework of evolutionary theory, the degree to which cultural evolution is autonomous from genetic evolution, and the extent to which cultural change should be seen as a Darwinian process. We argue that the nonselection components of evolutionary change are much more important for culture than for genes, and that this and other important differences from the genetic case mean that different approaches and emphases are needed for cultural than genetic processes.
A transport equation for the evolution of shock amplitudes along rays
Giovanni Russo
1991-05-01
Full Text Available A new asymptotic method is derived for the study of the evolution of weak shocks in several dimension. The method is based on the Generalized Wavefront Expansion derived in [1]. In that paper the propagation of a shock into a known background was studied under the assumption that shock is weak, i.e. Mach Number =1+O(ε, ε ≪ 1, and that the perturbation of the field varies over a length scale O(ε. To the lowest order, the shock surface evolves along the rays associated with the unperturbed state. An infinite system of compatibility relations was derived for the jump in the field and its normal derivatives along the shock, but no valid criterion was found for a truncation of the system. Here we show that the infinite hierarchy is equivalent to a single equation that describes the evolution of the shock along the rays. We show that this method gives equivalent results to those obtained by Weakly Nonlinear Geometrical Optics [2].
STUDY ON RESTRAINING THE RESIDUAL VIBRATION OF FLEXIBLE ARM BY PLANNING ACCELERATION
Zhu Jian; Shao Hao; Wang Xingsong
2000-01-01
The method of planning acceleration is discussed to restrain the residual vibration of flexible arm.Based on the built mathematical model of the flexible arm,the equations of vibration with acceleration,vibration frequency,damping and time are obtained theoretically.According to the vibration frequency and damping,the suitable acceleration is executed experimentally to the flexible arm at the corresponding time.The result shows that this way can give rise to good effect to restrain the residual vibration.
Zhu Shundong [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China)], E-mail: zhusd1965@sina.com
2008-09-15
The tanh method is used to find travelling wave solutions to various wave equations. In this paper, the extended tanh function method is further improved by the generalizing Riccati equation mapping method and picking up its new solutions. In order to test the validity of this approach, the (2 + 1)-dimensional Boiti-Leon-Pempinelle equation is considered. As a result, the abundant new non-travelling wave solutions are obtained.
Yan, Shaomin; Li, Zhenchong; Wu, Guang
2010-04-01
The understanding of evolutionary mechanism is important, and equally important is to describe the evolutionary process. If so, we would know where the biological evolution will go. At species level, we would know whether and when a species will extinct or be prosperous. At protein level, we would know when a protein family will mutate more. In our previous study, we explored the possibility of using the differential equation to describe the evolution of protein family from influenza A virus based on the assumption that the mutation process is the exchange of entropy between protein family and its environment. In this study, we use the analytical solution of system of differential equations to fit the evolution of matrix protein 1 family from influenza A virus. Because the evolutionary process goes along the time course, it can be described by differential equation. The results show that the evolution of a protein family can be fitted by the analytical solution. With the obtained fitted parameters, we may predict the evolution of matrix protein 1 family from influenza A virus. Our model would be the first step towards the systematical modeling of biological evolution and paves the way for further modeling.
柳银萍; 李志斌
2003-01-01
Based on a 0 of elliptic equation, a new algebraic method to construct a series of exact solutions for nonlinear evolution equations is proposed, meanwhile, its complete implementation TRWS in Maple is presented. The TRWS can output a series of travelling wave solutions entirely automatically, which include polynomial solutions, exponential function solutions, triangular function solutions, hyperbolic function solutions, rational function solutions, Jacobi elliptic function solutions, and Weierstrass elliptic function solutions. The effectiveness of the package is illustrated by applying it to a variety of equations. Not only are previously known solutions recovered but also new solutions and more general form of solutions are obtained.
Kovács, M; Lindgren, F
2012-01-01
We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation.
Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México DF (Mexico); Schuch, Dieter [Institut für Theoretische Physik, JW Goethe-Universität Frankfurt am Main, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany); Castaños, Octavio, E-mail: ocasta@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México DF (Mexico); Rosas-Ortiz, Oscar [Physics Department, Cinvestav, A. P. 14-740, 07000 México D. F. (Mexico)
2015-09-15
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.
Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado
1997-10-01
The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.
Diffusion-equation representations of landform evolution in the simplest circumstances: Appendix C
Hanks, Thomas C.
2009-01-01
The diffusion equation is one of the three great partial differential equations of classical physics. It describes the flow or diffusion of heat in the presence of temperature gradients, fluid flow in porous media in the presence of pressure gradients, and the diffusion of molecules in the presence of chemical gradients. [The other two equations are the wave equation, which describes the propagation of electromagnetic waves (including light), acoustic (sound) waves, and elastic (seismic) waves radiated from earthquakes; and LaPlace’s equation, which describes the behavior of electric, gravitational, and fluid potentials, all part of potential field theory. The diffusion equation reduces to LaPlace’s equation at steady state, when the field of interest does not depend on t. Poisson’s equation is LaPlace’s equation with a source term.
范恩贵
2001-01-01
A Riccati equation involving a parameter and symbolic computation are used to uniformly construct the different forms of travelling wave solutions for nonlinear evolution equations.It is shown that the sign of the parameter can be applied in judging the existence of various forms of travelling wave solutions.An efficiency of this method is demonstrated on some equations,which include Burgers-Huxley equation,Caudrey-Dodd-Gibbon-Kawada equation,generalized Benjamin-Bona-Mahony equation and generalized Fisher equation.
Frequency-Uniform Decomposition, Function Spaces , and Applications to Nonlinear Evolution Equations
Shaolei Ru
2013-01-01
Full Text Available By combining frequency-uniform decomposition with (, we introduce a new class of function spaces (denoted by . Moreover, we study the Cauchy problem for the generalized NLS equations and Ginzburg-Landau equations in .
Soliton solutions of some nonlinear evolution equations with time-dependent coefficients
Hitender Kumar; Anand Malik; Fakir Chand
2013-02-01
In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schrödinger equation and (, ) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.
Targut (O)zi(s); Imail Asian
2009-01-01
With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher's equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G'/G-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered.
Transversely Compressed- and Restrained Shear Joints
Schmidt, Jacob Wittrup; Hansen, Christian Skodborg
2013-01-01
. This paper presents theoretical model which can predict the response of transversely compressed and restrained single- and double lap shear joints. The interface material model is based on a cohesive law in the shear-slip plane with a descending branch and a uniform frictional stress added due...... to the friction in the crack, emanating from the transverse pressure or restraint. The theoretical model is compared with experimental results from transversely compressed single- and double shear joints. Also theoretical predictions of a mechanical integrated sleeve-wedge anchorage load capacity are carried out...
From the Fermi-Pasta-Ulam Model to Higher-Order Nonlinear Evolution Equations
Kudryashov, Nikolay A.
2016-02-01
We consider generalizations of the Korteweg-de Vries equation of the fifth and seventh order obtained from the Fermi-Pasta-Ulam problem. Analytical properties of the equation are investigated taking into account the Painlevé test. It is shown that the equations of the fifth and seventh order do not have the Painlevé property. We demonstrate that there are expansions of the solution in the Laurent series and as a consequence we can find exact solutions of the equations. Solitary wave and elliptic solutions of the fifth and seventh order equations are presented.
Mottaghizadeh, Marzieh; Taghavi Shahri, Fatemeh; Eslami, Parvin
2017-10-01
In this paper we present a new and efficient analytical solutions for evolving the QCD⊗QED DGLAP evolution equations in Mellin space and obtain the parton distribution functions (PDFs) in perturbative QCD including the QED corrections. The validity of our analytical solutions, which have done in the next to leading order QCD and the leading order QED approximations, are checked with the initial parton distributions from newly released CT14QED global analysis code (Schmidt et al., 2016 [9]). The evolved parton distribution functions are in good agreement with CT14QED PDFs set and also with those from APFEL (Bertone et al., 2014 [7]) program. Finally, we derived the impact of the NLO QED corrections to the QCD⊗QED DGLAP evolution equations.
Nuclear SMAD2 Restrains Proliferation of Glioblastoma
Yunhu Yu
2015-03-01
Full Text Available Aims: Although TGFβ receptor signaling has been shown to play a role in regulation of the growth and metastasis of glioblastoma multiforme (GBM, the downstream pathway through either SMAD2 or SMAD3 has not been elucidated. In this study, we investigate whether nuclear SMAD2 can restrain the proliferation of glioblastoma. Methods: A total of 23 resected specimens from GBM patients were collected for SMAD2 detection. Human GBM cell line A172, U87mg, D341m and Hs683 were maintained in Dulbecco's modified Eagle's medium and transfected with SMAD2 and SMAD3 shRNA plasmids. Gene expression was detected by RT-qPCR and Western and cell growth were detected by MTT assay. Results: Our results showed that the phosphorylated SMAD2 (pSMAD2, the nuclear and functional form of SMAD2 levels in GBM were significantly lower than the paired normal brain tissue in patients. Depletion of SMAD2, but not SMAD3, significantly abolished the inhibitory effects of TGFβ1 on the growth of GBM cells, possibly through pSMAD2-mediated increases in cell-cycle inhibitor, p27. Conclusion: Our data suggest that TGFβ/SMAD2 signaling cascades restrains growth of GBM.
Monavari, Mehran; Sandfeld, Stefan; Zaiser, Michael
2016-10-01
Plasticity is governed by the evolution of, in general anisotropic, systems of dislocations. We seek to faithfully represent this evolution in terms of density-like variables which average over the discrete dislocation microstructure. Starting from T. Hochrainer's continuum theory of dislocations (CDD) (Hochrainer, 2015), we introduce a methodology based on the 'Maximum Information Entropy Principle' (MIEP) for deriving closed-form evolution equations for dislocation density measures of different order. These equations provide an optimum representation of the kinematic properties of systems of curved and connected dislocation lines with the information contained in a given set of density measures. The performance of the derived equations is benchmarked against other models proposed in the literature, using discrete dislocation dynamics simulations as a reference. As a benchmark problem we study dislocations moving in a highly heterogeneous, persistent-slip-band like geometry. We demonstrate that excellent agreement with discrete simulations can be obtained in terms of a very small number of averaged dislocation fields containing information about the edge and screw components of the total and excess (geometrically necessary) dislocation densities. From these the full dislocation orientation distribution which emerges as dislocations move through a channel-wall structure can be faithfully reconstructed.
A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations
Zhang Zhi-Yong; Yong Xue-Lin; Chen Yu-Fu
2009-01-01
A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.
Amar Debbouche
2012-01-01
Full Text Available We introduce a new concept called implicit evolution system to establish the existence results of mild and strong solutions of a class of fractional nonlocal nonlinear integrodifferential system, then we prove the exact null controllability result of a class of fractional evolution nonlocal integrodifferential control system in Banach space. As an application that illustrates the abstract results, two examples are provided.
Do All Integrable Evolution Equations Have the Painlevé Property?
K.M. Tamizhmani
2007-06-01
Full Text Available We examine whether the Painlevé property is necessary for the integrability of partial differential equations (PDEs. We show that in analogy to what happens in the case of ordinary differential equations (ODEs there exists a class of PDEs, integrable through linearisation, which do not possess the Painlevé property. The same question is addressed in a discrete setting where we show that there exist linearisable lattice equations which do not possess the singularity confinement property (again in analogy to the one-dimensional case.
Naher, Hasibun; Abdullah, Farah Aini
2013-01-01
In this article, new (G′/G)-expansion method and new generalized (G′/G)-expansion method is proposed to generate more general and abundant new exact traveling wave solutions of nonlinear evolution equations...
On the Cauchy Problem of Evolution p-Laplacian Equation with Nonlinear Gradient Term
Mingyu CHEN; Junning ZHAO
2009-01-01
The authors study the existence of solution to p-Laplacian equation with non-linear forcing term under optimal assumptions on the initial data,which are assumed to be measures.The existence of local solution is obtained.
Bruno de Andrade
2009-01-01
Full Text Available We study the existence and uniqueness of almost automorphic (resp., pseudo-almost automorphic solutions to a first-order differential equation with linear part dominated by a Hille-Yosida type operator with nondense domain.
49 CFR 1103.22 - Restraining clients from improprieties.
2010-10-01
... 49 Transportation 8 2010-10-01 2010-10-01 false Restraining clients from improprieties. 1103.22... Practitioner's Duties and Responsibilities Toward A Client § 1103.22 Restraining clients from improprieties. A practitioner should see that his clients act with the same restraint that the practitioner himself uses...
Mechanical Analysis of Concrete Specimen under Restrained Condition
MA Xinwei; NIU Changren; R D Hooton
2005-01-01
In order to quantify the development of the tensile stresses and obtain a reliable estimation of the cracking risk, the concrete was subjected to restrained conditions. The fully restrained condition was achieved by keeping the length constant of a concrete specimen. Comparing the free shrinkage with the restrained shrinkage,tensile creep could be discriminated from shrinkage. The testing method was introduced in details, and the mechanical behaviors under tensile load were analyzed. Results show that concrete exhibits a pronounced viscoelasticity. Under restrained condition, the self induced tensile stress increases with time. The lower the water to cement ratio, the larger the tensile stress at the same age. The tensile creep of hardening concrete is much larger than that of hardened concrete. The relationships among autogenous shrinkage under free condition, elastic strain and creep under restrained condition are described, and the mathematical model for the calculation of elastic strain and creep is proposed.
Long Wei
2014-01-01
Full Text Available In a recent paper (Zhang (2013, the author claims that he has proposed two rules to modify Ibragimov’s theorem on conservation laws to “ensure the theorem can be applied to nonlinear evolution equations with any mixed derivatives.” In this letter, we analysis the paper. Indeed, the so-called “modification rules” are needless and the theorem of Ibragimov can be applied to construct conservation laws directly for nonlinear equations with any mixed derivatives as long as the formal Lagrangian is rewritten in symmetric form. Moreover, the conservation laws obtained by the so-called “modification rules” in the paper under discussion are equivalent to the one obtained by Ibragimov’s theorem.
ZHANG Han; LUO Jun; REN Ting-Ting; SUN Xian-Ping
2010-01-01
@@ We report the experimental demonstration of decoherence dynamics of entanglement for the four Bell states in two-qubit nuclear-spin systems on ensemble quantum computers.Using artificial error operators to simulate noisy channels,we experimentally investigate the effect of noises on the four Bell states,and furthermore observe the time evolution of entanglement for the four Bell states in different noisy channels by calculating concurrences.Our experimental results show that the concurrences of the different Bell states under the same artificial error operations have the same values within the experimental error,and are independent of the different Bell states.These experimental results verify the theoretical evolution equation developed by Konrad et al.[Nature Phys.4 (2008) 99]for two-qubit entanglement.
Yan, Zuomao; Lu, Fangxia
2016-08-01
In this paper, we introduce the optimal control problems governed by a new class of impulsive stochastic partial neutral evolution equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, the analytic semigroup theory, fractional powers of closed operators, and suitable fixed point theorems, we prove an existence result of mild solutions for the control systems in the α-norm without the assumptions of compactness. Next, we derive the existence conditions of optimal pairs of these systems. Finally, application to a nonlinear impulsive stochastic parabolic optimal control system is considered.
Y.G. Cao; W.K. Chow; N.K. Fong
2011-01-01
With a self-similar parameter b（At） = Hi/λi, where At is the Atwood number, Hi and λi are the a.mplluae and wavelength of bubble （i = 1） and spike （i = 2） respectively, we derive analytically the solutions to the buoyancy-drag equation recently proposed for dynamical evolution of Rayleigh-Taylor and Richtmyer-Meshkov mixing zone. Numerical solutions are obtained with a simple form ofb（At）--- 1/（1 ＋ At） and comparisons with recent LEM （linear electric motor） experiments are made, and an agreement is found with properly chosen initial conditions.
Nemirovskii, Sergey K.
2006-01-01
The evolution a network of vortex loops due to the fusion and breakdown in the turbulent superfluid helium is studied. We perform investigation on the base of the "rate equation" for the distribution function $n(l)$ of number of loops in space of their length $l$. There are two mechanisms for change of quantity $n(l)$. Firstly, the function changes due to deterministic process of mutual friction, when the length grows or decreases depending on orientation. Secondly, the change of $n(l)$ occur...
Evolution equations in generalized Stepanov-like pseudo almost automorphic spaces
Toka Diagana
2012-03-01
Full Text Available In this article, first we introduce and study the concept of $mathbb{S}_{gamma}^p$-pseudo almost automorphy (or generalized Stepanov-like pseudo almost automorphy, which is more general than the notion of Stepanov-like pseudo almost automorphy due to Diagana. We next study the existence of solutions to some classes of nonautonomous differential equations of Sobolev type in $mathbb{S}_{gamma}^p$-pseudo almost automorphic spaces. To illustrate our abstract result, we will study the existence and uniqueness of a pseudo almost automorphic solution to the heat equation with a negative time-dependent diffusion coefficient.
Generalized Kudryashov method for solving some (3+1-dimensional nonlinear evolution equations
Md. Shafiqul Islam
2015-06-01
Full Text Available In this work, we have applied the generalized Kudryashov methods to obtain the exact travelling wave solutions for the (3+1-dimensional Jimbo-Miwa (JM equation, the (3+1-dimensional Kadomtsev-Petviashvili (KP equation and the (3+1-dimensional Zakharov-Kuznetsov (ZK. The attained solutions show distinct physical configurations. The constraints that will guarantee the existence of specific solutions will be investigated. These solutions may be useful and desirable for enlightening specific nonlinear physical phenomena in genuinely nonlinear dynamical systems.
Persistence of solutions to nonlinear evolution equations in weighted Sobolev spaces
Xavier Carvajal Paredes
2010-11-01
Full Text Available In this article, we prove that the initial value problem associated with the Korteweg-de Vries equation is well-posed in weighted Sobolev spaces $mathcal{X}^{s,heta}$, for $s geq 2heta ge 2$ and the initial value problem associated with the nonlinear Schrodinger equation is well-posed in weighted Sobolev spaces $mathcal{X}^{s,heta}$, for $s geq heta geq 1$. Persistence property has been proved by approximation of the solutions and using a priori estimates.
Hasibun Naher
2013-03-01
Full Text Available In this article, new (G′/G-expansion method and new generalized (G′/G-expansion method is proposed to generate more general and abundant new exact traveling wave solutions of nonlinear evolution equations. The novelty and advantages of these methods is exemplified by its implementation to the KdV equation. The results emphasize the power of proposed methods in providing distinct solutions of different physical structures in nonlinear science. Moreover, these methods could be more effectively used to deal with higher dimensional and higher order nonlinear evolution equations which frequently arise in many scientific real time application fields.
Late-time evolution of cosmological models with fluids obeying a Shan-Chen-like equation of state
Bini, Donato; Geralico, Andrea
2016-01-01
Classical as well as quantum features of the late-time evolution of cosmological models with fluids obeying a Shan-Chen-like equation of state are studied. The latter is of the type $p=w_{\\rm eff}(\\rho)\\,\\rho$, and has been used in previous works to describe, e.g., a possible scenario for the growth of the dark-energy content of the present Universe. At the classical level the fluid dynamics in a spatially flat Friedmann-Robertson-Walker background implies the existence of two possible equilibrium solutions depending on the model parameters, associated with (asymptotic) finite pressure and energy density. We show that no future cosmological singularity is developed during the evolution for this specific model. The corresponding quantum effects in the late-time behavior of the system are also investigated within the framework of quantum geometrodynamics, i.e., by solving the (minisuperspace) Wheeler-DeWitt equation in the Born-Oppenheimer approximation, constructing wave-packets and analyzing their behavior.
A non-local evolution equation model of cell-cell adhesion in higher dimensional space.
Dyson, Janet; Gourley, Stephen A; Webb, Glenn F
2013-01-01
A model for cell-cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell-cell adhesion, J. Theor. Biol. 243 (2006), pp. 98-113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion attributable to cells having formed bonds with other nearby cells. Using the theory of fractional powers of analytic semigroup generators and working in spaces with bounded uniformly continuous derivatives, the local existence of classical solutions is proved. Positivity and boundedness of solutions is then established, leading to global existence of solutions. Finally, the asymptotic behaviour of solutions about the spatially uniform state is considered. The model is illustrated by simulations that can be applied to in vitro wound closure experiments.
Maximal Dimension of Invariant Subspaces to Systems of Nonlinear Evolution Equations
Shoufeng SHEN; ChangZheng QU; Yongyang JIN; Lina JI
2012-01-01
In this paper,the dimension of invariant subspaces admitted by nonlinear systems is estimated under certain conditions.It is shown that if the two-component nonlinear vector differential operator F =(F1,F2) with orders {k1,k2} (k1 ≥ k2) preserves the invariant subspace W1n1 × W2n2 (n1 ≥ n2),then n1 - n2 ≤ k2,n1 ≤ 2(k1 + k2) + 1,where Wqnq is the space generated by solutions of a linear ordinary differential equation of order nq (q =1,2).Several examples including the (1+1)-dimensional diffusion system and It(o)'s type,Drinfel'd-Sokolov-Wilson's type and Whitham-Broer-Kaup's type equations are presented to illustrate the result.Furthermore,the estimate of dimension for m-component nonlinear systems is also given.
Optical analogues of the Newton-Schrödinger equation and boson star evolution.
Roger, Thomas; Maitland, Calum; Wilson, Kali; Westerberg, Niclas; Vocke, David; Wright, Ewan M; Faccio, Daniele
2016-11-14
Many gravitational phenomena that lie at the core of our understanding of the Universe have not yet been directly observed. An example in this sense is the boson star that has been proposed as an alternative to some compact objects currently interpreted as being black holes. In the weak field limit, these stars are governed by the Newton-Schrodinger equation. Here we present an optical system that, under appropriate conditions, identically reproduces such equation in two dimensions. A rotating boson star is experimentally and numerically modelled by an optical beam propagating through a medium with a positive thermal nonlinearity and is shown to oscillate in time while also stable up to relatively high densities. For higher densities, instabilities lead to an apparent breakup of the star, yet coherence across the whole structure is maintained. These results show that optical analogues can be used to shed new light on inaccessible gravitational objects.
A unified approach to the large deviations for small perturbations of random evolution equations
胡亦钧
1997-01-01
Let be the processes governed by the following stochastic differential equations:where v (t) is a random process independent of the Brownian motion B(·).Some large deviation (LD) properties of are proved.For a particular case,an explicit representation of the rate function is also given,which solves a problem posed by Eizenberg and Freidlin.In the meantime,an abstract LD theorem is obtained.
A class of stochastic evolutions that scale to the porous medium equation
Feng, Shui [McMaster Univ., Hamilton, Ontario (Canada); Iscoe, I. [McMaster Univ., Hamilton, Ontario (Canada)]|[Algorithmics, Toronto, Ontario (Canada); Seppaelaeinen, T. [Iowa State Univ., Ames, IA (United States)
1996-11-01
A class of reversible Markov jump processes on a periodic lattice is described and a result about their scaling behavior stated: Under diffusion scaling, the empirical measure converges to a solution of the porous medium equation on the d-dimensional torus. The process can be viewed as a randomly interacting configuration of sticks that evolves through exchanges of stick pieces between nearest neighbors through a zero-range pressure mechanism, with conservation of total stick length.
ON EXPONENTIAL STABILITY OF NON-AUTONOMOUS STOCHASTIC SEMILINEAR EVOLUTION EQUATIONS
夏学文; 刘凯
2002-01-01
Sufficient conditions for the exponential stability of a class of nonlinear, nonautonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.
Sakhnovich, Lev A; Roitberg, Inna Ya
2013-01-01
This monograph fits theclearlyneed for books with a rigorous treatment of theinverse problems for non-classical systems and that of initial-boundary-value problems for integrable nonlinear equations. The authorsdevelop a unified treatment of explicit and global solutions via the transfer matrix function in a form due to Lev A. Sakhnovich. The book primarily addresses specialists in the field. However, it is self-contained andstarts with preliminaries and examples, and hencealso serves as an introduction for advanced graduate students in the field.
牛晓花; 潘祖梁
2006-01-01
A new method based on Lie-B(a)cklund symmetry method to solve the perturbed nonlinear evolution equations is presented. New approximate solutions of perturbed nonlinear evolution equations stemming from the exact solutions of unperturbed equations are obtained.This method is a generalization of Burde's Lie point symmetry technique.
Recovery of the Time-Evolution Equation of Time-Delay Systems from Time Series
Bünner, M J; Kittel, A; Parisi, J; Meyer, Th.
1997-01-01
We present a method for time series analysis of both, scalar and nonscalar time-delay systems. If the dynamics of the system investigated is governed by a time-delay induced instability, the method allows to determine the delay time. In a second step, the time-delay differential equation can be recovered from the time series. The method is a generalization of our recently proposed method suitable for time series analysis of {\\it scalar} time-delay systems. The dynamics is not required to be settled on its attractor, which also makes transient motion accessible to the analysis. If the motion actually takes place on a chaotic attractor, the applicability of the method does not depend on the dimensionality of the chaotic attractor - one main advantage over all time series analysis methods known until now. For demonstration, we analyze time series, which are obtained with the help of the numerical integration of a two-dimensional time-delay differential equation. After having determined the delay time, we recover...
An analytic solution to LO coupled DGLAP evolution equations: a new pQCD tool
Block, Martin M; Ha, Phuoc; McKay, Douglas W
2010-01-01
We have analytically solved the LO pQCD singlet DGLAP equations using Laplace transform techniques. Newly-developed highly accurate numerical inverse Laplace transform algorithms allow us to write fully decoupled solutions for the singlet structure function F_s(x,Q^2)and G(x,Q^2) as F_s(x,Q^2)={\\cal F}_s(F_{s0}(x), G_0(x)) and G(x,Q^2)={\\cal G}(F_{s0}(x), G_0(x)). Here {\\cal F}_s and \\cal G are known functions of the initial boundary conditions F_{s0}(x) = F_s(x,Q_0^2) and G_{0}(x) = G(x,Q_0^2), i.e., the chosen starting functions at the virtuality Q_0^2. For both G and F_s, we are able to either devolve or evolve each separately and rapidly, with very high numerical accuracy, a computational fractional precision of O(10^{-9}). Armed with this powerful new tool in the pQCD arsenal, we compare our numerical results from the above equations with the published MSTW2008 and CTEQ6L LO gluon and singlet F_s distributions, starting from their initial values at Q_0^2=1 GeV^2 and 1.69 GeV^2, respectively, using their ...
Optical analogues of the Newton-Schr\\"odinger equation and boson star evolution
Roger, Thomas; Wilson, Kali; Westerberg, Niclas; Vocke, David; Wright, Ewan M; Faccio, Daniele
2016-01-01
Many gravitational phenomena that lie at the core of our understanding of the Universe have not yet been directly observed. An example in this sense is the boson star that has been proposed as an alternative to some compact objects currently interpreted as being black holes. In the weak field limit, these stars are governed by the Newton-Schrodinger equation (NSE). Here we present an optical system that, under appropriate conditions, identically reproduces the NSE in two dimensions. A rotating boson star is experimentally and numerically modelled by an optical beam propagating through a medium with a positive thermal nonlinearity and is shown to oscillate in time while also stable up to relatively high densities. For higher densities, instabilities lead to an apparent breakup of the star, yet coherence across the whole structure is maintained. These results show that optical analogues can be used to shed new light on inaccessible gravitational objects.
First correction to JIMWLK evolution from the classical equations of motion
Albacete, J L; Milhano, J G
2007-01-01
We calculate some ${\\cal O}(\\alpha_s^2)$ corrections to the JIMWLK kernel in the framework of the light-cone wave function approach to the high energy limit of QCD. The contributions that we consider originate from higher order corrections in the strong coupling and in the density of the projectile to the solution of the classical Yang-Mills equations of motion that determine the Weizs\\"acker-Williams fields of the projectile. We study the structure of these corrections in the dipole limit, showing that they are subleading in the limit of large number of colours $N$, and that they cannot be fully recast in the form of dipole degrees of freedom.
Numerical Solution of the Evolution Equation for Orbital Angular Momentum of Partons in the Nucleon
Martin, O; Schäfer, A
1999-01-01
The evolution of orbital angular momentum distributions within the radiative parton model is studied. We use different scenarios for the helicity weighted parton distributions and consider a broad range of input distributions for orbital angular momentum. In all cases we are lead to the conclusion that the absolute value of the average angular momentum per parton peaks at relatively large $x\\approx 0.1$ for perturbatively accessible scales. Furthermore, in all scenarios considered here the average orbital angular momentum per parton is several times larger for gluons than for quarks which favours gluon initiated reactions to measure orbital angular momentum. The large gluon polarization typically obtained in NLO-fits to DIS data is primarily canceled by the gluon orbital angular momentum.
Chen, Mei-Dan; Li, Xian; Wang, Yao; Li, Biao
2017-06-01
With symbolic computation, some lump solutions are presented to a (3+1)-dimensional nonlinear evolution equation by searching the positive quadratic function from the Hirota bilinear form of equation. The quadratic function contains six free parameters, four of which satisfy two determinant conditions guaranteeing analyticity and rational localization of the solutions, while the others are free. Then, by combining positive quadratic function with exponential function, the interaction solutions between lump solutions and the stripe solitons are presented on the basis of some conditions. Furthermore, we extend this method to obtain more general solutions by combining of positive quadratic function and hyperbolic cosine function. Thus the interaction solutions between lump solutions and a pair of resonance stripe solitons are derived and asymptotic property of the interaction solutions are analyzed under some specific conditions. Finally, the dynamic properties of these solutions are shown in figures by choosing the values of the parameters. Supported by National Natural Science Foundation of China under Grant Nos. 11271211, 11275072, and 11435005, Ningbo Natural Science Foundation under Grant No. 2015A610159 and the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No. xkzw11502 and K.C. Wong Magna Fund in Ningbo University
Study of Buckling Restrained Braces in Steel Frame Building
Mr. Y. D. Kumbhar
2014-08-01
Full Text Available Conventional braces have limited deformation ductility capacity, and exhibit unsymmetrical hysteretic cycles, with marked strength deterioration when loaded in compression. To overcome the above mentioned problems, a new type of brace was developed in Japan called as buckling restrained braces, designated as BRB’s. These braces are designed such that buckling is inhibited to occur, exhibiting adequate behavior and symmetrical hysteretic curves under the action of both tensile and compressive cycles, produced by the action of seismic and wind forces. This paper presents experimental results concerning the lateral load carrying capacity of steel frame model by use of buckling restrained brace. This paper also includes the comparative study of lateral load carrying capacity of frame model for bare frame, frame with Conventional brace and frame with buckling restrained brace.
关于交通成本演化方程的假设及经济分析%Economic Analysis of Traffic Flow with an Evolution Equation
FENG Su-wei
2005-01-01
Based on two main hypotheses of traffic economical equilibrium and the relationship between traffic density and the demand,an evolution equation of traffic cost was proposed to describe the change of cost under decreasing toll. Economical explanation of the model and a numerical case were given to demonstrate the constraint between the marginal traffic demand and the flow velocity.
Experimental Study of Damage Evolution in Circular Stirrup-Confined Concrete
Zuohua Li
2016-04-01
Full Text Available This paper presents an experimental study on circular stirrup-confined concrete specimens under uniaxial and monotonic load. The effects of stirrup volume ratio, stirrup yield strength and concrete strength on damage evolution of stirrup-confined concrete were investigated. The experimental results showed that the strength and ductility of concrete are improved by appropriate arrangement of the stirrup confinement. Firstly, the concrete damage evolution can be relatively restrained with the increase of the stirrup volume ratio. Secondly, higher stirrup yield strength usually causes larger confining pressures and slower concrete damage evolution. In contrast, higher concrete strength leads to higher brittleness, which accelerates the concrete damage evolution. A plastic strain expression is obtained through curve fitting, and a damage evolution equation for circular stirrup-confined concrete is proposed by introducing a confinement factor (C based on the experimental data. The comparison results demonstrate that the proposed damage evolution model can accurately describe the experimental results.
Lu, Yanfei; Lekszycki, Tomasz
2016-10-01
During fracture healing, a series of complex coupled biological and mechanical phenomena occurs. They include: (i) growth and remodelling of bone, whose Young's modulus varies in space and time; (ii) nutrients' diffusion and consumption by living cells. In this paper, we newly propose to model these evolution phenomena. The considered features include: (i) a new constitutive equation for growth simulation involving the number of sensor cells; (ii) an improved equation for nutrient concentration accounting for the switch between Michaelis-Menten kinetics and linear consumption regime; (iii) a new constitutive equation for Young's modulus evolution accounting for its dependence on nutrient concentration and variable number of active cells. The effectiveness of the model and its predictive capability are qualitatively verified by numerical simulations (using COMSOL) describing the healing of bone in the presence of damaged tissue between fractured parts.
Flow-Induced Vibration of A Nonlinearly Restrained Curved Pipe Conveying Fluid
王琳; 倪樵; 黄玉盈
2004-01-01
Investigated in this study is the flow-induced vibration of a nonlinearly restrained curved pipe conveying fluid. The nonlinear equation of motion is derived by equilibrium of forces on microelement of the system under consideration. The spatial coordinate of the system is discretized by DQM (differential quadrature method). On the basis of the boundary conditions, the dynamic equation is solved by the Newton-Raphson iteration method. The numerical solutions reveal several complex dynamic motions for the variation of the fluid velocity parameter, such as limit cycle motion, buckling and so on. The result obtained also shows that the sub parameter regions corresponding to the several motions may change with the variation of some parameters of the curved pipe. The present study supplies a new reference for investigating the nonlinear dynamic response of some other structures.
Rezzolla, L; Markovic, D M; Shapiro, S L; Rezzolla, Luciano; Lamb, Frederick L.; Markovic, Dragoljub; Shapiro, Stuart L.
2001-01-01
The instability of r-mode oscillations in rapidly rotating neutron stars has attracted attention as a potential mechanism for producing high frequency, almost periodic gravitational waves. The analyses carried so far have shown the existence of these modes and have considered damping by shear and bulk viscosity. However, the magnetohydrodynamic coupling of the modes with a stellar magnetic field and its role in the damping of the instability has not been fully investigated yet. Following our introductory paper (Rezzolla, Lamb and Shapiro 2000), we here discuss in more detail the existence of secular higher-order kinematical effects which will produce toroidal fluid drifts. We also define the sets of equations that account for the time evolution of the magnetic fields produced by these secular velocity fields and show that the magnetic fields produced can reach equipartition in less than a year. The full numerical calculations as well as the evaluation of the impact of strong magnetic fields on the onset and e...
Chang Jiang ZHU; Zhi Yong ZHANG; Hui YIN
2006-01-01
In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects:{ψt = -(1 - α)ψ - θx + αψxx, (E)θt = -(1 - α)θ + vψx + (χθ)x + αθxx,with initial data(ψ,θ)(x, 0) = (ψ0(x),θ0(x)) → (χ±,θ±) as x →±∞, (Ⅰ)where α and v are positive constants such that α＜ 1, v ＜ 4α(1 - α). Under the assumption that|ψ+ - ψ-| + |θ+ - θ-| is sufficiently small, we show the global existence of the solutions to Cauchy problem (E) and (I) if the initial data is a small perturbation. And the decay rates of the solutions with exponential rates also are obtained. The analysis is based on the energy method.
Akbar, M Ali; Mohd Ali, Norhashidah Hj; Mohyud-Din, Syed Tauseef
2013-01-01
Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics. In the present paper, the alternative (G'/G)-expansion method has been further modified by introducing the generalized Riccati equation to construct new exact solutions. In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way. These solutions may be imperative and significant for the explanation of some practical physical phenomena. It is shown that the modified alternative (G'/G)-expansion method an efficient and advance mathematical tool for solving nonlinear partial differential equations in mathematical physics.
Nonlinear Vibration of an Elastically Restrained Tapered Beam
Karimpour, S; Ganji, S.S; Barari, Amin;
2012-01-01
This paper presents the analytical simulation of an elastically restrained tapered cantilever beam using the energy balance method (EBM) and the iteration perturbation method (IPM). To assess the accuracy of solutions, we compare the results with the harmonic balance method (HBM). The obtained re...
Qin, Bo; Tian, Bo; Wang, Yu-Feng; Shen, Yu-Jia; Wang, Ming
2017-10-01
Under investigation in this paper are the Belov-Chaltikian (BC), Leznov and Blaszak-Marciniak (BM) lattice equations, which are associated with the conformal field theory, UToda(m_1,m_2) system and r-matrix, respectively. With symbolic computation, the Bell-polynomial approach is developed to directly bilinearize those three sets of differential-difference nonlinear evolution equations (NLEEs). This Bell-polynomial approach does not rely on any dependent variable transformation, which constitutes the key step and main difficulty of the Hirota bilinear method, and thus has the advantage in the bilinearization of the differential-difference NLEEs. Based on the bilinear forms obtained, the N-soliton solutions are constructed in terms of the N × N Wronskian determinant. Graphic illustrations demonstrate that those solutions, more general than the existing results, permit some new properties, such as the solitonic propagation and interactions for the BC lattice equations, and the nonnegative dark solitons for the BM lattice equations.
王云虎; 陈勇
2011-01-01
In the present letter, we get the appropriate bilinear forms of （2 ＋ 1）-dimensional KdV equation, extended （2 ＋ 1）-dimensional shallow water wave equation and （2 ＋ 1）-dimensional Sawada -Kotera equation in a quick and natural manner, namely by appling the binary Bell polynomials. Then the Hirota direct method and Riemann theta function are combined to construct the periodic wave solutions of the three types nonlinear evolution equations. And the corresponding figures of the periodic wave solutions are given. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.
史定华; 徐洪; 熊勇; 王远第
2002-01-01
For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time-dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi-group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.
张英世; 张行
2004-01-01
On the basis about studying free bending for box beam with rectangular crosssection filled by honeycomb core, supplementary displacements and stresses of restrained bending for such beam were analyzed. The hypothesis for separated variables was adopted to solve displacement. According to this, three aspect equations of geometrical, physical and balance were obtained. With Galerkin's method, it is summed up as two-order ordinary differential equations with the attenuation character. Analysis makes clear that attenuation speed of stress is concerned with a big load or a small one, geometric dimensions of crosssection of beam, and physical parameter of material.
Shahriar, M S; Krishnamurthy, Subramanian; Tu, Y; Pati, G S; Tseng, S
2013-01-01
The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and redistribution. For finding solutions of this equation, it is convenient first to reformulate the Liouville equation by defining a vector corresponding to the elements of the density operator, and determining the corresponding time-evolution matrix. For a system of N energy levels, the size of the evolution matrix is N2xN2. When N is very large, evaluating the elements of these matrices becomes very cumbersome. We describe a novel algorithm that can produce the evolution matrix in an automated fashion for an arbitrary value of N. As a non-trivial example, we apply this algorithm to a fifteen-level atomic system used for producing optically controlled polarization rotation. We also point out how such a code can be extended for use in an atomic system with arbitrary number of energy le...
Partial Differential Equations
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.
Parametric vibrations of a restrained beam with an end mass under displacement excitation
Gürgöze, M.
1986-07-01
This paper is concerned with the stability and the steady state response of the main parametric resonance vibrations of a simply supported vertical beam. The beam carries a concentrated mass and is restrained at one end and subjected to a periodic axial displacement excitation at the other end. This system can be looked upon as a dynamic model of the vibrations of an engine valve mechanism. Non-linear terms arising from moderately large curvatures, longitudinal inertia of the beam elements and concentrated mass are included in the equation of motion. By using the one mode approximation and applying Galerkin's method, the governing partial differential equation is reduced to a non-linear ordinary differential equation with a periodic coefficient. The boundaries of the main parametric instability region of the linearized equation are obtained. The harmonic balance method is applied to solve the equation and an analytical expression for the dynamic response in the vicinity of the main parametric resonance is derived. The effects of various parameters on the boundaries of the instability region and the dynamic response are investigated.
Auzinger, Winfried
2016-07-28
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.
Winckler, N; Shevelko, V P; Al-Turany, M; Kollegger, T; Stöhlker, Th
2017-01-01
A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.
Winckler, N.; Rybalchenko, A.; Shevelko, V. P.; Al-Turany, M.; Kollegger, T.; Stöhlker, Th.
2017-02-01
A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.
Social ultrasonic vocalization in awake head-restrained mouse
Benjamin Weiner
2016-12-01
Full Text Available Numerous animal species emit vocalizations in response to various social stimuli. The neural basis of vocal communication has been investigated in monkeys, songbirds, rats, bats and invertebrates resulting in deep insights into motor control, neural coding and learning. Mice, which recently became very popular as a model system for mammalian neuroscience, also utilize ultrasonic vocalizations (USVs during mating behavior. However, our knowledge is lacking of both the behavior and its underlying neural mechanism. We developed a novel method for head-restrained male mice (HRMM to interact with non-restrained female mice (NRFM and show that mice can emit USVs in this context. We first recorded USVs in free arena with non-restrained male mice (NRMM and NRFM. Of the NRMM, which vocalized in the free arena, the majority could be habituated to also vocalize while head-restrained but only when a female mouse was present in proximity. The USVs emitted by HRMM are similar to the USVs of NRMM in the presence of a female mouse in their spectral structure, inter syllable interval distribution and USV sequence length, and therefore are interpreted as social USVs. By analyzing vocalizations of NRMM, we established criteria to predict which individuals are likely to vocalize while head fixed based on the USV rate and average syllable duration. To characterize the USVs emitted by HRMM, we analyzed the syllable composition of HRMM and NRMM and found that USVs emitted by HRMM have higher proportions of USVs with complex spectral representation, supporting previous studies showing that mice social USVs are context dependent. Our results suggest a way to study the neural mechanisms of production and control of social vocalization in mice using advanced methods requiring head fixation.
Visual associative learning in restrained honey bees with intact antennae.
Scott E Dobrin
Full Text Available A restrained honey bee can be trained to extend its proboscis in response to the pairing of an odor with a sucrose reward, a form of olfactory associative learning referred to as the proboscis extension response (PER. Although the ability of flying honey bees to respond to visual cues is well-established, associative visual learning in restrained honey bees has been challenging to demonstrate. Those few groups that have documented vision-based PER have reported that removing the antennae prior to training is a prerequisite for learning. Here we report, for a simple visual learning task, the first successful performance by restrained honey bees with intact antennae. Honey bee foragers were trained on a differential visual association task by pairing the presentation of a blue light with a sucrose reward and leaving the presentation of a green light unrewarded. A negative correlation was found between age of foragers and their performance in the visual PER task. Using the adaptations to the traditional PER task outlined here, future studies can exploit pharmacological and physiological techniques to explore the neural circuit basis of visual learning in the honey bee.
刘明姬; 吕悦; 吕显瑞
2007-01-01
In this paper, we establish sufficient conditions for the controllability of nonlinear neutral evolution equations with nonlocal conditions. The result is obtained by using Krasnoselski-Schaefer type fixed point theorem.
张英世; 张行
2004-01-01
Differential equation of restrained torsion for rectangular-section box bar with honeycomb core was established and solved by using the method of undetermined function.Non-dimension normal stress, shear stress acting in the faceplate and shear stress acting in the honeycomb-core and warping displacement were deduced. Numerical analysis shows the normal stress attenuates quickly along x-axis. Normal stress acting on the cross section at a distance of 20 h from the fixed end is only one per cent of that acting on the fixed end.
Naige Wang
2017-03-01
Full Text Available The incompletely restrained cable-suspension swing system driven by two cables is introduced in this article. Based on wrench of forces theory and Lagrange’s equation of first kind, the static and dynamics models of incompletely restrained cable-suspension swing system driven by two cables are established, respectively. In order to obtain an intuitive understanding of the trajectory analysis, a dynamics model consisting of governing equation and geometric constraint conditions which is a set of the mixed differential-algebraic equation in mathematics is established. A typical feedback controller and an inverse model were set up to estimate the driving function. The effective workspace, which is used to guarantee an efficient swing process, mostly depends on the geometrical shape rather than the volume itself which was calculated by trajectory analysis. In order to estimate system features and ensure a limited range of tension in underconstrained spatial cable system, the probable location of unbalanced loading was evaluated by pointwise evaluation techniques during normal work.
Cracking Tendency of Restrained Concrete at Early Ages
BA Hengjing; SU Anshuang; GAO Xiaojian; TAO Qi
2008-01-01
A modified testing system characterized by full automation, steady operation and high accuracy of strain and stress measurements was developed to determine the cracking tendency of high strength concrete (HSC) in restrained condition at early ages. The shrinkage stress and the tensile creep behavior of HSC at early ages were investigated. The influence of W/C ratio and curing conditions on the early-age shrinkage stress and tensile creep was evaluated. It was found that the lower W/C ratio and drying curing condition resulted in higher shrinkage stress, stress induced tensile creep and greater cracking tendency.
Bar, D
2002-01-01
Using the Gell-Mann-Hartle-Griffiths formalism in the framework of the Flesia-Piron form of the Lax-Phillips theory we show that the Schr\\"oedinger equation may be derived as a condition of stability of histories. This mechanism is realized in a mathematical structure closely related to the Zeno effect.
Dhar A.K.
2015-05-01
Full Text Available Fourth order nonlinear evolution equations, which are a good starting point for the study of nonlinear water waves, are derived for deep water surface capillary gravity waves in the presence of second waves in which air is blowing over water. Here it is assumed that the space variation of the amplitude takes place only in a direction along which the group velocity projection of the two waves overlap. A stability analysis is made for a uniform wave train in the presence of a second wave train. Graphs are plotted for the maximum growth rate of instability wave number at marginal stability and wave number separation of fastest growing sideband component against wave steepness. Significant improvements are noticed from the results obtained from the two coupled third order nonlinear Schrödinger equations.
Sacripanti, A. [ENEA, Rome (Italy). Direzione Sicurezza Nazionale e Protezione Sanitaria; Dal Monte, A. [CONI, Rome (Italy). Ist. di Scienza dello Sport; Rossi, L.; Fabbri, M. [ENEA, Casaccia (Italy)
1993-12-31
The foundation, evolution and related improvements of the new heat and mass transfer equation, used in the joint research of CONI-ENEA (the Italian National Agency for Energy, New Technologies and the Environment) - FILPJ are shown in this report. Emphasis is given to the experimental history and the changes that are justified in a more formal approach on the basis of theoretical thermodynamics or similarity and dimensional theory. The new form of the equation in the computer code actually utilized in the research is given in the appendix.
Camelio, Giovanni; Lovato, Alessandro; Gualtieri, Leonardo; Benhar, Omar; Pons, José A.; Ferrari, Valeria
2017-08-01
In a core-collapse supernova, a huge amount of energy is released in the Kelvin-Helmholtz phase subsequent to the explosion, when the proto-neutron star cools and deleptonizes as it loses neutrinos. Most of this energy is emitted through neutrinos, but a fraction of it can be released through gravitational waves. We model the evolution of a proto-neutron star in the Kelvin-Helmholtz phase using a general relativistic numerical code, and a recently proposed finite temperature, many-body equation of state; from this we consistently compute the diffusion coefficients driving the evolution. To include the many-body equation of state, we develop a new fitting formula for the high density baryon free energy at finite temperature and intermediate proton fraction. We estimate the emitted neutrino signal, assessing its detectability by present terrestrial detectors, and we determine the frequencies and damping times of the quasinormal modes which would characterize the gravitational wave signal emitted in this stage.
Lu, Jian; Dong, Yuxia; Ng, Emily C; Siehl, Daniel L
2017-05-01
One of applications of directed evolution is to desensitize an enzyme to an inhibitor. kcat,1/KM and KI are three dimensions that when multiplied measure an enzyme's intrinsic capacity for catalysis in the presence of an inhibitor. The ideal values for the individual dimensions depend on substrate and inhibitor concentrations under the conditions of the application. When attempting to optimize those values by directed evolution, (kcat/KM)*KI can be an informative parameter for evaluating libraries of variants, but throughput is limited. We describe a manipulation of the Michaelis-Menten equation for competitive inhibition that isolates (kcat/KM)*KI on one side of the equation. If velocity is measured at constant enzyme and substrate concentrations with two different inhibitor concentrations (one of which can be 0), the data are sufficient to calculate (kcat/KM)*KI with just two rate measurements. The procedure is validated by correlating values obtained by the rapid method with those obtained by substrate saturation kinetics. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Lalung, M.; Phukan, P.; Sarma, J. K.
2017-09-01
In this work we have solved the nonlinear GLR-MQ evolution equation upto next-to-leading order (NLO) by considering NLO terms of the gluon-gluon splitting functions and running coupling constant α s (Q 2). Here, we have incorporated a Regge-like behaviour of gluon distribution in order to obtain a solution of the GLR-MQ equation in the range of 5G e V 2 ≤ Q 2 ≤ 25G e V 2. We have studied the Q 2 evolution of the gluon distribution function G(x, Q 2) and its nonlinear effects at small-x. It can be observed from our analysis that the nonlinearities increase with decrease in the correlation radius R of two interacting gluons, as expected. We have compared our result of G(x, Q 2) as Q 2 increases and x decreases, for two different values of R, viz. R = 2G e V -1 and 5 G e V -1. We have also checked the sensitivity of the Regge intercept λ G on our results. We compare our computed results with those obtained by the global analysis to parton distribution functions (PDFs) by various collaborations where LHC data have been included viz. ABM12, CT14, MMHT14, PDF4LHC15, NNPDF3.0 and CJ15. Besides we have also shown comparison of our results with HERA PDF data viz. HERAPDF15.
Interactive effects of emotional and restrained eating on responses to chocolate and affect.
Macht, Michael; Mueller, Jochen
2007-12-01
To examine differences and interactions between emotional and restrained-eating healthy adults (56 women, 53 men) were classified into emotional or restrained eaters, and persons scoring high or low on both dimensions. Participants tasted different types of chocolate (with 30, 70, 85, or 99% cocoa content) and completed questionnaires on affect and attitudes towards chocolate. Emotional eaters reported increased craving for and increased consumption of chocolate, whereas restrained eaters experienced chocolate-related guilt. However, restrained eaters rated plain chocolate (70% and 85% cocoa) as more pleasant than other groups. Persons scoring high on both dimensions showed heightened negative affect and may be prone to disturbances of eating and affect.
Zia, H.; Simpson, G.
2013-12-01
The interaction between flowing surface water and sediment transport has numerous important applications in Earth science, including controls on river patterns, drainage basin evolution and morphological changes induced by extreme events such as tsunamis and dam breaks. Many of these problems can be investigated with the mathematical model of the shallow water equations coupled to conservation of sediment concentration and empirical functions for bed friction, substrate erosion and deposition. However, this system of equations is highly nonlinear, requiring fast and robust numerical methods. In this study, we investigate the solution of the shallow water equations coupled to sediment transports via the Non-oscillatory Central Differencing (NOC ) method, a second order scheme based on a predictor-corrector method. The scheme is chosen for its relative stability and robustness. The NOC scheme is especially favorable in situations where the water depth approaches zero and for steady flow conditions, both of which cause problems with more naive schemes. The model is verified by comparing computed results with documented solutions. We are currently using the model to investigate coupling between flow and sediment transport in alluvial rivers.
LU Chang-gen; CAO Wei-dong; QIAN Jian-hua
2006-01-01
A new method for direct numerical simulation of incompressible Navier-Stokes equations is studied in the paper. The compact finite difference and the non-linear terms upwind compact finite difference schemes on non-uniform meshes in x and y directions are developed respectively. With the Fourier spectral expansion in the spanwise direction, three-dimensional N-S equation are converted to a system of two-dimensional equations. The third-order mixed explicit-implicit scheme is employed for time integration. The treatment of the three-dimensional non-reflecting outflow boundary conditions is presented, which is important for the numerical simulations of the problem of transition in boundary layers, jets, and mixing layer. The numerical results indicate that high accuracy, stabilization and efficiency are achieved by the proposed numerical method. In addition, a theory model for the coherent structure in a laminar boundary layer is also proposed, based on which the numerical method is implemented to the non-linear evolution of coherent structure. It is found that the numerical results of the distribution of Reynolds stress, the formation of high shear layer, and the event of ejection and sweeping, match well with the observed characteristics of the coherent structures in a turbulence boundary layer.
Soustova, Irina; Gorshkov, Konstantin; Ermoshkin, Alexey; Ostrovsky, Lev; Sofonof, Alexandr
2017-04-01
Previously, we have proposed an approach approximate description of the evolution of solitons, permitting the view of composite structures, formed a more simple stationary waves-kinks. The key point in the proposed approach is the transition from traditional descriptions of the evolution of solitons as coherent entities( essentially, particles,characterized by one coordinate, speed, etc.) to the description of the dynamics of being their kinks. The use of this approach allowed to investigate non-quasi-stationary processes arising from the interaction of solitons and their propagation in media with variable parameters , when the magnitude of disturbances become comparable and even significantly smaller-scale solitary waves. To non-quasi-stationary behavior of solitons leads and evolution is not flat fronts of solitary waves. The study of these processes is of interest as from fundamental and applied points of view. In the present work using this approach is discussed a simple from such problems with cylindrically converging(and diverging) composite solitons in the framework of the Gardner equation, the augmented term is responsible for the cylindrical geometry tasks.
Bezak, V
2002-01-01
The Waxman-Peck theory of the population genetics is discussed in regard of soil bacteria. Each bacterium is understood as a carrier of a phenotypic parameter p. The central aim is the calculation of the probability density with respect to p of the carriers living at time t>0. The theory involves two small parameters: the mutation probability $\\mu$ and a parameter $\\gamma$ involved in a function w(p) defining the fitness of the bacteria to survive the generation time $\\tau$ and give birth to offspring. The mutation from a state p to a state q is defined by a Gaussian. The author focuses attention on an equation generalizing Waxman's equation. The author solves this equation in the standard style of a perturbation theory and discusses how the solution depends on the choice of the fitness function w(p). In a sense, the function $c(p)=1-w(p)/w(0)$ is analogous to the dispersion function E(p) of fictitious quasiparticles. With a general function c(p), the distribution function ${\\mathit\\Phi}(p,t;0)$ is composed o...
Blood vessels restrain pancreas branching, differentiation and growth.
Magenheim, Judith; Ilovich, Ohad; Lazarus, Alon; Klochendler, Agnes; Ziv, Oren; Werman, Roni; Hija, Ayat; Cleaver, Ondine; Mishani, Eyal; Keshet, Eli; Dor, Yuval
2011-11-01
How organ size and form are controlled during development is a major question in biology. Blood vessels have been shown to be essential for early development of the liver and pancreas, and are fundamental to normal and pathological tissue growth. Here, we report that, surprisingly, non-nutritional signals from blood vessels act to restrain pancreas growth. Elimination of endothelial cells increases the size of embryonic pancreatic buds. Conversely, VEGF-induced hypervascularization decreases pancreas size. The growth phenotype results from vascular restriction of pancreatic tip cell formation, lateral branching and differentiation of the pancreatic epithelium into endocrine and acinar cells. The effects are seen both in vivo and ex vivo, indicating a perfusion-independent mechanism. Thus, the vasculature controls pancreas morphogenesis and growth by reducing branching and differentiation of primitive epithelial cells.
Developmental Partial Differential Equations
Duteil, Nastassia Pouradier; Rossi, Francesco; Boscain, Ugo; Piccoli, Benedetto
2015-01-01
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's evolution. In other words, the manifold's evolution depends on the solution to the PDE, and vice versa the differential operator of the PDE depends on the manifold's geometry. DPDE is used to study a diffusion equation with source on a growing surface whose gro...
Bezák, V
2003-02-01
The Waxman-Peck theory of population genetics is discussed in regard of soil bacteria. Each bacterium is understood as a carrier of a phenotypic parameter p. The central objective is the calculation of the probability density with respect to p, Phi(p,t;p(0)), of the carriers living at time t>0, provided that initially at t(0)=0, all bacteria carried the phenotypic parameter p(0)=0. The theory involves two small parameters: the mutation probability mu and a parameter gamma involved in a function w(p) defining the fitness of the bacteria to survive the generation time tau and give birth to an offspring. The mutation from a state p to a state q is defined by a Gaussian with a dispersion sigma(2)(m). The author focuses our attention on a function phi(p,t) which determines uniquely the function Phi(p,t;p(0)) and satisfies a linear equation (Waxman's equation). The Green function of this equation is mathematically identical with the one-particle Bloch density matrix, where mu characterizes the order of magnitude of the potential energy. (In the x representation, the potential energy is proportional to the inverted Gaussian with the dispersion sigma(2)(m)). The author solves Waxman's equation in the standard style of a perturbation theory and discusses how the solution depends on the choice of the fitness function w(p). In a sense, the function c(p)=1-w(p)/w(0) is analogous to the dispersion function E(p) of fictitious quasiparticles. In contrast to Waxman's approximation, where c(p) was taken as a quadratic function, c(p) approximately gammap(2), the author exemplifies the problem with another function, c(p)=gamma[1-exp(-ap(2))], where gamma is small but a may be large. The author shows that the use of this function in the theory of the population genetics is the same as the use of a nonparabolic dispersion law E=E(p) in the density-matrix theory. With a general function c(p), the distribution function Phi(p,t;0) is composed of a delta-function component, N
Gianini, Loren M.; Smith, Jane Ellen
2008-01-01
The purpose of the current study was to examine the eating behavior, self-esteem, and social anxiety of restrained and non-restrained eaters exposed to an interpersonal stressor. Sixty female undergraduate students completed questionnaires and took part in a stressor and taste test. Results indicated that self-esteem was not predictive of eating…
Restrained eating and self-esteem in premenopausal and postmenopausal women.
Drobnjak, Suzana; Atsiz, Semra; Ditzen, Beate; Tuschen-Caffier, Brunna; Ehlert, Ulrike
2014-01-01
There has been limited research about disordered eating in middle-aged women, and to date, few data exist about restrained eating behavior in postmenopausal women. Therefore, the aim of this study was to examine eating behavior with a specific focus on menopause as an associated factor in restrained eating. Beyond this, we were interested in how postmenopausal status and self-esteem would interact to determine eating patterns in women in middle age. We conducted an online survey in women aged between 40 and 66. Eating behavior was assessed with the Eating Disorder Examination-Questionnaire (EDE-Q) in premenopausal (N = 318) and postmenopausal women (N = 250). All participants rated their self-esteem using the Rosenberg Self-Esteem Scale (RSE) and reported their weight, height, waist circumference, and hip circumference. 15.7% of all participants showed clinically meaningful scores on restrained eating. Postmenopausal women showed significantly higher scores on the EDE-Q subscale of restrained eating as compared to premenopausal women, but when controlling for body mass index, however, this finding was no longer significant. Further exploratory analyses suggest that particularly low or high self-esteem levels are associated with restrained eating. Self-esteem might serve as a mediator between menopausal status and restrained eating, however results of these additional analyses were inconsistent. Restrained eating may appear in middle-aged women. Particularly in postmenopausal women, restrained eating might be associated with lower and higher self-esteem.
EXPERIMENTAL TESTING OF DRAW-BEAD RESTRAINING FORCE IN SHEET METAL FORMING
J.H. Yang; J. Chen; D.N. He; X. Y. Ruan
2003-01-01
Due to complexities of draw-bead restraining force calculated according to theory anddepending on sheet metal forming properties experiment testing system, a simplifiedmethod to calculate draw-bead restraining force is put forward by experimental methodin cup-shaped drawing process. The experimental results were compared with numer-ical results and proved agreement. It shows the method is effective.
Ebert, S [Swiss Federal Institute of Technology (ETH), Zurich, 8092 Zurich (Switzerland); Eom, S J [Swiss Federal Institute of Technology (ETH), Zurich, 8092 Zurich (Switzerland); Schuderer, J [Foundation for Research on Information Technologies in Society (IT' IS), Zeughausstrasse 43, 8004 Zurich (Switzerland); Apostel, U [Fraunhofer Institute for Toxicology and Experimental Medicine, Nicolai-Fuchs-Strasse 1, 30625 Hannover (Germany); Tillmann, T [Fraunhofer Institute for Toxicology and Experimental Medicine, Nicolai-Fuchs-Strasse 1, 30625 Hannover (Germany); Dasenbrock, C [Fraunhofer Institute for Toxicology and Experimental Medicine, Nicolai-Fuchs-Strasse 1, 30625 Hannover (Germany); Kuster, N [Swiss Federal Institute of Technology (ETH), Zurich, 8092 Zurich (Switzerland)
2005-11-07
The objective of this study was the determination of the thermal regulatory and the thermal breakdown thresholds for in-tube restrained B6C3F1 and NMRI mice exposed to radiofrequency electromagnetic fields at 905 MHz. Different levels of the whole-body averaged specific absorption rate (SAR 0, 2, 5, 7.2, 10, 12.6 and 20 W kg{sup -1}) have been applied to the mice inside the 'Ferris Wheel' exposure setup at 22 {+-} 2 {sup 0}C and 30-70% humidity. The thermal responses were assessed by measurement of the rectal temperature prior, during and after the 2 h exposure session. For B6C3F1 mice, the thermal response was examined for three different weight groups (20 g, 24 g, 29 g), both genders and for pregnant mice. Additionally, NMRI mice with a weight of 36 g were investigated for an interstrain comparison. The thermal regulatory threshold of in-tube restrained mice was found at SAR levels between 2 W kg{sup -1} and 5 W kg{sup -1}, whereas the breakdown of regulation was determined at 10.1 {+-} 4.0 W kg{sup -1}(K = 2) for B6C3F1 mice and 7.7 {+-} 1.6 W kg{sup -1}(K = 2) for NMRI mice. Based on a simplified power balance equation, the thresholds show a clear dependence upon the metabolic rate and weight. NMRI mice were more sensitive to thermal stress and respond at lower SAR values with regulation and breakdown. The presented data suggest that the thermal breakdown for in-tube restrained mice, whole-body exposed to radiofrequency fields, may occur at SAR levels of 6 W kg{sup -1}(K = 2) at laboratory conditions.
Neill, David
2012-01-01
In this review Alzheimer's disease is seen as a maladaptive interaction between human brain evolution and senescence. It is predicted to occur in everyone although does not necessarily lead to dementia. The pathological process is initiated in relation to a senescence mediated functional down-regulation in the posteromedial cortex (Initiation Phase). This leads to a loss of glutamatergic excitatory input to layer II entorhinal cortex neurons. A human specific maladaptive neuroplastic response is initiated in these neurons leading to neuronal dysfunction, NFT formation and death. This leads to further loss of glutamatergic excitatory input and propagation of the maladaptive response along excitatory pathways linking evolutionary progressed vulnerable neurons (Propagation Phase). Eventually neurons are affected in many brain areas resulting in dementia. Possible therapeutic approaches include enhancing glutamatergic transmission. The theory may have implications with regards to how Alzheimer's disease is classified.
Donets, E E; Boyadjiev, T L
2003-01-01
We study both analytically and numerically a coupled system of spherically symmetric SU(2) Yang-Mills-dilaton equation in 3+1 Minkowski space-time. It has been found that the system admits a hidden scale invariance which becomes transparent if a special ansatz for the dilaton field is used. This choice corresponds to transition to a frame rotated in the $\\ln r-t$ plane at a definite angle. We find an infinite countable family of self-similar solutions which can be parametrized by the $N$ - the number of zeros of the relevant Yang-Mills function. According to the performed linear perturbation analysis, the lowest solution with N=0 only occurred to be stable. The Cauchy problem has been solved numerically for a wide range of smooth finite energy initial data. It has been found that if the initial data exceed some threshold, the resulting solutions in a compact region shrinking to the origin, attain the lowest N=0 stable self-similar profile, which can pretend to be a global stable attractor in the Cauchy proble...
Restraining orders and foreigner’s right to respect for privacy and family life in Europe
Rosmerlin Estupiñán Silva
2012-09-01
Full Text Available The immigration enforcement in Europe produces a constant tension between the sovereign exercise of border control and the state’s duty to respect human rights. In this regard, the European Court of Human Rights has developed a case law that seeks to restore the harmony between respect for private and family life of foreigners and the legitimacy of restraining orders issued by States. This reflective paper studies the application of Article 8 of the European Convention on Human Rights: “Right to respect for private and family life”, taking into account the so-called national margin of appreciation of States and the analysis of proportionality in the case law of the Court. Then, the analysis shows the evolution of case law in the matter, ending with a balance between the effectiveness of Article 8 of the Convention, given the tightening of the conditions and guarantees allowed to the foreign population in Europe, and the adaptation of national legislation with the decisions of the Court
A constrained theory for single crystal shape memory wires with application to restrained recovery
Rizzoni, Raffaella
2011-07-01
The theory of thin wires developed in Dret and Meunier (Comptes Rendus de l'Académie des Sciences. Série I. Mathématique 337:143-147, 2003) is adapted to phase-transforming materials with large elastic moduli in the sense discussed in James and Rizzoni (J Elast 59:399-436, 2000). The result is a one-dimensional constitutive model for shape memory wires, characterized by a small number of material constants. The model is used to analyze self-accommodated and detwinned microstructures and to study superelasticity. It also turns out that the model successfully reproduces the behavior of shape memory wires in experiments of restrained recovery (Tsoi et al. in Mater Sci Eng A 368:299-310, 2004; Tsoi in 50:3535-3544, 2002; S̆ittner et al. in Mater Sci Eng A 286:298-311, 2000; vokoun in Smart Mater Struct 12:680-685, 2003; Zheng and Cui in Intermetallics 12:1305-1309, 2004; Zheng et al. in J Mater Sci Technol 20(4):390-394, 2004). In particular, the model is able to predict the shift to higher transformation temperatures on heating. The model also captures the effect of prestraining on the evolution of the recovery stress and of the martensite volume fraction.
Endotracheal Intubation Done in Field Conditions of Restrained Space
S. Gavrilovic
2010-01-01
Full Text Available Endotracheal intubation used as a method of cardiopulmonal resuscitation and advanced life support in a field condition frequently represents a problem even to very experienced resuscitatiors because of its extremly complex circumstances. The author’s aim of this work is to suggest his own way of the patient’s intubation in a field condition by the application of the method which has not been described in the literature yet. A several dozen of patients have been intubated by this method in such conditions which did not represent even the minimum for intubation done in a conventional way, but they were enough to prove our method. Maximum performing time for the sample was 15 seconds. We consider that, using this method, the endo-tracheal intubation can be realized in all conditions up to now thought untouchable. This method requires only 30 to 35 cm wider space than patient’s shoulders occupate and 20 to 30 cm extra of his height. The only noted inadequacy is the risk in spine injury intubation, but with more careful treatment it can be avoided. Key words: Endotracheal intubation, cardiopul-monal resuscitation, field condition, restrained space.
Full scale tests of all-steel buckling restrained braces
Ma, Ning; Wu, Bin; Li, Hui; Ou, Jinping; Yang, Weibiao
2009-03-01
Buckling-restrained braces (BRBs) are widely used seismic response-controlling members with excellent energy dissipation capacity without buckling at design deformation. However, the property of all-steel BRBs with cruciform cross section encased in a square steel tube remains insufficiently studied. In this paper, the properties of this kind of BRBs, which were used in two office buildings in Beijing, were examined by full-scale test. First, initial design was done according to the client's requirement. Then, two full-scale specimens were tested under uniaxial quasi-static cyclic loading. The test results indicate that there should be no welding in yielding portion of the core. Finally, the full-scale subassemblage test was done with an improved BRB and gusset plates installed in a frame. The result shows that the brace exhibited high energy dissipation capacity and stable hysteretic characteristic. According to the results from above tests, some important issues are summarized to provide advices for practical applications.
Seismic Energy Demand of Buckling-Restrained Braced Frames
Choi, Hyunhoon; Kim, Jinkoo
2008-07-01
In this study seismic analyses of steel structures were carried out to examine the effect of ground motion characteristics and structural properties on energy demands using 60 earthquake ground motions recorded in different soil conditions, and the results were compared with those of previous works. Analysis results show that ductility ratios and the site conditions have significant influence on input energy. The ratio of hysteretic to input energy is considerably influenced by the ductility ratio and the strong motion duration. It is also observed that as the predominant periods of the input energy spectra are significantly larger than those of acceleration response spectra used in the strength design, the strength demand on a structure designed based on energy should be checked especially in short period structures. For that reason framed structures with buckling-restrained-braces (BRBs) were designed in such a way that all the input energy was dissipated by the hysteretic energy of the BRBs, and the results were compared with those designed by conventional strength-based design procedure.
Stromal response to Hedgehog signaling restrains pancreatic cancer progression.
Lee, John J; Perera, Rushika M; Wang, Huaijun; Wu, Dai-Chen; Liu, X Shawn; Han, Shiwei; Fitamant, Julien; Jones, Phillip D; Ghanta, Krishna S; Kawano, Sally; Nagle, Julia M; Deshpande, Vikram; Boucher, Yves; Kato, Tomoyo; Chen, James K; Willmann, Jürgen K; Bardeesy, Nabeel; Beachy, Philip A
2014-07-29
Pancreatic ductal adenocarcinoma (PDA) is the most lethal of common human malignancies, with no truly effective therapies for advanced disease. Preclinical studies have suggested a therapeutic benefit of targeting the Hedgehog (Hh) signaling pathway, which is activated throughout the course of PDA progression by expression of Hh ligands in the neoplastic epithelium and paracrine response in the stromal fibroblasts. Clinical trials to test this possibility, however, have yielded disappointing results. To further investigate the role of Hh signaling in the formation of PDA and its precursor lesion, pancreatic intraepithelial neoplasia (PanIN), we examined the effects of genetic or pharmacologic inhibition of Hh pathway activity in three distinct genetically engineered mouse models and found that Hh pathway inhibition accelerates rather than delays progression of oncogenic Kras-driven disease. Notably, pharmacologic inhibition of Hh pathway activity affected the balance between epithelial and stromal elements, suppressing stromal desmoplasia but also causing accelerated growth of the PanIN epithelium. In striking contrast, pathway activation using a small molecule agonist caused stromal hyperplasia and reduced epithelial proliferation. These results indicate that stromal response to Hh signaling is protective against PDA and that pharmacologic activation of pathway response can slow tumorigenesis. Our results provide evidence for a restraining role of stroma in PDA progression, suggesting an explanation for the failure of Hh inhibitors in clinical trials and pointing to the possibility of a novel type of therapeutic intervention.
Grammatical-Restrained Hidden Conditional Random Fields for Bioinformatics applications
Martelli Pier
2009-10-01
Full Text Available Abstract Background Discriminative models are designed to naturally address classification tasks. However, some applications require the inclusion of grammar rules, and in these cases generative models, such as Hidden Markov Models (HMMs and Stochastic Grammars, are routinely applied. Results We introduce Grammatical-Restrained Hidden Conditional Random Fields (GRHCRFs as an extension of Hidden Conditional Random Fields (HCRFs. GRHCRFs while preserving the discriminative character of HCRFs, can assign labels in agreement with the production rules of a defined grammar. The main GRHCRF novelty is the possibility of including in HCRFs prior knowledge of the problem by means of a defined grammar. Our current implementation allows regular grammar rules. We test our GRHCRF on a typical biosequence labeling problem: the prediction of the topology of Prokaryotic outer-membrane proteins. Conclusion We show that in a typical biosequence labeling problem the GRHCRF performs better than CRF models of the same complexity, indicating that GRHCRFs can be useful tools for biosequence analysis applications. Availability GRHCRF software is available under GPLv3 licence at the website http://www.biocomp.unibo.it/~savojard/biocrf-0.9.tar.gz.
Folate Deficiency Could Restrain Decidual Angiogenesis in Pregnant Mice.
Li, Yanli; Gao, Rufei; Liu, Xueqing; Chen, Xuemei; Liao, Xinggui; Geng, Yanqing; Ding, Yubin; Wang, Yingxiong; He, Junlin
2015-08-04
The mechanism of birth defects induced by folate deficiency was focused on mainly in fetal development. Little is known about the effect of folate deficiency on the maternal uterus, especially on decidual angiogenesis after implantation which establishes vessel networks to support embryo development. The aim of this study was to investigate the effects of folate deficiency on decidual angiogenesis. Serum folate levels were measured by electrochemiluminescence. The status of decidual angiogenesis was examined by cluster designation 34 (CD34) immunohistochemistry and the expression of angiogenic factors, including vascular endothelial growth factor A (VEGFA), placental growth factor (PLGF), and VEGF receptor 2 (VEGFR2) were also tested. Serum levels of homocysteine (Hcy), follicle stimulating hormone (FSH), luteinizing hormone (LH), prolactin (PRL), progesterone (P4), and estradiol (E2) were detected by Enzyme-linked immunosorbent assay. The folate-deficient mice had a lower folate level and a higher Hcy level. Folate deficiency restrained decidual angiogenesis with significant abnormalities in vascular density and the enlargement and elongation of the vascular sinus. It also showed a reduction in the expressions of VEGFA, VEGFR2, and PLGF. In addition, the serum levels of P4, E2, LH, and PRL were reduced in folate-deficient mice, and the expression of progesterone receptor (PR) and estrogen receptor α (ERα) were abnormal. These results indicated that folate deficiency could impaire decidual angiogenesis and it may be related to the vasculotoxic properties of Hcy and the imbalance of the reproductive hormone.
Folate Deficiency Could Restrain Decidual Angiogenesis in Pregnant Mice
Yanli Li
2015-08-01
Full Text Available The mechanism of birth defects induced by folate deficiency was focused on mainly in fetal development. Little is known about the effect of folate deficiency on the maternal uterus, especially on decidual angiogenesis after implantation which establishes vessel networks to support embryo development. The aim of this study was to investigate the effects of folate deficiency on decidual angiogenesis. Serum folate levels were measured by electrochemiluminescence. The status of decidual angiogenesis was examined by cluster designation 34 (CD34 immunohistochemistry and the expression of angiogenic factors, including vascular endothelial growth factor A (VEGFA, placental growth factor (PLGF, and VEGF receptor 2 (VEGFR2 were also tested. Serum levels of homocysteine (Hcy, follicle stimulating hormone (FSH, luteinizing hormone (LH, prolactin (PRL, progesterone (P4, and estradiol (E2 were detected by Enzyme-linked immunosorbent assay. The folate-deficient mice had a lower folate level and a higher Hcy level. Folate deficiency restrained decidual angiogenesis with significant abnormalities in vascular density and the enlargement and elongation of the vascular sinus. It also showed a reduction in the expressions of VEGFA, VEGFR2, and PLGF. In addition, the serum levels of P4, E2, LH, and PRL were reduced in folate-deficient mice, and the expression of progesterone receptor (PR and estrogen receptor α (ERα were abnormal. These results indicated that folate deficiency could impaire decidual angiogenesis and it may be related to the vasculotoxic properties of Hcy and the imbalance of the reproductive hormone.
Coincident Phosphatidic Acid Interaction Restrains Drp1 in Mitochondrial Division.
Adachi, Yoshihiro; Itoh, Kie; Yamada, Tatsuya; Cerveny, Kara L; Suzuki, Takamichi L; Macdonald, Patrick; Frohman, Michael A; Ramachandran, Rajesh; Iijima, Miho; Sesaki, Hiromi
2016-09-15
Mitochondria divide to control their size, distribution, turnover, and function. Dynamin-related protein 1 (Drp1) is a critical mechanochemical GTPase that drives constriction during mitochondrial division. It is generally believed that mitochondrial division is regulated during recruitment of Drp1 to mitochondria and its oligomerization into a division apparatus. Here, we report an unforeseen mechanism that regulates mitochondrial division by coincident interactions of Drp1 with the head group and acyl chains of phospholipids. Drp1 recognizes the head group of phosphatidic acid (PA) and two saturated acyl chains of another phospholipid by penetrating into the hydrophobic core of the membrane. The dual phospholipid interactions restrain Drp1 via inhibition of oligomerization-stimulated GTP hydrolysis that promotes membrane constriction. Moreover, a PA-producing phospholipase, MitoPLD, binds Drp1, creating a PA-rich microenvironment in the vicinity of a division apparatus. Thus, PA controls the activation of Drp1 after the formation of the division apparatus.
Folate Deficiency Could Restrain Decidual Angiogenesis in Pregnant Mice
Li, Yanli; Gao, Rufei; Liu, Xueqing; Chen, Xuemei; Liao, Xinggui; Geng, Yanqing; Ding, Yubin; Wang, Yingxiong; He, Junlin
2015-01-01
The mechanism of birth defects induced by folate deficiency was focused on mainly in fetal development. Little is known about the effect of folate deficiency on the maternal uterus, especially on decidual angiogenesis after implantation which establishes vessel networks to support embryo development. The aim of this study was to investigate the effects of folate deficiency on decidual angiogenesis. Serum folate levels were measured by electrochemiluminescence. The status of decidual angiogenesis was examined by cluster designation 34 (CD34) immunohistochemistry and the expression of angiogenic factors, including vascular endothelial growth factor A (VEGFA), placental growth factor (PLGF), and VEGF receptor 2 (VEGFR2) were also tested. Serum levels of homocysteine (Hcy), follicle stimulating hormone (FSH), luteinizing hormone (LH), prolactin (PRL), progesterone (P4), and estradiol (E2) were detected by Enzyme-linked immunosorbent assay. The folate-deficient mice had a lower folate level and a higher Hcy level. Folate deficiency restrained decidual angiogenesis with significant abnormalities in vascular density and the enlargement and elongation of the vascular sinus. It also showed a reduction in the expressions of VEGFA, VEGFR2, and PLGF. In addition, the serum levels of P4, E2, LH, and PRL were reduced in folate-deficient mice, and the expression of progesterone receptor (PR) and estrogen receptor α (ERα) were abnormal. These results indicated that folate deficiency could impaire decidual angiogenesis and it may be related to the vasculotoxic properties of Hcy and the imbalance of the reproductive hormone. PMID:26247969
Quantum mechanics/molecular mechanics restrained electrostatic potential fitting.
Burger, Steven K; Schofield, Jeremy; Ayers, Paul W
2013-12-05
We present a quantum mechanics/molecular mechanics (QM/MM) method to evaluate the partial charges of amino acid residues for use in MM potentials based on their protein environment. For each residue of interest, the nearby residues are included in the QM system while the rest of the protein is treated at the MM level of theory. After a short structural optimization, the partial charges of the central residue are fit to the electrostatic potential using the restrained electrostatic potential (RESP) method. The resulting charges and electrostatic potential account for the individual environment of the residue, although they lack the transferable nature of library partial charges. To evaluate the quality of the QM/MM RESP charges, thermodynamic integration is used to measure the pKa shift of the aspartic acid residues in three different proteins, turkey egg lysozyme, beta-cryptogein, and Thioredoxin. Compared to the AMBER ff99SB library values, the QM/MM RESP charges show better agreement between the calculated and experimental pK(a) values for almost all of the residues considered.
一类非线性发展方程的复合型双孤子新解∗%New complexion two-soliton solutions of a class of nonlinear evolution equation
套格图桑; 伊丽娜
2015-01-01
通过下列步骤，构造了一类非线性发展方程的无穷序列复合型双孤子新解：步骤一，给出两种函数变换，把一类非线性发展方程化为二阶非线性常微分方程；步骤二，再通过函数变换，二阶非线性常微分方程转化为一阶非线性常微分方程组，并获得了该方程组的首次积分；步骤三，利用首次积分与两种椭圆方程的新解与Bäcklund变换，构造了一类非线性发展方程的无穷序列复合型双孤子新解。%New infinite sequence complexion two-soliton solutions of a kind of nonlinear evolution equation are constructed with the help of function transformations and two kinds of elliptic equations. Step one,according to two function transformations, a kind of nonlinear evolution equation is changed into a nonlinear ordinary differential equation of second order. Step two, using function transformation, the nonlinear ordinary differential equation of second order is transformed into a set of nonlinear ordinary differential equations of first order, and the first integral of the set of equations is obtained. Finally, the first integral with new solutions and Bäcklund transformation of two kinds of elliptic equations are used to search for new infinite sequence complexion two-soliton solutions of a kind of nonlinear evolution equation.
夏铁成; 于发军; 陈登远
2005-01-01
An extension of the Lie algebra An-1 has been proposed [Phys. Lett. A, 2003, 310:19-24]. In this paper, the new Lie algebra was used to construct a new higher dimensional loop algebra G. Based on the loop algebra G, the integrable couplings system of the NLS-MKdV equations hierarchy was obtained. As its reduction case, generalized nonlinear NLS-MKdV equations were obtained. The method proposed in this letter can be applied to other hierarchies of evolution equations.
Coelho, Jennifer S; Nederkoorn, Chantal; Jansen, Anita
2014-04-01
The cue-reactivity model, which is based on conditioning processes, posits that repeated food exposure (in the absence of consumption) should decrease cue reactivity. To examine whether repeated chocolate exposure attenuates cravings and intake, relative to those exposed to an acute cue, a 2 (repeated vs acute cue) × 2 (restrained vs unrestrained eaters) design was employed. Fifty female participants were recruited. Repeated exposure reduced cravings in unrestrained eaters (relative to acute exposure), but increased cravings in restrained eaters. An interaction between restraint and exposure emerged on intake, such that restrained eaters ate less after acute exposure than did unrestrained eaters.
EXPERIMENTAL TESTING OF DRAW—BEAD RESTRAINING FORCE IN SHEET METAL FORMING
J.H.Yang; J.Chen; 等
2003-01-01
Due to complexities of draw-bead restraining force calculated according to theory and depending on sheet metal forming properties experiment testing system,a simplified method to calculate draw-bead restraining force is put forward by experimental method in cup-shaped drawing process.The experimental results were compared with numer-ical results and proved agreement.It shows the method is effective.
Peláez-Fernández, María Angeles; Extremera, Natalio
2011-11-01
The present research explored the effects of pre-exposure to temptation primes and dieting primes on food intake, goal accessibility and explicit automatic evaluations of food-enjoyment and dieting goals among restrained and unrestrained eaters. Participants (n= 166) were randomly assigned to three conditions: food-cue, dieting, or control, in which they were exposed to incidental presentation of gourmet, fashion or geographic magazines, respectively. Words related to the goals of dieting and/or food- enjoyment were presented in a computer decision task following the incidental presentation of gourmet, dieting, and geographic magazine photographs. The computer task and the presentation of food were counterbalanced. Participants' food intake was assessed in a taste-rating task. Restrained eaters ate more than did unrestrained eaters across the three conditions. Restrained eaters who were exposed to food cues ate more than did restrained eaters in the control condition and they evaluated the goal of dieting more negatively compared to restrained eaters in the other two conditions. These findings were inconsistent with 'Counteractive Self-Control Theory' but consistent with previous studies on the effects of food-cue exposure in restrained eaters.
Arvieu, R.; Carbonell, J.; Gignoux, C.; Mangin-Brinet, M. [Inst. des Sciences Nucleaires, Grenoble-1 Univ., 38 (France); Rozmej, P. [Uniwersytet Marii Curie-Sklodowskiej, Lublin (Poland)
1997-12-31
The time evolution of coherent rotational wave packets associated to a diatomic molecule or to a deformed nucleus has been studied. Assuming a rigid body dynamics the J(J+1) law leads to a mechanism of cloning: the way function is divided into wave packets identical to the initial one at specific time. Applications are studied for a nuclear wave packed formed by Coulomb excitation. Exact boundary conditions at finite distance for the solution of the time-dependent Schroedinger equation are derived. A numerical scheme based on Crank-Nicholson method is proposed to illustrate its applicability in several examples. (authors) 3 refs.
Abstract methods in partial differential equations
Carroll, Robert W
2012-01-01
Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.
New application to Riccati equation
Taogetusang; Sirendaoerji; Li, Shu-Min
2010-08-01
To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation. Based on the tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamoto-Sivashinsky equation and the set of (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.
Kurbel, Sven
2014-01-07
Based on avian and mammalian fossils found in the northeastern Chinese province of Liaoning and physiological traits linked to homeothermy, a hypothesis of evolution of homeothermic animals is proposed. It is based on the importance of muscle function in cold environment, as a strong selection pressure that favors endothermic metabolism during periods of cold climates. The presented hypothesis postulates that in progressively cooling environment, animals will develop thermal insulation, increased basal metabolism if food is available, and torpor when food is scarce. Since late Permian, Triassic and Cretaceous global temperatures were high, an exceptional place that gradually became cold was needed for the homeothermy evolution. South China Craton is here proposed as a plausible candidate for that role since it drifted across the Paleo-Tethys ocean, from equator to high northern latitudes in a journey that lasted from 250 to 200Myr ago. After this small continent collided with North China Craton some 200Myr ago, the already cold-adapted animals had spread to large, mostly empty spaces on the North China Craton, due to their evolutionary advantage of making active living in the cold environment. The most advantageous early homeothermic animals went further north to the cold Liaoning to start an oasis that delivered modern birds during next 50Myr. Modern mammals possibly evolved somewhere in the cold vicinity. This made Liaoning and similarly cold places the cradles of early birds and early mammals since for the following millions of years these places remained too cold for poikilotherms to enter and warm enough for homeotherms to dwell, until the Cretaceous-Paleogene extinction event and subsequent global cooling that diminished poikilotherms. Homeothermy was probably even more important as a survival advantage in cooler climates of Paleogene, when mammals and birds became dominant animals. This interpretation is probably supported by a recent report that a small
Studies on effect of stress preconditioning in restrain stress-induced behavioral alterations.
Kaur, Rajneet; Jaggi, Amteshwar Singh; Singh, Nirmal
2010-02-01
Stress preconditioning has been documented to confer on gastroprotective effects on stress-induced gastric ulcerations. However, the effects of prior exposure of stress preconditioning episodes on stress-induced behavioral changes have not been explored yet. Therefore the present study was designed to investigate the ameliorative effects of stress preconditioning in immobilization stress-induced behavioral alterations in rats. The rats were subjected to restrain stress by placing in restrainer (5.5 cm in diameter and 18 cm in length) for 3.5 h. Stress preconditioning was induced by subjecting the rats to two cycles of restraint and restrain-free periods of 15 min each. Furthermore, a similar type of stress preconditioning was induced using different time cycles of 30 and 45 min. The extent and severity of the stress-induced behavioral alterations were assessed using different behavioral tests such as hole-board test, social interaction test, open field test, and actophotometer. Restrain stress resulted in decrease in locomotor activity, frequency of head dips and rearing in hole board, line crossing and rearing in open field, and decreased following and increased avoidance in social interaction test. Stress preconditioning with two cycles of 15, 30 or 45 min respectively, did not attenuate stress-induced behavioral changes to any extent. It may be concluded that stress preconditioning does not seem to confer any protective effect in modulating restrain stress-induced behavioral alterations.
Nayan Mani Nath; Mrinal Kumar Das; Jayanta Kumar Sarma
2015-10-01
This is an attempt to study how the features of Regge theory, along with QCD predictions, lead towards the understanding of unpolarized non-singlet structure functions $F_{2}^{\\text{NS}}$ (, 2) and 3 (, 2) at low and low 2 . Combining the features of perturbative quantum chromodynamics (pQCD) and Regge theory, an ansatz for $F_{2}^{\\text{NS}}$ (, 2) and 3 (, 2) structure functions at small was obtained, which when used as the initial input to Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) equation, gives the 2 evolution of the non-singlet structure functions. The non-singlet structure functions, evolved in accordance with DGLAP evolution equations up to next-next-to-leading order are studied phenomenologically in comparison with the available experimental and parametrization results taken from NMC, CCFR, NuTeV, CORUS, CDHSW, NNPDF and MSTW Collaborations and a very good agreement is observed in this regard.
Chaotic region of elastically restrained single-walled carbon nanotube
Hu, Weipeng; Song, Mingzhe; Deng, Zichen; Zou, Hailin; Wei, Bingqing
2017-02-01
The occurrence of chaos in the transverse oscillation of the carbon nanotube in all of the precise micro-nano mechanical systems has a strong impact on the stability and the precision of the micro-nano systems, the conditions of which are related with the boundary restraints of the carbon nanotube. To generalize some transverse oscillation problems of the carbon nanotube studied in current references, the elastic restraints at both ends of the single-walled carbon nanotube are considered by means of rotational and translational springs to investigate the effects of the boundary restraints on the chaotic properties of the carbon nanotube in this paper. Based on the generalized multi-symplectic theory, both the generalized multi-symplectic formulations for the governing equation describing the transverse oscillation of the single-walled carbon nanotube subjected to the transverse load and the constraint equations resulting from the elastic restraints are presented firstly. Then, the structure-preserving scheme with discrete constraint equations is constructed to simulate the transverse oscillation process of the carbon nanotube. Finally, the chaotic region of the carbon nanotube is captured, and the oscillations of the two extreme cases (including simply supported and cantilever) are investigated in the numerical investigations. From the numerical results, it can be concluded that the relative bending stiffness coefficient and the absolute bending stiffness coefficients at both ends of the carbon nanotube are two important factors that affect the chaotic region of the carbon nanotube, which provides guidance on the design and manufacture of precise micro-nano mechanical systems. In addition, the different routes to the chaos of the carbon nanotube in two extreme cases are revealed.
Prolongation structures for supersymmetric equations
Roelofs, G.H.M.; Hijligenberg, van den N.W.
1990-01-01
The well known prolongation technique of Wahlquist and Estabrook (1975) for nonlinear evolution equations is generalized for supersymmetric equations and applied to the supersymmetric extension of the KdV equation of Manin-Radul. Using the theory of Kac-Moody Lie superalgebras, the explicit form of
On the statistical equivalence of restrained-ensemble simulations with the maximum entropy method.
Roux, Benoît; Weare, Jonathan
2013-02-28
An issue of general interest in computer simulations is to incorporate information from experiments into a structural model. An important caveat in pursuing this goal is to avoid corrupting the resulting model with spurious and arbitrary biases. While the problem of biasing thermodynamic ensembles can be formulated rigorously using the maximum entropy method introduced by Jaynes, the approach can be cumbersome in practical applications with the need to determine multiple unknown coefficients iteratively. A popular alternative strategy to incorporate the information from experiments is to rely on restrained-ensemble molecular dynamics simulations. However, the fundamental validity of this computational strategy remains in question. Here, it is demonstrated that the statistical distribution produced by restrained-ensemble simulations is formally consistent with the maximum entropy method of Jaynes. This clarifies the underlying conditions under which restrained-ensemble simulations will yield results that are consistent with the maximum entropy method.
Lattimore, Paul; Caswell, Noreen
2004-04-01
This study examined the effects of active (AC) and passive coping (PC) stress tasks on food intake in female restrained (n = 20) and unrestrained eaters (n = 20) Participants completed a reaction time task (AC), a cold-pressor test (PC), and a relaxation control condition separated by 1-week intervals. Food intake was assessed after each task. Self-reported anxiety, heart rate and blood pressure (BP) were measured before and after each task. Restraint was measured using the Dutch Eating Behaviour Questionnaire. Significant increases in BP were evident in the AC task only. Stress tasks produced significant increases in self-rated anxiety. Restrained eaters consumed more than unrestrained following the reaction time task, while the opposite was observed following relaxation. The findings of this study show that disinhibited eating of restrained eaters can be triggered by the distracting effects of a cognitively demanding task and may be independent of anxiety experienced.
The tanh-coth method combined with the Riccati equation for solving non-linear equation
Bekir, Ahmet [Dumlupinar University, Art-Science Faculty, Department of Mathematics, Kuetahya (Turkey)], E-mail: abekir@dumlupinar.edu.tr
2009-05-15
In this work, we established abundant travelling wave solutions for some non-linear evolution equations. This method was used to construct solitons and traveling wave solutions of non-linear evolution equations. The tanh-coth method combined with Riccati equation presents a wider applicability for handling non-linear wave equations.
Research on the Defects Restraining Ability of Power Supply Transacting Electrocircuit
GAO Jun; CHEN Chuan-bo
2006-01-01
Adopting the mechanism model and the system identification method, the power supply transacting electrocircuit (integrate manostat) is analyzed, and the restraining ability and the response for power supply transacting electrocircuit to overcome various battery defects are studied. The effects of the power supply yawp on the normal functions of the radio fuze are investigated. The research indicate that the shortcomings of the integration manostat as battery defects can be regarded as steady noise, and the restraining ability of the integration manostat to battery defects isn't less than 50 dB.
Stability of axially restrained steel columns under temperature action
无
2010-01-01
The in-plane elastic buckling of a steel column under thermal loading is investigated. The column is pinned at its ends, with two linear elastic springs that model the restraint provided by adjacent members in a structural assemblage or an elastic foundation. Across a section, the temperature is assumed to be linearly distributed. Based on a nonlinear strain-displacement relationship, the energy method is used to obtain the equilibrium and buckling equations. Then the buckling of columns with three different thermal loading cases is studied. The results show that the analytical formulas can be used to evaluate the critical temperature for elastic buckling. The thermal gradient plays a positive role in improving the stability of columns. Comparing these predictions with uniform temperature distribution over cross section, it can be shown that the buckling load is seriously underestimated. It can also be found that axial restraints can significantly affect the column elastic buckling loads. The critical temperature decreases with an increase of restraint stiffness. Furthermore, the effect of axial stiffness increases when increasing the thermal gradients and decreasing the slenderness ratio of columns.
李向正
2012-01-01
The bounded bell shape algebraic solitary wave solutions of nonlinear evolution equations are researched in this paper. The Kolmogorov-Petrovskii-Piskunov (KPP for short) equation,compound KdV-mKdV equation and mKdV equation are chose to as examples. The theory of planar dynamical systems is applied to study the existence conditions of algebraic solitary wave solutions. The algebraic solitary wave solutions of these three equations are obtained respectively. And a method for solving this type solutions is proposed, which is called algebraic solitary wave solution method(ASW method for short).%本文以非线性发展方程的有界钟状代数孤波解为研究对象,以Kolmogorov-Petrovskii-Piskunov(简称KPP)方程、组合KdV-mKdV方程和mKdV方程为例,利用平面动力系统知识,分析有界钟状代数孤立波解出现的条件,提出求解的方法,称之为代数孤波解解法(简称ASW解法),分别获得这三个方程的代数孤立波解.
Burkett, Corey A.; Bemis, Sean P.; Benowitz, Jeff A.
2016-12-01
The tallest mountain in North America, Denali (formerly Mount McKinley, 6,190 m), is situated inside an abrupt bend in the right-lateral strike-slip Denali fault. This anomalous topography is clearly associated with the complex geometry of the Denali fault, but how this restraining bend has evolved in conjunction with the regional topography is unknown. To constrain how this bend in the Denali fault is deforming, we document the Quaternary fault-related deformation north of the Denali fault through combined geologic mapping, active fault characterization, and analysis of background seismicity. Our mapping illustrates an east-west change in faulting style where normal faults occur east of the fault bend and thrust faults predominate to the west. The complex and elevated regional seismicity corroborates the style of faulting adjacent to the fault bend and provides additional insight into the change in local stress field in the crust adjacent to the bend. The style of active faulting and seismicity patterns define a deforming zone that accommodates the southwestward migration of this restraining bend. Fault slip rates for the active faults north of the Denali fault, derived from offset glacial outwash surfaces, indicate that the Mount McKinley restraining bend is migrating along the Denali fault at a late Pleistocene/Holocene rate of 2-6 mm/yr. Ongoing thermochronologic and structural studies of the Mount McKinley restraining bend will extend these constraints on the migration and evolution of the restraining bend deeper in time and to the south of the Denali fault.
1 in 5 U.S. Kids Killed in Crashes Not Restrained Properly
... https://medlineplus.gov/news/fullstory_165912.html 1 in 5 U.S. Kids Killed in Crashes Not Restrained Properly Finding highlights importance of ... save young lives, researchers now report that one in every five children killed in car crashes in ...
Emotional, external and restrained eating behaviour and BMI trajectories in adolescence
Snoek, Harriëtte M.; Engels, Rutger C.M.E.; Strien, Van Tatjana; Otten, Roy
2013-01-01
Individual differences in eating behaviours might partly explain the variations in development of weight gain and subsequent overweight and obesity. In the current study, identified trajectories of BMI in adolescence and their associations with restrained, emotional and external eating were tested.
van Rooij, F.B.; ten Haaf, J.; Verhoeff, A.P.
2013-01-01
In 2009, the Netherlands introduced a 10-day temporary restraining order (TRO) intended for adult perpetrators of domestic violence to defuse dangerous situations and to reduce recidivism by combining a legal action with social services. For this study, 18 victims and 10 perpetrators were interviewe
Zhou, Yizhou; Gao, Xiao; Chen, Hong; Kong, Fanchang
2017-08-01
Restrained eating for weight control and loss is becoming highly prevalent in many affluent societies, while most of the restrained eaters are rather unsuccessful in the long term. According to the strength model of self-control, the disinhibition effect of restrained eaters may occur after the depletion of self-control resources. However, no work has examined the direct impact of self-control resources on inhibitory control ability of restrained eaters. This study investigated the influences of self-control resources on the food-related inhibitory control among high-restraint/low-disinhibition restrained eaters, high-restraint/high-disinhibition restrained eaters and unrestrained eaters using stop signal task. Results reveal that there's no difference of food-related inhibitory control between three groups when the self-control resources are non-depleted, while high-restraint/high-disinhibition restrained eaters showing a decrease of food-related inhibitory control after ego-depletion. This disinhibition effect only seems to occur in samples of restrained eaters with a high tendency toward overeating. Copyright © 2017 Elsevier Ltd. All rights reserved.
Werthmann, Jessica; Jansen, Anita; Roefs, Anne
2016-01-01
Attention bias for food could be a cognitive pathway to overeating in obesity and restrained eating. Yet, empirical evidence for individual differences (e.g., in restrained eating and body mass index) in attention bias for food is mixed. We tested experimentally if temporarily induced health versus
Partial differential equations
Friedman, Avner
2008-01-01
This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we
EXACT TRAVELLING WAVE SOLUTIONS TO BBM EQUATION
无
2009-01-01
Abundant new travelling wave solutions to the BBM (Benjamin-Bona-Mahoni) equation are obtained by the generalized Jacobian elliptic function method. This method can be applied to other nonlinear evolution equations.
Nestola, Yago; Storti, Fabrizio; Cavozzi, Cristian; Magistroni, Corrado; Meda, Marco; Piero Righetti, Fabrizio
2016-04-01
Structural inheritance plays a fundamental role during crustal deformation because pre-existing fault and shear zones typically provide weakness zone suitable to fail again when affected by a new regional stress field. Re-activation of structural inheritance is expected to unavoidably increase the complexity of structural architectures, whose geometric and kinematic patterns can significantly deviate from what expected in newly deformed crustal sectors. Availability of templates from analogue models can provide a very effective tool to help unraveling such a structural complexity. For this purpose, we simulated the reworking of a set of basement hosted pre-existing fault zones at strike-slip restraining fault bends. In the models, the mechanical stratigraphy consists of a basement, made of a mixture of dry kaolin and sand to slightly increase cohesion, and a sedimentary cover made by pure dry sand. Inherited fault zones are confined to the basement and coated by a thin veneer of silicone putty. In the experimental programme, the geometry of the left-lateral restraining bend is maintained the same, with a bending angle of 30° of the restraining fault segment. The strike of the inherited fault zones, measured counterclockwise with respect to that of the master strike-slip fault zone outside the restraining bend, was 0°, 30°, and 60° in different experiments, respectively. An end member experiment without inheritance was also run for comparison. Our experimental results show that the angle that the inherited fault zones make with the restraining bend plays a fundamental role in governing the deformation pattern. When structural inheritance is near parallel to the master strike-slip fault zone, synthetic shears form and severely compartmentalize the transpressional pop-up anticline growing on top of the restraining bend. Fault-bounded blocks undergo sinistral escape during transpression. On the other hand, when structural inheritance makes a high angle to the
Simple Derivation of the Lindblad Equation
Pearle, Philip
2012-01-01
The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…
Experimental and numerical study of restraining force development in inclined draw beads
Raghavan, K. S.; Narainen, R.; Smith, L. M.
2013-12-01
Inclined (angled) draw bead geometries are becoming increasingly common as body styling requirements necessitate external panel shapes with considerable curvature. The restraining force that develops as material undergoes bending and frictional contact varies with bead geometry, material strength level and ambient lubrication conditions. In this study, an FEA based parametric approach is used to model the effects of material strength, friction condition, and binder angle on draw bead restraining force (DBRF). A finite element draw bead simulation was calibrated to experimental data for a 250 MPa electro-galvanized bake-hardenable specimen. The experimental data is used to confirm that the DBRF vs. binder angle curve roughly follows a concave shaped second order function with a maximum somewhere in the positive binder angle domain.
The danger signal S100B integrates pathogen- and danger-sensing pathways to restrain inflammation.
Sorci, Guglielmo; Giovannini, Gloria; Riuzzi, Francesca; Bonifazi, Pierluigi; Zelante, Teresa; Zagarella, Silvia; Bistoni, Francesco; Donato, Rosario; Romani, Luigina
2011-03-01
Humans inhale hundreds of Aspergillus conidia without adverse consequences. Powerful protective mechanisms may ensure prompt control of the pathogen and inflammation. Here we reveal a previously unknown mechanism by which the danger molecule S100B integrates pathogen- and danger-sensing pathways to restrain inflammation. Upon forming complexes with TLR2 ligands, S100B inhibited TLR2 via RAGE, through a paracrine epithelial cells/neutrophil circuit that restrained pathogen-induced inflammation. However, upon binding to nucleic acids, S100B activated intracellular TLRs eventually resolve danger-induced inflammation via transcriptional inhibition of S100B. Thus, the spatiotemporal regulation of TLRs and RAGE by S100B provides evidence for an evolving braking circuit in infection whereby an endogenous danger protects against pathogen-induced inflammation and a pathogen-sensing mechanism resolves danger-induced inflammation.
The danger signal S100B integrates pathogen- and danger-sensing pathways to restrain inflammation.
Guglielmo Sorci
2011-03-01
Full Text Available Humans inhale hundreds of Aspergillus conidia without adverse consequences. Powerful protective mechanisms may ensure prompt control of the pathogen and inflammation. Here we reveal a previously unknown mechanism by which the danger molecule S100B integrates pathogen- and danger-sensing pathways to restrain inflammation. Upon forming complexes with TLR2 ligands, S100B inhibited TLR2 via RAGE, through a paracrine epithelial cells/neutrophil circuit that restrained pathogen-induced inflammation. However, upon binding to nucleic acids, S100B activated intracellular TLRs eventually resolve danger-induced inflammation via transcriptional inhibition of S100B. Thus, the spatiotemporal regulation of TLRs and RAGE by S100B provides evidence for an evolving braking circuit in infection whereby an endogenous danger protects against pathogen-induced inflammation and a pathogen-sensing mechanism resolves danger-induced inflammation.
Chen, Lianfeng; Zheng, Tianran; Chen, Qing; Zhang, Jun
2013-12-01
Advanced high strength steels (AHSS) are used more and more in automotive industry for increasing crashworthiness and weight reduction. Improving metal flow and reduce friction are important to forming the part and decrease part reject rates of AHSS. The present study focused on friction characteristics and drawbead restraining force of Dual Phase (DP) steels with or without coating, such as DP980, DP780, DP590, DP780+Z, DP780+ZF, DP590+Z, using experimental approach. The effect of material properties, temperature, sliding velocity, surface roughness, dry and lubricant on friction behavior of DP steels is investigated. The contrast of DP steels with mild IF steel is carried out. The restraining force draw through different radius of drawbead is evaluated. This study is benefit to the set up of technique parameters during sheet metal forming simulation.
A generalized advection dispersion equation
Abdon Atangana
2014-02-01
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of the operator are presented. The operator is used to generalize the advection dispersion equation. The generalized equation differs from the standard equation in four properties. The generalized equation is solved via the variational iteration technique. Some illustrative figures are presented.
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
Towards an understanding of nurturing and restraining relational patterns in school communities
2012-01-01
This study aimed to understand the nature of nurturing and restraining relationships in a school communiy. The inquiry entailed a single instrumental case study of a selected school community in a semi-urban context in South Africa. Participants were learners (n=720), teachers (n=33) and administrative and terrain staff members (N=8) as well as two parents. Data on participants' perceptions of relationships in the school community were collected using work sessions/nominal group techniques, v...
Minimum Reinforcement in Concrete Structures under Restrained Shrinkage and Thermal Actions
Christiansen, Morten Bo; Nielsen, Mogens Peter
1999-01-01
The present paper deals with minimum reinforcement to ensure limitation of crack widths in concrete structures subjected to small imposed strains, such as those from restrained shrinkage or thermal actions. A theory is presented, which models the behaviour of a tensile member from zero load...... to first yielding of reinforcement. The theory takes into account the formation of each crack. However, concluding the paper, a simple design formula is given, which provides the amount of reinforcement, necessary to ensure a given crack width....
Upgrading the seismic capacity of existing RC buildings using buckling restrained braces
Hamdy Abou-Elfath
2017-06-01
Full Text Available Many existing RC buildings do not meet the lateral strength requirements of current seismic codes and are vulnerable to significant damage or collapse in the event of future earthquakes. In the past few decades, buckling-restrained braces have become increasingly popular as a lateral force resisting system because of their capability of improving the strength, the stiffness and the energy absorbing capacity of structures. This study evaluates the seismic upgrading of a 6-story RC-building using single diagonal buckling restrained braces. Seismic evaluation in this study has been carried out by static pushover analysis and time history earthquake analysis. Ten ground motions with different PGA levels are used in the analysis. The mean plus one standard deviation values of the roof-drift ratio, the maximum story drift ratio, the brace ductility factors and the member strain responses are used as the basis for the seismic performance evaluations. The results obtained in this study indicate that strengthening of RC buildings with buckling restrained braces is an efficient technique as it significantly increases the PGA capacity of the RC buildings. The results also indicate the increase in the PGA capacity of the RC building with the increase in the amount of the braces.
In-Situ-measurement of restraining forces during forming of rectangular cups
Singer, M.; Liewald, M.
2016-11-01
This contribution introduces a new method for evaluating the restraining forces during forming of rectangular cups with the goal of eliminating the disadvantages of the currently used scientifically established measurement procedures. With this method forming forces are measured indirectly by the elastic deformation of die structure caused by locally varying tribological system. Therefore, two sensors were integrated into the punch, which measure the restraining forces during the forming process. Furthermore, it was possible to evaluate the effects of different lubricants showing the time dependent trend as a function of stroke during the forming of the materials DP600 and DC04. A main advantage of this testing method is to get real friction corresponding data out of the physical deep drawing process as well as the measurement of real acting restraining forces at different areas of the deep drawing part by one single test. Measurement results gained by both sensors have been integrated into LS-Dyna simulation in which the coefficient of friction was regarded as a function of time. The simulated and deep drawn parts afterwards are analysed and compared to specific areas with regard to locally measured thickness of part. Results show an improvement of simulation quality when using locally varying, time dependent coefficients of friction compared to commonly used constant values.
Inertial manifold of the atmospheric equations
李建平; 丑纪范
1999-01-01
For a class of nonlinear evolution equations, their global attractors are studied and the existence of their inertial manifolds is discussed using the truncated method. Then, on the basis of the properties of operators of the atmospheric equations, it is proved that the operator equation of the atmospheric motion with dissipation and external forcing belongs to the class of nonlinear evolution equations. Therefore, it is known that there exists an inertial manifold of the atmospheric equations if the spectral gap condition for the dissipation operator is satisfied. These results furnish a basis for further studying the dynamical properties of global attractor of the atmospheric equations and for designing better numerical scheme.
New Jacobi Elliptic Function Solutions for the Zakharov Equations
Yun-Mei Zhao
2012-01-01
Full Text Available A generalized (G′/G-expansion method is proposed to seek the exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the Zakharov equations. As a result, some new Jacobi elliptic function solutions of the Zakharov equations are obtained. This method can also be applied to other nonlinear evolution equations in mathematical physics.
Bejger, M; Haensel, P; Zdunik, J L; Fortin, M
2016-01-01
We explore the implications of a strong first-order phase transition region in the dense matter equation of state in the interiors of rotating neutron stars, and the resulting creation of two disjoint families of neutron-stars' configurations (the so-called high-mass twins). Rotating, axisymmetric and stationary stellar configurations are obtained numerically in the framework of general relativity, and their global parameters and stability are studied. The equation of state-induced instability divides stable neutron star configurations into two disjoint families: neutron stars (second family) and hybrid stars (third family), with an overlapping region in mass, the high-mass twin star region. These two regions are divided by an instability strip. Its existence has interesting astrophysical consequences for rotating neutron stars. We note that it provides a "natural" explanation for the rotational frequency cutoff in the observed distribution of neutron stars spins, and for the apparent lack of back-bending in ...
Povstenko, Y. Z.
2010-11-01
In the case of time-fractional diffusion-wave equation considered in the spatial domain -∞Mainardi [F. Mainardi, Fractional relaxation-oscillation and fractional diffusion-wave phenomena, Chaos Solitons Fractals 7 (1996) 1461-1477]. In the present paper, we supplement Mainardi’s results with additional numerical calculations illustrating the behavior of the solution and solve the corresponding problems for axisymmetric and central symmetric cases. The obtained results show an unusual behavior of solutions.
Differential Equations as Actions
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
Solid-State NMR-Restrained Ensemble Dynamics of a Membrane Protein in Explicit Membranes.
Cheng, Xi; Jo, Sunhwan; Qi, Yifei; Marassi, Francesca M; Im, Wonpil
2015-04-21
Solid-state NMR has been used to determine the structures of membrane proteins in native-like lipid bilayer environments. Most structure calculations based on solid-state NMR observables are performed using simulated annealing with restrained molecular dynamics and an energy function, where all nonbonded interactions are represented by a single, purely repulsive term with no contributions from van der Waals attractive, electrostatic, or solvation energy. To our knowledge, this is the first application of an ensemble dynamics technique performed in explicit membranes that uses experimental solid-state NMR observables to obtain the refined structure of a membrane protein together with information about its dynamics and its interactions with lipids. Using the membrane-bound form of the fd coat protein as a model membrane protein and its experimental solid-state NMR data, we performed restrained ensemble dynamics simulations with different ensemble sizes in explicit membranes. For comparison, a molecular dynamics simulation of fd coat protein was also performed without any restraints. The average orientation of each protein helix is similar to a structure determined by traditional single-conformer approaches. However, their variations are limited in the resulting ensemble of structures with one or two replicas, as they are under the strong influence of solid-state NMR restraints. Although highly consistent with all solid-state NMR observables, the ensembles of more than two replicas show larger orientational variations similar to those observed in the molecular dynamics simulation without restraints. In particular, in these explicit membrane simulations, Lys(40), residing at the C-terminal side of the transmembrane helix, is observed to cause local membrane curvature. Therefore, compared to traditional single-conformer approaches in implicit environments, solid-state NMR restrained ensemble simulations in explicit membranes readily characterize not only protein
Lloyd K. Williams
1987-01-01
Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
Neural Mechanism of Restrained Eating%限制性饮食的神经机制
周一舟; 陈红; 高笑
2012-01-01
This paper introduced the ERP and brain mechanism studies on the dimension of cognitive restraint and tendency toward disinhibitive eating respectively, and put forward the restrained model of "cool-hot" processing. Future stud-ies are also advanced.%本文分别从认知限制和去抑制进食倾向两个维度回顾了限制性饮食的ERP和脑成像研究,初步提出限制性饮食者对食物的“冷—热”加工模型,并对今后的研究提出了展望.
Time-dependent Early-age Behaviors of Concrete under Restrained Condition
MA Xinwei; CAO Lixin; R D Hooton; H Lam; NIU Changren
2007-01-01
To investigate the early-age behaviors of concrete under a restrained condition, a set of apparatus was developed. In this way, the tensile creep and other early-age properties can be investigated in depth. By measuring the modulus of elasticity of concrete, synchronous shrinkage of concrete and steel rings and free shrinkage of concrete, the deformations of concrete ring can be quantified respectively. The experimental results show the tensile stress in concrete is time-dependent, and the stress at cracking is much lower than the tensile strength at that age; the tensile creep plays an important role in relaxing the tensile stress and postponing the cracking of concrete.
Barroga, Edward F
2014-11-01
Peer review is the pillar of the integrity of science communication. It is often beset with flaws as well as accusations of unreliability and lack of predictive validity. 'Rational cheating' by reviewers is a threat to the validity of peer review. It may diminish the value of good papers by unfavourable appraisals of the reviewers whose own works have lower scientific merits. This article analyzes the mechanics and defects of peer review and focuses on rational cheating in peer review, its implications, and options to restrain it.
Awasthi, Saurabh; Saraswathi, N T
2016-06-01
Vanillin a major component of vanilla bean extract is commonly used a natural flavoring agent. Glycation is known to induce aggregation and fibrillation of globular proteins such as albumin, hemoglobin. Here we report the inhibitory potential of vanillin toward early and advanced glycation modification and amyloid like aggregation of albumin based on the determination of both early and advanced glycation and conformational changes in albumin using circular dichroism. Inhibition of aggregation and fibrillation of albumin was determined based on amyloid specific dyes i.e., Congo red and Thioflavin T and microscopic imaging. It was evident that vanillin restrains glycation of albumin and exhibits protective effect toward its native conformation.
Kerr, I. D.; Sankararamakrishnan, R; Smart, O.S.; Sansom, M S
1994-01-01
A parallel bundle of transmembrane (TM) alpha-helices surrounding a central pore is present in several classes of ion channel, including the nicotinic acetylcholine receptor (nAChR). We have modeled bundles of hydrophobic and of amphipathic helices using simulated annealing via restrained molecular dynamics. Bundles of Ala20 helices, with N = 4, 5, or 6 helices/bundle were generated. For all three N values the helices formed left-handed coiled coils, with pitches ranging from 160 A (N = 4) to...
Constraint-Preserving Scheme for Maxwell's Equations
Tsuchiya, Takuya
2016-01-01
We derive the discretized Maxwell's equations using the discrete variational derivative method (DVDM), calculate the evolution equation of the constraint, and confirm that the equation is satisfied at the discrete level. Numerical simulations showed that the results obtained by the DVDM are superior to those obtained by the Crank-Nicolson scheme. In addition, we study the two types of the discretized Maxwell's equations by the DVDM and conclude that if the evolution equation of the constraint is not conserved at the discrete level, then the numerical results are also unstable.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Buckling Behavior of Long Anisotropic Plates Subjected to Elastically Restrained Thermal Expansion
Nemeth, Michael P.
2002-01-01
An approach for synthesizing buckling results for, and behavior of, thin balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and elastically restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates that are subjected to combined mechanical loads and is based on useful nondimensional parameters. In addition, stiffness-weighted laminate thermal-expansion parameters and compliance coefficients are derived that are used to determine critical temperatures in terms of physically intuitive mechanical-buckling coefficients. The effects of membrane orthotropy and membrane anisotropy are included in the general formulation. Many results are presented for some common laminates that are intended to facilitate a structural designer's transition to the use of generic buckling design curves. Several curves that illustrate the fundamental parameters used in the analysis are presented, for nine contemporary material systems, that provide physical insight into the buckling response in addition to providing useful design data. Examples are presented that demonstrate the use of generic design curves. The analysis approach and generic results indicate the effects and characteristics of elastically restrained laminate thermal expansion or contraction, membrane orthotropy and anisotropy, and flexural orthotropy and anisotropy in a very general and unifying manner.
Thoracic Duct Narrowing-Innovative Technique Restraining Weight Gain in Rats.
Rosenzweig, Barak; Barshack, Iris; Harats, Dror; Shaish, Aviv
2015-12-01
The lymphatic system is responsible for the absorption of fats from the digestive system, conveying 60-70 % of ingested fat to the blood stream. From the anatomical point of view, all the lymphatic drainage from the lower half of the body converges in the abdomen to enter the thoracic duct. This experimental study aim was to study the result of thoracic duct narrowing (TDN), an innovative surgical technique, on weight gain restrain in high-fat diet-fed rats. Forty-seven rats were allocated into three groups: thoracic duct narrowing ("S"-surgery), sham operation ("CS"-control surgery), and no surgery ("C"-control). All rats were fed with high-fat, cholesterol-rich diet. Food consumption and metabolic syndrome parameters including weight gain, plasma lipids and glucose, blood pressure, and viscera weight and histopathology were analyzed. Thoracic duct narrowing was proved simple and safe surgical procedure in the rat model. TDN induced weight gain restrain, associated with mild hepatic steatosis compared to moderate-severe hepatic steatosis in control groups. Splenomegaly and splenic fatty histiocytes were shown in the treated animals. TDN improved several parameters of the metabolic syndrome in high-fat diet-fed rats. TDN carries the potential of innovative obesity treatment using the lymphatic route of lipid absorption.
Bcl6 Sets a Threshold for Antiviral Signaling by Restraining IRF7 Transcriptional Program.
Xu, Feng; Kang, Yanhua; Zhuang, Ningtong; Lu, Zhe; Zhang, Hang; Xu, Dakang; Ding, Yina; Yin, Hongping; Shi, Liyun
2016-01-05
The coordination of restraining and priming of antiviral signaling constitute a fundamental aspect of immunological functions. However, we currently know little about the molecular events that can translate the pathogenic cues into the appropriate code for antiviral defense. Our present study reports a specific role of B cell lymphoma (Bcl)6 as a checkpoint in the initiation of the host response to cytosolic RNA viruses. Remarkably, Bcl6 specifically binds to the interferon-regulatory factor (IRF)7 loci and restrains its transcription, thereby functioning as a negative regulator for interferon (IFN)-β production and antiviral responses. The signal-controlled turnover of the Bcl6, most likely mediated by microRNA-127, coordinates the antiviral response and inflammatory sequelae. Accordingly, de-repression of Bcl6 resulted in a phenotypic conversion of macrophages into highly potent IFN-producing cells and rendered mice more resistant to pathogenic RNA virus infection. The failure to remove the Bcl6 regulator, however, impedes the antiviral signaling and exaggerates viral pneumonia in mice. We thus reveal a novel key molecular checkpoint to orchestrate antiviral innate immunity.
Ductility demands on buckling-restrained braced frames under earthquake loading
Fahnestock, Larry A.; Sause, Richard; Ricles, James M.; Lu, Le-Wu
2003-12-01
Accurate estimates of ductility demands on buckling-restrained braced frames (BRBFs) are crucial to performance-based design of BRBFs. An analytical study on the seismic behavior of BRBFs has been conducted at the ATLSS Center, Lehigh University to prepare for an upcoming experimental program. The analysis program DRAIN-2DX was used to model a one-bay, four-story prototype BRBF including material and geometric nonlinearities. The buckling-restrained brace (BRB) model incorporates both isotropic and kinematic hardening. Nonlinear static pushover and time-history analyses were performed on the prototype BRBF. Performance objectives for the BRBs were defined and used to evaluate the time-history analysis results. Particular emphasis was placed on global ductility demands and ductility demands on the BRBs. These demands were compared with anticipated ductility capacities. The analysis results, along with results from similar previous studies, are used to evaluate the BRBF design provisions that have been recommended for codification in the United States. The results show that BRB maximum ductility demands can be as high as 20 to 25. These demands significantly exceed those anticipated by the BRBF recommended provisions. Results from the static pushover and time-history analyses are used to demonstrate why the ductility demands exceed those anticipated by the recommended provisions. The BRB qualification testing protocol contained in the BRBF recommended provisions is shown to be inadequate because it requires only a maximum ductility demand of at most 7.5. Modifications to the testing protocol are recommended.
Dynamical Analysis of Long Fiber-Reinforced Laminated Plates with Elastically Restrained Edges
Liz G. Nallim
2012-01-01
Full Text Available This paper presents a variational formulation for the free vibration analysis of unsymmetrically laminated composite plates with elastically restrained edges. The study includes a micromechanics approach that allows starting the study considering each layer as constituted by long unidirectional fibers in a continuous matrix. The Mori-Tanaka method is used to predict the mechanical properties of each lamina as a function of the elastic properties of the components and of the fiber volume fraction. The resulting mechanical properties for each lamina are included in a general Ritz formulation developed to analyze the free vibration response of thick laminated anisotropic plates resting on elastic supports. Comprehensive numerical examples are computed to validate the present method, and the effects of the different mechanical and geometrical parameters on the dynamical behavior of different laminated plates are shown. New results for general unsymmetrical laminates with elastically restrained edges are also presented. The analytical approximate solution obtained in this paper can also be useful as a basis to deal with optimization problems under, for instance, frequency constraints.
Head excursion of restrained human volunteers and hybrid III dummies in steady state rollover tests.
Moffatt, Edward; Hare, Barry; Hughes, Raymond; Lewis, Lance; Iiyama, Hiroshi; Curzon, Anne; Cooper, Eddie
2003-01-01
Seatbelts provide substantial benefits in rollover crashes, yet occupants still receive head and neck injuries from contacting the vehicle roof interior when the roof exterior strikes the ground. Prior research has evaluated rollover restraint performance utilizing anthropomorphic test devices (dummies), but little dynamic testing has been done with human volunteers to learn how they move during rollovers. In this study, the vertical excursion of the head of restrained dummies and human subjects was measured in a vehicle being rotated about its longitudinal roll axis at roll rates from 180-to-360 deg/sec and under static inversion conditions. The vehicle's restraint design was the commonly used 3-point seatbelt with continuous loop webbing and a sliding latch plate. This paper presents an analysis of the observed occupant motion and provides a comparison of dummy and human motion under similar test conditions. Thirty-five tests (eighteen static and seventeen dynamic) were completed using two different sizes of dummies and human subjects in both near and far-side roll directions. The research indicates that far-side rollovers cause the restrained test subjects to have greater head excursion than near-side rollovers, and that static inversion testing underestimates head excursion for far-side occupants. Human vertical head excursion of up to 200 mm was found at a roll rate of 220 deg/sec. Humans exhibit greater variability in head excursion in comparison to dummies. Transfer of seatbelt webbing through the latch plate did not correlate directly with differences in head excursion.
Mathematical modeling and full-scale shaking table tests for multi-curve buckling restrained braces
C. S. Tsai; Yungchang Lin; Wenshin Chen; H. C. Su
2009-01-01
Buckling restrained braces (BRBs) have been widely applied in seismic mitigation since they were introduced in the 1970s. However, traditional BRBs have several disadvantages caused by using a steel tube to envelope the mortar to prevent the core plate from buckling, such as: complex interfaces between the materials used, uncertain precision, and time consumption during the manufacturing processes. In this study, a new device called the multi-curve buckling restrained brace (MC-BRB) is proposed to overcome these disadvantages. The new device consists of a core plate with multiple neck portions assembled to form multiple energy dissipation segments, and the enlarged segment, lateral support elements and constraining elements to prevent the BRB from buckling. The enlarged segment located in the middle of the core plate can be welded to the lateral support and constraining elements to increase buckling resistance and to prevent them from sliding during earthquakes. Component tests and a series of shaking table tests on a full-scale steel structure equipped with MC-BRBs were carried out to investigate the behavior and capability of this new BRB design for seismic mitigation. The experimental results illustrate that the MC-BRB possesses a stable mechanical behavior under cyclic loadings and provides good protection to structures during earthquakes. Also, a mathematical model has been developed to simulate the mechanical characteristics of BRBs.
Geneviève Painchaud Guérard
2016-01-01
Full Text Available Nutrition claims may help people to adopt healthier eating habits, but little is known about the potential cognitive effects of such claims on appetite sensations. The main purpose of this study was to evaluate the impact of nutrition claims and individual factors on perceived appetite sensations. According to a three (“healthy” versus “diet” (i.e., satiating versus “hedonic” by two (restrained or not restrained by two (normal-weight or overweight/obese by two (men versus women factorial design, 164 males and 188 females aged 18–65 were invited to taste an oatmeal-raisin snack in a blinded and ad libitum context. Visual analog scales (150 mm were used to evaluate appetite sensations before and over 1 h after consumption period. BMI and Restraint Scale were used to categorize participants according to their weight and restraint status. No main condition effect was observed for any of the four appetite sensations. However, subgroups analysis revealed significant differences among specific subgroups. A main effect of sex was also observed for all appetite sensations with men reporting higher levels of desire to eat, hunger and prospective food consumption, and lower levels of fullness than women. These findings highlight the importance of considering individual characteristics in interaction when studying appetite sensations.
Doucet, Éric; Pomerleau, Sonia
2016-01-01
Nutrition claims may help people to adopt healthier eating habits, but little is known about the potential cognitive effects of such claims on appetite sensations. The main purpose of this study was to evaluate the impact of nutrition claims and individual factors on perceived appetite sensations. According to a three (“healthy” versus “diet” (i.e., satiating) versus “hedonic”) by two (restrained or not restrained) by two (normal-weight or overweight/obese) by two (men versus women) factorial design, 164 males and 188 females aged 18–65 were invited to taste an oatmeal-raisin snack in a blinded and ad libitum context. Visual analog scales (150 mm) were used to evaluate appetite sensations before and over 1 h after consumption period. BMI and Restraint Scale were used to categorize participants according to their weight and restraint status. No main condition effect was observed for any of the four appetite sensations. However, subgroups analysis revealed significant differences among specific subgroups. A main effect of sex was also observed for all appetite sensations with men reporting higher levels of desire to eat, hunger and prospective food consumption, and lower levels of fullness than women. These findings highlight the importance of considering individual characteristics in interaction when studying appetite sensations. PMID:27725885
Postnikov, Sergey; Hernandez, Xavier; Capozziello, Salvatore
2014-01-01
We study the dark energy equation of state as a function of redshift in a non-parametric way, without imposing any {\\it a priori} $w(z)$ (ratio of pressure over energy density) functional form. As a check of the method, we test our scheme through the use of synthetic data sets produced from different input cosmological models which have the same relative errors and redshift distribution as the real data. Using the luminosity-time $L_{X}-T_{a}$ correlation for GRB X-ray afterglows (the Dainotti et al. correlation), we are able to utilize GRB sample from the {\\it Swift} satellite as probes of the expansion history of the Universe out to $z \\approx 10$. Within the assumption of a flat FLRW universe and combining SNeIa data with BAO constraints, the resulting maximum likelihood solutions are close to a constant $w=-1$. If one imposes the restriction of a constant $w$, we obtain $w=-0.99 \\pm 0.06$ (consistent with a cosmological constant) with the present day Hubble constant as $H_{0}=70.0 \\pm 0.6$ ${\\rm km} \\, {\\...
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Dovey, Terence M; Torab, Tina; Yen, Dorothy; Boyland, E J; Halford, Jason C G
2017-05-01
The objective of this study was to explore the impact of different advertising messages on adults' snack choice. Eighty participants (18-24 years old) were offered the choice between two snack packs following exposure to one of three advertising conditions. The snack packs contained either healthy or high fat, sugar or salt (HFSS) foods. Participants were exposed to commercials containing either non-food products, healthy food products or HFSS food products and their subsequent choice of snack pack was recorded. The Dutch Eating Behaviour Questionnaire (DEBQ) was used to assess the impact of external, restrained and emotional eating behaviour on snack pack selection following exposure to advertisements. The majority of unrestrained participants preferentially choose the HFSS snack pack irrespective of advertisement condition. In contrast, high restrained individuals exposed to the healthy eating advertisement condition preferentially selected the healthy snack pack while those in other advertisement conditions refused to take either snack pack. The healthy eating message, when distributed through mass media, resonated with restrained eaters only. Exposure to healthy food adverts provoked restrained eaters into choosing a snack pack; while exposure to other messages results in restrained eaters refusing to take any foods. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.
Wang Changfeng
2014-10-01
Full Text Available During an earthquake, the nonlinearity of the bridge structure mainly occurs at the supports, bridge piers and restrainers. When entering nonlinear stage, members of the bridge structure affect the elasto-plastic seismic response of the whole structure to a certain extent; for multi-span continuous bridges, longitudinal restrainers can be installed on the movable piers to optimise the distribution of seismic force and enable the movable piers to bear a certain amount of seismic effect. In order to evaluate the effect of nonlinearity of restrainer and supports on the elasto-plastic seismic response of continuous girder bridge, analytical models of continuous girder bridge structure considering the nonlinearity of movable supports, restrainers and bridge piers were built and the nonlinear time history analysis was conducted to evaluate the effect of nonlinearity of restraining devices and supports on the elasto-plastic seismic response of continuous girder bridge. Relevant structural measures and recommendation were made to reduce the seismic response of the fixed piers of the continuous girder bridge.
Pfattheicher, Stefan; Sassenrath, Claudia
2014-01-01
By applying regulatory focus theory (RFT) to the context of eating behavior, the present research examines the relations between individual differences in the two motivational orientations as conceptualized in RFT, that is, prevention-focused and promotion-focused self-regulation and emotional, external, and restrained eating. Building on a representative study conducted in the Netherlands (N = 4,230), it is documented that individual differences in prevention focus are positively related to emotional eating whereas negligible associations are found in regards to external and restrained eating. Individual differences in promotion focus are positively related to external eating whereas negligible associations are found in regards to emotional and restrained eating. In relating RFT to different eating styles we were able to document significant relations of basic self-regulatory orientations with regard to essential daily behavior associated with health and well-being. The implications for changing eating styles are discussed.
Cavanagh, Kevin V; Kruja, Blina; Forestell, Catherine A
2014-11-01
The goal of the current study was to determine whether provision of brand and caloric information affects sensory perception and consumption of a food in restrained (n=84) and unrestrained eaters (n=104). Using a between-subjects 2 × 2 × 3 design, female restrained and unrestrained eaters were asked to taste and rate a cookie that was labeled with a brand associated with healthful eating (Kashi(®)) or one associated with unhealthful eating (Nabisco(®)). Additionally, some participants were presented with a nutrition label alongside the brand name indicating that one serving contained 130 calories (Low-Calorie Condition), or 260 calories (High-Calorie Condition). The remaining participants were not shown a nutrition label (No Label Condition). Results indicated that those in the No Label or the High-Calorie Condition perceived the healthful branded cookie to have a better flavor than those who received the unhealthful branded cookie regardless of their restraint status. However, restrained eaters in the No Label Condition consumed more of the healthful than the unhealthful branded cookie, whereas those in the Low-Calorie Condition consumed more of the unhealthful than the healthful branded cookie. In contrast, unrestrained eaters ate more of the healthful branded cookie regardless of the caloric information provided. Thus, although restrained and unrestrained eaters' perceptions are similarly affected by branding and caloric information, brands and caloric information interact to affect restrained eaters' consumption. This study reveals that labeling foods as low calorie may create a halo effect which may lead to over-consumption of these foods in restrained eaters. Copyright © 2014 Elsevier Ltd. All rights reserved.
Effective equations for the quantum pendulum from momentous quantum mechanics
Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)
2012-08-24
In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.
Vittes, Katherine A; Webster, Daniel W; Frattaroli, Shannon; Claire, Barbara E; Wintemute, Garen J
2013-05-01
Persons under certain domestic violence restraining orders in California are required to surrender any firearms in their possession within 24 hours of service. The California Department of Justice funded a pilot program in which Sheriff's Offices in two counties developed a system for better enforcing the firearm surrender requirement. As part of a larger process evaluation, 17 restraining order recipients were interviewed about their experiences with and feelings about the removal of firearms from their abusers. Most women surveyed wanted firearms removed and felt safer as a result of their removal. Implications of the findings are discussed.
Nemeth, Michael P.
2004-01-01
An approach for synthesizing buckling results for thin balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and elastically restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexural anisotropic plates that are subjected to combined mechanical loads. In addition, stiffness-weighted laminate thermal-expansion parameters and compliance coefficients are derived that are used to determine critical temperatures in terms of physically intuitive mechanical-buckling coefficients. Many results are presented for some common laminates that are intended to facilitate a structural designer s transition to the use of the generic buckling design curves. Several curves that illustrate the fundamental parameters used in the analysis are presented, for nine contemporary material systems, that provide physical insight into the buckling response in addition to providing useful design data. Examples are presented that demonstrate the use of the generic design curves.
Lee Kyungkoo
2008-01-01
Full Text Available An analytical method to model failure of steel beam plastic hinges due to local buckling and low-cycle fatigue is proposed herein. This method is based on the plastic collapse mechanism approach and a yield-line plastic hinge (YLPH model whose geometry is based on buckled shapes of beam plastic hinges observed in experiments. Two limit states, strength degradation failure induced by local buckling and low-cycle fatigue fracture, are considered. The proposed YLPH model was developed for FEMA-350 WUF-W, RBS and Free Flange connections and validated in comparisons to experimental data. This model can be used to estimate the seismic rotation capacity of fully restrained beam-column connections in special steel moment-resisting frames under both monotonic and cyclic loading conditions.
Body image and restrained eating in blind and sighted women: A preliminary study.
Ashikali, Eleni-Marina; Dittmar, Helga
2010-03-01
Sociocultural theory attributes the high levels of body image concerns and disordered eating in Western women to the promotion of an unrealistically thin body ideal. This study investigated body dissatisfaction, restrained eating, and attitudes toward appearance in visually impaired and sighted women. There were 21 congenitally blind, 11 blinded later in life, and 60 sighted. Blind women were more satisfied with their body and dieted less than sighted women. Appearance attitudes, particularly thin-ideal internalization, accounted for differences in body dissatisfaction and dieting among the three groups of women. Possible explanations for our findings are considered, including the importance of visual exposure to the media's thin ideal, as well as the usefulness of future research on blind women. Copyright 2010 Elsevier Ltd. All rights reserved.
Size-dependent thermal buckling of heated nanowires with ends axially restrained
Wang, Yu; Wang, Zhi-Qiao; Lv, Jian-Guo
2014-02-01
Nanowires (NWs) are being actively explored for applications as nanoscale building blocks of sensors, actuators and nanoelectromechanical systems (NEMS). Temperature changes can induce an axial force within NWs due to the thermal expansion and may lead to buckling. The thermal buckling behaviors of ends-axially-restrained nanowires, subjected to a uniform temperature rise, are studied based on Bernoulli-Euler beam theory including the surface thermoelastic effects. Besides the surface elastic modulus, the influences of surface thermal expansion coefficient are incorporated into the model presented herein to describe size-dependent thermoelastic behaviors of nanowires. The results show that the critical buckling temperature and postbuckling deflection are significantly affected by surface thermoelastic effects and the influences become more prominent as the thickness of nanowire decreases. The corresponding influences of the slenderness ratio are also discussed. This research is helpful not only in understanding the thermal buckling properties of nanowires but also in designing the nanowire-based sensor and thermal actuator.
Size-dependent thermal buckling of heated nanowires with ends axially restrained
Wang, Yu [School of Engineering and Technology, China University of Geosciences, Beijing 100083 (China); Key Laboratory on Deep GeoDrilling Technology, Ministry of Land and Resources, China University of Geosciences, Beijing 100083 (China); Wang, Zhi-Qiao, E-mail: zqwang@cugb.edu.cn [School of Engineering and Technology, China University of Geosciences, Beijing 100083 (China); Key Laboratory on Deep GeoDrilling Technology, Ministry of Land and Resources, China University of Geosciences, Beijing 100083 (China); Lv, Jian-Guo [School of Engineering and Technology, China University of Geosciences, Beijing 100083 (China); Key Laboratory on Deep GeoDrilling Technology, Ministry of Land and Resources, China University of Geosciences, Beijing 100083 (China)
2014-02-01
Nanowires (NWs) are being actively explored for applications as nanoscale building blocks of sensors, actuators and nanoelectromechanical systems (NEMS). Temperature changes can induce an axial force within NWs due to the thermal expansion and may lead to buckling. The thermal buckling behaviors of ends-axially-restrained nanowires, subjected to a uniform temperature rise, are studied based on Bernoulli–Euler beam theory including the surface thermoelastic effects. Besides the surface elastic modulus, the influences of surface thermal expansion coefficient are incorporated into the model presented herein to describe size-dependent thermoelastic behaviors of nanowires. The results show that the critical buckling temperature and postbuckling deflection are significantly affected by surface thermoelastic effects and the influences become more prominent as the thickness of nanowire decreases. The corresponding influences of the slenderness ratio are also discussed. This research is helpful not only in understanding the thermal buckling properties of nanowires but also in designing the nanowire-based sensor and thermal actuator.
Differences in thoracic injury causation patterns between seat belt restrained children and adults.
Arbogast, Kristy B; Locey, Caitlin M; Zonfrillo, Mark R
2012-01-01
The objective of this research was to delineate age-based differences in specific thoracic injury diagnoses for seat belt restrained rear seat occupants and describe the associated injury causation in order to provide insight into how the load of the seat belt is transferred to occupants of various sizes. Using data from the Crash Investigation Research and Engineering Network (CIREN), 20 cases of rear seated, lap and shoulder belt restrained occupants with AIS2+ thoracic injuries in frontal crashes were reviewed. Seven were children and adolescents age 8-15 years, 5 were 16-24 years, 3 were 25-54 years, and 5 were 55+ years. Six of the seven 8-15 year olds sustained injuries to the lung in the form of pulmonary contusion or pneumothorax. Only three of the seven sustained a skeletal (sternum or rib) fracture; only one of these three involved multiple ribs bilaterally. In contrast, four of the five 16-24 year olds sustained at least one rib fracture - often multiple and bilateral. The adult cohort (25+ years) was involved in predominantly more minor crashes; however they all sustained complex rib fractures - seven of the eight involved multiple ribs, four of the eight were also bilateral. Belt compression - either from the shoulder belt or the lap belt - was identified as the primary cause of the thoracic injuries. Often, there was clear evidence of the location of belt loading from AIS 1 chest contusions or abrasions. These findings have implications for age-based thoracic injury criteria suggesting that that different metrics may be needed for different age groups.
Weisz, K; Shafer, R H; Egan, W; James, T L
1994-01-11
The solution structure of the DNA decamer d(CATTTGCATC)-d(GATGCAAATG), comprising the octamer motif of immunoglobulin genes, is determined by restrained molecular dynamics (rMD) simulations. The restraint data set includes interproton distances and torsion angles for the deoxyribose sugar ring which were previously obtained by a complete relaxation matrix analysis of the two-dimensional nuclear Overhauser enhancement (2D NOE) intensities and by the quantitative simulation of cross-peaks in double-quantum-filtered correlated (2QF-COSY) spectra. The influence of torsion angles and the number of experimental distance restraints on the structural refinement has been systematically examined. Omitting part of the experimental NOE-derived distances results in reduced restraint violations and lower R factors but impairs structural convergence in the rMD refinement. Eight separate restrained molecular dynamics simulations were carried out for 20 ps each, starting from either energy-minimized A- or B-DNA. Mutual atomic root-mean-square (rms) differences among the refined structures are well below 1 A and comparable to the rms fluctuations of the atoms about their average position, indicating convergence to essentially identical structures. The average refined structure was subjected to an additional 100 ps of rMD simulations and analyzed in terms of average torsion angles and helical parameters. The B-type duplex exhibits clear sequence-dependent variations in its geometry with a narrow minor groove at the T3.A3 tract and a large positive roll at the subsequent TG.CA step. This is accompanied by a noticeable bend of the global helix axis into the major groove. There is also evidence of significant flexibility of the sugar-phosphate backbone with rapid interconversion among different conformers.
Elfhag, K; Tynelius, P; Rasmussen, F
2007-06-08
We studied sugar-sweetened soft drinks and light soft drinks in their associations to psychological constructs of eating behavior and demographic data for adults and children. Soft drink intakes were assessed by consumption of soft drinks in number of days the last week, and eating behavior was measured by the Dutch Eating Behaviour Questionnaire (DEBQ). The sample included 3265 men and women, and their 12-year old children, originating from Swedish national databases. Associations to younger age and lower education in adults were in particular apparent for sugar-sweetened soft drinks. Consumption of sugar-sweetened soft drinks was further associated to less restrained and more external eating in adults. In contrast, light soft drinks were associated with higher BMI, more restrained eating and also more emotional eating in adults. For the children these associations were generally weaker. Sugar-sweetened soft drinks are consumed by persons with a lower education, who furthermore are less prone to attempt to restrict their calorie intake, and by some of those who are sensitive to external stimuli of foods. Light soft drinks are rather chosen by the more heavy persons who try to restrict their energy intake perhaps in order to control the body weight, and more unexpectedly, by adults who eat for comfort. Being more sensitive to an external stimulus of food such as taste seems to imply proneness to consume sugar-sweetened soft drinks instead of the light versions. Light soft drinks may be perceived as an adequate substitute in the use of foods for comfort, meaning the sweet taste may be sufficient for this purpose.
Soliton states of Maxwell’s equations and nonlinear Schrodinger equation
陈翼强
1997-01-01
Similarities and fundamental differences between Maxwell’s equations and nonlinear Schrodinger equation in predicting a soliton evolution in a uniform nonlinear anisotropic medium are analyzed.It is found that in some cases,the soliton solutions to the nonlinear Schrodinger equation cannot be recovered from Maxwell’s equations while in others the soliton solutions to Maxwell’s equations are lost from the nonlinear Schrodinger equation through approximation,although there are cases where the soliton solutions to the two sets of the equations demonstrate only quantitative difference.The origin of the differences is also discussed.
Boyce, Jessica A; Kuijer, Roeline G; Gleaves, David H
2013-09-01
Although viewing media body ideals promotes body dissatisfaction and problematic eating among women (e.g., extreme restraint/overeating), some argue that women only report such negative effects because they think that they are meant to (i.e., demand characteristics). Because restrained eaters are trying to lose weight, they might be vulnerable to such media exposure. However, because of demand characteristics, evidence is mixed. Therefore, we minimized demand characteristics and explored whether media body ideals would trigger restrained eaters to report negative (negative mood, weight dissatisfaction) or positive (positive mood, weight satisfaction) effects. We also hypothesized that this change (negative or positive) would encourage food intake. Restrained and unrestrained eaters (n=107) memorized media or control images. Restrained eaters exposed to media images reported decreased weight satisfaction and increased negative mood, but their food intake was not significantly affected. Perhaps paying advertent attention to the images caused goal-related negative affect, which triggered restraint. Copyright © 2013 Elsevier Ltd. All rights reserved.
Li, Lun; Li, Aibing; Murphy, Michael A.; Fu, Yuanyuan V.
2016-09-01
Three-dimensional shear wave velocity and radial anisotropy models of the crust and upper mantle beneath the NE Tibetan plateau are constructed from new measurements of Love wave dispersions (20-77s) and previously obtained Rayleigh wave dispersions (20-87s) using a two-plane-wave method. The mid-lower crust is characterized with positive anisotropy (VSH > VSV) with large strength beneath the Qinling and Qilian Mountains and small values beneath the Anyemaqen Mountain. The large positive anisotropy can be explained by horizontal alignment of anisotropic minerals in the mid-lower crust due to crustal flow. The mantle lithosphere above 90 km is largely isotropic while weak positive anisotropy appears beneath 90 km, which probably marks the lithosphere-asthenosphere boundary (LAB). A low shear wave velocity anomaly and relatively negative radial anisotropy are imaged in the entire lithosphere beneath the restraining bend in the eastern Kunlun fault, consistent with a weak lithosphere experiencing vertical thickening under horizontal compression. The asthenosphere at the restraining bend is characterized by significant low velocity and positive radial anisotropy, reflecting that the asthenosphere here is probably hotter, has more melts, and deforms more easily than the surrounding region. We propose that the lithosphere at the restraining bend was vertically thickened and subsequently delaminated locally, and induced asthenosphere upwelling. This model explains the observations of velocity and anisotropy anomalies in the lithosphere and asthenosphere as well as geological observations of rapid rock uplift at the restraining bend of the Kunlun fault.
Hilbert space methods in partial differential equations
Showalter, Ralph E
1994-01-01
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
Stämpfli, Aline E; Stöckli, Sabrina; Brunner, Thomas A
2017-03-01
Losing weight is a goal for many people, but it is hard to pursue. However, dieting cues in the environment hold promise for improving individuals' eating behavior. For example, exposure to thin, human-like sculptures by the artist Alberto Giacometti has been found to promote healthy snack choices at a vending machine. Whether health- or weight-related processes drive such effects has not yet been determined. However, a detailed understanding of the content-related drivers of environmental cues' effects provides the first indications regarding a cue's possible use. Therefore, two laboratory studies were conducted. They examined the Giacometti sculptures' effects on unhealthy and healthy food intake (Study 1) and on the completion of weight- and health-related fragmented words (Study 2). Study 1 indicated that the sculptures are weight-related by showing that they reduced food intake independent of food healthiness. Furthermore, the "Giacometti effect" was moderated by restrained eating. Restrained eaters, who are known for their weight-control goal, ate less after having been exposed to the thin sculptures. The results of Study 2 pointed in the same direction. Restrained eaters completed more weight-related words after being exposed to the sculptures. Overall, these studies suggest that the thin sculptures are primarily weight-related cues and particularly helpful for restrained eaters. Environmental weight-control cues such as the Giacometti sculptures could act as a counterforce to our obesogenic environment and help restrained eaters pursue their weight-control goal. In this way, they could nudge food decisions in a healthier direction.
Algebraic dynamics solution and algebraic dynamics algorithm of Burgers equations
2008-01-01
Algebraic dynamics solution and algebraic dynamics algorithm of nonlinear partial differential evolution equations in the functional space are applied to Burgers equation. The results indicate that the approach is effective for analytical solutions to Burgers equation, and the algorithm for numerical solutions of Burgers equation is more stable, with higher precision than other existing finite difference algo-rithms.
Restrictions on the geometry of the periodic vorticity equation
Escher, Joachim
2010-01-01
We prove that several evolution equations arising as mathematical models for fluid motion cannot be realized as metric Euler equations on the Lie group of all smooth and orientation-preserving diffeomorphisms on the circle. These include the quasi-geostrophic model equation, the axisymmetric Euler flow in higher space dimensions, and De Gregorio's vorticity model equation.
Probability representation of kinetic equation for open quantum system
Man'ko, V I; Shchukin, E V
2003-01-01
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
Comportamento de restrição alimentar e obesidade Restrained eating behavior and obesity
Fabiana Bernardi
2005-02-01
Full Text Available A obesidade é uma doença de alta prevalência no mundo e é responsável por sérias repercussões orgânicas e psicossociais, desde a infância até a vida adulta. O comportamento alimentar tem bases biológicas e sociais e, associado, à obesidade, torna-se um processo ainda mais complexo pelos aspectos psicológicos envolvidos, os quais se expressam por meio de humor depressivo, ansiedade, sentimento de culpa e, também, por mecanismos fisiológicos, como a resistência ao jejum na vigência de dietas restritivas. Há evidências de que, em indivíduos obesos, comportamentos de compulsão alimentar e ou restrição são mais freqüentes e parecem ser, em parte, responsáveis pelos fracassos observados no tratamento da obesidade. As restrições e auto-imposições das pessoas que fazem dieta, parecem ter um efeito rebote, resultando em compulsão alimentar, a qual pode associar-se a conseqüências psicológicas, como a perda da auto-estima, mudanças de humor e distração. As reflexões desta revisão sugerem que os programas para redução de peso corporal devem enfocar as bases do comportamento alimentar e desenvolver, efetivamente, ações interdisciplinares que permitam obter resultados eficazes no tratamento da obesidade.Obesity is a widespread disease in the world, responsible for serious organic and psychosocial repercussions, from infancy to adulthood. Eating behavior has biological as well as social bases. Associated to obesity, it becomes an even more complex process, since it is accompanied by psychological aspects showing symptoms such as depressive moods, anxiety, feelings of guilt, and physiological mechanisms as, for instance, the resistance to fast during restrictive diets. Obese individuals prevalently present behaviors such as binge or restrained eating, both leading to failure in the treatment of obesity. Restrained eating refers to the tendency to restrict food intake consciously, in order to prevent weight gain or to
Barr, Yael; Fogarty, Jennifer
2010-01-01
During the Orion landing and recovery subsystem design review, June 2009, it was noted that the human system and various vehicle systems, the environmental control and life support (ECLSS) and guidance, navigation and control (GN&C) systems for example, are negatively affected by Orion assuming a stable 2 (upside down; Figure A) configuration post landing. The stable 2 configuration is predicted to occur about 50% of the time based on Apollo landing data and modeling of the current capsule. The stable 2 configuration will be countered by an active up-righting system (crew module up-righting system; CMUS). Post landing balloons will deploy and inflate causing the vehicle to assume or maintain the stable 1 (up-right; Figure B) configuration. During the design review it was proposed that the up-righting system could be capable of righting the vehicle within 60 seconds. However, this time limit posed a series of constraints on the design which made it less robust than desired. The landing and recovery subsystem team requested an analysis of Orion vehicle systems as well as the human system with regard to the effect of stable 2 in order to determine if an up-righting response time greater than 60 seconds could be tolerated. The following report focuses on the assessment of the human system in the posture assumed when Orion is in the stable 2 configuration. Stable 2 will place suited, seated, and restrained crewmembers in a prone (facedown), head-up position for a period of time dependent on the functionality of the up-righting systems, ability of the crew to release themselves from the seat and restraints, and/or time to arrival of rescue forces. Given that the Orion seat and restraint system design is not complete and therefore, not available for evaluation, Space Medicine assessed how long a healthy but deconditioned crewmember could stay in this prone, restrained position and the physiological consequences of this posture by researching terrestrial analogs and
Extended Auxiliary Equation Method and Its Applications to Three Generalized NLS Equations
Gui-qiong Xu
2014-01-01
Full Text Available The auxiliary equation method proposed by Sirendaoreji is extended to construct new types of elliptic function solutions of nonlinear evolution equations. The effectiveness of the extended method is demonstrated by applications to the RKL model, the generalized derivative NLS equation and the Kundu-Eckhaus equation. Not only are the Jacobian elliptic function solutions are derived, but also the solitary wave solutions and trigonometric function solutions are obtained in a unified way.
Elsayed Mohamed Elsayed ZAYED
2014-07-01
Full Text Available In this article, many new exact solutions of the (2+1-dimensional nonlinear Boussinesq-Kadomtsev-Petviashvili equation and the (1+1-dimensional nonlinear heat conduction equation are constructed using the Riccati equation mapping method. By means of this method, many new exact solutions are successfully obtained. This method can be applied to many other nonlinear evolution equations in mathematical physics.doi:10.14456/WJST.2014.14
Integrable systems of partial differential equations determined by structure equations and Lax pair
Bracken, Paul, E-mail: bracken@panam.ed [Department of Mathematics, University of Texas, Edinburg, TX 78541-2999 (United States)
2010-01-11
It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a constraint equation is selected and imposed on the system of equations. This allows for the possibility of selecting the coefficients in the second fundamental form in a general way.
Zhi Hong-Yan; Zhao Xue-Qin; Zhang Hong-Qing
2005-01-01
Based on the study of tanh function method and the coupled projective Riccati equation method, we propose a new algorithm to search for explicit exact solutions of nonlinear evolution equations. We use the higher-order Schrodinger equation and mKdV equation to illustrate this algorithm. As a result, more new solutions are obtained, which include new solitary solutions, periodic solutions, and singular solutions. Some new solutions are illustrated in figures.
Stochastic Evolution Equations Driven by Fractional Noises
2016-11-28
Stochastic Calculus , Monte Carlo Methods and Mathematical Finance, University of Le Mans, October 6-9, 2015. "Parabolic Anderson model driven by...is based on the techniques of Malliavin calculus or stochastic calculus of variations. In the second part of this project, we have studied two...xi|2Hi−2, where Hi > 1 2 and condition (10) is satisfied if and only if ∑d i=1Hi > d− 1. This particular structure has been examined in [20]. ( ii
Tricomi, Francesco Giacomo
1957-01-01
This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Lienard Equation and Exact Solutions for Some Soliton-Producing Nonlinear Equations
ZHANG Wei-Guo; CHANG Qian-Shun; ZHANG Qi-Ren
2004-01-01
In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.
A Diffusion Equation for Quantum Adiabatic Systems
Jain, S R
1998-01-01
For ergodic adiabatic quantum systems, we study the evolution of energy distribution as the system evolves in time. Starting from the von Neumann equation for the density operator, we obtain the quantum analogue of the Smoluchowski equation on coarse-graining over the energy spectrum. This result brings out the precise notion of quantum diffusion.
An alternative to exact renormalization equations
Alexandre, Jean
2005-01-01
An alternative point of view to exact renormalization equations is discussed, where quantum fluctuations of a theory are controlled by the bare mass of a particle. The procedure is based on an exact evolution equation for the effective action, and recovers usual renormalization results.
Multisymplectic Geometry for the Seismic Wave Equation
CHEN Jing-Bo
2004-01-01
The multisymplectic geometry for the seismic wave equation is presented in this paper.The local energy conservation law,the local momentum evolution equations,and the multisymplectic form are derived directly from the variational principle.Based on the covariant Legendre transform,the multisymplectic Hamiltonian formulation is developed.Multisymplectic discretization and numerical experiments are also explored.
Buckling Behavior of Long Anisotropic Plates Subjected to Fully Restrained Thermal Expansion
Nemeth, Michael P.
2003-01-01
An approach for synthesizing buckling results and behavior for thin, balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and which are fully-restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates that are subjected to combined mechanical loads and is based on useful nondimensional parameters. In addition, stiffness-weighted laminate thermal-expansion parameters are derived and used to determine critical temperature changes in terms of physically intuitive mechanical buckling coefficients. The effects of membrane orthotropy and anisotropy are included. Many results are presented for some common laminates that are intended to facilitate a structural designer's transition to the use of the generic buckling design curves that are presented in the paper. Several generic buckling design curves are presented that provide physical insight into buckling response and provide useful design data. Examples are presented that demonstrate the use of generic design curves. The analysis approach and generic results indicate the effects and characteristics of laminate thermal expansion, membrane orthotropy and anisotropy, and flexural orthotropy and anisotropy in a very general, unifying manner.
Assessment of early-age cracking of high-performance concrete in restrained ring specimens
Quang-phu NGUYEN NGUYEN
2010-03-01
Full Text Available High-performance concrete (HPC is stronger and more durable than conventional concrete. However, shrinkage and shrinkage cracking are common phenomena in HPC, especially early-age cracking. This study assessed early-age cracking of HPC for two mixtures using restrained ring tests. The two mixtures were produced with water/binder mass ratio (mW/mB of 0.22 and 0.40, respectively. The results show that, with greater steel thickness, the higher degree of restraint resulted in a higher interface pressure and earlier cracking. With steel thickness of 6 mm, 19 mm, and 30 mm, the age of cracking were, respectively, 12 days, 8 days, and 5.4 days with the mW/mB = 0.22 mixture; and 22.5 days, 12.6 days, and 7.1 days with the mW/mB = 0.40 mixture. Cases of the same steel thickness show that the ring specimens with a thicker concrete wall crack later. With the mW/mB = 0.22 mixture, concrete walls with thicknesses of 37.5 mm, 75 mm, and 112.5 mm cracked at 3.4 days, 8.0 days, and 9.8 days, respectively; with the mW/mB = 0.40 mixture, the ages of cracking were 7.1 days, 12.6 days, and 16.0 days, respectively.
Ductility demands on buckling-restrained braced frames under earthquake loading
Larry A. Fahnestock; Richard Sause; James M. Ricles; Le-Wu Lu
2003-01-01
Accurate estimates of ductility demands on buckling-restrained braced frames (BRBFs) are crucial to performance-based design of BRBFs. An analytical study on the seismic behavior of BRBFs has been conducted at the ATLSS Center, Lehigh University to prepare for an upcoming experimental program. The analysis program DRAIN-2DX was used to model a one-bay, four-story prototype BRBF including material and geometric nonlinearities. The bucklingrestrained brace (BRB) model incorporates both isotropic and kinematic hardening. Nonlinear static pushover and timehistory analyses were performed on the prototype BRBF. Performance objectives for the BRBs were defined and uscd to evaluate thc time-history analysis results. Particular emphasis was placed on global ductility demands and ductility demands oa the BRBs. These demands were compared with anticipated ductility capacities. The analysis results, along with results from similar previous studics, are used to evaluate the BRBF design provisions that have been recommended for codification in the United States. Thc results show that BRB maximum ductility demands can be as high as 20 to 25. These demands significantly exceed those anticipated by the BRBF recommended provisions. Results from the static pushover and timehistory analyses are used to demonstrate why the ductility demands exceed those anticipated by the recommended provisions.The BRB qualification testing protocol contained in the BRBF recommended provisions is shown to be inadequate because it requires only a maximum ductility demand of at most 7.5. Modifications to the testing protocol are recommended.
Debe, D.A.; Carlson, M.J.; Chan, S.I; Goddard, W.A. III [California Inst. of Tech., Pasadena, CA (United States); Sadanobu, Jiro [Teijin Limited, Iwakuni, Yamaguchi (Japan). Polymer and Materials Research Labs.
1999-04-15
The authors present the generate-and-select hierarchy for tertiary protein structure prediction. The foundation of this hierarchy is the Restrained Generic Protein (RGP) Direct Monte Carlo method. The RGP method is a highly efficient off-lattice residue buildup procedure that can quickly generate the complete set of topologies that satisfy a very small number of interresidue distance restraints. For three restraints uniformly distributed in a 72-residue protein, the authors demonstrate that the size of this set is {approximately}10{sup 4}. The RGP method can generate this set of structures in less than 1 h using a Silicon Graphics R10000 single processor workstation. Following structure generation, a simple criterion that measures the burial of hydrophobic and hydrophilic residues can reliably select a reduced set of {approximately}10{sup 2} structures that contains the native topology. A minimization of the structures in the reduced set typically ranks the native topology in the five lowest energy folds. Thus, using this hierarchical approach, the authors suggest that de novo prediction of moderate resolution globular protein structure can be achieved in just a few hours on a single processor workstation.
YY1 restrained cell senescence through repressing the transcription of p16.
Wang, Xiuli; Feng, Yunpeng; Xu, Liang; Chen, Yuli; Zhang, Yu; Su, Dongmei; Ren, Guoling; Lu, Jun; Huang, Baiqu
2008-10-01
The transcription factor YY1 has been implicated to play a role in cell growth control. In this report, we demonstrate that YY1 was able to suppress NCI-H460 cell senescence through regulating the expression of p16(INK4a), a cyclin-dependent kinase inhibitor. We also show that YY1 participated in the repression of p16(INK4a) expression in 293T cells through an epigenetic mechanism involving histone acetylation modification. Specifically, HDAC3 and HDAC4 inhibited the p16(INK4a) promoter activity. The chromatin immunoprecipitation (ChIP) assays verified that HDAC3 and HDAC4 were recruited to p16(INK4a) promoter by YY1. Moreover, co-immunoprecipitation assays revealed that these three protein factors formed a complex. Furthermore, knockdown of these factors induced cell enlargement and flattened morphology and significantly increased the SA-beta-gal activity, a biochemical marker of cell senescence. Overall, data from this study suggest that YY1, HDAC3 and HDAC4 restrained cell senescence by repressing p16(INK4a) expression through an epigenetic modification of histones.
A Long Noncoding RNA lincRNA-EPS Acts as a Transcriptional Brake to Restrain Inflammation.
Atianand, Maninjay K; Hu, Wenqian; Satpathy, Ansuman T; Shen, Ying; Ricci, Emiliano P; Alvarez-Dominguez, Juan R; Bhatta, Ankit; Schattgen, Stefan A; McGowan, Jason D; Blin, Juliana; Braun, Joerg E; Gandhi, Pallavi; Moore, Melissa J; Chang, Howard Y; Lodish, Harvey F; Caffrey, Daniel R; Fitzgerald, Katherine A
2016-06-16
Long intergenic noncoding RNAs (lincRNAs) are important regulators of gene expression. Although lincRNAs are expressed in immune cells, their functions in immunity are largely unexplored. Here, we identify an immunoregulatory lincRNA, lincRNA-EPS, that is precisely regulated in macrophages to control the expression of immune response genes (IRGs). Transcriptome analysis of macrophages from lincRNA-EPS-deficient mice, combined with gain-of-function and rescue experiments, revealed a specific role for this lincRNA in restraining IRG expression. Consistently, lincRNA-EPS-deficient mice manifest enhanced inflammation and lethality following endotoxin challenge in vivo. lincRNA-EPS localizes at regulatory regions of IRGs to control nucleosome positioning and repress transcription. Further, lincRNA-EPS mediates these effects by interacting with heterogeneous nuclear ribonucleoprotein L via a CANACA motif located in its 3' end. Together, these findings identify lincRNA-EPS as a repressor of inflammatory responses, highlighting the importance of lincRNAs in the immune system.
Messner, Simon; Schuermann, David; Altmeyer, Matthias; Kassner, Ingrid; Schmidt, Darja; Schär, Primo; Müller, Stefan; Hottiger, Michael O
2009-11-01
Poly(ADP-ribose) polymerase 1 (PARP1) is a chromatin-associated nuclear protein and functions as a molecular stress sensor. At the cellular level, PARP1 has been implicated in a wide range of processes, such as maintenance of genome stability, cell death, and transcription. PARP1 functions as a transcriptional coactivator of nuclear factor kappaB (NF-kappaB) and hypoxia inducible factor 1 (HIF1). In proteomic studies, PARP1 was found to be modified by small ubiquitin-like modifiers (SUMOs). Here, we characterize PARP1 as a substrate for modification by SUMO1 and SUMO3, both in vitro and in vivo. PARP1 is sumoylated at the single lysine residue K486 within its automodification domain. Interestingly, modification of PARP1 with SUMO does not affect its ADP-ribosylation activity but completely abrogates p300-mediated acetylation of PARP1, revealing an intriguing crosstalk of sumoylation and acetylation on PARP1. Genetic complementation of PARP1-depleted cells with wild-type and sumoylation-deficient PARP1 revealed that SUMO modification of PARP1 restrains its transcriptional coactivator function and subsequently reduces gene expression of distinct PARP1-regulated target genes.
Cerebral regulatory T cells restrain microglia/macrophage-mediated inflammatory responses via IL-10
Xie, Luokun; Choudhury, Gourav Roy; Winters, Ali; Yang, Shao-Hua; Jin, Kunlin
2014-01-01
Forkhead box P3 (Foxp3)+ regulatory T (Treg) cells maintain the immune tolerance and prevent inflammatory responses in the periphery. However, the presence of Treg cells in the central nervous system under steady state has not been studied. Here, for the first time, we show a substantial TCRαβ+CD4+Foxp3+ T-cell population (cerebral Treg cells) in the normal rat cerebrum, constituting more than 15% of the cerebral CD4+ T-cell compartment. Cerebral Treg cells showed an activated/memory phenotype and expressed many Treg-cell signature genes at higher levels than peripheral Treg cells. Consistent with their activated/memory phenotype, cerebral Treg cells robustly restrained the LPS-induced inflammatory responses of brain microglia/macrophages, suggesting a role in maintaining the cerebral homeostasis by inhibiting the neuroinflammation. In addition, brain astrocytes were the helper cells that sustained Foxp3 expression in Treg cells through IL-2/STAT5 signaling, showing that the interaction between astrocytes and Treg cells contributes to the maintenance of Treg-cell identity in the brain. Taken together, our work represents the first study to characterize the phenotypic and functional features of Treg cells in the normal rat cerebrum. Our data have provided a novel insight for the contribution of Treg cells to the immunosurveillance and immunomodulation in the cerebrum under steady state. PMID:25329858
Frattaroli, Shannon; McGinty, Emma E; Barnhorst, Amy; Greenberg, Sheldon
2015-06-01
The gun violence restraining order (GVRO) is a new tool for preventing gun violence. Unlike traditional approaches to prohibiting gun purchase and possession, which rely on a high threshold (adjudication by criminal justice or mental health systems) before intervening, the GVRO allows family members and intimate partners who observe a relative's dangerous behavior and believe it may be a precursor to violence to request a GVRO through the civil justice system. Once issued by the court, a GVRO authorizes law enforcement to remove any guns in the respondent's possession and prohibits the respondent from purchasing new guns. In September 2014, California's governor signed AB1014 into law, making California the first U.S. state to enact a GVRO law. This article describes the GVRO and the rationale behind the concept, considers case examples to assess the potential impact of the GVRO as a strategy for preventing gun violence, and reviews the content of the California law. Copyright © 2015 John Wiley & Sons, Ltd.
Charoenpanich, Pornsri; Soto, Maria J; Becker, Anke; McIntosh, Matthew
2015-04-01
Microbial cooperative behaviours, such as quorum sensing (QS), improve survival and this explains their prevalence throughout the microbial world. However, relatively little is known about the mechanisms by which cooperation promotes survival. Furthermore, cooperation typically requires costly contributions, e.g. exopolysaccharides, which are produced from limited resources. Inevitably, cooperation is vulnerable to damaging mutations which results in mutants that are relieved of the burden of contributing but nonetheless benefit from the contributions of their parent. Unless somehow prevented, such mutants may outcompete and replace the parent. The bacterium Sinorhizobium meliloti uses QS to activate the production of copious levels of exopolysaccharide (EPS). Domestication of this bacterium is typified by the appearance of spontaneous mutants incapable of EPS production, which take advantage of EPS production by the parent and outcompete the parent. We found that all of the mutants were defect in QS, implying that loss of QS is a typical consequence of the domestication of this bacterium. This instability was traced to several QS-regulated processes, including a QS-dependent restraint of growth, providing the mutant with a significant growth advantage. A model is proposed whereby QS restrains population growth to prevent overcrowding and prepares the population for the survival of severe conditions.
NEMO inhibits programmed necrosis in an NFκB-independent manner by restraining RIP1.
Marie Anne O'Donnell
Full Text Available TNF can trigger two opposing responses: cell survival and cell death. TNFR1 activates caspases that orchestrate apoptosis but some cell types switch to a necrotic death when treated with caspase inhibitors. Several genes that are required to orchestrate cell death by programmed necrosis have been identified, such as the kinase RIP1, but very little is known about the inhibitory signals that keep this necrotic cell death pathway in check. We demonstrate that T cells lacking the regulatory subunit of IKK, NFκB essential modifier (NEMO, are hypersensitive to programmed necrosis when stimulated with TNF in the presence of caspase inhibitors. Surprisingly, this pro-survival activity of NEMO is independent of NFκB-mediated gene transcription. Instead, NEMO inhibits necrosis by binding to ubiquitinated RIP1 to restrain RIP1 from engaging the necrotic death pathway. In the absence of NEMO, or if ubiquitination of RIP1 is blocked, necrosis ensues when caspases are blocked. These results indicate that recruitment of NEMO to ubiquitinated RIP1 is a key step in the TNFR1 signaling pathway that determines whether RIP1 triggers a necrotic death response.
A Novel Restraining Device for Small Animal Imaging Exams: Validation in Rabbits
Carlos Henrique Barbosa
2015-01-01
Full Text Available Objective. To develop, validate, and patent a Restraining Device for Small Animal Imaging Exams (RDSAIE that allows exams to be comfortably conducted without risks to animals and professionals. Methods. A RDSAIE with a mobile cover and shelf was built with transparent acrylic material. A total of six anesthetized rabbits were used to perform the following imaging exams of the skull: Cone Beam Computed Tomography, Magnetic Resonance Imaging, and Scintigraphy. Results. The device showed great functionality and full visibility of the animal behavior, which remained fully stabilized and immobilized in either the horizontal or vertical position without the need for a person to remain in the test room to assist them. The procedures were performed without difficulty, and images of good resolution and without artifacts were obtained. Conclusion. The RDSAIE is comfortable, safe, efficient, and ergonomic. It allows the easy placement of animals in different body positions, including the vertical, the maintenance of postural stability, and full visibility. It may be constructed for animals heavier than 4 kg and it is adaptable for translational studies in anima nobile.
Hall, Peter A; Lowe, Cassandra; Vincent, Corita
2014-08-01
Prior studies have documented a negative relationship between strength of executive control resources (ECRs) and frequency of snack food consumption. However, little is known about what effect environmental cues (restraining versus facilitating) have on the engagement of such control resources. We presented 88 healthy adults with standardized tests of ECRs followed by a bogus taste test for three appetitive snack foods. Participants were randomly assigned to receive instructions to eat the bare minimum to make their ratings ("restraint condition"), eat as much as they like ("facilitation condition") or no special instructions. We surreptitiously measured the weight of food consumed during the taste test. Findings revealed a main effect of treatment condition, such that those in the restraint condition ate significantly less than those in either of the other conditions; however, this main effect was qualified by an ECR by treatment condition interaction. Specifically, those in the facilitation condition showed a strong negative association between ECR strength and amount of food consumed, whereas those in the restraint and control conditions did not. Findings suggest that the effect of ECR strength on consumption of snack food varies substantially by the characteristics of contextual cues.
Ischemia Reperfusion Unveils Impaired Capacity of Older Adults to Restrain Oxidative Insult
Davies, Sean S.; Traustadóttir, Tinna; Stock, Anthoney A.; Ye, Fei; Shyr, Yu; Harman, S. Mitchell; Roberts, L. Jackson
2009-01-01
Age independently predicts poor outcome in a variety of medical settings including sepsis, trauma, severe burns, and surgery. Since these conditions are associated with oxidative stress, we hypothesized that the capacity to constrain oxidative insult diminishes with age, leading to more extensive oxidative damage during trauma. To test this hypothesis, we used supra-systolic inflation of an arm blood pressure cuff to safely induce localized forearm ischemia/reperfusion (I/R) and quantified plasma F2-isoprostane (IsoP) levels in serial blood samples. Prior to I/R, IsoP levels were similar in young (20-33 yrs) and older adults (62-81 yrs). After I/R challenge, the magnitude and duration of increased IsoP levels was significantly greater in older adults. Because aging is associated with declining levels of sex hormones that contribute to regulation of antioxidant enzyme expression, we then examined the response to I/R in older women receiving hormone replacement therapy, and found these women did not manifest the amplified IsoP response found in untreated older women. These finding demonstrate that aging impairs the ability to restrain oxidative damage after an acute insult, which may contribute to the increased vulnerability of older adults to traumatic conditions, and establishes a useful method to identify effective interventions to ameliorate this deficiency. PMID:19596063
Id1 restrains p21 expression to control endothelial progenitor cell formation.
Alessia Ciarrocchi
Full Text Available Loss of Id1 in the bone marrow (BM severely impairs tumor angiogenesis resulting in significant inhibition of tumor growth. This phenotype has been associated with the absence of circulating endothelial progenitor cells (EPCs in the peripheral blood of Id1 mutant mice. However, the manner in which Id1 loss in the BM controls EPC generation or mobilization is largely unknown. Using genetically modified mouse models we demonstrate here that the generation of EPCs in the BM depends on the ability of Id1 to restrain the expression of its target gene p21. Through a series of cellular and functional studies we show that the increased myeloid commitment of BM stem cells and the absence of EPCs in Id1 knockout mice are associated with elevated p21 expression. Genetic ablation of p21 rescues the EPC population in the Id1 null animals, re-establishing functional BM-derived angiogenesis and restoring normal tumor growth. These results demonstrate that the restraint of p21 expression by Id1 is one key element of its activity in facilitating the generation of EPCs in the BM and highlight the critical role these cells play in tumor angiogenesis.
Hydration Process and Crack Tendency of Concrete Based on Resistivity and Restrained Shrinkage Crack
MUAZU Bawa Samaila; WEI Xiaosheng; WANG Lei
2016-01-01
Hydration process, crack potential and setting time of concrete grade C30, C40 and C50 were monitored by using a non-contact electrical resistivity apparatus, a novel plastic ring mould and penetration resistance methods, respectively. The results show the highest resistivity of C30 at the early stage until a point when C50 accelerated and overtook the others. It has been experimentally conifrmed that the crossing point of C30 and C50 corresponds to the ifnal setting time of C50. From resistivity derivative curve, four different stages were observed upon which the hydration process is classiifed; these are dissolution, induction, acceleration and deceleration periods. Consequently, restrained shrinkage crack and setting time results demonstrated that C50 set and cracked the earliest. The cracking time of all the samples occurred within a reasonable experimental period thus the novel plastic ring is a convenient method for predicting concrete’s crack potential. The highest inlfection time (ti) obtained from resistivity curve and the ifnal setting time (tf) were used with crack time (tc) in coming up with mathematical models for the prediction of concrete’s cracking age for the range of concrete grade considered. Finally, an ANSYS numerical simulation supports the experimental ifndings in terms of the earliest crack age of C50 and the crack location.
Early age damage quantification of actively restrained concrete using inverse analysis
Albanna, Ali
Early-age cracking can be a significant problem in concrete pavements, floors, and bridge decks. Cracking occurs when the volumetric changes associated with drying, hydration, and temperature reduction are prevented. Good knowledge about the characteristics of early age concrete is necessary to achieve reliable crack control. Volumetric changes due to shrinkage depend on the type of concrete and its components. It has been found that light weight aggregates can work as internal reservoir to supply the concrete matrix with water that is needed during the early age; this process is called internal curing. Also fibers can give more ductility to the concrete and produce less shrinkage. There is a need to better understand the effects of early age uniaxial restraint on long term concrete mechanical performance. In this study, two types of concrete were studied (high performance fiber reinforced concrete and ordinary concrete) under actively restrained loading conditions to assess the effect on the long term fracture toughness and energy. Single edge notched specimens having dimensions of 250 mm x 150 mm x 75 mm and a notch to depth ratio of 0.33 were caste and used in both direct tension and three point bending. The direct tension tests were carried out on a direct tension loading frame constructed in house that was supplied with two mechanical jacks and load cell.
Quantum molecular master equations
Brechet, Sylvain D.; Reuse, Francois A.; Maschke, Klaus; Ansermet, Jean-Philippe
2016-10-01
We present the quantum master equations for midsize molecules in the presence of an external magnetic field. The Hamiltonian describing the dynamics of a molecule accounts for the molecular deformation and orientation properties, as well as for the electronic properties. In order to establish the master equations governing the relaxation of free-standing molecules, we have to split the molecule into two weakly interacting parts, a bath and a bathed system. The adequate choice of these systems depends on the specific physical system under consideration. Here we consider a first system consisting of the molecular deformation and orientation properties and the electronic spin properties and a second system composed of the remaining electronic spatial properties. If the characteristic time scale associated with the second system is small with respect to that of the first, the second may be considered as a bath for the first. Assuming that both systems are weakly coupled and initially weakly correlated, we obtain the corresponding master equations. They describe notably the relaxation of magnetic properties of midsize molecules, where the change of the statistical properties of the electronic orbitals is expected to be slow with respect to the evolution time scale of the bathed system.
Solitons and cnoidal waves of the Klein–Gordon–Zakharov equation in plasmas
Ghodrat Ebadi; E V Krishnan; Anjan Biswas
2012-08-01
This paper studies the Klein–Gordon–Zakharov equation with power-law nonlinearity. This is a coupled nonlinear evolution equation. The solutions for this equation are obtained by the travelling wave hypothesis method, (′/) method and the mapping method.
2-dimensional Radical Symmetric Solutions for Modified Landau-Lifshitz Equation
曾明
2006-01-01
@@ Landau-Lifshitz equation is a nonlinear parabolic equation describing micromagnetic evolution[1]. In [2] A. Visintin proposed a modified Landau-Lifshitz equation to account for dry friction in domain-wall displacement due to magnetic inclusion, which reads
Schrodinger Equation for an Open System
毕桥; H.E.Ruda
2002-01-01
We present a Schrodinger (Liouville) type of equation for a quantum open system. It has a correlated part, and various master equations may be its special cases. It also has significant applications for constructing decoherencefree subspace for quantum computation. It is related to the original Schrodinger (Liouville) equation for the total system through a non-unitary similarity transformation. It is unnecessary for its correlated part to be self-adjoint,so there is a complex spectrum for the corresponding Hamiltonian (Liouvillian), which enables the time evolution of states to be asymmetric. This shows just the correlation to produce evolution of world.
Extension of the Schrodinger equation
Somsikov, Vyacheslav
2017-03-01
Extension of the Schrodinger equation is submitted by removing its limitations appearing due to the limitations of the formalism of Hamilton, based on which this equation was obtained. For this purpose the problems of quantum mechanics arising from the limitations of classical mechanics are discussed. These limitations, in particular, preclude the use of the Schrodinger equation to describe the time symmetry violation. The extension of the Schrodinger equation is realized based on the principle of duality symmetry. According to this principle the dynamics of the systems is determined by the symmetry of the system and by the symmetry of the space. The extension of the Schrodinger equation was obtained from the dual expression of energy, represented in operator form. For this purpose the independent micro - and macro-variables that determine respectively the dynamics of quantum particle system relative to its center of mass and the movement of the center of mass in space are used. The solution of the extended Schrodinger equation for the system near equilibrium is submitted. The main advantage of the extended Schrodinger equation is that it is applicable to describe the interaction and evolution of quantum systems in inhomogeneous field of external forces.
Wallis, D J; Hetherington, M M
2004-08-01
Restrained and emotional eaters overeat in response to stress. To compare differential effects of cognitive demand and ego-threatening stressors on subsequent chocolate intake, 38 females completed a neutral (control), an ego threatening and an incongruent Stroop colour-naming task on three separate occasions. Participants were assigned to four groups based on median-split scores on the restrained and emotional eating scales of the Dutch Eating Behaviour Questionnaire-high restraint/high emotional, high restraint/low emotional, low restraint/high emotional and low restraint/low emotional. Higher response latencies were observed in the incongruent task, confirming its greater cognitive (attentional) demand. Overall intake was enhanced by 23% after ego-threat and 15% after the incongruent Stroop task relative to control. Restraint was associated with greater intake after both ego-threat and the incongruent task than in the control condition. In contrast, emotional eating was associated with greater intake after only the ego-threat, relative to control. A positive association between reaction time and subsequent intake in all conditions for high restraint/low emotional eaters provided support for the limited capacity hypothesis. Enhanced intake in emotional eaters is proposed to relate to escape from self-awareness. These findings demonstrate differential effects of threat and demand on stress-related eating in restrained and emotional eaters.
Are "uncharacteristic" earthquakes spatially linked to strike-slip restraining bends?
Mann, P.
2011-12-01
, the Haiti earthquake of 2010 showed similar "uncharacteristic" elements: the large M 7.2 shock generated high intensity ground shaking on a previously unknown subsurface thrust fault, produced extensive slope failures, produced a broad pattern of vertical uplift extending several kilometers north of the main EPGF trace - but did not produce clear surface rupture on land or along the seafloor. This talk links the elements of "uncharacteristic" ruptures to their generation at strike-slip restraining bends. Key restraining bend elements for the nucleation of "uncharacteristic" ruptures include a broader and more diffuse area of strain accumulation, the presence of propagating, blind thrust faults commonly parallel with but off axis of the main topographic bend, and broad areas of tectonic uplift above the blind thrust faults. Bend faults tend to remain unrecognized because their recurrence intervals are much longer than the adjacent straight segments of the strike-slip fault.
Harrell, John W; Schrage, William G
2014-01-15
Poor cerebrovascular function in metabolic syndrome (MetSyn) likely contributes to elevated risk of cerebrovascular disease in this growing clinical population. Younger MetSyn adults without clinical evidence of cerebrovascular disease exhibit preserved hypercapnic vasodilation yet markedly impaired hypoxic vasodilation, but the mechanisms behind reduced hypoxic vasodilation are unknown. Based on data from rats, we tested the hypothesis that younger adults with MetSyn exhibit reduced cerebral hypoxic vasodilation due to loss of vasodilating prostaglandins. Middle cerebral artery velocity (MCAv) was measured with transcranial Doppler ultrasound in adults with MetSyn (n = 13, 33 ± 3 yr) and healthy controls (n = 15, 31 ± 2 yr). Isocapnic hypoxia was induced by titrating inspired oxygen to lower arterial saturation to 90% and 80% for 5 min each. Separately, hypercapnia was induced by increasing end-tidal CO2 10 mmHg above baseline levels. Cyclooxygenase inhibition (100 mg indomethacin) was conducted in a randomized double-blind, placebo controlled design. MCAv was normalized for group differences in blood pressure (healthy: 89 ± 2 mmHg vs. MetSyn: 102 ± 2 mmHg) as cerebrovascular conductance index (CVCi), and used to assess cerebral vasodilation. Hypoxia increased CVCi in both groups; however, vasodilation was ∼55% lower in MetSyn at SpO2 = 80% (P vasodilation in healthy controls, and unexpectedly increased dilation in MetSyn (P vasodilation was similar between groups, as was the decrease in vasodilation with indomethacin. These data indicate increased production of vasoconstrictor prostaglandins restrains hypoxic cerebral vasodilation in MetSyn, preventing them from responding appropriately to this important physiological stressor.
The role of tobacco promoting and restraining factors in smoking intentions among Ghanaian youth
Doku David
2012-08-01
Full Text Available Abstract Background In Western countries, the relationship between smoking intentions and smoking behaviour is well established. However, youth smoking intentions and associated factors in developing countries are largely unexplored and the former may occur for a variety of reasons. We investigated youth smoking intentions in Ghana with regard to several tobacco promoting and restraining factors, including environmental, familial, attitudinal and knowledge measures. Methods A school-based survey of a representative sample of 12-20-year-olds was conducted in 2008 in Ghana (N = 1338, response rate 89.7%. Results In a bivariate model, both among ever and never smokers, allowing smoking on school compound, exposure to tobacco advertisement and parental smoking were associated with future intention to smoke. Compared to those who agreed that smoking is harmful to health, smoking is difficult to quit and that tobacco should not be sold to minors, those who disagreed or were not sure were more likely to have an intention to smoke. In the multivariate analyses, these associations persisted, except that the attitude measures concerning the difficulty of quitting smoking once started and tobacco sales ban were no longer significantly associated with smoking intentions. Conclusions These findings underscore the importance of school smoking policy, parental smoking behaviour and knowledge of the harmful effects of tobacco use in determining Ghanaian youths’ future smoking intentions. Because current high percentages of smoking intentions may turn into high smoking rates in the future, the introduction of effective tobacco control measures at all levels of society to prevent youth smoking in Ghana may be essential.
Chuncheng Xie
Full Text Available In this study, we examined the effect of chronic administration of simvastatin immediately after status epilepticus (SE on rat brain with temporal lobe epilepsy (TLE. First, we evaluated cytokines expression at 3 days post KA-lesion in hippocampus and found that simvastatin-treatment suppressed lesion-induced expression of interleukin (IL-1β and tumor necrosis factor-α (TNF-α. Further, we quantified reactive astrocytosis using glial fibrillary acidic protein (GFAP staining and neuron loss using Nissl staining in hippocampus at 4-6 months after KA-lesion. We found that simvastatin suppressed reactive astrocytosis demonstrated by a significant decrease in GFAP-positive cells, and attenuated loss of pyramidal neurons in CA3 and interneurons in dentate hilar (DH. We next assessed aberrant mossy fiber sprouting (MFS that is known to contribute to recurrence of spontaneous seizure in epileptic brain. In contrast to the robust MFS observed in saline-treated animals, the extent of MFS was restrained by simvastatin in epileptic rats. Attenuated MFS was related to decreased neuronal loss in CA3 and DH, which is possibly a mechanism underlying decreased hippocampal susceptibility in animal treated with simvastatin. Electronic encephalography (EEG was recorded during 4 to 6 months after KA-lesion. The frequency of abnormal spikes in rats with simvastatin-treatment decreased significantly compared to the saline group. In summary, simvastatin treatment suppressed cytokines expression and reactive astrocytosis and decreased the frequency of discharges of epileptic brain, which might be due to the inhibition of MFS in DH. Our study suggests that simvastatin administration might be a possible intervention and promising strategy for preventing SE exacerbating to chronic epilepsy.