Asymptotically periodic solutions of Volterra integral equations
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Muhammad N. Islam
2016-03-01
Full Text Available We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.
Asymptotic Methods for Solitary Solutions and Compactons
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Ji-Huan He
2012-01-01
Full Text Available This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.
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G. M. N’Guérékata
2018-01-01
Full Text Available The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.
Asymptotic Solutions of Serial Radial Fuel Shuffling
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Xue-Nong Chen
2015-12-01
Full Text Available In this paper, the mechanism of traveling wave reactors (TWRs is investigated from the mathematical physics point of view, in which a stationary fission wave is formed by radial fuel drifting. A two dimensional cylindrically symmetric core is considered and the fuel is assumed to drift radially according to a continuous fuel shuffling scheme. A one-group diffusion equation with burn-up dependent macroscopic coefficients is set up. The burn-up dependent macroscopic coefficients were assumed to be known as functions of neutron fluence. By introducing the effective multiplication factor keff, a nonlinear eigenvalue problem is formulated. The 1-D stationary cylindrical coordinate problem can be solved successively by analytical and numerical integrations for associated eigenvalues keff. Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher keff than the outward one. The 2-D eigenvalue problem has to be solved by a more complicated method, namely a pseudo time stepping iteration scheme. Its 2-D asymptotic solutions are obtained together with certain eigenvalues keff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor kinf and the normalized power are presented for two different drifting speeds.
An asymptotic solution of large-$N$ $QCD$
Bochicchio, Marco
2014-01-01
We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-poin...
An asymptotic solution of large-N QCD
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Bochicchio Marco
2014-01-01
Full Text Available We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-N QCD, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic S-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic S-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the LS Z reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-N QCD, and in particular on any string solution.
An asymptotic solution of large-N QCD
Bochicchio, Marco
2014-11-01
We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-N QCD, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic S-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic S-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the LS Z reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-N QCD, and in particular on any string solution.
Asymptotic behaviour of solutions of a nonlinear transport equation
C.J. van Duijn (Hans); M.A. Peletier (Mark)
1996-01-01
textabstractWe investigate the asymptotic behaviour of solutions of the convection- diffusion equation $$ b(u)_t + divleft( u q - n u right) = 0 qquad hbox{for r = |x| > e quadhbox{andquad t>0, $$ where $q=l/r, er $, $l>0$. The asymptotic limits that we consider are $ttoinfty$ and $e downto0$. We
On oscillation and asymptotic behaviour of solutions of forced first ...
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 111; Issue 3. On Oscillation and Asymptotic Behaviour of Solutions of Forced First Order Neutral Differential Equations. N Parhi R N Rath. Volume 111 Issue 3 August 2001 pp ... Keywords. Oscillation; nonoscillation; neutral equations; asymptotic behaviour.
Asymptotic shape of solutions to nonlinear eigenvalue problems
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Tetsutaro Shibata
2005-03-01
Full Text Available We consider the nonlinear eigenvalue problem $$ -u''(t = f(lambda, u(t, quad u mbox{greater than} 0, quad u(0 = u(1 = 0, $$ where $lambda > 0$ is a parameter. It is known that under some conditions on $f(lambda, u$, the shape of the solutions associated with $lambda$ is almost `box' when $lambda gg 1$. The purpose of this paper is to study precisely the asymptotic shape of the solutions as $lambda o infty$ from a standpoint of $L^1$-framework. To do this, we establish the asymptotic formulas for $L^1$-norm of the solutions as $lambda o infty$.
Asymptotics of solutions to semilinear stochastic wave equations
Chow, Pao-Liu
2006-01-01
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions, the existence theorem for a unique global solution is given. Next the questions of bounded solutions and the exponential stability of an equilibrium solution, in mean-square and the almost sure sense, are studied. Then...
Solute transport through porous media using asymptotic dispersivity
Indian Academy of Sciences (India)
Abstract. In this paper, multiprocess non-equilibrium transport equation has been used, which accounts for both physical and chemical non-equilibrium for reactive transport through porous media. An asymptotic distance dependent dispersivity is used to embrace the concept of scale-dependent dispersion for solute ...
The Asymptotic Solution for the Steady Variable-Viscosity Free ...
African Journals Online (AJOL)
Under an arbitrary time-dependent heating of an infinite vertical plate (or wall), the steady viscosity-dependent free convection flow of a viscous incompressible fluid is investigated. Using the asymptotic method of solution on the governing equations of motion and energy, the resulting Ordinary differential equations were ...
Solute transport through porous media using asymptotic dispersivity
Indian Academy of Sciences (India)
In this paper, multiprocess non-equilibrium transport equation has been used, which accounts for both physical and chemical non-equilibrium for reactive transport through porous media. An asymptotic distance dependent dispersivity is used to embrace the concept of scale-dependent dispersion for solute transport in ...
Uniqueness and asymptotic stability properties of the critical solution ...
African Journals Online (AJOL)
In this research, the Volterra prey/predator model system is modified by introducing time-lag functions f (t - h) into the state parameters to account for the ... The asymptotic stability properties of the critical solution are investigated using the quadratic matrix equation and symmetric linear matrix inequality test. Results obtained ...
Asymptotic solutions of diffusion models for risk reserves
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S. Shao
2003-01-01
Full Text Available We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armed with asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate governing the conditional probability of ruin over a finite time in terms of interest rate.
Solution branches for nonlinear problems with an asymptotic oscillation property
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Lin Gong
2015-10-01
Full Text Available In this article we employ an oscillatory condition on the nonlinear term, to prove the existence of a connected component of solutions of a nonlinear problem, which bifurcates from infinity and asymptotically oscillates over an interval of parameter values. An interesting and immediate consequence of such oscillation property of the connected component is the existence of infinitely many solutions to the nonlinear problem for all parameter values in that interval.
Precise asymptotic behavior of solutions to damped simple pendulum equations
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Tetsutaro Shibata
2009-11-01
Full Text Available We consider the simple pendulum equation $$displaylines{ -u''(t + epsilon f(u'(t = lambdasin u(t, quad t in I:=(-1, 1,cr u(t > 0, quad t in I, quad u(pm 1 = 0, }$$ where $0 < epsilon le 1$, $lambda > 0$, and the friction term is either $f(y = pm|y|$ or $f(y = -y$. Note that when $f(y = -y$ and $epsilon = 1$, we have well known original damped simple pendulum equation. To understand the dependance of solutions, to the damped simple pendulum equation with $lambda gg 1$, upon the term $f(u'(t$, we present asymptotic formulas for the maximum norm of the solutions. Also we present an asymptotic formula for the time at which maximum occurs, for the case $f(u = -u$.
Asymptotic shape of solutions to the perturbed simple pendulum problems
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Tetsutaro Shibata
2007-05-01
Full Text Available We consider the positive solution of the perturbed simple pendulum problem $$ u''(r + frac{N-1}{r}u'(r - g(u(t + lambda sin u(r = 0, $$ with $0 < r < R$, $ u'(0 = u(R = 0$. To understand well the shape of the solution $u_lambda$ when $lambda gg 1$, we establish the leading and second terms of $Vert u_lambdaVert_q$ ($1 le q < infty$ with the estimate of third term as $lambda o infty$. We also obtain the asymptotic formula for $u_lambda'(R$ as $lambda o infty$.
On the asymptotic behaviour of solutions of an asymptotically Lotka-Volterra model
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Attila Dénes
2016-09-01
Full Text Available We make more realistic our model [Nonlinear Anal. 73(2010, 650-659] on the coexistence of fishes and plants in Lake Tanganyika. The new model is an asymptotically autonomous system whose limiting equation is a Lotka-Volterra system. We give conditions for the phenomenon that the trajectory of any solution of the original non-autonomous system "rolls up"' onto a cycle of the limiting Lotka-Volterra equation as $t\\to\\infty$, which means that the limit set of the solution of the non-autonomous system coincides with the cycle. A counterexample is constructed showing that the key integral condition on the coefficient function in the original non-autonomous model cannot be dropped. Computer simulations illustrate the results.
Thermodynamical description of stationary, asymptotically flat solutions with conical singularities
Herdeiro, Carlos; Rebelo, Carmen
2010-01-01
We examine the thermodynamical properties of a number of asymptotically flat, stationary (but not static) solutions having conical singularities, with both connected and non-connected event horizons, using the thermodynamical description recently proposed in arXiv:0912.3386 [gr-qc]. The examples considered are the double-Kerr solution, the black ring rotating in either S^2 or S^1 and the black Saturn, where the balance condition is not imposed for the latter two solutions. We show that not only the Bekenstein-Hawking area law is recovered from the thermodynamical description but also the thermodynamical angular momentum is the ADM angular momentum. We also analyse the thermodynamical stability and show that, for all these solutions, either the isothermal moment of inertia or the specific heat at constant angular momentum is negative, at any point in parameter space. Therefore, all these solutions are thermodynamically unstable in the grand canonical ensemble.
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
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Golovaty Yuriy
2017-04-01
Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.
Weighted Asymptotically Periodic Solutions of Linear Volterra Difference Equations
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Josef Diblík
2011-01-01
Full Text Available A linear Volterra difference equation of the form x(n+1=a(n+b(nx(n+∑i=0nK(n,ix(i, where x:N0→R, a:N0→R, K:N0×N0→R and b:N0→R∖{0} is ω-periodic, is considered. Sufficient conditions for the existence of weighted asymptotically periodic solutions of this equation are obtained. Unlike previous investigations, no restriction on ∏j=0ω-1b(j is assumed. The results generalize some of the recent results.
Asymptotics of weakly collapsing solutions of nonlinear Schroedinger equation
Ovchinnikov, Yu N
2001-01-01
One studied possible types of asymptotic behavior of weakly collapsing solution of the 3-rd nonlinear Schroedinger equation. It is shown that within left brace A, C sub 1 right brace parameter space there are two neighboring lines along which the amplitude of oscillation terms is exponentially small as to C sub 1 parameter. The same lines locates values of left brace A, C sub 1 right brace parameters at which the energy is equal to zero. With increase of C sub 1 parameter the accuracy of numerical determination of points with zero energy drops abruptly
Periodic Solutions and S-Asymptotically Periodic Solutions to Fractional Evolution Equations
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Jia Mu
2017-01-01
Full Text Available This paper deals with the existence and uniqueness of periodic solutions, S-asymptotically periodic solutions, and other types of bounded solutions for some fractional evolution equations with the Weyl-Liouville fractional derivative defined for periodic functions. Applying Fourier transform we give reasonable definitions of mild solutions. Then we accurately estimate the spectral radius of resolvent operator and obtain some existence and uniqueness results.
Solution of internal erosion equations by asymptotic expansion
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Dubujet P.
2012-07-01
Full Text Available One dimensional coupled soil internal erosion and consolidation equations are considered in this work for the special case of well determined sand and clay mixtures with a small proportion of clay phase. An enhanced modelling of the effect of erosion on elastic soil behavior was introduced through damage mechanics concepts. A modified erosion law was proposed. The erosion phenomenon taking place inside the soil was shown to act like a perturbation affecting the classical soil consolidation equation. This interpretation has enabled considering an asymptotic expansion of the coupled erosion consolidation equations in terms of a perturbation parameter linked to the maximum expected internal erosion. A robust analytical solution was obtained via direct integration of equations at order zero and an adequate finite difference scheme that was applied at order one.
Ground state solutions for asymptotically periodic Schrodinger equations with critical growth
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Hui Zhang
2013-10-01
Full Text Available Using the Nehari manifold and the concentration compactness principle, we study the existence of ground state solutions for asymptotically periodic Schrodinger equations with critical growth.
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
Sachdev, PL
2010-01-01
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/boundary conditions. This title presents the constructive mathematical techniques. It deals with the asymptotic methods which include self-similarity, balancing argument, and matched asymptotic expansions
Asymptotic Solution of the Theory of Shells Boundary Value Problem
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I. V. Andrianov
2007-01-01
Full Text Available This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i it is devoted to the fundamental principles of asymptotic approaches, and (ii it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.
Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions
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Vladimir V. Varlamov
1999-01-01
classical solution is proved and the solution is constructed in the form of a series. The major term of its long-time asymptotics is calculated explicitly and a uniform in space estimate of the residual term is given.
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Zhanhua Yu
2011-01-01
Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.
Renormalized asymptotic solutions of the Burgers equation and the Korteweg-de Vries equation
Zakharov, Sergei V.
2015-01-01
The Cauchy problem for the Burgers equation and the Korteweg-de Vries equation is considered. Uniform renormalized asymptotic solutions are constructed in cases of a large initial gradient and a perturbed initial weak discontinuity.
Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation
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Yuncheng You
2008-12-01
Full Text Available The asymptotic dynamics of high-order temporal-spatial derivatives of the two-dimensional vorticity and velocity of an incompressible, viscous fluid flow in $mathbb{R}^2$ are studied, which is equivalent to the 2D Navier-Stokes equation. It is known that for any integrable initial vorticity, the 2D vorticity solution converges to the Oseen vortex. In this paper, sharp exterior decay estimates of the temporal-spatial derivatives of the vorticity solution are established. These estimates are then used and combined with similarity and $L^p$ compactness to show the asymptotical attraction rates of temporal-spatial derivatives of generic 2D vorticity and velocity solutions by the Oseen vortices and velocity solutions respectively. The asymptotic estimates and the asymptotic attraction rates of all the derivatives obtained in this paper are independent of low or high Reynolds numbers.
Asymptotic Solutions of Time-Space Fractional Coupled Systems by Residual Power Series Method
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Wenjin Li
2017-01-01
Full Text Available This paper focuses on the asymptotic solutions to time-space fractional coupled systems, where the fractional derivative and integral are described in the sense of Caputo derivative and Riemann-Liouville integral. We introduce the Residual Power Series (for short RPS method to construct the desired asymptotic solutions. Furthermore, we apply this method to some time-space fractional coupled systems. The simplicity and efficiency of RPS method are shown by the application.
Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis
Harada, Tomohiro; Maeda, Hideki; Carr, B. J.
2008-01-01
Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=(γ-1)μ with 0antigravity. This extends the previous analysis of spherically symmetric self-similar solutions for fluids with positive pressure (γ>1). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically “quasi-Friedmann,” in the sense that they exhibit an angle deficit at large distances. In the 0<γ<2/3 case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in an accompanying paper to obtain and physically interpret numerical solutions.
Asymptotic behavior of solutions to a system of Schrodinger equations
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Xavier Carvajal
2017-07-01
Full Text Available This article concerns the behaviour of solutions to a coupled system of Schrodinger equations that has applications in many physical problems, especially in nonlinear optics. In particular, when the solution exists globally, we obtain the growth of the solutions in the energy space. Finally, some conditions are also obtained for having blow-up in this space.
On oscillation and asymptotic behaviour of solutions of forced first ...
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
In most of our results, the assumptions are stronger than (1). It seems that it is possible to obtain an example of a neutral differential equation in the critical case such that (1) holds but the equation admits a nonoscillatory solution which does not tend to zero as t → ∞. A similar example is obtained in the discrete case by Yu ...
Asymptotic stability of multi-soliton solutions for nonlinear Schroedinger eqations
Perelman, G.
2003-01-01
We consider the Cauchy problem for the nonlinear Schroedinger eqiation with initial data close to a sum of N decoupled solitons. Under some suitable assumptions on the spectral structure of the one soliton linearizations we prove that for large time the asymptotics of the solution is given by a sum of solitons with slightly modified parameters and a small dispersive term.
Mikhailov, E. A.; Teplyakov, I. O.
2017-11-01
The flow generated in the conductive medium with the electromagnetic force appearing when non-uniform electric current interacts with the own magnetic field was considered. The problem was solved analytically using Stokes approximation in a hemispherical geometry. Also numerical solution was obtained and comparing with the oldest mode of analytical one was carried out. The numerical and asymptotic results are quite similar.
Directory of Open Access Journals (Sweden)
Yan-Tao Bian
2014-04-01
Full Text Available In this article, we study weighted asymptotic behavior of solutions to the semilinear integro-differential equation $$ u'(t=Au(t+\\alpha\\int_{-\\infty}^{t}e^{-\\beta(t-s}Au(sds+f(t,u(t, \\quad t\\in \\mathbb{R}, $$ where $\\alpha, \\beta \\in \\mathbb{R}$, with $\\beta > 0, \\alpha \
High-frequency asymptotics of solutions of ODE in a Banach space
Sazonov, L. I.
2017-12-01
We construct and justify high-frequency asymptotic expansions of solutions for some class of linear ODE in a Banach space. In particular, we obtain new results in the case when the averaged ODE are degenerate. The author is deceased. The editors are grateful to A. B. Morgulis, who finished the paper after the author’s death.
Asymptotic behavior of solutions to a degenerate quasilinear parabolic equation with a gradient term
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Huilai Li
2015-12-01
Full Text Available This article concerns the asymptotic behavior of solutions to the Cauchy problem of a degenerate quasilinear parabolic equations with a gradient term. A blow-up theorem of Fujita type is established and the critical Fujita exponent is formulated by the spacial dimension and the behavior of the coefficient of the gradient term at infinity.
ASYMPTOTICALLY OPTIMAL HIGH-ORDER ACCURATE ALGORITHMS FOR THE SOLUTION OF CERTAIN ELLIPTIC PDEs
Energy Technology Data Exchange (ETDEWEB)
Leonid Kunyansky, PhD
2008-11-26
The main goal of the project, "Asymptotically Optimal, High-Order Accurate Algorithms for the Solution of Certain Elliptic PDE's" (DE-FG02-03ER25577) was to develop fast, high-order algorithms for the solution of scattering problems and spectral problems of photonic crystals theory. The results we obtained lie in three areas: (1) asymptotically fast, high-order algorithms for the solution of eigenvalue problems of photonics, (2) fast, high-order algorithms for the solution of acoustic and electromagnetic scattering problems in the inhomogeneous media, and (3) inversion formulas and fast algorithms for the inverse source problem for the acoustic wave equation, with applications to thermo- and opto- acoustic tomography.
Directory of Open Access Journals (Sweden)
H. Ullah
2015-01-01
Full Text Available The two-dimensional nonlinear wave equations are considered. Solution to the problem is approximated by using optimal homotopy asymptotic method (OHAM. The residual and convergence of the proposed method to nonlinear wave equation are presented through graphs. The resultant analytic series solution of the two-dimensional nonlinear wave equation shows the effectiveness of the proposed method. The comparison of results has been made with the existing results available in the literature.
Tables of generalized Airy functions for the asymptotic solution of the differential equation
Nosova, L N
1965-01-01
Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations contains tables of the special functions, namely, the generalized Airy functions, and their first derivatives, for real and pure imaginary values. The tables are useful for calculations on toroidal shells, laminae, rode, and for the solution of certain other problems of mathematical physics. The values of the functions were computed on the ""Strela"" highspeed electronic computer.This book will be of great value to mathematicians, researchers, and students.
On the asymptotic behaviour of 2D stationary Navier-Stokes solutions with symmetry conditions
Decaster, Agathe; Iftimie, Dragoş
2017-10-01
We consider the 2D stationary incompressible Navier-Stokes equations in ℝ2. Under suitable symmetry, smallness and decay at infinity conditions on the forcing we determine the behaviour at infinity of the solutions. Moreover, when the forcing is small, satisfies suitable symmetry conditions and decays at infinity like a vector field homogeneous of degree -3, we show that there exists a unique small solution whose asymptotic behaviour at infinity is homogeneous of degree -1.
Existence and asymptotic behavior of solutions for Henon equations in hyperbolic spaces
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Haiyang He
2013-09-01
Full Text Available In this article, we consider the existence and asymptotic behavior of solutions for the Henon equation $$\\displaylines{ -\\Delta_{\\mathbb{B}^N}u=(d(x^{\\alpha}|u|^{p-2}u, \\quad x\\in \\Omega\\cr u=0 \\quad x\\in \\partial \\Omega, }$$ where $\\Delta_{\\mathbb{B}^N}$ denotes the Laplace Beltrami operator on the disc model of the Hyperbolic space $\\mathbb{B}^N$, $d(x=d_{\\mathbb{B}^N}(0,x$, $\\Omega \\subset \\mathbb{B}^N$ is geodesic ball with radius $1$, $\\alpha>0, N\\geq 3$. We study the existence of hyperbolic symmetric solutions when $2
asymptotic behavior of the ground state solution when p tends to the critical exponent $2^* =\\frac{2N}{N-2}$ with $N\\geq 3$.
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Jafar Biazar
2015-01-01
Full Text Available We combine the Adomian decomposition method (ADM and Adomian’s asymptotic decomposition method (AADM for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from Adomian’s asymptotic decomposition method for Riccati equations and in such cases when we do not find any region of overlap between the obtained approximate solutions by the two proposed methods, we connect the two approximations by the Padé approximant of the near-field approximation. We illustrate the efficiency of the technique for several specific examples of the Riccati equation for which the exact solution is known in advance.
Asymptotic behaviour of solutions for porous medium equation with periodic absorption
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Yin Jingxue
2001-01-01
Full Text Available This paper is concerned with porous medium equation with periodic absorption. We are interested in the discussion of asymptotic behaviour of solutions of the first boundary value problem for the equation. In contrast to the equation without sources, we show that the solutions may not decay but may be attracted into any small neighborhood of the set of all nontrivial periodic solutions, as time tends to infinity. As a direct consequence, the null periodic solution is unstable. We have presented an accurate condition on the sources for solutions to have such a property. Whereas in other cases of the sources, the solutions might decay with power speed, which implies that the null periodic solution is stable.
On the Asymptotic Behavior of Positive Solutions of Certain Fractional Differential Equations
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Said R. Grace
2015-01-01
Full Text Available This paper deals with the asymptotic behavior of positive solutions of certain forced fractional differential equations of the form DcαCyt=et+ft, xt, c>1, α∈0,1, where yt=atx′t′, c0=y(c/Γ(1 =yc, and c0 is a real constant. From the obtained results, we derive a technique which can be applied to some related fractional differential equations.
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Qiong Liu
2012-01-01
Full Text Available We study the following fourth-order elliptic equations: Δ2+Δ=(,,∈Ω,=Δ=0,∈Ω, where Ω⊂ℝ is a bounded domain with smooth boundary Ω and (, is asymptotically linear with respect to at infinity. Using an equivalent version of Cerami's condition and the symmetric mountain pass lemma, we obtain the existence of multiple solutions for the equations.
Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations
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Aimin Liu
2014-01-01
Full Text Available This work is concerned with the quadratic-mean asymptotically almost periodic mild solutions for a class of stochastic functional differential equations dxt=Atxt+Ft,xt,xtdt+H(t,xt,xt∘dW(t. A new criterion ensuring the existence and uniqueness of the quadratic-mean asymptotically almost periodic mild solutions for the system is presented. The condition of being uniformly exponentially stable of the strongly continuous semigroup {Tt}t≥0 is essentially removed, which is generated by the linear densely defined operator A∶D(A⊂L2(ℙ,ℍ→L2(ℙ,ℍ, only using the exponential trichotomy of the system, which reflects a deeper analysis of the behavior of solutions of the system. In this case the asymptotic behavior is described through the splitting of the main space into stable, unstable, and central subspaces at each point from the flow’s domain. An example is also given to illustrate our results.
Asymptotic behavior of solutions to nonlinear initial-value fractional differential problems
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Mohammed D. Kassim
2016-10-01
Full Text Available We study the boundedness and asymptotic behavior of solutions for a class of nonlinear fractional differential equations. These equations involve two Riemann-Liouville fractional derivatives of different orders. We determine fairly large classes of nonlinearities and appropriate underlying spaces where solutions are bounded, exist globally and decay to zero as a power type function. Our results are obtained by using generalized versions of Gronwall-Bellman inequality, appropriate regularization techniques and several properties of fractional derivatives. Three examples are given to illustrate our results.
Ritchie, R.H.; Sakakura, A.Y.
1956-01-01
The formal solutions of problems involving transient heat conduction in infinite internally bounded cylindrical solids may be obtained by the Laplace transform method. Asymptotic series representing the solutions for large values of time are given in terms of functions related to the derivatives of the reciprocal gamma function. The results are applied to the case of the internally bounded infinite cylindrical medium with, (a) the boundary held at constant temperature; (b) with constant heat flow over the boundary; and (c) with the "radiation" boundary condition. A problem in the flow of gas through a porous medium is considered in detail.
Asymptotics for the multiple pole solutions of the nonlinear Schrödinger equation
Schiebold, Cornelia
2017-07-01
Multiple pole solutions consist of groups of weakly bound solitons. For the (focusing) nonlinear Schrödinger equation the double pole solution was constructed by Zakharov and Shabat. In the sequel particular cases have been discussed in the literature, but it has remained an open problem to understand multiple pole solutions in their full complexity. In the present work this problem is solved, in the sense that a rigorous and complete asymptotic description of the multiple pole solutions is given. More precisely, the asymptotic paths of the solitons are determined and their position- and phase-shifts are computed explicitly. As a corollary we generalize the conservation law known for the N-solitons. In the special case of one wave packet, our result confirms a conjecture of Olmedilla. Our method stems from an operator theoretic approach to integrable systems. To facilitate comparison with the literature, we also establish the link to the construction of multiple pole solutions via the inverse scattering method. The work is rounded off by many examples and Mathematica plots and a detailed discussion of the transition to the next level of degeneracy.
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Mohamed Abdalla Darwish
2014-01-01
Full Text Available We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach space BC(ℝ+. We show that this equation has at least one asymptotically stable solution.
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Alok Dhaundiyal
2016-10-01
Full Text Available This article focuses on the influence of relevant parameters of biomass pyrolysis on the numerical solution of the isothermal nth-order distributed activation energy model (DAEM using the Rayleigh distribution as the initial distribution function F(E of the activation energies. In this study, the integral upper limit, the frequency factor, the reaction order and the scale parameters are investigated. This paper also derived the asymptotic approximation for the DAEM. The influence of these parameters is used to calculate the kinetic parameters of the isothermal nth-order DAEM with the help of thermo-analytical results of TGA/DTG analysis.
Asymptotic behavior of positive solutions of a semilinear Dirichlet problem outside the unit ball
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Habib Maagli
2013-04-01
Full Text Available In this article, we are concerned with the existence, uniqueness and asymptotic behavior of a positive classical solution to the semilinear boundary-value problem $$displaylines{ -Delta u=a(xu^{sigma }quadext{in }D, cr lim _{|x|o 1}u(x= lim_{|x|o infty}u(x =0. }$$ Here D is the complement of the closed unit ball of $mathbb{R} ^n$ ($ngeq 3$, $sigma<1$ and the function a is a nonnegative function in $C_{m loc}^{gamma}(D$, $0
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Fazle Mabood
2015-01-01
Full Text Available The heat flow patterns profiles are required for heat transfer simulation in each type of the thermal insulation. The exothermic reaction models in porous medium can prescribe the problems in the form of nonlinear ordinary differential equations. In this research, the driving force model due to the temperature gradients is considered. A governing equation of the model is restricted into an energy balance equation that provides the temperature profile in conduction state with constant heat source on the steady state. The proposed optimal homotopy asymptotic method (OHAM is used to compute the solutions of the exothermic reactions equation.
Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes
Chesler, Paul M.; Yaffe, Laurence G.
2014-07-01
A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics, convenient exploitation of the residual diffeomorphism freedom, and use of spectral methods for discretizing and solving the resulting differential equations. Relevant issues and choices leading to this approach are discussed in detail. Three examples, motivated by applications to non-equilibrium dynamics in strongly coupled gauge theories, are discussed as instructive test cases. These are gravitational descriptions of homogeneous isotropization, collisions of planar shocks, and turbulent fluid flows in two spatial dimensions.
Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus
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Safa Dridi
2015-01-01
Full Text Available In this paper, we establish existence and asymptotic behavior of a positive classical solution to the following semilinear boundary value problem: \\[-\\Delta u=q(xu^{\\sigma }\\;\\text{in}\\;\\Omega,\\quad u_{|\\partial\\Omega}=0.\\] Here \\(\\Omega\\ is an annulus in \\(\\mathbb{R}^{n}\\, \\(n\\geq 3\\, \\(\\sigma \\lt 1\\ and \\(q\\ is a positive function in \\(\\mathcal{C}_{loc}^{\\gamma }(\\Omega \\, \\(0\\lt\\gamma \\lt 1\\, satisfying some appropriate assumptions related to Karamata regular variation theory. Our arguments combine a method of sub- and supersolutions with Karamata regular variation theory.
Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces
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Anna Kisiolek
2005-01-01
Full Text Available We consider the second-order nonlinear difference equations of the form Δ(rn−1Δxn−1+pnf(xn−k=hn. We show that there exists a solution (xn, which possesses the asymptotic behaviour ‖xn−a∑j=0n−1(1/rj+b‖=o(1, a,b∈ℝ. In this paper, we extend the results of Agarwal (1992, Dawidowski et al. (2001, Drozdowicz and Popenda (1987, M. Migda (2001, and M. Migda and J. Migda (1988. We suppose that f has values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.
An Asymptotic Theory for the Re-Equilibration of a Micellar Surfactant Solution
Griffiths, I. M.
2012-01-01
Micellar surfactant solutions are characterized by a distribution of aggregates made up predominantly of premicellar aggregates (monomers, dimers, trimers, etc.) and a region of proper micelles close to the peak aggregation number, connected by an intermediate region containing a very low concentration of aggregates. Such a distribution gives rise to a distinct two-timescale reequilibration following a system dilution, known as the t1 and t2 processes, whose dynamics may be described by the Becker-Döring equations. We use a continuum version of these equations to develop a reduced asymptotic description that elucidates the behavior during each of these processes.© 2012 Society for Industrial and Applied Mathematics.
Hybrid resonance and long-time asymptotic of the solution to Maxwell's equations
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Després, Bruno, E-mail: despres@ann.jussieu.fr [Laboratory Jacques Louis Lions, University Pierre et Marie Curie, Paris VI, Boîte courrier 187, 75252 Paris Cedex 05 (France); Weder, Ricardo, E-mail: weder@unam.mx [Departamento de Física Matemática, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-126, DF 01000 (Mexico)
2016-03-22
We study the long-time asymptotic of the solutions to Maxwell's equation in the case of an upper-hybrid resonance in the cold plasma model. We base our analysis in the transfer to the time domain of the recent results of B. Després, L.M. Imbert-Gérard and R. Weder (2014) [15], where the singular solutions to Maxwell's equations in the frequency domain were constructed by means of a limiting absorption principle and a formula for the heating of the plasma in the limit of vanishing collision frequency was obtained. Currently there is considerable interest in these problems, in particular, because upper-hybrid resonances are a possible scenario for the heating of plasmas, and since they can be a model for the diagnostics involving wave scattering in plasmas. - Highlights: • The upper-hybrid resonance in the cold plasma model is considered. • The long-time asymptotic of the solutions to Maxwell's equations is studied. • A method based in a singular limiting absorption principle is proposed.
Asymptotic solutions of glass temperature profiles during steady optical fibre drawing
Taroni, M.
2013-03-12
In this paper we derive realistic simplified models for the high-speed drawing of glass optical fibres via the downdraw method that capture the fluid dynamics and heat transport in the fibre via conduction, convection and radiative heating. We exploit the small aspect ratio of the fibre and the relative orders of magnitude of the dimensionless parameters that characterize the heat transfer to reduce the problem to one- or two-dimensional systems via asymptotic analysis. The resulting equations may be readily solved numerically and in many cases admit exact analytic solutions. The systematic asymptotic breakdown presented is used to elucidate the relative importance of furnace temperature profile, convection, surface radiation and conduction in each portion of the furnace and the role of each in controlling the glass temperature. The models derived predict many of the qualitative features observed in real industrial processes, such as the glass temperature profile within the furnace and the sharp transition in fibre thickness. The models thus offer a desirable route to quick scenario testing, providing valuable practical information about the dependencies of the solution on the parameters and the dominant heat-transport mechanism. © 2013 Springer Science+Business Media Dordrecht.
Asymptotic solutions for flow in microchannels with ridged walls and arbitrary meniscus protrusion
Kirk, Toby
2017-11-01
Flow over structured surfaces exhibiting apparent slip, such as parallel ridges, have received much attention experimentally and numerically, but analytical and asymptotic solutions that account for the microstructure have so far been limited to unbounded geometries such as shear-driven flows. Analysis for channel flows has been limited to (close to) flat interfaces spanning the grooves between ridges, but in applications the interfaces (menisci) can highly protrude and have a significant impact on the apparent slip. In this presentation, we consider pressure-driven flow through a microchannel with longitudinal ridges patterning one or both walls. With no restriction on the meniscus protrusion, we develop explicit formulae for the slip length using a formal matched asymptotic expansion. Assuming the ratio of channel height to ridge period is large, the periodicity is confined to an inner layer close to the ridges, and the expansion is found to all algebraic orders. As a result, the error is exponentially small and, under a further ``diluteness'' assumption, the explicit formulae are compared to finite element solutions. They are found to have a very wide range of validity in channel height (even when the menisci can touch the opposing wall) and so are useful for practitioners.
Li, Can; Deng, Wei-Hua
2014-07-01
Following the fractional cable equation established in the letter [B.I. Henry, T.A.M. Langlands, and S.L. Wearne, Phys. Rev. Lett. 100 (2008) 128103], we present the time-space fractional cable equation which describes the anomalous transport of electrodiffusion in nerve cells. The derivation is based on the generalized fractional Ohm's law; and the temporal memory effects and spatial-nonlocality are involved in the time-space fractional model. With the help of integral transform method we derive the analytical solutions expressed by the Green's function; the corresponding fractional moments are calculated; and their asymptotic behaviors are discussed. In addition, the explicit solutions of the considered model with two different external current injections are also presented.
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J. Kalas
2012-01-01
Full Text Available The asymptotic behaviour for the solutions of a real two-dimensional system with a bounded nonconstant delay is studied under the assumption of instability. Our results improve and complement previous results by J. Kalas, where the sufficient conditions assuring the existence of bounded solutions or solutions tending to origin for $t$ approaching infinity are given. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle.
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Bologna, Mauro, E-mail: mauroh69@libero.i [Instituto de Alta Investigacion, Universidad de Tarapaca-Casilla 7-D Arica (Chile)
2010-09-17
This paper addresses the problem of finding an asymptotic solution for first- and second-order integro-differential equations containing an arbitrary kernel, by evaluating the corresponding inverse Laplace and Fourier transforms. The aim of the paper is to go beyond the Tauberian theorem in the case of integral-differential equations which are widely used by the scientific community. The results are applied to the convolute form of the Lindblad equation setting generic conditions on the kernel in such a way as to generate a positive definite density matrix, and show that the structure of the eigenvalues of the correspondent Liouvillian operator plays a crucial role in determining the positivity of the density matrix.
Bochicchio, Marco
2016-05-01
Employing a new class of string theories we construct a family of S -matrix amplitudes that factorize over linear Regge trajectories, and that are good candidates to be asymptotically free, i.e. to lead to asymptotically-free correlation functions working out the LS Z formulae the other way around. In particular, we propose a candidate for a string solution of QCD with NF massless quarks in the large-N 't Hooft limit, for the glueball and meson spectrum, and for certain S-matrix amplitudes in the collinear limit. The solution extends to massive quarks of equal mass.
Asymptotically flat scalar, Dirac and Proca stars: Discrete vs. continuous families of solutions
Herdeiro, Carlos A. R.; Pombo, Alexandre M.; Radu, Eugen
2017-10-01
The existence of localized, approximately stationary, lumps of the classical gravitational and electromagnetic field - geons - was conjectured more than half a century ago. If one insists on exact stationarity, topologically trivial configurations in electro-vacuum are ruled out by no-go theorems for solitons. But stationary, asymptotically flat geons found a realization in scalar-vacuum, where everywhere non-singular, localized field lumps exist, known as (scalar) boson stars. Similar geons have subsequently been found in Einstein-Dirac theory and, more recently, in Einstein-Proca theory. We identify the common conditions that allow these solutions, which may also exist for other spin fields. Moreover, we present a comparison of spherically symmetric geons for the spin 0 , 1 / 2 and 1, emphasizing the mathematical similarities and clarifying the physical differences, particularly between the bosonic and fermionic cases. We clarify that for the fermionic case, Pauli's exclusion principle prevents a continuous family of solutions for a fixed field mass; rather only a discrete set exists, in contrast with the bosonic case.
Asymptotically flat scalar, Dirac and Proca stars: Discrete vs. continuous families of solutions
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Carlos A.R. Herdeiro
2017-10-01
Full Text Available The existence of localized, approximately stationary, lumps of the classical gravitational and electromagnetic field – geons – was conjectured more than half a century ago. If one insists on exact stationarity, topologically trivial configurations in electro-vacuum are ruled out by no-go theorems for solitons. But stationary, asymptotically flat geons found a realization in scalar-vacuum, where everywhere non-singular, localized field lumps exist, known as (scalar boson stars. Similar geons have subsequently been found in Einstein–Dirac theory and, more recently, in Einstein–Proca theory. We identify the common conditions that allow these solutions, which may also exist for other spin fields. Moreover, we present a comparison of spherically symmetric geons for the spin 0,1/2 and 1, emphasizing the mathematical similarities and clarifying the physical differences, particularly between the bosonic and fermionic cases. We clarify that for the fermionic case, Pauli's exclusion principle prevents a continuous family of solutions for a fixed field mass; rather only a discrete set exists, in contrast with the bosonic case.
Asymptotic behaviour as t\\to \\infty of the solutions of the generalized Korteweg-de Vries equation
Naumkin, P. I.; Shishmarev, I. A.
1996-06-01
Asymptotic formulae representing for large time the solution of the Cauchy problem are obtained for the generalized Korteweg-de Vries equation with non-linear term to an integer power greater than three. The error terms are estimated. The method is based on the perturbation theory with respect to a parameter characterizing the smallness of the initial data.
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Javed Ali
2012-01-01
Full Text Available We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHAM. The proposed method is capable to handle a wide variety of linear and nonlinear problems effectively. The numerical results given by OHAM are compared with the exact solutions and the solutions obtained by Adomian decomposition (ADM, variational iteration (VIM, homotopy perturbation (HPM, and variational iteration decomposition method (VIDM. The results show that the proposed method is more effective and reliable.
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Bezyaev Vladimir Ivanovich
2014-09-01
Full Text Available The authors present an efficient algorithm different from the previously known to construct the asymptotics of solutions of nonautonomous systems of ordinary differential equations with meromorphic matrix. Schrödinger equation, Dirac system, Lippman-Schwinger equation and other equations of quantum mechanics with spherically symmetric and meromorphic potentials may be reduced to such systems. The Schrödinger equation and the Dirac system describe the stationary states of an electron in a Coulomb field with a fixed point charge in the description of the relativistic and nonrelativistic hydrogen atom. The Lippman-Schwinger equation of scattering theory describes the results of collision and interaction of quantum-mechanical particles in mathematical language after these particles have already diverged a long way from one another and ceased to interact. The observed algorithm supplements the known results and allows you to approach the analysis of the problems of this type with a fairly simple and at the same time, a universal point of view.
An asymptotic solution of the Schroedinger equation for the elliptic wire in the magnetic field
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Bejenari, I; Kantser, V [Institute of Electronic Engineering and Industrial Technologies, Academiei str., 3/3, MD2028 Chisinau (Moldova, Republic of)], E-mail: bejenari@iieti.asm.md
2008-10-03
An asymptotic solution of the Schroedinger equation with non-separable variables is obtained for a particle confined to an infinite elliptic cylinder potential well under an applied uniform longitudinal magnetic field. Using the standard-problem method, dimension-quantized eigenvalues have been calculated when the magnetic length is large enough in comparison with the half of the distance between the boundary ellipse focuses. In semi-classical approximation, the confined electron (hole) states are divided into the boundary states (BS), ring states (RS), hyperbolic caustic states (HCS) and harmonic oscillator states (HOS). For large angular momentum quantum numbers and small radial quantum numbers, the BS and RS are grouped into the 'whispering gallery' mode. They associate with particles moving along the wire cross section boundary. The motion is limited from the wire core by the elliptic caustic. Consisting of the HCS and HOS, the 'jumping ball' modes correspond to the states of particle moving along a wire diameter when the angular momentum quantum number is much less than the radial quantum number. In this case, the motion is restricted by the hyperbolic caustics and two boundary ellipse arcs. For excited hole states in a Bi wire, the energy spectrum and space probability distribution are analyzed.
Bulatov, Vitaly V
2012-01-01
The dynamics of internal waves in stratified media, such as the ocean or atmosphere, is highly dependent on the topography of their floor. A closed-form analytical solution can be derived only in cases when the water distribution density and the shape of the floor are modeled with specific functions. In a general case when the characteristics of stratified media and the boundary conditions are arbitrary, the dynamics of internal waves can be only approximated with numerical methods. However, numerical solutions do not describe the wave field qualitatively. At the same time, the need for a qualitative analysis of the far field of internal waves arises in studies applying remote sensing methods in space-based radar applications. In this case, the dynamics of internal waves can be described using asymptotic models. In this paper, we derive asymptotic solutions to the problem of characterizing the far field of internal gravity waves propagating in a stratified medium with a smoothly varying floor.
Asymptotic Solution of a Model for Bilayer Organic Diodes and Solar Cells
Richardson, Giles
2012-11-15
Organic diodes and solar cells are constructed by placing together two organic semiconducting materials with dissimilar electron affinities and ionization potentials. The electrical behavior of such devices has been successfully modeled numerically using conventional drift diffusion together with recombination (which is usually assumed to be bimolecular) and thermal generation. Here a particular model is considered and the dark current-voltage curve and the spatial structure of the solution across the device is extracted analytically using asymptotic methods. We concentrate on the case of Shockley-Read-Hall recombination but note the extension to other recombination mechanisms. We find that there are three regimes of behavior, dependent on the total current. For small currents-i.e., at reverse bias or moderate forward bias-the structure of the solution is independent of the total current. For large currents-i.e., at strong forward bias-the current varies linearly with the voltage and is primarily controlled by drift of charges in the organic layers. There is then a narrow range of currents where the behavior undergoes a transition between the two regimes. The magnitude of the parameter that quantifies the interfacial recombination rate is critical in determining where the transition occurs. The extension of the theory to organic solar cells generating current under illumination is discussed as is the analogous current-voltage curves derived where the photo current is small. Finally, by comparing the analytic results to real experimental data, we show how the model parameters can be extracted from the shape of current-voltage curves measured in the dark. © 2012 Society for Industrial and Applied Mathematics.
Large gyres as a shallow-water asymptotic solution of Euler's equation in spherical coordinates.
Constantin, A; Johnson, R S
2017-04-01
Starting from the Euler equation expressed in a rotating frame in spherical coordinates, coupled with the equation of mass conservation and the appropriate boundary conditions, a thin-layer (i.e. shallow water) asymptotic approximation is developed. The analysis is driven by a single, overarching assumption based on the smallness of one parameter: the ratio of the average depth of the oceans to the radius of the Earth. Consistent with this, the magnitude of the vertical velocity component through the layer is necessarily much smaller than the horizontal components along the layer. A choice of the size of this speed ratio is made, which corresponds, roughly, to the observational data for gyres; thus the problem is characterized by, and reduced to an analysis based on, a single small parameter. The nonlinear leading-order problem retains all the rotational contributions of the moving frame, describing motion in a thin spherical shell. There are many solutions of this system, corresponding to different vorticities, all described by a novel vorticity equation: this couples the vorticity generated by the spin of the Earth with the underlying vorticity due to the movement of the oceans. Some explicit solutions are obtained, which exhibit gyre-like flows of any size; indeed, the technique developed here allows for many different choices of the flow field and of any suitable free-surface profile. We comment briefly on the next order problem, which provides the structure through the layer. Some observations about the new vorticity equation are given, and a brief indication of how these results can be extended is offered.
Maksimova, N.V.; Akhmetov, R. G.
2013-01-01
The work deals with a boundary value problem for a quasilinear partial elliptical equation. The equation describes a stationary process of convective diffusion near a cylinder and takes into account the value of a chemical reaction for large Peclet numbers and for large constant of chemical reaction. The quantity the rate constant of the chemical reaction and Peclet number is assumed to have a constant value. The leading term of the asymptotics of the solution is constructed in the boundary l...
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Yaojun Ye
2010-01-01
Full Text Available The initial boundary value problem for a class of nonlinear higher-order wave equation with damping and source term utt+Au+a|ut|p−1ut=b|u|q−1u in a bounded domain is studied, where A=(−Δm, m≥1 is a nature number, and a,b>0 and p,q>1 are real numbers. The existence of global solutions for this problem is proved by constructing the stable sets and shows the asymptotic stability of the global solutions as time goes to infinity by applying the multiplier method.
Maci, S.; Neto, A.
2004-01-01
This second part of a two-paper sequence deals with the uniform asymptotic description of the Green's function of an infinite slot printed between two different homogeneous dielectric media. Starting from the magnetic current derived in Part I, the dyadic green's function is first formulated in
Asymptotic solution on the dynamic buckling of a column stressed by ...
African Journals Online (AJOL)
This paper analysis the dynamic stability of a dynamically oscillatory system with slowly varying time dependent parameters. It utilizes the concept of multiple times scaling in an asymptotic evaluation of the dynamic buckling load of the imperfect elastic structure under investigation. Unlike most similar investigations to date ...
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Liaqat Ali
2016-09-01
Full Text Available In this research work a new version of Optimal Homotopy Asymptotic Method is applied to solve nonlinear boundary value problems (BVPs in finite and infinite intervals. It comprises of initial guess, auxiliary functions (containing unknown convergence controlling parameters and a homotopy. The said method is applied to solve nonlinear Riccati equations and nonlinear BVP of order two for thin film flow of a third grade fluid on a moving belt. It is also used to solve nonlinear BVP of order three achieved by Mostafa et al. for Hydro-magnetic boundary layer and micro-polar fluid flow over a stretching surface embedded in a non-Darcian porous medium with radiation. The obtained results are compared with the existing results of Runge-Kutta (RK-4 and Optimal Homotopy Asymptotic Method (OHAM-1. The outcomes achieved by this method are in excellent concurrence with the exact solution and hence it is proved that this method is easy and effective.
Russell, John
2000-11-01
A modified Orr-Sommerfeld equation that applies to the asymptotic suction boundary layer was reported by Bussmann & Münz in a wartime report dated 1942 and by Hughes & Reid in J.F.M. ( 23, 1965, p715). Fundamental systems of exact solutions of the Orr-Sommerfeld equation for this mean velocity distribution were reported by D. Grohne in an unpublished typescript dated 1950. Exact solutions of the equation of Bussmann, Münz, Hughes, & Reid were reported by P. Baldwin in Mathematika ( 17, 1970, p206). Grohne and Baldwin noticed that these exact solutions may be expressed either as Barnes integrals or as convolution integrals. In a later paper (Phil. Trans. Roy. Soc. A, 399, 1985, p321), Baldwin applied the convolution integrals in the contruction of large-Reynolds number asymptotic approximations that hold uniformly. The present talk discusses the subtleties that arise in the construction of such convolution integrals, including several not reported by Grohne or Baldwin. The aim is to recover the full set of seven solutions (one well balanced, three balanced, and three dominant-recessive) postulated by W.H. Reid in various works on the uniformly valid solutions.
Wu, Junde; Zhou, Fujun
2017-05-01
In this paper we study a free boundary problem modeling the growth of solid tumor spheroid. It consists of two elliptic equations describing nutrient diffusion and pressure distribution within tumor, respectively. The new feature is that nutrient concentration on the boundary is less than external supply due to a Gibbs-Thomson relation and the problem has two radial stationary solutions, which differs from widely studied tumor spheroid model with surface tension effect. We first establish local well-posedness by using a functional approach based on Fourier multiplier method and analytic semigroup theory. Then we investigate stability of each radial stationary solution. By employing a generalized principle of linearized stability, we prove that the radial stationary solution with a smaller radius is always unstable, and there exists a positive threshold value γ* of cell-to-cell adhesiveness γ, such that the radial stationary solution with a larger radius is asymptotically stable for γ >γ*, and unstable for 0 < γ <γ*.
On global asymptotic stability of solutions of a system of ordinary differential equations
Filimonov, M. Yu.
2017-12-01
To investigate global asymptotic stability in general of an equilibrium position of an autonomous system of ordinary differential equations, considered by V.A. Pliss, a function different from the Lyapunov functions is applied. V.A. Pliss proved that for this system it is impossible to construct the Lyapunov function as a sum of a quadratic form and an integral of some nonlinear function defined by the right-hand side of the system.
Sameh Turki
2012-01-01
This paper deals with the existence and the asymptotic behavior of positive continuous solutions of the nonlinear elliptic system \\(\\Delta u=p(x)u^{\\alpha}v^r\\), \\(\\Delta v = q(x)u^s v^{\\beta}\\), in the half space \\(\\mathbb{R}^n_+ :=\\{x=(x_1,..., x_n)\\in \\mathbb{R}^n : x_n \\gt 0\\}\\), \\(n \\geq 2\\), where \\(\\alpha, \\beta \\gt 1\\) and \\(r, s \\geq 0\\). The functions \\(p\\) and \\(q\\) are required to satisfy some appropriate conditions related to the Kato class \\(K^{\\infty}(\\mathbb{R}^n_+)\\). Our app...
Sekerzh-Zen'kovich, S. Ya.
2017-10-01
Statement of the hydrodynamic problem in the framework of the potential tsunami model with "simple" source whose solution is chosen as the reference one. Generalized Cauchy problem for the Boussinesq equation and its reduction to the classical one. Analytical solution of the Cauchy problem for the Boussinesq equation. An explanation of the incorrectness of the formulation of the problem. Derivation of an approximate equation for the correct setting of the Cauchy problem. The known reference solution of the problem. An analytical solution of the correct problem and the derivation of its asymptotic representation in the "far zone." Comparison of the graphs of the temporal history of wave height calculated by the formulas of the asymptotic and reference solutions. Estimation of the accuracy of the asymptotic solution by a three-level scale. Discussion. A remark concerning the referees.
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Edgardo Alvarez
2016-10-01
Full Text Available We study weighted pseudo almost automorphic solutions for the nonlinear fractional difference equation $$ \\Delta^{\\alpha}u(n=Au(n+1+f(n, u(n,\\quad n\\in \\mathbb{Z}, $$ for $0<\\alpha \\leq 1$, where A is the generator of an $\\alpha$-resolvent sequence $\\{S_{\\alpha}(n\\}_{n\\in\\mathbb{N}_0}$ in $\\mathcal{B}(X$. We prove the existence and uniqueness of a weighted pseudo almost automorphic solution assuming that f(.,. is weighted almost automorphic in the first variable and satisfies a Lipschitz (local and global type condition in the second variable. An analogous result is also proved for $\\mathcal{S}$-asymptotically $\\omega$-periodic solutions.
Aguareles, M.
2014-06-01
In this paper we consider an oscillatory medium whose dynamics are modeled by the complex Ginzburg-Landau equation. In particular, we focus on n-armed spiral wave solutions of the complex Ginzburg-Landau equation in a disk of radius d with homogeneous Neumann boundary conditions. It is well-known that such solutions exist for small enough values of the twist parameter q and large enough values of d. We investigate the effect of boundaries on the rotational frequency of the spirals, which is an unknown of the problem uniquely determined by the parameters d and q. We show that there is a threshold in the parameter space where the effect of the boundary on the rotational frequency switches from being algebraic to exponentially weak. We use the method of matched asymptotic expansions to obtain explicit expressions for the asymptotic wavenumber as a function of the twist parameter and the domain size for small values of q. © 2014 Elsevier B.V. All rights reserved.
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Hiroshi Matsuzawa
2006-01-01
Full Text Available In this article, we consider the semilinear elliptic problem $$ -varepsilon^{2}Delta u=h(|x|^2(u-a(|x|(1-u^2 $$ in $B_1(0$ with the Neumann boundary condition. The function $a$ is a $C^1$ function satisfying $|a(x|< 1$ for $xin [0,1]$ and $a'(0=0$. In particular we consider the case $a(r=0$ on some interval $Isubset [0,1]$. The function $h$ is a positive $C^1$ function satisfying $h'(0=0$. We investigate an asymptotic profile of the global minimizer corresponding to the energy functional as $varepsilono 0$. We use the variational procedure used in [4] with a few modifications prompted by the presence of the function $h$.
Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions
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Diabate Nabongo
2008-01-01
Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.
Stable subharmonic solutions and asymptotic behavior in reaction-diffusion equations
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P. Polacik
2000-01-01
Full Text Available Time-periodic reaction-diffusion equations can be discussed in the context of discrete-time strongly monotone dynamical systems. It follows from the general theory that typical trajectories approach stable periodic solutions. Among these periodic solutions, there are some that have the same period as the equation, but, possibly, there might be others with larger minimal periods (these are called subharmonic solutions. The problem of existence of stable subharmonic solutions is therefore of fundamental importance in the study of the behavior of solutions. We address this problem for two classes of reaction diffusion equations under Neumann boundary conditions. Namely, we consider spatially inhomogeneous equations, which can have stable subharmonic solutions on any domain, and spatially homogeneous equations, which can have such solutions on some (necessarily non-convex domains.
Asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^n
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Meng-Rong Li
2013-11-01
Full Text Available In this article we study properties of positive solutions of the ordinary differential equation $t^2u''=u^n$ for $1
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Traytak, Sergey D., E-mail: sergtray@mail.ru [Centre de Biophysique Moléculaire, CNRS-UPR4301, Rue C. Sadron, 45071 Orléans (France); Le STUDIUM (Loire Valley Institute for Advanced Studies), 3D av. de la Recherche Scientifique, 45071 Orléans (France); Semenov Institute of Chemical Physics RAS, 4 Kosygina St., 117977 Moscow (Russian Federation)
2014-06-14
The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problem and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.
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Messaris, Gerasimos A. T., E-mail: messaris@upatras.gr [Department of Physics, Division of Theoretical Physics, University of Patras, GR 265 04 Rion (Greece); School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras (Greece); Hadjinicolaou, Maria [School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras (Greece); Karahalios, George T. [Department of Physics, Division of Theoretical Physics, University of Patras, GR 265 04 Rion (Greece)
2016-08-15
The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses
Directory of Open Access Journals (Sweden)
Zhoujin Cui
2007-01-01
Full Text Available This paper investigates the local existence of the nonnegative solution and the finite time blow-up of solutions and boundary layer profiles of diffusion equations with nonlocal reaction sources; we also study the global existence and that the rate of blow-up is uniform in all compact subsets of the domain, the blow-up rate of |u(t|∞ is precisely determined.
Asymptotic behaviour of solutions to a system of Schrödinger equations
Czech Academy of Sciences Publication Activity Database
Carvajal, X.; Gamboa, P.; Nečasová, Šárka; Nguyen, H. H.; Vero, O.
2017-01-01
Roč. 2017, č. 171 (2017), s. 1-23 ISSN 1072-6691 R&D Projects: GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : coupled Schrodinger system * energy conservation * global solution * growth of solutions Subject RIV: BA - General Mathematics Impact factor: 0.954, year: 2016 https://ejde.math.txstate.edu/Volumes/2017/171/abstr.html
Thermal stability analysis of nonlinearly charged asymptotic AdS black hole solutions
Dehghani, M.; Hamidi, S. F.
2017-08-01
In this paper, the four-dimensional nonlinearly charged black hole solutions have been considered in the presence of the power Maxwell invariant electrodynamics. Two new classes of anti-de Sitter (AdS) black hole solutions have been introduced according to different amounts of the parameters in the nonlinear theory of electrodynamics. The conserved and thermodynamical quantities of either of the black hole classes have been calculated from geometrical and thermodynamical approaches, separately. It has been shown that the first law of black hole thermodynamics is satisfied for either of the AdS black hole solutions we just obtained. Through the canonical and grand canonical ensemble methods, the black hole thermal stability or phase transitions have been analyzed by considering the heat capacities with the fixed black hole charge and fixed electric potential, respectively. It has been found that the new AdS black holes are stable if some simple conditions are satisfied.
Gilliam, Ashley E.; Wunsch, Jared; Lerman, Abraham
2017-09-01
Systems of simultaneous or parallel chemical reactions of the type A → B → C → Other products are often treated as first order or pseudo-first order. For a system of simultaneous first and second order reactions — dB/dt = kABA - kBCB2 and dC/dt = kBCB2 - kCC, where A, B, and C are concentrations, t is time, and the reaction rate parameters kAB and kC in yr-1 are 1st-order and kBC in cm3 molecule-1 yr-1 is 2nd-order — no explicit solution is available, as far as we are aware. This paper presents explicit and asymptotic solutions of simultaneous 1st- and 2nd order Riccati equations and applies them to a simplified sequence of gas reactions in the atmosphere of Titan, the largest satellite of Saturn: CH4 methane (1st order, k12) → CH3 methyl (2nd order, k23) → C2H6 ethane (1st order, k3) → Other products. The Titan's atmosphere contains methane (CH4) at the present-day partial pressure of 0.1 bar, out of a total atmospheric pressure made up by nitrogen (N2) of 1.5 bar, comparable to Earth's. Methyl CH3 and ethane C2H6 are minor components. On Titan, methyl (CH3) is an intermediate product from methane to ethane, the latter raining out as liquid on Titan's surface. The main points of this paper are: (1) the asymptotic solutions that approximate near-steady state of Titan's atmosphere about 4.5 billion years after its accretion; (2) the computed present-day concentrations of the three gases in Titan's scale atmosphere (i.e., scale atmosphere is a model of an isothermal well mixed reservoir); and (3) the agreement between Titan's reported and computed atmospheric concentrations of CH4, CH3, and C2H6. The reaction rate parameters of the species are constants representative of their mean values during the satellite's cooling history. The present-day concentrations of methyl (CH3) and ethane (C2H6) are several orders of magnitude lower than the concentration of methane (CH4). Since Titan's accretion about 4.5 billion years B.P., steady-state concentrations
Said-Houari, Belkacem
2012-03-01
In this paper, we consider a viscoelastic wave equation with an absorbing term and space-time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term. © 2011 Elsevier Inc.
Positive solutions with specific asymptotic behavior for a polyharmonic problem on R^{n}
Directory of Open Access Journals (Sweden)
Abdelwaheb Dhifli
2015-01-01
Full Text Available This paper is concerned with positive solutions of the semilinear polyharmonic equation \\((-\\Delta^{m} u = a(x{u}^{\\alpha}\\ on \\(\\mathbb{R}^{n}\\, where \\(m\\ and \\(n\\ are positive integers with \\(n\\gt 2m\\, \\(\\alpha\\in (-1,1\\. The coefficient \\(a\\ is assumed to satisfy \\[a(x\\approx{(1+|x|}^{-\\lambda}L(1+|x|\\quad \\text{for}\\quad x\\in \\mathbb{R}^{n},\\] where \\(\\lambda\\in [2m,\\infty\\ and \\(L\\in C^{1}([1,\\infty\\ is positive with \\(\\frac{tL'(t}{L(t}\\longrightarrow 0\\ as \\(t\\longrightarrow \\infty\\; if \\(\\lambda=2m\\, one also assumes that \\(\\int_{1}^{\\infty}t^{-1}L(tdt\\lt \\infty\\. We prove the existence of a positive solution \\(u\\ such that \\[u(x\\approx{(1+|x|}^{-\\widetilde{\\lambda}}\\widetilde{L}(1+|x| \\quad\\text{for}\\quad x\\in \\mathbb{R}^{n},\\] with \\(\\widetilde{\\lambda}:=\\min(n-2m,\\frac{\\lambda-2m}{1-\\alpha}\\ and a function \\(\\widetilde{L}\\, given explicitly in terms of \\(L\\ and satisfying the same condition at infinity. (Given positive functions \\(f\\ and \\(g\\ on \\(\\mathbb{R}^{n}\\, \\(f\\approx g\\ means that \\(c^{-1}g\\leq f\\leq cg\\ for some constant \\(c\\gt 1\\.
Directory of Open Access Journals (Sweden)
Hai Zhang
2017-01-01
Full Text Available This paper investigates the existence and globally asymptotic stability of equilibrium solution for Riemann-Liouville fractional-order hybrid BAM neural networks with distributed delays and impulses. The factors of such network systems including the distributed delays, impulsive effects, and two different fractional-order derivatives between the U-layer and V-layer are taken into account synchronously. Based on the contraction mapping principle, the sufficient conditions are derived to ensure the existence and uniqueness of the equilibrium solution for such network systems. By constructing a novel Lyapunov functional composed of fractional integral and definite integral terms, the globally asymptotic stability criteria of the equilibrium solution are obtained, which are dependent on the order of fractional derivative and network parameters. The advantage of our constructed method is that one may directly calculate integer-order derivative of the Lyapunov functional. A numerical example is also presented to show the validity and feasibility of the theoretical results.
Large gyres as a shallow-water asymptotic solution of Euler’s equation in spherical coordinates
Johnson, R. S.
2017-01-01
Starting from the Euler equation expressed in a rotating frame in spherical coordinates, coupled with the equation of mass conservation and the appropriate boundary conditions, a thin-layer (i.e. shallow water) asymptotic approximation is developed. The analysis is driven by a single, overarching assumption based on the smallness of one parameter: the ratio of the average depth of the oceans to the radius of the Earth. Consistent with this, the magnitude of the vertical velocity component through the layer is necessarily much smaller than the horizontal components along the layer. A choice of the size of this speed ratio is made, which corresponds, roughly, to the observational data for gyres; thus the problem is characterized by, and reduced to an analysis based on, a single small parameter. The nonlinear leading-order problem retains all the rotational contributions of the moving frame, describing motion in a thin spherical shell. There are many solutions of this system, corresponding to different vorticities, all described by a novel vorticity equation: this couples the vorticity generated by the spin of the Earth with the underlying vorticity due to the movement of the oceans. Some explicit solutions are obtained, which exhibit gyre-like flows of any size; indeed, the technique developed here allows for many different choices of the flow field and of any suitable free-surface profile. We comment briefly on the next order problem, which provides the structure through the layer. Some observations about the new vorticity equation are given, and a brief indication of how these results can be extended is offered. PMID:28484341
Energy Technology Data Exchange (ETDEWEB)
Dranishnikov, A N [Steklov Mathematical Institute, Russian Academy of Sciences (Russian Federation)
2000-12-31
In this paper we study the similarity between local topology and its global analogue, so-called asymptotic topology. In the asymptotic case, the notions of dimension, cohomological dimension, and absolute extensor are introduced and some basic facts about them are proved. The Higson corona functor establishing a connection between macro- and micro-topology is considered. A relationship between problems of general asymptotic topology and the Novikov conjecture on higher signatures is discussed. Some new results concerning the Novikov conjecture and other related conjectures are presented.
Peters, C. (Principal Investigator)
1980-01-01
A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes.
Energy Technology Data Exchange (ETDEWEB)
Griesbaum, R.; Ehrhard, P.; Mueller, U.
1994-05-01
Based on the approximate solution for the liminar far wake of an isothermal cylinder, we derive a model for the far wake of a weakly-heated cylinder. Forced flow is upward against gravity, while the problem is considered to be two-dimensional and steady. A scaled version of boundary layer equations in conjunction with Boussinesq`s approximation are the basis for an asymptotic expansion using the small parameter {epsilon}=1/{radical}Re. Two leading orders of this expansion are discussed. In a first order we find the well-known flow field associated with the linearized far wake of a cylinder in conjunction with a gaussian temperature profile resulting from heat input. There are, however, no buoyancy forces present in the momentum equation of this approximation. The second order accounts for nonlinearities of momentum and heat transport and includes buoyant effects. The typical properties of this heated far wake, as e.g. kinematic or thermal boundary layer thickness and velocity or temperature amplitudes are discussed in their functional dependancy on the parameters. The parameters considered are the Reynolds-number, the Pradtl-number, the Grashof-number, as well as geometry. (orig.) [Deutsch] Ausgehend von der Naeherungsloesung fuer den laminaren, isothermen Zylindernachlauf wird der laminare Nachlauf hinter einem schwach beheizten Zylinder modelliert. Der Zylinder wird entgegen der Richtung des Schwerevektors angestroemt. Das Problem wird zweidimensional und stationaer betrachtet. Unter Verwendung der Boussinesq-Approximation bilden die skalierten Grenzschichtgleichungen die Basis zur Beschreibung dieser Stroemung. Die gesuchten asymptotischen Loesungen werden nach dem Parameter {epsilon}=1/{radical}Re entwickelt. Die ersten beiden Ordnungen dieser Entwicklung werden betrachtet. Die Loesung der ersten Ordnung liefert das bekannte Stromfeld des linearisierten Zylindernachlaufs. Darueber hinaus ist das Temperaturprofil durch die eingebrachte Waerme gekennzeichnet. Die
Sarwar, S.; Rashidi, M. M.
2016-07-01
This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.
On asymptotics for difference equations
Rafei, M.
2012-01-01
In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Medviďová-Lukáčová, M.; Nečasová, Šárka; Novotný, A.; She, Bangwei
2018-01-01
Roč. 16, č. 1 (2018), s. 150-183 ISSN 1540-3459 R&D Projects: GA ČR GA16-03230S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method * asymptotic preserving schemes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.865, year: 2016 http://epubs.siam.org/doi/10.1137/16M1094233
Rimbert, Nicolas; Séro-Guillaume, Olivier
2004-05-01
In this paper, it will be shown that “totally skewed to the left” log-stable distributions are suitable asymptotic solutions to a fragmentation equation. This result generalizes Kolmogorov’s work on log-normal distribution for the drops’ size number distribution of particles under pulverization. Indeed, Kolmogorov’s discrete process is extended to a continuous time Markov process for the volume distribution instead of the number distribution. New hypotheses are then introduced which lead to log-stable distributions as asymptotic solutions of the fragmentation equation. Log-stable laws are then used to fit experimental probability distribution function (pdf) of Simmons and Hanratty measuring drop sizes in a horizontal annular gas-liquid flow at high Weber number [Int. J. Multiphase Flow 27, 861 (2001)]. Log-stable pdf better fits to the experimental pdf than usual empirical spray pdf and especially, because of the heavy tail of the associated stable distribution, in the small drops part of the distribution.
Vinas, A. F.; Scudder, J. D.
1986-01-01
A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., theta sub Bn, yields N, V sub s and M sub A), the conservation constants and the self-consistent asymptotic magnetofluid variables, that uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all theta sub Bn angles regardless of the shock strength or geometry. Explicit proof of uniqueness of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented.
Asymptotically flat multiblack lenses
Tomizawa, Shinya; Okuda, Taika
2017-03-01
We present an asymptotically flat and stationary multiblack lens solution with biaxisymmetry of U (1 )×U (1 ) as a supersymmetric solution in the five-dimensional minimal ungauged supergravity. We show that the spatial cross section of each degenerate Killing horizon admits different lens space topologies of L (n ,1 )=S3/Zn as well as a sphere S3. Moreover, we show that, in contrast to the higher-dimensional Majumdar-Papapetrou multiblack hole and multi-Breckenridge-Myers-Peet-Vafa (BMPV) black hole spacetime, the metric is smooth on each horizon even if the horizon topology is spherical.
Directory of Open Access Journals (Sweden)
Imed Bachar
2014-01-01
Full Text Available We are interested in the following fractional boundary value problem: Dαu(t+atuσ=0, t∈(0,∞, limt→0t2-αu(t=0, limt→∞t1-αu(t=0, where 1<α<2, σ∈(-1,1, Dα is the standard Riemann-Liouville fractional derivative, and a is a nonnegative continuous function on (0,∞ satisfying some appropriate assumptions related to Karamata regular variation theory. Using the Schauder fixed point theorem, we prove the existence and the uniqueness of a positive solution. We also give a global behavior of such solution.
Directory of Open Access Journals (Sweden)
Nita Jain
2015-09-01
Full Text Available The work presented in this paper is focused on deductive group-theoretic transformations to develop the similarity solution of steady, laminar, incompressible quasi three dimensional boundary layer flow governing power law fluid. The application of one-parameter group reduces the number of independent variables to one and consequently the system of governing, highly non-linear partial differential equations reduces to a self similar, non-linear ordinary differential equation with appropriate auxiliary conditions. The numerical solution for a power law fluid considered for small cross flow is obtained systematically using MSABC in dimensionless form.
Asymptotic freedom, asymptotic flatness and cosmology
Kiritsis, Elias
2013-01-01
Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free $\\beta$-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability and other problems of such inflationary models.
Rahali, Radouane
2013-03-01
In this paper, we investigate the decay property of a Timoshenko system in thermoelasticity of type III in the whole space where the heat conduction is given by the Green and Naghdi theory. Surprisingly, we show that the coupling of the Timoshenko system with the heat conduction of Green and Naghdi\\'s theory slows down the decay of the solution. In fact we show that the L-2-norm of the solution decays like (1 + t)(-1/8), while in the case of the coupling of the Timoshenko system with the Fourier or Cattaneo heat conduction, the decay rate is of the form (1 + t)(-1/4) [25]. We point out that the decay rate of (1 + t)(-1/8) has been obtained provided that the initial data are in L-1 (R) boolean AND H-s (R); (s >= 2). If the wave speeds of the fi rst two equations are di ff erent, then the decay rate of the solution is of regularity-loss type, that is in this case the previous decay rate can be obtained only under an additional regularity assumption on the initial data. In addition, by restricting the initial data to be in H-s (R) boolean AND L-1,L-gamma (R) with gamma is an element of [0; 1], we can derive faster decay estimates with the decay rate improvement by a factor of t(-gamma/4).
Nockowska-Rosiak, Magdalena
2016-01-01
This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ \\Delta \\left( r_{n} \\Delta \\left( x_{n}+q_{n}x_{n-\\tau}\\right)\\right)= a_{n}f(x_{n-\\sigma})+b_n%, \\ n\\geq n_0 $$ with respect to $(q_n)$. For $q_n\\to1$, $q_n\\in(0,1)$ the standard fixed point approach is not sufficed to get the existence of the bounded solution, so we combine this method with an approximation technique to achieve our goal. Moreover, for $p\\ge 1$ a...
Qin, Yuming
2016-01-01
This book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic systems, thermoelastic systems of types II and III, as well as Timoshenko-type systems with past history. Part of the book is based on the research conducted by the authors and their collaborators in recent years. The book will benefit interested beginners in the field and experts alike.
AdS3 to dS3 transition in the near horizon of asymptotically de Sitter solutions
Sadeghian, S.; Vahidinia, M. H.
2017-08-01
We consider two solutions of Einstein-Λ theory which admit the extremal vanishing horizon (EVH) limit, odd-dimensional multispinning Kerr black hole (in the presence of cosmological constant) and cosmological soliton. We show that the near horizon EVH geometry of Kerr has a three-dimensional maximally symmetric subspace whose curvature depends on rotational parameters and the cosmological constant. In the Kerr-dS case, this subspace interpolates between AdS3 , three-dimensional flat and dS3 by varying rotational parameters, while the near horizon of the EVH cosmological soliton always has a dS3 . The feature of the EVH cosmological soliton is that it is regular everywhere on the horizon. In the near EVH case, these three-dimensional parts turn into the corresponding locally maximally symmetric spacetimes with a horizon: Kerr-dS3 , flat space cosmology or BTZ black hole. We show that their thermodynamics match with the thermodynamics of the original near EVH black holes. We also briefly discuss the holographic two-dimensional CFT dual to the near horizon of EVH solutions.
Asymptotic vacua with higher derivatives
Energy Technology Data Exchange (ETDEWEB)
Cotsakis, Spiros, E-mail: skot@aegean.gr [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kadry, Seifedine, E-mail: Seifedine.Kadry@aum.edu.kw [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kolionis, Georgios, E-mail: gkolionis@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece); Tsokaros, Antonios, E-mail: atsok@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece)
2016-04-10
We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Asymptotically Safe Dark Matter
DEFF Research Database (Denmark)
Sannino, Francesco; Shoemaker, Ian M.
2015-01-01
We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....
The Asymptotic Approach to the Twin Paradox
National Research Council Canada - National Science Library
Spiridon Dumitru
2008-01-01
The argument of twins' asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant...
The Asymptotic Approach to the Twin Paradox
National Research Council Canada - National Science Library
Dumitru S
2008-01-01
The argument of twins’ asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant...
Asymptotics and Borel summability
Costin, Ovidiu
2008-01-01
Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.To give a sense of how new methods are us
The Asymptotic Approach to the Twin Paradox
Directory of Open Access Journals (Sweden)
Dumitru S.
2008-04-01
Full Text Available The argument of twins’ asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant. Consequently the respective solution proves itself as unreliable thing and the Twin Paradox is re-established as an open problem which require further investigations.
The Asymptotic Approach to the Twin Paradox
Directory of Open Access Journals (Sweden)
Dumitru S.
2008-04-01
Full Text Available The argument of twins' asymmetry, essentially put forward in the common solution of the Twin Paradox, is revealed to be inoperative in some asymptotic situations in which the noninertial effects are insignificant. Consequently the respective solution proves itself as unreliable thing and the Twin Paradox is re-established as an open problem which require further investigations.
Large Deviations and Asymptotic Methods in Finance
Gatheral, Jim; Gulisashvili, Archil; Jacquier, Antoine; Teichmann, Josef
2015-01-01
Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find th...
Nonstandard asymptotic analysis
Berg, Imme
1987-01-01
This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the t...
Asymptotic stability of a catalyst particle
DEFF Research Database (Denmark)
Wedel, Stig; Michelsen, Michael L.; Villadsen, John
1977-01-01
The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0. These a......The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0...
Optimal asymptotic cloning machines
Chiribella, Giulio; Yang, Yuxiang
2014-06-01
We pose the question whether the asymptotic equivalence between quantum cloning and quantum state estimation, valid at the single-clone level, still holds when all clones are examined globally. We conjecture that the answer is affirmative and present a large amount of evidence supporting our conjecture, developing techniques to derive optimal asymptotic cloners and proving their equivalence with estimation in virtually all scenarios considered in the literature. Our analysis covers the case of arbitrary finite sets of states, arbitrary families of coherent states, arbitrary phase- and multiphase-covariant sets of states, and two-qubit maximally entangled states. In all these examples we observe that the optimal asymptotic cloners enjoy a universality property, consisting in the fact that scaling of their fidelity does not depend on the specific details of the input states, but only on the number of free parameters needed to specify them.
Ramnath, Rudrapatna V
2012-01-01
This book addresses the task of computation from the standpoint of asymptotic analysis and multiple scales that may be inherent in the system dynamics being studied. This is in contrast to the usual methods of numerical analysis and computation. The technical literature is replete with numerical methods such as Runge-Kutta approach and its variations, finite element methods, and so on. However, not much attention has been given to asymptotic methods for computation, although such approaches have been widely applied with great success in the analysis of dynamic systems. The presence of differen
The Asymptotic Expansion Method via Symbolic Computation
Directory of Open Access Journals (Sweden)
Juan F. Navarro
2012-01-01
Full Text Available This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.
Asymptotic symmetry algebra of conformal gravity
Irakleidou, Maria; Lovrekovic, Iva
2017-11-01
We compute asymptotic symmetry algebras of conformal gravity. Due to more general boundary conditions allowed in conformal gravity in comparison to those in Einstein gravity, we can classify the corresponding algebras. The highest algebra for nontrivial boundary conditions is five dimensional and it leads to global geon solution with nonvanishing charges.
Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices
Cha, Ye Sle; Sakovich, Anna
2016-01-01
We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case in the asymptotically flat setting, whenever a geometrically motivated system of elliptic equations admits a solution.
Asymptotic behavior of a system of linear fractional difference equations
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Nurkanović M
2005-01-01
Full Text Available We investigate the global asymptotic behavior of solutions of the system of difference equations , , , where the parameters , , , and are positive numbers and the initial conditions and are arbitrary nonnegative numbers. We obtain some asymptotic results for the positive equilibrium of this system.
Quadratic maps without asymptotic measure
Hofbauer, Franz; Keller, Gerhard
1990-02-01
An interval map is said to have an asymptotic measure if the time averages of the iterates of Lebesgue measure converge weakly. We construct quadratic maps which have no asymptotic measure. We also find examples of quadratic maps which have an asymptotic measure with very unexpected properties, e.g. a map with the point mass on an unstable fix point as asymptotic measure. The key to our construction is a new characterization of kneading sequences.
ASYMPTOTICS OF a PARTICLES TRANSPORT PROBLEM
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Kuzmina Ludmila Ivanovna
2017-11-01
Full Text Available Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.
Konosevich, B. I.
2014-07-01
The error of the Wentzel-Kramers-Brillouin solution of the equations describing the angular motion of the axis of symmetry of rotation of a rigid body (projectile) is estimated. It is established that order of this estimate does not depend on whether the low-frequency oscillations of the axis of symmetry are damped or not
Nguyen, Van Minh
In this paper we present a new approach to the spectral theory of non-uniformly continuous functions and a new framework for the Loomis-Arendt-Batty-Vu theory. Our approach is direct and free of C-semigroups, so the obtained results, that extend previous ones, can be applied to large classes of evolution equations and their solutions.
Scheven, U. M.; Harris, R.; Johns, M. L.
2008-12-01
The experimental characterization of voidspaces in porous media generally includes measurements of volume averaged scalar properties such as porosity, dispersivity, or the hydrodynamic radius rh = V/S, where V and S are the volume and surface area of the pore space respectively. Displacement encoding NMR experiments have made significant contributions to this characterization. It is clear, however, that NMR derived dispersivities in packed beds—the one random porous system for which there exist canonical but incompatible theoretical predictions with few or no adjustable parameters—can be affected by the same experimental complications which have substantially contributed to the puzzling scatter in published dispersion results based on elution experiments. Notable among these are macroscopic flow heterogeneities near walls, and inhomogeneous flow injection. Using the first three cumulants we delineate a transition from a pre-asymptotic to a quasi-asymptotic dispersion regime and determine the true dispersivity of the random pack of spheres.
Energy Technology Data Exchange (ETDEWEB)
Litim, Daniel F. [Department of Physics and Astronomy, University of Sussex,Falmer Campus, Brighton, BN1 9QH (United Kingdom); Sannino, Francesco [CP-Origins & the Danish Institute for Advanced Study Danish IAS, University of Southern Denmark,Campusvej 55, DK-5230 Odense (Denmark)
2014-12-31
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.
DEFF Research Database (Denmark)
Litim, Daniel F.; Sannino, Francesco
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet...... fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed....
Asymptotics of perturbed soliton for Davey-Stewartson; 2, equation
Gadylshin, R R
1998-01-01
It is shown that, under a small perturbation of lump (soliton) for Davey-Stewartson (DS-II) equation, the scattering data gain the nonsoliton structure. As a result, the solution has the form of Fourier type integral. Asymptotic analysis shows that, in spite of dispertion, the principal term of the asymptotic expansion for the solution has the solitary wave form up to large time.
Kravchenko, Vladislav V.; Torba, Sergii M.
2017-01-01
A representation for a solution $u(\\omega,x)$ of the equation $-u"+q(x)u=\\omega^2 u$, satisfying the initial conditions $u(\\omega,0)=1$, $u'(\\omega,0)=i\\omega$ is derived in the form \\[ u(\\omega,x)=e^{i\\omega x}\\left( 1+\\frac{u_1(x)}{\\omega}+ \\frac{u_2(x)}{\\omega^2}\\right) +\\frac{e^{-i\\omega x}u_3(x)}{\\omega^2}-\\frac{1}{\\omega^2}\\sum_{n=0}^{\\infty} i^{n}\\alpha_n(x)j_n(\\omega x), \\] where $u_m(x)$, $m=1,2,3$ are given in a closed form, $j_n$ stands for a spherical Bessel function of order $n$ ...
Asymptotic structures of cardinals
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Oleksandr Petrenko
2014-07-01
Full Text Available A ballean is a set X endowed with some family F of its subsets, called the balls, in such a way that (X,F can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal k, we define F using a natural order structure on k. We characterize balleans up to coarse equivalence, give the criterions of metrizability and cellularity, calculate the basic cardinal invariant of these balleans. We conclude the paper with discussion of some special ultrafilters on cardinal balleans.
Ho, Pei-Ming
2017-04-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Asymptotic Behavior of Certain Integrodifferential Equations
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Said Grace
2016-01-01
Full Text Available This paper deals with asymptotic behavior of nonoscillatory solutions of certain forced integrodifferential equations of the form: atx′t′=e(t+∫ct(t-sα-1k(t,sf(s,x(sds, c>1, 0<α<1. From the obtained results, we derive a technique which can be applied to some related integrodifferential as well as integral equations.
Asymptotic independence for unimodal densities
Balkema, G.; Nolde, N.
2010-01-01
Asymptotic independence of the components of random vectors is a concept used in many applications. The standard criteria for checking asymptotic independence are given in terms of distribution functions (DFs). DFs are rarely available in an explicit form, especially in the multivariate case. Often
Asymptotic Safety, Fractals, and Cosmology
Reuter, Martin; Saueressig, Frank
These lecture notes introduce the basic ideas of the asymptotic safety approach to quantum Einstein gravity (QEG). In particular they provide the background for recent work on the possibly multi-fractal structure of the QEG space-times. Implications of asymptotic safety for the cosmology of the early Universe are also discussed.
Essentially asymptotically stable homoclinic networks
Driesse, R.; Homburg, A.J.
2009-01-01
Melbourne [An example of a nonasymptotically stable attractor, Nonlinearity 4(3) (1991), pp. 835-844] discusses an example of a robust heteroclinic network that is not asymptotically stable but which has the strong attracting property called essential asymptotic stability. We establish that this
Asymptotic-induced numerical methods for conservation laws
Garbey, Marc; Scroggs, Jeffrey S.
1990-01-01
Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques.
An asymptotically exact theory of functionally graded piezoelectric shells
Le, Khanh Chau
2016-01-01
An asymptotically exact two-dimensional theory of functionally graded piezoelectric shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application, analytical solution to the problem of forced vibration of a functionally graded piezoceramic cylindrical shell with thickness polarization fully covered by electrodes and excited by a harmonic voltage is found.
Dynamics and Asymptotics of Brane-Worlds
Antoniadis, I.; Cotsakis, S.; Klaoudatou, I.
2015-01-01
The self-tuning mechanism aims to provide a way to address the cosmological constant problem by guarantying the existence of flat brane solutions independently of the brane tension value. In recent work we have studied the asymptotics of different models of brane-worlds, and here we highlight certain interesting behaviors we have encountered in our search for appropriate conditions to avoid finite-distance singularities in flat brane solutions. Finding such conditions offers a framework within which the self-tuning mechanism could be realized.
Convergence Theorem for Finite Family of Total Asymptotically Nonexpansive Mappings
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E.U. Ofoedu
2015-11-01
Full Text Available In this paper we introduce an explicit iteration process and prove strong convergence of the scheme in a real Hilbert space $H$ to the common fixed point of finite family of total asymptotically nonexpansive mappings which is nearest to the point $u \\in H$. Our results improve previously known ones obtained for the class of asymptotically nonexpansive mappings. As application, iterative method for: approximation of solution of variational Inequality problem, finite family of continuous pseudocontractive mappings, approximation of solutions of classical equilibrium problems and approximation of solutions of convex minimization problems are proposed. Our theorems unify and complement many recently announced results.
Asymptotic stability results for retarded differential systems | Igobi ...
African Journals Online (AJOL)
The transcendental character of the polynomial equation of the retarded differential system makes it difficult to express its solution explicitly. This has cause a set back in the asymptotic stability analysis of the system solutions. Various acceptable mathematical techniques have been used to address the issue. In this paper ...
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I. V. Samoilenko
2005-01-01
Full Text Available We study the asymptotic expansion for solution of singularly perturbed equation for functional of Markovian evolution in Rd. The view of regular and singular parts of solution is found.
Spherical convective dynamos in the rapidly rotating asymptotic regime
Aubert, Julien; Fournier, Alexandre
2016-01-01
Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a unidimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state...
Top mass from asymptotic safety
Eichhorn, Astrid; Held, Aaron
2018-02-01
We discover that asymptotically safe quantum gravity could predict the top-quark mass. For a broad range of microscopic gravitational couplings, quantum gravity could provide an ultraviolet completion for the Standard Model by triggering asymptotic freedom in the gauge couplings and bottom Yukawa and asymptotic safety in the top-Yukawa and Higgs-quartic coupling. We find that in a part of this range, a difference of the top and bottom mass of approximately 170GeV is generated and the Higgs mass is determined in terms of the top mass. Assuming no new physics below the Planck scale, we construct explicit Renormalization Group trajectories for Standard Model and gravitational couplings which link the transplanckian regime to the electroweak scale and yield a top pole mass of Mt,pole ≈ 171GeV.
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
Traversable asymptotically flat wormholes in Rastall gravity
Moradpour, H.; Sadeghnezhad, N.; Hendi, S. H.
2017-12-01
There are some gravitational theories in which the ordinary energy-momentum conservation law is not valid in the curved spacetime. Rastall gravity is one of the known theories in this regard which includes a non-minimal coupling between geometry and matter fields. Equipped with the basis of such theory, we study the properties of traversable wormholes with flat asymptotes. We investigate the possibility of exact solutions by a source with the baryonic matter state parameter. Our survey indicates that Rastall theory has considerable effects on the wormhole characteristics. In addition, we study various case studies and show that the weak energy condition may be met for some solutions. We also give a discussion regarding to traversability of such wormhole geometry with phantom sources.
Asymptotic methods in mechanics of solids
Bauer, Svetlana M; Smirnov, Andrei L; Tovstik, Petr E; Vaillancourt, Rémi
2015-01-01
The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russi...
Elastohydrodynamic lubrication for line and point contacts asymptotic and numerical approaches
Kudish, Ilya I
2013-01-01
Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches describes a coherent asymptotic approach to the analysis of lubrication problems for heavily loaded line and point contacts. This approach leads to unified asymptotic equations for line and point contacts as well as stable numerical algorithms for the solution of these elastohydrodynamic lubrication (EHL) problems. A Unique Approach to Analyzing Lubrication Problems for Heavily Loaded Line and Point Contacts The book presents a robust combination of asymptotic and numerical techniques to solve EHL p
Asymptotics and Numerics for Laminar Flow over Finite Flat Plate
Dijkstra, D.; Kuerten, J.G.M.; Kaper, Hans G.; Garbey, Mare; Pieper, Gail W.
1992-01-01
A compilation of theoretical results from the literature on the finite flat-plate flow at zero incidence is presented. This includes the Blasius solution, the Triple Deck at the trailing edge, asymptotics in the wake, and properties near the edges of the plate. In addition, new formulas for skin
Asymptotic description of a test particle around a Schwarzschild black hole
Rosales-Vera, Marco
2018-03-01
In this paper, the movement of a test particle around a Schwarzschild black hole is revisited. Using matched asymptotic expansions, approximate analytical expressions for the orbit of the test particle in the case of large eccentricity are found. The asymptotic solutions are compared with numerical and analytical results.
Asymptotic expansion of unsteady gravity flow of a power-law fluid ...
African Journals Online (AJOL)
We present a paper on the asymptotic expansion of unsteady non-linear rheological effects of a power-law fluid under gravity. The fluid flows through a porous medium. The asymptotic expansion is employed to obtain solution of the nonlinear problem. The results show the existence of traveling waves. It is assumed that the ...
On the asymptotic structure of a Navier-Stokes flow past a rotating body
Kyed, Mads
2014-01-01
Consider a rigid body moving with a prescribed constant non-zero velocity and rotating with a prescribed constant non-zero angular velocity in a three-dimensional Navier-Stokes liquid. The asymptotic structure of a steady-state solution to the corresponding equations of motion is analyzed. In particular, an asymptotic expansion of the corresponding velocity field is obtained.
Optimal Homotopy Asymptotic Method for Solving System of Fredholm Integral Equations
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Bahman Ghazanfari
2013-08-01
Full Text Available In this paper, optimal homotopy asymptotic method (OHAM is applied to solve system of Fredholm integral equations. The effectiveness of optimal homotopy asymptotic method is presented. This method provides easy tools to control the convergence region of approximating solution series wherever necessary. The results of OHAM are compared with homotopy perturbation method (HPM and Taylor series expansion method (TSEM.
Asymptotic Dichotomy in a Class of Odd-Order Nonlinear Differential Equations with Impulses
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Kunwen Wen
2013-01-01
Full Text Available We investigate the oscillatory and asymptotic behavior of a class of odd-order nonlinear differential equations with impulses. We obtain criteria that ensure every solution is either oscillatory or (nonoscillatory and zero convergent. We provide several examples to show that impulses play an important role in the asymptotic behaviors of these equations.
Asymptotics of weighted random sums
DEFF Research Database (Denmark)
Corcuera, José Manuel; Nualart, David; Podolskij, Mark
2014-01-01
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral...
Thermodynamics of asymptotically safe theories
DEFF Research Database (Denmark)
Rischke, Dirk H.; Sannino, Francesco
2015-01-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...
Naturalness of asymptotically safe Higgs
DEFF Research Database (Denmark)
Pelaggi, Giulio M.; Sannino, Francesco; Strumia, Alessandro
2017-01-01
that the scalars can be lighter than Λ. Although we do not have an answer to whether the Standard Model hypercharge coupling growth toward a Landau pole at around Λ ~ 1040GeV can be tamed by non-perturbative asymptotic safety, our results indicate that such a possibility is worth exploring. In fact, if successful...
Ruin problems and tail asymptotics
DEFF Research Database (Denmark)
Rønn-Nielsen, Anders
The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived...
Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients
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Eleni Bisognin
2008-03-01
Full Text Available In this work we study the asymptotic behavior of solutions of a dissipative plate equation in $mathbb{R}^N$ with periodic coefficients. We use the Bloch waves decomposition and a convenient Lyapunov function to derive a complete asymptotic expansion of solutions as $to infty$. In a first approximation, we prove that the solutions for the linear model behave as the homogenized heat kernel.
Global Asymptotic Stability for Linear Fractional Difference Equation
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A. Brett
2014-01-01
Full Text Available Consider the difference equation xn+1=(α+∑i=0kaixn-i/(β+∑i=0kbixn-i, n=0,1,…, where all parameters α,β,ai,bi, i=0,1,…,k, and the initial conditions xi, i∈{-k,…,0} are nonnegative real numbers. We investigate the asymptotic behavior of the solutions of the considered equation. We give easy-to-check conditions for the global stability and global asymptotic stability of the zero or positive equilibrium of this equation.
Contact mechanics of articular cartilage layers asymptotic models
Argatov, Ivan
2015-01-01
This book presents a comprehensive and unifying approach to articular contact mechanics with an emphasis on frictionless contact interaction of thin cartilage layers. The first part of the book (Chapters 1–4) reviews the results of asymptotic analysis of the deformational behavior of thin elastic and viscoelastic layers. A comprehensive review of the literature is combined with the authors’ original contributions. The compressible and incompressible cases are treated separately with a focus on exact solutions for asymptotic models of frictionless contact for thin transversely isotropic layers bonded to rigid substrates shaped like elliptic paraboloids. The second part (Chapters 5, 6, and 7) deals with the non-axisymmetric contact of thin transversely isotropic biphasic layers and presents the asymptotic modelling methodology for tibio-femoral contact. The third part of the book consists of Chapter 8, which covers contact problems for thin bonded inhomogeneous transversely isotropic elastic layers, and Cha...
Asymptotic symmetries and electromagnetic memory
Pasterski, Sabrina
2017-09-01
Recent investigations into asymptotic symmetries of gauge theory and gravity have illuminated connections between gauge field zero-mode sectors, the corresponding soft factors, and their classically observable counterparts — so called "memories". Namely, low frequency emissions in momentum space correspond to long time integrations of the corre-sponding radiation in position space. Memory effect observables constructed in this manner are non-vanishing in typical scattering processes, which has implications for the asymptotic symmetry group. Here we complete this triad for the case of large U(1) gauge symmetries at null infinity. In particular, we show that the previously studied electromagnetic memory effect, whereby the passage of electromagnetic radiation produces a net velocity kick for test charges in a distant detector, is the position space observable corresponding to th Weinberg soft photon pole in momentum space scattering amplitudes.
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R. Fares
2012-01-01
Full Text Available We study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and some a priori estimates, we construct an asymptotic solution. The existence of a junction region between the two rectangles imposes to consider, as part of the asymptotic solution, some boundary layer correctors that correspond to this region. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. By means of the a priori estimates, we justify our asymptotic construction, by obtaining a small error between the exact and the asymptotic solutions.
Asymptotic prime partitions of integers
Bartel, Johann; Bhaduri, R. K.; Brack, Matthias; Murthy, M. V. N.
2017-05-01
In this paper, we discuss P (n ) , the number of ways a given integer n may be written as a sum of primes. In particular, an asymptotic form Pas(n ) valid for n →∞ is obtained analytically using standard techniques of quantum statistical mechanics. First, the bosonic partition function of primes, or the generating function of unrestricted prime partitions in number theory, is constructed. Next, the density of states is obtained using the saddle-point method for Laplace inversion of the partition function in the limit of large n . This gives directly the asymptotic number of prime partitions Pas(n ) . The leading term in the asymptotic expression grows exponentially as √{n /ln(n ) } and agrees with previous estimates. We calculate the next-to-leading-order term in the exponent, proportional to ln[ln(n )]/ln(n ) , and we show that an earlier result in the literature for its coefficient is incorrect. Furthermore, we also calculate the next higher-order correction, proportional to 1 /ln(n ) and given in Eq. (43), which so far has not been available in the literature. Finally, we compare our analytical results with the exact numerical values of P (n ) up to n ˜8 ×106 . For the highest values, the remaining error between the exact P (n ) and our Pas(n ) is only about half of that obtained with the leading-order approximation. But we also show that, unlike for other types of partitions, the asymptotic limit for the prime partitions is still quite far from being reached even for n ˜107 .
Root Asymptotics of Spectral Polynomials
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B. Shapiro
2007-01-01
Full Text Available We have been studying the asymptotic energy distribution of the algebraic part of the spectrum of the one-dimensional sextic anharmonic oscillator. We review some (both old and recent results on the multiparameter spectral problem and show that our problem ranks among the degenerate cases of Heine-Stieltjes spectral problem, and we derive the density of the corresponding probability measure.
Holography and Colliding gravitational shock waves in asymptotically AdS5 spacetime.
Chesler, Paul M; Yaffe, Laurence G
2011-01-14
Using holography, we study the collision of planar shock waves in strongly coupled N=4 supersymmetric Yang-Mills theory. This requires the numerical solution of a dual gravitational initial value problem in asymptotically anti-de Sitter spacetime.
Holography and Colliding Gravitational Shock Waves in Asymptotically AdS5 Spacetime
Chesler, Paul M.; Yaffe, Laurence G.
2011-01-01
Using holography, we study the collision of planar shock waves in strongly coupled N=4 supersymmetric Yang-Mills theory. This requires the numerical solution of a dual gravitational initial value problem in asymptotically anti-de Sitter spacetime.
Asymptotic stability of steady compressible fluids
Padula, Mariarosaria
2011-01-01
This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory. The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A h...
Asymptotically Lifshitz spacetimes with universal horizons in (1 +2 ) dimensions
Basu, Sayandeb; Bhattacharyya, Jishnu; Mattingly, David; Roberson, Matthew
2016-03-01
Hořava gravity theory possesses global Lifshitz space as a solution and has been conjectured to provide a natural framework for Lifshitz holography. We derive the conditions on the two-derivative Hořava gravity Lagrangian that are necessary for static, asymptotically Lifshitz spacetimes with flat transverse dimensions to contain a universal horizon, which plays a similar thermodynamic role as the Killing horizon in general relativity. Specializing to z =2 in 1 +2 dimensions, we then numerically construct such regular solutions over the whole spacetime. We calculate the mass for these solutions and show that, unlike the asymptotically anti-de Sitter case, the first law applied to the universal horizon is straightforwardly compatible with a thermodynamic interpretation.
Asymptotics of the filtration problem for suspension in porous media
Directory of Open Access Journals (Sweden)
Kuzmina Ludmila Ivanovna
2015-01-01
Full Text Available The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and are stuck at the inlet of pores that are smaller than the particle size. It is considered that one particle can clog only one small pore and vice versa. The particles stuck in the pores remain motionless and form a deposit. The concentrations of suspended and retained particles satisfy a quasilinear hyperbolic system of partial differential equations of the first order, obtained as a result of macro-averaging of micro-stochastic diffusion equations. Initially the porous media contains no particles and both concentrations are equal to zero; the suspension supplied to the porous media inlet has a constant concentration of suspended particles. The flow of particles moves in the porous media with a constant speed, before the wave front the concentrations of suspended and retained particles are zero. Assuming that the filtration coefficient is small we construct an asymptotic solution of the filtration problem over the concentration front. The terms of the asymptotic expansions satisfy linear partial differential equations of the first order and are determined successively in an explicit form. It is shown that in the simplest case the asymptotics found matches the known asymptotic expansion of the solution near the concentration front.
Numerical Relativity and Asymptotic Flatness
Deadman, E.; Stewart, J. M.
2009-01-01
It is highly plausible that the region of space-time far from an isolated gravitating body is, in some sense, asymptotically Minkowskian. However theoretical studies of the full nonlinear theory, initiated by Bondi et al. (1962), Sachs (1962) and Newman & Unti (1962), rely on careful, clever, a-priori choices of chart (and tetrad) and so are not readily accessible to the numerical relativist, who chooses her/his chart on the basis of quite different grounds. This paper seeks to close this gap...
Modeling broadband poroelastic propagation using an asymptotic approach
Energy Technology Data Exchange (ETDEWEB)
Vasco, Donald W.
2009-05-01
An asymptotic method, valid in the presence of smoothly-varying heterogeneity, is used to derive a semi-analytic solution to the equations for fluid and solid displacements in a poroelastic medium. The solution is defined along trajectories through the porous medium model, in the manner of ray theory. The lowest order expression in the asymptotic expansion provides an eikonal equation for the phase. There are three modes of propagation, two modes of longitudinal displacement and a single mode of transverse displacement. The two longitudinal modes define the Biot fast and slow waves which have very different propagation characteristics. In the limit of low frequency, the Biot slow wave propagates as a diffusive disturbance, in essence a transient pressure pulse. Conversely, at low frequencies the Biot fast wave and the transverse mode are modified elastic waves. At intermediate frequencies the wave characteristics of the longitudinal modes are mixed. A comparison of the asymptotic solution with analytic and numerical solutions shows reasonably good agreement for both homogeneous and heterogeneous Earth models.
Ultraviolet asymptotics of glueball propagators
Bochicchio, Marco; Muscinelli, Samuele P.
2013-08-01
We point out that perturbation theory in conjunction with the renormalization group ( RG) puts a severe constraint on the structure of the large- N non-perturbative glueball propagators in SU( N) pure Y M, in QCD and in = 1 SU SY QCD with massless quarks, or in any confining asymptotically-free gauge theory massless in perturbation theory. For the scalar and pseudoscalar glueball propagators in pure Y M and QCD with massless quarks we check in detail the RG-improved estimate to the order of the leading and next-to-leading logarithms by means of a remarkable three-loop computation by Chetyrkin et al. We investigate as to whether the aforementioned constraint is satisfied by any of the scalar or pseudoscalar glueball propagators computed in the framework of the AdS String/ large- N Gauge Theory correspondence and of a recent proposal based on a Topological Field Theory underlying the large- N limit of Y M . We find that none of the proposals for the scalar or the pseudoscalar glueball propagators based on the AdS String/large- N Gauge Theory correspondence satisfies the constraint, actually as expected, since the gravity side of the correspondence is in fact strongly coupled in the ultraviolet. On the contrary, the Topological Field Theory satisfies the constraint that follows by the asymptotic freedom.
Asymptotically Free Gauge Theories. I
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Asymptotic Behavior for a Class of Nonclassical Parabolic Equations
Yanjun Zhang; Qiaozhen Ma
2013-01-01
This paper is devoted to the qualitative analysis of a class of nonclassical parabolic equations ut-εΔut-ωΔu+f(u)=g(x) with critical nonlinearity, where ε∈[0,1] and ω>0 are two parameters. Firstly, we establish some uniform decay estimates for the solutions of the problem for g(x)∈H-1(Ω), which are independent of the parameter ε. Secondly, some uniformly (with respect to ε∈[0,1]) asymptotic regularity about the solutions has been established for g(x)∈L2(Ω), which shows that the solutions are ...
Non-Tikhonov Asymptotic Properties of Cardiac Excitability
Biktashev, V. N.; Suckley, R.
2004-10-01
Models of electric excitability of cardiac cells can be studied by singular perturbation techniques. To do this one should take into account parameters appearing in equations in nonstandard ways. The physical reason for this is near-perfect switch behavior of ionic current gates. This leads to a definition of excitability different from the currently accepted one. The asymptotic structure revealed by our analysis can be used to devise simplified caricature models, to obtain approximate analytical solutions, and to facilitate numerical simulations.
Local asymptotic stability for nonlinear quadratic functional integral equations
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Bapurao Dhage
2008-03-01
Full Text Available In the present study, using the characterizations of measures of noncompactness we prove a theorem on the existence and local asymptotic stability of solutions for a quadratic functional integral equation via a fixed point theorem of Darbo. The investigations are placed in the Banach space of real functions defined, continuous and bounded on an unbounded interval. An example is indicated to demonstrate the natural realizations of abstract result presented in the paper.
On the accuracy of the asymptotic theory for cylindrical shells
DEFF Research Database (Denmark)
Niordson, Frithiof; Niordson, Christian
1999-01-01
We study the accuracy of the lowest-order bending theory of shells, derived from an asymptotic expansion of the three-dimensional theory of elasticity, by comparing the results of this theory for a cylindrical shell with clamped ends with the results of a solution to the three-dimensional problem....... The results are also compared with those of some commonly used engineering shell theories....
On the accuracy of the asymptotic theory for cylindrical shells
DEFF Research Database (Denmark)
Niordson, Frithiof; Niordson, Christian
1999-01-01
We study the accuracy of the lowest-order bending theory of shells, derived from an asymptotic expansion of the three-dimensional theory of elasticity, by comparing the results of this shell theory for a cylindrical shell with clamped ends with the results of a solution to the three......-dimensional problem. The results are also compared with those of some commonly used engineering shell theories....
Gauge hierarchy problem in asymptotically safe gravity - The resurgence mechanism
Wetterich, Christof; Yamada, Masatoshi
2017-07-01
The gauge hierarchy problem could find a solution within the scenario of asymptotic safety for quantum gravity. We discuss a ;resurgence mechanism; where the running dimensionless coupling responsible for the Higgs scalar mass first decreases in the ultraviolet regime and subsequently increases in the infrared regime. A gravity induced large anomalous dimension plays a crucial role for the required ;self-tuned criticality; in the ultraviolet regime beyond the Planck scale.
Asymptotic and oscillatory behavior of second order neutral quantum equations with maxima
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Douglas Anderson
2009-03-01
Full Text Available In this study, the behavior of solutions to certain second order quantum ($q$-difference equations with maxima are considered. In particular, the asymptotic behavior of non-oscillatory solutions is described, and sufficient conditions for oscillation of all solutions are obtained.
A note on asymptotically anti-de Sitter quantum spacetimes in loop quantum gravity
Bodendorfer, Norbert
2015-01-01
A framework conceptually based on the conformal techniques employed to study the structure of the gravitational field at infinity is set up in the context of loop quantum gravity to describe asymptotically anti-de Sitter quantum spacetimes. A conformal compactification of the spatial slice is performed, which, in terms of the rescaled metric, has now finite volume, and can thus be conveniently described by spin networks states. The conformal factor used is a physical scalar field, which has the necessary asymptotics for many asymptotically AdS black hole solutions.
Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks.
Chen, Boshan; Chen, Jiejie
2015-08-01
We study the global asymptotic ω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ω-periodic or autonomous fractional-order neural networks cannot generate exactly ω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymptotically converge to the same nonconstant ω-periodic function that may be not a solution. Copyright © 2015 Elsevier Ltd. All rights reserved.
Asymptotic dimension of relatively hyperbolic groups
Osin, D. V.
2004-01-01
Suppose that a finitely generated group $G$ is hyperbolic relative to a collection of subgroups $\\{H_1, ..., H_m\\} $. We prove that if each of the subgroups $H_1, ..., H_m$ has finite asymptotic dimension, then asymptotic dimension of $G$ is also finite.
Asymptotically informative prior for Bayesian analysis
Yuan, A.; de Gooijer, J.G.
2011-01-01
In classical Bayesian inference the prior is treated as fixed, it is asymptotically negligible, thus any information contained in the prior is ignored from the asymptotic first order result. However, in practice often an informative prior is summarized from previous similar or the same kind of
Term structure modeling and asymptotic long rate
Yao, Y.
1999-01-01
This paper examines the dynamics of the asymptotic long rate in three classes of term structure models. It shows that, in a frictionless and arbitrage-free market, the asymptotic long rate is a non-decreasing process. This gives an alternative proof of the same result of Dybvig et al. (Dybvig, P.H.,
Asymptotic Floquet states of non-Markovian systems
Magazzú, Luca; Denisov, Sergey; Hänggi, Peter
2017-10-01
We propose a method to find asymptotic states of a class of periodically modulated open systems which are outside the range of validity of the Floquet theory due to the presence of memory effects. The method is based on a Floquet treatment of the time-local, memoryless dynamics taking place in a minimally enlarged state space where the original system is coupled to auxiliary—typically nonphysical—variables. A projection of the Floquet solution into the physical subspace returns the sought asymptotic state of the system. The spectral gap of the Floquet propagator acting in the enlarged state space can be used to estimate the relaxation time. We illustrate the method with a modulated quantum random walk model.
Asymptotically near-optimal RRT for fast, high-quality, motion planning
Salzman, Oren; Halperin, Dan
2013-01-01
We present Lower Bound Tree-RRT (LBT-RRT), a single-query sampling-based algorithm that is asymptotically near-optimal. Namely, the solution extracted from LBT-RRT converges to a solution that is within an approximation factor of 1+epsilon of the optimal solution. Our algorithm allows for a continuous interpolation between the fast RRT algorithm and the asymptotically optimal RRT* and RRG algorithms. When the approximation factor is 1 (i.e., no approximation is allowed), LBT-RRT behaves like ...
Asymptotic ray theory of linear viscoelastic media
Nechtschein, Stephane
The Asymptotic Ray Theory (ART) has become a frequently used technique for the numerical modeling of seismic wave propagation in complex geological models. This theory was originally developed for elastic structures with the ray amplitude computation performed in the time domain. ART is now extended to linear viscoelastic media, the linear theory of viscoelasticity being used to simulate the dispersive properties peculiar to anelastic materials. This extension of ART is based on the introduction of a frequency dependent amplitude term having the same properties as in the elastic case and on a frequency dependent complex phase function. Consequently the ray amplitude computation is now performed in the frequency domain, the final solution being obtained by carrying out an Inverse Fourier Transform. Since ART is used, the boundary conditions for the kinematic and dynamic properties of the waves only have to be satisfied locally. This results in a much simpler Snell's Law for linear viscoelastic media, which in fact turns out to be of the same form as for the elastic case. No complex angle is involved. Furthermore the rays, the ray parameters, the geometrical spreading are all real values implying that the direction of the attenuation vector is always along the ray. The reflection and transmission coefficients were therefore rederived. These viscoelastic ART coefficients behave differently from those obtained with the Plane Wave method. Their amplitude and phase curves are always close to those computed for perfectly elastic media and they smoothly approach the elastic reflection/transmission coefficients when the quality factors increase to infinity. These same ART coefficients also display some non-physical results depending on the choice of the quality factors. This last feature might be useful to determine whether or not the two media making up the interface can be regarded as linear viscoelastic. Finally the results obtained from synthetic seismogram computations
The asymptotic probabilistic genetic algorithm
Galushin, P.; Semenkin, E.
2009-01-01
This paper proposes the modification of probabilistic genetic algorithm, which uses genetic operators, not affecting the particular solutions, but the probabilities distribution of solution vector's components. This paper also compares the reliability and efficiency of the base algorithm and proposed modification using the set of test optimization problems and bank loan portfolio problem.
Asymptotic methods for wave and quantum problems
Karasev, M V
2003-01-01
The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper "Quantization and Intrinsic Dynamics" a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approxi
Asymptotic behavior for a quadratic nonlinear Schrodinger equation
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Pavel I. Naumkin
2008-02-01
Full Text Available We study the initial-value problem for the quadratic nonlinear Schrodinger equation $$displaylines{ iu_{t}+frac{1}{2}u_{xx}=partial _{x}overline{u}^{2},quad xin mathbb{R},; t>1, cr u(1,x=u_{1}(x,quad xin mathbb{R}. }$$ For small initial data $u_{1}in mathbf{H}^{2,2}$ we prove that there exists a unique global solution $uin mathbf{C}([1,infty ;mathbf{H}^{2,2}$ of this Cauchy problem. Moreover we show that the large time asymptotic behavior of the solution is defined in the region $|x|leq Csqrt{t}$ by the self-similar solution $frac{1}{sqrt{t}}MS(frac{x}{sqrt{t}}$ such that the total mass $$ frac{1}{sqrt{t}}int_{mathbb{R}}MS(frac{x}{sqrt{t}} dx=int_{mathbb{R}}u_{1}(xdx, $$ and in the far region $|x|>sqrt{t}$ the asymptotic behavior of solutions has rapidly oscillating structure similar to that of the cubic nonlinear Schrodinger equations.
A quantum kinematics for asymptotically flat spacetimes
Campiglia, Miguel
2014-01-01
We construct a quantum kinematics for asymptotically flat spacetimes based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying Loop Quantum Gravity (LQG) which supports, in addition to the usual LQG operators, the action of `background exponential operators' which are connection dependent operators labelled by `background' $su(2)$ electric fields. KS states have, in addition to the LQG state label corresponding to 1 dimensional excitations of the triad, a label corresponding to a `background' electric field which describes 3 dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields which label the {\\em states} and the background electric fields which label the {\\em operators}. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We...
Global dynamics and asymptotics for monomial scalar field potentials and perfect fluids
Alho, Artur; Uggla, Claes
2015-01-01
We consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat FLRW cosmology. We apply local and global dynamical systems techniques to a new three-dimensional dynamical systems reformulation of the field equations on a compact state space. This leads to a visual global description of the solution space and asymptotic behavior. At late times we employ averaging techniques to prove statements about how the relationship between the equation of state of the fluid and the monomial exponent of the scalar field affects asymptotic source dominance and asymptotic manifest self-similarity breaking. We also situate the `attractor' solution in the three-dimensional state space and show that it corresponds to the one-dimensional unstable center manifold of a de Sitter fixed point, located on an unphysical boundary associated with the dynamics at early times. By deriving a center manifold expansion we obtain approximate expressions for the attractor solution. We subsequently improve th...
Asymptotic and Numerical Methods for Rapidly Rotating Buoyant Flow
Grooms, Ian G.
This thesis documents three investigations carried out in pursuance of a doctoral degree in applied mathematics at the University of Colorado (Boulder). The first investigation concerns the properties of rotating Rayleigh-Benard convection -- thermal convection in a rotating infinite plane layer between two constant-temperature boundaries. It is noted that in certain parameter regimes convective Taylor columns appear which dominate the dynamics, and a semi-analytical model of these is presented. Investigation of the columns and of various other properties of the flow is ongoing. The second investigation concerns the interactions between planetary-scale and mesoscale dynamics in the oceans. Using multiple-scale asymptotics the possible connections between planetary geostrophic and quasigeostrophic dynamics are investigated, and three different systems of coupled equations are derived. Possible use of these equations in conjunction with the method of superparameterization, and extension of the asymptotic methods to the interactions between mesoscale and submesoscale dynamics is ongoing. The third investigation concerns the linear stability properties of semi-implicit methods for the numerical integration of ordinary differential equations, focusing in particular on the linear stability of IMEX (Implicit-Explicit) methods and exponential integrators applied to systems of ordinary differential equations arising in the numerical solution of spatially discretized nonlinear partial differential equations containing both dispersive and dissipative linear terms. While these investigations may seem unrelated at first glance, some reflection shows that they are in fact closely linked. The investigation of rotating convection makes use of single-space, multiple-time-scale asymptotics to deal with dynamics strongly constrained by rotation. Although the context of thermal convection in an infinite layer seems somewhat removed from large-scale ocean dynamics, the asymptotic
Asymptotics of work distributions in a stochastically driven system
Manikandan, Sreekanth K.; Krishnamurthy, Supriya
2017-12-01
We determine the asymptotic forms of work distributions at arbitrary times T, in a class of driven stochastic systems using a theory developed by Nickelsen and Engel (EN theory) [D. Nickelsen and A. Engel, Eur. Phys. J. B 82, 207 (2011)], which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in path integral form, are characterised by having quadratic augmented actions. We first illustrate EN theory, for a deterministically driven system - the breathing parabola model, and show that within its framework, the Crooks fluctuation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial, which also determines the exact moment-generating-function at arbitrary times. We then extend our analysis to a stochastically driven system, studied in references [S. Sabhapandit, EPL 89, 60003 (2010); A. Pal, S. Sabhapandit, Phys. Rev. E 87, 022138 (2013); G. Verley, C. Van den Broeck, M. Esposito, New J. Phys. 16, 095001 (2014)], for both equilibrium and non-equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary T. For dissipated work in the steady state, we compare the large T asymptotic behaviour of our solution to the functional form obtained in reference [New J. Phys. 16, 095001 (2014)]. In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with numerical simulations. Our solutions are exact in the low noise (β → ∞) limit.
Asymptotic Behavior of the Maximum Entropy Routing in Computer Networks
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Milan Tuba
2013-01-01
Full Text Available Maximum entropy method has been successfully used for underdetermined systems. Network design problem, with routing and topology subproblems, is an underdetermined system and a good candidate for maximum entropy method application. Wireless ad-hoc networks with rapidly changing topology and link quality, where the speed of recalculation is of crucial importance, have been recently successfully investigated by maximum entropy method application. In this paper we prove a theorem that establishes asymptotic properties of the maximum entropy routing solution. This result, besides being theoretically interesting, can be used to direct initial approximation for iterative optimization algorithms and to speed up their convergence.
Nonspherically Symmetric Collapse in Asymptotically AdS Spacetimes
Bantilan, Hans; Figueras, Pau; Kunesch, Markus; Romatschke, Paul
2017-11-01
We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative cosmological constant in five spacetime dimensions and obtain a family of nonspherically symmetric solutions, including those that form two distinct black holes on the axis. We find that these configurations collapse faster than spherically symmetric ones of the same mass and radial compactness. Similarly, they require less mass to collapse within a fixed time.
Gatignol, Renée; Croizet, Cédric
2017-04-01
Asymptotic models are constructed to investigate the basic physical phenomena of thermal flows of a mixture of two monatomic gases inside a two-dimensional microchannel. The steady flows are described by the Navier-Stokes-Fourier balance equations, with additional coupling terms in momentum and energy equations, and with first-order slip boundary conditions for the velocities and jump boundary conditions for the temperatures on the two walls. The small parameter equal to the ratio of the two longitudinal and transverse lengths is introduced, and then an asymptotic model is proposed. It corresponds to small Mach numbers and small or moderate Knudsen numbers. Attention is paid to the first-order asymptotic solutions. Results are given and discussed for different cases: the mass flow rates, the molecular weights of the gases, and the temperature gradients along the walls. Comparisons between the first-order asymptotic solutions and Direct Simulation Monte Carlo (DSMC) simulations corresponding to the same physical data show rather good agreement. It should be noted that obtaining an asymptotic solution is very fast compared to obtaining a DSMC result.
Sharp asymptotics for Einstein-$\\lambda$-dust flows
Friedrich, Helmut
2016-01-01
We consider the Einstein-dust equations with positive cosmological constant $\\lambda$ on manifolds with time slices diffeomorphic to an orientable, compact 3-manifold $S$. It is shown that the set of standard Cauchy data for the Einstein-$\\lambda$-dust equations on $S$ contains an open (in terms of suitable Sobolev norms) subset of data that develop into solutions which admit at future time-like infinity a space-like conformal boundary ${\\cal J}^+$ that is $C^{\\infty}$ if the data are of class $C^{\\infty}$ and of correspondingly lower smoothness otherwise. As a particular case follows a strong stability result for FLRW solutions. The solutions can conveniently be characterized in terms of their asymptotic end data induced on ${\\cal J}^+$, only a linear equation must be solved to construct such data. In the case where the energy density $\\hat{\\rho}$ is everywhere positive such data can be constructed without solving any differential equation at all.
Conference on Boundary and Interior Layers : Computational and Asymptotic Methods
Stynes, Martin; Zhang, Zhimin
2017-01-01
This volume collects papers associated with lectures that were presented at the BAIL 2016 conference, which was held from 14 to 19 August 2016 at Beijing Computational Science Research Center and Tsinghua University in Beijing, China. It showcases the variety and quality of current research into numerical and asymptotic methods for theoretical and practical problems whose solutions involve layer phenomena. The BAIL (Boundary And Interior Layers) conferences, held usually in even-numbered years, bring together mathematicians and engineers/physicists whose research involves layer phenomena, with the aim of promoting interaction between these often-separate disciplines. These layers appear as solutions of singularly perturbed differential equations of various types, and are common in physical problems, most notably in fluid dynamics. This book is of interest for current researchers from mathematics, engineering and physics whose work involves the accurate app roximation of solutions of singularly perturbed diffe...
Sharp Asymptotics for Einstein-{λ}-Dust Flows
Friedrich, Helmut
2017-03-01
We consider the Einstein-dust equations with positive cosmological constant {λ} on manifolds with time slices diffeomorphic to an orientable, compact 3-manifold {S}. It is shown that the set of standard Cauchy data for the Einstein-{λ}-dust equations on {S} contains an open (in terms of suitable Sobolev norms) subset of data which develop into solutions that admit at future time-like infinity a space-like conformal boundary J^+ that is C^{∞} if the data are of class C^{∞} and of correspondingly lower smoothness otherwise. The class of solutions considered here comprises non-linear perturbations of FLRW solutions as very special cases. It can conveniently be characterized in terms of asymptotic end data induced on J^+. These data must only satisfy a linear differential equation. If the energy density is everywhere positive they can be constructed without solving differential equations at all.
Asymptotically AdS spacetimes with a timelike Kasner singularity
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Ren, Jie [Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2016-07-21
Exact solutions to Einstein’s equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution’s appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The entanglement entropy and Wilson loops are discussed. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimensional reduction.
Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion
Cui, Xia; Yuan, Guang-wei; Shen, Zhi-jun
2016-05-01
Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-order accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion.
Directory of Open Access Journals (Sweden)
Maria de Hoyos Guajardo, Ph.D. Candidate, M.Sc., B.Eng.
2004-11-01
Full Text Available The theory that is presented below aims to conceptualise how a group of undergraduate students tackle non-routine mathematical problems during a problem-solving course. The aim of the course is to allow students to experience mathematics as a creative process and to reflect on their own experience. During the course, students are required to produce a written ‘rubric’ of their work, i.e., to document their thoughts as they occur as well as their emotionsduring the process. These ‘rubrics’ were used as the main source of data.Students’ problem-solving processes can be explained as a three-stage process that has been called ‘solutioning’. This process is presented in the six sections below. The first three refer to a common area of concern that can be called‘generating knowledge’. In this way, generating knowledge also includes issues related to ‘key ideas’ and ‘gaining understanding’. The third and the fourth sections refer to ‘generating’ and ‘validating a solution’, respectively. Finally, once solutions are generated and validated, students usually try to improve them further before presenting them as final results. Thus, the last section deals with‘improving a solution’. Although not all students go through all of the stages, it may be said that ‘solutioning’ considers students’ main concerns as they tackle non-routine mathematical problems.
Asymptotics of eigenfunctions for Sturm-Liouville problem in difference equations
Bas, Erdal; Ozarslan, Ramazan
2016-06-01
In this study, Sturm-Liouville problem with variable coefficient, potential function q (n), for difference equation is considered. The representation of solutions is obtained by variation of parameters method for two different initial value problems and trigonometric solutions are found by means of complex characteristic roots. It is proved that these results hold the equation by using summation by parts method. Two estimations of asymptotic expansion of the solutions are established.
Non-Abelian Higgs models: Paving the way for asymptotic freedom
Gies, Holger; Zambelli, Luca
2017-07-01
Asymptotically free renormalization group trajectories can be constructed in non-Abelian Higgs models with the aid of generalized boundary conditions imposed on the renormalized action. We detail this construction within the languages of simple low-order perturbation theory, effective field theory, as well as modern functional renormalization group equations. We construct a family of explicit scaling solutions using a controlled weak-coupling expansion in the ultraviolet, and obtain a standard Wilsonian renormalization group relevance classification of perturbations about scaling solutions. We obtain global information about the quasifixed function for the scalar potential by means of analytic asymptotic expansions and numerical shooting methods. Further analytical evidence for such asymptotically free theories is provided in the large-N limit. We estimate the long-range properties of these theories and identify initial/boundary conditions giving rise to a conventional Higgs phase.
The optimal homotopy asymptotic method engineering applications
Marinca, Vasile
2015-01-01
This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011, and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five application...
Exact Asymptotics of Bivariate Scale Mixture Distributions
Hashorva, Enkelejd
2009-01-01
Let (RU_1, R U_2) be a given bivariate scale mixture random vector, with R>0 being independent of the bivariate random vector (U_1,U_2). In this paper we derive exact asymptotic expansions of the tail probability P{RU_1> x, RU_2> ax}, a \\in (0,1] as x tends infintiy assuming that R has distribution function in the Gumbel max-domain of attraction and (U_1,U_2) has a specific tail behaviour around some absorbing point. As a special case of our results we retrieve the exact asymptotic behaviour ...
Asymptotically flat spacetimes with BMS3 symmetry
Compère, Geoffrey; Fiorucci, Adrien
2017-10-01
We construct the phase space of 3-dimensional asymptotically flat spacetimes that forms the bulk metric representation of the BMS group consisting of both supertranslations and superrotations. The asymptotic symmetry group is a unique copy of the BMS group at both null infinities and spatial infinity. The BMS phase space obeys a notion of holographic causality and can be parametrized by boundary null fields. This automatically leads to the antipodal identification of bulk fields between past and future null infinity in the absence of a global conical defect.
Dujardin, G. M.
2009-08-12
This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas\\' transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over. © 2009 The Royal Society.
Asymptotic behavior of solutions of forced fractional differential equations
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Said Grace
2016-09-01
where $y(t=\\left( a(tx^{\\prime }(t\\right ^{\\prime }$, $c_{0}=\\frac{y(c}{\\Gamma (1}=y(c$, and $c_{0}$ is a real constant. The technique used in obtaining their results will apply to related fractional differential equations with Caputo derivatives of any order. Examples illustrate the results obtained in this paper.
Diffusion on Viscous Fluids, Existence and Asymptotic Properties of Solutions,
1983-09-01
Matematica - Politecuico di Milano (1982). 11.* P. Secchi "On the Initial Value ProbleM for the Nquations of Notion of Viscous Incompressible Fluids In...of two viscous Incompressible Fluids’, preprint DepartLmento dl matematica - Politecuico di Milano (1982). -15- 11. P. Secchi 00n the XnitiaI Value
Asymptotic Stability Results of Solutions of Neutral Delay Systems ...
African Journals Online (AJOL)
In this paper, a retarded delay system is transformed to a class of neutral delay system using the differentiability condition of the functional on the Banach space. The Leibnez-Newton formula and symmetric properties of some chosen matrices are utilized to formulate a Lyapunov functional of the transformed system, which ...
Bulk Viscous Matter-dominated Universes: Asymptotic Properties
Avelino, Arturo; Gonzalez, Tame; Nucamendi, Ulises; Quiros, Israel
2013-01-01
By means of a combined study of the type Ia supernovae test,together with a study of the asymptotic properties in the equivalent phase space -- through the use of the dynamical systems tools -- we demonstrate that the bulk viscous matter-dominated scenario is not a good model to explain the accepted cosmological paradigm, at least, under the parametrization of bulk viscosity considered in this paper. The main objection against such scenarios is the absence of conventional radiation and matter-dominated critical points in the phase space of the model. This entails that radiation and matter dominance are not generic solutions of the cosmological equations, so that these stages can be implemented only by means of very particular solutions. Such a behavior is in marked contradiction with the accepted cosmological paradigm which requires of an earlier stage dominated by relativistic species, followed by a period of conventional non-relativistic matter domination, during which the cosmic structure we see was formed...
Formation of compression waves with multiscale asymptotics in the Burgers and KdV models
Zakharov, Sergei V.
2015-01-01
The Cauchy problem for the Burgers equation with a small dissipation and an initial weak discontinuity and the Cauchy problem with a large initial gradient for a quasilinear parabolic equation and for the Korteweg-de Vries (KdV) equation are considered. Multiscale asymptotics of solutions corresponding to shock waves are constructed. Some results can also be applied to rarefaction waves.
Asymptotic freedom in the early big bang and the isotropy of the cosmic microwave background
Stecker, F. W.
1980-01-01
It is suggested that a superunified field theory incorporating gravity and possessing asymptotic freedom could provide a solution to the problem of the isotropy of the universal 3 K background radiation. Thermal equilibrium could be established in this context through interactions occurring in a temporally indefinite pre-Planckian era.
Asymptotic freedom in the early big-bang and the isotropy of the cosmic microwave background
Stecker, F. W.
1979-01-01
The isotropy of the universal 3K background radiation is discussed and a superunified field theory incorporating gravity and possessing asymptotic freedom is suggested to provide a solution to the problem. Thermal equilibrium is established in this context through interactions occurring in a temporally indefinite preplanckian era.
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
Directory of Open Access Journals (Sweden)
Leonid Berezansky
2005-04-01
Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.
The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces
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Rabian Wangkeeree
2012-01-01
Full Text Available We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.
DEFF Research Database (Denmark)
Jensen, Tom Nørgaard; Wisniewski, Rafal
2014-01-01
directional actuator constraints is addressed. The proposed solution consists of a set of decentralized positively constrained proportional control actions. The results show that the closed-loop system always has a globally asymptotically stable equilibrium point independently on the number of end...
On iterative procedures of asymptotic inference
K.O. Dzhaparidze (Kacha)
1983-01-01
textabstractAbstract An informal discussion is given on performing an unconstrained maximization or solving non‐linear equations of statistics by iterative methods with the quadratic termination property. It is shown that if a miximized function, e.g. likelihood, is asymptotically quadratic, then
Term structure extrapolation and asymptotic forward rates
de Kort, J.; Vellekoop, M.H.
2015-01-01
We investigate different inter- and extrapolation methods for term structures under different constraints in order to generate market-consistent estimates which describe the asymptotic behavior of forward rates. Our starting point is the method proposed by Smith and Wilson, which is used by the
Fixed Point Theorems for Asymptotically Contractive Multimappings
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M. Djedidi
2012-01-01
Full Text Available We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. Some existence results of coincidence points and eigenvalues for multimappings are given.
Supersymmetric asymptotic safety is not guaranteed
DEFF Research Database (Denmark)
Intriligator, Kenneth; Sannino, Francesco
2015-01-01
in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those...
Asymptotic symmetries, holography and topological hair
Mishra, Rashmish K.; Sundrum, Raman
2018-01-01
Asymptotic symmetries of AdS4 quantum gravity and gauge theory are derived by coupling the holographically dual CFT3 to Chern-Simons gauge theory and 3D gravity in a "probe" (large-level) limit. Despite the fact that the three-dimensional AdS4 boundary as a whole is consistent with only finite-dimensional asymptotic symmetries, given by AdS isometries, infinite-dimensional symmetries are shown to arise in circumstances where one is restricted to boundary subspaces with effectively two-dimensional geometry. A canonical example of such a restriction occurs within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS4 quantum gravity. An AdS4 analog of Minkowski "super-rotation" asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT2 structure (in a large central charge limit), via AdS3 foliation of AdS4 and the AdS3/CFT2 correspondence. The maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D gravities have Chern-Simons formulation, manifesting their topological character. Chern-Simons structure is also shown to be emergent in the Poincare patch of AdS4, as soft/boundary limits of 4D gauge theory, rather than "put in by hand" as an external probe. This results in a finite effective Chern-Simons level. Several of the considerations of asymptotic symmetry structure are found to be simpler for AdS4 than for Mink4, such as non-zero 4D particle masses, 4D non-perturbative "hard" effects, and consistency with unitarity. The last of these in particular is greatly simplified because in some set-ups the time dimension is explicitly shared by each level of description: Lorentzian AdS4, CFT3 and CFT2. Relatedly, the CFT2 structure clarifies the sense in which the infinite asymptotic charges constitute a useful form of "hair" for black holes and other complex 4D states. An AdS4 analog of Minkowski "memory" effects is derived, but with late-time memory of earlier events being replaced by (holographic) "shadow" effects. Lessons
An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation
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Hakeem Ullah
2014-01-01
Full Text Available We consider the approximate solution of the coupled Schrödinger-KdV equation by using the extended optimal homotopy asymptotic method (OHAM. We obtained the extended OHAM solution of the problem and compared with the exact, variational iteration method (VIM and homotopy perturbation method (HPM solutions. The obtained solution shows that extended OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.
Exploring central opacity and asymptotic scenarios in elastic hadron scattering
Fagundes, D. A.; Menon, M. J.; Silva, P. V. R. G.
2016-02-01
In the absence of a global description of the experimental data on elastic and soft diffractive scattering from the first principles of QCD, model-independent analyses may provide useful phenomenological insights for the development of the theory in the soft sector. With that in mind, we present an empirical study on the energy dependence of the ratio X between the elastic and total cross sections; a quantity related to the evolution of the hadronic central opacity. The dataset comprises all the experimental information available on proton-proton and antiproton-proton scattering in the c.m. energy interval 5 GeV-8 TeV. Generalizing previous works, we discuss four model-independent analytical parameterizations for X, consisting of sigmoid functions composed with elementary functions of the energy and three distinct asymptotic scenarios: either the standard black disk limit or scenarios above or below that limit. Our two main conclusions are the following: (1) although consistent with the experimental data, the black disk does not represent an unique solution; (2) the data reductions favor a semi-transparent scenario, with asymptotic average value for the ratio X bar = 0.30 ± 0.12. In this case, within the uncertainty, the asymptotic regime may already be reached around 1000 TeV. We present a comparative study of the two scenarios, including predictions for the inelastic channel (diffraction dissociation) and the ratio associated with the total cross-section and the elastic slope. Details on the selection of our empirical ansatz for X and physical aspects related to a change of curvature in this quantity at 80-100 GeV, indicating the beginning of a saturation effect, are also presented and discussed.
Asymptotics of QCD traveling waves with fluctuations and running coupling effects
Beuf, Guillaume
2008-09-01
Extending the Balitsky-Kovchegov (BK) equation independently to running coupling or to fluctuation effects due to pomeron loops is known to lead in both cases to qualitative changes of the traveling-wave asymptotic solutions. In this paper we study the extension of the forward BK equation, including both running coupling and fluctuations effects, extending the method developed for the fixed coupling case [E. Brunet, B. Derrida, A.H. Mueller, S. Munier, Phys. Rev. E 73 (2006) 056126, cond-mat/0512021]. We derive the exact asymptotic behavior in rapidity of the probabilistic distribution of the saturation scale.
Laminar flow and convective transport processes scaling principles and asymptotic analysis
Brenner, Howard
1992-01-01
Laminar Flow and Convective Transport Processes: Scaling Principles and Asymptotic Analysis presents analytic methods for the solution of fluid mechanics and convective transport processes, all in the laminar flow regime. This book brings together the results of almost 30 years of research on the use of nondimensionalization, scaling principles, and asymptotic analysis into a comprehensive form suitable for presentation in a core graduate-level course on fluid mechanics and the convective transport of heat. A considerable amount of material on viscous-dominated flows is covered.A unique feat
Asymptotic approximations for non-integer order derivatives of monomials
Aşiru, Muniru A.
2015-02-01
In this note, we develop new, simple and very accurate asymptotic approximations for non-integer order derivatives of monomial functions by using the more accurate asymptotic approximations for large factorials that have recently appeared in the literature.
Induction motor IFOC based speed-controlled drive with asymptotic disturbance compensation
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Stojić Đorđe M.
2012-01-01
Full Text Available This paper presents the design of digitally controlled speed electrical drive, with the asymptotic compensation of external disturbances, implemented by using the IFOC (Indirect Field Oriented Control torque controlled induction motor. The asymptotic disturbance compensation is achieved by using the DOB (Disturbance Observer with the IMP (Internal Model Principle. When compared to the existing IMP-based DOB solutions, in this paper the robust stability and disturbance compensation are improved by implementing the minimal order DOB filter. Also, the IMP-based DOB design is improved by employing the asymptotic compensation of all elemental or more complex external disturbances. The dynamic model of the IFOC torque electrical drive is, also, included in the speed-controller and DOB section design. The simulation and experimental measurements presented in the paper illustrate the effectiveness and robustness of the proposed control scheme.
Asymptotic modelling of a thermopiezoelastic anisotropic smart plate
Long, Yufei
Motivated by the requirement of modelling for space flexible reflectors as well as other applications of plate structures in engineering, a general anisotropic laminated thin plate model and a monoclinic Reissner-Mindlin plate model with thermal deformation, two-way coupled piezoelectric effect and pyroelectric effect is constructed using the variational asymptotic method, without any ad hoc assumptions. Total potential energy contains strain energy, electric potential energy and energy caused by temperature change. Three-dimensional strain field is built based on the concept of warping function and decomposition of the rotation tensor. The feature of small thickness and large in-plane dimension of plate structure helped to asymptotically simplify the three-dimensional analysis to a two-dimensional analysis on the reference surface and a one-dimensional analysis through the thickness. For the zeroth-order approximation, the asymptotically correct expression of energy is derived into the form of energetic equation in classical laminated plate theory, which will be enough to predict the behavior of plate structures as thin as a space flexible reflector. A through-the-thickness strain field can be expressed in terms of material constants and two-dimensional membrane and bending strains, while the transverse normal and shear stresses are not predictable yet. In the first-order approximation, the warping functions are further disturbed into a high order and an asymptotically correct energy expression with derivatives of the two-dimensional strains is acquired. For the convenience of practical use, the expression is transformed into a Reissner-Mindlin form with optimization implemented to minimize the error. Transverse stresses and strains are recovered using the in-plane strain variables. Several numerical examples of different laminations and shapes are studied with the help of analytical solutions or shell elements in finite element codes. The constitutive relation is
Gravitational geons in asymptotically anti-de Sitter spacetimes
Martinon, Grégoire; Fodor, Gyula; Grandclément, Philippe; Forgács, Peter
2017-06-01
We report on numerical constructions of fully non-linear geons in asymptotically anti-de Sitter (AdS) spacetimes in four dimensions. Our approach is based on 3 + 1 formalism and spectral methods in a gauge combining maximal slicing and spatial harmonic coordinates. We are able to construct several families of geons seeded by different families of spherical harmonics. We can reach unprecedentedly high amplitudes, with mass of order ∼1/2 of the AdS length, and with deviations of the order of 50% compared to third order perturbative approaches. The consistency of our results with numerical resolution is carefully checked and we give extensive precision monitoring techniques. All global quantities, such as mass and angular momentum, are computed using two independent frameworks that agree with each other at the 0.1% level. We also provide strong evidence for the existence of ‘excited’ (i.e. with one radial node) geon solutions of Einstein equations in asymptotically AdS spacetimes by constructing them numerically.
Asymptotically simple spacetimes and mass loss due to gravitational waves
Saw, Vee-Liem
The cosmological constant Λ used to be a freedom in Einstein’s theory of general relativity (GR), where one had a proclivity to set it to zero purely for convenience. The signs of Λ or Λ being zero would describe universes with different properties. For instance, the conformal structure of spacetime directly depends on Λ: null infinity ℐ is a spacelike, null, or timelike hypersurface, if Λ > 0, Λ = 0, or Λ 0 in Einstein’s theory of GR. A quantity that depends on the conformal structure of spacetime, especially on the nature of ℐ, is the Bondi mass which in turn dictates the mass loss of an isolated gravitating system due to energy carried away by gravitational waves. This problem of extending the Bondi mass to a universe with Λ > 0 has spawned intense research activity over the past several years. Some aspects include a closer inspection on the conformal properties, working with linearization, attempts using a Hamiltonian formulation based on “linearized” asymptotic symmetries, as well as obtaining the general asymptotic solutions of de Sitter-like spacetimes. We consolidate on the progress thus far from the various approaches that have been undertaken, as well as discuss the current open problems and possible directions in this area.
Numerical Solution for an Epicycloid Crack
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Nik Mohd Asri Nik Long
2014-01-01
linear equations. Numerical solution for the shear stress intensity factors, maximum stress intensity, and strain energy release rate is obtained. Our results give an excellent agreement to the existing asymptotic solutions.
Gerbi, Stéphane
2011-12-01
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.
Asymptotic expansions for the Gaussian unitary ensemble
DEFF Research Database (Denmark)
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian...... aj(g), j ¿ N, as distributions (in the sense of L. Schwarts). We derive a similar asymptotic expansion for the covariance Cov{Trn[f(Xn)], Trn[g(Xn)]}, where f is a function of the same kind as g, and Trn = n trn. Special focus is drawn to the case where and for ¿, µ in C\\R. In this case the mean...
Kink fluctuation asymptotics and zero modes
Energy Technology Data Exchange (ETDEWEB)
Izquierdo, A.A. [Universidad de Salamanca, Departamento de Matematica Aplicada and IUFFyM, Salamanca (Spain); Guilarte, J.M. [Universidad de Salamanca, Departamento de Fisica Fundamental and IUFFyM, Salamanca (Spain)
2012-10-15
In this paper we propose a refinement of the heat-kernel/zeta function treatment of kink quantum fluctuations in scalar field theory, further analyzing the existence and implications of a zero-energy fluctuation mode. Improved understanding of the interplay between zero modes and the kink heat-kernel expansion delivers asymptotic estimations of one-loop kink mass shifts with remarkably higher precision than previously obtained by means of the standard Gilkey-DeWitt heat-kernel expansion. (orig.)
Theorems for asymptotic safety of gauge theories
Bond, Andrew D.; Litim, Daniel F.
2017-06-01
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.
Long-time asymptotics for the derivative nonlinear Schrödinger equation on the half-line
Arruda, Lynnyngs Kelly; Lenells, Jonatan
2017-11-01
We derive asymptotic formulas for the solution of the derivative nonlinear Schrödinger equation on the half-line under the assumption that the initial and boundary values lie in the Schwartz class. The formulas clearly show the effect of the boundary on the solution. The approach is based on a nonlinear steepest descent analysis of an associated Riemann–Hilbert problem.
Asymptotic expansions and the possibilities to drop the hypotheses in the prandtl problem
Georgievskii, D. V.
2009-02-01
The plane problem on the quasistatic compression of a thin perfectly plastic layer between undeformable rough plates (the Prandtl problem) has a well-known analytic solution at all points sufficiently far from the midsection and endpoints of the layer. Both the static and the kinematic component of this solution were obtained on the basis of the Prandtl hypothesis [1] stating that the tangential stress is linear along the layer thickness and is maximal in absolute value on the plate surfaces. (If the plates are perfectly rough, then this maximum value coincides with the shear yield stress.) The Prandtl hypothesis was widely confirmed in experiments carried out after the paper [1] had been published. At the same time, it is natural to ask whether one can construct a classical solution of this problem without imposing any static or kinematic hypotheses on the unknown variables and whether there exist any other mathematical solutions in which these hypotheses do not hold and which themselves are not observed in experiments. In the present paper, we use asymptotic analysis with a natural small geometric parameter and uniquely determine an exact solution (in the sense of finiteness of the number of terms in the asymptotic expansion), which coincides with the Prandtl solution generalized to the case of an arbitrary roughness coefficient of the plates. We rigorously show that such asymptotics cannot hold near the layer midsection, where we construct another, internal asymptotic expansion. In the abovementioned sense, the solution corresponding to the internal expansion is also exact and models the compression of a thin vertical strip in the middle of the layer. We realize two possible versions of matching of the two expansions in the cross-section whose distance from the midsection is equal to the layer thickness.
Avoidance of singularities in asymptotically safe Quantum Einstein Gravity
Energy Technology Data Exchange (ETDEWEB)
Kofinas, Georgios [Research Group of Geometry, Dynamical Systems and Cosmology,Department of Information and Communication Systems Engineering,University of the Aegean, Karlovassi 83200, Samos (Greece); Zarikas, Vasilios [Department of Electrical Engineering, Theory Division, ATEI of Central Greece,35100 Lamia (Greece); Department of Physics, Aristotle University of Thessaloniki,54124 Thessaloniki (Greece)
2015-10-30
New general spherically symmetric solutions have been derived with a cosmological “constant” Λ as a source. This Λ term is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed point. The importance of these solutions comes from the fact that they may describe the near to the centre region of black hole spacetimes as this is modified by the Renormalization Group scaling behaviour of the fields. The consistent set of field equations which respect the Bianchi identities is derived and solved. One of the solutions (with conventional sign of temporal-radial metric components) is timelike geodesically complete, and although there is still a curvature divergent origin, this is never approachable by an infalling massive particle which is reflected at a finite distance due to the repulsive origin. Another family of solutions (of both signatures) range from a finite radius outwards, they cannot be extended to the centre of spherical symmetry, and the curvature invariants are finite at the minimum radius.
Polynomial asymptotic stability of damped stochastic differential equations
Directory of Open Access Journals (Sweden)
John Appleby
2004-08-01
Full Text Available The paper studies the polynomial convergence of solutions of a scalar nonlinear It\\^{o} stochastic differential equation\\[dX(t = -f(X(t\\,dt + \\sigma(t\\,dB(t\\] where it is known, {\\it a priori}, that $\\lim_{t\\rightarrow\\infty} X(t=0$, a.s. The intensity of the stochastic perturbation $\\sigma$ is a deterministic, continuous and square integrable function, which tends to zero more quickly than a polynomially decaying function. The function $f$ obeys $\\lim_{x\\rightarrow 0}\\mbox{sgn}(xf(x/|x|^\\beta = a$, for some $\\beta>1$, and $a>0$.We study two asymptotic regimes: when $\\sigma$ tends to zero sufficiently quickly the polynomial decay rate of solutions is the same as for the deterministic equation (when $\\sigma\\equiv0$. When $\\sigma$ decays more slowly, a weaker almost sure polynomial upper bound on the decay rate of solutions is established. Results which establish the necessity for $\\sigma$ to decay polynomially in order to guarantee the almost sure polynomial decay of solutions are also proven.
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.
Baranwal, Vipul K; Pandey, Ram K; Singh, Om P
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations
Baranwal, Vipul K.; Pandey, Ram K.
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems. PMID:27437484
Asymptotic Waveform Evaluation (AWE) Technique for Frequency Domain Electromagnetic Analysis
Cockrell, C. R.; Beck, F. B.
1996-01-01
The Asymptotic Waveform Evaluation (AWE) technique is applied to a generalized frequency domain electromagnetic problem. Most of the frequency domain techniques in computational electromagnetics result in a matrix equation, which is solved at a single frequency. In the AWE technique, the Taylor series expansion around that frequency is applied to the matrix equation. The coefficients of the Taylor's series are obtained in terms of the frequency derivatives of the matrices evaluated at the expansion frequency. The coefficients hence obtained will be used to predict the frequency response of the system over a frequency range. The detailed derivation of the coefficients (called 'moments') is given along with an illustration for electric field integral equation (or Method of Moments) technique. The radar cross section (RCS) frequency response of a square plate is presented using the AWE technique and is compared with the exact solution at various frequencies.
INVESTIGATION OF STURM-LIOUVILLE PROBLEM SOLVABILITY IN THE PROCESS OF ASYMPTOTIC SERIES CREATION
Directory of Open Access Journals (Sweden)
A. I. Popov
2015-09-01
Full Text Available Subject of Research. Creation of asymptotic expansions for solutions of partial differential equations with small parameter reduces, usually, to consequent solving of the Sturm-Liouville problems chain. To find some term of the series, the non-homogeneous Sturm-Liouville problem with the inhomogeneity depending on the previous term needs to be solved. At the same time, the corresponding homogeneous problem has a non-trivial solution. Hence, the solvability problem occures for the non-homogeneous Sturm-Liouville problem for functions or formal power series. The paper deals with creation of such asymptotic expansions. Method. To prove the necessary condition, we use conventional integration technique of the whole equation and boundary conditions. To prove the sufficient condition, we create an appropriate Cauchy problem (which is always solvable and analyze its solution. We deal with the general case of power series and make no hypotheses about the series convergence. Main Result. Necessary and sufficient conditions of solvability for the non-homogeneous Sturm-Liouville problem in general case for formal power series are proved in the paper. As a particular case, the result is valid for functions instead of formal power series. Practical Relevance. The result is usable at creation of the solutions for partial differential equation in the form of power series. The result is general and is applicable to particular cases of such solutions, e.g., to asymptotic series or to functions (convergent power series.
Callan-Symanzik equation and asymptotic freedom in the Marr-Shimamoto model
Scarfone, Leonard M.
2010-05-01
The exactly soluble nonrelativistic Marr-Shimamoto model was introduced in 1964 as an example of the Lee model with a propagator and a nontrivial vertex function. An exactly soluble relativistic version of this model, known as the Zachariasen model, has been found to be asymptotically free in terms of coupling constant renormalization at an arbitrary spacelike momentum and on the basis of exact solutions of the Gell-Mann-Low equations. This is accomplished with conventional cut-off regularization by setting up the Yukawa and Fermi coupling constants at Euclidean momenta in terms of on mass-shell couplings and then taking the asymptotic limit. In view of this background, it may be expected that an investigation of the nonrelativistic Marr-Shimamoto theory may also exhibit asymptotic freedom in view of its manifest mathematical similarity to that of the Zachariasen model. To prove this point, the present paper prefers to examine asymptotic freedom in the nonrelativistic Marr-Shimamoto theory using the powerful concepts of the renormalization group and the Callan-Symanzik equation, in conjunction with the specificity of dimensional regularization and on-shell renormalization. This approach is based on calculations of the Callan-Symanzik coefficients and determinations of the effective coupling constants. It is shown that the Marr-Shimamoto theory is asymptotically free for dimensions D 3 occurring in periodic intervals over the range of 0
Asymptotic Representations of Quantum Affine Superalgebras
Zhang, Huafeng
2017-08-01
We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of Kirillov-Reshetikhin modules based on a cyclicity result that we established previously on tensor products of these modules, and realize their inductive limits as modules over its Borel subalgebra, the so-called q-Yangian. A new generic asymptotic limit of the same inductive systems is proposed, resulting in modules over the full quantum affine superalgebra. We derive generalized Baxter's relations in the sense of Frenkel-Hernandez for representations of the full quantum group.
Asymptotically safe inflation from quadratic gravity
Bonanno, Alfio
2015-01-01
Asymptotically Safe theories of gravity have recently received much attention. In this work we discuss a class of inflationary models derived from quantum-gravity modification of quadratic gravity according to the induced scaling around the non-Gaussian fixed point at very high energies. It is argued that the presence of a three dimensional ultraviolet critical surface generates operators of non-integer power of the type $R^{2-\\theta/2}$ in the effective Lagrangian, where $\\theta>0$ is a critical exponent. The requirement of a successful inflationary model in agreement with the recent Planck 2015 data puts important constraints on the strenght of this new type of couplings.
Discrete dispersion models and their Tweedie asymptotics
DEFF Research Database (Denmark)
Jørgensen, Bent; Kokonendji, Célestin C.
2016-01-01
in this approach, whereas several overdispersed discrete distributions, such as the Neyman Type A, Pólya-Aeppli, negative binomial and Poisson-inverse Gaussian, turn out to be Poisson-Tweedie factorial dispersion models with power dispersion functions, analogous to ordinary Tweedie exponential dispersion models......-Tweedie asymptotic framework where Poisson-Tweedie models appear as dilation limits. This unifies many discrete convergence results and leads to Poisson and Hermite convergence results, similar to the law of large numbers and the central limit theorem, respectively. The dilation operator also leads to a duality...
Lectures on the asymptotic theory of ideals
Rees, D
1988-01-01
In this book Professor Rees introduces and proves some of the main results of the asymptotic theory of ideals. The author's aim is to prove his Valuation Theorem, Strong Valuation Theorem, and Degree Formula, and to develop their consequences. The last part of the book is devoted to mixed multiplicities. Here the author develops his theory of general elements of ideals and gives a proof of a generalised degree formula. The reader is assumed to be familiar with basic commutative algebra, as covered in the standard texts, but the presentation is suitable for advanced graduate students. The work
Asymptotic granularity reduction and its application
Su, Shenghui; Lü, Shuwang; Fan, Xiubin
2011-01-01
It is well known that the inverse function of y = x with the derivative y' = 1 is x = y, the inverse function of y = c with the derivative y' = 0 is inexistent, and so on. Hence, on the assumption that the noninvertibility of the univariate increasing function y = f(x) with x > 0 is in direct proportion to the growth rate reflected by its derivative, the authors put forward a method of comparing difficulties in inverting two functions on a continuous or discrete interval called asymptotic gra...
On the Asymptotics of Takeuchi Numbers
Prellberg, Thomas
2000-01-01
I present an asymptotic formula for the Takeuchi numbers $T_n$. In particular, I give compelling numerical evidence and present a heuristic argument showing that $$T_n\\sim C_T B_n\\exp{1\\over2}{W(n)}^2$$as $n$ tends to infinity, where $B_n$ are the Bell numbers, W(n) is Lambert's $W$ function, and $C_T=2.239...$ is a constant. Moreover, I show that the method presented here can be generalized to derive conjectures for related problems.
Subordinated diffusion and continuous time random walk asymptotics.
Dybiec, Bartłomiej; Gudowska-Nowak, Ewa
2010-12-01
Anomalous transport is usually described either by models of continuous time random walks (CTRWs) or, otherwise, by fractional Fokker-Planck equations (FFPEs). The asymptotic relation between properly scaled CTRW and fractional diffusion process has been worked out via various approaches widely discussed in literature. Here, we focus on a correspondence between CTRWs and time and space fractional diffusion equation stemming from two different methods aimed to accurately approximate anomalous diffusion processes. One of them is the Monte Carlo simulation of uncoupled CTRW with a Lévy α-stable distribution of jumps in space and a one-parameter Mittag-Leffler distribution of waiting times. The other is based on a discretized form of a subordinated Langevin equation in which the physical time defined via the number of subsequent steps of motion is itself a random variable. Both approaches are tested for their numerical performance and verified with known analytical solutions for the Green function of a space-time fractional diffusion equation. The comparison demonstrates a trade off between precision of constructed solutions and computational costs. The method based on the subordinated Langevin equation leads to a higher accuracy of results, while the CTRW framework with a Mittag-Leffler distribution of waiting times provides efficiently an approximate fundamental solution to the FFPE and converges to the probability density function of the subordinated process in a long-time limit. © 2010 American Institute of Physics.
Asymptotical analysis and Padé approximation in problems on diffusion-controlled cracks propagation
Directory of Open Access Journals (Sweden)
Alla V. Balueva
2012-07-01
Full Text Available In this work, we consider the diffusion-controlled axisymmetric fracture in an infinite space, and half-space. An important example of diffusion-controlled fracture growth is given by hydrogen induced cracking. In metals, hydrogen is typically dissolved in the proton form. When protons reach the crack surface, they recombine with electrons and form molecular hydrogen in the crack cavity. Then, the fracture can propagate even in the absence of any external loading, that is, only under the excessive pressure of gas hydrogen accumulated inside the crack. Our results show that in the long-time asymptotic approximation (based on the quasi-static solution, the diffusion-controlled delamination propagates with constant velocity. We determine a maximum critical concentration that limits the use of the quasi-static solution. A transient solution, representing a short time asymptotic approximation, is used when the concentration of gas exceeds the critical concentration. We then match these two end-member cases by using the method of Padé approximations and present closed-form solutions for both internal and near-surface diffusion-controlled crack propagation at different time scales. Keywords: diffusion, crack propagation, asymptotic analysis, Padé approximation. Mathematics Subject Classification: 74A45, 74N25, 41A21.
Frenod, Emmanuel
2013-01-01
In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes.
Integrable theories that are asymptotically CFT
Evans, J M; Jonathan M Evans; Timothy J Hollowood
1995-01-01
A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level k. In contrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered here may be termed ``asymptotically CFT''. These theories have previously been conjectured to be quantum integrable; we confirm this by proposing a factorizable S-matrix to describe their infra-red behaviour and then carrying out a stringent test of this proposal. The test involves coupling the theory to a conserved charge and evaluating the response of the free-energy both in perturbation theory to one loop and directly from the S-matrix via the Thermodynamic Bethe Ansatz with a chemical potential at zero temperature. Comparison of these results provides convincing evidence in favour of the proposed S-matrix; it also yields the universal coefficients of the beta-func...
Asymptotic accuracy of two-class discrimination
Energy Technology Data Exchange (ETDEWEB)
Ho, T.K.; Baird, H.S. [AT& T Bell Laboratories, Murray Hill, NJ (United States)
1994-12-31
Poor quality-e.g. sparse or unrepresentative-training data is widely suspected to be one cause of disappointing accuracy of isolated-character classification in modern OCR machines. We conjecture that, for many trainable classification techniques, it is in fact the dominant factor affecting accuracy. To test this, we have carried out a study of the asymptotic accuracy of three dissimilar classifiers on a difficult two-character recognition problem. We state this problem precisely in terms of high-quality prototype images and an explicit model of the distribution of image defects. So stated, the problem can be represented as a stochastic source of an indefinitely long sequence of simulated images labeled with ground truth. Using this sequence, we were able to train all three classifiers to high and statistically indistinguishable asymptotic accuracies (99.9%). This result suggests that the quality of training data was the dominant factor affecting accuracy. The speed of convergence during training, as well as time/space trade-offs during recognition, differed among the classifiers.
Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers
Marinca, Vasile; Ene, Remus-Daniel; Bereteu, Liviu
2017-10-01
Dynamic response time is an important feature for determining the performance of magnetorheological (MR) dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.
Optimal homotopy asymptotic method for solving fractional relaxation-oscillation equation
Directory of Open Access Journals (Sweden)
Mohammad Hamarsheh
2015-11-01
Full Text Available In this paper, an approximate analytical solution of linear fractional relaxation-oscillation equations in which the fractional derivatives are given in the Caputo sense, is obtained by the optimal homotopy asymptotic method (OHAM. The studied OHAM is based on minimizing the residual error. The results given by OHAM are compared with the exact solutions and the solutions obtained by generalized Taylor matrix method. The reliability and efficiency of the proposed approach are demonstrated in three examples with the aid of the symbolic algebra program Maple.
Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity
Directory of Open Access Journals (Sweden)
Anyin Xia
2013-01-01
Full Text Available The asymptotic behavior of the solution for the Dirichlet problem of the parabolic equation with nonlocal term ut=urr+ur/r+f(u/(a+2πb∫01f(urdr2, for 00,u1,t=u′(0,t=0, for t>0, ur,0=u0r, for 0≤r≤1. The model prescribes the dimensionless temperature when the electric current flows through two conductors, subject to a fixed potential difference. One of the electrical resistivity of the axis-symmetric conductor depends on the temperature and the other one remains constant. The main results show that the temperature remains uniformly bounded for the generally decreasing function f(s, and the global solution of the problem converges asymptotically to the unique equilibrium.
Transport of radionuclides in stochastic media. Pt. 1: The quasi-asymptotic approximation
Energy Technology Data Exchange (ETDEWEB)
Devooght, J.; Smidts, O.F. [Universite Libre de Bruxelles (Belgium). Service de Metrologie Nucleaire
1996-04-01
A three-dimensional quasi-asymptotic approximate equation is developed for the transport of radionuclides in a stochastic velocity field. This approximation is derived from an integro-differential equation of transport in stochastic media, commonly encountered in hydrogeology. The quasi-asymptotic equation turns out to be a generalised Telegrapher`s equation as found by Williams in the particular context of fractured media. We obtain the Telegrapher`s equation without specifying the causes responsible for the random velocity field. Our model may thus be applied in porous media as well as in fractured media. We give the developments leading to the analytical solution of the three-dimensional Telegrapher`s equation for constant parameters. This solution is then visualised for a source in the form of a square wave. (Author).
Optimal homotopy asymptotic method for solving Volterra integral equation of first kind
Directory of Open Access Journals (Sweden)
N. Khan
2014-09-01
Full Text Available In this paper, authors demonstrate the efficiency of optimal homotopy asymptotic method (OHAM. This is done by solving nonlinear Volterra integral equation of first kind. OHAM is applied to Volterra integral equations which involves exponential, trigonometric function as their kernels. It is observed that solution obtained by OHAM is more accurate than existing techniques, which proves its validity and stability for solving Volterra integral equation of first kind.
Optimal homotopy asymptotic method for solving Volterra integral equation of first kind
Khan, N; Hashmi, M.S.; Iqbal, S.; Mahmood, T
2014-01-01
In this paper, authors demonstrate the efficiency of optimal homotopy asymptotic method (OHAM). This is done by solving nonlinear Volterra integral equation of first kind. OHAM is applied to Volterra integral equations which involves exponential, trigonometric function as their kernels. It is observed that solution obtained by OHAM is more accurate than existing techniques, which proves its validity and stability for solving Volterra integral equation of first kind.
On asymptotic stability in energy space of ground states of NLS in 2D
Cuccagna, Scipio; Tarulli, Mirko
2009-01-01
We transpose work by K.Yajima and by T.Mizumachi to prove dispersive and smoothing estimates for dispersive solutions of the linearization at a ground state of a Nonlinear Schr\\"odinger equation (NLS) in 2D. As an application we extend to dimension 2D a result on asymptotic stability of ground states of NLS proved in the literature for all dimensions different from 2.
On asymptotic stability in energy space of ground states of NLS in 2D
Cuccagna, Scipio; Tarulli, Mirko
2009-07-01
We transpose work by K.Yajima and by T.Mizumachi to prove dispersive and smoothing estimates for dispersive solutions of the linearization at a ground state of a Nonlinear Schr\\"odinger equation (NLS) in 2D. As an application we extend to dimension 2D a result on asymptotic stability of ground states of NLS proved in the literature for all dimensions different from 2.
Gauge hierarchy problem in asymptotically safe gravity — The resurgence mechanism
Directory of Open Access Journals (Sweden)
Christof Wetterich
2017-07-01
Full Text Available The gauge hierarchy problem could find a solution within the scenario of asymptotic safety for quantum gravity. We discuss a “resurgence mechanism” where the running dimensionless coupling responsible for the Higgs scalar mass first decreases in the ultraviolet regime and subsequently increases in the infrared regime. A gravity induced large anomalous dimension plays a crucial role for the required “self-tuned criticality” in the ultraviolet regime beyond the Planck scale.
Asymptotic behaviour for a thermoelastic problem of a microbeam with thermoelasticity of type III
Directory of Open Access Journals (Sweden)
Roberto Díaz
2017-11-01
Full Text Available In this paper we study the asymptotic behavior of a equation modeling a microbeam moving transversally, coupled with an equation describing a heat pulse on it. Such pulse is given by a type III of the Green–Naghdi model, providing a more realistic model of heat flow from a physics point of view. We use semigroups theory to prove existence and uniqueness of solutions of our model, and multiplicative techniques to prove exponentially stable of its associated semigroup.
Directory of Open Access Journals (Sweden)
Liang-cai Zhao
2012-01-01
Full Text Available The purpose of this paper is to introduce a class of total quasi-ϕ-asymptotically nonexpansive-nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the corresponding results announced by some authors recently.
A universal asymptotic regime in the hyperbolic nonlinear\\ud Schrodinger equation
Ablowitz, Mark; Ma, Yi-Ping; Rumanov, Igor
2017-01-01
The appearance of a fundamental long-time asymptotic regime in the two space one time dimensional hyperbolic nonlinear Schrodinger (HNLS) equation is discussed. Based on analytical and numerical simulations, a wide range of initial conditions corresponding to initial lumps of moderate energy are found to approach a quasi-self-similar solution. Even relatively large initial amplitudes, which imply strong nonlinear effects, eventually lead to local structures resembling those of the self-simila...
Saw, Vee-Liem
2016-01-01
We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $\\Lambda$, using the Newman-Penrose formalism. Our approach is based exclusively on the physical spacetime, i.e. no reference of conformal rescaling nor conformal spacetime is made, at least not explicitly. By investigating the Schwarzschild-de Sitter spacetime in spherical coordinates, we subsequently stipulate the fall-offs of the null tetrad and spin coefficients for asymptotically de Sitter spacetimes such that the terms which would give rise to the Bondi mass-loss due to energy carried by gravitational radiation (i.e. involving $\\sigma^o$) must be non-zero. After solving the vacuum Newman-Penrose equations asymptotically, we obtain the Bondi mass-loss formula by integrating the Bianchi identity involving $D'\\Psi_2$ over a compact 2-surface on $\\mathcal{I}$. Whilst our original intention was to study asymptotically de Sitter spacetimes, the use of spherical coordinates implies that this readily applies for $\\Lambd...
Asymptotic variance of grey-scale surface area estimators
DEFF Research Database (Denmark)
Svane, Anne Marie
Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in isotropic and sufficiently smooth settings, resulting...... in a general asymptotic bound. For compact convex sets with nowhere vanishing Gaussian curvature, the asymptotics can be described more explicitly. As in the case of volume estimators, the variance is decomposed into a lattice sum and an oscillating term of at most the same magnitude....
Soft pion theorem, asymptotic symmetry and new memory effect
Hamada, Yuta; Sugishita, Sotaro
2017-11-01
It is known that soft photon and graviton theorems can be regarded as the Ward-Takahashi identities of asymptotic symmetries. In this paper, we consider soft theorem for pions, i.e., Nambu-Goldstone bosons associated with a spontaneously broken axial symmetry. The soft pion theorem is written as the Ward-Takahashi identities of the S-matrix under asymptotic transformations. We investigate the asymptotic dynamics, and find that the conservation of charges generating the asymptotic transformations can be interpreted as a pion memory effect.
Asymptotic expansions for high-contrast elliptic equations
Calo, Victor M.
2014-03-01
In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in [Domain decomposition preconditioners for multiscale flows in high-contrast media, Multiscale Model Simul. 8 (2010) 1461-1483] where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high-and low-conductivity inclusions. © 2014 World Scientific Publishing Company.
Bulk viscous matter-dominated Universes: asymptotic properties
Energy Technology Data Exchange (ETDEWEB)
Avelino, Arturo [Departamento de Física, Campus León, Universidad de Guanajuato, León, Guanajuato (Mexico); García-Salcedo, Ricardo [Centro de Investigacion en Ciencia Aplicada y Tecnologia Avanzada - Legaria del IPN, México D.F. (Mexico); Gonzalez, Tame [Departamento de Ingeniería Civil, División de Ingeniería, Universidad de Guanajuato, Guanajuato (Mexico); Nucamendi, Ulises [Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, CP. 58040 Morelia, Michoacán (Mexico); Quiros, Israel, E-mail: avelino@fisica.ugto.mx, E-mail: rigarcias@ipn.mx, E-mail: tamegc72@gmail.com, E-mail: ulises@ifm.umich.mx, E-mail: iquiros6403@gmail.com [Departamento de Matemáticas, Centro Universitario de Ciencias Exactas e Ingenierías (CUCEI), Corregidora 500 S.R., Universidad de Guadalajara, 44420 Guadalajara, Jalisco (Mexico)
2013-08-01
By means of a combined use of the type Ia supernovae and H(z) data tests, together with the study of the asymptotic properties in the equivalent phase space — through the use of the dynamical systems tools — we demonstrate that the bulk viscous matter-dominated scenario is not a good model to explain the accepted cosmological paradigm, at least, under the parametrization of bulk viscosity considered in this paper. The main objection against such scenarios is the absence of conventional radiation and matter-dominated critical points in the phase space of the model. This entails that radiation and matter dominance are not generic solutions of the cosmological equations, so that these stages can be implemented only by means of unique and very specific initial conditions, i. e., of very unstable particular solutions. Such a behavior is in marked contradiction with the accepted cosmological paradigm which requires of an earlier stage dominated by relativistic species, followed by a period of conventional non-relativistic matter domination, during which the cosmic structure we see was formed. Also, we found that the bulk viscosity is positive just until very late times in the cosmic evolution, around z < 1. For earlier epochs it is negative, been in tension with the local second law of thermodynamics.
The asymptotic complexity of merging networks
DEFF Research Database (Denmark)
Miltersen, Peter Bro; Paterson, Mike; Tarui, Jun
1996-01-01
Let M(m,n) be the minimum number of comparatorsneeded in a comparator network that merges m elements x1≤x2≤&cdots;≤xm and n elements y1≤y2≤&cdots;≤yn , where n≥m . Batcher's odd-even merge yields the following upper bound: Mm,n≤1 2m+nlog 2m+on; in particular, Mn,n≤nlog 2n+On. We prove the following...... lower bound that matches the upper bound above asymptotically as n≥m→∞: Mm,n≥1 2m+nlog 2m-Om; in particular, Mn,n≥nlog 2n-On. Our proof technique extends to give similarily tight lower bounds for the size of monotone Boolean circuits for merging, and for the size of switching networks capable...... of realizing the set of permutations that arise from merging....
Asymptotic freedom beyond the leading order
Buras, Andrzej J; Ross, D A; Sachrajda, Christopher T C
1977-01-01
The authors make a quantitative analysis of the full G/sup 2/ interaction corrections to the leading Q/sup 2/ dependence of nu W/sub 2/ at x>or=0.4, as given by an asymptotically free gauge theory. It turns out that due to partial cancellations between various contributions the g/sup 2/ corrections are small. The best fit with the SLAC ep data after including the g/sup 2/ corrections is almost identical to that without these corrections, the only effect being a change in Lambda , the one free parameter, which sets the scale of the theory. On the other hand the effect of including target mass corrections is to improve the agreement of the prediction for nu W/sub 2//sup ep/ with data for large values of x. (20 refs).
Asymptotic representation of relaxation oscillations in lasers
Grigorieva, Elena V
2017-01-01
In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
Motion Parallax is Asymptotic to Binocular Disparity
Stroyan, Keith
2010-01-01
Researchers especially beginning with (Rogers & Graham, 1982) have noticed important psychophysical and experimental similarities between the neurologically different motion parallax and stereopsis cues. Their quantitative analysis relied primarily on the "disparity equivalence" approximation. In this article we show that retinal motion from lateral translation satisfies a strong ("asymptotic") approximation to binocular disparity. This precise mathematical similarity is also practical in the sense that it applies at normal viewing distances. The approximation is an extension to peripheral vision of (Cormac & Fox's 1985) well-known non-trig central vision approximation for binocular disparity. We hope our simple algebraic formula will be useful in analyzing experiments outside central vision where less precise approximations have led to a number of quantitative errors in the vision literature.
Correlation at low temperature;2, Asymptotics
Bach, V
2003-01-01
The present paper is a continuation of our paper [Bach-Moller mp_arc 02-215] where the truncated two-point correlation function for a class of lattice spin systems was proved to have exponential decay at low temperature, under a weak coupling assumption. In this paper we compute the asymptotics of the correlation function as the temperature goes to zero. This paper thus extends [Bach-Jecko-Sjostrand, mp_arc 98-552] in two directions: The Hamiltonian function is allowed to have several local minima other than a unique global minimum, and we do not require translation invariance of the Hamiltonian function. We are in particular able to handle spin systems on a general lattice.
Asymptotic theory of weakly dependent random processes
Rio, Emmanuel
2017-01-01
Presenting tools to aid understanding of asymptotic theory and weakly dependent processes, this book is devoted to inequalities and limit theorems for sequences of random variables that are strongly mixing in the sense of Rosenblatt, or absolutely regular. The first chapter introduces covariance inequalities under strong mixing or absolute regularity. These covariance inequalities are applied in Chapters 2, 3 and 4 to moment inequalities, rates of convergence in the strong law, and central limit theorems. Chapter 5 concerns coupling. In Chapter 6 new deviation inequalities and new moment inequalities for partial sums via the coupling lemmas of Chapter 5 are derived and applied to the bounded law of the iterated logarithm. Chapters 7 and 8 deal with the theory of empirical processes under weak dependence. Lastly, Chapter 9 describes links between ergodicity, return times and rates of mixing in the case of irreducible Markov chains. Each chapter ends with a set of exercises. The book is an updated and extended ...
Asymptotic properties of restricted naming games
Bhattacherjee, Biplab; Datta, Amitava; Manna, S. S.
2017-07-01
Asymptotic properties of the symmetric and asymmetric naming games have been studied under some restrictions in a community of agents. In one version, the vocabulary sizes of the agents are restricted to finite capacities. In this case, compared to the original naming games, the dynamics takes much longer time for achieving the consensus. In the second version, the symmetric game starts with a limited number of distinct names distributed among the agents. Three different quantities are measured for a quantitative comparison, namely, the maximum value of the total number of names in the community, the time at which the community attains the maximal number of names, and the global convergence time. Using an extensive numerical study, the entire set of three power law exponents characterizing these quantities are estimated for both the versions which are observed to be distinctly different from their counter parts of the original naming games.
Asymptotically Honest Confidence Regions for High Dimensional
DEFF Research Database (Denmark)
Caner, Mehmet; Kock, Anders Bredahl
While variable selection and oracle inequalities for the estimation and prediction error have received considerable attention in the literature on high-dimensional models, very little work has been done in the area of testing and construction of confidence bands in high-dimensional models. However...... of the asymptotic covariance matrix of an increasing number of parameters which is robust against conditional heteroskedasticity. To our knowledge we are the first to do so. Next, we show that our confidence bands are honest over sparse high-dimensional sub vectors of the parameter space and that they contract...... at the optimal rate. All our results are valid in high-dimensional models. Our simulations reveal that the desparsified conservative Lasso estimates the parameters much more precisely than the desparsified Lasso, has much better size properties and produces confidence bands with markedly superior coverage rates....
Lattice quantum gravity and asymptotic safety
Laiho, J.; Bassler, S.; Coumbe, D.; Du, D.; Neelakanta, J. T.
2017-09-01
We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we argue that the target symmetry is the general coordinate invariance of the theory. After introducing and fine-tuning a nontrivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with 3 /2 , a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue that the number of relevant couplings in the continuum theory is one, once symmetry breaking by the lattice regulator is accounted for. Such a theory is maximally predictive, with no adjustable parameters. The cosmological constant in Planck units is the only relevant parameter, which serves to set the lattice scale. The cosmological constant in Planck units is of order 1 in the ultraviolet and undergoes renormalization group running to small values in the infrared. If these findings hold up under further scrutiny, the lattice may provide a nonperturbative definition of a renormalizable quantum field theory of general relativity with no adjustable parameters and a cosmological constant that is naturally small in the infrared.
Asymptotic stability of an Euler-Bernoulli beam coupled to non-linear spring-damper systems
Gorrec, Yann Le; Zwart, Hans; Ramirez, Hector
2017-01-01
The stability of an undamped Euler Bernoulli beam connected to non-linear mass spring damper systems is addressed. It is shown that under mild assumptions on the local behaviour of the non-linear springs and dampers the solutions exist and the system is globally asymptotically stable.
New wormhole solutions on the brane
Parsaei, F.; Riazi, N.
2015-01-01
In this paper, static wormholes in the brane-world scenario are studied. We show that the existence of extra terms coming from the bulk help construct exact solutions that satisfy the null energy condition. Two important classes of solutions found earlier are analyzed in more depth in order to determine the conditions necessary for consistent solutions. Two new classes of solutions with different asymptotic behavior are also introduced. We focus on the conservation of the stress-energy tensor to achieve new solutions which have the important property of asymptotic flatness. Some main mathematical and physical properties of the solutions are addressed.
Asymptotic representation theorems for poverty indices | Lo | Afrika ...
African Journals Online (AJOL)
Abstract. We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotic of the bulk of poverty indices and issues in poverty ...
Asymptotic size determines species abundance in the marine size spectrum
DEFF Research Database (Denmark)
Andersen, Ken Haste; Beyer, Jan
2006-01-01
The majority of higher organisms in the marine environment display indeterminate growth; that is, they continue to grow throughout their life, limited by an asymptotic size. We derive the abundance of species as a function of their asymptotic size. The derivation is based on size-spectrum theory...
Comparison of the asymptotic stability properties for two multirate strategies
V. Savcenco (Valeriu)
2007-01-01
textabstractThis paper contains a comparison of the asymptotic stability properties for two multirate strategies. For each strategy, the asymptotic stability regions are presented for a 2 x 2 test problem and the differences between the results are discussed. The considered multirate schemes use
Journal Afrika Statistika ISSN 0852-0305 Asymptotic representation ...
African Journals Online (AJOL)
Abstract. We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotic of the bulk of poverty indices and issues in poverty ...
Numerical algorithms for uniform Airy-type asymptotic expansions
N.M. Temme (Nico)
1997-01-01
textabstractAiry-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing
An efficient locally asymptotic parametric test in nonlinear ...
African Journals Online (AJOL)
Abstract. In this paper we deal with a locally asymptotic stringent test for a general class of nonlinear time series heteroscedastic models. Based on the local asymptotic normality (LAN) property of these models, we propose a scoretyp test statistic for testing hypotheses on the parameters appearing in the mean and variance ...
Asymptotic distribution of products of sums of independent random ...
Indian Academy of Sciences (India)
453007 Henan, China. E-mail: bigduckwyl@163.com; duhongxia24@gmail.com. MS received 7 April 2012; revised 10 October 2012. Abstract. In the paper we consider the asymptotic distribution of products of weighted sums of independent random variables. Keywords. Asymptotic distribution; products of sums. 1.
Asymptotic expansions for high-contrast linear elasticity
Poveda, Leonardo A.
2015-03-01
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.
Numerical and asymptotic aspects of parabolic cylinder functions
N.M. Temme (Nico)
2000-01-01
textabstractSeveral uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic expansions given earlier by F.W.J. Olver. Some of his
Large-time behavior of solutions of linear dispersive equations
Dix, Daniel B
1997-01-01
This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension. Complete matched and uniformly-valid asymptotic expansions are obtained and sharp error estimates are proved. Using the method of steepest descent much new information on the regularity and spatial asymptotics of the solutions are also obtained. Applications to nonlinear dispersive equations are discussed. This monograph is intended for researchers and graduate students of partial differential equations. Familiarity with basic asymptotic, complex and Fourier analysis is assumed.
An Optimal Homotopy Asymptotic Approach Applied to Nonlinear MHD Jeffery-Hamel Flow
Directory of Open Access Journals (Sweden)
Vasile Marinca
2011-01-01
Full Text Available A simple and effective procedure is employed to propose a new analytic approximate solution for nonlinear MHD Jeffery-Hamel flow. This technique called the Optimal Homotopy Asymptotic Method (OHAM does not depend upon any small/large parameters and provides us with a convenient way to control the convergence of the solution. The examples given in this paper lead to the conclusion that the accuracy of the obtained results is growing along with increasing the number of constants in the auxiliary function, which are determined using a computer technique. The results obtained through the proposed method are in very good agreement with the numerical results.
Oliveira, José J.
2017-10-01
In this paper, we investigate the global convergence of solutions of non-autonomous Hopfield neural network models with discrete time-varying delays, infinite distributed delays, and possible unbounded coefficient functions. Instead of using Lyapunov functionals, we explore intrinsic features between the non-autonomous systems and their asymptotic systems to ensure the boundedness and global convergence of the solutions of the studied models. Our results are new and complement known results in the literature. The theoretical analysis is illustrated with some examples and numerical simulations.
Asymptotic behaviors of a cell-to-cell HIV-1 infection model perturbed by white noise
Liu, Qun
2017-02-01
In this paper, we analyze a mathematical model of cell-to-cell HIV-1 infection to CD4+ T cells perturbed by stochastic perturbations. First of all, we investigate that there exists a unique global positive solution of the system for any positive initial value. Then by using Lyapunov analysis methods, we study the asymptotic property of this solution. Moreover, we discuss whether there is a stationary distribution for this system and if it owns the ergodic property. Numerical simulations are presented to illustrate the theoretical results.
Energy Technology Data Exchange (ETDEWEB)
Shin, U.; Miller, W.F. Jr. [California Univ., Berkeley, CA (United States)]|[Los Alamos National Lab., NM (United States); Morel, J.E. [Los Alamos National Lab., NM (United States)
1994-10-01
Using conventional diffusion limit analysis, we asymptotically compare three competitive time-dependent equations (the telegrapher`s equation, the time-dependent Simplified P{sub 2} (SP{sub 2}) equation, and the time-dependent Simplified Evcn-Parity (SEP) equation). The time-dependent SP{sub 2} equation contains higher order asymptotic approximations of the time-dependent transport equation than the other equations in a physical regime in which the time-dependent diffusion equation is the leading order approximation. In addition, we derive the multigroup modified time-dependent SP{sub 2} equation from the multigroup time-dependent transport equation by means of an asymptotic expansion in which the multigroup time-dependent diffusion equation is the leading, order approximation. Numerical comparisons of the timedependent diffusion, the telegrapher`s, the time-dependent SP{sub 2}, and S{sub 8} solutions in 2-D X-Y geometry show that, in most cases, the SP{sub 2} solutions contain most of the transport corrections for the diffusion approximation.
Dilts, James
2016-01-01
For each set of (freely chosen) seed data, the conformal method reduces the Einstein constraint equations to a system of elliptic equations, the conformal constraint equations. We prove an admissibility criterion, based on a (conformal) prescribed scalar curvature problem, which provides a necessary condition on the seed data for the conformal constraint equations to (possibly) admit a solution. We then consider sets of asymptotically Euclidean (AE) seed data for which solutions of the conformal constraint equations exist, and examine the blowup properties of these solutions as the seed data sets approach sets for which no solutions exist. We also prove that there are AE seed data sets which include a Yamabe nonpositive metric and lead to solutions of the conformal constraints. These data sets allow the mean curvature function to have zeroes.
Characterization of (asymptotically) Kerr-de Sitter-like spacetimes at null infinity
Mars, Marc; Paetz, Tim-Torben; Senovilla, José M. M.; Simon, Walter
2016-08-01
We investigate solutions ({M},g) to Einstein's vacuum field equations with positive cosmological constant Λ which admit a smooth past null infinity {{I}}- à la Penrose and a Killing vector field whose associated Mars-Simon tensor (MST) vanishes. The main purpose of this work is to provide a characterization of these spacetimes in terms of their Cauchy data on {{I}}-. Along the way, we also study spacetimes for which the MST does not vanish. In that case there is an ambiguity in its definition which is captured by a scalar function Q. We analyze properties of the MST for different choices of Q. In doing so, we are led to a definition of ‘asymptotically Kerr-de Sitter-like spacetimes’, which we also characterize in terms of their asymptotic data on {{I}}-. Preprint UWThPh-2016-5.
A multiscale asymptotic analysis of time evolution equations on the complex plane
Energy Technology Data Exchange (ETDEWEB)
Braga, Gastão A., E-mail: gbraga@mat.ufmg.br [Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 30161-970 Belo Horizonte, MG (Brazil); Conti, William R. P., E-mail: wrpconti@gmail.com [Departamento de Ciências do Mar, Universidade Federal de São Paulo, Rua Dr. Carvalho de Mendonça 144, 11070-100 Santos, SP (Brazil)
2016-07-15
Using an appropriate norm on the space of entire functions, we extend to the complex plane the renormalization group method as developed by Bricmont et al. The method is based upon a multiscale approach that allows for a detailed description of the long time asymptotics of solutions to initial value problems. The time evolution equation considered here arises in the study of iterations of the block spin renormalization group transformation for the hierarchical N-vector model. We show that, for initial conditions belonging to a certain Fréchet space of entire functions of exponential type, the asymptotics is universal in the sense that it is dictated by the fixed point of a certain operator acting on the space of initial conditions.
Asymptotic behavior of a competitive system of linear fractional difference equations
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Nurkanović M
2006-01-01
Full Text Available We investigate the global asymptotic behavior of solutions of the system of difference equations xn+1 = (a+xn/(b+yn, yn+1 = (d+yn/(e+xn, n = 0,1,..., where the parameters a, b, d, and e are positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers. In certain range of parameters, we prove the existence of the global stable manifold of the unique positive equilibrium of this system which is the graph of an increasing curve. We show that the stable manifold of this system separates the positive quadrant of initial conditions into basins of attraction of two types of asymptotic behavior. In the case where a = d and b = e, we find an explicit equation for the stable manifold to be y = x.
Kotlyarov, Vladimir; Minakov, Alexander
2015-07-01
We study the long-time asymptotic behavior of the Cauchy problem for the modified Korteweg—de Vries equation with an initial function of the step type. This function rapidly tends to zero as x\\to +∞ and to some positive constant c as x\\to -∞ . In 1989 Khruslov and Kotlyarov have found (Khruslov and Kotlyarov 1989 Inverse Problems 5 1075-88) that for a large time the solution breaks up into a train of asymptotic solitons located in the domain 4{c}2t-{C}N{ln}t\\lt x≤slant 4{c}2t ({C}N is a constant). The number N of these solitons grows unboundedly as t\\to ∞ . In 2010 Kotlyarov and Minakov have studied temporary asymptotics of the solution of the Cauchy problem on the whole line (Kotlyarov and Minakov 2010 J. Math. Phys. 51 093506) and have found that in the domain -6{c}2t\\lt x\\lt 4{c}2t this solution is described by a modulated elliptic wave. We consider here the modulated elliptic wave in the domain 4{c}2t-{C}N{ln}t\\lt x\\lt 4{c}2t. Our main result shows that the modulated elliptic wave also breaks up into solitons, which are similar to the asymptotic solitons in Khruslov and Kotlyarov (1989 Inverse Problems 5 1075-88), but differ from them in phase. It means that the modulated elliptic wave does not represent the asymptotics of the solution in the domain 4{c}2t-{C}N{ln}t\\lt x\\lt 4{c}2t. The correct asymptotic behavior of the solution is given by the train of asymptotic solitons given in Khruslov and Kotlyarov (1989 Inverse Problems 5 1075-88). However, in the asymptotic regime as t\\to ∞ in the region 4{c}2t-\\displaystyle \\frac{N+1/4}{c}{ln}t\\lt x\\lt 4{c}2t-\\displaystyle \\frac{N-3/4}{c}{ln}t we can watch precisely a pair of solitons with numbers N. One of them is the asymptotic soliton while the other soliton is generated from the elliptic wave. Their phases become closer to each other for a large N, i.e. these solitons are also close to each other. This result gives the answer on a very important question about matching of the asymptotic
Photodetachment cross-section evaluation using asymptotic considerations
Babilotte, Philippe; Vandevraye, Mickael
2017-06-01
Mathematical calculations are given concerning the evaluation of the negative ions photodetachment cross-section σ , into a so-called saturation regime. The interaction between a negative ion particle beam and a laser beam is examined under theoretical aspects. A quantitative criterion S is proposed to define the saturation threshold between the linear and the saturated domains, which are both present in this saturation regime. The asymptotic behaviours extracted at the low and high energy limits are used to determine this threshold quantitative criterion S and to evaluate also the photodetachment cross-section σ . The case of a symmetric gaussian photodetachment laser beam shape is examined according to the proposed formalism, which can be used either for the photo-detachment or photo-ionization processes, and could be potentially used into technological solutions for negative ion neutralisation processes (such as neutral beam injector) in the future fusion energy devices. Estimations onto the errors related to the use of this methodology are given.
Viscous asymptotically flat Reissner-Nordström black branes
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Gath, Jakob; Pedersen, Andreas Vigand [Niels Bohr Institute, University of Copenhagen,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark)
2014-03-12
We study electrically charged asymptotically flat black brane solutions whose world-volume fields are slowly varying with the coordinates. Using familiar techniques, we compute the transport coefficients of the fluid dynamic derivative expansion to first order. We show how the shear and bulk viscosities are modified in the presence of electric charge and we compute the charge diffusion constant which is not present for the neutral black p-brane. We compute the first order dispersion relations of the effective fluid. For small values of the charge the speed of sound is found to be imaginary and the brane is thus Gregory-Laflamme unstable as expected. For sufficiently large values of the charge, the sound mode becomes stable, however, in this regime the hydrodynamic mode associated with charge diffusion is found to be unstable. The electrically charged brane is thus found to be (classically) unstable for all values of the charge density in agreement with general thermodynamic arguments. Finally, we show that the shear viscosity to entropy bound is saturated, as expected, while the proposed bounds for the bulk viscosity to entropy can be violated in certain regimes of the charge of the brane.
Viscous asymptotically flat Reissner-Nordström black branes
Gath, Jakob; Pedersen, Andreas Vigand
2014-03-01
We study electrically charged asymptotically flat black brane solutions whose world-volume fields are slowly varying with the coordinates. Using familiar techniques, we compute the transport coefficients of the fluid dynamic derivative expansion to first order. We show how the shear and bulk viscosities are modified in the presence of electric charge and we compute the charge diffusion constant which is not present for the neutral black p-brane. We compute the first order dispersion relations of the effective fluid. For small values of the charge the speed of sound is found to be imaginary and the brane is thus Gregory-Laflamme unstable as expected. For sufficiently large values of the charge, the sound mode becomes stable, however, in this regime the hydrodynamic mode associated with charge diffusion is found to be unstable. The electrically charged brane is thus found to be (classically) unstable for all values of the charge density in agreement with general thermodynamic arguments. Finally, we show that the shear viscosity to entropy bound is saturated, as expected, while the proposed bounds for the bulk viscosity to entropy can be violated in certain regimes of the charge of the brane.
The time-dependent simplified P{sub 2} equations: Asymptotic analyses and numerical experiments
Energy Technology Data Exchange (ETDEWEB)
Shin, U.; Miller, W.F. Jr. [Los Alamos National Lab., NM (United States)
1998-01-01
Using an asymptotic expansion, the authors found that the modified time-dependent simplified P{sub 2} (SP{sub 2}) equations are robust, high-order, asymptotic approximations to the time-dependent transport equation in a physical regime in which the conventional time-dependent diffusion equation is the leading-order approximation. Using diffusion limit analysis, they also asymptotically compared three competitive time-dependent equations (the telegrapher`s equation, the time-dependent SP{sub 2} equations, and the time-dependent simplified even-parity equation). As a result, they found that the time-dependent SP{sub 2} equations contain higher-order asymptotic approximations to the time-dependent transport equation than the other competitive equations. The numerical results confirm that, in the vast majority of cases, the time-dependent SP{sub 2} solutions are significantly more accurate than the time-dependent diffusion and the telegrapher`s solutions. They have also shown that the time-dependent SP{sub 2} equations have excellent characteristics such as rotational invariance (which means no ray effect), good diffusion limit behavior, guaranteed positivity in diffusive regimes, and significant accuracy, even in deep-penetration problems. Through computer-running-time tests, they have shown that the time-dependent SP{sub 2} equations can be solved with significantly less computational effort than the conventionally used, time-dependent S{sub N} equations (for N > 2) and almost as fast as the time-dependent diffusion equation. From all these results, they conclude that the time-dependent SP{sub 2} equations should be considered as an important competitor for an improved approximately transport equations solver. Such computationally efficient time-dependent transport models are important for problems requiring enhanced computational efficiency, such as neutronics/fluid-dynamics coupled problems that arise in the analyses of hypothetical nuclear reactor accidents.
Qualitative and Asymptotic Theory of Detonations
Faria, Luiz
2014-11-09
Shock waves in reactive media possess very rich dynamics: from formation of cells in multiple dimensions to oscillating shock fronts in one-dimension. Because of the extreme complexity of the equations of combustion theory, most of the current understanding of unstable detonation waves relies on extensive numerical simulations of the reactive compressible Euler/Navier-Stokes equations. Attempts at a simplified theory have been made in the past, most of which are very successful in describing steady detonation waves. In this work we focus on obtaining simplified theories capable of capturing not only the steady, but also the unsteady behavior of detonation waves. The first part of this thesis is focused on qualitative theories of detonation, where ad hoc models are proposed and analyzed. We show that equations as simple as a forced Burgers equation can capture most of the complex phenomena observed in detonations. In the second part of this thesis we focus on rational theories, and derive a weakly nonlinear model of multi-dimensional detonations. We also show, by analysis and numerical simulations, that the asymptotic equations provide good quantitative predictions.
Asymptotic Behaviour of the QED Perturbation Series
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Idrish Huet
2017-01-01
Full Text Available I will summarize the present state of a long-term effort to obtain information on the large-order asymptotic behaviour of the QED perturbation series through the effective action. Starting with the constant-field case, I will discuss the Euler-Heisenberg Lagrangian in various dimensions and up to the three-loop level. This Lagrangian holds the information on the N-photon amplitudes in the low-energy limit, and combining it with Spinor helicity methods explicit all-N results can be obtained at the one-loop and, for the “all +” amplitudes, also at the two-loop level. For the imaginary part of the Euler-Heisenberg Lagrangian, an all-loop formula has been conjectured independently by Affleck, Alvarez, and Manton for Scalar QED and by Lebedev and Ritus for Spinor QED. This formula can be related through a Borel dispersion relation to the leading large-N behaviour of the N-photon amplitudes. It is analytic in the fine structure constant, which is puzzling and suggests a diagrammatic investigation of the large-N limit in perturbation theory. Preliminary results of such a study for the 1+1 dimensional case throw doubt on the validity of the conjecture.
Solvable Optimal Velocity Models and Asymptotic Trajectory
Nakanishi, K; Igarashi, Y; Bando, M
1996-01-01
In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay $T$. This leads to a global pattern formation in time development of vehicles' motion, and gives rise to a closed trajectory on $\\Delta x$-$v$ (headway-velocity) plane connecting congested and free flow points. To obtain the closed trajectory analytically, we propose a new approach to the pattern formation, which makes it possible to reduce the coupled car following equations to a single difference-differential equation (Rondo equation). To demonstrate our approach, we employ a class of linear models which are exactly solvable. We also introduce the concept of ``asymptotic traj...
Black holes in an asymptotically safe gravity theory with higher derivatives
Cai, Yi-Fu; Easson, Damien A.
2010-09-01
We present a class of spherically symmetric vacuum solutions to an asymptotically safe theory of gravity containing high-derivative terms. We find quantum corrected Schwarzschild-(anti)-de Sitter solutions with running gravitational coupling parameters. The evolution of the couplings is determined by their corresponding renormalization group flow equations. These black holes exhibit properties of a classical Schwarzschild solution at large length scales. At the center, the metric factor remains smooth but the curvature singularity, while softened by the quantum corrections, persists. The solutions have an outer event horizon and an inner Cauchy horizon which equate when the physical mass decreases to a critical value. Super-extremal solutions with masses below the critical value correspond to naked singularities. The Hawking temperature of the black hole vanishes when the physical mass reaches the critical value. Hence, the black holes in the asymptotically safe gravitational theory never completely evaporate. For appropriate values of the parameters such stable black hole remnants make excellent dark matter candidates.
Asymptotic distribution of zeros of polynomials satisfying difference equations
Krasovsky, I. V.
2003-01-01
We propose a way to find the asymptotic distribution of zeros of orthogonal polynomials pn(x) satisfying a difference equation of the formB(x)pn(x+[delta])-C(x,n)pn(x)+D(x)pn(x-[delta])=0.We calculate the asymptotic distribution of zeros and asymptotics of extreme zeros of the Meixner and Meixner-Pollaczek polynomials. The distribution of zeros of Meixner polynomials shows some delicate features. We indicate the relation of our technique to the approach based on the Nevai-Dehesa-Ullman distribution.
Sufficient conditions for polynomial asymptotic behaviour of the stochastic pantograph equation
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John Appleby
2016-08-01
Full Text Available This paper studies the asymptotic growth and decay properties of solutions of the stochastic pantograph equation with multiplicative noise. We give sufficient conditions on the parameters for solutions to grow at a polynomial rate in $p$-th mean and in the almost sure sense. Under stronger conditions the solutions decay to zero with a polynomial rate in $p$-th mean and in the almost sure sense. When polynomial bounds cannot be achieved, we show for a different set of parameters that exponential growth bounds of solutions in $p$-th mean and an almost sure sense can be obtained. Analogous results are established for pantograph equations with several delays, and for general finite dimensional equations.
An asymptotic model in acoustics: acoustic drift equations.
Vladimirov, Vladimir A; Ilin, Konstantin
2013-11-01
A rigorous asymptotic procedure with the Mach number as a small parameter is used to derive the equations of mean flows which coexist and are affected by the background acoustic waves in the limit of very high Reynolds number.
Preheating in an asymptotically safe quantum field theory
DEFF Research Database (Denmark)
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-01-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J....... High Energy Phys. 01 (2016) 081]. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. Since the models contain many scalar fields which are intrinsically coupled to the inflaton there is the possibility of parametric resonance....... Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081] must contain. This bound also depends on the total number of e-foldings of the inflationary phase....
Pseudo-random number generator based on asymptotic deterministic randomness
Energy Technology Data Exchange (ETDEWEB)
Wang Kai [Department of Radio Engineering, Southeast University, Nanjing (China)], E-mail: kaiwang@seu.edu.cn; Pei Wenjiang; Xia Haishan [Department of Radio Engineering, Southeast University, Nanjing (China); Cheung Yiuming [Department of Computer Science, Hong Kong Baptist University, Hong Kong (China)
2008-06-09
A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks.
Radial asymptotics of Lemaitre-Tolman-Bondi dust models
Sussman, Roberto A
2010-01-01
We examine the radial asymptotic behavior of spherically symmetric Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along radial rays, which are spacelike geodesics parametrized by proper length $\\ell$, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing quasi-local scalars defined as integral functions along the rays, we obtain a complete and covariant representation of the models, leading to an initial value parametrization in which all scalars can be given by scaling laws depending on two metric scale factors and two basic initial value functions. Considering regular "open" LTB models whose space slices allow for a diverging $\\ell$, we provide the conditions on the radial coordinate so that its asymptotic limit corresponds to the limit as $\\ell\\to\\infty$. The "asymptotic state" is then defined as this limit, together with asymptotic series expansion around it, evaluated for all metric functions, covariant scalars (local and quasi-local) and their fluctuations. By ...
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
On the generalized asymptotically nonspreading mappings in convex metric spaces
Directory of Open Access Journals (Sweden)
Withun Phuengrattana
2017-04-01
Full Text Available In this article, we propose a new class of nonlinear mappings, namely, generalized asymptotically nonspreading mapping, and prove the existence of fixed points for such mapping in convex metric spaces. Furthermore, we also obtain the demiclosed principle and a delta-convergence theorem of Mann iteration for generalized asymptotically nonspreading mappings in CAT(0 spaces.
Comparison of the asymptotic stability properties for two multirate strategies
Savcenco, V Valeriu
2007-01-01
textabstractThis paper contains a comparison of the asymptotic stability properties for two multirate strategies. For each strategy, the asymptotic stability regions are presented for a 2 x 2 test problem and the differences between the results are discussed. The considered multirate schemes use Rosenbrock type methods as the main time integration method and have one level of temporal local refinement. Some remarks on the relevance of the results for 2 x 2 test problems are presented.
Singularity-free gravitational collapse and asymptotic safety
Torres, Ramón
2014-06-01
A general class of quantum improved stellar models with interiors composed of non-interacting (dust) particles is obtained and analyzed in a framework compatible with asymptotic safety. First, the effective exterior, based on the Quantum Einstein Gravity approach to asymptotic safety is presented and, second, its effective compatible dust interiors are deduced. The resulting stellar models appear to be devoid of shell-focusing singularities.
Asymptotic estimation of shift parameter of a quantum state
Holevo, A. S.
2003-01-01
We develop an asymptotic theory of estimation of a shift parameter in a pure quantum state to study the relation between entangled and unentangled covariant estimates in the analytically most transparent way. After recollecting basics of estimation of shift parameter in Sec. 2, we study the structure of the optimal covariant estimate in Sec. 3, showing how entanglement comes into play for several independent trials. In Secs. 4,5 we give the asymptotics of the performance of the optimal covari...
Some late-time asymptotics of general scalar-tensor cosmologies
Energy Technology Data Exchange (ETDEWEB)
Barrow, John D [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Shaw, Douglas J [Astronomy Unit, Queen Mary University, Mile End Rd., London E1 4NS (United Kingdom)
2008-04-21
We study the asymptotic behaviour of isotropic and homogeneous universes in general scalar-tensor gravity theories containing a p = -{rho} vacuum fluid stress and other sub-dominant matter stresses. It is shown that in order for there to be an approach to a de Sitter spacetime at large 4-volumes the coupling function, {omega}({phi}), which defines the scalar-tensor theory, must diverge faster than |{phi}{sub {infinity}} - {phi}|{sup -1+{epsilon}} for all {epsilon} > 0 as {phi} {yields} {phi}{sub {infinity}} {ne} 0 for large values of the time. Thus, for a given theory, specified by {omega}({phi}), there must exist some {phi}{sub {infinity}} element of (0, {infinity}) such that {omega} {yields} {infinity} and {omega}'/{omega}{sup 2+{epsilon}} {yields} 0 as {phi} {yields} {phi}{sub {infinity}} in order for cosmological solutions of the theory to approach de Sitter expansion at late times. We also classify the possible asymptotic time variations of the gravitation 'constant' G(t) at late times in scalar-tensor theories. We show that (unlike in general relativity) the problem of a profusion of 'Boltzmann brains' at late cosmological times can be avoided in scalar-tensor theories, including Brans-Dicke theory, in which {phi} {yields} {infinity} and {omega} {approx}o({phi}{sup 1/2}) at asymptotically late times.
Asymptotics for moist deep convection I: refined scalings and self-sustaining updrafts
Hittmeir, Sabine; Klein, Rupert
2017-10-01
Moist processes are among the most important drivers of atmospheric dynamics, and scale analysis and asymptotics are cornerstones of theoretical meteorology. Accounting for moist processes in systematic scale analyses therefore seems of considerable importance for the field. Klein and Majda (Theor Comput Fluid Dyn 20:525-551, 2006) proposed a scaling regime for the incorporation of moist bulk microphysics closures in multiscale asymptotic analyses of tropical deep convection. This regime is refined here to allow for mixtures of ideal gases and to establish consistency with a more general multiple scales modeling framework for atmospheric flows. Deep narrow updrafts, the so-called hot towers, constitute principal building blocks of larger scale storm systems. They are analyzed here in a sample application of the new scaling regime. A single quasi-one-dimensional upright columnar cloud is considered on the vertical advective (or tower life cycle) time scale. The refined asymptotic scaling regime is essential for this example as it reveals a new mechanism for the self-sustainance of such updrafts. Even for strongly positive convectively available potential energy, a vertical balance of buoyancy forces is found in the presence of precipitation. This balance induces a diagnostic equation for the vertical velocity, and it is responsible for the generation of self-sustained balanced updrafts. The time-dependent updraft structure is encoded in a Hamilton-Jacobi equation for the precipitation mixing ratio. Numerical solutions of this equation suggest that the self-sustained updrafts may strongly enhance hot tower life cycles.
Efficient asymptotic frame selection for binary black hole spacetimes using asymptotic radiation
O'Shaughnessy, R; Healy, J; Meeks, Z; Shoemaker, D
2011-01-01
Previous studies have demonstrated that gravitational radiation reliably encodes information about the natural emission direction of the source (e.g., the orbital plane). In this paper, we demonstrate that these orientations can be efficiently estimated by the principal axes of , an average of the action of rotation group generators on the Weyl tensor at asymptotic infinity. Evaluating this average at each time provides the instantaneous emission direction. Further averaging across the entire signal yields an average orientation, closely connected to the angular components of the Fisher matrix. The latter direction is well-suited to data analysis and parameter estimation when the instantaneous emission direction evolves significantly. Finally, in the time domain, the average provides fast, invariant diagnostics of waveform quality.
On the asymptotic behavior for a nonlocal difusion equation with an absorption term on a lattice
Directory of Open Access Journals (Sweden)
Théodore K. Boni
2008-11-01
Full Text Available In this paper, we consider the following initial value problem:U_i'(t =sum_{jin B} J_{i-j}(U_j(t - U_i(t, t geq 0, iin BU_i(0=varphi_i >0, iin Bwhere B is a bounded subset of Z^d, p > 1, J_ h = (J_i_{iinB} is a kernel which is nonnegative, symmetric, bounded and sum_{j in Z^d} Jj = 1. We describe the asymptotic behavior of the solution of the above problem.
Relativistic stars in Starobinsky gravity with the matched asymptotic expansions method
Arapoǧlu, Savaş; ćıkıntoǧlu, Sercan; Ekşi, K. Yavuz
2017-10-01
We study the structure of relativistic stars in R +α R2 theory using the method of matched asymptotic expansion to handle the higher order derivatives in field equations arising from the higher order curvature term. We find solutions, parametrized by α , for uniform density stars. We obtain the mass-radius relations and study the dependence of maximum mass on α . We find that Mmax is almost linearly proportional to α . For each α the maximum mass configuration has the biggest compactness parameter (η =G M /R c2), and we argue that the general relativistic stellar configuration corresponding to α =0 is the least compact among these.
Asymptotically linear Schrodinger equation with zero on the boundary of the spectrum
Directory of Open Access Journals (Sweden)
Dongdong Qin
2015-08-01
Full Text Available This article concerns the Schr\\"odinger equation $$\\displaylines{ -\\Delta u+V(xu=f(x, u, \\quad \\text{for } x\\in\\mathbb{R}^N,\\cr u(x\\to 0, \\quad \\text{as } |x| \\to \\infty, }$$ where V and f are periodic in x, and 0 is a boundary point of the spectrum $\\sigma(-\\Delta+V$. Assuming that f(x,u is asymptotically linear as $|u|\\to\\infty$, existence of a ground state solution is established using some new techniques.
Low and high frequency asymptotics acoustic, electromagnetic and elastic wave scattering
Varadan, VK
2013-01-01
This volume focuses on asymptotic methods in the low and high frequency limits for the solution of scattering and propagation problems. Each chapter is pedagogical in nature, starting with the basic foundations and ending with practical applications. For example, using the Geometrical Theory of Diffraction, the canonical problem of edge diffraction is first solved and then used in solving the problem of diffraction by a finite crack. In recent times, the crack problem has been of much interest for its applications to Non-Destructive Evaluation (NDE) of flaws in structural materials.
Numerical Simulations of Asymptotically AdS Spacetimes
Bantilan, Hans
In this dissertation, we introduce a numerical scheme to construct asymptotically anti-de Sitter spacetimes with Lorentzian signature, focusing on cases that preserve five-dimensional axisymmetry. We study the field theories that are dual to these spacetimes by appealing to the AdS/CFT correspondence in the regime where the gravity dual is completely described by Einstein gravity. The numerical scheme is based on generalized harmonic evolution, and we begin by obtaining initial data defined on some Cauchy hypersurface. For the study described in this dissertation, we use a scalar field to source deviations from pure AdS5, and obtain data that correspond to highly deformed black holes. We evolve this initial data forward in time, and follow the subsequent ringdown. What is novel about this study is that the initial horizon geometry cannot be considered a small perturbation of the final static horizon, and hence we are probing an initial non-linear phase of the evolution of the bulk spacetime. On the boundary, we find that the dual CFT stress tensor behaves like that of a thermalized N = 4 SYM fluid. We find that the equation of state of this fluid is consistent with conformal invariance, and that its transport coefficients match those previously calculated for an N = 4 SYM fluid via holographic methods. Modulo a brief transient that is numerical in nature, this matching appears to hold from the initial time onwards. We transform these solutions computed in global AdS onto a Minkowski piece of the boundary, and examine the temperature of the corresponding fluid flows. Under this transformation, the spatial profile of temperature at the initial time resembles a Lorentz-flattened pancake centered at the origin of Minkowski space. By interpreting the direction along which the data is flattened as the beam-line direction, our initial data can be thought of as approximating a head-on heavy ion collision at its moment of impact.
Asymptotic behavior for cross coupled parabolic equations
Directory of Open Access Journals (Sweden)
Yingzhen XUE
2017-04-01
Full Text Available In order to better describe the heat transfer process of three kinds of mixed substances, namely the reaction of the reactants in the three chemical reactions, a class of three variable cross coupling with non parabolic equations of the whole existence of local source and non local boundary flow and the finite time blow up problem with breaking method for the solution of the first commonly used feature value structure are studied. The structure of the equations of the upper and lower solutions by using the method of ordinary differential equation reference is broken, with comparison theorem, the proof shows that obtained by local source power function and exponential function of parabolic equations is broken, with the sufficient conditions for global existence of clegerate purubolic equations solutions cross coupled by local source power function and non local sources exponential function are proved, as soon as the solution of blowing up in finite time degradation of non local sources of cross coupling, providing better support for the theory of heat transfer and chemical reaction problem.
Asymptotic analysis for personalized web search
Volkovich, Y.; Litvak, Nelli
2010-01-01
PageRank with personalization is used in Web search as an importance measure for Web documents. The goal of this paper is to characterize the tail behavior of the PageRank distribution in the Web and other complex networks characterized by power laws. To this end, we model the PageRank as a solution
Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size.
King, Richard B; Stanford, Kristin M; Jones, Peter C; Bekker, Kent
2016-01-01
Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females) and annual growth increments of individuals of unknown age (1,152 males, 730 females). We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631-820 mm snout-vent length in males and from 835-1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further investigation.
Numerical Analysis of Asymptotic Stability of Equilibrium Points
Directory of Open Access Journals (Sweden)
A. A. Vorkel
2017-01-01
Full Text Available The aim of this study is to numerically analyze an asymptotic stability of the equilibrium points of autonomous systems of ordinary differential equations on the basis of the asymptotic stability criterion given in the article and the functional localization method of invariant compact sets. The article formulates the necessary and sufficient conditions for an asymptotic stability in terms of invariant compact sets and positively invariant sets and describes a functional localization method. Presents appropriate localization theorems for invariant compact sets of dynamical systems.To investigate the asymptotic stability is proposed an algorithm for a numerical iteration procedure to construct the localizing bounds for invariant compact sets contained in a given initial set. Application of the asymptotic stability criterion is based on the results of this procedure. The author of the article verifies the conditions of the appropriate theorem and confirms the use of this criterion.The examples of two- and three-dimensional systems of differential equations demonstrate a principle of the iteration procedure. The article also gives an example of the system with a limit cycle and it shows that the developed numerical algorithm and the functional localization method of invariant compact sets can be used to analyze stability of the limit cycles.Thanks to the method described in the article, when analyzing an asymptotic stability of equilibrium points, finding a Lyapunov function and calculating eigenvalues of a matrix of linear approximation are non-essential. Thus, it is possible to avoid labour-intensive work with complex analytical structures.The numerical iteration procedure can be used in systems of different dimensions and makes the presented algorithm of asymptotic stability analysis universal.
Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size
King, Richard B.
2016-01-01
Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females) and annual growth increments of individuals of unknown age (1,152 males, 730 females). We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631–820 mm snout-vent length in males and from 835–1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further investigation. PMID
Vainshtein solutions without superluminal modes
Gabadadze, Gregory; Kimura, Rampei; Pirtskhalava, David
2015-06-01
The Vainshtein mechanism suppresses the fifth force at astrophysical distances, while enabling it to compete with gravity at cosmological scales. Typically, Vainshtein solutions exhibit superluminal perturbations. However, a restricted class of solutions with special boundary conditions was shown to be devoid of the faster-than-light modes. Here we extend this class by finding solutions in a theory of quasidilaton, amended by derivative terms consistent with its symmetries. Solutions with Minkowski asymptotics are not stable, while the ones that exhibit the Vainshtein mechanism by transitioning to cosmological backgrounds are free of ghosts, tachyons, gradient instability, and superluminality, for all propagating modes present in the theory. These solutions require a special choice of the strength and signs of nonlinear terms, as well as a choice of asymptotic cosmological boundary conditions.
Large gauge symmetries and asymptotic states in QED
Energy Technology Data Exchange (ETDEWEB)
Gabai, Barak; Sever, Amit [School of Physics and Astronomy, Tel Aviv University,Ramat Aviv 69978 (Israel)
2016-12-19
Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles’ momenta and may be associated to the vacuum. The soft theorem’s manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.
Arkhincheev, V E
2017-03-01
The new asymptotic behavior of the survival probability of particles in a medium with absorbing traps in an electric field has been established in two ways-by using the scaling approach and by the direct solution of the diffusion equation in the field. It has shown that at long times, this drift mechanism leads to a new temporal behavior of the survival probability of particles in a medium with absorbing traps.
Perasso, Antoine; Razafison, Ulrich
2014-01-01
In this article is studied an infection load-structured SI model with exponential growth of the infection, that incorporates a potential external source of contamination. We perform the analysis of the time asymptotic behavior of the solution by exhibiting epidemiological thresholds, such as the basic reproduction number, that ensure extinction or persistence of the disease in the contagion process. Moreover, a numerical scheme adapted to the model is developped and analyzed. This scheme is t...
Asymptotic chaos expansions in finance theory and practice
Nicolay, David
2014-01-01
Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (suc...
Asymptotic Analysis in MIMO MRT/MRC Systems
Directory of Open Access Journals (Sweden)
Zhou Quan
2006-01-01
Full Text Available Through the analysis of the probability density function of the squared largest singular value of a complex Gaussian matrix at the origin and tail, we obtain two asymptotic results related to the multi-input multi-output (MIMO maximum-ratio-transmission/maximum-ratio-combining (MRT/MRC systems. One is the asymptotic error performance (in terms of SNR in a single-user system, and the other is the asymptotic system capacity (in terms of the number of users in the multiuser scenario when multiuser diversity is exploited. Similar results are also obtained for two other MIMO diversity schemes, space-time block coding and selection combining. Our results reveal a simple connection with system parameters, providing good insights for the design of MIMO diversity systems.
Vacuum energy in asymptotically flat 2+1 gravity
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Olivera Miskovic
2017-04-01
Full Text Available We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern–Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein–Hilbert term in the bulk plus half of the Gibbons–Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.
Vacuum energy in asymptotically flat 2 + 1 gravity
Miskovic, Olivera; Olea, Rodrigo; Roy, Debraj
2017-04-01
We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern-Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein-Hilbert term in the bulk plus half of the Gibbons-Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.
Vacuum energy in asymptotically flat 2 + 1 gravity
Energy Technology Data Exchange (ETDEWEB)
Miskovic, Olivera, E-mail: olivera.miskovic@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Olea, Rodrigo, E-mail: rodrigo.olea@unab.cl [Departamento de Ciencias Físicas, Universidad Andres Bello, Sazié 2212, Piso 7, Santiago (Chile); Roy, Debraj, E-mail: roy.debraj@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile)
2017-04-10
We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern–Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein–Hilbert term in the bulk plus half of the Gibbons–Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.
Selected asymptotic methods with applications to electromagnetics and antennas
Fikioris, George; Bakas, Odysseas N
2013-01-01
This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include som
Asymptotic analysis of the Poisson-Boltzmann equation describing electrokinetics in porous media
Allaire, Grégoire; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey
2013-03-01
We consider the Poisson-Boltzmann equation in a periodic cell, representative of a porous medium. It is a model for the electrostatic distribution of N chemical species diluted in a liquid at rest, occupying the pore space with charged solid boundaries. We study the asymptotic behaviour of its solution depending on a parameter β, which is the square of the ratio between a characteristic pore length and the Debye length. For small β we identify the limit problem which is still a nonlinear Poisson equation involving only one species with maximal valence, opposite to the average of the given surface charge density. This result justifies the Donnan effect, observing that the ions for which the charge is that of the solid phase are expelled from the pores. For large β we prove that the solution behaves like a boundary layer near the pore walls and is constant far away in the bulk. Our analysis is valid for Neumann boundary conditions (namely for imposed surface charge densities) and establishes rigorously that solid interfaces are uncoupled from the bulk fluid so that simplified additive theories, such as the popular Derjaguin, Landau, Verwey and Overbeek approach, can be used. We show that the asymptotic behaviour is completely different in the case of Dirichlet boundary conditions (namely for imposed surface potential).
Asymptotically spacelike warped anti-de Sitter spacetimes in generalized minimal massive gravity
Setare, M. R.; Adami, H.
2017-06-01
In this paper we show that warped AdS3 black hole spacetime is a solution of the generalized minimal massive gravity (GMMG) and introduce suitable boundary conditions for asymptotically warped AdS3 spacetimes. Then we find the Killing vector fields such that transformations generated by them preserve the considered boundary conditions. We calculate the conserved charges which correspond to the obtained Killing vector fields and show that the algebra of the asymptotic conserved charges is given as the semi direct product of the Virasoro algebra with U(1) current algebra. We use a particular Sugawara construction to reconstruct the conformal algebra. Thus, we are allowed to use the Cardy formula to calculate the entropy of the warped black hole. We demonstrate that the gravitational entropy of the warped black hole exactly coincides with what we obtain via Cardy’s formula. As we expect, the warped Cardy formula also gives us exactly the same result as we obtain from the usual Cardy’s formula. We calculate mass and angular momentum of the warped black hole and then check that obtained mass, angular momentum and entropy to satisfy the first law of the black hole mechanics. According to the results of this paper we believe that the dual theory of the warped AdS3 black hole solution of GMMG is a warped CFT.
On solutions of a Volterra integral equation with deviating arguments
Directory of Open Access Journals (Sweden)
M. Diana Julie
2009-04-01
Full Text Available In this article, we establish the existence and asymptotic characterization of solutions to a nonlinear Volterra integral equation with deviating arguments. Our proof is based on measure of noncompactness and the Schauder fixed point theorem.
Super-accelerating bouncing cosmology in asymptotically free non-local gravity
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [CSIC, Instituto de Estructura de la Materia, Madrid (Spain); Modesto, Leonardo [Fudan University, Department of Physics and Center for Field Theory and Particle Physics, Shanghai (China); Nicolini, Piero [Johann Wolfgang Goethe-Universitaet, Frankfurt Institute for Advanced Studies (FIAS) und Institut fuer Theoretische Physik, Frankfurt am Main (Germany)
2014-08-15
Recently, evidence has been collected that a class of gravitational theories with certain non-local operators is renormalizable. We consider one such model which, at the linear perturbative level, reproduces the effective non-local action for the light modes of bosonic closed string-field theory. Using the property of asymptotic freedom in the ultraviolet and fixing the classical behavior of the scale factor at late times, an algorithm is proposed to find general homogeneous cosmological solutions valid both at early and late times. Imposing a power-law classical limit, these solutions (including anisotropic ones) display a bounce, instead of a big-bang singularity, and super-accelerate near the bounce even in the absence of an inflaton or phantom field. (orig.)
Stability and square integrability of solutions of nonlinear fourth order differential equations
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Moussadek Remili
2016-05-01
Full Text Available The aim of the present paper is to establish a new result, which guarantees the asymptotic stability of zero solution and square integrability of solutions and their derivatives to nonlinear differential equations of fourth order.
Relaxing the parity conditions of asymptotically flat gravity
Compère, G.; Dehouck, F.
2011-01-01
Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counterterm
Asymptotic inference for jump diffusions with state-dependent intensity
Becheri, Gaia; Drost, Feico; Werker, Bas
2016-01-01
We establish the local asymptotic normality property for a class of ergodic parametric jump-diffusion processes with state-dependent intensity and known volatility function sampled at high frequency. We prove that the inference problem about the drift and jump parameters is adaptive with respect to
High energy asymptotics of the scattering amplitude for the ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
High energy asymptotics of the scattering amplitude for the. Schrödinger equation. D YAFAEV. Department of Mathematics, University Rennes-1, Campus Beaulieu, 35042 Rennes,. France. Abstract. We find an explicit function approximating at high energies the kernel of the scattering matrix with arbitrary accuracy.
Asymptotics of sums of lognormal random variables with Gaussian copula
DEFF Research Database (Denmark)
Asmussen, Søren; Rojas-Nandayapa, Leonardo
2008-01-01
Let (Y1, ..., Yn) have a joint n-dimensional Gaussian distribution with a general mean vector and a general covariance matrix, and let Xi = eYi, Sn = X1 + ⋯ + Xn. The asymptotics of P (Sn > x) as n → ∞ are shown to be the same as for the independent case with the same lognormal marginals. In part...
Chemical Analysis of Asymptotic Giant Branch Stars in M62
Lapenna, E.; Mucciarelli, A.; Ferraro, F. R.; Origlia, L.; Lanzoni, B.; Massari, D.; Dalessandro, E.
2015-01-01
We have collected UVES-FLAMES high-resolution spectra for a sample of 6 asymptotic giant branch (AGB) and 13 red giant branch (RGB) stars in the Galactic globular cluster (GC) M62 (NGC 6266). Here we present the detailed abundance analysis of iron, titanium, and light elements (O, Na, Mg, and Al).
Precise asymptotics for complete moment convergence in Hilbert ...
Indian Academy of Sciences (India)
... Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 122; Issue 1. Precise Asymptotics for Complete Moment Convergence in Hilbert Spaces. Keang Fu Juan Chen. Volume 122 Issue 1 February 2012 ...
Exact overflow asymptotics for queues with many Gaussian inputs
Debicki, Krzysztof; Mandjes, M.R.H.
2003-01-01
In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the
Asymptotic linear estimation of the quantile function of a location ...
African Journals Online (AJOL)
Specific results are discussed for the ABLUE of Qξ for the location-scale exponential and double exponential distributions. As a further application of the exponential results, we discuss the asymptotically best optimal spacings for the location-scale logistic distribution. Keywords: Quantiles; Order statistics; Optimal spacing; ...
A Review on asymptotic normality of sums of associated random ...
African Journals Online (AJOL)
Association between random variables is a generalization of independence of these random variables. This concept is more and more commonly used in current trends in any research elds in Statistics. In this paper, we proceed to a simple, clear and rigorous introduction to it. We will present the fundamental asymptotic ...
Hardy-Weinberg law: asymptotic approach to a generalized form.
Stark, A E
1976-09-17
The equilibrium frequencies of a generalized Hardy-Weinberg law are approached at a geometric rate under assortative mating, irrespective of the initial genotypic frequencies. The asymptotic form is similar to that of Wright, and the pattern of assortative mating is based on deviations from the mean genotypic value.
Ergodic Retractions for Families of Asymptotically Nonexpansive Mappings
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Saeidi Shahram
2010-01-01
Full Text Available We prove some theorems for the existence of ergodic retractions onto the set of common fixed points of a family of asymptotically nonexpansive mappings. Our results extend corresponding results of Benavides and Ramírez (2001, and Li and Sims (2002.
Asymptotic estimates of viscoelastic Green's functions near the wavefront
Hanyga, Andrzej
2014-01-01
Asymptotic behavior of viscoelastic Green's functions near the wavefront is expressed in terms of a causal function $g(t)$ defined in \\cite{SerHanJMP} in connection with the Kramers-Kronig dispersion relations. Viscoelastic Green's functions exhibit a discontinuity at the wavefront if $g(0) < \\infty$. Estimates of continuous and discontinuous viscoelastic Green's functions near the wavefront are obtained.
Asymptotic-bound-state model for Feshbach resonances
Tiecke, T.G.; Goosen, M.R.; Walraven, J.T.M.; Kokkelmans, S.J.J.M.F.
2010-01-01
We present an asymptotic-bound-state model which can be used to accurately describe all Feshbach resonance positions and widths in a two-body system. With this model we determine the coupled bound states of a particular two-body system. The model is based on analytic properties of the two-body
Parabolic cyclinder functions : examples of error bounds for asymptotic expansions
R. Vidunas; N.M. Temme (Nico)
2002-01-01
textabstractSeveral asymptotic expansions of parabolic cylinder functions are discussedand error bounds for remainders in the expansions are presented. Inparticular Poincaré-type expansions for large values of the argument$z$ and uniform expansions for large values of the parameter areconsidered.
Precise asymptotics for complete moment convergence in Hilbert ...
Indian Academy of Sciences (India)
(Math. Sci.) Vol. 122, No. 1, February 2012, pp. 87–97. c Indian Academy of Sciences. Precise asymptotics for complete moment convergence in Hilbert spaces ... School of Statistics and Mathematics, Zhejiang Gongshang University, .... Now we start to introduce some Propositions, and the proof of our main result is based.
A note on properties of iterative procedures of asymptotic evidence
Paardekooper, H.C.H.; Steens, H.B.A.; Van der Hoek, G.
1989-01-01
The theoretical results obtained by Dzhaparidze (1983) are based on a theorem dealing with the asymptotically normality of an estimator which is the result of a Newton-like iteration method. The paper establishes a new theorem that supports the use of a more robust BFGS Quasi Newton method with
Holographic reconstruction and renormalization in asymptotically Ricci-flat spacetimes
Caldeira Costa, R.N.
2012-01-01
In this work we elaborate on an extension of the AdS/CFT framework to a sub-class of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family
From A to Z: Asymptotic expansions by van Zwet
Albers, Willem/Wim; de Gunst, Mathisca; Klaasen, Chris; van der Vaart, Aad
2001-01-01
Refinements of first order asymptotic results axe reviewed, with a number of Ph.D. projects supervised by van Zwet serving as stepping stones. Berry-Esseen bounds and Edgeworth expansions are discussed for R-, L- and [/-statistics. After these special classes, the question about a general second
From A to Z: asymptotic expansions by van Zwet
Albers, Willem/Wim; de Gunst, M.C.M.; Klaassen, C.A.J.; van der Vaart, A.W.
2001-01-01
Refinements of first order asymptotic results are reviewed, with a number of Ph.D. projects supervised by van Zwet serving as stepping stones. Berry-Esseen bounds and Edgeworth expansions are discussed for R-, L- and U-statistics. After these special classes, the question about a general second
Tail asymptotics for dependent subexponential diﬀerences
DEFF Research Database (Denmark)
Albrecher, H; Asmussen, Søren; Kortschak, D.
We study the asymptotic behavior of P(X − Y > u) as u → ∞, where X is subexponential and X, Y are positive random variables that may be dependent. We give criteria under which the subtraction of Y does not change the tail behavior of X. It is also studied under which conditions the comonotonic...
Asymptotic tensor rank of graph tensors: beyond matrix multiplication
M. Christandl (Matthias); P. Vrana (Péter); J. Zuiddam (Jeroen)
2016-01-01
textabstractWe present an upper bound on the exponent of the asymptotic behaviour of the tensor rank of a family of tensors defined by the complete graph on $k$ vertices. For $k\\geq4$, we show that the exponent per edge is at most 0.77, outperforming the best known upper bound on the exponent per
Quantum local asymptotic normality and other questions of quantum statistics
Kahn, Jonas
2008-01-01
This thesis is entitled Quantum Local Asymptotic Normality and other questions of Quantum Statistics ,. Quantum statistics are statistics on quantum objects. In classical statistics, we usually start from the data. Indeed, if we want to predict the weather, and can measure the wind or the
Asymptotic symmetries in de Sitter and inflationary spacetimes
DEFF Research Database (Denmark)
Ferreira, Ricardo J. Z.; Sandora, McCullen; Sloth, Martin S.
2017-01-01
Soft gravitons produced by the expansion of de Sitter can be viewed as the Nambu-Goldstone bosons of spontaneously broken asymptotic symmetries of the de Sitter spacetime. We explicitly construct the associated charges, and show that acting with the charges on the vacuum creates a new state...
DEFF Research Database (Denmark)
Farrokhzad, F.; Mowlaee, P.; Barari, Amin
2011-01-01
The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified......, and this process produces noise in the obtained answers. This paper deals with solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Optimal Homotopy Asymptotic...... Method (OHAM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate to systems of non-linear differential equation....
Directory of Open Access Journals (Sweden)
Mahmoud Bayat
Full Text Available This review features a survey of some recent developments in asymptotic techniques and new developments, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the achieved approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to over-come the shortcomings.In this review we have applied different powerful analytical methods to solve high nonlinear problems in engineering vibrations. Some patterns are given to illustrate the effectiveness and convenience of the methodologies.
On Asymptotically Lacunary Statistical Equivalent Sequences of Order α in Probability
Directory of Open Access Journals (Sweden)
Işık Mahmut
2017-01-01
Full Text Available In this study, we introduce and examine the concepts of asymptotically lacunary statistical equivalent of order α in probability and strong asymptotically lacunary equivalent of order α in probability. We give some relations connected to these concepts.
On Asymptotically Lacunary Statistical Equivalent Sequences of Order α in Probability
Işık Mahmut; Akbaş Kübra Elif
2017-01-01
In this study, we introduce and examine the concepts of asymptotically lacunary statistical equivalent of order α in probability and strong asymptotically lacunary equivalent of order α in probability. We give some relations connected to these concepts.
Lindsay, A. E.; Spoonmore, R. T.; Tzou, J. C.
2016-10-01
A hybrid asymptotic-numerical method is presented for obtaining an asymptotic estimate for the full probability distribution of capture times of a random walker by multiple small traps located inside a bounded two-dimensional domain with a reflecting boundary. As motivation for this study, we calculate the variance in the capture time of a random walker by a single interior trap and determine this quantity to be comparable in magnitude to the mean. This implies that the mean is not necessarily reflective of typical capture times and that the full density must be determined. To solve the underlying diffusion equation, the method of Laplace transforms is used to obtain an elliptic problem of modified Helmholtz type. In the limit of vanishing trap sizes, each trap is represented as a Dirac point source that permits the solution of the transform equation to be represented as a superposition of Helmholtz Green's functions. Using this solution, we construct asymptotic short-time solutions of the first-passage-time density, which captures peaks associated with rapid capture by the absorbing traps. When numerical evaluation of the Helmholtz Green's function is employed followed by numerical inversion of the Laplace transform, the method reproduces the density for larger times. We demonstrate the accuracy of our solution technique with a comparison to statistics obtained from a time-dependent solution of the diffusion equation and discrete particle simulations. In particular, we demonstrate that the method is capable of capturing the multimodal behavior in the capture time density that arises when the traps are strategically arranged. The hybrid method presented can be applied to scenarios involving both arbitrary domains and trap shapes.
Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas
Grigor'ev, Yu. N.; Ershov, I. V.
2017-01-01
An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.
Pucci, Patrizia; Saldi, Sara
2017-09-01
This paper is devoted to the question of global and local asymptotic stability for nonlinear damped Kirchhoff systems, with homogeneous Dirichlet boundary conditions, under fairly natural assumptions on the external force f = f (t , x , u), the distributed damping Q = Q (t , x , u ,ut), the perturbation term μ | u| p - 2 u and the dissipative term ϱ (t) M ([u]sp) |ut| p - 2ut, with ϱ ≥ 0 and in Lloc1 (R0+), when the initial data are in a special region. Here u = (u1 , … ,uN) = u (t , x) represents the vectorial displacement, with N ≥ 1. Particular attention is devoted to the asymptotic behavior of the solutions in the linear case specified in Section 5. Finally, the results are extended to problems where the fractional p-Laplacian is replaced by a more general elliptic nonlocal integro-differential operator. The paper extends in several directions recent theorems and covers also the so-called degenerate case, that is the case in which M is zero at zero.
Asymptotic fragility, near AdS2 holography and T\\overline{T}
Dubovsky, Sergei; Gorbenko, Victor; Mirbabayi, Mehrdad
2017-09-01
We present the exact solution for the scattering problem in the flat space Jackiw-Teitelboim (JT) gravity coupled to an arbitrary quantum field theory. JT gravity results in a gravitational dressing of field theoretical scattering amplitudes. The exact expression for the dressed S-matrix was previously known as a solvable example of a novel UV asymptotic behavior, dubbed asymptotic fragility. This dressing is equivalent to the T\\overline{T} deformation of the initial quantum field theory. JT gravity coupled to a single mass-less boson provides a promising action formulation for an integrable approximation to the worldsheet theory of confining strings in 3D gluodynamics. We also derive the dressed S-matrix as a flat space limit of the near AdS2 holography. We show that in order to preserve the flat space unitarity the conventional Schwarzian dressing of boundary correlators needs to be slightly extended. Finally, we propose a new simple expression for flat space amplitudes of massive particles in terms of correlators of holographic CFT's.
Structure and asymptotic theory for nonlinear models with GARCH errors
Directory of Open Access Journals (Sweden)
Felix Chan
2015-01-01
Full Text Available Nonlinear time series models, especially those with regime-switching and/or conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper, we derive sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is essential, among other reasons, to establish the conditions under which the traditional LM linearity tests based on Taylor expansions are valid. We also provide sufficient conditions for consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors.
Asymptotic Expansions of the Contact Angle in Nonlocal Capillarity Problems
Dipierro, Serena; Maggi, Francesco; Valdinoci, Enrico
2017-10-01
We consider a family of nonlocal capillarity models, where surface tension is modeled by exploiting the family of fractional interaction kernels |z|^{-n-s}, with s\\in (0,1) and n the dimension of the ambient space. The fractional Young's law (contact angle condition) predicted by these models coincides, in the limit as s→ 1^-, with the classical Young's law determined by the Gauss free energy. Here we refine this asymptotics by showing that, for s close to 1, the fractional contact angle is always smaller than its classical counterpart when the relative adhesion coefficient σ is negative, and larger if σ is positive. In addition, we address the asymptotics of the fractional Young's law in the limit case s→ 0^+ of interaction kernels with heavy tails. Interestingly, near s=0, the dependence of the contact angle from the relative adhesion coefficient becomes linear.
Asymptotic analysis of multicell massive MIMO over Rician fading channels
Sanguinetti, Luca
2017-06-20
This work considers the downlink of a multicell massive MIMO system in which L base stations (BSs) of N antennas each communicate with K single-antenna user equipments randomly positioned in the coverage area. Within this setting, we are interested in evaluating the sum rate of the system when MRT and RZF are employed under the assumption that each intracell link forms a MIMO Rician uncorrelated fading channel. The analysis is conducted assuming that N and K grow large with a non-trivial ratio N/K under the assumption that the data transmission in each cell is affected by channel estimation errors, pilot contamination, and an arbitrary large scale attenuation. Numerical results are used to validate the asymptotic analysis in the finite system regime and to evaluate the network performance under different settings. The asymptotic results are also instrumental to get insights into the interplay among system parameters.
The asymptotic convergence factor for a polygon under a perturbation
Energy Technology Data Exchange (ETDEWEB)
Li, X. [Georgia Southern Univ., Statesboro, GA (United States)
1994-12-31
Let Ax = b be a large system of linear equations, where A {element_of} C{sup NxN}, nonsingular and b {element_of} C{sup N}. A few iterative methods for solving have recently been presented in the case where A is nonsymmetric. Many of their algorithms consist of two phases: Phase I: estimate the extreme eigenvalues of A; Phase II: construct and apply an iterative method based on the estimates. For convenience, it is rewritten as an equivalent fixed-point form, x = Tx + c. Let {Omega} be a compact set excluding 1 in the complex plane, and let its complement in the extended complex plane be simply connected. The asymptotic convergence factor (ACF) for {Omega}, denoted by {kappa}({Omega}), measures the rate of convergence for the asymptotically optimal semiiterative methods for solving, where {sigma}(T) {contained_in} {Omega}.
Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian
2011-01-01
The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... considerable effect on the final estimations of the method, in particular on the coefficient of variation of the estimated failure probability. Based on these observations, a simple optimization algorithm is proposed which distributes the support points so that the coefficient of variation of the method...... is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high...
Upper bound on the Abelian gauge coupling from asymptotic safety
Eichhorn, Astrid; Versteegen, Fleur
2018-01-01
We explore the impact of asymptotically safe quantum gravity on the Abelian gauge coupling in a model including a charged scalar, confirming indications that asymptotically safe quantum fluctuations of gravity could trigger a power-law running towards a free fixed point for the gauge coupling above the Planck scale. Simultaneously, quantum gravity fluctuations balance against matter fluctuations to generate an interacting fixed point, which acts as a boundary of the basin of attraction of the free fixed point. This enforces an upper bound on the infrared value of the Abelian gauge coupling. In the regime of gravity couplings which in our approximation also allows for a prediction of the top quark and Higgs mass close to the experimental value [1], we obtain an upper bound approximately 35% above the infrared value of the hypercharge coupling in the Standard Model.
On the asymptotic expansion of the Bergman kernel
Seto, Shoo
Let (L, h) → (M, o) be a polarized Kahler manifold. We define the Bergman kernel for H0(M, Lk), holomorphic sections of the high tensor powers of the line bundle L. In this thesis, we will study the asymptotic expansion of the Bergman kernel. We will consider the on-diagonal, near-diagonal and far off-diagonal, using L2 estimates to show the existence of the asymptotic expansion and computation of the coefficients for the on and near-diagonal case, and a heat kernel approach to show the exponential decay of the off-diagonal of the Bergman kernel for noncompact manifolds assuming only a lower bound on Ricci curvature and C2 regularity of the metric.
Higher order corrections to asymptotic-de Sitter inflation
Mohsenzadeh, M.; Yusofi, E.
2017-08-01
Since trans-Planckian considerations can be associated with the re-definition of the initial vacuum, we investigate further the influence of trans-Planckian physics on the spectra produced by the initial quasi-de Sitter (dS) state during inflation. We use the asymptotic-dS mode to study the trans-Planckian correction of the power spectrum to the quasi-dS inflation. The obtained spectra consist of higher order corrections associated with the type of geometry and harmonic terms sensitive to the fluctuations of space-time (or gravitational waves) during inflation. As an important result, the amplitude of the power spectrum is dependent on the choice of c, i.e. the type of space-time in the period of inflation. Also, the results are always valid for any asymptotic dS space-time and particularly coincide with the conventional results for dS and flat space-time.
TAIL ASYMPTOTICS OF LIGHT-TAILED WEIBULL-LIKE SUMS
DEFF Research Database (Denmark)
Asmussen, Soren; Hashorva, Enkelejd; Laub, Patrick J.
2017-01-01
We consider sums of n i.i.d. random variables with tails close to exp{-x(beta)} for some beta > 1. Asymptotics developed by Rootzen (1987) and Balkema, Kluppelberg, and Resnick (1993) are discussed from the point of view of tails rather than of densities, using a somewhat different angle......, and supplemented with bounds, results on a random number N of terms, and simulation algorithms....
Asymptotic behaviour of the Weyl tensor in higher dimensions
Czech Academy of Sciences Publication Activity Database
Ortaggio, Marcello; Pravdová, Alena
2014-01-01
Roč. 90, č. 10 (2014), s. 104011 ISSN 1550-7998 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : higher-dimensional gravity * asymptotic structure * classical general relativity Subject RIV: BA - General Mathematics Impact factor: 4.643, year: 2014 http://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.104011
Asymptotic behavior of Maxwell fields in higher dimensions
Czech Academy of Sciences Publication Activity Database
Ortaggio, Marcello
2014-01-01
Roč. 90, č. 12 (2014), s. 124020 ISSN 1550-7998 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : higher-dimensional gravity * asymptotic structure * classical general relativity Subject RIV: BA - General Mathematics Impact factor: 4.643, year: 2014 http://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.124020
Framework for an asymptotically safe standard model via dynamical breaking
Abel, Steven; Sannino, Francesco
2017-09-01
We present a consistent embedding of the matter and gauge content of the Standard Model into an underlying asymptotically safe theory that has a well-determined interacting UV fixed point in the large color/flavor limit. The scales of symmetry breaking are determined by two mass-squared parameters with the breaking of electroweak symmetry being driven radiatively. There are no other free parameters in the theory apart from gauge couplings.
Asymptotic estimation of xi^{(2n)}(1/2)
Coffey, Mark W.
2009-06-01
We verify a very recent conjecture of Farmer and Rhoades on the asymptotic rate of growth of the derivatives of the Riemann xi function at s=1/2 . We give two separate proofs of this result, with the more general method not restricted to s=1/2 . We briefly describe other approaches to our results, give a heuristic argument, and mention supporting numerical evidence.
Bounds and asymptotics for orthogonal polynomials for varying weights
Levin, Eli
2018-01-01
This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals. Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics. This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices. .
Asymptotic analysis of Lévy-driven tandem queues
P.M.D. Lieshout (Pascal); M.R.H. Mandjes (Michel)
2008-01-01
htmlabstractWe analyze tail asymptotics of a two-node tandem queue with spectrally-positive Lévy input. A first focus lies in the tail probabilities of the type ¿(Q 1>¿ x,Q 2>(1¿¿)x), for ¿¿(0,1) and x large, and Q i denoting the steady-state workload in the ith queue. In case of light-tailed input,
Non-linear and signal energy optimal asymptotic filter design
Directory of Open Access Journals (Sweden)
Josef Hrusak
2003-10-01
Full Text Available The paper studies some connections between the main results of the well known Wiener-Kalman-Bucy stochastic approach to filtering problems based mainly on the linear stochastic estimation theory and emphasizing the optimality aspects of the achieved results and the classical deterministic frequency domain linear filters such as Chebyshev, Butterworth, Bessel, etc. A new non-stochastic but not necessarily deterministic (possibly non-linear alternative approach called asymptotic filtering based mainly on the concepts of signal power, signal energy and a system equivalence relation plays an important role in the presentation. Filtering error invariance and convergence aspects are emphasized in the approach. It is shown that introducing the signal power as the quantitative measure of energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. The property of structural energy dissipativeness is one of the most important and fundamental features of resulting filters. Therefore, it is natural to call them asymptotic filters. The notion of the asymptotic filter is carried in the paper as a proper tool in order to unify stochastic and non-stochastic, linear and nonlinear approaches to signal filtering.
Yedlin, M. J.; Virieux, J.; van Vorst, D. G.
2010-12-01
obtained by using the new uniform asymptotic expansion ansatz, which supplants the usual homogeneous transfer function employed. Examples will be presented for synthetic data sets, to illustrate the differences between these two transfer functions. References [1] E. Zauderer. 1971, Uniform asymptotic solutions of the reduced wave equation. Journal of Mathematical Analysis and Application 30, pp. 157-171. [2] M. J. Yedlin. 1987, Uniform asymptotic solution for the Green’s function for the two-dimensional acoustic equation. J. Acoust. Soc. Am. 81(2) pp. 238-243. [3] J. Tromp, C. Tape and Q. Liu. 2005, Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophysical Journal International 160(1), pp. 195-216. [4] I. Iturbe, P. Roux, J. Virieux and B. Nicolas. 2009, Travel-time sensitivity kernels versus diffraction patterns obtained through double beam-forming in shallow water. J. Acoust. Soc. Am. 126(2), pp. 713-720. [5] J. R. Ernst, A. G. Green, H. Maurer and K. Holliger. 2007, Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data. Geophysics 72, pp. J53-J64.
Directory of Open Access Journals (Sweden)
Justine Yasappan
2013-01-01
Full Text Available Fluids subject to thermal gradients produce complex behaviors that arise from the competition with gravitational effects. Although such sort of systems have been widely studied in the literature for simple (Newtonian fluids, the behavior of viscoelastic fluids has not been explored thus far. We present a theoretical study of the dynamics of a Maxwell viscoelastic fluid in a closed-loop thermosyphon. This sort of fluid presents elastic-like behavior and memory effects. We study the asymptotic properties of the fluid inside the thermosyphon and the exact equations of motion in the inertial manifold that characterizes the asymptotic behavior. We derive, for the first time, the mathematical derivations of the motion of a viscoelastic fluid in the interior of a closed-loop thermosyphon under the effects of natural convection and a given external temperature gradient.
Asymptotics for the Ostrovsky-Hunter Equation in the Critical Case
Directory of Open Access Journals (Sweden)
Fernando Bernal-Vílchis
2017-01-01
Full Text Available We consider the Cauchy problem for the Ostrovsky-Hunter equation ∂x∂tu-b/3∂x3u-∂xKu3=au, t,x∈R2, u0,x=u0x, x∈R, where ab>0. Define ξ0=27a/b1/4. Suppose that K is a pseudodifferential operator with a symbol K^ξ such that K^±ξ0=0, Im K^ξ=0, and K^ξ≤C. For example, we can take K^ξ=ξ2-ξ02/ξ2+1. We prove the global in time existence and the large time asymptotic behavior of solutions.
An Asymptotic-Preserving Method for a Relaxation of the Navier-Stokes-Korteweg Equations
Chertock, Alina; Neusser, Jochen
2015-01-01
The Navier-Stokes-Korteweg (NSK) equations are a classical diffuse-interface model for compressible two-phase flow. As direct numerical simulations based on the NSK system are quite expensive and in some cases even impossible, we consider a relaxation of the NSK system, for which robust numerical methods can be designed. However, time steps for explicit numerical schemes depend on the relaxation parameter and therefore numerical simulations in the relaxation limit are very inefficient. To overcome this restriction, we propose an implicit-explicit asymptotic-preserving finite volume method. We prove that the new scheme provides a consistent discretization of the NSK system in the relaxation limit and demonstrate that it is capable of accurately and efficiently computing numerical solutions of problems with realistic density ratios and small interfacial widths.
Directory of Open Access Journals (Sweden)
Alexandre Cabot
2009-04-01
Full Text Available We investigate the asymptotic properties as $to infty$ of the differential equation $$ ddot{x}(t+a(tdot{x}(t+ abla G(x(t=0, quad tgeq 0 $$ where $x(cdot$ is $mathbb{R}$-valued, the map $a:mathbb{R}_+o mathbb{R}_+$ is non increasing, and $G:mathbb{R} o mathbb{R}$ is a potential with locally Lipschitz continuous derivative. We identify conditions on the function $a(cdot$ that guarantee or exclude the convergence of solutions of this problem to points in $mathop{ m argmin} G$, in the case where $G$ is convex and $mathop{ m argmin} G$ is an interval. The condition $$ int_0^{infty} e^{-int_0^t a(s, ds}dt
Asymptotic theory for the dynamic of networks with heterogenous social capital allocation
Ubaldi, Enrico; Karsai, Márton; Vezzani, Alessandro; Burioni, Raffaella; Vespignani, Alessandro
2015-01-01
The structure and dynamic of social network are largely determined by the heterogeneous interaction activity and social capital allocation of individuals. These features interplay in a non-trivial way in the formation of network and challenge a rigorous dynamical system theory of network evolution. Here we study seven real networks describing temporal human interactions in three different settings: scientific collaborations, Twitter mentions, and mobile phone calls. We find that the node's activity and social capital allocation can be described by two general functional forms that can be used to define a simple stochastic model for social network dynamic. This model allows the explicit asymptotic solution of the Master Equation describing the system dynamic, and provides the scaling laws characterizing the time evolution of the social network degree distribution and individual node's ego network. The analytical predictions reproduce with accuracy the empirical observations validating the theoretical approach....
A diffusion model for two parallel queues with processor sharing: transient behavior and asymptotics
Directory of Open Access Journals (Sweden)
Charles Knessl
1999-01-01
Full Text Available We consider two identical, parallel M/M/1 queues. Both queues are fed by a Poisson arrival stream of rate λ and have service rates equal to μ. When both queues are non-empty, the two systems behave independently of each other. However, when one of the queues becomes empty, the corresponding server helps in the other queue. This is called head-of-the-line processor sharing. We study this model in the heavy traffic limit, where ρ=λ/μ→1. We formulate the heavy traffic diffusion approximation and explicitly compute the time-dependent probability of the diffusion approximation to the joint queue length process. We then evaluate the solution asymptotically for large values of space and/or time. This leads to simple expressions that show how the process achieves its stead state and other transient aspects.
Vaidya-like exact solutions with torsion
Blagojević, M
2015-01-01
Starting from the Oliva-Tempo-Troncoso black hole, a solution of the Bergshoeff-Hohm-Townsend massive gravity, a new class of the Vaidya-like exact solutions with torsion is constructed in the three-dimensional Poincar\\'e gauge theory. A particular subclass of these solutions is shown to possess the asymptotic conformal symmetry. The related canonical energy contains a contribution stemming from torsion.
On IR solutions in Horava gravity theories
Nastase, Horatiu
2009-01-01
In this note we search for large distance solutions of Horava gravity. In the case of the "detailed balance" action, gravity solutions asymptote to IR only above the cosmological constant ($\\sim$horizon) scale. However, if one adds IR dominant terms $\\alpha R^{(3)}+\\beta \\Lambda_W$, one can recover general relativity solutions on usual scales in the real Universe, provided one fine-tunes the cosmological constant, reobtaining the usual cosmological constant problem. We comment on pp wave solu...
Asymptotic domination of cold relativistic MHD winds by kinetic energy flux
Begelman, Mitchell C.; Li, Zhi-Yun
1994-01-01
We study the conditions which lead to the conversion of most Poynting flux into kinetic energy flux in cold, relativistic hydromagnetic winds. It is shown that plasma acceleration along a precisely radial flow is extremely inefficient due to the near cancellation of the toroidal magnetic pressure and tension forces. However, if the flux tubes in a flow diverge even slightly faster than radially, the fast magnetosonic point moves inward from infinity to a few times the light cylinder radius. Once the flow becomes supermagnetosonic, further divergence of the flux tubes beyond the fast point can accelerate the flow via the 'magnetic nozzle' effect, thereby further converting Poynting flux to kinetic energy flux. We show that the Grad-Shafranov equation admits a generic family of kinetic energy-dominated asymptotic wind solutions with finite total magnetic flux. The Poynting flux in these solutions vanishes logarithmically with distance. The way in which the flux surfaces are nested within the flow depends only on the ratio of angular velocity to poliodal 4-velocity as a function of magnetic flux. Radial variations in flow structure can be expressed in terms of a pressure boundary condition on the outermost flux surface, provided that no external toriodal field surrounds the flow. For a special case, we show explicitly how the flux surfaces merge gradually to their asymptotes. For flows confined by an external medium of pressure decreasing to zero at infinity we show that, depending on how fast the ambient pressure declines, the final flow state could be either a collimated jet or a wind that fills the entire space. We discuss the astrophysical implications of our results for jets from active galactic nuclei and for free pulsar winds such as that believed to power the Crab Nebula.
Wu, Chih-Ping; Li, Wei-Chen
2017-05-01
A three-dimensional (3D) asymptotic formulation is developed for the buckling analysis of simply-supported, single-layered nanoplates/graphene sheets (SLNP and SLGS) embedded in an elastic medium and under biaxial compressive loads. In the formulation, the Eringen nonlocal elasticity theory is used to capture the small length scale effect, and the interaction between the SLNP/SLGS and its surrounding medium is simulated using a Pasternak-type foundation. After performing the mathematical processes of nondimensionalization, asymptotic expansion and successive integration, we finally obtain recursive sets of governing equations for various order problems. The nonlocal classical plate theory (CPT) is derived as a first-order approximation of the 3D nonlocal elasticity theory, and the governing equations for higher-order problems retain the same differential operators as those of nonlocal CPT, although with different nonhomogeneous terms. Some accurate nonlocal elasticity solutions of the critical load parameters of simply-supported, biaxially-loaded SLNP/SLGS with and without being embedded in the elastic medium are given to demonstrate the performance of the 3D asymptotic nonlocal elasticity theory.
Effect of plate permeability on nonlinear stability of the asymptotic suction boundary layer.
Wedin, Håkan; Cherubini, Stefania; Bottaro, Alessandro
2015-07-01
The nonlinear stability of the asymptotic suction boundary layer is studied numerically, searching for finite-amplitude solutions that bifurcate from the laminar flow state. By changing the boundary conditions for disturbances at the plate from the classical no-slip condition to more physically sound ones, the stability characteristics of the flow may change radically, both for the linearized as well as the nonlinear problem. The wall boundary condition takes into account the permeability K̂ of the plate; for very low permeability, it is acceptable to impose the classical boundary condition (K̂=0). This leads to a Reynolds number of approximately Re(c)=54400 for the onset of linearly unstable waves, and close to Re(g)=3200 for the emergence of nonlinear solutions [F. A. Milinazzo and P. G. Saffman, J. Fluid Mech. 160, 281 (1985); J. H. M. Fransson, Ph.D. thesis, Royal Institute of Technology, KTH, Sweden, 2003]. However, for larger values of the plate's permeability, the lower limit for the existence of linear and nonlinear solutions shifts to significantly lower Reynolds numbers. For the largest permeability studied here, the limit values of the Reynolds numbers reduce down to Re(c)=796 and Re(g)=294. For all cases studied, the solutions bifurcate subcritically toward lower Re, and this leads to the conjecture that they may be involved in the very first stages of a transition scenario similar to the classical route of the Blasius boundary layer initiated by Tollmien-Schlichting (TS) waves. The stability of these nonlinear solutions is also investigated, showing a low-frequency main unstable mode whose growth rate decreases with increasing permeability and with the Reynolds number, following a power law Re(-ρ), where the value of ρ depends on the permeability coefficient K̂. The nonlinear dynamics of the flow in the vicinity of the computed finite-amplitude solutions is finally investigated by direct numerical simulations, providing a viable scenario for
Nonoscillatory half-linear difference equations and recessive solutions
Directory of Open Access Journals (Sweden)
Mauro Marini
2005-05-01
Full Text Available Recessive and dominant solutions for the nonoscillatory half-linear difference equation are investigated. By using a uniqueness result for the zero-convergent solutions satisfying a suitable final condition, we prove that recessive solutions are the Ã¢Â€Âœsmallest solutions in a neighborhood of infinity,Ã¢Â€Â like in the linear case. Other asymptotic properties of recessive and dominant solutions are treated too.
On selfdual spin-connections and asymptotic safety
Directory of Open Access Journals (Sweden)
U. Harst
2016-02-01
Full Text Available We explore Euclidean quantum gravity using the tetrad field together with a selfdual or anti-selfdual spin-connection as the basic field variables. Setting up a functional renormalization group (RG equation of a new type which is particularly suitable for the corresponding theory space we determine the non-perturbative RG flow within a two-parameter truncation suggested by the Holst action. We find that the (anti-selfdual theory is likely to be asymptotically safe. The existing evidence for its non-perturbative renormalizability is comparable to that of Einstein–Cartan gravity without the selfduality condition.
Subexponential loss rate asymptotics for Lévy processes
DEFF Research Database (Denmark)
Andersen, Lars Nørvang
2011-01-01
We consider a Lévy process reflected in barriers at 0 and K > 0. The loss rate is the mean of the local time at K at time 1 when the process is started in stationarity, and is a natural continuous-time analogue of the stationary expected loss rate for a reflected random walk. We derive asymptotics...... for the loss rate when K tends to infinity, when the mean of the Lévy process is negative and the positive jumps are subexponential. In the course of this derivation, we achieve a formula, which is a generalization of the celebrated Pollaczeck-Khinchine formula....
Asymptotic formulae for likelihood-based tests of new physics
Cowan, Glen; Cranmer, Kyle; Gross, Eilam; Vitells, Ofer
2011-02-01
We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to account for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wald. We motivate and justify the use of a representative data set, called the "Asimov data set", which provides a simple method to obtain the median experimental sensitivity of a search or measurement as well as fluctuations about this expectation.
Asymptotic formulae for likelihood-based tests of new physics
Energy Technology Data Exchange (ETDEWEB)
Cowan, Glen [Royal Holloway, University of London, Physics Department, Egham (United Kingdom); Cranmer, Kyle [New York University, Physics Department, New York, NY (United States); Gross, Eilam; Vitells, Ofer [Weizmann Institute of Science, Rehovot (Israel)
2011-02-15
We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to account for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wald. We motivate and justify the use of a representative data set, called the ''Asimov data set'', which provides a simple method to obtain the median experimental sensitivity of a search or measurement as well as fluctuations about this expectation. (orig.)
Shrinkage singularities of amplitudes and weak interaction cross- section asymptotic
Dolgov, A D; Okun, Lev Borisovich
1972-01-01
The so called shrinkage singularities of amplitudes caused by shrinkage of diffraction peak at asymptotically high energies are discussed given the condition that the amplitude singularities are not stronger than t/sup 2/ ln t (as is case for neutrino pair exchange diagrams) then total cross-section sigma /sub tot/ cannot increase faster at s to infinity than s/sup 1/3/. If shrinkage singularities are absent then sigma /sub tot/ cannot increase as any power of s. All the conclusions are valid, if the dispersion relations with finite number of subtractions exist at t
Asymptotic behavior of observables in the asymmetric quantum Rabi model
Semple, J.; Kollar, M.
2018-01-01
The asymmetric quantum Rabi model with broken parity invariance shows spectral degeneracies in the integer case, that is when the asymmetry parameter equals an integer multiple of half the oscillator frequency, thus hinting at a hidden symmetry and accompanying integrability of the model. We study the expectation values of spin observables for each eigenstate and observe characteristic differences between the integer and noninteger cases for the asymptotics in the deep strong coupling regime, which can be understood from a perturbative expansion in the qubit splitting. We also construct a parent Hamiltonian whose exact eigenstates possess the same symmetries as the perturbative eigenstates of the asymmetric quantum Rabi model in the integer case.
Asymptotic Analysis and Spatial Coupling of Counter Braids
Rosnes, Eirik; Amat, Alexandre Graell i
2016-01-01
A counter braid (CB) is a novel counter architecture introduced by Lu et al. in 2007 for per-flow measurements on high-speed links. CBs achieve an asymptotic compression rate (under optimal decoding) that matches the entropy lower bound of the flow size distribution. In this paper, we apply the concept of spatial coupling to CBs to improve their belief propagation (BP) threshold, and analyze the performance of the resulting spatially-coupled CBs (SC-CBs). We introduce an equivalent bipartite ...
Asymptotic geometry in higher products of rank one Hadamard spaces
Link, Gabriele
2013-01-01
Given a product X of locally compact rank one Hadamard spaces, we study asymptotic properties of certain discrete isometry groups. First we give a detailed description of the structure of the geometric limit set and relate it to the limit cone; moreover, we show that the action of the group on a quotient of the regular geometric boundary of X is minimal and proximal. This is completely analogous to the case of Zariski dense discrete subgroups of semi-simple Lie groups acting on the associated...
Asymptotics of Rydberg states for the hydrogen atom
Energy Technology Data Exchange (ETDEWEB)
Thomas, L.E. [Virginia Univ., Charlottesville, VA (United States). Dept. of Mathematics; Villegas-Blas, C. [Universidad Nacional Autonoma de Mexico, Instituto de Matematicas, Unidad Cuernavaca, A. P. 273-3 Admon. 3, Cuernavaca Morelos 62251 (Mexico)
1997-08-01
The asymptotics of Rydberg states, i.e., highly excited bound states of the hydrogen atom Hamiltonian, and various expectations involving these states are investigated. We show that suitable linear combinations of these states, appropriately rescaled and regarded as functions either in momentum space or configuration space, are highly concentrated on classical momentum space or configuration space Kepler orbits respectively, for large quantum numbers. Expectations of momentum space or configuration space functions with respect to these states are related to time-averages of these functions over Kepler orbits. (orig.)
Asymptotic Theory for the Probability Density Functions in Burgers Turbulence
Weinan, E; Eijnden, Eric Vanden
1999-01-01
A rigorous study is carried out for the randomly forced Burgers equation in the inviscid limit. No closure approximations are made. Instead the probability density functions of velocity and velocity gradient are related to the statistics of quantities defined along the shocks. This method allows one to compute the anomalies, as well as asymptotics for the structure functions and the probability density functions. It is shown that the left tail for the probability density function of the velocity gradient has to decay faster than $|\\xi|^{-3}$. A further argument confirms the prediction of E et al., Phys. Rev. Lett. {\\bf 78}, 1904 (1997), that it should decay as $|\\xi|^{-7/2}$.
Joint Asymptotic Distributions of Smallest and Largest Insurance Claims
Directory of Open Access Journals (Sweden)
Hansjörg Albrecher
2014-07-01
Full Text Available Assume that claims in a portfolio of insurance contracts are described by independent and identically distributed random variables with regularly varying tails and occur according to a near mixed Poisson process. We provide a collection of results pertaining to the joint asymptotic Laplace transforms of the normalised sums of the smallest and largest claims, when the length of the considered time interval tends to infinity. The results crucially depend on the value of the tail index of the claim distribution, as well as on the number of largest claims under consideration.
Asymptotic Limits for Transport in Binary Stochastic Mixtures
Energy Technology Data Exchange (ETDEWEB)
Prinja, A. K. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-05-01
The Karhunen-Loeve stochastic spectral expansion of a random binary mixture of immiscible fluids in planar geometry is used to explore asymptotic limits of radiation transport in such mixtures. Under appropriate scalings of mixing parameters - correlation length, volume fraction, and material cross sections - and employing multiple- scale expansion of the angular flux, previously established atomic mix and diffusion limits are reproduced. When applied to highly contrasting material properties in the small cor- relation length limit, the methodology yields a nonstandard reflective medium transport equation that merits further investigation. Finally, a hybrid closure is proposed that produces both small and large correlation length limits of the closure condition for the material averaged equations.
Application of the Asymptotic Taylor Expansion Method to Bistable Potentials
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Okan Ozer
2013-01-01
Full Text Available A recent method called asymptotic Taylor expansion (ATEM is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.
Asymptotically Efficient Identification of Known-Sensor Hidden Markov Models
Mattila, Robert; Rojas, Cristian R.; Krishnamurthy, Vikram; Wahlberg, Bo
2017-12-01
We consider estimating the transition probability matrix of a finite-state finite-observation alphabet hidden Markov model with known observation probabilities. The main contribution is a two-step algorithm; a method of moments estimator (formulated as a convex optimization problem) followed by a single iteration of a Newton-Raphson maximum likelihood estimator. The two-fold contribution of this letter is, firstly, to theoretically show that the proposed estimator is consistent and asymptotically efficient, and secondly, to numerically show that the method is computationally less demanding than conventional methods - in particular for large data sets.
Asymptotic Stability for a Class of Nonlinear Difference Equations
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Chang-you Wang
2010-01-01
Full Text Available We study the global asymptotic stability of the equilibrium point for the fractional difference equation xn+1=(axn-lxn-k/(α+bxn-s+cxn-t, n=0,1,…, where the initial conditions x-r,x-r+1,…,x1,x0 are arbitrary positive real numbers of the interval (0,α/2a,l,k,s,t are nonnegative integers, r=max{l,k,s,t} and α,a,b,c are positive constants. Moreover, some numerical simulations are given to illustrate our results.
Asymptotic Ergodic Capacity Analysis of Composite Lognormal Shadowed Channels
Ansari, Imran Shafique
2015-05-01
Capacity analysis of composite lognormal (LN) shadowed links, such as Rician-LN, Gamma-LN, and Weibull-LN, is addressed in this work. More specifically, an exact closed-form expression for the moments of the end-to-end signal-to-noise ratio (SNR) of a single composite link transmission system is presented in terms of well- known elementary functions. Capitalizing on these new moments expressions, we present asymptotically tight lower bounds for the ergodic capacity at high SNR. All the presented results are verified via computer-based Monte-Carlo simulations. © 2015 IEEE.
Ke, Zijun; Zhang, Zhiyong Johnny
2017-09-12
Autocorrelation and partial autocorrelation, which provide a mathematical tool to understand repeating patterns in time series data, are often used to facilitate the identification of model orders of time series models (e.g., moving average and autoregressive models). Asymptotic methods for testing autocorrelation and partial autocorrelation such as the 1/T approximation method and the Bartlett's formula method may fail in finite samples and are vulnerable to non-normality. Resampling techniques such as the moving block bootstrap and the surrogate data method are competitive alternatives. In this study, we use a Monte Carlo simulation study and a real data example to compare asymptotic methods with the aforementioned resampling techniques. For each resampling technique, we consider both the percentile method and the bias-corrected and accelerated method for interval construction. Simulation results show that the surrogate data method with percentile intervals yields better performance than the other methods. An R package pautocorr is used to carry out tests evaluated in this study. © 2017 The British Psychological Society.
Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations
Craps, Ben; Jai-akson, Puttarak; Vanhoof, Joris
2015-01-01
Spherically symmetric perturbations in AdS-scalar field systems of small amplitude epsilon approximately periodic on time scales of order 1/epsilon^2 (in the sense that no significant transfer of energy between the AdS normal modes occurs) have played an important role in considerations of AdS stability. They are seen as anchors of stability islands where collapse of small perturbations to black holes does not occur. (This collapse, if it happens, typically develops on time scales of the order 1/epsilon^2.) We construct an analytic treatment of the frequency spectra of such quasiperiodic perturbations, paying special attention to the large frequency asymptotics. For the case of a self-interacting phi^4 scalar field in a non-dynamical AdS background, we arrive at a fairly complete analytic picture involving quasiperiodic spectra with an exponential suppression modulated by a power law at large mode numbers. For the case of dynamical gravity, the structure of the large frequency asymptotics is more complicated....
arXiv Naturalness of asymptotically safe Higgs
Pelaggi, Giulio Maria; Strumia, Alessandro; Vigiani, Elena
2017-01-01
We extend the list of theories featuring a rigorous interacting ultraviolet fixed point by constructing the first theory featuring a Higgs-like scalar with gauge, Yukawa and quartic interactions. We show that the theory enters a perturbative asymptotically safe regime at energies above a physical scale $\\Lambda$. We determine the salient properties of the theory and use it as a concrete example to test whether scalars masses unavoidably receive quantum correction of order $\\Lambda$. Having at our dispose a calculable model allowing us to precisely relate the IR and UV of the theory we demonstrate that the scalars can be lighter than $\\Lambda$. Although we do not have an answer to whether the Standard Model hypercharge coupling growth towards a Landau pole at around $\\Lambda \\sim 10^{40}$ GeV can be tamed by non-perturbative asymptotic safety, our results indicate that such a possibility is worth exploring. In fact, if successful, it might also offer an explanation for the unbearable lightness of the Higgs.
Quantum gravity on foliated spacetimes: Asymptotically safe and sound
Biemans, Jorn; Platania, Alessia; Saueressig, Frank
2017-04-01
Asymptotic safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the Arnowitt-Deser-Misner formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the non-Gaussian fixed-point characteristic for asymptotic safety the setting exhibits a second family of non-Gaussian fixed points with a positive Newton's constant and real critical exponents. The presence of these new fixed points alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the ɛ -expansion around two dimensions, Monte Carlo simulations based on lattice quantum gravity, and the discretized Wheeler-DeWitt equation.
The asymptotic behavior of Buneman instability in dissipative plasma
Rostomyan, Eduard V.
2017-10-01
The problem of time evolution of initial perturbation excited at the development of the Buneman instability (BI) in plasma with dissipation is solved. Developing fields are presented in the form of a wave train with slowly varying amplitude. It is shown that the evolution of the initial pulse in space and time is given by the differential equation of third order. The equation is solved and the expression for the asymptotic pulse shape is obtained. The expression gives the most complete information on the instability: the space-time distribution of the fields, growth rates, velocities of unstable perturbations, the influence of the collisions/dissipation on the instability, its character, (absolute/convective), etc. All these characteristics of the BI are carried out by analyzing the expression for the shape. The obtained results may be applied to any system in which the red-shifted electron stream oscillations resonantly interact with ions. Asymptotic shapes of the BI are presented for various levels of dissipation.
Deformation limits on two-parameter fracture mechanics in terms of higher order asymptotics
Crane, D. L.; Anderson, T. L.
1994-09-01
This report addresses the limitations of two-parameter fracture mechanics. We performed an asymptotic analysis of the general power series representation of the crack tip stress potential in an elastic plastic material that obeys a Ramberg-Osgood constitutive law. Expansion of the power series over a substantial number of terms yields. only three independent coefficients for low. and medium-hardening materials. The first independent The second and third independent coefficients, K2 and K4 are a function of geometry and loading level. A two-parameter theory implies that the crack tip stress fields have two degrees of freedom, but the asymptotic analysis implies that three parameters are required to characterize near-tip conditions. Thus two-parameter fracture theory is a valid engineering model only when there is an approximately unique relationship between K2 and K4. We performed elastic-plastic finite element analyses on several geometries and evaluated K2 and K4 as a function of deformation level. A reference,two-parameter solution (which gives a unique relation between K2 and K4) was provided by the modified boundary layer (MBL) geometry. Results indicate that the near tip stresses in all but the deeply cracked SENT (a/W-.5.O.9) and SENT (a/W-0.9) lend themselves to a two-parameter characterization. However, the deeply cracked SENT and SENT specimens maintain a high level of constraint to relatively large deformation levels. Thus single-parameter fracture mechanics is fairly robust for these high constraint geometries, but two-parameter theory is of little value when constraint loss eventually occurs.
Uezu, Tatsuya
1997-11-01
In learning under external disturbance, it is expected that some tolerance in the system will optimize the learning process. In this paper, we give one example of this in learning from stochastic rules by the Gibbs algorithm. Using the replica method, we show that for the case of output noise, there exists an optimal temperature at which the generalization error is a minimum. This temperature exists even in the limit of large training sets and is determined by the stable replica symmetric solution. On the other hand, for other types of noise no such temperature exists and the asymptotic behaviour is determined by the one-step replica symmetric breaking solution. Further, the asymptotic expressions for learning curves are derived. They are precisely the same as those for the minimum-error algorithm.
Asymptotic Expansions and Bootstrapping Distributions for Dependent Variables: A Martingale Approach
Mykland, Per Aslak
1992-01-01
The paper develops a one-step triangular array asymptotic expansion for continuous martingales which are asymptotically normal. Mixing conditions are not required, but the quadratic variations of the martingales must satisfy a law of large numbers and a central limit type condition. From this result we derive expansions for the distributions of estimators in asymptotically ergodic differential equation models, and also for the bootstrapping estimators of these distributions.
On the asymptotic behavior of the Durbin-Watson statistic for ARX processes in adaptive tracking
Bercu, Bernard; Portier, Bruno; Vazquez, V.
2012-01-01
International audience; A wide literature is available on the asymptotic behavior of the Durbin-Watson statistic for autoregressive models. However, it is impossible to find results on the Durbin-Watson statistic for autoregressive models with adaptive control. Our purpose is to fill the gap by establishing the asymptotic behavior of the Durbin Watson statistic for ARX models in adaptive tracking. On the one hand, we show the almost sure convergence as well as the asymptotic normality of the ...
Coulomb-distorted plane wave: Partial wave expansion and asymptotic forms
Hornyak, I.; Kruppa, A. T.
2013-05-01
Partial wave expansion of the Coulomb-distorted plane wave is determined and studied. Dominant and sub-dominant asymptotic expansion terms are given and leading order three-dimensional asymptotic form is derived. The generalized hypergeometric function 2F2(a, a; a + l + 1, a - l; z) is expressed with the help of confluent hypergeometric functions and the asymptotic expansion of 2F2(a, a; a + l + 1, a - l; z) is simplified.
Directory of Open Access Journals (Sweden)
Kim Jong
2011-01-01
Full Text Available Abstract We consider a hybrid projection method for finding a common element in the fixed point set of an asymptotically quasi-ϕ-nonexpansive mapping and in the solution set of an equilibrium problem. Strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. 2000 Mathematics subject classification: 47H05, 47H09, 47H10, 47J25
Test of the second order asymptotic theory with low degree solar gravity modes
Energy Technology Data Exchange (ETDEWEB)
Barry, C.T.; Rosenwald, R.D.; Gu, Y.; Hill, H.A
1988-01-01
Further testing of first and second order asymptotic theory predictions for solar gravity modes is possible with the work of gu and Hill in which the number of classified low-degree gravity mode multiplets was increased from 31 to 53. In an extension of the work where the properties of 31 multiplets were analyzed in the framework of first order asymptotic theory, a new analysis has been performed using the properties of the 53 classified multiplets. The result of this analysis again shows the inadequacy of first order asymptotic theory for describing the eigenfrequency spectrum and clearly demonstrates the necessity of using second order asymptotic theory. 30 refs.
Time-asymptotic interactions of two ensembles of Cucker-Smale flocking particles
Ha, Seung-Yeal; Ko, Dongnam; Zhang, Xiongtao; Zhang, Yinglong
2017-07-01
We study the time-asymptotic interactions of two ensembles of Cucker-Smale flocking particles. For this, we use a coupled hydrodynamic Cucker-Smale system and discuss two frameworks, leading to mono-cluster and bi-cluster flockings asymptotically depending on initial configurations, coupling strengths, and the far-field decay property of communication weights. Under the proposed two frameworks, we show that mono-cluster and bi-cluster flockings emerge asymptotically exponentially fast and algebraically slow, respectively. Our asymptotic analysis uses the Lyapunov functional approach and a Lagrangian formulation of the coupled system.
A classification scheme for nonoscillatory solutions of a higher order neutral difference equation
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available Nonoscillatory solutions of a nonlinear neutral type higher order difference equations are classified by means of their asymptotic behaviors. By means of the Kranoselskii's fixed point theorem, existence criteria are then provided for justification of such classification.
New generalized nonspherical black hole solutions
Kleihaus, Burkhard; Radu, Eugen; Rodriguez, Maria J
2010-01-01
We present numerical evidence for the existence of several types of static black hole solutions with a nonspherical event horizon topology in $d\\geq 6$ spacetime dimensions. These asymptotically flat configurations are found for a specific metric ansatz and can be viewed as higher dimensional counterparts of the $d=5$ static black rings, dirings and black Saturn. Similar to that case, they are supported against collapse by conical singularities. The issue of rotating generalizations of these solutions is also considered.
Asymptotically safe gravity and nonsingular inflationary big bang with vacuum birth
Kofinas, Georgios; Zarikas, Vasilios
2016-11-01
General nonsingular accelerating cosmological solutions for an initial cosmic period of pure vacuum birth era are derived. This vacuum era is described by a varying cosmological "constant" suggested by the renormalization group flow of asymptotic safety scenario near the ultraviolet fixed point. In this scenario, a natural exit from inflation to the standard decelerating cosmology occurs when the energy scale lowers and the cosmological constant becomes insignificant. In the following period where matter is also present, cosmological solutions with characteristics similar to the vacuum case are generated. Remarkably the set of equations allows for particle production and entropy generation. Alternatively, in the case of nonzero bulk viscosity, entropy production and reheating is found. As for the equations of motion, they modify Einstein equations by adding covariant kinetic terms of the cosmological constant which respect the Bianchi identities. An advance of the proposed framework is that it ensures a consistent description of both a quantum vacuum birth of the universe and a subsequent cosmic era in the presence of matter.
Exact solution for a one-dimensional model for reptation.
Drzewiński, Andrzej; van Leeuwen, J M J
2006-05-01
We discuss the exact solution for the properties of the recently introduced "necklace" model for reptation. The solution gives the drift velocity, diffusion constant, and renewal time for asymptotically long chains. Its properties are also related to a special case of the Rubinstein-Duke model in one dimension.
Uniqueness of singular solution of semilinear elliptic equation
Indian Academy of Sciences (India)
Information Science, Henan University, Kaifeng 475004, People's Republic of China. E-mail: laibaishun@henu.edu.cn ... Keywords. Nonhomogeneous semilinear elliptic equation; positive solutions; asymptotic behavior; singular solutions. 1. Introduction. In this paper, we study the elliptic equation u + K(|x|)up + μf (|x|) = 0,.
Rugate filter design: An analytical approach using uniform WKB solutions
Perelman, N.; Averbukh, I.
1996-03-01
An analytical approach to the design of rugate filters with a smooth amplitude modulation of the sine-wave index is developed. The approach is based on the uniform WKB solutions (asymptotic expansions) of the coupled-wave equations. A closed-form solution for the inverse problem (finding the refractive index profile for a given reflectance shape inside the stop band) is found.
A Neumann problem for a system depending on the unknown boundary values of the solution
Directory of Open Access Journals (Sweden)
Pablo Amster
2013-01-01
Full Text Available A semilinear system of second order ODEs under Neumann conditions is studied. The system has the particularity that its nonlinear term depends on the (unknown Dirichlet values $y(0$ and $y(1$ of the solution. Asymptotic and non-asymptotic sufficient conditions of Landesman-Lazer type for existence of solutions are given. We generalize our previous results for a scalar equation, and a well known result by Nirenberg for a nonlinearity independent of $y(0$ and $y(1$.
Asymptotic analysis of downlink MISO systems over Rician fading channels
Falconet, Hugo
2016-06-24
In this work, we focus on the ergodic sum rate in the downlink of a single-cell large-scale multi-user MIMO system in which the base station employs N antennas to communicate with K single-antenna user equipments. A regularized zero-forcing (RZF) scheme is used for precoding under the assumption that each link forms a spatially correlated MIMO Rician fading channel. The analysis is conducted assuming N and K grow large with a non trivial ratio and perfect channel state information is available at the base station. Recent results from random matrix theory and large system analysis are used to compute an asymptotic expression of the signal-to-interference-plus-noise ratio as a function of the system parameters, the spatial correlation matrix and the Rician factor. Numerical results are used to evaluate the performance gap in the finite system regime under different operating conditions. © 2016 IEEE.
Asymptotic approximation method of force reconstruction: Proof of concept
Sanchez, J.; Benaroya, H.
2017-08-01
An important problem in engineering is the determination of the system input based on the system response. This type of problem is difficult to solve as it is often ill-defined, and produces inaccurate or non-unique results. Current reconstruction techniques typically involve the employment of optimization methods or additional constraints to regularize the problem, but these methods are not without their flaws as they may be sub-optimally applied and produce inadequate results. An alternative approach is developed that draws upon concepts from control systems theory, the equilibrium analysis of linear dynamical systems with time-dependent inputs, and asymptotic approximation analysis. This paper presents the theoretical development of the proposed method. A simple application of the method is presented to demonstrate the procedure. A more complex application to a continuous system is performed to demonstrate the applicability of the method.
Asymptotic coherence of gluons and of q-bosons
Energy Technology Data Exchange (ETDEWEB)
Nelson, C.A.
1993-12-31
In theoretical physics one of the most important aspects of coherent states is that they can often be simply and reliably used to investigate the quantum coherence and correlation properties of new dynamical, quantum field theories. First, this paper reviews the coherent/degenerate state treatment of the infra-red dynamics of perturbative QCD. This based on the asymptotic behavior of the Hamiltonian operator as {vert_bar}t{vert_bar} {yields} {infinity} in the interaction representation. Second, the paper reviews the usage of q-analogue coherent states {vert_bar}z>{sub q} to deduce coherence and uncertainty properties of the q-analogue quantized radiation field in the {vert_bar}z>{sub q} ``classical limit`` where {vert_bar}z{vert_bar} is large. Third, for future applications, a new ``projector`` definition of the usual coherent states and of the squeezed states is reported.
The large Reynolds number - Asymptotic theory of turbulent boundary layers.
Mellor, G. L.
1972-01-01
A self-consistent, asymptotic expansion of the one-point, mean turbulent equations of motion is obtained. Results such as the velocity defect law and the law of the wall evolve in a relatively rigorous manner, and a systematic ordering of the mean velocity boundary layer equations and their interaction with the main stream flow are obtained. The analysis is extended to the turbulent energy equation and to a treatment of the small scale equilibrium range of Kolmogoroff; in velocity correlation space the two-thirds power law is obtained. Thus, the two well-known 'laws' of turbulent flow are imbedded in an analysis which provides a great deal of other information.
Asymptotic freedom in the Hamiltonian approach to binding of color
Directory of Open Access Journals (Sweden)
Gómez-Rocha María
2017-01-01
Full Text Available We derive asymptotic freedom and the SU(3 Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian Hs, which is a matrix written in a basis that depend on the scale (or size parameter s. The effective Hamiltonians Hs and the (regularized canonical Hamiltonian H0 are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
Asymptotic freedom in the Hamiltonian approach to binding of color
Gómez-Rocha, María
2017-03-01
We derive asymptotic freedom and the SU(3) Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian Hs, which is a matrix written in a basis that depend on the scale (or size) parameter s. The effective Hamiltonians Hs and the (regularized) canonical Hamiltonian H0 are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.
Asymptotic analysis of radiation extinction of stretched premixed flames
Energy Technology Data Exchange (ETDEWEB)
Ju, Y.; Masuya, G. [Tohoku Univ., Sendai (Japan). Dept. of Aeronautics and Space Engineering; Liu, F. [National Research Council, Ottawa, Ontario (Canada). Inst. for Chemical Prpcess and Environmental Technology; Hattori, Yuji [Tohoku Univ., Sendai (Japan). Inst. of Fluid Science; Riechelmann, D. [Ishikawajima-Harima Heavy Industry, Tokyo (Japan). Research Inst.
2000-01-01
The flammability limit, radiation extinction of stretched premixed flame and effect of non-unity Lewis numbers are analyzed by the large-activated-energy asymptotic method. Particular attention is paid to the effect of Lewis number, the upstream and downstream radiation heat losses as well as the non-linearity of radiation. Explicit expressions for the flame temperature, extinction limit and flammability limit are obtained. The C-shaped extinction curve is reproduced. The dependence of radiation heat loss and the Lewis number effect on the stretch rate and flame separation distance is investigated. The effects of fuel Lewis number, oxidizer Lewis number, upstream radiation heat loss and the non-linearity of radiation on the C-shaped extinction curve are also examined. The results demonstrate a significant influence of these parameters on the radiation extinction and flammability limit and provide a good explanation to the experimental results and numerical simulations. (Author)
An introduction to covariant quantum gravity and asymptotic safety
Percacci, Roberto
2017-01-01
This book covers recent developments in the covariant formulation of quantum gravity. Developed in the 1960s by Feynman and DeWitt, by the 1980s this approach seemed to lead nowhere due to perturbative non-renormalizability. The possibility of non-perturbative renormalizability or "asymptotic safety," originally suggested by Weinberg but largely ignored for two decades, was revived towards the end of the century by technical progress in the field of the renormalization group. It is now a very active field of research, providing an alternative to other approaches to quantum gravity. Written by one of the early contributors to this subject, this book provides a gentle introduction to the relevant ideas and calculational techniques. Several explicit calculations gradually bring the reader close to the current frontier of research. The main difficulties and present lines of development are also outlined.
An asymptotic state of the critical ionization velocity phenomenon
Goertz, C. K.; Machida, S.; Smith, R. A.
1985-01-01
The paper considers the problem of how the momentum of ions created by electron impact ionization of neutrals moving at a speed v(0) perpendicular to the magnetic field through a background plasma is coupled to this plasma. It has been found that the plasma accelerates, and the relative velocity between neutrals and plasma decreases. If this decrease is rapid and large enough, the critical ionization velocity (CIV) phenomenon may turn off. Equations for the evolution of plasma density, electron and ion thermal energy, and plasma velocity have been derived. It was found that the CIV process reaches an asymptotic quasi-steady state, in which the ionization rate reaches a constant value which depends on the properties of the surrounding medium and the value of v(0).
The complex dynamics of products and its asymptotic properties.
Directory of Open Access Journals (Sweden)
Orazio Angelini
Full Text Available We analyse global export data within the Economic Complexity framework. We couple the new economic dimension Complexity, which captures how sophisticated products are, with an index called logPRODY, a measure of the income of the respective exporters. Products' aggregate motion is treated as a 2-dimensional dynamical system in the Complexity-logPRODY plane. We find that this motion can be explained by a quantitative model involving the competition on the markets, that can be mapped as a scalar field on the Complexity-logPRODY plane and acts in a way akin to a potential. This explains the movement of products towards areas of the plane in which the competition is higher. We analyse market composition in more detail, finding that for most products it tends, over time, to a characteristic configuration, which depends on the Complexity of the products. This market configuration, which we called asymptotic, is characterized by higher levels of competition.
Fields Institute International Symposium on Asymptotic Methods in Stochastics
Kulik, Rafal; Haye, Mohamedou; Szyszkowicz, Barbara; Zhao, Yiqiang
2015-01-01
This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.
Turbomachinery computational fluid dynamics: asymptotes and paradigm shifts.
Dawes, W N
2007-10-15
This paper reviews the development of computational fluid dynamics (CFD) specifically for turbomachinery simulations and with a particular focus on application to problems with complex geometry. The review is structured by considering this development as a series of paradigm shifts, followed by asymptotes. The original S1-S2 blade-blade-throughflow model is briefly described, followed by the development of two-dimensional then three-dimensional blade-blade analysis. This in turn evolved from inviscid to viscous analysis and then from steady to unsteady flow simulations. This development trajectory led over a surprisingly small number of years to an accepted approach-a 'CFD orthodoxy'. A very important current area of intense interest and activity in turbomachinery simulation is in accounting for real geometry effects, not just in the secondary air and turbine cooling systems but also associated with the primary path. The requirements here are threefold: capturing and representing these geometries in a computer model; making rapid design changes to these complex geometries; and managing the very large associated computational models on PC clusters. Accordingly, the challenges in the application of the current CFD orthodoxy to complex geometries are described in some detail. The main aim of this paper is to argue that the current CFD orthodoxy is on a new asymptote and is not in fact suited for application to complex geometries and that a paradigm shift must be sought. In particular, the new paradigm must be geometry centric and inherently parallel without serial bottlenecks. The main contribution of this paper is to describe such a potential paradigm shift, inspired by the animation industry, based on a fundamental shift in perspective from explicit to implicit geometry and then illustrate this with a number of applications to turbomachinery.
Stability of Stationary Solutions of the Multifrequency Radiation Diffusion Equations
Energy Technology Data Exchange (ETDEWEB)
Hald, O H; Shestakov, A I
2004-01-20
A nondimensional model of the multifrequency radiation diffusion equation is derived. A single material, ideal gas, equation of state is assumed. Opacities are proportional to the inverse of the cube of the frequency. Inclusion of stimulated emission implies a Wien spectrum for the radiation source function. It is shown that the solutions are uniformly bounded in time and that stationary solutions are stable. The spatially independent solutions are asymptotically stable, while the spatially dependent solutions of the linearized equations approach zero.
Most, S.; Jia, N.; Bijeljic, B.; Nowak, W.
2016-12-01
Pre-asymptotic characteristics are almost ubiquitous when analyzing solute transport processes in porous media. These pre-asymptotic aspects are caused by spatial coherence in the velocity field and by its heterogeneity. For the Lagrangian perspective of particle displacements, the causes of pre-asymptotic, non-Fickian transport are skewed velocity distribution, statistical dependencies between subsequent increments of particle positions (memory) and dependence between the x, y and z-components of particle increments. Valid simulation frameworks should account for these factors. We propose a particle tracking random walk (PTRW) simulation technique that can use empirical pore-space velocity distributions as input, enforces memory between subsequent random walk steps, and considers cross dependence. Thus, it is able to simulate pre-asymptotic non-Fickian transport phenomena. Our PTRW framework contains an advection/dispersion term plus a diffusion term. The advection/dispersion term produces time-series of particle increments from the velocity CDFs. These time series are equipped with memory by enforcing that the CDF values of subsequent velocities change only slightly. The latter is achieved through a random walk on the axis of CDF values between 0 and 1. The virtual diffusion coefficient for that random walk is our only fitting parameter. Cross-dependence can be enforced by constraining the random walk to certain combinations of CDF values between the three velocity components in x, y and z. We will show that this modelling framework is capable of simulating non-Fickian transport by comparison with a pore-scale transport simulation and we analyze the approach to asymptotic behavior.
Delay-dependent asymptotic stability for neural networks with time-varying delays
Directory of Open Access Journals (Sweden)
Xiaofeng Liao
2006-01-01
ensure local and global asymptotic stability of the equilibrium of the neural network. Our results are applied to a two-neuron system with delayed connections between neurons, and some novel asymptotic stability criteria are also derived. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature. Some numerical examples are included to demonstrate our results.
On the tail asymptotics of the area swept under the Brownian storage graph
Arendarczyk, M.; Dȩbicki, K.; Mandjes, M.
2014-01-01
In this paper, the area swept under the workload graph is analyzed: with {Q(t): t≥0} denoting the stationary workload process, the asymptotic behavior of πT(u)(u):=P(∫T(u)0Q(r)dr>u) is analyzed. Focusing on regulated Brownian motion, first the exact asymptotics of πT(u)(u) are given for the case
Explanation of Second-Order Asymptotic Theory Via Information Spectrum Method
Hayashi, Masahito
We explain second-order asymptotic theory via the information spectrum method. From a unified viewpoint based on the generality of the information spectrum method, we consider second-order asymptotic theory for use in fixed-length data compression, uniform random number generation, and channel coding. Additionally, we discuss its application to quantum cryptography, folklore in source coding, and security analysis.
Assessing model fit in latent class analysis when asymptotics do not hold
van Kollenburg, Geert H.; Mulder, Joris; Vermunt, Jeroen K.
2015-01-01
The application of latent class (LC) analysis involves evaluating the LC model using goodness-of-fit statistics. To assess the misfit of a specified model, say with the Pearson chi-squared statistic, a p-value can be obtained using an asymptotic reference distribution. However, asymptotic p-values
Yuan, Ke-Hai; Bentler, Peter M.
2002-01-01
Examined the asymptotic distributions of three reliability coefficient estimates: (1) sample coefficient alpha; (2) reliability estimate of a composite score following factor analysis; and (3) maximal reliability of a linear combination of item scores after factor analysis. Findings show that normal theory based asymptotic distributions for these…
An asymptotic expansion for product integration applied to Cauchy principal value integrals
Wesseling, P.
1975-01-01
Product integration methods for Cauchy principal value integrals based on piecewise Lagrangian interpolation are studied. It is shown that for this class of quadrature methods the truncation error has an asymptotic expansion in integer powers of the step-size, and that a method with an asymptotic
Scaling solutions for dilaton quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Henz, T.; Pawlowski, J.M., E-mail: j.pawlowski@thphys.uni-heidelberg.de; Wetterich, C.
2017-06-10
Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between scalar field and renormalization scale k is varied. In the Einstein frame the quantum effective action corresponding to the scaling solutions becomes independent of k. The field equations derived from this effective action can be used directly for cosmology. Scale symmetry is spontaneously broken by a non-vanishing cosmological value of the scalar field. For the cosmology corresponding to our scaling solutions, inflation arises naturally. The effective cosmological constant becomes dynamical and vanishes asymptotically as time goes to infinity.
Scaling solutions for dilaton quantum gravity
Henz, T.; Pawlowski, J. M.; Wetterich, C.
2017-06-01
Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between scalar field and renormalization scale k is varied. In the Einstein frame the quantum effective action corresponding to the scaling solutions becomes independent of k. The field equations derived from this effective action can be used directly for cosmology. Scale symmetry is spontaneously broken by a non-vanishing cosmological value of the scalar field. For the cosmology corresponding to our scaling solutions, inflation arises naturally. The effective cosmological constant becomes dynamical and vanishes asymptotically as time goes to infinity.
Mabood, Fazle; Khan, Waqar A; Ismail, Ahmad Izani Md
2013-01-01
In this article, an approximate analytical solution of flow and heat transfer for a viscoelastic fluid in an axisymmetric channel with porous wall is presented. The solution is obtained through the use of a powerful method known as Optimal Homotopy Asymptotic Method (OHAM). We obtained the approximate analytical solution for dimensionless velocity and temperature for various parameters. The influence and effect of different parameters on dimensionless velocity, temperature, friction factor, and rate of heat transfer are presented graphically. We also compared our solution with those obtained by other methods and it is found that OHAM solution is better than the other methods considered. This shows that OHAM is reliable for use to solve strongly nonlinear problems in heat transfer phenomena.
Asymptotic theory of evolution and failure of self-sustained detonations
Kasimov, Aslan R.; Stewart, D. Scott
2005-02-01
Based on a general theory of detonation waves with an embedded sonic locus that we have previously developed, we carry out asymptotic analysis of weakly curved slowly varying detonation waves and show that the theory predicts the phenomenon of detonation ignition and failure. The analysis is not restricted to near Chapman-Jouguet detonation speeds and is capable of predicting quasi-steady, normal detonation shock speed versus curvature (D-κ) curves with multiple turning points. An evolution equation that retains the shock acceleration, skew2dot{D}, namely a skew2dot{D}-D-κ relation is rationally derived which describes the dynamics of pre-existing detonation waves. The solutions of the equation for spherical detonation are shown to reproduce the ignition/failure phenomenon observed in both numerical simulations of blast wave initiation and in experiments. A single-step chemical reaction described by one progress variable is employed, but the kinetics is sufficiently general and is not restricted to Arrhenius form, although most specific calculations are performed for Arrhenius kinetics. As an example, we calculate critical energies of direct initiation for hydrogen-oxygen mixtures and find close agreement with available experimental data.
Asymptotically optimal probes for noisy interferometry via quantum annealing to criticality
Durkin, Gabriel A.
2016-10-01
Quantum annealing is explored as a resource for quantum information beyond solution of classical combinatorial problems. Envisaged as a generator of robust interferometric probes, we examine a Hamiltonian of N ≫1 uniformly coupled spins subject to a transverse magnetic field. The discrete many-body problem is mapped onto dynamics of a single one-dimensional particle in a continuous potential. This reveals all the qualitative features of the ground state beyond typical mean-field or large classical spin models. It illustrates explicitly a graceful warping from an entangled unimodal to bimodal ground state in the phase transition region. The transitional "Goldilocks" probe has a component distribution of width N2 /3 and exhibits characteristics for enhanced phase estimation in a decoherent environment. In the presence of realistic local noise and collective dephasing, we find this probe state asymptotically saturates ultimate precision bounds calculated previously. By reducing the transverse field adiabatically, the Goldilocks probe is prepared in advance of the minimum gap bottleneck, allowing the annealing schedule to be terminated "early." Adiabatic time complexity of probe preparation is shown to be linear in N .
Khong, Y. T.; Nordin, N.; Seri, S. M.; Mohammed, A. N.; Sapit, A.; Taib, I.; Abdullah, K.; Sadikin, A.; Razali, M. A.
2017-09-01
The present work aims to numerically investigate the effect of varying turning angle, ϕ = 30° - 90° on the performance of 2-D turning diffuser and to develop the performance correlations via integrating the turning angle using Asymptotic Computational Fluid Dynamics (ACFD) technique. Standard k-ε adopting enhanced wall treatment of y+ ≈ 1.1 appeared as the best validated model to represent the actual cases with deviation of ±4.7%. Results show that the pressure recovery, Cp and flow uniformity, σout are distorted of respectively 37% and 28% with the increment of turning angle from 30° to 90°. The flow separation starts to emerge within the inner wall, S=0.91Lin/W1 when 45° turning diffuser is applied and its scale is enlarged by further increasing the turning angle. The performance correlations of 2-D turning diffuser are successfully developed with deviation to the full CFD solution approximately of ±7.1%.
Asymptotic analysis of a pile-up of regular edge dislocation walls
Hall, Cameron L.
2011-12-01
The idealised problem of a pile-up of regular dislocation walls (that is, of planes each containing an infinite number of parallel, identical and equally spaced dislocations) was presented by Roy et al. [A. Roy, R.H.J. Peerlings, M.G.D. Geers, Y. Kasyanyuk, Materials Science and Engineering A 486 (2008) 653-661] as a prototype for understanding the importance of discrete dislocation interactions in dislocation-based plasticity models. They noted that analytic solutions for the dislocation wall density are available for a pile-up of regular screw dislocation walls, but that numerical methods seem to be necessary for investigating regular edge dislocation walls. In this paper, we use the techniques of discrete-to-continuum asymptotic analysis to obtain a detailed description of a pile-up of regular edge dislocation walls. To leading order, we find that the dislocation wall density is governed by a simple differential equation and that boundary layers are present at both ends of the pile-up. © 2011 Elsevier B.V.
Motion of particles on a Four-Dimensional Asymptotically AdS Black Hole with Scalar Hair
Gonzalez, P A; Vasquez, Yerko
2015-01-01
Motivated by black hole solutions with matter fields outside their horizon, we study the effect of these matter fields in the motion of massless and massive particles. We consider as background a four-dimensional asymptotically AdS black hole with scalar hair. The geodesics are studied numerically and we discuss about the differences in the motion of particles between the four-dimensional asymptotically AdS black holes with scalar hair and their no-hair limit, that is, Schwarzschild AdS black holes. Mainly, we found that there are bounded orbits like planetary orbits in this background. However, the periods associated to circular orbits are modified by the presence of the scalar hair. Besides, we found that some classical tests such as perihelion precession, deflection of light and gravitational time delay have the standard value of general relativity plus a correction term coming from the cosmological constant and the scalar hair. Finally, we found a specific value of the parameter associated to the scalar h...
Motion of particles on a four-dimensional asymptotically AdS black hole with scalar hair
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, P.A.; Olivares, Marco [Universidad Diego Portales, Facultad de Ingenieria, Santiago (Chile); Vasquez, Yerko [Universidad de La Serena, Departamento de Fisica, Facultad de Ciencias, La Serena (Chile)
2015-10-15
Motivated by black hole solutions with matter fields outside their horizon, we study the effect of these matter fields on the motion of massless and massive particles. We consider as background a four-dimensional asymptotically AdS black hole with scalar hair. The geodesics are studied numerically and we discuss the differences in the motion of particles between the four-dimensional asymptotically AdS black holes with scalar hair and their no-hair limit, that is, Schwarzschild AdS black holes. Mainly, we found that there are bounded orbits like planetary orbits in this background. However, the periods associated to circular orbits are modified by the presence of the scalar hair. Besides, we found that some classical tests such as perihelion precession, deflection of light, and gravitational time delay have the standard value of general relativity plus a correction term coming from the cosmological constant and the scalar hair. Finally, we found a specific value of the parameter associated to the scalar hair, in order to explain the discrepancy between the theory and the observations, for the perihelion precession of Mercury and light deflection. (orig.)
Asymptotic performance of regularized quadratic discriminant analysis based classifiers
Elkhalil, Khalil
2017-12-13
This paper carries out a large dimensional analysis of the standard regularized quadratic discriminant analysis (QDA) classifier designed on the assumption that data arise from a Gaussian mixture model. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under some mild assumptions, we show that the asymptotic classification error converges to a deterministic quantity that depends only on the covariances and means associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized QDA and can be used to determine the optimal regularization parameter that minimizes the misclassification error probability. Despite being valid only for Gaussian data, our theoretical findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from popular real data bases, thereby making an interesting connection between theory and practice.
3D face recognition with asymptotic cones based principal curvatures
Tang, Yinhang
2015-05-01
The classical curvatures of smooth surfaces (Gaussian, mean and principal curvatures) have been widely used in 3D face recognition (FR). However, facial surfaces resulting from 3D sensors are discrete meshes. In this paper, we present a general framework and define three principal curvatures on discrete surfaces for the purpose of 3D FR. These principal curvatures are derived from the construction of asymptotic cones associated to any Borel subset of the discrete surface. They describe the local geometry of the underlying mesh. First two of them correspond to the classical principal curvatures in the smooth case. We isolate the third principal curvature that carries out meaningful geometric shape information. The three principal curvatures in different Borel subsets scales give multi-scale local facial surface descriptors. We combine the proposed principal curvatures with the LNP-based facial descriptor and SRC for recognition. The identification and verification experiments demonstrate the practicability and accuracy of the third principal curvature and the fusion of multi-scale Borel subset descriptors on 3D face from FRGC v2.0.
Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?
Directory of Open Access Journals (Sweden)
Mehmet Fatih Öçal
2017-01-01
Full Text Available Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students’ learning during graphing functions. However, the display of graphs of functions that students sketched by hand may be relatively different when compared to the correct forms sketched using graphing software. The possible misleading effects of this situation brought a discussion of a misconception (asymptote misconception on graphing functions. The purpose of this study is two- fold. First of all, this study investigated whether using graphing software (GeoGebra in this case helps students to determine and resolve this misconception in calculus classrooms. Second, the reasons for this misconception are sought. The multiple case study was utilized in this study. University students in two calculus classrooms who received instructions with (35 students or without GeoGebra assisted instructions (32 students were compared according to whether they fell into this misconception on graphing basic functions (1/x, lnx, ex. In addition, students were interviewed to reveal the reasons behind this misconception. Data were analyzed by means of descriptive and content analysis methods. The findings indicated that those who received GeoGebra assisted instruction were better in resolving it. In addition, the reasons behind this misconception were found to be teacher-based, exam-based and some other factors.