PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS
Institute of Scientific and Technical Information of China (English)
FEIGUIHUA; QIUQINGJIU
1997-01-01
The authors establish the existence of nontrival periodic solutions of the asymptotically linear Hamiltomian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.
On generalized Nariai solutions and their asymptotics
Beyer, Florian
2009-01-01
In this paper, we consider the class of generalized Nariai solutions of Einstein's field equations in vacuum with a positive cosmological constant. According to the cosmic no-hair conjecture, generic expanding solutions isotropize and approach the de-Sitter solution asymptotically, at least locally in space. The generalized Nariai solutions, however, show quite unusual asymptotics and hence should be non-generic in some sense. In the first part of the paper, we list the necessary facts and characterize the asymptotic behavior geometrically. In the second part, we study the question of non-genericity, which we are able to confirm within the class of spatially homogeneous solutions. It turns out that perturbations of the three isometry classes of generalized Nariai solutions are related to different mass regimes of Schwarzschild de-Sitter solutions. In subsequent papers, we will continue this research in more general classes of solutions.
Asymptotically periodic solutions of Volterra integral equations
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
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.
Asymptotic Behavior of Solutions to a Linear Volterra Integrodifferential System
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Yue-Wen Cheng
2013-01-01
Full Text Available We investigate the asymptotic behavior of solutions to a linear Volterra integrodifferential system , We show that under some suitable conditions, there exists a solution for the above integrodifferential system, which is asymptotically equivalent to some given functions. Two examples are given to illustrate our theorem.
Asymptotic Solutions of Serial Radial Fuel Shuffling
Directory of Open Access Journals (Sweden)
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
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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.
Asymptotic traveling wave solution for a credit rating migration problem
Liang, Jin; Wu, Yuan; Hu, Bei
2016-07-01
In this paper, an asymptotic traveling wave solution of a free boundary model for pricing a corporate bond with credit rating migration risk is studied. This is the first study to associate the asymptotic traveling wave solution to the credit rating migration problem. The pricing problem with credit rating migration risk is modeled by a free boundary problem. The existence, uniqueness and regularity of the solution are obtained. Under some condition, we proved that the solution of our credit rating problem is convergent to a traveling wave solution, which has an explicit form. Furthermore, numerical examples are presented.
Uniformly Asymptotic Stability and Existence of Periodic Solutions and Almost Periodic Solutions
Institute of Scientific and Technical Information of China (English)
林发兴
1994-01-01
We introduce the concepts of uniformly stable solutions and uniformly-asymptotically stable solutions, and then give the relation between Lyapunov function and those concepts. Furthermore, we establish the theorem that an almost periodic system or periodic system has uniformly-asymptotically stable solutions and Lipschitz’ condition has an almost periodic solution or periodic solution.
Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation
Institute of Scientific and Technical Information of China (English)
HUANG Qiong-Wei; TANG Jia-Shi
2011-01-01
Stability and dynamic bifurcation in the perturbed Kuramoto-Sivashinsky (KS) equation with Dirichlet boundary condition are investigated by using central manifold reduction procedure.The result shows, as the bifurcation parameter crosses a critical value, the system undergoes a pitchfork bifurcation to produce two asymptotically stable solutions.Furthermore, when the distance from bifurcation is of comparable order ∈2 (｜∈｜ (≤) 1), the first two terms in e-expansions for the new asymptotic bifurcation solutions are derived by multiscale expansion method.Such information is useful to the bifurcation control.
EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF TRAVELING WAVE SOLUTIONS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper studies the asymptotic stability of traveling wave solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinear stability and some “nice structure” of the spectrum of an associated operator implies the linear stability. By using the method of variation of parameter, the author defines some complex analytic function, called the Evans function. The zeros of the Evans function corresponds to the eigenvalues of the associated linear operator. By calculating the zeros of the Evans function, the asymptotic stability of the travling wave solutions is established.
Asymptotic stability of solutions to elastic systems with structural damping
Directory of Open Access Journals (Sweden)
Hongxia Fan
2014-11-01
Full Text Available In this article, we study the asymptotic stability of solutions for the initial value problems of second order evolution equations in Banach spaces, which can model elastic systems with structural damping. The discussion is based on exponentially stable semigroups theory. Applications to the vibration equation of elastic beams with structural damping are also considered.
MULTIPLE SOLUTIONS TO AN ASYMPTOTICALLY LINEAR ROBIN BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
Under some weaker conditions,we prove the existence of at least two solutions to an asymptotically linear elliptic problem with Robin boundary value condition,using truncation arguments.Our results are also valid for the case of the so-called resonance at infinity.
The Asymptotic Behavior for Numerical Solution of a Volterra Equation
Institute of Scientific and Technical Information of China (English)
Da Xu
2003-01-01
Long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type are studied. The methods are based on the first-second order backward difference methods. The memory term is approximated by the convolution quadrature and the interpolant quadrature. Discretization of the spatial partial differential operators by the finite element method is also considered.
A Note on Solutions for Asymptotically Linear Elliptic Systems
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper, we axe concerned with the elliptic system of -△u+V(x)u=g(=x,v),x=∈RN,-△v+V(x)v=f(x, u), x∈RN, where V(x) is a continuous potential well, f, g are continuous and asymptotically linear as t→∞. The existence of a positive solution and ground state solution are established via variational methods.
Asymptotic behavior of singular solutions to semilinear fractional elliptic equations
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Guowei Lin
2014-02-01
Full Text Available In this article we study the asymptotic behavior of positive singular solutions to the equation $$ (-\\Delta^{\\alpha} u+u^p=0\\quad\\text{in } \\Omega\\setminus\\{0\\}, $$ subject to the conditions $u=0$ in $\\Omega^c$ and $\\lim_{x\\to0}u(x=\\infty$, where $p\\geq1$, $\\Omega$ is an open bounded regular domain in $\\mathbb{R}^N$ ($N\\ge2$ containing the origin, and $(-\\Delta^\\alpha$ with $\\alpha\\in(0,1$ denotes the fractional Laplacian. We show that the asymptotic behavior of positive singular solutions is controlled by a radially symmetric solution with $\\Omega$ being a ball.
Asymptotic Reissner-Nordstr\\"om solution within nonlinear electrodynamics
Kruglov, S I
2016-01-01
A model of nonlinear electrodynamics coupled with the gravitational field is studied. We obtain the asymptotic black hole solutions at $r\\rightarrow 0$ and $r\\rightarrow \\infty$. The asymptotic at $r\\rightarrow 0$ is shown, and we find corrections to the Reissner-Nordstr\\"om solution and Coulomb's law at $r\\rightarrow\\infty$. The mass of the black hole is evaluated having the electromagnetic origin. We investigate the thermodynamics of charged black holes and their thermal stability. The critical point corresponding to the second-order phase transition (where heat capacity diverges) is found. If the mass of the black hole is greater than the critical mass, the black hole becomes unstable.
Asymptotic Reissner-Nordström solution within nonlinear electrodynamics
Kruglov, S. I.
2016-08-01
A model of nonlinear electrodynamics coupled with the gravitational field is studied. We obtain the asymptotic black hole solutions at r →0 and r →∞ . The asymptotic at r →0 is shown, and we find corrections to the Reissner-Nordström solution and Coulomb's law at r →∞ . The mass of the black hole is evaluated having the electromagnetic origin. We investigate the thermodynamics of charged black holes and their thermal stability. The critical point corresponding to the second-order phase transition (where heat capacity diverges) is found. If the mass of the black hole is greater than the critical mass, the black hole becomes unstable.
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 $f(u = -u$.
AN ASYMPTOTIC SOLUTION OF VELOCITY FIELD IN SHIP WAVES
Institute of Scientific and Technical Information of China (English)
WU Yun-gang; TAO Ming-de
2006-01-01
The stationary phase method in conventional Lighthill's two-stage scheme to get the expressions of the velocity field was given up in this paper. The method that Ursell had used in deducing the elevation expression of ship wave was adopted, and an asymptotic solution of velocity field of ship waves on an inviscid fluid that is perfectly fit for the region inside and outside the critical lines was obtained. It is very convenient to be used in SAR technique.
Solute transport through porous media using asymptotic dispersivity
Indian Academy of Sciences (India)
P K Sharma; Teodrose Atnafu Abgaze
2015-08-01
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 heterogeneous porous media. Semi-analytical solution has been derived of the governing equations with an asymptotic distance dependent dispersivity by using Laplace transform technique and the power series method. For application of analytical model, we simulated observed experimental breakthrough curves from 1500 cm long soil column experiments conducted in the laboratory. The simulation results of break-through curves were found to deviate from the observed breakthrough curves for both mobile–immobile and multiprocess non-equilibrium transport with constant dispersion models. However, multiprocess non-equilibrium with an asymptotic dispersion model gives better fit of experimental breakthrough curves through long soil column and hence it is more useful for describing anomalous solute transport through hetero-geneous porous media. The present model is simpler than the stochastic numerical method.
Asymptotic solution for EI Nino-southern oscillation of nonlinear model
Institute of Scientific and Technical Information of China (English)
MO Jia-qi; LIN Wan-tao
2008-01-01
A class of nonlinear coupled system for E1 Nino-Southern Oscillation (ENSO) model is considered. Using the asymptotic theory and method of variational iteration, the asymptotic expansion of the solution for ENSO models is obtained.
Asymptotic solution for heat convection-radiation equation
Energy Technology Data Exchange (ETDEWEB)
Mabood, Fazle; Ismail, Ahmad Izani Md [School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia); Khan, Waqar A. [Department of Engineering Sciences, National University of Sciences and Technology, PN Engineering College, Karachi, 75350 (Pakistan)
2014-07-10
In this paper, we employ a new approximate analytical method called the optimal homotopy asymptotic method (OHAM) to solve steady state heat transfer problem in slabs. The heat transfer problem is modeled using nonlinear two-point boundary value problem. Using OHAM, we obtained the approximate analytical solution for dimensionless temperature with different values of a parameter ε. Further, the OHAM results for dimensionless temperature have been presented graphically and in tabular form. Comparison has been provided with existing results from the use of homotopy perturbation method, perturbation method and numerical method. For numerical results, we used Runge-Kutta Fehlberg fourth-fifth order method. It was found that OHAM produces better approximate analytical solutions than those which are obtained by homotopy perturbation and perturbation methods, in the sense of closer agreement with results obtained from the use of Runge-Kutta Fehlberg fourth-fifth order method.
ASYMPTOTIC ESTIMATION FOR SOLUTION OF A CLASS OF SEMI-LINEAR ROBIN PROBLEMS
Institute of Scientific and Technical Information of China (English)
Cheng Ouyang
2005-01-01
A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic expansion of solution for the problem is constructed and the uniform validity of the solution is obtained by using the method of upper and lower solution.
Asymptotic Solution to the Rayleigh Problem of Dynamic Soaring
Bousquet, Gabriel D; Slotine, Jean-Jacques E
2015-01-01
It is believed that albatrosses power their flight through dynamic soaring, a technique where energy is extracted from horizontally blowing shear winds. The Rayleigh model of dynamic soaring, also called the two layer model, makes a 2-dimensional approximation of the wind field and glider trajectory. This note considers the "Rayleigh problem" of finding the minimum wind necessary for the existence of energy neutral gliding cycles. We utilize a 3-degree of freedom glider model with quadratic drag. Asymptotic solutions in the limit of large glide ratios are obtained. The optimal motion is a traveling trajectory constituted of a succession of small partial turns. It is over 50% more efficient at preserving airspeed than full half-turn based trajectories.
Ground state solutions for asymptotically periodic Schrodinger equations with critical growth
Directory of Open Access Journals (Sweden)
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.
Levchenko, E. A.; Trifonov, A. Yu.; Shapovalov, A. V.
2015-11-01
Asymptotic solutions of the multidimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation with an influence function that is invariant with respect to a spatial shift are constructed. The asymptotic solutions are perturbations of a spatially-homogeneous quasistationary exact solution. General expressions are illustrated by the example of a two-dimensional equation with a Gaussian initial condition.
Asymptotic Behavior of Soliton Solutions with a Double Spectral Parameter for Principal Chiral Field
Institute of Scientific and Technical Information of China (English)
SONG Quan-Fu; ZHOU Zi-Xiang
2005-01-01
The soliton solutions with a double spectral parameter for the principal chiral field are derived by Darboux transformation. The asymptotic behavior of the solutions as time tends to infinity is obtained and the speeds of the peaks in the asymptotic solutions are not constants.
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
Institute of Scientific and Technical Information of China (English)
Wei-hua Mao; An-hua Wan
2006-01-01
The oscillatory and asymptotic behavior of the solutions for third order nonlinear impulsive delay differential equations are investigated. Some novel criteria for all solutions to be oscillatory or be asymptotic are established. Three illustrative examples are proposed to demonstrate the effectiveness of the conditions.
Directory of Open Access Journals (Sweden)
Park Jong Yeoul
2007-01-01
Full Text Available We study the existence of global weak solutions for a hyperbolic differential inclusion with a source term, and then investigate the asymptotic stability of the solutions by using Nakao lemma.
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.
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.
On the minimal speed and asymptotics of the wave solutions for the lotka volterra system
Hou, Xiaojie
2010-01-01
e study the minimal wave speed and the asymptotics of the traveling wave solutions of a competitive Lotka Volterra system. The existence of the traveling wave solutions is derived by monotone iteration. The asymptotic behaviors of the wave solutions are derived by comparison argument and the exponential dichotomy, which seems to be the key to understand the geometry and the stability of the wave solutions. Also the uniqueness and the monotonicity of the waves are investigated via a generalized sliding domain method.
Asymptotic Properties of Solutions of Parabolic Equations Arising from Transient Diffusions
Institute of Scientific and Technical Information of China (English)
A.M. Il'in; R.Z. Khasminskii; G. Yin
2002-01-01
This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.
ASYMPTOTIC SOLUTION OF ACTIVATOR INHIBITOR SYSTEMS FOR NONLINEAR REACTION DIFFUSION EQUATIONS
Institute of Scientific and Technical Information of China (English)
Jiaqi MO; Wantao LIN
2008-01-01
A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.
Directory of Open Access Journals (Sweden)
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.
Institute of Scientific and Technical Information of China (English)
黎勇; 陈丽
2002-01-01
In this paper, we study the asymptotic behavior of global smooth solution to the initial boundary problem for the 1-D energy transport model in semiconductor science. We prove that the smooth solution of the problem converges to a stationary solution exponentially fast as t - ∞ when the initial data is a small perturbation of the stationary solution.
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.
S-asymptotically -periodic Solutions of R-L Fractional Derivative-Integral Equation
Institute of Scientific and Technical Information of China (English)
WANG Bing
2015-01-01
The aim of this paper is to study the S-asymptotically ω-periodic solutions of R-L fractional derivative-integral equation:is a linear densely defined operator of sectorial type on a completed Banach space X, f is a continuous function satisfying a suitable Lipschitz type condition. We will use the contraction mapping theory to prove problem (1) and (2) has a unique S-asymptotically ω-periodic solution if the function f satisfies Lipshcitz condition.
Institute of Scientific and Technical Information of China (English)
李大鸣; 张红萍; 高永祥
2002-01-01
A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
Asymptotic Stability and Balanced Growth Solution of the Singular Dynamic Input-Output System＊
Institute of Scientific and Technical Information of China (English)
ChonghuiGuo; HuanwenTang
2004-01-01
The dynamic input-output system is well known in economic theory and practice. In this paper the asymptotic stability and balanced growth solution of the dynamic input-output system are considered. Under three natural assumptions, we obtain four theorems about asymptotic stability and balanced growth solution of the dynamic input-output system and bring together in a unified manner some contributions scattered in the literature.
Asymptotics for the greatest zeros of solutions of a particular O.D.E.
Directory of Open Access Journals (Sweden)
Silvia Noschese
1994-05-01
Full Text Available This paper deals with the Liouville-Stekeloff method for approximating solutions of homogeneous linear ODE and a general result due to Tricomi which provides estimates for the zeros of functions by means of the knowledge of an asymptotic representation. From the classical tools we deduce information about the asymptotics of the greatest zeros of a class of solutions of a particular ODE, including the classical Hermite polynomials.
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.
Institute of Scientific and Technical Information of China (English)
王金良; 周笠
2003-01-01
In this paper,our main aim is to study the existence and uniqueness of the periodic solution of delayed Logistic equation and its asymptotic behavior.In case the coefficients are periodic,we give some sufficient conditions for the existence and uniqueness of periodic solution.Furthermore,we also study the effect of time-delay on the solution.
Asymptotic Behavior of Solutions to the Generalized BBM-Burgers Equation
Institute of Scientific and Technical Information of China (English)
Mi-na Jiang; Yan-ling Xu
2005-01-01
We investigate the asymptotic behavior of solutions of the initial-boundary value problem for the generalized BBM-Burgers equation ut + f(u)x = uxx +uxxt on the half line with the conditions u(0, t) =u-, u(∞, t) = u+ and u- ＜ u+, where the corresponding Cauchy problem admits the rarefaction wave as an asymptotic states. In the present problem, because of the Dirichlet boundary, the asymptotic states are divided into five cases depending on the signs of the characteristic speeds f′(u±) of boundary state u- = u(0) and the far fields states u+ = u(∞). In all cases both global existence of the solution and asymptotic behavior are shown under the smallness conditions.
Mishima, T; Mishima, Takashi; Iguchi, Hideo
2006-01-01
New axisymmetric stationary solutions of the vacuum Einstein equations in five-dimensional asymptotically flat spacetimes are given by solitonic solution-generating techniques. We show the equivalence between these solutions and the four-dimensional multi-solitonic ones derived from particular class of four-dimensional Weyl solutions. The solutions constructed here include different black rings from the ones obtained by Emparan and Reall.
Portilheiro, Manuel
2010-01-01
We study a nonlinear porous medium type equation involving the infinity Laplacian operator. We first consider the problem posed on a bounded domain and prove existence of maximal nonnegative viscosity solutions. Uniqueness is obtained for strictly positive solutions with Lipschitz in time data. We also describe the asymptotic behaviour for the Dirichlet problem in the class of maximal solutions. We then discuss the Cauchy problem posed in the whole space. As in the standard porous medium equation (PME), solutions which start with compact support exhibit a free boundary propagating with finite speed, but such propagation takes place only in the direction of the spatial gradient. The description of the asymptotic behaviour of the Cauchy Problem shows that the asymptotic profile and the rates of convergence and propagation agree for large times with a one-dimensional PME.
Solutions of the Nonlinear Schrodinger Equation with Prescribed Asymptotics at Infinity
Gonzalez, John B
2009-01-01
We prove local existence and uniqueness of solutions for the one-dimensional nonlinear Schr\\"odinger (NLS) equations $iu_t + u_{xx} \\pm |u|^2 u = 0$ in classes of smooth functions that admit an asymptotic expansion at infinity in decreasing powers of $x$. We show that an asymptotic solution differs from a genuine solution by a Schwartz class function which solves a generalized version of the NLS equation. The latter equation is solved by discretization methods. The proofs closely follow previous work done by the author and others on the Korteweg-De Vries (KdV) equation and the modified KdV equations.
Asymptotic stability of solutions to the nonisentropic hydrodynamic model for semiconductors
Institute of Scientific and Technical Information of China (English)
XU Jiang; FANG Da-yuan
2008-01-01
In this paper, the asymptotic stability of smooth solutions to the multidimensional nonisentropic hydrodynamic model for semiconductors is established, under the assumption that the initial data are a small perturbation of the stationary solutions for the thermal equilibrium state, whose proofs mainly depend on the basic energy methods.
Asymptotic Behavior of Solutions to a Class of Systems of Delay Differential Equations
Institute of Scientific and Technical Information of China (English)
Tai Shan YI; Li Hong HUANG
2007-01-01
The authors investigate the asymptotic behavior of solutions to a class of systems of delaydifferential equations.It is shown that every bounded solution of such a class of systems tends to aconstant vector as t→∞.Our results improve and extend some corresponding ones already known.
Asymptotic Behavior of Global Solution for Nonlinear Generalized Euler-Possion-Darboux Equation
Institute of Scientific and Technical Information of China (English)
LIANGBao-song; CHENZhen
2004-01-01
J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.
ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION ON TIME SCALES
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,we investigate a second order impulsive differential equation on time scales.Sufficient conditions are given to guarantee that the solutions tend to zero.The notable effect of impulse upon the asymptotic behavior of solutions is stressed in this paper.At last,we illustrate our results with two examples.
Directory of Open Access Journals (Sweden)
Qiong Wu
2015-01-01
Full Text Available Mild solutions generated by a a, k-regularized family to fractional stochastic relaxation equations are studied. The main objective is to establish the existence and uniqueness of square-mean asymptotically almost automorphic mild solutions to linear and semilinear case of these equations. Under different hypotheses, some new theorems concerning the main objective are derived.
Asymptotic Growth of Solutions of Neutral Type Systems
Energy Technology Data Exchange (ETDEWEB)
Sklyar, G. M., E-mail: sklar@univ.szczecin.pl; Polak, P., E-mail: piotr.polak@wmf.univ.szczecin.pl [University of Szczecin, Institute of Mathematics (Poland)
2013-06-15
We consider a differential system of neutral type with distributed delay. We obtain a precise norm estimation of semigroup generated by the operator corresponding to the system in question. Our result is based on a spectral analysis of the operator and some uniform estimation of norms of the exponentials of matrices. We also discuss the stability properties of corresponding solutions and the existence of the fastest growing solution.
Serov, S A
2013-01-01
In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert's and Enskog's methods are discussed. The equations system of multicomponent non-equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asymptotic) method for solution of the system of kinetic Boltzmann equations. It is shown, that the velocity distribution functions of particles, obtained by the proposed method and by Enskog's method, within Enskog's approach, are equivalent up to the infinitesimal first order terms of the asymptotic expansion, but, generally speaking, differ in the next order. Interpretation of turbulent gas flow is proposed, as stratified on components gas flow, which is described by the derived equations system of multicomponent non-equilibrium gas dynamics.
Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painleve' Equation: II
Kitaev, A V
2010-01-01
The degenerate third Painleve' equation, $u"(t)=(u'(t))^2/u(t)-u'(t)/t+1/t(-8c u^2(t)+2ab)+b^2/u(t)$, where $c=+/-1$, $b>0$, and $a$ is a complex parameter, is studied via the Isomonodromy Deformation Method. Asymptotics of general regular and singular solutions $u(t)$ as $t -> +/-\\infty$ and $t -> +/-i\\infty$ are derived and parametrized in terms of the monodromy data of the associated 2X2 linear auxiliary problem introduced in the first part of this work [1]. Using these results, three-real-parameter families of solutions that have infinite sequences of zeroes and poles that are asymptotically located along the real and imaginary axes are distinguished: asymptotics of these zeroes and poles are also obtained.
S-asymptotically periodic solutions for partial differential equations with finite delay
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William Dimbour
2011-09-01
Full Text Available In this article, we give some sufficient conditions for the existence and uniqueness of S-asymptotically periodic (mild solutions for some partial functional differential equations. To illustrate our main result, we study a diffusion equation with delay.
Asymptotic and Oscillatory Behavior of Solutions of First Order Neutral Differential Equations
Institute of Scientific and Technical Information of China (English)
王其如; 李黎
1993-01-01
This paper has made researches on first order neutral differential equations with varia-ble coefficients and several deviations.The asymptotic behavior of nonoscillatory solutions of the equations are discussed.Necessary and sufficient conditions and several sufficient conditions for the oscillations of the equations are obtained.The relevent results in [1-3] are improved and genera-lized.
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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 \
Error estimates for asymptotic solutions of dynamic equations on time scales
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Gro Hovhannisyan
2007-02-01
Full Text Available We establish error estimates for first-order linear systems of equations and linear second-order dynamic equations on time scales by using calculus on a time scales [1,4,5] and Birkhoff-Levinson's method of asymptotic solutions [3,6,8,9].
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Sakovich, Anna, E-mail: sakovich@math.kth.s [Institutionen foer Matematik, Kungliga Tekniska Hoegskolan, 100 44 Stockholm (Sweden)
2010-12-21
We follow the approach employed by Y Choquet-Bruhat, J Isenberg and D Pollack in the case of closed manifolds and establish existence and non-existence results for constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds.
Multiple Solutions for a Fourth-order Asymptotically Linear Elliptic Problem
Institute of Scientific and Technical Information of China (English)
Ai Xia QIAN; Shu Jie LI
2006-01-01
Under simple conditions, we prove the existence of three solutions for a fourth-order asymptotically linear elliptic boundary value problem. For the resonance case at infinity, we do not need to assume any more conditions to ensure the boundedness of the (PS) sequence of the corresponding functional.
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.
Asymptotic solutions for laminar flow in a channel with uniformly accelerating rigid porous walls
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A theoretical investigation was done for the generalized Berman problem, which arises in steady laminar flow of an incompressible viscous fluid along a channel with accelerating rigid porous walls. The existence of multiple solutions and its conditions were established by taking into account exponentially small terms in matched asymptotic expansion. The correctness of the analytical predictions was verified by numerical results.
The asymptotics of a solution of a parabolic equation as time increases without bound
Energy Technology Data Exchange (ETDEWEB)
Degtyarev, Denis O; Il' in, Arlen M
2012-11-30
A boundary-value problem for a second order parabolic equation on a half-line is considered. A uniform asymptotic approximation to a solution to within any power of t{sup -1} is constructed and substantiated. Bibliography: 8 titles.
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Zhanhua Yu
2011-01-01
convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results.
ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS TO THE EULER-POISSON SYSTEM IN SEMICONDUCTORS
Institute of Scientific and Technical Information of China (English)
琚强昌
2002-01-01
In this paper, we establish the global existence and the asymptotic behavior of smooth solution to the initial-boundary value problem of Euler-Poisson system which is used as the bipolar hydrodynamic model for semiconductors with the nonnegative constant doping profile.
Asymptotic property of solutions to the random cauchy problem for wave equations
Dôku, Isamu
1986-01-01
Based on the existence and uniqueness theorem for random wave equations, we consider asymptotic behaviors of solutions to the random initial value problem. We describe conditions for the equipartition of stochastic energy (or SE for short) by making use of the random spectral theory and, according to Goldstein's semigroup method, we prove the asymptotically equipartitioned SE theorem and the so-called virial theorem of classical mechanics, and also study the probabilistic characterization of the conditions for equipartition. In addition, we show at last the equipartition of SE from a finite time onwards.
Weak asymptotic solution for a non-strictly hyperbolic system of conservation laws-II
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Manas Ranjan Sahoo
2016-04-01
Full Text Available In this article we introduce a concept of entropy weak asymptotic solution for a system of conservation laws and construct the same for a prolonged system of conservation laws which is highly non-strictly hyperbolic. This is first done for Riemann type initial data by introducing $\\delta,\\delta',\\delta''$ waves along a discontinuity curve and then for general initial data by piecing together the Riemann solutions.
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.
TIME-ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR GENERAL NAVIER-STOKES EQUATIONS IN EVEN SPACE-DIMENSION
Institute of Scientific and Technical Information of China (English)
Xu Hongmei
2001-01-01
We study the time-asymptotic behavior of solutions to general NavierStokes equations in even and higher than two space-dimensions. Through the pointwise estimates of the Green function of the linearized system, we obtain explicit expressions of the time-asymptotic behavior of the solutions. The result coincides with weak Huygan's principle.
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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.
Institute of Scientific and Technical Information of China (English)
LIU Hong-Zhun; PAN Zu-Liang; LI Peng
2006-01-01
In this article, we will derive an equality, where the Taylor series expansion around ε = 0for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted.By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-B(a)cklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-B(a)cklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.
Institute of Scientific and Technical Information of China (English)
Tang Zhongwei
2006-01-01
The author first analyzes the existence of ground state solutions and cylindrically symmetric solutions and then the asymptotic behavior of the ground state solution of the equation -Au = φ(r)up-1, u ＞ 0 in RN, u ∈ D1,2(RN), where N ≥ 3, x =(x',z) ∈ RK × RN-K,2 ≤ K ≤ N,r = |x'|. It is proved that for 2(N-s)/(N-2) ＜p ＜ 2* = 2N/(N - 2), 0 ＜ s ＜ 2, the above equation has a ground state solution and a cylindrically symmetric solution. For p = 2*, the above equation does not have a ground state solution but a cylindrically symmetric.solution, and when p close to 2*, the ground state solutions are not cylindrically symmetric. On the other hand, it is proved that as p close to 2*, the ground state solution up has a unique maximum point xp = (x'p, zp) and as p → 2*, |x'p| → r0 which attains the maximum of φ on RN. The asymptotic behavior ofground state solution up is also given, which also deduces that the ground state solutionis not cylindrically symmetric as p goes to 2*.
Institute of Scientific and Technical Information of China (English)
薛强; 梁冰; 刘晓丽; 李宏艳
2003-01-01
The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport , a coupled mathematical model of contaminant transport in unsaturated zone has been established based on fluid-solid interaction mechanics theory. The asymptotical solutions to the nonlinear coupling mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of pore pressure,pore water velocity and contaminant concentration in unsaturated zone has been presented under the conditions of with coupling and without coupling gas phase. An example problem was used to provide a quantitative verification and validation of the model. The asymptotical solution was compared with Faust model solution. The comparison results show reasonable agreement between asymptotical solution and Faust solution, and the gas effect and media deformation has a large impact on the contaminant transport. The theoretical basis is provided for forecasting contaminant transport and the determination of the relationship among pressure-saturation-permeability in laboratory.
Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem
Institute of Scientific and Technical Information of China (English)
TANG Rong-rong
2009-01-01
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter e and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of O(ε2).
Institute of Scientific and Technical Information of China (English)
郭柏灵; 苗长兴
1995-01-01
The final value problem for the classical coupled Klein-Gordon-Schrodinger equations is studied in . This leads to the construction of the modified wave operator Ω, for certain scattered data. When initial functions belong to (Ω) which denotes the range domain of Ω, the global existence and asymptotic behavior of solutions of Cauchy problem tor the coupled Klein-Gordon-Schrodinger equations are proved.
On asymptotic time decay of solutions to a parabolic equation in unbounded domains
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P. Maremonti
1991-05-01
Full Text Available Estimates on the asymptotic behaviour of solutions to a parabolic equation are given, when the I.B.V.P. is posed in particular domains. More precisely, the domain Ω is unbounded, unbounded in any direction, and Ω is enclosed in a wedge or in a cone of two or three-dimensional Euclidean space. It is proved that the order of decay is increasing for decreasing opening of the wedge or of the cone.
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.
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Jacqueline Fleckinger
2001-12-01
Full Text Available We study the asymptotic behavior of positive solutions $u$ of $$ -Delta_p u(x = V(x u(x^{p-1}, quad p>1; x in Omega,$$ and related partial differential inequalities, as well as conditions for existence of such solutions. Here, $Omega$ contains the exterior of a ball in $mathbb{R}^N$ $1
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.
Asymptotic solution for high vorticity regions in incompressible 3D Euler equations
Agafontsev, D S; Mailybaev, A A
2016-01-01
Incompressible 3D Euler equations develop high vorticity in very thin pancake-like regions from generic large-scale initial conditions. In this work we propose an exact solution of the Euler equations for the asymptotic pancake evolution. This solution combines a shear flow aligned with an asymmetric straining flow, and is characterized by a single asymmetry parameter and an arbitrary transversal vorticity profile. The analysis is based on detailed comparison with numerical simulations performed using a pseudo-spectral method in anisotropic grids of up to 972 x 2048 x 4096.
Asymptotic Smoothing Effect of Solutions to Davey-Stewartson Systems on the Whole Plane
Institute of Scientific and Technical Information of China (English)
Cai Di ZHAO; Yong Sheng LI; Sheng Fan ZHOU
2007-01-01
This paper discusses the Cauchy problem of elliptic-elliptic-type Davey-Stewartson systems with zero-order dissipation on R2. Making use of the Fourier spectral projector, together with a long time comparison between the solutions to the Davey-Stewartson systems and to an auxiliary problem,we prove that the global attractor in H1 (R2) for the addressed Davey-Stewartson systems is a compact subset of H2(R2), and thus reveal the asymptotic smoothing effect of the solutions for the systems.
Asymptotic analysis of singular solutions of the scalar and mean curvature equations
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Gonzalo García
2005-01-01
Full Text Available We show that positive solutions of a semilinear elliptic problem in the Sobolev critical exponent with Newmann conditions, related to conformal deformation of metrics in ℝ+n, are asymptotically symmetric in a neighborhood of the origin. As a consequence, we prove for a related problem of conformal deformation of metrics in ℝ+n that if a solution satisfies a Kazdan-Warner-type identity, then the conformal metric can be realized as a smooth metric on S+n.
Exact Asymptotic Expansion of Singular Solutions for the (2+1-D Protter Problem
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Lubomir Dechevski
2012-01-01
Full Text Available We study three-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems in ℝ2. In contrast to the planar Darboux problem the three-dimensional version is not well posed, since its homogeneous adjoint problem has an infinite number of classical solutions. On the other hand, it is known that for smooth right-hand side functions there is a uniquely determined generalized solution that may have a strong power-type singularity at one boundary point. This singularity is isolated at the vertex of the characteristic light cone and does not propagate along the cone. The present paper describes asymptotic expansion of the generalized solutions in negative powers of the distance to this singular point. We derive necessary and sufficient conditions for existence of solutions with a fixed order of singularity and give a priori estimates for the singular solutions.
Asymptotic Behaviors of the Solutions to Scalar Viscous Conservation Laws on Bounded Interval
Institute of Scientific and Technical Information of China (English)
Quansen Jiu; Tao Pan
2003-01-01
This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value problem for scalar viscous conservations laws ut + f(u)x = uxx on [0, 1], with the boundary condition u(0, t) =u_,u(1,t) = u+ and the initial data u(x, 0) = u0(x), where u_ ≠ u+ and f is a given function satisfying f″ (u) ＞ 0 for u under consideration. By means of energy estimates method and under some more regular conditions on the initial data, both the global existence and the asymptotic behavior are obtained. When u_ ＜ u+, which corresponds to rarefaction waves in inviscid conservation laws, no smallness conditions are needed. While for u_ ＞ u+, which corresponds to shock waves in inviscid conservation laws, it is established for weak shock waves, which means that |u_ - u+| is small. Moreover, exponential decay rates are both given.
Grava, T
2012-01-01
We study numerically the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\\epsilon^{2}u_{xxx}=0$ for $\\epsilon\\ll1$ and give a quantitative comparison of the numerical solution with various asymptotic formulae for small $\\epsilon$ in the whole $(x,t)$-plane. The matching of the asymptotic solutions is studied numerically.
Asymptotic solution of the turbulent mixing layer for velocity ratio close to unity
Higuera, F. J.; Jimenez, J.; Linan, A.
1996-01-01
The equations describing the first two terms of an asymptotic expansion of the solution of the planar turbulent mixing layer for values of the velocity ratio close to one are obtained. The first term of this expansion is the solution of the well-known time-evolving problem and the second, which includes the effects of the increase of the turbulence scales in the stream-wise direction, obeys a linear system of equations. Numerical solutions of these equations for a two-dimensional reacting mixing layer show that the correction to the time-evolving solution may explain the asymmetry of the entrainment and the differences in product generation observed in flip experiments.
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Zhihe Jin
2011-12-01
Full Text Available This work investigates transient heat conduction in a functionally graded plate (FGM plate subjected to gradual cooling/heating at its boundaries. The thermal properties of the FGM are assumed to be continuous and piecewise differentiable functions of the coordinate in the plate thickness direction. A linear ramp function describes the cooling/heating rates at the plate boundaries. A multi-layered material model and Laplace transform are employed to obtain the transformed temperatures at the interfaces between the layers. An asymptotic analysis and an integration technique are then used to obtain a closed form asymptotic solution of the temperature field in the FGM plate for short times. The thermal stress intensity factor (TSIF for an edge crack in the FGM plate calculated based on the asymptotic temperature solution shows that the asymptotic solution can capture the peak TSIFs under the finite cooling rate conditions.
Institute of Scientific and Technical Information of China (English)
Zhang Zhijiun
2008-01-01
By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem △u = k(x)g(u),u>0, x∈Ω, u|(e)Ω = +∞, where Ω is a bounded domain with smooth boundary in RN; g ∈ C1[0,∞), g(0) = g'(0) = 0, and there exists p > 1, such that lims→∞ g(sξ)/g(s)=ξp, (A)ξ > 0, and k∈Cαloc(Ω) is non-negative non-trivial in Ω which may be singular on the boundary.
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.
Pullback Asymptotic Behavior of Solutions for a 2D Non-autonomous Non-Newtonian Fluid
Liu, Guowei
2016-10-01
This paper studies the pullback asymptotic behavior of solutions for the non-autonomous incompressible non-Newtonian fluid in 2D bounded domains. Firstly, with a little high regularity of the force, the semigroup method and ɛ -regularity method are used to establish the existence of compact pullback absorbing sets. Then, with a minimal regularity of the force, by verifying the flattening property also known as the "Condition (C)", the author proves the existence of pullback attractors for the universe of fixed bounded sets and for the another universe given by a tempered condition. Furthermore, the regularity of pullback attractors is given.
Asymptotic L1-decay of solutions of the porous medium equation to self-similarity
Carrillo de la Plata, José Antonio; G. Toscani
2000-01-01
We consider the flow of gas in an N-dimensional porous medium with initial density v0(x) ≥ 0. The density v(x, t) then satisfies the nonlinear degenerate parabolic equation vt = ∆vm where m > 1 is a physical constant. Assuming that R (1 + |x|2)v0(x) dx < ∞, we prove that v(x, t) behaves asymptotically, as t → ∞, like the Barenblatt-Pattle solution V (|x|, t). We prove that the L1-distance decays at a rate t1/((N+2)m−N). Moreover, if N = 1, we obtain an explicit time decay for the L∞-distance ...
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.
Budd, Christopher J
2015-01-01
We study the asymptotic behaviour of sharp front solutions arising from the nonlinear diffusion equation \\theta_t = (D(\\theta)\\theta_x)_x, where the diffusivity is an exponential function D({\\theta}) = D_o exp(\\beta\\theta). This problem arises in the study of unsaturated flow in porous media where {\\theta} represents the liquid saturation. For the physical parameters corresponding to actual porous media, the diffusivity at the residual saturation is D(0) = D_o << 1 so that the diffusion problem is nearly degenerate. Such problems are characterised by wetting fronts that sharply delineate regions of saturated and unsaturated flow, and that propagate with a well-defined speed. Using matched asymptotic expansions in the limit of large {\\beta}, we derive an analytical description of the solution that is uniformly valid throughout the wetting front. This is in contrast with most other related analyses that instead truncate the solution at some specific wetting front location, which is then calculated as part...
A two-parameter family of exact asymptotically flat solutions to the Einstein-scalar field equations
Energy Technology Data Exchange (ETDEWEB)
Nikonov, V V; Tchemarina, Ju V; Tsirulev, A N [Department of Mathematics, Tver State University, Sadovyi per. 35, Tver 170002 (Russian Federation)], E-mail: tsirulev@tversu.ru
2008-07-07
We consider a static spherically symmetric real scalar field, minimally coupled to Einstein gravity. A two-parameter family of exact asymptotically flat solutions is obtained by using the inverse problem method. This family includes non-singular solutions, black holes and naked singularities. For each of these solutions the respective potential is partially negative but positive near spatial infinity. (comments, replies and notes)
Asymptotic self-similar solutions with a characteristic time-scale
Waxman, Eli
2010-01-01
For a wide variety of initial and boundary conditions, adiabatic one dimensional flows of an ideal gas approach self-similar behavior when the characteristic length scale over which the flow takes place, $R$, diverges or tends to zero. It is commonly assumed that self-similarity is approached since in the $R\\to\\infty(0)$ limit the flow becomes independent of any characteristic length or time scales. In this case the flow fields $f(r,t)$ must be of the form $f(r,t)=t^{\\alpha_f}F(r/R)$ with $R\\propto(\\pm t)^\\alpha$. We show that requiring the asymptotic flow to be independent only of characteristic length scales imply a more general form of self-similar solutions, $f(r,t)=R^{\\delta_f}F(r/R)$ with $\\dot{R}\\propto R^\\delta$, which includes the exponential ($\\delta=1$) solutions, $R\\propto e^{t/\\tau}$. We demonstrate that the latter, less restrictive, requirement is the physically relevant one by showing that the asymptotic behavior of accelerating blast-waves, driven by the release of energy at the center of a co...
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.
Hybrid resonance and long-time asymptotic of the solution to Maxwell's equations
Després, Bruno
2015-01-01
We study the long-time asymptotic of the solutions to Maxwell's equation in the case of a hybrid resonance in the cold plasma model. We base our analysis in the transfer to the time domain of the recent results of B. Despr\\'es, L.M. Imbert-G\\'erard and R. Weder, J. Math. Pures Appl. {\\bf 101} ( 2014) 623-659, where the singular solutions to Maxwell's equations in the frequency domain where 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 because hybrid resonances are a possible scenario for the heating of plasmas in the future ITER Tokamak.
A remark on the asymptotic form of BPS multi-dyon solutions and their conserved charges
Constantinidis, C. P.; Ferreira, L. A.; Luchini, G.
2015-12-01
We evaluate the gauge invariant, dynamically conserved charges, recently obtained from the integral form of the Yang-Mills equations, for the BPS multi-dyon solutions of a Yang-Mills-Higgs theory associated to any compact semi-simple gauge group G. Those charges are shown to correspond to the eigenvalues of the next-to-leading term of the asymptotic form of the Higgs field at spatial infinity, and so coinciding with the usual topological charges of those solutions. Such results show that many of the topological charges considered in the literature are in fact dynamical charges, which conservation follows from the global properties of classical Yang-Mills theories encoded into their integral dynamical equations. The conservation of those charges can not be obtained from the differential form of Yang-Mills equations.
A remark on the asymptotic form of BPS multi-dyon solutions and their conserved charges
Constantinidis, C P; Luchini, G
2015-01-01
We evaluate the gauge invariant, dynamically conserved charges, recently obtained from the integral form of the Yang-Mills equations, for the BPS multi-dyon solutions of a Yang-Mills-Higgs theory associated to any compact semi-simple gauge group G. Those charges are shown to correspond to the eigenvalues of the next-to-leading term of the asymptotic form of the Higgs field at spatial infinity, and so coinciding with the usual topological charges of those solutions. Such results show that many of the topological charges considered in the literature are in fact dynamical charges, which conservation follows from the global properties of classical Yang-Mills theories encoded into their integral dynamical equations. The conservation of those charges can not be obtained from the differential form of Yang-Mills equations.
Hybrid resonance and long-time asymptotic of the solution to Maxwell's equations
Després, Bruno; Weder, Ricardo
2016-03-01
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.
Institute of Scientific and Technical Information of China (English)
Zhi-zhong Sun; Long-Jun Shen
2003-01-01
In this paper, the solution of back-Euler implicit difference scheme for a semi-linearparabolic equation is proved to converge to the solution of difference scheme for the corre-sponding semi-linear elliptic equation as t tends to infinity. The long asymptotic behaviorof its discrete solution is obtained which is analogous to that of its continuous solution. Atlast, a few results are also presented for Crank-Nicolson scheme.
Institute of Scientific and Technical Information of China (English)
Wenrong DAI
2006-01-01
In this paper, we study the asymptotic behavior of global classical solutions of the Cauchy problem for general quasilinear hyperbolic systems with constant multiple and weakly linearly degenerate characteristic fields. Based on the existence of global classical solution proved by Zhou Yi et al., we show that, when t tends to infinity, the solution approaches a combination of C1 travelling wave solutions, provided that the total variation and the L1 norm of initial data are sufficiently small.
Qandalji, K Rasem
2011-01-01
We show that based on the general solution, given by Corrigan, Olive, Fairlie and Nuyts, in the region outside the monopole's core; the equations of motion in the Higgs vacuum (i.e. outside the monopole's core) will not allow asymptotically non-singular extended non-trivial non-Dyonic (including, also, all static) solutions of the 't Hooft-Polyakov monopole. In other words, unless the monopole's magnetic charge is shielded (by some mechanism), the Dirac string is inevitable asymptotically, in the region outside the monopole's core, for all non-Dyonic solutions that are admissible by the equations of motion. That we show that the non-dyonic solutions (based on Corrigan et al) will include all "admissible" static solutions and their gauge transform might be interpreted as that all admissible dyonic solutions (based on Corrigan et al) are composite solutions.
Behzadan, A
2015-01-01
In this article we consider the conformal decomposition of Einstein's constraint equations introduced by Lichnerowicz, Choquet-Bruhat, and York, on asymptotically flat (AF) manifolds. Using the non-CMC fixed-point framework developed in 2009 by Holst, Nagy, and Tsogtgerel and by Maxwell, we establish existence of coupled non-CMC weak solutions for AF manifolds. As is the case for the analogous existence results for non-CMC solutions on closed manifolds and compact manifolds with boundary, our results here avoid the near-CMC assumption by assuming that the freely specifiable part of the data given by the traceless-transverse part of the rescaled extrinsic curvature and the matter fields are sufficiently small. The non-CMC rough solutions results here for AF manifolds may be viewed as extending to AF manifolds the 2009 and 2014 results on rough far-from-CMC positive Yamabe solutions for closed and compact manifolds with boundary. Similarly, our results may be viewed as extending the recent 2014 results for AF m...
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Majda Chaieb
2016-01-01
Full Text Available Let \\(\\Omega\\ be a bounded domain in \\(\\mathbb{R}^{n}\\ (\\(n\\geq 2\\ with a smooth boundary \\(\\partial \\Omega\\. We discuss in this paper the existence and the asymptotic behavior of positive solutions of the following semilinear elliptic system \\[\\begin{aligned} -\\Delta u&=a_{1}(xu^{\\alpha}v^{r}\\quad\\text{in}\\;\\Omega ,\\;\\;\\,u|_{\\partial\\Omega}=0,\\\\ -\\Delta v&=a_{2}(xv^{\\beta}u^{s}\\quad\\text{in}\\;\\Omega ,\\;\\;\\,v|_{\\partial\\Omega }=0.\\end{aligned}\\] Here \\(r,s\\in \\mathbb{R}\\, \\(\\alpha,\\beta \\lt 1\\ such that \\(\\gamma :=(1-\\alpha(1-\\beta-rs\\gt 0\\ and the functions \\(a_{i}\\ (\\(i=1,2\\ are nonnegative and satisfy some appropriate conditions with reference to Karamata regular variation theory.
Asymptotic profiles for a travelling front solution of a biological equation
Chapuisat, Guillemette
2010-01-01
We are interested in the existence of depolarization waves in the human brain. These waves propagate in the grey matter and are absorbed in the white matter. We consider a two-dimensional model $u_t=\\Delta u + f(u) \\1_{|y|\\leq R} - \\alpha u \\1_{|y|>R}$, with $f$ a bistable nonlinearity taking effect only on the domain $\\Rm\\times [-R,R]$, which represents the grey matter layer. We study the existence, the stability and the energy of non-trivial asymptotic profiles of possible travelling fronts. For this purpose, we present dynamical systems technics and graphic criteria based on Sturm-Liouville theory and apply them to the above equation. This yields three different behaviours of the solution $u$ after stimulation, depending of the thickness $R$ of the grey matter. This may partly explain the difficulties to observe depolarization waves in the human brain and the failure of several therapeutic trials.
Kiselev, O M
1999-01-01
The asymptotic solution for the Painleve-2 equation with small parameter is considered. The solution has algebraic behavior before point $t_*$ and fast oscillating behavior after the point $t_*$. In the transition layer the behavior of the asymptotic solution is more complicated. The leading term of the asymptotics satisfies the Painleve-1 equation and some elliptic equation with constant coefficients, where the solution of the Painleve-1 equation has poles. The uniform smooth asymptotics are constructed in the interval, containing the critical point $t_*$.
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Min Jia
2012-01-01
Full Text Available We study a model arising from porous media, electromagnetic, and signal processing of wireless communication system -tαx(t=f(t,x(t,x'(t,x”(t,…,x(n-2(t, 0
Institute of Scientific and Technical Information of China (English)
Cuimei ZHANG; Wencheng CHEN; Yu YANG
2006-01-01
In this paper, we study the existence and global asymptotic stability of positive periodic solutions of a delayed periodic predator-prey system with Holling Ⅱ type functional response. By use of the continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions are obtained.
Qin, Yuming; Zhang, Jianlin
2016-12-01
In this paper, we establish the global existence, uniqueness and asymptotic behavior of cylindrically symmetric solutions for the 3D infrarelativistic model with radiation in H^i× (H^i)^3× H^i× H^{i+1}(i=1,2,4) . The key point is that the smallness of initial data is not needed.
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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.
An asymptotic solution of large-$N$ $QCD$, and of large-$N$ $\\mathcal{N}=1$ $SUSY$ $QCD$
Bochicchio, Marco
2014-01-01
We find an asymptotic solution for two- and three-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$ (and of massless large-$N$ $\\cal{N}$ $=1$ $SUSY$ $QCD$), in terms of glueball and meson propagators (and of their $SUSY$ partners), by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap. The asymptotically-free bootstrap exploits the lowest-order conformal invariance of connected correlators of gauge invariant composite operators in perturbation theory, the renormalization-group improvement, and a recently-proved asymptotic structure theorem for glueball and meson propagators (and for their $SUSY$ partners), that involves the unknown particle spectrum and the anomalous dimension of operators for fixed spin. In principle the asymptotically-free bootstrap extends to all the higher-spin two- and three-point correlators whose lowest-order conformal limit is non-vanishing in perturbation theory, and by means of the o...
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Tongqing Lu
2014-01-01
Full Text Available In a thin film-substrate system in-plane compressive stress is commonly generated in the film due to thermal mismatch in operation or fabrication process. If the stress exceeds a critical value, part of the film may buckle out of plane along the defective interface. After buckling delamination, the interface crack at the ends may propagate. In the whole process, the compliance of the substrate compared with the film plays an important role. In this work, we study a circular film subject to compressive stress on an infinitely thick substrate. We study the effects of compliance of the substrate by modeling the system as a plate on an elastic foundation. The critical buckling condition is formulated. The asymptotic solutions of post-buckling deformation and the corresponding energy release rate of the interface crack are obtained with perturbation methods. The results show that the more compliant the substrate is, the easier for the film to buckle and easier for the interface crack to propagate after buckling.
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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.
Holst, Michael
2014-01-01
In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold M with interior boundary S. Building on recent results for both the asymptotically Euclidean and compact with boundary settings, we show existence of far-from-CMC and near-CMC solutions to the conformal formulation of the Einstein constraints when nonlinear Robin boundary conditions are imposed on S, similar to those analyzed previously by Dain (2004), by Maxwell (2004, 2005), and by Holst and Tsogtgerel (2013) as a model of black holes in various CMC settings, and by Holst, Meier, and Tsogtgerel (2013) in the setting of far-from-CMC solutions on compact manifolds with boundary. These "marginally trapped surface" Robin conditions ensure that the expansion scalars along null geodesics perpendicular to the boundary region S are non-positive, which is considered the correct mathematical model for black holes in the context of the Einstein constraint equations. Assumi...
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.
Asymptotic solutions of the axisymmetric moist Hadley circulation in a model with two vertical modes
Energy Technology Data Exchange (ETDEWEB)
Burns, Samuel P. [Columbia University, Department of Applied Physics and Applied Mathematics, New York, NY (United States); New York University, Courant Institute, New York, NY (United States); Sobel, Adam H.; Polvani, Lorenzo M. [Columbia University, Department of Applied Physics and Applied Mathematics, New York, NY (United States)
2006-11-15
A simplified model of the moist axisymmetric Hadley circulation is examined in the asymptotic limit in which surface drag is strong and the meridional wind is weak compared to the zonal wind. Our model consists of the quasi-equilibrium tropical circulation model (QTCM) equations on an axisymmetric aquaplanet equatorial beta-plane. This model includes two vertical momentum modes, one baroclinic and one barotropic. Prior studies use either continuous stratification, or a shallow water system best viewed as representing the upper troposphere. The analysis here focuses on the interaction of the baroclinic and barotropic modes, and the way in which this interaction allows the constraints on the circulation known from the fully stratified case to be satisfied in an approximate way. The dry equations, with temperature forced by Newtonian relaxation towards a prescribed radiative equilibrium, are solved first. To leading order, the resulting circulation has a zonal wind profile corresponding to uniform angular momentum at a level near the tropopause, and zero zonal surface wind, owing to the cancelation of the barotropic and baroclinic modes there. The weak surface winds are calculated from the first-order corrections. The broad features of these solutions are similar to those obtained in previous studies of the dry Hadley circulation. The moist equations are solved next, with a fixed sea surface temperature at the lower boundary and simple parameterizations of surface fluxes, deep convection, and radiative transfer. The solutions yield the structure of the barotropic and baroclinic winds, as well as the temperature and moisture fields. In addition, we derive expressions for the width and strength of the equatorial precipitating region (ITCZ) and the width of the entire Hadley circulation. The ITCZ width is on the order of a few degrees in the absence of any horizontal diffusion and is relatively insensitive to parameter variations. (orig.)
Exact Solution of Klein-Gordon Equation by Asymptotic Iteration Method
Institute of Scientific and Technical Information of China (English)
Eser Ol(g)ar
2008-01-01
Using the asymptotic iteration method (AIM) we obtain the spectrum of the Klein-Gordon equation for some choices of scalar and vector potentials. In particular, it is shown that the AIM exactly reproduces the spectrum of some solvable potentials.
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Zhijun Zhang
2006-08-01
Full Text Available We show the exact asymptotic behaviour near the boundary for the classical solution to the Dirichler problem $$ -Delta =k(xg(u+lambda |abla u|^q, quad u>0,; xin Omega,quad uig|_{partial{Omega}}=0, $$ where $Omega$ is a bounded domain with smooth boundary in $mathbb R^N$. We use the Karamata regular varying theory, a perturbed argument, and constructing comparison functions.
Luo, Tao; Xin, Zhouping; Zeng, Huihui
2016-11-01
The nonlinear asymptotic stability of Lane-Emden solutions is proved in this paper for spherically symmetric motions of viscous gaseous stars with the density dependent shear and bulk viscosities which vanish at the vacuum, when the adiabatic exponent {γ} lies in the stability regime {(4/3, 2)}, by establishing the global-in-time regularity uniformly up to the vacuum boundary for the vacuum free boundary problem of the compressible Navier-Stokes-Poisson systems with spherical symmetry, which ensures the global existence of strong solutions capturing the precise physical behavior that the sound speed is {C^{{1}/{2}}}-Hölder continuous across the vacuum boundary, the large time asymptotic uniform convergence of the evolving vacuum boundary, density and velocity to those of Lane-Emden solutions with detailed convergence rates, and the detailed large time behavior of solutions near the vacuum boundary. Those uniform convergence are of fundamental importance in the study of vacuum free boundary problems which are missing in the previous results for global weak solutions. Moreover, the results obtained in this paper apply to much broader cases of viscosities than those in Fang and Zhang (Arch Ration Mech Anal 191:195-243, 2009) for the theory of weak solutions when the adiabatic exponent {γ} lies in the most physically relevant range. Finally, this paper extends the previous local-in-time theory for strong solutions to a global-in-time one.
Asymptotic solution of natural convection problem in a square cavity heated from below
Grundmann, M; Mojtabi, A; vantHof, B
1996-01-01
Studies a two-dimensional natural convection in a porous, square cavity using a regular asymptotic development in powers of the Rayleigh number. Carries the approximation through to the 34th order. Analyses convergence of the resulting series for the Nusselt number in both monocellular and multicell
Institute of Scientific and Technical Information of China (English)
马西奎; 韩社教
2002-01-01
Based on the multipole expansion theory of the potential, a satisfactory interpretation is put forward of the exact nature of the approximations of asymptotic boundary condition (called the ABC) techniques for the numerical solutions of open-boundary static electromagnetic-field problems, and a definite physical meaning is bestowed on ABC, which provide a powerful theoretical background for laying down the operating rules and the key to the derivation of asymptotic boundary conditions. This paper is also intended to reveal the shortcomings of the conventional higher-order ABC, and at the same time to give the concept of a new type of higher-order ABC, and to present a somewhat different formulation of the new nth-order ABC. In order to test its feasibility, several simple problems of electrostatic potentials are analyzed. The results are found to be much better than those of conventional higher-order ABCs.
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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.
Rigorous asymptotics of traveling-wave solutions to the thin-film equation and Tanner’s law
Giacomelli, Lorenzo; Gnann, Manuel V.; Otto, Felix
2016-09-01
We are interested in traveling-wave solutions to the thin-film equation with zero microscopic contact angle (in the sense of complete wetting without precursor) and inhomogeneous mobility {{h}3}+{λ3-n}{{h}n} , where h, λ, and n\\in ≤ft(\\frac{3}{2},\\frac{7}{3}\\right) denote film height, slip parameter, and mobility exponent, respectively. Existence and uniqueness of these solutions have been established by Maria Chiricotto and the first of the authors in previous work under the assumption of sub-quadratic growth as h\\to ∞ . In the present work we investigate the asymptotics of solutions as h\\searrow 0 (the contact-line region) and h\\to ∞ . As h\\searrow 0 we observe, to leading order, the same asymptotics as for traveling waves or source-type self-similar solutions to the thin-film equation with homogeneous mobility h n and we additionally characterize corrections to this law. Moreover, as h\\to ∞ we identify, to leading order, the logarithmic Tanner profile, i.e. the solution to the corresponding unperturbed problem with λ =0 that determines the apparent macroscopic contact angle. Besides higher-order terms, corrections turn out to affect the asymptotic law as h\\to ∞ only by setting the length scale in the logarithmic Tanner profile. Moreover, we prove that both the correction and the length scale depend smoothly on n. Hence, in line with the common philosophy, the precise modeling of liquid-solid interactions (within our model, the mobility exponent) does not affect the qualitative macroscopic properties of the film.
Garbarz, Alan; Vásquez, Yerko
2008-01-01
We study exact solutions to Cosmological Topologically Massive Gravity (CTMG) coupled to Topologically Massive Electrodynamics (TME) at special values of the coupling constants. For the particular case of the so called chiral point l\\mu_G=1, vacuum solutions (with vanishing gauge field) are exhibited. These correspond to a one-parameter deformation of GR solutions, and are continuously connected to the extremal Banados-Teitelboim-Zanelli black hole (BTZ) with bare constants J=-lM. In CTMG this extremal BTZ turns out to be massless, and thus it can be regarded as a kind of ground state. For certain range of parameters, our solution exhibits an event horizon located at finite geodesic distance. Although the solution is not asymptotically AdS_3 in the sense of Brown-Henneaux boundary conditions, it does obey the weakened asymptotic recently proposed by Grumiller and Johansson. Consequently, we discuss the computation of the conserved chages in terms of the stress-tensor in the boundary, and we find that the sign...
Nal, P L
2002-01-01
We consider the asymptotic stability and the boundedness with probability one of solutions of linear lto stochastic differential equations not reduced to the Cauchy form and give some numerical examples to show that our sufficient conditions for the asymptotic stability with probability one of solutions are more general and more effective than those of Korenevskij and Mitropoloshij. Moreover, our results can also be applied to the case when the unperturbed linear deterministic system is not assumed to be stable.
Dai, Hui-Hui
2011-01-01
A polymer network can imbibe water, forming an aggregate called hydrogel, and undergo large and inhomogeneous deformation with external mechanical constraint. Due to the large deformation, nonlinearity plays a crucial role, which also causes the mathematical difficulty for obtaining analytical solutions. Based on an existing model for equilibrium states of a swollen hydrogel with a core-shell structure, this paper seeks analytical solutions of the deformations by perturbation methods for three cases, i.e. free-swelling, nearly free-swelling and general inhomogeneous swelling. Particularly for the general inhomogeneous swelling, we introduce an extended method of matched asymptotics to construct the analytical solution of the governing nonlinear second-order variable-coefficient differential equation. The analytical solution captures the boundary layer behavior of the deformation. Also, analytical formulas for the radial and hoop stretches and stresses are obtained at the two boundary surfaces of the shell, ma...
Institute of Scientific and Technical Information of China (English)
Ying-hui ZHANG; Zhong TAN
2011-01-01
In this paper,we are concerned with the asymptotic behaviour of a weak solution to the NavierStokes equations for compressible barotropic flow in two space dimensions with the pressure function satisfying p(ρ) =a(ρ)logd(ρ) for large (ρ).Here d ＞ 2,a ＞ 0.We introduce useful tools from the theory of Orlicz spaces and construct a suitable function which approximates the density for time going to infinity.Using properties of this function,we can prove the strong convergence of the density to its limit state.The behaviour of the velocity field and kinetic energy is also briefly discussed.
Institute of Scientific and Technical Information of China (English)
Hideo KUBO; K(o)ji KUBOTA
2006-01-01
This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t → -∞ in the energy norm, and to show it has a free profile as t → +∞. Our approach is based on the work of [11]. Namely we use a weighted L∞ norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper.
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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.
Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.
2016-08-01
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 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 augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the
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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Bloom Clifford O.
1996-01-01
Full Text Available The asymptotic behavior as λ → ∞ of the function U ( x , λ that satisfies the reduced wave equation L λ [ U ] = ∇ ⋅ ( E ( x ∇ U + λ 2 N 2 ( x U = 0 on an infinite 3-dimensional region, a Dirichlet condition on ∂ V , and an outgoing radiation condition is investigated. A function U N ( x , λ is constructed that is a global approximate solution as λ → ∞ of the problem satisfied by U ( x , λ . An estimate for W N ( x , λ = U ( x , λ − U N ( x , λ on V is obtained, which implies that U N ( x , λ is a uniform asymptotic approximation of U ( x , λ as λ → ∞ , with an error that tends to zero as rapidly as λ − N ( N = 1 , 2 , 3 , ... . This is done by applying a priori estimates of the function W N ( x , λ in terms of its boundary values, and the L 2 norm of r L λ [ W N ( x , λ ] on V . It is assumed that E ( x , N ( x , ∂ V and the boundary data are smooth, that E ( x − I and N ( x − 1 tend to zero algebraically fast as r → ∞ , and finally that E ( x and N ( x are slowly varying; ∂ V may be finite or infinite. The solution U ( x , λ can be interpreted as a scalar potential of a high frequency acoustic or electromagnetic field radiating from the boundary of an impenetrable object of general shape. The energy of the field propagates through an inhomogeneous, anisotropic medium; the rays along which it propagates may form caustics. The approximate solution (potential derived in this paper is defined on and in a neighborhood of any such caustic, and can be used to connect local “geometrical optics” type approximate solutions that hold on caustic free subsets of V .The result of this paper generalizes previous work of Bloom and Kazarinoff [C. O. BLOOM and N. D. KAZARINOFF, Short Wave Radiation Problems in Inhomogeneous Media: Asymptotic Solutions, SPRINGER VERLAG, NEW YORK, NY, 1976].
Kazinski, P. O.; Shipulya, M. A.
2011-06-01
We present a study of planar physical solutions to the Lorentz-Dirac equation in a constant electromagnetic field. In this case, we reduced the Lorentz-Dirac equation to one second-order differential equation. We obtained the asymptotics of physical solutions to this equation at large proper times. It turns out that, in a crossed constant uniform electromagnetic field with vanishing invariants, a charged particle enters a universal regime at large times. We found that the ratios of momentum components that tend to constants are determined only by the external field. This effect is essentially due to a radiation reaction. There is no such effect for the Lorentz equation in this field.
Kazinski, P O
2010-01-01
We present a study of planar physical solutions to the Lorentz-Dirac equation in a constant electromagnetic field. In this case, we reduced the Lorentz-Dirac equation to the one second order differential equation. We found the asymptotics of physical solutions to this equation at large proper times. It turns out that, in the crossed constant uniform electromagnetic field with vanishing invariants, a charged particle goes to a universal regime at large times. We found the ratio of momentum components which tends to a constant determined only by the external field. This effect is essentially due to a radiation reaction. There is no such an effect for the Lorentz equation in this field.
Maximal admissible faces and asymptotic bounds for the normal surface solution space
Burton, Benjamin A
2010-01-01
The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significant improvements upon the best known asymptotic bounds on the number of admissible vertices, using polytopes in both the standard normal surface coordinate system and the streamlined quadrilateral coordinate system. To achieve these results we examine the layout of admissible points within these polytopes. We show that these points correspond to well-behaved substructures of the face lattice, and we study properties of the corresponding "admissible faces". Key lemmata include upper bounds on the number of maximal admissible faces of each dimension, and a bijection between the maximal admissible faces in the two coordinate systems mentioned above.
Asymptotic solutions of forced nonlinear second order differential equations and their extensions
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Angelo B. Mingarelli
2007-03-01
Full Text Available Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear differential equations on a half-axis. In addition, we extend the methods and present new similar results for integral equations and Volterra-Stieltjes integral equations, a framework whose benefits include the unification of second order difference and differential equations. In so doing, we enlarge the class of nonlinearities and in some cases remove the distinction between superlinear, sublinear, and linear differential equations that is normally found in the literature. An update of papers, past and present, in the theory of Volterra-Stieltjes integral equations is also presented.
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.
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
Institute of Scientific and Technical Information of China (English)
Li Xiao-Jing
2008-01-01
This paper studies a time delay equation for sea-air oscillator model. The existence and asymptotic estimates of periodic solutions of corresponding problem are obtained by employing the technique of upper and lower solution, and by using the continuation theorem of coincidence degree theory.
Traytak, Sergey D
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.
Energy Technology Data Exchange (ETDEWEB)
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.
On de Sitter solutions in asymptotically safe $f(R)$ theories
Falls, Kevin; Nikolakopoulos, Kostas; Rahmede, Christoph
2016-01-01
The availability of scaling solutions in renormalisation group improved versions of cosmology are investigated in the high-energy limit. We adopt $f(R)$-type models of quantum gravity which display an interacting ultraviolet fixed point at shortest distances. Expanding the gravitational fixed point action to very high order in the curvature scalar, we detect a convergence-limiting singularity in the complex field plane. Resummation techniques including Pad\\'e approximants as well as infinite order approximations of the effective action are used to maximise the domain of validity. We find that the theory displays near de Sitter solutions as well as an anti-de Sitter solution in the UV whereas real de Sitter solutions, for small curvature, appear to be absent. The significance of our results for inflation, and implications for more general models of quantum gravity are discussed.
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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 PROPERTY OF THE TIME-DEPENDENT SOLUTION OF A RELIABILITY MODEL
Institute of Scientific and Technical Information of China (English)
Geni Gupur; GUO Baozhu
2005-01-01
We discuss a transfer line consisting of a reliable machine, an unreliable machine and a storage buffer. This transfer line can be described by a group of partial differential equations with integral boundary conditions. First we show that the operator corresponding to these equations generates a positive contraction C0-semigroup T(t), and prove that T(t) is a quasi-compact operator. Next we verify that 0 is an eigenvalue of this operator and its adjoint operator with geometric multiplicity one. Last, by using the above results we obtain that the time-dependent solution of these equations converges strongly to their steady-state solution.
ON THE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF CERTAIN FIFTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Cemil Tunc
2003-01-01
The sufficient conditions are given for all solutions of certain non-autonomous differential equation to be uniformly bounded and convergence to zero as t →∞ . The result given includes and improves that result obtained by Abou-El-Ela & Sadek.
Asymptotically simple solutions of the vacuum Einstein equations in even dimensions
Anderson, M T; Anderson, Michael T.; Chrusciel, Piotr T.
2004-01-01
We show that a set of conformally invariant equations derived from the Fefferman-Graham tensor can be used to construct global solutions of the vacuum Einstein equations, in all even dimensions. This gives, in particular, a new, simple proof of Friedrich's result on the future hyperboloidal stability of Minkowski space-time, and extends its validity to even dimensions.
On the asymptotic behavior of solutions of certain third-order nonlinear differential equations
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Cemil Tunç
2005-01-01
Full Text Available We establish sufficient conditions under which all solutions of the third-order nonlinear differential equation x ⃛+ψ(x,x˙,x¨x¨+f(x,x˙=p(t,x,x˙,x¨ are bounded and converge to zero as t→∞.
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.
Tsuboi, Zengo
2012-01-01
We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra U_q(gl(M|N)^). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of U_q(gl(M|N))in the FRT formulation and obtain explicit solutions of the graded Yang-Baxter equation in terms of q-oscillator superalgebras. These solutions correspond to L-operators for Baxter Q operators. We define model independent universal Q-operators as the supertrace of the universal R-matrix and write universal T-operators in terms of these Q-operators based on shift operators on the supercharacters. These include our previous work on U_q(sl(2|1)^) case [arXiv:0805.4274] in part, and also give a cue for operator realization of our Wronskian-like formulas on T-and Q-functions in [arXiv:0906.2039, arXiv:1109.5524].
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Lijuan Zhang
2014-01-01
Full Text Available An iterative algorithm for finding a common element of the set of common fixed points of a finite family of asymptotically nonextensive nonself mappings and the set of solutions for equilibrium problems is discussed. A strong convergence theorem of common element is established in a uniformly smooth and uniformly convex Banach space.
Institute of Scientific and Technical Information of China (English)
黄家寅
2004-01-01
By using "the method of modified two-variable ", "the method of mixing perturbation" and introducing four small parameters, the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied. And the uniformly valid asymptotic solution of Nth- order for ε 1 and Mth- order for ε 2of the deflection functions and stress function are obtained.
Asymptotic Steady State Solution to a Bow Shock with an Infinite Mach Number
Yalinewich, Almog
2015-01-01
The problem of a cold gas flowing past a stationary object is considered. It is shown that at large distances from the obstacle the shock front forms a parabolic solid of revolution. The interior of the shock front is obtained by solution of the hydrodynamic equations in parabolic coordinates. The results are verified with a hydrodynamic simulation. The drag force and expected spectra are calculated for such shock, both in case of an optically thin and thick media. Finally, relations to astrophysical bow shocks and other analytic works on oblique shocks are discussed.
Asymptotic properties of solutions of the Maxwell Klein Gordon equation with small data
Bieri, Lydia; Shahshahani, Sohrab
2014-01-01
We prove peeling estimates for the small data solutions of the Maxwell Klein Gordon equations with non-zero charge and with a non-compactly supported scalar field, in $(3+1)$ dimensions. We obtain the same decay rates as in an earlier work by Lindblad and Sterbenz, but giving a simpler proof. In particular we dispense with the fractional Morawetz estimates for the electromagnetic field, as well as certain space-time estimates. In the case that the scalar field is compactly supported we can avoid fractional Morawetz estimates for the scalar field as well. All of our estimates are carried out using the double null foliation and in a gauge invariant manner.
Amirkhanov, I V; Zhidkova, I E; Vasilev, S A
2000-01-01
Asymptotics of eigenfunctions and eigenvalues has been obtained for a singular perturbated relativistic analog of Schr`dinger equation. A singular convergence of asymptotic expansions of the boundary problems to degenerated problems is shown for a nonrelativistic Schr`dinger equation. The expansions obtained are in a good agreement with a numeric experiment.
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Le Thi Phuong Ngoc
2016-01-01
Full Text Available This paper is devoted to the study of a nonlinear Carrier wave equation in an annular membrane associated with Robin-Dirichlet conditions. Existence and uniqueness of a weak solution are proved by using the linearization method for nonlinear terms combined with the Faedo-Galerkin method and the weak compact method. Furthermore, an asymptotic expansion of a weak solution of high order in a small parameter is established.
Asymptotic solutions for the case of nearly symmetric gravitational lens systems
Wertz, O.; Pelgrims, V.; Surdej, J.
2012-08-01
Gravitational lensing provides a powerful tool to determine the Hubble parameter H0 from the measurement of the time delay Δt between two lensed images of a background variable source. Nevertheless, knowledge of the deflector mass distribution constitutes a hurdle. We propose in the present work interesting solutions for the case of nearly symmetric gravitational lens systems. For the case of a small misalignment between the source, the deflector and the observer, we first consider power-law (ɛ) axially symmetric models for which we derive an analytical relation between the amplification ratio and source position which is independent of the power-law slope ɛ. According to this relation, we deduce an expression for H0 also irrespective of the value ɛ. Secondly, we consider the power-law axially symmetric lens models with an external large-scale gravitational field, the shear γ, resulting in the so-called ɛ-γ models, for which we deduce simple first-order equations linking the model parameters and the lensed image positions, the latter being observable quantities. We also deduce simple relations between H0 and observables quantities only. From these equations, we may estimate the value of the Hubble parameter in a robust way. Nevertheless, comparison between the ɛ-γ and singular isothermal ellipsoid (SIE) models leads to the conclusion that these models remain most often distinct. Therefore, even for the case of a small misalignment, use of the first-order equations and precise astrometric measurements of the positions of the lensed images with respect to the centre of the deflector enables one to discriminate between these two families of models. Finally, we confront the models with numerical simulations to evaluate the intrinsic error of the first-order expressions used when deriving the model parameters under the assumption of a quasi-alignment between the source, the deflector and the observer. From these same simulations, we estimate for the case of the
Institute of Scientific and Technical Information of China (English)
王文彬; 刘淑梅
2005-01-01
In this paper, we study the asymptotic behavior of the solutions to the initial boundary value problem for unipolar drift diffusion equations for semiconductors. Under the proper assumptions on doping profile and initial value, we prove that the smooth solutions to these evolutionary problems tend to the unique stationary solution exponentially as time tends to infinity.
Carro, Adrian; Miguel, Maxi San
2012-01-01
We study a model for continuous-opinion dynamics under bounded confidence. In particular, we analyze the importance of the initial distribution of opinions in determining the asymptotic configuration. Thus, we sketch the structure of attractors of the dynamical system, by means of the numerical computation of the time evolution of the agents density. We show that, for a given bound of confidence, a consensus can be encouraged or prevented by certain initial conditions. Furthermore, a noisy perturbation is added to the system with the purpose of modeling the free will of the agents. As a consequence, the importance of the initial condition is partially replaced by that of the statistical distribution of the noise. Nevertheless, we still find evidence of the influence of the initial state upon the final configuration for a short range of the bound of confidence parameter.
Institute of Scientific and Technical Information of China (English)
梁保松; 陈振
2004-01-01
J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.
Grooms, Ian
2014-01-01
The non-hydrostatic, quasigeostrophic approximation for rapidly rotating Rayleigh-B\\'enard convection admits a class of exact `single mode' solutions. These solutions correspond to steady laminar convection with a separable structure consisting of a horizontal planform characterized by a single wavenumber multiplied by a vertical amplitude profile, with the latter given as the solution of a nonlinear boundary value problem. The heat transport associated with these solutions is studied in the regime of strong thermal forcing (large reduced Rayleigh number $\\widetilde{Ra}$). It is shown that the Nusselt number $Nu$, a nondimensional measure of the efficiency of heat transport by convection, for this class of solutions is bounded below by $Nu\\gtrsim \\widetilde{Ra}^{3/2}$, independent of the Prandtl number, in the limit of large reduced Rayleigh number. Matching upper bounds include only logarithmic corrections, showing the accuracy of the estimate. Numerical solutions of the nonlinear boundary value problem for ...
Composite asymptotic expansions
Fruchard, Augustin
2013-01-01
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance pro...
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J. Diblík
2012-01-01
Full Text Available We study a frequently investigated class of linear difference equations Δv(n=−p(nv(n−k with a positive coefficient p(n and a single delay k. Recently, it was proved that if the function p(n is bounded above by a certain function, then there exists a positive vanishing solution of the considered equation, and the upper bound was found. Here we improve this result by finding even the lower bound for the positive solution, supposing the function p(n is bounded above and below by certain functions.
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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.
Asymptotically hyperbolic connections
Fine, Joel; Krasnov, Kirill; Scarinci, Carlos
2015-01-01
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising "evolution" equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the obstruction appears at third order in the expansion. Another interesting feature of the connection formulation is that the "counter terms" required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-d...
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).
Asymptotically Almost Periodic Mild Solutions of Neutral Differential Equations%一类中立型微分方程的渐近概周期温和解
Institute of Scientific and Technical Information of China (English)
姚慧丽; 李雪鑫; 付作娴
2012-01-01
The research of almost periodic type function is aroused by mathematical workers at home and broad. Especially, it is applied to differential equation. In this paper, the existence of asymptotically almost periodic mild solution for a class of neutral differential equation is discussed by fixed theorem and some knowledge on C0-semigroup. The research is made on the basis of some literature for almost periodic mild solution. Then we expand the scope of the equations and applied the conclusions to more general problems.%概周期型函数的研究受到了国内外越来越多数学工作者的关注,特别是将其应用到微分方程中.利用不动点定理,结合算子半群有关理论,讨论了一类中立型微分方程的渐近概周期温和解的存在性.本文的研究问题是在一些文献对这类方程的概周期温和解研究的基础上进行的,扩大了方程解的范围,这样能够使结论应用到更一般的问题中.
Institute of Scientific and Technical Information of China (English)
张长海; 梁久祯; 刘明珠
2000-01-01
This paper deals with the stability analysis of numerical solutionof linear -methods for delay differential equations. We focuson the linear test equation x(t)=ax(t)+bx(［t］), where a,b areconstants and ［t］ is the largest-integer function. Sufficent conditionsare given for the numerical solution to be asymptotic stable
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.
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.
Asymptotically hyperbolic connections
Fine, Joel; Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos
2016-09-01
General relativity in four-dimensions can be equivalently described as a dynamical theory of {SO}(3)˜ {SU}(2)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analogue of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising ‘evolution’ equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the unconstrained by Einstein equations ‘stress-energy tensor’ appears at third order in the expansion. Another interesting feature of the connection formulation is that the ‘counter terms’ required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-defined requires the cosmological constant to be quantised. Finally, in the connection setting one can deform the 4D Einstein condition in an interesting way, and we show that asymptotically hyperbolic connection expansion is universal and valid for any of the deformed theories.
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 vacua with higher derivatives
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Spiros Cotsakis
2016-04-01
Full Text Available 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...
Confinement versus asymptotic freedom
Dubin, A Yu
2002-01-01
I put forward the low-energy confining asymptote of the solution $$ (valid for large macroscopic contours C of the size $>>1/\\Lambda_{QCD}$) to the large N Loop equation in the D=4 U(N) Yang-Mills theory with the asymptotic freedom in the ultraviolet domain. Adapting the multiscale decomposition characteristic of the Wilsonean renormgroup, the proposed Ansatz for the loop-average is composed in order to sew, along the lines of the bootstrap approach, the large N weak-coupling series for high-momentum modes with the $N\\to{\\infty}$ limit of the recently suggested stringy representation of the 1/N strong-coupling expansion Dub4 applied to low-momentum excitations. The resulting low-energy stringy theory can be described through such superrenormalizable deformation of the noncritical Liouville string that, being devoid of ultraviolet divergences, does not possess propagating degrees of freedom at short-distance scales $<<1/{\\sqrt{\\sigma_{ph}}}$, where $\\sigma_{ph}\\sim{(\\Lambda_{QCD})^{2}}$ is the physical s...
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....
ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
SHEN Yi; JIANG Ming-hui; LIAO Xiao-xin
2006-01-01
Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of t he solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.
Universal asymptotic umbrella for hydraulic fracture modeling
Linkov, Aleksandr M
2014-01-01
The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.
Asymptotic analysis of mode Ⅰ propagating crack-tip field in a creeping material
Institute of Scientific and Technical Information of China (English)
WANG Zhen-qing; ZHAO Qi-cheng; LIANG Wen-yan; FU Zhang-jian
2003-01-01
Adopting an elastic-viscoplastic, the asymptotic problem of mode I propagating crack-tip field is investigated. Various asymptotic solutions resulting from the analysis of crack growing programs are presented. The analysis results show that the quasi-statically growing crack solutions are the special case of the dynamic propagating solutions. Therefore these two asymptotic solutions can be unified.
Asymptotics of Random Contractions
Hashorva, Enkelejd; Tang, Qihe
2010-01-01
In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an extreme value distribution and the distribution function of $S$ satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.
ASYMPTOTIC QUANTIZATION OF PROBABILITY DISTRIBUTIONS
Institute of Scientific and Technical Information of China (English)
Klaus P(o)tzelberger
2003-01-01
We give a brief introduction to results on the asymptotics of quantization errors.The topics discussed include the quantization dimension,asymptotic distributions of sets of prototypes,asymptotically optimal quantizations,approximations and random quantizations.
Weakly asymptotically hyperbolic manifolds
Allen, Paul T; Lee, John M; Allen, Iva Stavrov
2015-01-01
We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature invariants decay at infinity, identifying a conformally invariant tensor which serves as an obstruction to "higher order decay" of the Riemann curvature operator. Finally, we establish Fredholm results for geometric elliptic operators, extending the work of Rafe Mazzeo and John M. Lee to this setting. As an application, we show that any weakly asymptotically hyperbolic metric is conformally related to a weakly asymptotically hyperbolic metric of constant negative curvature.
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...
Asymptotics of a horizontal liquid bridge
Haynes, M.; O'Brien, S. B. G.; Benilov, E. S.
2016-04-01
This paper uses asymptotic techniques to find the shape of a two dimensional liquid bridge suspended between two vertical walls. We model the equilibrium bridge shape using the Laplace-Young equation. We use the Bond number as a small parameter to deduce an asymptotic solution which is then compared with numerical solutions. The perturbation approach demonstrates that equilibrium is only possible if the contact angle lies within a hysteresis interval and the analysis relates the width of this interval to the Bond number. This result is verified by comparison with a global force balance. In addition, we examine the quasi-static evolution of such a two dimensional bridge.
Asymptotic analysis of the Nörlund and Stirling polynomials
Directory of Open Access Journals (Sweden)
Mark Daniel Ward
2012-04-01
Full Text Available We provide a full asymptotic analysis of the N{\\"o}rlund polynomials and Stirling polynomials. We give a general asymptotic expansion---to any desired degree of accuracy---when the parameter is not an integer. We use singularity analysis, Hankel contours, and transfer theory. This investigation was motivated by a need for such a complete asymptotic description, with parameter 1/2, during this author's recent solution of Wilf's 3rd (previously Unsolved Problem.
Liapunov structure and asymptotic expressions of linear differential systems
Institute of Scientific and Technical Information of China (English)
高维新
1996-01-01
With a view to the researches on asymptotic properties for linear differential systems,the characteristic number is transformed into functional dass which can indicate the change trend of the norm for solution,so the invariant structure is given under Liapunov changes and feasible computational method of asymptotic expressions for linear differential systems with variant coefficients,and various asymptotic conclusions induding the necessary and sufllcient conditions of stability are got.
Pratiwi, B. N.; Suparmi, A.; Cari, C.; Husein, A. S.; Yunianto, M.
2016-08-01
We apllied asymptotic iteration method (AIM) to obtain the analytical solution of the Dirac equation in case exact pseudospin symmetry in the presence of modified Pcischl- Teller potential and trigonometric Scarf II non-central potential. The Dirac equation was solved by variables separation into one dimensional Dirac equation, the radial part and angular part equation. The radial and angular part equation can be reduced into hypergeometric type equation by variable substitution and wavefunction substitution and then transform it into AIM type equation to obtain relativistic energy eigenvalue and wavefunctions. Relativistic energy was calculated numerically by Matlab software. And then relativistic energy spectrum and wavefunctions were visualized by Matlab software. The results show that the increase in the radial quantum number nr causes decrease in the relativistic energy spectrum. The negative value of energy is taken due to the pseudospin symmetry limit. Several quantum wavefunctions were presented in terms of the hypergeometric functions.
Asymptotic behaviour for a diffusion equation governed by nonlocal interactions
Ovono, Armel Andami
2010-01-01
In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the parabolic problem $L^\\infty $ estimates of solution based on using the Moser iterations and existence of global attractor. We finish our study by the issue of asymptotic behaviour in some cases when $t\\to \\infty$.
Asymptotic symmetry algebra of conformal gravity
Irakleidou, M
2016-01-01
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 non-trivial boundary conditions is five dimensional and it leads to global geon solution with non-vanishing charges.
脉冲-扩散周期竞争系统解的渐近行为%Asymptotic Behavior of Solutions of Periodic Impulse-Diffusion Competition System
Institute of Scientific and Technical Information of China (English)
窦家维; 李开泰
2003-01-01
研究了在周期变化环境中具有扩散及种群密度可能发生突变的两竞争种群动力系统的数学模型.模型由反应扩散方程组以及初边值及脉冲条件组成.文章建立了研究模型的上下解方法,获得了一些比较原理.利用脉冲常微分方程的比较定理以及利用相应的脉冲常微分方程的解控制和估计所讨论模型的解,研究了系统模型的解的渐近性质.%The mathematical model of two competing species dynamical system in a periodically changing environment with diffusion and instantaneous changes in the population densities is investigated. The model is described by a coupled system of reaction-diffusion equations together with some initial boundary value and impulses conditions. The upper-lower Solution method is established and some comparison principles are obtained. The asymptotic prope. rties of the system are researched by using the comparison theorem of impulsive ordinary differential equations and using the solutions of dominating inpulsive ordinary differential equation to control and estimate the solutions of the system.
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
Asymptotically anti-de Sitter Proca Stars
Duarte, Miguel
2016-01-01
We show that complex, massive spin-1 fields minimally coupled to Einstein's gravity with a negative cosmological constant, admit asymptotically anti-de Sitter self-gravitating solutions. Focusing on 4-dimensional spacetimes, we start by obtaining analytical solutions in the test-field limit, where the Proca field equations can be solved in a fixed anti-de Sitter background, and then find fully non-linear solutions numerically. These solutions are a natural extension of the recently found asymptotically flat Proca stars and share similar properties with scalar boson stars. In particular, we show that they are stable against spherically symmetric linear perturbations for a range of fundamental frequencies limited by their point of maximum mass. We finish with an overview of the behavior of Proca stars in $5$ dimensions.
Santucci, F.; Santini, P. M.
2016-10-01
We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.
Asymptotic analysis of outwardly propagating spherical flames
Institute of Scientific and Technical Information of China (English)
Yun-Chao Wu; Zheng Chen
2012-01-01
Asymptotic analysis is conducted for outwardly propagating spherical flames with large activation energy.The spherical flame structure consists of the preheat zone,reaction zone,and equilibrium zone.Analytical solutions are separately obtained in these three zones and then asymptotically matched.In the asymptotic analysis,we derive a correlation describing the spherical flame temperature and propagation speed changing with the flame radius.This correlation is compared with previous results derived in the limit of infinite value of activation energy.Based on this correlation,the properties of spherical flame propagation are investigated and the effects of Lewis number on spherical flame propagation speed and extinction stretch rate are assessed.Moreover,the accuracy and performance of different models used in the spherical flame method are examined.It is found that in order to get accurate laminar flame speed and Markstein length,non-linear models should be used.
Institute of Scientific and Technical Information of China (English)
刘凯丽; 窦家维
2012-01-01
研究了一类具有脉冲的周期L-V系统,利用脉冲微分方程的比较原理、Floquet理论及分析技巧,分析了系统周期解的存在性及系统解的全局渐近性质.并将所得到的一般结果应用于一类捕食-被捕食系统,获得了该系统正周期解的存在唯一及全局吸引的条件,进一步讨论了系统中种群灭绝的有关性质,给出一个实例进行数值模拟,阐明了所获得的理论结果.%In this paper, a class of periodic L-V impulsive system is studied. The comparison principle of impulsive differential equation, Roquet theory and some analysis techniques are used to analyse the existence of the system periodic solution and global asymptotic properties of the system. Furthermore, the general results obtained are applied to a predator-prey system, so as to obtain the existence and uniqueness of positive periodic solution to the system. Some relevant nature of extinction of population species is further discussed. Also, this paper presents a practical example to carry out the numerical simulation and to illustrate the obtained theoretical results.
Asymptotical Properties for Parabolic Systems of Neutral Type
Institute of Scientific and Technical Information of China (English)
CUI Bao-tong; HAN Mao-an
2005-01-01
Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis. The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.
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.......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...
Litim, Daniel F
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.
Asymptotic expansions in nonlinear rotordynamics
Day, William B.
1987-01-01
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
Institute of Scientific and Technical Information of China (English)
屈哲; 陶可勤
2015-01-01
欧拉-泊松方程的椭圆函数周期解渐近性收敛模型是实现浮点数据模糊加密核心基础，广泛应用在通信编码和数据加密等领域。对浮点数据的模糊加密能有效保证网络中实时数据交互通信的安全，通过对浮点数据模糊加密稀疏集准确构造建模，提高加密性能。提出采用欧拉-泊松方程的椭圆函数周期解渐近性收敛数学建模的方法实现对浮点数据进行模糊加密，利用压缩映射原理来完成特征解分区处理，给出在控制单元的作用下对浮点数据进行密钥重整，求得欧拉-泊松方程椭圆函数在不定搜索下的三孤波解。通过数学推导证明了欧拉-泊松方程椭圆函数的周期解式渐进收敛性，实现对大数据库的数据加密，实验得出该加密数学模型的收敛性能较好，性能优越。%The elliptic function periodic solutions of the Euler Poisson equations asymptotic convergence of the model is the realization of floating-point data encryption based fuzzy core, widely used in the communication code and data encryption and other fields. The fuzzy of floating-point data encryption can effectively guarantee the real-time data communication net⁃work security, based on fuzzy set accurate floating-point data encryption sparse structure modeling, improve the encryption performance. Proposed elliptic function periodic using Euler Poisson equation method for the solution of asymptotic conver⁃gence of mathematical modeling to achieve floating-point fuzzy data encryption, by using the contraction mapping principle to complete the characteristic solution separately are given in the control unit under the action of the floating point data are key reforming, obtained the Euler Poisson equations of elliptic function in indefinite search the three solitary wave solu⁃tions. Through mathematical derivation of gradual convergence of the cycle solution of Euler Poisson equations of elliptic function is
Asymptotic admissibility of priors and elliptic differential equations
Hartigan, J A
2010-01-01
We evaluate priors by the second order asymptotic behavior of the corresponding estimators.Under certain regularity conditions, the risk differences between efficient estimators of parameters taking values in a domain D, an open connected subset of R^d, are asymptotically expressed as elliptic differential forms depending on the asymptotic covariance matrix V. Each efficient estimator has the same asymptotic risk as a 'local Bayes' estimate corresponding to a prior density p. The asymptotic decision theory of the estimators identifies the smooth prior densities as admissible or inadmissible, according to the existence of solutions to certain elliptic differential equations. The prior p is admissible if the quantity pV is sufficiently small near the boundary of D. We exhibit the unique admissible invariant prior for V=I,D=R^d-{0). A detailed example is given for a normal mixture model.
Ho, Pei-Ming
2016-01-01
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.
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.
Asymptotic Behaviour Near a Nonlinear Sink
Calder, Matt S
2010-01-01
In this paper, we will explore an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Moreover, we will address the writing of one component in terms of the other in the case of a planar system. Examples will be given, notably the Michaelis-Menten mechanism of enzyme kinetics.
Asymptotic Symmetries from finite boxes
Andrade, Tomas
2015-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincar\\'e asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Research on temperature profiles of honeycomb regenerator with asymptotic analysis
Institute of Scientific and Technical Information of China (English)
AI Yuan-fang; MEI Chi; HUANG Guo-dong; JIANG Shao-jian; CHEN Hong-rong
2006-01-01
An asymptotic semi-analytical method for heat transfer in counter-flow honeycomb regenerator is proposed. By introducing a combined heat-transfer coefficient between the gas and solid phase, a heat transfer model is built based on the thin-walled assumption. The dimensionless thermal equation is deduced by considering solid heat conduction along the passage length. The asymptotic analysis is used for the small parameter of heat conduction term in equation. The first order asymptotic solution to temperature distribution under weak solid heat conduction is achieved after Laplace transformation through the multiple scales method and the symbolic manipulation function in MATLAB. Semi-analytical solutions agree with tests and finite-difference numerical results. It is proved possible for the asymptotic analysis to improve the effectiveness, economics and precision of thermal research on regenerator.
Asymptotically Safe Grand Unification
Bajc, Borut
2016-01-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
Asymptotically safe grand unification
Bajc, Borut; Sannino, Francesco
2016-12-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
High frequency asymptotics of antenna/structure interactions
Coats, J.
2002-01-01
This thesis is motivated by the need to calculate the electromagnetic fields produced by sources radiating in the presence of conductors. We begin by reviewing existing theory concerning sources in the presence of flat structures. Various extensions to the canonical Sommerfeld problem are considered. In particular we investigate the asymptotic solution for a finite source that focusses its energy at a point. In chapter 5 we review and extend the asymptotic results concerning illuminat...
An asymptotically exact theory of smart sandwich shells
Le, Khanh Chau
2016-01-01
An asymptotically exact two-dimensional theory of elastic-piezoceramic sandwich 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 circular elastic plate partially covered by two piezoceramic patches with thickness polarization excited by a harmonic voltage is found.
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.
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.
Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations
Directory of Open Access Journals (Sweden)
Zhinan Xia
2014-01-01
Full Text Available We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.
Global asymptotic stability of positive equilibrium in a 3-species cooperating model with time delay
Institute of Scientific and Technical Information of China (English)
WANG Chang-you
2007-01-01
The asymptotic behavior of the time-dependent solution for a 3-species cooperating model was investigated with the effects of both diffusion and time delay taken into consideration. We proved the global asymptotic stability of a positive steady-state solution to the model problem by using coupled upper and lower solutions for a more general reaction-diffusion system that gives a common framework for 3-species cooperating model problems. The result of global asymptotic stability implies that the model system coexistence is permanent. Some global asymptotic stability results for 2-species cooperating reaction-diffusion systems are included in the discussion, and some known results are extended.
Quantum fields from global propagators on asymptotically Minkowski and extended de Sitter spacetimes
Vasy, András
2015-01-01
We consider the wave equation on asymptotically Minkowski spacetimes and the Klein-Gordon equation on even asymptotically de Sitter spaces. In both cases we show that the extreme difference of propagators (i.e. retarded propagator minus advanced, or Feynman minus anti-Feynman), defined as Fredholm inverses, induces a symplectic form on the space of solutions with wave front set confined to the radial sets. Furthermore, we construct isomorphisms between the solution spaces and symplectic spaces of asymptotic data. As an application of this result we obtain distinguished Hadamard two-point functions from asymptotic data. Ultimately, we prove that the corresponding Quantum Field Theory on asymptotically de Sitter spacetimes induces canonically a QFT beyond the future and past conformal horizon, i.e. on two even asymptotically hyperbolic spaces. Specifically, we show this to be true both at the level of symplectic spaces of solutions and at the level of Hadamard two-point functions.
Oscillatory and Asymptotic Behavior of a Second-Order Nonlinear Functional Differential Equations
Institute of Scientific and Technical Information of China (English)
张全信; 高丽; 王少英
2012-01-01
This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of second order nonlinear functional differential equations. By using the generalized Riccati transformation and the integral averaging technique, new oscillation criteria and asymptotic behavior are obtained for all solutions of the equation. Our results generalize and improve some known theorems.
Institute of Scientific and Technical Information of China (English)
冯月才
2004-01-01
The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.
Asymptotic Behavior of the Finite Difference and the Finite Element Methods for Parabolic Equations
Institute of Scientific and Technical Information of China (English)
LIU Yang; FENG Hui
2005-01-01
The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continuous time.
Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
Nanopoulos, Dimitri
2010-01-01
In this paper, we study irregular singular solution to Hitchin's equation and use it to describe four dimensional $N=2$ asymptotically free gauge theories. For $SU(2)$ $A$ type quiver, two kinds of irregular singularities besides one regular singularity are needed for the solution of Hitchin's equation; We then classify irregular singularities needed for the general $SU(N)$ $A$ type quiver.
Asymptotic problems for stochastic partial differential equations
Salins, Michael
Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.
Asymptotics of a singularly perturbed GUE partition function
Mezzadri, F
2010-01-01
We study the double scaling asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble with weight exp(-z^2/2x^2 + t/x - x^2/2). We derive the asymptotics of the partition function when z and t are of O(N^(-1/2)). Our results are obtained using the Deift-Zhou steepest descent method and are expressed in terms of a solution of a fourth order nonlinear differential equation. We also compute the asymptotic limit of such a solution when zN^(1/2) -> 0. The behavior of this solution, together with fact that the partition function is an odd function in the variable t, allows us to reduce such a fourth order differential equation into a second order nonlinear ODE.
Asymptotically flat space-times: an enigma
Newman, Ezra T.
2016-07-01
We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory—absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) asymptotically flat space-times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of Newman-Unti (NU) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-space that has no immediate relationship with space-time. In fact these relations appear in two such spaces, H-space and its dual space \\bar{H}.
A Note on Asymptotic Contractions
Directory of Open Access Journals (Sweden)
Marina Arav
2006-12-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space X to converge to its unique fixed point, uniformly on each bounded subset of X.
A Note on Asymptotic Contractions
Directory of Open Access Journals (Sweden)
Castillo Santos Francisco Eduardo
2007-01-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space to converge to its unique fixed point, uniformly on each bounded subset of .
Asymptotic Dynamics of Monopole Walls
Cross, R
2015-01-01
We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs curve using the Newton polytope and amoeba. In particular, we show that the monopole wall splits into subwalls when any of its moduli become large. The long-distance gauge and Higgs field interactions of these subwalls are abelian, allowing us to derive an asymptotic metric for the monopole wall moduli space.
Homogenization and asymptotics for small transaction costs
Soner, H Mete
2012-01-01
We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic control problem which can be solved in closed form in the one-dimensional case. Unlike the existing literature, we consider a general utility function and general dynamics for the underlying assets. Our arguments are based on ideas from the homogenization theory and use the convergence tools from the theory of viscosity solutions. The multidimensional case is studied in our accompanying paper using the same approach.
BIHARMONIC EQUATIONS WITH ASYMPTOTICALLY LINEAR NONLINEARITIES
Institute of Scientific and Technical Information of China (English)
Liu Yue; Wang Zhengping
2007-01-01
This article considers the equation △2u = f(x, u)with boundary conditions either u|(a)Ω = (a)u/(a)n|(a)Ω = 0 or u|(a)Ω = △u|(a)Ω = 0, where f(x,t) is asymptotically linear with respect to t at infinity, and Ω is a smooth bounded domain in RN, N ＞ 4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x, t).
Singular asymptotic expansions in nonlinear rotordynamics
Day, W. B.
1985-01-01
During hot firing ground testing of the Space shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.
Vacuum polarization in asymptotically Lifshitz black holes
Quinta, Gonçalo M.; Flachi, Antonino; Lemos, José P. S.
2016-06-01
There has been considerable interest in applying the gauge-gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed, focused on incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes and, to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, nonminimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti-de Sitter black holes. The basics are similar to previous calculations; however, in the Lifshitz case, one needs to extend the previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulas are shown to reduce to the anti-de Sitter (AdS) case studied before once the value of the dynamical exponent is set to unity and the metric functions are accordingly chosen. The analytical results we present are general and can be applied to a variety of cases, in fact, to all spherically symmetric Lifshitz black hole solutions. We also implement the numerical analysis choosing some known Lifshitz black hole solutions as illustration.
Polynomial Asymptotes of the Second Kind
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
On the asymptotic expansion of complete Ricci-flat Kahler metrics on quasi-projective manifolds
Santoro, Bianca
2012-01-01
In this work, we describe the asymptotic behavior of complete metrics with prescribed Ricci curvature on open Kahler manifolds that can be compactified by the addition of a smooth and ample divisor. First, we construct a explicit sequence of Kahler metrics with special approximating properties. Using those metrics as starting point, we are able to work out the asymptotic behavior of the solutions given in the work of Tian-Yau, in particular obtaining their full asymptotic expansion.
Asymptotic properties of the inhomogeneous Lotka-Von Foerster system.
Inaba, H
1988-01-01
"In this paper, we investigate an extension of the multistate stable population model, which makes allowances for migration. The model is formulated as an inhomogeneous system of first order partial differential equations with integral boundary conditions. First, we construct its classical solution. Next, we reformulate the system as an abstract inhomogeneous Cauchy problem on a Banach space, and give its mild solution by using the population semigroup. Our main purpose is to investigate the asymptotic behavior of the mild solution." (SUMMARY IN FRE)
Institute of Scientific and Technical Information of China (English)
程燕; 周津; 邱国新
2012-01-01
The singularly perturbed boundary initial boundary value problems of nonlinear hyperbolic differential equations with time delays are considered. The uniform validity of the constructed asymptotic expansion is given and proved.%研究了有时滞的双曲型微分方程的初边值问题的奇摄动,给出并证明了形式渐近解的一致有效性.
Nonabelian Higgs models: paving the way for asymptotic freedom
Gies, Holger
2016-01-01
Asymptotically free renormalization group trajectories can be constructed in nonabelian 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 RG relevance classification of perturbations about scaling solutions. We obtain global information about the quasi-fixed 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.
A new class of asymptotically non-chaotic vacuum singularities
Energy Technology Data Exchange (ETDEWEB)
Klinger, Paul, E-mail: paul.klinger@univie.ac.at
2015-12-15
The BKL conjecture, stated in the 1960s and early 1970s by Belinski, Khalatnikov and Lifschitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated chaotic behaviour in the generic case, but simpler non-chaotic one in cases with symmetry assumptions or certain kinds of matter fields. Here we construct a new class of four-dimensional vacuum spacetimes containing spacelike singularities which show non-chaotic behaviour. In contrast with previous constructions, no symmetry assumptions are made. Rather, the metric is decomposed in Iwasawa variables and conditions on the asymptotic evolution of some of them are imposed. The constructed solutions contain five free functions of all space coordinates, two of which are constrained by inequalities. We investigate continuous and discrete isometries and compare the solutions to previous constructions. Finally, we give the asymptotic behaviour of the metric components and curvature.
Scalar hairy black holes and solitons in asymptotically flat spacetimes
Nucamendi, U; Nucamendi, Ulises; Salgado, Marcelo
2003-01-01
A numerical analysis shows that a class of scalar-tensor theories of gravity with a scalar field minimally and nonminimally coupled to the curvature allows static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. In the limit when the horizon radius of the black hole tends to zero, regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential $V(\\phi)$ of the theory is ``finetuned'' such that its local minimum is also a zero of the potential, the scalar field settling asymptotically at that minimum. The configurations, although unstable under spherically symmetric linear perturbations, are regular and thus can serve as counterexamples to the no-scalar-hair conjecture.
Holography of 3D Asymptotically Flat Black Holes
Fareghbal, Reza
2014-01-01
We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking flat-space limit (zero cosmological constant limit) of New Massive Gravity (NMG). We propose that the dual field theory of the flat-space limit of NMG can be described by a Contracted Conformal Field Theory (CCFT). Using Flat/CCFT correspondence we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. Furthermore, by taking appropriate limit of the Cardy formula in the parent CFT, we find a Cardy-like formula which reproduces the Wald's entropy of the 3D asymptotically flat black hole.
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...
Holography of 3D asymptotically flat black holes
Fareghbal, Reza; Hosseini, Seyed Morteza
2015-04-01
We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking the flat-space limit (zero cosmological constant limit) of new massive gravity. We propose that the dual field theory of the flat-space limit of new massive gravity can be described by a contracted conformal field theory which is invariant under the action of the BMS3 group. Using the flat/contracted conformal field theory correspondence, we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. We check that our expressions of the mass and angular momentum fit with the first law of black hole thermodynamics. Furthermore, by taking the appropriate limit of the Cardy formula in the parent conformal field theory, we find a Cardy-like formula which reproduces the Wald's entropy of the 3D asymptotically flat black hole.
Asymptotics of trimmed CUSUM statistics
Berkes, István; Schauer, Johannes; 10.3150/10-BEJ318
2012-01-01
There is a wide literature on change point tests, but the case of variables with infinite variances is essentially unexplored. In this paper we address this problem by studying the asymptotic behavior of trimmed CUSUM statistics. We show that in a location model with i.i.d. errors in the domain of attraction of a stable law of parameter $0<\\alpha <2$, the appropriately trimmed CUSUM process converges weakly to a Brownian bridge. Thus, after moderate trimming, the classical method for detecting change points remains valid also for populations with infinite variance. We note that according to the classical theory, the partial sums of trimmed variables are generally not asymptotically normal and using random centering in the test statistics is crucial in the infinite variance case. We also show that the partial sums of truncated and trimmed random variables have different asymptotic behavior. Finally, we discuss resampling procedures which enable one to determine critical values in the case of small and mo...
Asymptotic behaviour of electro-$\\Lambda$ spacetimes
Saw, Vee-Liem
2016-01-01
We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $\\Lambda$ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with $\\Lambda=0$. Using these asymptotic solutions, we discuss the mass-loss of an isolated electro-gravitating system with cosmological constant. In a universe with $\\Lambda>0$, the physics of electromagnetic (EM) radiation is relatively straightforward compared to those of gravitational radiation: 1) It is clear that outgoing EM radiation results in a decrease to the Bondi mass of the isolated system. 2) It is also perspicuous that if any incoming EM radiation from elsewhere is present, those beyond the isolated system's cosmological horizon would eventually arrive at the spacelike $\\mathcal{I}$ and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with the Bondi mass-loss formula in any un...
Superradiant instabilities of asymptotically anti-de Sitter black holes
Green, Stephen R.; Hollands, Stefan; Ishibashi, Akihiro; Wald, Robert M.
2016-06-01
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension d≥slant 4. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, { E }. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ergoregions, initial data can be constructed such that { E }\\lt 0, so all such black holes are unstable. To obtain such initial data, we first construct an approximate solution to the constraint equations using the WKB method, and then we use the Corvino-Schoen technique to obtain an exact solution. We also discuss the case of charged asymptotically anti-de Sitter black holes with generalized ergoregions.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Higher dimensional nonclassical eigenvalue asymptotics
Camus, Brice; Rautenberg, Nils
2015-02-01
In this article, we extend Simon's construction and results [B. Simon, J. Funct. Anal. 53(1), 84-98 (1983)] for leading order eigenvalue asymptotics to n-dimensional Schrödinger operators with non-confining potentials given by Hn α = - Δ + ∏ i = 1 n |x i| α i on ℝn (n > 2), α ≔ ( α 1 , … , α n ) ∈ ( R+ ∗ ) n . We apply the results to also derive the leading order spectral asymptotics in the case of the Dirichlet Laplacian -ΔD on domains Ωn α = { x ∈ R n : ∏ j = 1 n }x j| /α j α n < 1 } .
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...... by an underlying Harris recurrent Markov process some asymptotic results for the ruin probability are derived. Finally, a paper, which is separate in content from the rest of the thesis, treats a RESTART problem in the situation, where failures occur with decreasing intensity....
Asymptotic Rayleigh instantaneous unit hydrograph
Troutman, B.M.; Karlinger, M.R.
1988-01-01
The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude, N, tends asymptotically, as N grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, {Mathematical expression}, where ?? is a mean link wave travel time. ?? 1988 Springer-Verlag.
Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients
Directory of Open Access Journals (Sweden)
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.
New explicit global asymptotic stability criteria for higher order difference equations
El-Morshedy, Hassan A.
2007-12-01
New explicit sufficient conditions for the asymptotic stability of the zero solution of higher order difference equations are obtained. These criteria can be applied to autonomous and nonautonomous equations. The celebrated Clark asymptotic stability criterion is improved. Also, applications to models from mathematical biology and macroeconomics are given.
Asymptotic Dichotomy in a Class of Odd-Order Nonlinear Differential Equations with Impulses
Directory of Open Access Journals (Sweden)
Kunwen Wen
2013-01-01
Full Text Available We investigate the oscillatory and asymptotic behavior of a class of odd-order nonlinear differential equations with impulses. We obtain criteria that ensure every solution is either oscillatory or (nonoscillatory and zero convergent. We provide several examples to show that impulses play an important role in the asymptotic behaviors of these equations.
Asymptotic Speed of Wave Propagation for A Discrete Reaction-Diffusion Equation
Institute of Scientific and Technical Information of China (English)
Xiu-xiang Liu; Pei-xuan Weng
2006-01-01
We deal with asymptotic speed of wave propagation for a discrete reaction-diffusion equation. We find the minimal wave speed c* from the characteristic equation and show that c* is just the asymptotic speed of wave propagation. The isotropic property and the existence of solution of the initial value problem for the given equation are also discussed.
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
DISSIPATION AND DISPERSION APPROXIMATION TO HYDRODYNAMICAL EQUATIONS AND ASYMPTOTIC LIMIT
Institute of Scientific and Technical Information of China (English)
Hsiao Ling; Li Hailiang
2008-01-01
The compressible Euler equations with dissipation and/or dispersion correction are widely used in the area of applied sciences, for instance, plasma physics,charge transport in semiconductor devices, astrophysics, geophysics, etc. We consider the compressible Euler equation with density-dependent (degenerate) viscosities and capillarity, and investigate the global existence of weak solutions and asymptotic limit.
Asymptotic analysis of the Carrier-Pearson problem
Directory of Open Access Journals (Sweden)
Chunqing Lu
2003-02-01
Full Text Available This paper provides a rigorous analysis of the asymptotic behavior of the solution for the boundary-value problem begin{gather*} epsilon ^2u''+u^2-1 =0,quad -1
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
Institute of Scientific and Technical Information of China (English)
XUE Hongqi; SONG Lixin
2002-01-01
A grouped data model for Weibull distribution is considered. Under mild con-ditions, the maximum likelihood estimators(MLE) are shown to be identifiable, strongly consistent, asymptotically normal, and satisfy the law of iterated logarithm. Newton iter- ation algorithm is also considered, which converges to the unique solution of the likelihood equation. Moreover, we extend these results to a random case.
ASYMPTOTIC BEHAVIOR OF DELAY DISCRETETIME NEURAL NETWORKS WITH CRITICAL THRESHOLD
Institute of Scientific and Technical Information of China (English)
ZhangHongqiang; LiuKaiyu
2005-01-01
This paper is concerned with a delay discrete-time system arising as a discrete-time network of two neurons with McCulloch-Pitts nonlinearity. We obtain the asymptotic behaviors of the solutions of the system for some cases.The results obtained improve and extend the corresponding results established recently by Zhou, Yu and Huang [1].
Asymptotic Linear Stability of Solitary Water Waves
Pego, Robert L.; Sun, Shu-Ming
2016-12-01
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (that is, symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.
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...
Multichannel Scattering Problem with Non-trivial Asymptotic Non-adiabatic Coupling
Yakovlev, S L; Elander, N; Belyaev, A K
2016-01-01
The multichannel scattering problem in an adiabatic representation is considered. The non-adiabatic coupling matrix is assumed to have a non-trivial constant asymptotic behavior at large internuclear separations. The asymptotic solutions at large internuclear distances are constructed. It is shown that these solutions up to the first order of perturbation theory are identical to the asymptotic solutions of the re-projection approach, which was proposed earlier as a remedy for the electron translation problem in the context of the Born-Oppenheimer treatment.
Inaccurate usage of asymptotic formulas
Maj, R; Maj, Radoslaw; Mrowczynski, Stanislaw
2004-01-01
The asymptotic form of the plane-wave decomposition into spherical waves, which is often used, in particular, to express the scattering amplitude through the phase shifts, is incorrect. We precisely explain why it is incorrect and show how to circumvent mathematical inconsistency.
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...
Asymptotic heat transfer model in thin liquid films
Chhay, Marx; Gisclon, Marguerite; Ruyer-Quil, Christian
2015-01-01
In this article, we present a modelling of heat transfer occuring through a liquid film flowing down a vertical wall. This model is formally derived thanks to asymptotic developpment, by considering the physical ratio of typical length scales of the study. A new Nusselt thermal solution is proposed, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms in the asymptotic model are numerically pointed out. The comparisons are provided against the resolution of the full Fourier equations in a steady state frame.
The Asymptotic Limit for the 3D Boussinesq System
Institute of Scientific and Technical Information of China (English)
LI Lin-rui; WANG Ke; HONG Ming-li
2016-01-01
In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coeﬃcient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosityν=0 or zero diffusivityη=0) in 2D case separately.
Counting spanning trees on fractal graphs and their asymptotic complexity
Anema, Jason A.; Tsougkas, Konstantinos
2016-09-01
Using the method of spectral decimation and a modified version of Kirchhoff's matrix-tree theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely ramified fractal is given in theorem 3.4. We show how spectral decimation implies the existence of the asymptotic complexity constant and obtain some bounds for it. Examples calculated include the Sierpiński gasket, a non-post critically finite analog of the Sierpiński gasket, the Diamond fractal, and the hexagasket. For each example, the asymptotic complexity constant is found.
On a new approach to asymptotic stabilization problems
Ivanchikov, A. A.; Kornev, A. A.; Ozeritskii, A. V.
2009-12-01
A numerical algorithm for solving the asymptotic stabilization problem by the initial data to a fixed hyperbolic point with a given rate is proposed and justified. The stabilization problem is reduced to projecting the resolving operator of the given evolution process on a strongly stable manifold. This approach makes it possible to apply the results to a wide class of semidynamical systems including those corresponding to partial differential equations. By way of example, a numerical solution of the problem of the asymptotic stabilization of unstable trajectories of the two-dimensional Chafee-Infante equation in a circular domain by the boundary conditions is given.
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...
On transfinite extension of asymptotic dimension
Radul, Taras
2006-01-01
We prove that a transfinite extension of asymptotic dimension asind is trivial. We introduce a transfinite extension of asymptotic dimension asdim and give an example of metric proper space which has transfinite infinite dimension.
Vacuum polarization in asymptotically Lifshitz black holes
Quinta, Gonçalo M; Lemos, José P S
2016-01-01
There has been considerable interest in applying the gauge/gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed aiming at incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes, and to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, non-minimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti de Sitter black holes. The basics are similar to previous calculations, however in the Lifshitz case one needs to extend previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulae are shown to reduce to the AdS case studied before once the value of the dynamical exponent is set to...
Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model
Directory of Open Access Journals (Sweden)
Shengmao Fu
2013-01-01
Full Text Available The global asymptotic behavior of a nonautonomous competitor-competitor-mutualist model is investigated, where all the coefficients are time-dependent and asymptotically approach periodic functions, respectively. Under certain conditions, it is shown that the limit periodic system of this asymptotically periodic model admits two positive periodic solutions (u1T,u2T,u3T, (u1T,u2T,u3T such that uiT≤uiT (i=1,2,3, and the sector {(u1,u2,u3:uiT≤ui≤uiT, i=1,2,3} is a global attractor of the asymptotically periodic model. In particular, we derive sufficient conditions that guarantee the existence of a positive periodic solution which is globally asymptotically stable.
ASYMPTOTIC THEORY OF INITIAL VALUE PROBLEMS FOR NONLINEAR PERTURBED KLEIN-GORDON EQUATIONS
Institute of Scientific and Technical Information of China (English)
GAN Zai-hui; ZHANG Jian
2005-01-01
The asymptotic theory of initial value problems for a class of nonlinear perturbed Klein-Gordon equations in two space dimensions is considered. Firstly, using the contraction mapping principle, combining some priori estimates and the convergence of Bessel function, the well-posedness of solutions of the initial value problem in twice continuous differentiable space was obtained according to the equivalent integral equation of initial value problem for the Klein-Gordon equations. Next, formal approximations of initial value problem was constructed by perturbation method and the asymptotic validity of the formal approximation is got. Finally, an application of the asymptotic theory was given, the asymptotic approximation degree of solutions for the initial value problem of a specific nonlinear Klein-Gordon equation was analyzed by using the asymptotic approximation theorem.
Directory of Open Access Journals (Sweden)
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.
Localized travelling waves in the asymptotic suction boundary layer
Kreilos, Tobias; Schneider, Tobias M
2016-01-01
We present two spanwise-localized travelling wave solutions in the asymptotic suction boundary layer, obtained by continuation of solutions of plane Couette flow. One of the solutions has the vortical structures located close to the wall, similar to spanwise-localized edge states previously found for this system. The vortical structures of the second solution are located in the free stream far above the laminar boundary layer and are supported by a secondary shear gradient that is created by a large-scale low-speed streak. The dynamically relevant eigenmodes of this solution are concentrated in the free stream, and the departure into turbulence from this solution evolves in the free stream towards the walls. For invariant solutions in free-stream turbulence, this solution thus shows that that the source of energy of the vortical structures can be a dynamical structure of the solution itself, instead of the laminar boundary layer.
Asymptotic safety goes on shell
Benedetti, Dario
2012-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.
Composite Operators in Asymptotic Safety
Pagani, Carlo
2016-01-01
We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dimensional quantum gravity. Finally, we briefly argue that our construction paves the way to approach observables in the Asymptotic Safety program.
Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras
Institute of Scientific and Technical Information of China (English)
LI Jin-xiu; WANG Qin
2006-01-01
We introduce in this note the notions of asymptotic excision of proper metric spaces and asymptotic equivalence relation for subspaces of metric spaces, which are relevant in characterizing spatial ideals of the asymptotic coarse Roe algebras. We show that the lattice of the asymptotic equivalence classes of the subspaces of a proper metric space is isomorphic to the lattice of the spatial ideals of the asymptotic Roe algebra. For asymptotic excisions of the metric space, we also establish a Mayer-Vietoris sequence in K-theory of the asymptotic coarse Roe algebras.
Exact and asymptotic results for insurance risk models with surplus-dependent premiums
Albrecher, Hansjörg; Palmowski, Zbigniew; Regensburger, Georg; Rosenkranz, Markus
2011-01-01
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differential equations with variable coefficients. The algebraic structure of the Green's operators allows us to develop an intuitive way of tackling the asymptotic behavior of the solutions, leading to exponential-type expansions and Cram\\'er-type asymptotics. Furthermore, we obtain closed-form solutions for more specific cases of premium functions in the compound Poisson risk model.
ON THE ASYMPTOTIC BEHAVIOUR OF THE STEADY SUPERSONIC FLOWS AT INFINITY
Institute of Scientific and Technical Information of China (English)
ZHANG YONGQIAN
2005-01-01
This paper studies the asymptotic behaviour of steady supersonic flow past a piecewise smooth corner or bend. Under the hypothese that both vertex angle and the total variation of tangent along the boundary are small, it is shown that the solution can be obtained by a modified Glimm scheme, and that the asymptotic behaviour of the solution is determined by the velocity of incoming flow and the limit of the tangent of the boundary at infinity.
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...
Holographic Renormalization of Asymptotically Flat Gravity
Park, Miok
2012-01-01
We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotic flat and static spacetime for cylindrical boundary surface as $r \\rightarrow \\infty$, and find that the form of the boundary stress tensor is the same as the hyperbolic boundary case in 4 dimensions, but has additional terms in higher than 4 dimensions. We find that these additional terms are impotent and do not contribute to conserved charges. We also check the conservation of the boundary stress tensor in a sense that $\\mathcal{D}^a T_{ab} = 0$, and apply our result to the ($n+3$)-dimensional static black hole solution. As a result, we show that the stress boundary tensor with Mann-Marolf counterterm works well in standard boundary surfaces.
Asymptotic analysis of ultra-relativistic charge
Burton, D A; Tucker, R W; Burton, David A.; Gratus, Jonathan; Tucker, Robin W.
2006-01-01
This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneo...
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety 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 of an asymptotically free (perhaps magnetic dual) extension.
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.
Asymptotics for the Korteweg-de Vries-Burgers Equation
Institute of Scientific and Technical Information of China (English)
Nakao HAYASHI; Pavel I. NAUMKIN
2006-01-01
We study large time asymptotics of solutions to the Korteweg-de Vries-Burgers equation ut + uux - uxx + uxxx = 0, x ∈ R, t ＞ 0.We are interested in the large time asymptotics for the case when the initial data have an arbitrary size. We prove that ifthe initial data u0 ∈ Hs (R) ∩L1 (R), where s ＞ -1/2,then there exists a uniquesolution u (t,x) ∈ C∞ ((0, ∞);H∞ (R)) to the Cauchy problem for the Korteweg-de Vries-Burgers equation, which has asymptotics u (t) = t-1/2fM((·)t-1/2) + o(t-1/2) as t →∞, where fM is the self-similar solution for the Burgers equation. Moreover if xu0 (x) ∈ L1 (R),then the asymptotics are true u (t) = t-1/2fM((·)t-1/2) + O(t-1/2-γ),where γ∈ (0,1/2).
Asymptotic Analysis of Fiber-Reinforced Composites of Hexagonal Structure
Kalamkarov, Alexander L.; Andrianov, Igor V.; Pacheco, Pedro M. C. L.; Savi, Marcelo A.; Starushenko, Galina A.
2016-08-01
The fiber-reinforced composite materials with periodic cylindrical inclusions of a circular cross-section arranged in a hexagonal array are analyzed. The governing analytical relations of the thermal conductivity problem for such composites are obtained using the asymptotic homogenization method. The lubrication theory is applied for the asymptotic solution of the unit cell problems in the cases of inclusions of large and close to limit diameters, and for inclusions with high conductivity. The lubrication method is further generalized to the cases of finite values of the physical properties of inclusions, as well as for the cases of medium-sized inclusions. The analytical formulas for the effective coefficient of thermal conductivity of the fiber-reinforced composite materials of a hexagonal structure are derived in the cases of small conductivity of inclusions, as well as in the cases of extremely low conductivity of inclusions. The three-phase composite model (TPhM) is applied for solving the unit cell problems in the cases of the inclusions with small diameters, and the asymptotic analysis of the obtained solutions is performed for inclusions of small sizes. The obtained results are analyzed and illustrated graphically, and the limits of their applicability are evaluated. They are compared with the known numerical and asymptotic data in some particular cases, and very good agreement is demonstrated.
Asymptotic integration of differential and difference equations
Bodine, Sigrun
2015-01-01
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...
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.
Asymptotic properties of ground states of scalar field equations with a vanishing parameter
Moroz, Vitaly
2012-01-01
We study the leading order behaviour of positive solutions of the equation -\\Delta u +\\varepsilon u-|u|^{p-2}u+|u|^{q-2}u=0,\\qquad x\\in\\R^N, where $N\\ge 3$, $q>p>2$ and when $\\varepsilon>0$ is a small parameter. We give a complete characterization of all possible asymptotic regimes as a function of $p$, $q$ and $N$. The behavior of solutions depends sensitively on whether $p$ is less, equal or bigger than the critical Sobolev exponent $p^\\ast=\\frac{2N}{N-2}$. For $pp^\\ast$ the solution asymptotically coincides with the solution of the equation with $\\varepsilon=0$. In the most delicate case $p=p^\\ast$ the asymptotic behaviour of the solutions is given by a particular solution of the critical Emden--Fowler equation, whose choice depends on $\\varepsilon$ in a nontrivial way.
Li, Yongfeng; Cui, Jingan; Song, Xinyu
2009-01-01
In this paper, the nonautonomous competing two-species Lotka-Volterra models with impulsive effect are considered, where all the parameters are time-dependent and asymptotically approach the corresponding periodic functions. Under some conditions, it is shown that the semi-trivial positive solutions of the models asymptotically approach the semi-trivial positive periodic solutions of the corresponding periodic system. It is also shown that the positive solution of the models asymptotically approach the positive periodic solution of the corresponding periodic system.
Asymptotics of robust utility maximization
Knispel, Thomas
2012-01-01
For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\\lambda\\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.
Asymptotics for Associated Random Variables
Oliveira, Paulo Eduardo
2012-01-01
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting
Asymptotics of Lagged Fibonacci Sequences
Mertens, Stephan
2009-01-01
Consider "lagged" Fibonacci sequences $a(n) = a(n-1)+a(\\lfloor n/k\\rfloor)$ for $k > 1$. We show that $\\lim_{n\\to\\infty} a(kn)/a(n)\\cdot\\ln n/n = k\\ln k$ and we demonstrate the slow numerical convergence to this limit and how to deal with this slow convergence. We also discuss the connection between two classical results of N.G. de Bruijn and K. Mahler on the asymptotics of $a(n)$.
On Asymptotic Freedom and Confinement from Type-IIB Supergravity
Kehagias, A A
1999-01-01
We present a new type-IIB supergravity vacuum that describes the strong coupling regime of a non-supersymmetric gauge theory. The latter has a running coupling such that the theory becomes asymptotically free in the ultraviolet. It also has a running theta angle due to a non-vanishing axion field in the supergravity solution. We also present a worm-hole solution, which has finite action per unit four-dimensional volume and two asymptotic regions, a flat space and an AdS^5\\times S^5. The corresponding N=2 gauge theory, instead of being finite, has a running coupling. We compute the quark-antiquark potential in this case and find that it exhibits, under certain assumptions, area-law behaviour for large separations.
On asymptotic freedom and confinement from type-IIB supergravity
Kehagias, A.; Sfetsos, K.
1999-06-01
We present a new type-IIB supergravity vacuum that describes the strong coupling regime of a non-supersymmetric gauge theory. The latter has a running coupling such that the theory becomes asymptotically free in the ultraviolet. It also has a running theta angle due to a non-vanishing axion field in the supergravity solution. We also present a worm-hole solution, which has finite action per unit four-dimensional volume and two asymptotic regions, a flat space and an AdS5xS5. The corresponding N=2 gauge theory, instead of being finite, has a running coupling. We compute the quark-antiquark potential in this case and find that it exhibits, under certain assumptions, an area-law behaviour for large separations.
Asymptotically flat black holes with scalar hair: a review
Herdeiro, Carlos A R
2015-01-01
We consider the status of black hole solutions with non-trivial scalar fields but no gauge fields, in four dimensional asymptotically flat space-times, reviewing both classical results and recent developments. We start by providing a simple illustration on the physical difference between black holes in electro-vacuum and scalar-vacuum. Next, we review no-scalar-hair theorems. In particular, we detail an influential theorem by Bekenstein and stress three key assumptions: 1) the type of scalar field equation; 2) the spacetime symmetry inheritance by the scalar field; 3) an energy condition. Then, we list regular (on and outside the horizon), asymptotically flat BH solutions with scalar hair, organizing them by the assumption which is violated in each case and distinguishing primary from secondary hair. We provide a table summary of the state of the art.
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
Institute of Scientific and Technical Information of China (English)
XUEHongqi; SONGLixin
2002-01-01
A grouped data model for weibull distribution is considered.Under mild conditions .the maximum likelihood estimators(MLE)are shown to be identifiable,strongly consistent,asymptotically normal,and satisfy the law of iterated logarithm .Newton iteration algorthm is also condsidered,which converges to the unique solution of the likelihood equation.Moreover,we extend these results to a random case.
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....
Asymptotic analysis for vanishing acceleration in a thermoviscoelastic system
Directory of Open Access Journals (Sweden)
Elena Bonetti
2005-01-01
Full Text Available We have investigated a dynamic thermoviscoelastic system (2003, establishing existence and uniqueness results for a related initial and boundary values problem. The aim of the present paper is to study the asymptotic behavior of the solution to the above problem as the power of the acceleration forces goes to zero. In particular, well-posedness and regularity results for the limit (quasistatic problem are recovered.
Asymptotic safety goes on shell
Benedetti, Dario
2011-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge-dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector, and a new cut-off scheme. We find a non-trivial fixed point, with a value of the cosmological constant which is independent of the gauge-fixing parameters.
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.
Prozorov, A. A.; Trifonov, A. Yu.; Shapovalov, A. V.
2015-07-01
Asymptotic solutions of the nonlocal, one-dimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Grünwald-Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.
Asymptotic properties of the C-Metric
Sladek, Pavel
2010-01-01
The aim of this article is to analyze the asymptotic properties of the C-metric, using a general method specified in work of Tafel and coworkers, [1], [2], [3]. By finding an appropriate conformal factor $\\Omega$, it allows the investigation of the asymptotic properties of a given asymptotically flat spacetime. The news function and Bondi mass aspect are computed, their general properties are analyzed, as well as the small mass, small acceleration, small and large Bondi time limits.
Supersymmetric asymptotic safety is not guaranteed
DEFF Research Database (Denmark)
Intriligator, Kenneth; Sannino, Francesco
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety...... 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...
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.
Institute of Scientific and Technical Information of China (English)
Wang Kaiyong; Wang Yuebao; Yin Chuancun
2011-01-01
This article gives the equivalent conditions of the local asymptotics for the overshoot of a random walk with heavy-tailed increments, from which we find that the above asymptotics are different from the local asymptoties for the supremum of the random walk. To do this, the article first extends and improves some existing results about the solutions of renewal equations.
Institute of Scientific and Technical Information of China (English)
张正球; 王志成
2001-01-01
In this paper neutral delay differential equations of the form [x(t) + λc(t)x(t - σ]＇ + p(t)x(t - τ) - Q(t)x(t - σ) = 0 (1)are considered. Some sufficient conditions by which every solution of (1) tends to zero as t →∞ are established.
Asymptotic conditions of motion for radiating charged particles
Anderson, James L.
1997-10-01
Approximate asymptotic conditions on the motion of compact, electrically charged particles are derived within the framework of general relativity using the Einstein-Infeld-Hoffmann (EIH) surface integral method. While superficially similar to the Abraham-Lorentz and Lorentz-Dirac equations, these conditions differ from them in several fundamental ways. They are not equations of motion in the usual sense but rather a set of conditions which these motions must obey asymptotically in the future of an initial starting time. And furthermore, they do not admit the runaway solutions of these other equations. As in the original EIH work, they are integrability conditions gotten from integrating the empty-space (i.e., sourceless) Einstein-Maxwell equations of general relativity over closed two-surfaces surrounding the sources of the fields appearing in these equations. No additional ad hoc assumptions, such as the form of a force law or the introduction of inertial reaction terms, are required for this purpose, nor is there a need for any infinite mass renormalizations such as are required in other derivations since all integrals are over surfaces and thus finite. In addition to being asymptotic, the conditions of motion derived here are also approximate and apply, as do the original EIH equations, only to slowly moving systems. A ``slowness'' parameter ɛ is identified as the ratio of the light travel time across the system divided by a characteristic time, e.g., a period. Use is made of both the method of matched asymptotic expansions and the method of multiple time scales to obtain an asymptotic expansion in ɛ and the expansion is carried to sufficiently high order ɛ7 to obtain the lowest-order radiation reaction terms. The resulting conditions of motion are shown to not allow runaway motions.
Asymptotic analysis of laminated plates and shallow shells
Skoptsov, K. A.; Sheshenin, S. V.
2011-02-01
It was noted long ago [1] that the material strength theory develops both by improving computational methods and by widening the physical foundations. In the present paper, we develop a computational technique based on asymptotic methods, first of all, on the homogenization method [2, 3]. A modification of the homogenization method for plates periodic in the horizontal projection was proposed in [4], where the bending of a homogeneous plate with periodically repeating inhomogeneities on its surface was studied. A more detailed asymptotic analysis of elastic plates periodic in the horizontal projection can be found, e.g., in [5, 6]. In [6], three asymptotic approximations were considered, local problems on the periodicity cell were obtained for them, and the solvability of these problems was proved. In [7], it was shown that the techniques developed for plates periodic in the horizontal projection can also be used for laminated plates. In [7], this was illustrated by an example of asymptotic analysis of an isotropic plate symmetric with respect to the midplane. In what follows, these methods are generalized to the case of combined bending and extension of a longitudinal laminated plate up to the third approximation, which permits finding all components of the stress tensor. The study of the plate behavior is based on the method of homogenization of the three-dimensional problem of linear elasticity and does not use any hypotheses. It turns out that the Kirchhoff-Love hypothesis for the entire packet of layers is simply a consequence of the method in the zeroth approximation, and the bending stresses corresponding to the classical theory of laminated plates [8] are obtained in the first approximation. The successive approximations describe the behavior of the normal and the stress more precisely. In the present paper, the results obtained in [7] are refined, and the asymptotic solution is compared with the direct analysis of a laminated plate by the finite
Short time kernel asymptotics for Young SDE by means of Watanabe distribution theory
Inahama, Yuzuru
2011-01-01
In this paper we study short time asymptotics of a density function of the solution of a stochastic differential equation driven by fractional Brownian motion with Hurst parameter $H \\in (1/2, 1)$ when the coefficient vector fields satisfy an ellipticity condition at the starting point. We prove both on-diagonal and off-diagonal asymptotics under mild additional assumptions. Our main tool is Malliavin calculus, in particular, Watanabe's theory of generalized Wiener functionals.
Asymptotic stability of monostable wavefronts in discrete-time integral recursions
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in R2.We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior.Then,by employing the comparison principle and upper and lower solutions technique,we prove the asymptotic stability and uniqueness of such monostable wavefronts in the sense of phase shift and circumnutation.We also obtain some similar results in R.
Black branes in AdS: BPS bounds and asymptotic charges
Energy Technology Data Exchange (ETDEWEB)
Hristov, K. [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands); Faculty of Physics, Sofia University, Sofia 1164 (Bulgaria); Toldo, C.; Vandoren, S. [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)
2012-09-15
We focus on black branes and toroidal black holes in N = 2 gauged supergravities that asymptote to AdS{sub 4}, and derive formulas for the mass and central charge densities. We derive the corresponding BPS bound from the superalgebra of the asymptotic vacuum and illustrate our procedure with explicit examples of genuine black brane solutions with non-trivial scalars. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Impulsive control of stochastic system under the sense of stochastic asymptotical stability
Institute of Scientific and Technical Information of China (English)
Niu Yu-Jun; Ma Ge
2010-01-01
This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations,and establishes a comparison theory to ensure the trivial solution's stochastic asymptotical stability.From the comparison theory,it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterimpulsive control method,and numerical simulations are employed to verify the feasibility of this method.
On the asymptotic limit of the Navier-Stokes system on domains with rough boundaries
Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka; Wolf, Joerg
We study the asymptotic behavior of solutions to the incompressible Navier-Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter. Imposing the complete slip boundary conditions we show that in the asymptotic limit the fluid sticks completely to the boundary provided the oscillations are non-degenerate, meaning not oriented in a single direction.
An asymptotic model of the F layer
Oliver, W. L.
2012-01-01
A model of the F layer of the ionosphere is presented that consists of a bottomside asymptote that ignores transport and a topside asymptote that ignores chemistry. The asymptotes connect at the balance height dividing the chemistry and transport regimes. A combination of these two asymptotes produces a good approximation to the true F layer. Analogously, a model of F layer response to an applied vertical drift is presented that consists of two asymptotic responses, one that ignores transport and one that ignores chemistry. The combination of these asymptotic responses produces a good approximation to the response of the true F layer. This latter response is identical to the “servo” response of Rishbeth et al. (1978), derived from the continuity equation. The asymptotic approach bypasses the continuity equation in favor of “force balance” arguments and so replaces a differential equation with simpler algebraic equations. This new approach provides a convenient and intuitive mean for first-order estimates of the change in F layer peak height and density in terms of changes in neutral density, composition, temperature, winds, and electric fields. It is applicable at midlatitudes and at magnetically quiet times at high latitudes. Forensic inverse relations are possible but are not unique. The validity of the asymptotic relations is shown through numerical simulation.
Einstein Constraints on Asymptotically Euclidean Manifolds
Choquet-Bruhat, Y; York, J W; Choquet-Bruhat, Yvonne; Isenberg, James; York, James W.
2000-01-01
We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \\geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of existence. We also treat discontinuous scaled sources. In the last section we obtain new results in the case of non-constant mean curvature.
Charged rotating dilaton black holes with Kaluza-Klein asymptotics
Knoll, Christian; Nedkova, Petya
2016-03-01
We construct a class of stationary and axisymmetric solutions to the five-dimensional Einstein-Maxwell-dilaton gravity, which describe configurations of charged rotating black objects with Kaluza-Klein asymptotics. The solutions are constructed by uplifting a vacuum seed solution to six dimensions, performing a boost and a subsequent circle reduction. We investigate the physical properties of the charged solutions and obtain their general relations to the properties of the vacuum seed. We also derive the gyromagnetic ratio and the Smarr-like relations. As particular cases, we study three solutions, which describe a charged rotating black string, a charged rotating black ring on Kaluza-Klein bubbles, and a superposition of two black holes and a Kaluza-Klein bubble.
Penrose type inequalities for asymptotically hyperbolic graphs
Dahl, Mattias; Sakovich, Anna
2013-01-01
In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\\bH^n$. The graphs are considered as subsets of $\\bH^{n+1}$ and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the integrand for the asymptotically hyperbolic mass. Integrating this divergence we estimate the mass by an integral over an inner boundary. In case the inner boundary satisfies a convexity condition this can in turn be estimated in terms of the area of the inner boundary. The resulting estimates are similar to the conjectured Penrose inequality for asymptotically hyperbolic manifolds. The work presented here is inspired by Lam's article concerning the asymptotically Euclidean case.
Asymptotic properties of random matrices and pseudomatrices
Lenczewski, Romuald
2010-01-01
We study the asymptotics of sums of matricially free random variables called random pseudomatrices, and we compare it with that of random matrices with block-identical variances. For objects of both types we find the limit joint distributions of blocks and give their Hilbert space realizations, using operators called `matricially free Gaussian operators'. In particular, if the variance matrices are symmetric, the asymptotics of symmetric blocks of random pseudomatrices agrees with that of symmetric random blocks. We also show that blocks of random pseudomatrices are `asymptotically matricially free' whereas the corresponding symmetric random blocks are `asymptotically symmetrically matricially free', where symmetric matricial freeness is obtained from matricial freeness by an operation of symmetrization. Finally, we show that row blocks of square, lower-block-triangular and block-diagonal pseudomatrices are asymptotically free, monotone independent and boolean independent, respectively.
Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship
Institute of Scientific and Technical Information of China (English)
王启华; 荆炳义
2000-01-01
Here we study the problems of local asymptotic normality of the parametric family of distri-butions and asymptotic minimax efficient estimators when the observations are subject to right censor-ing. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and fur-thermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and furthermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
Asymptotic fingerprinting capacity for non-binary alphabets
Boesten, Dion
2011-01-01
We compute the channel capacity of non-binary fingerprinting under the Marking Assumption, in the limit of large coalition size c. The solution for the binary case was found by Huang and Moulin. They showed that asymptotically, the capacity is $1/(c^2 2\\ln 2)$, the interleaving attack is optimal and the arcsine distribution is the optimal bias distribution. In this paper we prove that the asymptotic capacity for general alphabet size q is $(q-1)/(c^2 2\\ln q)$. Our proof technique does not reveal the optimal attack or bias distribution. The fact that the capacity is an increasing function of q shows that there is a real gain in going to non-binary alphabets.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Institute of Scientific and Technical Information of China (English)
CHEN LiQun; C.W.LIM; HU QingQuan; DING Hu
2009-01-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach.The asymptotic solution is sought for a beam equation with a nonlinear boundary condition.The steady-state responses are determined in primary resonance and subharmonic resonance.The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition.Multivaluedness occurs in the relations as a consequence of the nonlinearity.The stability of steady-state responses is analyzed by use of the Lyapunov linearized sta-bility theory.The stability analysis predicts the jumping phenomenon for certain parameters.The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales.The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Chen, Liqun; Lim, C. W.; Hu, Qingquan; Ding, Hu
2009-09-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic Preserving schemes for highly oscillatory Vlasov–Poisson equations
Energy Technology Data Exchange (ETDEWEB)
Crouseilles, Nicolas [INRIA-Rennes Bretagne Atlantique, IPSO Project (France); Lemou, Mohammed [CNRS and IRMAR, Université de Rennes 1 and INRIA-Rennes Bretagne Atlantique, IPSO Project (France); Méhats, Florian, E-mail: florian.mehats@univ-rennes1.fr [IRMAR, Université de Rennes 1 and INRIA-Rennes Bretagne Atlantique, IPSO Project (France)
2013-09-01
This work is devoted to the numerical simulation of a Vlasov–Poisson model describing a charged particle beam under the action of a rapidly oscillating external field. We construct an Asymptotic Preserving numerical scheme for this kinetic equation in the highly oscillatory limit. This scheme enables to simulate the problem without using any time step refinement technique. Moreover, since our numerical method is not based on the derivation of the simulation of asymptotic models, it works in the regime where the solution does not oscillate rapidly, and in the highly oscillatory regime as well. Our method is based on a “two scale” reformulation of the initial equation, with the introduction of an additional periodic variable.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Institute of Scientific and Technical Information of China (English)
C.; W.; LIM
2009-01-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Singular solution of the Liouville equation under perturbation
Kalyakin, L A
1999-01-01
Small perturbation of the Liouville equation under singular initial data is considered. An asymptotics of the singular solution is constructed by the method which is similar to Bogolubov -- Krylov one. The main object is an asymptotics of the singular lines.
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.
Asymptotic dynamics of inertial particles with memory
Langlois, Gabriel Provencher; Haller, George
2014-01-01
Recent experimental and numerical observations have shown the significance of the Basset--Boussinesq memory term on the dynamics of small spherical rigid particles (or inertial particles) suspended in an ambient fluid flow. These observations suggest an algebraic decay to an asymptotic state, as opposed to the exponential convergence in the absence of the memory term. Here, we prove that the observed algebraic decay is a universal property of the Maxey--Riley equation. Specifically, the particle velocity decays algebraically in time to a limit that is $\\mathcal O(\\epsilon)$-close to the fluid velocity, where $0<\\epsilon\\ll 1$ is proportional to the square of the ratio of the particle radius to the fluid characteristic length-scale. These results follows from a sharp analytic upper bound that we derive for the particle velocity. For completeness, we also present a first proof of existence and uniqueness of global solutions to the Maxey--Riley equation, a nonlinear system of fractional-order differential equ...
Asymptotic theory for weakly non-linear wave equations in semi-infinite domains
Directory of Open Access Journals (Sweden)
Chirakkal V. Easwaran
2004-01-01
Full Text Available We prove the existence and uniqueness of solutions of a class of weakly non-linear wave equations in a semi-infinite region $0le x$, $t< L/sqrt{|epsilon|}$ under arbitrary initial and boundary conditions. We also establish the asymptotic validity of formal perturbation approximations of the solutions in this region.
ASYMPTOTICS OF INITIAL BOUNDARY VALUE PROBLEMS OF BIPOLAR HYDRODYNAMIC MODEL FOR SEMICONDUCTORS
Institute of Scientific and Technical Information of China (English)
Ju Qiangchang
2004-01-01
In this paper, we study the asymptotic behavior of the solutions to the bipolar hydrodynamic model with Dirichlet boundary conditions. It is shown that the initial boundary problem of the model admits a global smooth solution which decays to the steady state exponentially fast.
Asymptotics of thermal spectral functions
Caron-Huot, S
2009-01-01
We use operator product expansion (OPE) techniques to study the spectral functions of currents at finite temperature, in the high-energy time-like region $\\omega\\gg T$. The leading corrections to the spectral function of currents and stress tensors are proportional to $\\sim T^4$ expectation values in general, and the leading corrections $\\sim g^2T^4$ are calculated at weak coupling, up to one undetermined coefficient in the shear viscosity channel. Spectral functions in the asymptotic regime are shown to be infrared safe up to order $g^8T^4$. The convergence of sum rules in the shear and bulk viscosity channels is established in QCD to all orders in perturbation theory, though numerically significant tails $\\sim T^4/(\\log\\omega)^3$ are shown to exist in the bulk viscosity channel and to have an impact on sum rules recently proposed by Kharzeev and Tuchin. We argue that the spectral functions of currents and stress tensors in strongly coupled $\\mathcal{N}=4$ super Yang-Mills do not receive any medium-dependent...
On the Conditions for the Orbitally Asymptotical Stability of the Almost
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
@@This paper studies the behaviors of the solutions in the vicinity of a givenalmost periodic solution of the autonomous system x′=f(x), x Rn , (1) where f C1 (Rn ,Rn ). Since the periodic solutions of the autonomous system are not Liapunov asymptotic stable, we consider the weak orbitally stability. For the planar autonomous systems (n=2), the classical result of orbitally stability about its periodic solution with period w belongs to Poincare, i.e.
Asymptotic Safety, Emergence and Minimal Length
Percacci, R
2010-01-01
There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that 1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and 2) there is a precise sense in which asymptotic safety implies a minimal length. In so doing we also discuss possible signatures of asymptotic safety in scattering experiments.
Asymptotically AdS spacetimes with a timelike Kasner singularity
Ren, Jie
2016-07-01
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 behavior for a quadratic nonlinear Schrodinger equation
Directory of Open Access Journals (Sweden)
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.
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 Evolution of Random Unitary Operations
Novotny, J; Jex, I
2009-01-01
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.
The Lorentzian proper vertex amplitude: Asymptotics
Engle, Jonathan; Zipfel, Antonia
2015-01-01
In previous work, the Lorentzian proper vertex amplitude for a spin-foam model of quantum gravity was derived. In the present work, the asymptotics of this amplitude are studied in the semi-classical limit. The starting point of the analysis is an expression for the amplitude as an action integral with action differing from that in the EPRL case by an extra `projector' term which scales linearly with spins only in the asymptotic limit. New tools are introduced to generalize stationary phase methods to this case. For the case of boundary data which can be glued to a non-degenerate Lorentzian 4-simplex, the asymptotic limit of the amplitude is shown to equal the single Feynman term, showing that the extra term in the asymptotics of the EPRL amplitude has been eliminated.
Hermite polynomials and quasi-classical asymptotics
Energy Technology Data Exchange (ETDEWEB)
Ali, S. Twareque, E-mail: twareque.ali@concordia.ca [Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada); Engliš, Miroslav, E-mail: englis@math.cas.cz [Mathematics Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic and Mathematics Institute, Žitná 25, 11567 Prague 1 (Czech Republic)
2014-04-15
We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated quasi-classical asymptotics.
Nonsymmetric gravity does have acceptable global asymptotics
Cornish, N J
1994-01-01
"Reports of my death are greatly exaggerated" - Mark Twain. We consider the claim by Damour, Deser and McCarthy that nonsymmetric gravity theory has unacceptable global asymptotics. We explain why this claim is incorrect.
A Shortcut to LAD Estimator Asymptotics
1990-01-01
Using generalized functions of random variables and generalized Taylor series expansions, we provide almost trivial demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, autoregressions and autoregressions with in...
Asymptotic and Exact Expansions of Heat Traces
Energy Technology Data Exchange (ETDEWEB)
Eckstein, Michał, E-mail: michal@eckstein.pl [Jagiellonian University, Faculty of Physics, Astronomy and Applied Computer Science (Poland); Zając, Artur, E-mail: artur.zajac@uj.edu.pl [Jagiellonian University, Faculty of Mathematics and Computer Science (Poland)
2015-12-15
We study heat traces associated with positive unbounded operators with compact inverses. With the help of the inverse Mellin transform we derive necessary conditions for the existence of a short time asymptotic expansion. The conditions are formulated in terms of the meromorphic extension of the associated spectral zeta-functions and proven to be verified for a large class of operators. We also address the problem of convergence of the obtained asymptotic expansions. General results are illustrated with a number of explicit examples.
The trouble with asymptotically safe inflation
Fang, Chao
2013-01-01
In this paper we investigate the perturbation theory of the asymptotically safe inflation and we find that all modes of gravitational waves perturbation become ghosts in order to achieve a large enough number of e-folds. Formally we can calculate the power spectrum of gravitational waves perturbation, but we find that it is negative. It indicates that there is serious trouble with the asymptotically safe inflation.
Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps
Directory of Open Access Journals (Sweden)
Xinhong Zhang
2013-07-01
Full Text Available This article concerns the study of stochastic Gilpin-Ayala mutualism models with white noise and Poisson jumps. Firstly, an explicit solution for one-dimensional Gilpin-Ayala mutualism model with jumps is obtained and the asymptotic pathwise behavior is analyzed. Then, sufficient conditions for the existence of global positive solutions, stochastically ultimate boundedness and stochastic permanence are established for the n-dimensional model. Asymptotic pathwise behavior of n-dimensional Gilpin-Ayala mutualism model with jumps is also discussed. Finally numerical examples are introduced to illustrate the results developed.
Komech, A I; Stuart, D
2008-01-01
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\\"odinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schr\\"odinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as the Fermi Golden Rule.
Viscous flow in simple curved gaps. I - An asymptotic theory. II - Viscous stress and shape function
Fan, D.-N.; Tong, W.
1989-01-01
The present asymptotic theory for generalized incompressible two-dimensional steady flow in curved channels has been constructed in the limit when gas thickness approaches zero with its lateral dimensions fixed; successive asymptotic solution terms are analytically generated by quadratures. In the second part of this work, the curvature of the gap treated is arbitrary. It is established that each term in the series solution of velocity and pressure is the product of a scale factor and a universal shape functions. Various interaction modes between the volume rate-of-flow, curvature, and its variations, are identified and quantitatively characterized.
Canonical charges and asymptotic symmetry algebra of conformal gravity
Irakleidou, Maria; Preis, Florian
2014-01-01
We study canonical conformal gravity in four dimensions and construct the gauge generators and the associated charges. Using slightly generalized boundary conditions compared to those in \\cite{Grumiller:2013mxa} we find that the charges associated with space-time diffeomorphisms are finite and conserved in time. They are also shown to agree with the Noether charges found in \\cite{Grumiller:2013mxa}. However, there exists no charge associated with Weyl transformations. Consequently the asymptotic symmetry algebra is isomorphic to the Lie algebra of the boundary condition preserving diffeomorphisms. For illustrative purposes we apply the results to the Mannheim--Kazanas--Riegert solution of conformal gravity.
A Penrose inequality for asymptotically locally hyperbolic graphs
de Lima, Levi Lopes
2013-01-01
We use the inverse mean curvature flow to prove a sharp Alexandrov-Fenchel-type inequality for a class of hypersurfaces in certain locally hyperbolic manifolds. As an application we derive an optimal Penrose inequality for asymptotically locally hyperbolic graphs in any dimension $n\\geq 3$. When the horizon has the topology of a compact surface of genus at least one, this provides an affirmative answer, for this class of initial data sets, to a question posed by Gibbons, Chru\\'sciel and Simon on the validity of a Penrose-type inequality for black hole solutions carrying a higher genus horizon.
AN ASYMPTOTIC ANALYSIS METHOD FOR THE LINEAR SHELL
Institute of Scientific and Technical Information of China (English)
李开泰; 张文岭; 黄艾香
2004-01-01
In this paper, using the formal approach of asymptotic expansion for linear elastic shell we can get each term uk successively. According this metnod the leading term u0 will be identified by an elliptic boundary value problem, other terms will be obtained by the algebraic operations without solving partial differential equations. We give the variational formulation for the leading term U(x) and construct an approximate solution UKT(x,ζ):=U(x)+Ⅱ1Uζ+Ⅱ2Uζ2,then we give the estimation.
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.
Black hole remnant in asymptotic anti-de Sitter space
Energy Technology Data Exchange (ETDEWEB)
Wen, Wen-Yu [Chung Yuan Christian University, Department of Physics, Center for High Energy Physics, Chung Li City (China); National Taiwan University, Leung Center for Cosmology and Particle Astrophysics, Taipei (China); Wu, Shang-Yu [National Chiao Tung University, Department of Electrophysics, Hsinchu (China)
2015-12-15
The solution of a remnant was suggested for the black hole ground state after surface gravity is corrected for the loop quantum effect. On the other hand, a Schwarzschild black hole in asymptotic anti-de Sitter space would tunnel into the thermal soliton solution known as the Hawking-Page phase transition. In this letter, we investigate the low temperature phase of a three-dimensional Banados-Teitelboim-Zanelli (BTZ) black hole and four-dimensional AdS Schwarzschild black hole. We find that the thermal soliton is energetically favored rather than the remnant solution at low temperature in three dimensions, while a Planck-size remnant is still possible in four dimensions. Though the BTZ remnant seems energetically disfavored, we argue that it is still possible to find in the overcooled phase if strings were present, and its implication is discussed. (orig.)
Black hole remnant in asymptotic anti-de Sitter space
Energy Technology Data Exchange (ETDEWEB)
Wen, Wen-Yu, E-mail: steve.wen@gmail.com [Department of Physics, Center for High Energy Physics, Chung Yuan Christian University, Chung Li City, Taiwan (China); Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, 106, Taipei, Taiwan (China); Wu, Shang-Yu, E-mail: loganwu@gmail.com [Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan (China)
2015-12-21
The solution of a remnant was suggested for the black hole ground state after surface gravity is corrected for the loop quantum effect. On the other hand, a Schwarzschild black hole in asymptotic anti-de Sitter space would tunnel into the thermal soliton solution known as the Hawking–Page phase transition. In this letter, we investigate the low temperature phase of a three-dimensional Banados–Teitelboim–Zanelli (BTZ) black hole and four-dimensional AdS Schwarzschild black hole. We find that the thermal soliton is energetically favored rather than the remnant solution at low temperature in three dimensions, while a Planck-size remnant is still possible in four dimensions. Though the BTZ remnant seems energetically disfavored, we argue that it is still possible to find in the overcooled phase if strings were present, and its implication is discussed.
Guesmia, Senoussi
2008-05-01
We study here the asymptotic behavior of the solution of a hyperbolic problem defined on a cylindrical domain when l-->[infinity]. We show that, under very general assumptions, the solution of this problem converges faster than any power of towards the solution of another hyperbolic problem, defined on [0,T]×[omega], in any bounded subdomain. We give both necessary and sufficient conditions for this convergence to occur.
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.
Multiscale Asymptotic Analysis and Parallel Algorithm of Parabolic Equation in Composite Materials
Directory of Open Access Journals (Sweden)
Xin Wang
2014-01-01
Full Text Available An efficient parallel multiscale numerical algorithm is proposed for a parabolic equation with rapidly oscillating coefficients representing heat conduction in composite material with periodic configuration. Instead of following the classical multiscale asymptotic expansion method, the Fourier transform in time is first applied to obtain a set of complex-valued elliptic problems in frequency domain. The multiscale asymptotic analysis is presented and multiscale asymptotic solutions are obtained in frequency domain which can be solved in parallel essentially without data communications. The inverse Fourier transform will then recover the approximate solution in time domain. Convergence result is established. Finally, a novel parallel multiscale FEM algorithm is proposed and some numerical examples are reported.
ASYMPTOTIC SOLUTION TO MODEL FOR A CLASS OF VIRUS TRANSMISSION
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, a class of HIV virus transmission is considered. The transmissive dynamic model for the HIV virus is described. Using the functional-variational iteration theory, the rule for human group in the epidemic transmissive area is studied.
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 Behavior of Solutions for Nonlinear Volterra Discrete Equations
Directory of Open Access Journals (Sweden)
E. Messina
2008-01-01
Full Text Available We consider nonlinear difference equations of unbounded order of the form xi=bi−∑j=0iai,jfi−j(xj, i=0,1,2,…, where fj(x (j=0,…,i are suitable functions. We establish sufficient conditions for the boundedness and the convergence of xi as i→+∞. Some of these conditions are interesting mainly for studying stability of numerical methods for Volterra integral equations.
Relations between asymptotic and Fredholm representations
Manuilov, V M
1997-01-01
We prove that for matrix algebras $M_n$ there exists a monomorphism $(\\prod_n M_n/\\oplus_n M_n)\\otimes C(S^1) \\to {\\cal Q} $ into the Calkin algebra which induces an isomorphism of the $K_1$-groups. As a consequence we show that every vector bundle over a classifying space $B\\pi$ which can be obtained from an asymptotic representation of a discrete group $\\pi$ can be obtained also from a representation of the group $\\pi\\times Z$ into the Calkin algebra. We give also a generalization of the notion of Fredholm representation and show that asymptotic representations can be viewed as asymptotic Fredholm representations.
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...
Nanofluid surface wettability through asymptotic contact angle.
Vafaei, Saeid; Wen, Dongsheng; Borca-Tasciuc, Theodorian
2011-03-15
This investigation introduces the asymptotic contact angle as a criterion to quantify the surface wettability of nanofluids and determines the variation of solid surface tensions with nanofluid concentration and nanoparticle size. The asymptotic contact angle, which is only a function of gas-liquid-solid physical properties, is independent of droplet size for ideal surfaces and can be obtained by equating the normal component of interfacial force on an axisymmetric droplet to that of a spherical droplet. The technique is illustrated for a series of bismuth telluride nanofluids where the variation of surface wettability is measured and evaluated by asymptotic contact angles as a function of nanoparticle size, concentration, and substrate material. It is found that the variation of nanofluid concentration, nanoparticle size, and substrate modifies both the gas-liquid and solid surface tensions, which consequently affects the force balance at the triple line, the contact angle, and surface wettability.
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.
Semiclassical Asymptotics on Manifolds with Boundary
Koldan, Nilufer; Shubin, Mikhail
2008-01-01
We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by Kordyukov, Mathai and Shubin (2005), with a more extended use of quadratic forms instead of the operators. We also utilize some important ideas and technical elements from Helffer and Nier (2006), who were the first to supply a complete proof of the full semi-classical asymptotic expansions for the eigenvalues with fixed numbers.
de Reyna, Juan Arias
2012-01-01
A new derivation of the classic asymptotic expansion of the n-th prime is presented. A fast algorithm for the computation of its terms is also given, which will be an improvement of that by Salvy (1994). Realistic bounds for the error with $\\li^{-1}(n)$, after having retained the first m terms, for $1\\le m\\le 11$, are given. Finally, assuming the Riemann Hypothesis, we give estimations of the best possible $r_3$ such that, for $n\\ge r_3$, we have $p_n> s_3(n)$ where $s_3(n)$ is the sum of the first four terms of the asymptotic expansion.
Asymptotic stability of singularly perturbed differential equations
Artstein, Zvi
2017-02-01
Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.
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.
Institute of Scientific and Technical Information of China (English)
JI Xue-Feng; ZHOU Zi-Xiang
2005-01-01
@@ The asymptotic behaviour of the solitons with a double spectral parameter for the Bogomolny equation in (2+1)-dimensional anti de Sitter space is obtained. The asymptotic solution has two ridges close to each other which locates beside the geodesic of the Poincaré half-plane.
Directory of Open Access Journals (Sweden)
Huabin Chen
2011-01-01
Full Text Available By establishing two Lemmas, the exponential stability and the asymptotical stability for mild solution to the second-order neutral stochastic partial differential equations with infinite delay are obtained, respectively. Our results can generalize and improve some existing ones. Finally, an illustrative example is given to show the effectiveness of the obtained results.
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...
Asymptotic Behavior of the Newton-Boussinesq Equation in a Two-Dimensional Channel
Fucci, Guglielmo; Singh, Preeti
2007-01-01
We prove the existence of a global attractor for the Newton-Boussinesq equation defined in a two-dimensional channel. The asymptotic compactness of the equation is derived by the uniform estimates on the tails of solutions. We also establish the regularity of the global attractor.
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.
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
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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$.
Asymptotic behavior on the Hénon equation with supercritical exponent
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The main purpose of this paper is to analyze the asymptotic behavior of the radial solution of Hénon equation △ u = |x|αup-1, u > 0, x ∈ BR(0) Rn (n 3), u = 0, x ∈ BR(0), where p → p(α) = 2(n+α)/n-2 from left side, α > 0.
Gravitational collapse of thin shells of dust in asymptotically flat shape dynamics
Mercati, Flavio; Gomes, Henrique; Koslowski, Tim; Napoletano, Andrea
2017-02-01
In a recent paper, one of us studied spherically symmetric, asymptotically flat solutions of shape dynamics, finding that the spatial metric has characteristics of a wormhole—two asymptotically flat ends and a minimal-area sphere, or "throat," in between. In this paper, we investigate whether that solution can emerge as a result of gravitational collapse of matter. With this goal, we study the simplest kind of spherically symmetric matter: an infinitely-thin shell of dust. Our system can be understood as a model of a star accreting a thin layer of matter. We solve the dynamics of the shell exactly and find that, indeed, as it collapses, the shell leaves in its wake the wormhole metric. In the maximal-slicing time we use for asymptotically flat solutions, the shell only approaches the throat asymptotically and does not cross it in a finite amount of time (as measured by a clock "at infinity"). This leaves open the possibility that a more realistic cosmological solution of shape dynamics might see this crossing happening in a finite amount of time (as measured by the change of relational or shape degrees of freedom).
Asymptotic Behavior of Equilibrium Point for a Class of Nonlinear Difference Equation
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Gong Fei
2009-01-01
Full Text Available We study the asymptotic behavior of the solutions for the following nonlinear difference equation where the initial conditions are arbitrary nonnegative real numbers, are nonnegative integers, , and are positive constants. Moreover, some numerical simulations to the equation are given to illustrate our results.
Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation
Institute of Scientific and Technical Information of China (English)
Claude-Michel BRAUNER; Lina HU; Luca LORENZI
2013-01-01
The authors consider a free interface problem which stems from a gas-solid model in combustion with pattern formation.A third-order,fully nonlinear,self-consistent equation for the flame front is derived.Asymptotic methods reveal that the interface approaches a solution to the Kuramoto-Sivashinsky equation.Numerical results which illustrate the dynamics are presented.
On the asymptotic wavenumber of spiral waves in \\lambda -\\omega systems
Aguareles, M.; Baldomà, I.; M-Seara, T.
2017-01-01
In this paper we consider spiral wave solutions of a general class of λ -ω systems with a small twist parameter q and we prove that the asymptotic wavenumber of the spirals is a {{C}∞} -flat function of the perturbation parameter q.
On Asymptotic Behavior for Reaction Diffusion Equation with Small Time Delay
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Xunwu Yin
2011-01-01
Full Text Available We investigate the asymptotic behavior of scalar diffusion equation with small time delay ut-Δu=f(ut,u(t-τ. Roughly speaking, any bounded solution will enter and stay in the neighborhood of one equilibrium when the equilibria are discrete.
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.
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...
Spinning, Precessing, Black Hole Binary Spacetime via Asymptotic Matching
Nakano, Hiroyuki; Campanelli, Manuela; West, Eric J
2016-01-01
We briefly discuss a method to construct a global, analytic, approximate spacetime for precessing, spinning binary black holes. The spacetime construction is broken into three parts: the inner zones are the spacetimes close to each black hole, and are approximated by perturbed Kerr solutions; the near zone is far from the two black holes, and described by the post-Newtonian metric; and finally the wave (far) zone, where retardation effects need to be taken into account, is well modeled by the post-Minkowskian metric. These individual spacetimes are then stitched together using asymptotic matching techniques to obtain a global solution that approximately satisfies the Einstein field equations. Precession effects are introduced by rotating the black hole spin direction according to the precessing equations of motion, in a way that is consistent with the global spacetime construction.
Asymptotic Distributions for Tests of Combined Significance.
Becker, Betsy Jane
This paper discusses distribution theory and power computations for four common "tests of combined significance." These tests are calculated using one-sided sample probabilities or p values from independent studies (or hypothesis tests), and provide an overall significance level for the series of results. Noncentral asymptotic sampling…
THE COMPLETE ASYMPTOTIC EXPANSION FOR BASKAKOV OPERATORS
Institute of Scientific and Technical Information of China (English)
Chungou Zhang; Quane Wang
2007-01-01
In this paper, we derive the complete asymptotic expansion of classical Baskakov itly in terms of Stirling number of the first and second kind and another number G(I, p). As a corollary, we also get the Voronovskaja-type result for the operators.
Discrete Energy Asymptotics on a Riemannian circle
Brauchart, J S; Saff, E B
2009-01-01
We derive the complete asymptotic expansion in terms of powers of $N$ for the geodesic $f$-energy of $N$ equally spaced points on a rectifiable simple closed curve $\\Gamma$ in ${\\mathbb R}^p$, $p\\geq2$, as $N \\to \\infty$. For $f$ decreasing and convex, such a point configuration minimizes the $f$-energy $\\sum_{j\
Asymptotic estimates for generalized Stirling numbers
Chelluri, R.; Richmond, L.B.; Temme, N.M.
1999-01-01
Uniform asymptotic expansions are given for the Stirling numbers of the first kind for integral arguments and for the second kind as defined for real arguments by Flajolet and Prodinger. The logconcavity of the resulting real valued function of Flajolet and Prodinger is established for a range inclu
Toeplitz Quantization and Asymptotic Expansions: Geometric Construction
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Miroslav Englis
2009-02-01
Full Text Available For a real symmetric domain G_R/K_R, with complexification G_C/K_C, we introduce the concept of ''star-restriction'' (a real analogue of the ''star-products'' for quantization of Kähler manifolds and give a geometric construction of the G_R-invariant differential operators yielding its asymptotic expansion.
An asymptotically optimal nonparametric adaptive controller
Institute of Scientific and Technical Information of China (English)
郭雷; 谢亮亮
2000-01-01
For discrete-time nonlinear stochastic systems with unknown nonparametric structure, a kernel estimation-based nonparametric adaptive controller is constructed based on truncated certainty equivalence principle. Global stability and asymptotic optimality of the closed-loop systems are established without resorting to any external excitations.
The conformal approach to asymptotic analysis
Nicolas, Jean-Philippe
2015-01-01
This essay was written as an extended version of a talk given at a conference in Strasbourg on "Riemann, Einstein and geometry", organized by Athanase Papadopoulos in September 2014. Its aim is to present Roger Penrose's approach to asymptotic analysis in general relativity, which is based on conformal geometric techniques, focusing on historical and recent aspects of two specialized topics~: conformal scattering and peeling.
Breaking a magnetic zero locus: asymptotic analysis
Raymond, Nicolas
2014-01-01
25 pages; This paper deals with the spectral analysis of the Laplacian in presence of a magnetic field vanishing along a broken line. Denoting by $\\theta$ the breaking angle, we prove complete asymptotic expansions of all the lowest eigenpairs when $\\theta$ goes to $0$. The investigation deeply uses a coherent states decomposition and a microlocal analysis of the eigenfunctions.
Couplings and Asymptotic Exponentiality of Exit Times
Brassesco, S.; Olivieri, E.; Vares, M. E.
1998-10-01
The goal of this note is simply to call attention to the resulting simplification in the proof of asymptotic exponentiality of exit times in the Freidlin-Wentzell regime (as proved by F. Martinelli et al.) by using the coupling proposed by T. Lindvall and C. Rogers.
On the Asymptotic Distribution of Signal Fraction
Volobouev, Igor
2016-01-01
Condition of the asymptotic normality of the signal fraction estimate by maximum likelihood is derived under the null hypothesis of no signal. Consequences of this condition for determination of signal significance taking in to account the look elsewhere effect are discussed.
Resonance asymptotics in the generalized Winter model
Exner, P; Exner, Pavel; Fraas, Martin
2006-01-01
We consider a modification of the Winter model describing a quantum particle in presence of a spherical barrier given by a fixed generalized point interaction. It is shown that the three classes of such interactions correspond to three different types of asymptotic behaviour of resonances of the model at high energies.
Asymptotic iteration approach to supersymmetric bistable potentials
Institute of Scientific and Technical Information of China (English)
H. Ciftci; O. ozer; P. Roy
2012-01-01
We examine quasi exactly solvable bistable potentials and their supersymmetric partners within the framework of the asymptotic iteration method (AIM).It is shown that the AIM produces excellent approximate spectra and that sometimes it is found to be more useful to use the partner potential for computation. We also discuss the direct application of the AIM to the Fokker-Planck equation.
Higher Spin Black Holes in Three Dimensions: Comments on Asymptotics and Regularity
Banados, M; Theisen, S
2016-01-01
In the context of (2+1)--dimensional SL(N,R)\\times SL(N,R) Chern-Simons theory we explore issues related to regularity and asymptotics on the solid torus, for stationary and circularly symmetric solutions. We display and solve all necessary conditions to ensure a regular metric and metric-like higher spin fields. We prove that holonomy conditions are necessary but not sufficient conditions to ensure regularity, and that Hawking conditions do not necessarily follow from them. Finally we give a general proof that once the chemical potentials are turn on -- as demanded by regularity -- the asymptotics cannot be that of Brown-Henneaux.
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
Higher spin black holes in three dimensions: Remarks on asymptotics and regularity
Bañados, Máximo; Canto, Rodrigo; Theisen, Stefan
2016-07-01
In the context of (2 +1 )-dimensional S L (N ,R )×S L (N ,R ) Chern-Simons theory we explore issues related to regularity and asymptotics on the solid torus, for stationary and circularly symmetric solutions. We display and solve all necessary conditions to ensure a regular metric and metriclike higher spin fields. We prove that holonomy conditions are necessary but not sufficient conditions to ensure regularity, and that Hawking conditions do not necessarily follow from them. Finally we give a general proof that once the chemical potentials are turned on—as demanded by regularity—the asymptotics cannot be that of Brown-Henneaux.
Institute of Scientific and Technical Information of China (English)
Xu Rui(徐瑞); Chen Lansun(陈兰荪); M.A.J. Chaplain
2003-01-01
A delayed n-species nonautonomous Lotka-Volterra type competitive systemwithout dominating instantaneous negative feedback is investigated. By means of a suitableLyapunov functional, sufficient conditions are derived for the global asymptotic stability ofthe positive solutions of the system. As a corollary, it is shown that the global asymptoticstability of the positive solution is maintained provided that the delayed negative feedbacksdominate other interspecific interaction effects with delays and the delays are sufficientlysmall.
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.
Enhanced Asymptotic Symmetry Algebra of 2+1 Dimensional Flat Space
Detournay, Stéphane
2016-01-01
In this paper we present a new set of asymptotic boundary conditions for Einstein gravity in 2+1 dimensions with vanishing cosmological constant that are a generalization of the Barnich-Comp{\\`e}re boundary conditions gr-qc/0610130. These new boundary conditions lead to an asymptotic symmetry algebra that is generated by a $\\mathfrak{bms}_3$ algebra and two affine $\\hat{\\mathfrak{u}}(1)$ current algebras. We then apply these boundary conditions to Topologically Massive Gravity (TMG) and determine how the presence of the gravitational Chern-Simons term affects the central extensions of the asymptotic symmetry algebra. We furthermore determine the thermal entropy of solutions obeying our new boundary conditions for both Einstein gravity and TMG.
Elliptic Equations in Weighted Besov Spaces on Asymptotically Flat Riemannian Manifolds
Brauer, Uwe
2012-01-01
This paper deals with the applications of weighted Besov spaces to elliptic equations on asymptotically flat Riemannian manifolds, and in particular to the solutions of Einstein's constraints equations. We establish existence theorems for the Hamiltonian an momentum constraints with constant mean curvature and with a background metric which satisfies very low regularity assumptions. These results extend the regularity results of Holst, Nagy and Tsogtgerel about the constraint equations on compact manifolds in the Besov space $B_{p,p}^s$, to asymptotically flat manifolds. We also consider the Brill--Cantor criterion in the weighted Besov spaces. Our results improve the regularity assumptions on asymptotically flat manifolds Choquet--Bruhat, Isenberg and Pollack, and Maxwell, as well as they enable us to construct the initial data for the Einstein--Euler system.
The renormalization method based on the Taylor expansion and applications for asymptotic analysis
Liu, Cheng-shi
2016-01-01
Based on the Taylor expansion, we propose a renormalization method for asymptotic analysis. The standard renormalization group (RG) method for asymptotic analysis can be derived out from this new method, and hence the mathematical essence of the RG method is also recovered. The biggest advantage of the proposed method is that the secular terms in perturbation series are automatically eliminated, but in usual perturbation theory, we need more efforts and tricks to eliminate these terms. At the same time, the mathematical foundation of the method is simple and the logic of the method is very clear, therefore, it is very easy in practice. As application, we obtain the uniform valid asymptotic solutions to some problems including vector field, boundary layer and boundary value problems of nonlinear wave equations. Moreover, we discuss the normal form theory and reduction equations of dynamical systems. Furthermore, by combining the topological deformation and the RG method, a modified method namely the homotopy r...
Nonlinear mechanics of thin-walled structures asymptotics, direct approach and numerical analysis
Vetyukov, Yury
2014-01-01
This book presents a hybrid approach to the mechanics of thin bodies. Classical theories of rods, plates and shells with constrained shear are based on asymptotic splitting of the equations and boundary conditions of three-dimensional elasticity. The asymptotic solutions become accurate as the thickness decreases, and the three-dimensional fields of stresses and displacements can be determined. The analysis includes practically important effects of electromechanical coupling and material inhomogeneity. The extension to the geometrically nonlinear range uses the direct approach based on the principle of virtual work. Vibrations and buckling of pre-stressed structures are studied with the help of linearized incremental formulations, and direct tensor calculus rounds out the list of analytical techniques used throughout the book. A novel theory of thin-walled rods of open profile is subsequently developed from the models of rods and shells, and traditionally applied equations are proven to be asymptotically exa...
Asymptotically locally flat spacetimes and dynamical black flowers in three dimensions
Barnich, Glenn; Tempo, David; Troncoso, Ricardo
2015-01-01
The theory of massive gravity proposed by Bergshoeff, Hohm and Townsend is considered in the special case of the pure irreducibly fourth order quadratic Lagrangian. It is shown that the asymptotically locally flat black holes of this theory can be consistently deformed to "black flowers" that are no longer spherically symmetric. Moreover, we construct radiating spacetimes settling down to these black flowers in the far future. The generic case can be shown to fit within a relaxed set of asymptotic conditions as compared to the ones of general relativity at null infinity, while the asymptotic symmetries remain the same. Conserved charges as surface integrals at null infinity are constructed following a covariant approach, and their algebra represents BMS$_{3}$, but without central extensions. For solutions possessing an event horizon, we derive the first law of thermodynamics from these surface integrals.
Asymptotic expansion of the wavelet transform with error term
Pathak, R.S.; Pathak, Ashish
2014-01-01
UsingWong's technique asymptotic expansion for the wavelet transform is derived and thereby asymptotic expansions for Morlet wavelet transform, Mexican Hat wavelet transform and Haar wavelet transform are obtained.
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
Institute of Scientific and Technical Information of China (English)
张映辉; 吴国春
2014-01-01
We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.
Locally Asymptotic-norming Property and Kadec Property
Institute of Scientific and Technical Information of China (English)
王建华
2002-01-01
In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property κ, κ=Ⅰ,Ⅱ,Ⅲ,and discuss the relationship between the locally asymptotic-norming property and the Kadec Property.
Global dynamics of a Yang-Mills field on an asymptotically hyperbolic space
Bizoń, Piotr
2014-01-01
We consider a spherically symmetric (purely magnetic) SU(2) Yang-Mills field propagating on an ultrastatic spacetime with two asymptotically hyperbolic regions connected by a throat of radius $\\alpha$. Static solutions in this model are shown to exhibit an interesting bifurcation pattern in the parameter $\\alpha$. We relate this pattern to the Morse index of the static solution with maximal energy. Using a hyperboloidal approach to the initial value problem, we describe the relaxation to the ground state solution for generic initial data and unstable static solutions for initial data of codimension one, two, and three.
Asymptotic dynamics of three-dimensional gravity
Donnay, Laura
2016-01-01
These are the lectures notes of the course given at the Eleventh Modave Summer School in Mathematical Physics, 2015, aimed at PhD candidates and junior researchers in theoretical physics. We review in details the result of Coussaert-Henneaux-van Driel showing that the asymptotic dynamics of $(2+1)$- dimensional gravity with negative cosmological constant is described at the classical level by Liouville theory. Boundary conditions implement the asymptotic reduction in two steps: the first set reduces the $SL(2,\\mathbb R)\\times SL(2,\\mathbb R)$ Chern-Simons action, equivalent to the Einstein action, to a non-chiral $SL(2,\\mathbb R)$ Wess-Zumino-Witten model, while the second set imposes constraints on the WZW currents that reduce further the action to Liouville theory. We discuss the issues of considering the latter as an effective description of the dual conformal field theory describing AdS$_3$ gravity beyond the semi-classical regime.
On asymptotic flatness and Lorentz charges
Energy Technology Data Exchange (ETDEWEB)
Compere, Geoffrey [KdV Institute for Mathematics, Universiteit van Amsterdam (Netherlands); Dehouck, Francois; Virmani, Amitabh, E-mail: gcompere@uva.nl, E-mail: fdehouck@ulb.ac.be, E-mail: avirmani@ulb.ac.be [Physique Theorique et Mathematique, Universite Libre de Bruxelles, Bruxelles (Belgium)
2011-07-21
In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence-free tensors that we construct from the equations of motion. Second, we show that the integrability of Einstein's equations in the asymptotic expansion is sufficient to establish the equivalence between counter-term charges defined from the variational principle and charges defined by Ashtekar and Hansen. These results clarify earlier constructions of conserved charges in the hyperboloid representation of spatial infinity. In showing this, the parity condition on the mass aspect is not needed. Along the way in establishing these results, we prove two lemmas on tensor fields on three-dimensional de Sitter spacetime stated by Ashtekar-Hansen and Beig-Schmidt and state and prove three additional lemmas.
Theorems for Asymptotic Safety of Gauge Theories
Bond, Andrew D
2016-01-01
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 emphasized. 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.
Asymptotics of high order noise corrections
Sondergaard, N; Pálla, G; Voros, A; Sondergaard, Niels; Vattay, Gabor; Palla, Gergely; Voros, Andre
1999-01-01
We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and noise with finite moments. Using a perturbative expansion of the evolution operator we calculate high order corrections to its trace in the case of a quartic map and Gaussian noise. The leading contributions come from the period one orbits of the map. The asymptotic behaviour is investigated and is found to be independent up to a multiplicative constant of the distribution of noise.
Asymptotic Existence of Nearly Kirkman Systems
Institute of Scientific and Technical Information of China (English)
沈灏; 储文松
1994-01-01
It is proved in this paper that,for any given positive integer k≥2,there exists a constant v0=v0(k) such that for v≥v0,the necessary condition v=0 (mod k(k-)) for the existence of a nearly Kirkman system NKS (2,k,v) is also sufficient.Thus we have completely determined the asymptotic existence of NKS.
Asymptotic analysis of the Forward Search
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Bent
The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made....... The argument involves theory for a new class of weighted and marked empirical processes, quantile process theory, and a fixed point argument to describe the iterative element of the procedure....
Asymptotic Enumeration of RNA Structures with Pseudoknots
Jin, Emma Y
2007-01-01
In this paper we present the asymptotic enumeration of RNA structures with pseudoknots. We develop a general framework for the computation of exponential growth rate and the sub exponential factors for $k$-noncrossing RNA structures. Our results are based on the generating function for the number of $k$-noncrossing RNA pseudoknot structures, ${\\sf S}_k(n)$, derived in \\cite{Reidys:07pseu}, where $k-1$ denotes the maximal size of sets of mutually intersecting bonds. We prove a functional equation for the generating function $\\sum_{n\\ge 0}{\\sf S}_k(n)z^n$ and obtain for $k=2$ and $k=3$ the analytic continuation and singular expansions, respectively. It is implicit in our results that for arbitrary $k$ singular expansions exist and via transfer theorems of analytic combinatorics we obtain asymptotic expression for the coefficients. We explicitly derive the asymptotic expressions for 2- and 3-noncrossing RNA structures. Our main result is the derivation of the formula ${\\sf S}_3(n) \\sim \\frac{10.4724\\cdot 4!}{n(n...
INVESTIGATION OF STURM-LIOUVILLE PROBLEM SOLVABILITY IN THE PROCESS OF ASYMPTOTIC SERIES CREATION
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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.
ESTIMATION FOR THE ASYMPTOTIC BEHAVIOR OF THE DELAYED COMPETITION MODEL
Institute of Scientific and Technical Information of China (English)
Li Huifeng; Wang Jinliang
2008-01-01
In ecological dynamic systems, the competition between species is a very universal phenomenon, which can be described by the well-known Volterra-Lotka model in a diffusion form. Noticing that the living space usually changes in a seasonal manner and the population development of the species may also undergo time-delay im-pact, a developed form of this model is investigated in this article. The main approaches employed here are the upper-lower solution method and the energy-estimate technique. The results show that whether the species may sustain survival or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the time delay. For the survival case, the population evolutions of the two species may appear asymptotic periodicity with distinct upper bound and this bound depends heavily on the time delay. These results can be also checked by the intuitionistic numerical simulations.
Cubic Derivative Interactions and Asymptotic Dynamics of the Galileon Vacuum
De Arcia, Roberto; León, Genly; Nucamendi, Ulises; Quiros, Israel
2015-01-01
In this paper we apply the tools of the dynamical systems theory in order to uncover the whole asymptotic structure of the vacuum interactions of a galileon model with a cubic derivative interaction term. It is shown that, contrary to what occurs in the presence of background matter, the galileon interactions of vacuum appreciably modify the late-time cosmic dynamics. In particular, a local late-time attractor representing phantom behavior arises which is inevitably associated with a big rip singularity. It seems that the gravitational interactions of the background matter with the galileon screen the effects of the gravitational self-interactions of the galileon, thus erasing any potential modification of the late-time dynamics by the galileon vacuum processes. Unlike other galileon models inspired in the DGP scenario, self-accelerating solutions do not arise in this model.
Asymptotic Stability of Neutral Differential Equations with Unbounded Delay
Institute of Scientific and Technical Information of China (English)
YE Hai-ping; GAO Guo-zhu
2002-01-01
Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt [x(t)- P(t)x(h(t))] + Q(t)x(q(t)) -R(t)x(r(t))= 0, t ≥ t0,where P(t)∈ C([t0, ∞), R), Q(t), R(t) ∈ C([t0,∞ ), R+ ), and h, q, r: [ t0, ∞ ) → R are continuously differentiable and strictly increasing, h( t) ＜ t, q( t) ＜t, r(t) ＜ t for all t ≥ t0. In this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable.
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.
Asymptotic self-restabilization of a continuous elastic structure
Bosi, F.; Misseroni, D.; Dal Corso, F.; Neukirch, S.; Bigoni, D.
2016-12-01
A challenge in soft robotics and soft actuation is the determination of an elastic system that spontaneously recovers its trivial path during postcritical deformation after a bifurcation. The interest in this behavior is that a displacement component spontaneously cycles around a null value, thus producing a cyclic soft mechanism. An example of such a system is theoretically proven through the solution of the elastica and a stability analysis based on dynamic perturbations. It is shown that the asymptotic self-restabilization is driven by the development of a configurational force, of similar nature to the Peach-Koehler interaction between dislocations in crystals, which is derived from the principle of least action. A proof-of-concept prototype of the discovered elastic system is designed, realized, and tested, showing that this innovative behavior can be obtained in a real mechanical apparatus.
Generalized asymptotic expansions for coupled wavenumbers in fluid-filled cylindrical shells
Kunte, M. V.; Sarkar, Abhijit; Sonti, Venkata R.
2010-12-01
Analytical expressions are found for the coupled wavenumbers in an infinite fluid-filled cylindrical shell using the asymptotic methods. These expressions are valid for any general circumferential order ( n). The shallow shell theory (which is more accurate at higher frequencies) is used to model the cylinder. Initially, the in vacuo shell is dealt with and asymptotic expressions are derived for the shell wavenumbers in the high- and the low-frequency regimes. Next, the fluid-filled shell is considered. Defining a relevant fluid-loading parameter μ, we find solutions for the limiting cases of small and large μ. Wherever relevant, a frequency scaling parameter along with some ingenuity is used to arrive at an elegant asymptotic expression. In all cases, Poisson's ratio ν is used as an expansion variable. The asymptotic results are compared with numerical solutions of the dispersion equation and the dispersion relation obtained by using the more general Donnell-Mushtari shell theory ( in vacuo and fluid-filled). A good match is obtained. Hence, the contribution of this work lies in the extension of the existing literature to include arbitrary circumferential orders ( n).
asymptoticMK: A Web-Based Tool for the Asymptotic McDonald-Kreitman Test.
Haller, Benjamin C; Messer, Philipp W
2017-03-24
The McDonald-Kreitman (MK) test is a widely used method for quantifying the role of positive selection in molecular evolution. One key shortcoming of this test lies in its sensitivity to the presence of slightly deleterious mutations, which can severely bias its estimates. An asymptotic version of the MK test was recently introduced that addresses this problem by evaluating polymorphism levels for different mutation frequencies separately, and then extrapolating a function fitted to that data. Here we present asymptoticMK, a web-based implementation of this asymptotic McDonald-Kreitman test. Our web service provides a simple R-based interface into which the user can upload the required data (polymorphism and divergence data for the genomic test region and a neutrally evolving reference region). The web service then analyzes the data and provides plots of the test results. This service is free to use, open-source, and available at http://benhaller.com/messerlab/asymptoticMK.html. We provide results from simulations to illustrate the performance and robustness of the asymptoticMK test under a wide range of model parameters.
Directory of Open Access Journals (Sweden)
Xionghua Wu
2012-01-01
Full Text Available Let {}⊂(0,1 be such that →1 as →∞, let and be two positive numbers such that +=1, and let be a contraction. If be a continuous asymptotically pseudocontractive self-mapping of a nonempty bounded closed convex subset of a real reflexive Banach space with a uniformly Gateaux differentiable norm, under suitable conditions on the sequence {}, we show the existence of a sequence {} satisfying the relation =(1−/(+(/ and prove that {} converges strongly to the fixed point of , which solves some variational inequality provided is uniformly asymptotically regular. As an application, if be an asymptotically nonexpansive self-mapping of a nonempty bounded closed convex subset of a real Banach space with a uniformly Gateaux differentiable norm and which possesses uniform normal structure, we prove that the iterative process defined by 0∈,+1=(1−/(+(/+(/ converges strongly to the fixed point of .
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M. A. Davydova
2016-01-01
Full Text Available In the present work the model boundary value problem for a stationary singularly perturbed reaction-diﬀusion-advection equation arising at the description of gas impurity transfer processes in an ecosystem ”forest – swamp” is considered. Application of a boundary functions method and an asymptotic method of diﬀerential inequalities allow to construct an asymptotics of the boundary layer type solution, to prove the existence of the solution with such an asymptotics and its asymptotic stability by Lyapunov as the stationary solution of the corresponding parabolic problem with the deﬁnition of local area of boundary layer type solution formation. The latter has a certain importance for applications, since it allows to reveal the solution describing one of the most probable conditions of the ecosystem. In the ﬁnal part of the work suﬃcient conditions for existence of solutions with interior transitional layers (contrast structures are discussed.
Levchenko, E. A.; Shapovalov, A. V.; Trifonov, A. Yu
2016-07-01
In this paper we construct asymptotic solutions for the nonlocal multidimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation in the class of functions concentrated on a one-dimensional manifold (curve) using a semiclassical approximation technique. We show that the construction of these solutions can be reduced to solving a similar problem for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov in the class of functions concentrated at a point (zero-dimensional manifold) together with an additional operator condition. The general approach is exemplified by constructing a two-dimensional two-parametric solution, which describes quasi-steady-state patterns on a circumference.
Optimal homotopy asymptotic method for solving fractional relaxation-oscillation equation
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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 Analysis to a Diffusion Equation with a Weighted Nonlo cal Source
Institute of Scientific and Technical Information of China (English)
JIANG Liang-jun
2015-01-01
In this paper, we deal with the blow-up property of the solution to the diffusion equation ut=∆u+a(x)f(u) RΩh(u)dx, x∈Ω, t>0 subject to the null Dirichlet boundary condition. We will show that under certain conditions, the solution blows up in finite time and prove that the set of all blow-up points is the whole region. Especially, in case of f(s)=sp, h(s)=sq, 0≤p≤1, p+q>1, we obtain the asymptotic behavior of the blow up solution.
Taming perturbative divergences in asymptotically safe gravity
Energy Technology Data Exchange (ETDEWEB)
Benedetti, Dario, E-mail: dbenedetti@perimeterinstitute.c [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, N2L 2Y5, Waterloo ON (Canada); Machado, Pedro F., E-mail: p.f.machado@uu.n [Institute for Theoretical Physics, Utrecht University, 3508 TD Utrecht (Netherlands); Saueressig, Frank, E-mail: Frank.Saueressig@cea.f [Institut de Physique Theorique, CEA Saclay, F-91191 Gif-Sur-Yvette Cedex (France); CNRS URA 2306, F-91191 Gif-Sur-Yvette Cedex (France)
2010-01-01
We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may possess a non-trivial renormalization group fixed point controlling its UV behavior. We show that such a fixed point indeed exists within the truncations considered, lending strong support to the conjectured asymptotic safety of the theory. In particular, we demonstrate that the counterterms responsible for its perturbative non-renormalizability have no qualitative effect on this feature.
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
The ADM mass of asymptotically flat hypersurfaces
de Lima, Levi Lopes
2011-01-01
We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of infinity, thus extending Lam's recent results on Euclidean graphs to this broader context. As applications we exhibit, in any dimension, new classes of manifolds for which versions of the Positive Mass and Riemannian Penrose inequalities hold and discuss a notion of quasi-local mass in this setting. The proof explores a novel connection between the co-vector defining the ADM mass of a hypersurface as above and the Newton tensor associated to its shape operator, which takes place in the presence of an ambient Killing field.
Asymptotics for a generalization of Hermite polynomials
Alfaro, M; Peña, A; Rezola, M L
2009-01-01
We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties. Thus, our aim is to study the asymptotics of this sequence of nonstandard orthogonal polynomials. In fact, we obtain Mehler--Heine type formulas for these polynomials and, as a consequence, we prove that there exists an acceleration of the convergence of the smallest positive zeros of these generalized Hermite polynomials towards the origin.
Asymptotic curved interface models in piezoelectric composites
Serpilli, Michele
2016-10-01
We study the electromechanical behavior of a thin interphase, constituted by a piezoelectric anisotropic shell-like thin layer, embedded between two generic three-dimensional piezoelectric bodies by means of the asymptotic analysis in a general curvilinear framework. After defining a small real dimensionless parameter ε, which will tend to zero, we characterize two different limit models and their associated limit problems, the so-called weak and strong piezoelectric curved interface models, respectively. Moreover, we identify the non-classical electromechanical transmission conditions at the interface between the two three-dimensional bodies.
Vacuum Potential and its Asymptotic Variation
Dahal, Pravin
2016-09-01
The possible form of existence of dark energy is explained and the relation for its asymptotic variation is given. This has two huge implications in the understanding of the Universe. The first is that the theory predicts that the Universe should be in negative pressure state in the very early period as required for inflation and spontaneous symmetry breaking. The second is that the theory gives the reasonable answer to the astrophysical evidence of dark energy dominating the Universe. The author is presenting his research in the nature of dark energy. Some of the work is submitted for publication in the journal and is currently under review.
STABILITY OF SOLUTIONS TO CERTAIN FOURTH-ORDER DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to a certain fourth-order non-linear differential equation with delay are obtained.
Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity
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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.
Inspiralling, Non-Precessing, Spinning Black Hole Binary Spacetime via Asymptotic Matching
Ireland, Brennan; Nakano, Hiroyuki; Campanelli, Manuela
2015-01-01
We construct a new global, fully analytic, approximate spacetime which accurately describes the dynamics of non-precessing, spinning black hole binaries during the inspiral phase of the relativistic merger process. This approximate solution of the vacuum Einstein's equations can be obtained by asymptotically matching perturbed Kerr solutions near the two black holes to a post-Newtonian metric valid far from the two black holes. This metric is then matched to a post-Minkowskian metric even farther out in the wave zone. The procedure of asymptotic matching is generalized to be valid on all spatial hypersurfaces, instead of a small group of initial hypersurfaces discussed in previous works. This metric is well suited for long term dynamical simulations of spinning black hole binary spacetimes prior to merger, such as studies of circumbinary gas accretion which requires hundreds of binary orbits.
Asymptotic Expressions for Changes in the Surface Co-Seismic Strain on a Homogeneous Sphere
Tang, He; Sun, Wenke
2017-01-01
SUMMARYIn the dislocation theory for a spherical Earth model, the computation of surface co-seismic deformations using straightforward numerical methods is time-consuming and may encounter a series of convergence problems, especially for the near-field deformations due to shallow earthquakes. This study proposes an asymptotic method to approximate changes in the co-seismic surface strain that are caused by an arbitrary point dislocation in a homogeneous sphere. The corresponding expressions are in analytical form and can overcome these difficulties without the numerical integration of differential equations and summations of infinite associated Legendre series in practical applications. Importantly, in contrast with the classical solution for a half-space Earth model, the asymptotic solution can reflect the effect of the Earth's curvature.
Positive Solutions of Advanced Differential Systems
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Josef Diblík
2013-01-01
graph coordinates of two (lower and upper auxiliary vector functions. This result is applied to scalar advanced linear differential equations. Criteria of existence of positive solutions are given and their asymptotic behavior is discussed.
Hahn, Y. K.
2014-12-01
The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree-Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model.
ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS
Institute of Scientific and Technical Information of China (English)
Zeng Luchuan
2006-01-01
This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Ban ach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.
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.
Mohamed, Firdawati binti; Karim, Mohamad Faisal bin Abd
2015-10-01
Modelling physical problems in mathematical form yields the governing equations that may be linear or nonlinear for known and unknown boundaries. The exact solution for those equations may or may not be obtained easily. Hence we seek an analytical approximation solution in terms of asymptotic expansion. In this study, we focus on a singular perturbation in second order ordinary differential equations. Solutions to several perturbed ordinary differential equations are obtained in terms of asymptotic expansion. The aim of this work is to find an approximate analytical solution using the classical method of matched asymptotic expansion (MMAE). The Mathematica computer algebra system is used to perform the algebraic computations. The details procedures will be discussed and the underlying concepts and principles of the MMAE will be clarified. Perturbation problem for linear equation that occurs at one boundary and two boundary layers are discussed. Approximate analytical solution obtained for both cases are illustrated by graph using selected parameter by showing the outer, inner and composite solution separately. Then, the composite solution will be compare to the exact solution to show their accuracy by graph. By comparison, MMAE is found to be one of the best methods to solve singular perturbation problems in second order ordinary differential equation since the results obtained are very close to the exact solution.
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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.
Asymptotic behavior of a stochastic non-autonomous predator-prey model with impulsive perturbations
Wu, Ruihua; Zou, Xiaoling; Wang, Ke
2015-03-01
This paper is concerned with a stochastic non-autonomous Lotka-Volterra predator-prey model with impulsive effects. The asymptotic properties are examined. Sufficient conditions for persistence and extinction are obtained, our results demonstrate that the impulse has important effects on the persistence and extinction of the species. We also show that the solution is stochastically ultimate bounded under some conditions. Finally, several simulation figures are introduced to confirm our main results.
ASYMPTOTIC BEHAVIOUR AND EXPONENTIAL STABILITY FOR THERMOELASTIC PROBLEM WITH LOCALIZED DAMPING
Institute of Scientific and Technical Information of China (English)
GAO Hong-jun; ZHAO Yu-juan
2006-01-01
A semi-linear thermoelastic problem with localized damping is considered,which is one of the most important mathematical models in material science. The existence and decays exponentially to zero of solution of this problem are obtained. Moreover,the existence of absorbing sets is achieved in the non-homogeneous case. The result indicates that the system which we studied here is asymptotic stability.
On the high-order topological asymptotic expansion for shape functions
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Maatoug Hassine
2016-04-01
Full Text Available This article concerns the topological sensitivity analysis for the Laplace operator with respect to the presence of a Dirichlet geometry perturbation. Two main results are presented in this work. In the first result we discuss the influence of the considered geometry perturbation on the Laplace solution. In the second result we study the high-order topological derivatives. We derive a high-order topological asymptotic expansion for a large class of shape functions.
Asymptotic behavior of elliptic boundary-value problems with some small coefficients
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Senoussi Guesmia
2008-04-01
Full Text Available The aim of this paper is to analyze the asymptotic behavior of the solutions to elliptic boundary-value problems where some coefficients become negligible on a cylindrical part of the domain. We show that the dimension of the space can be reduced and find estimates of the rate of convergence. Some applications to elliptic boundary-value problems on domains becoming unbounded are also considered.
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Bin-Chao Deng
2014-01-01
Full Text Available This paper aims to use a hybrid algorithm for finding a common element of a fixed point problem for a finite family of asymptotically nonexpansive mappings and the set solutions of mixed equilibrium problem in uniformly smooth and uniformly convex Banach space. Then, we prove some strong convergence theorems of the proposed hybrid algorithm to a common element of the above two sets under some suitable conditions.
Asymptotic Weighted-Periodicity of the Impulsive Parabolic Equation with Time Delay
Institute of Scientific and Technical Information of China (English)
Jin-liang Wang; Hui-feng Li
2007-01-01
The main aim of this paper is to investigate the effects of the impulse and time delay on a type of parabolic equations. In view of the characteristics of the equation, a particular iteration scheme is adopted.The results show that Under certain conditions on the coefficients of the equation and the impulse, the solution oscillates in a particular manner-called "asymptotic weighted-periodicity".
Lattice Quantum Gravity and Asymptotic Safety
Laiho, J; Coumbe, D; Du, D; Neelakanta, J T
2016-01-01
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 identify the target symmetry as the Hamiltonian canonical symmetry, which is closely related to, but not identical to, four-dimensional diffeomorphism invariance. After introducing and fine-tuning a non-trivial 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 tha...
Relaxing the parity conditions of asymptotically flat gravity
Compère, Geoffrey; Dehouck, François
2011-12-01
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 which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincaré transformations as well as supertranslations and logarithmic translations are associated with finite and conserved charges which represent the asymptotic symmetry group. Lorentz charges as well as logarithmic translations transform anomalously under a change of regulator. Lorentz charges are generally nonlinear functionals of the asymptotic fields but reduce to well-known linear expressions when parity conditions hold. We also define a covariant phase space of asymptotically flat spacetimes with parity conditions but without restrictions on the Weyl tensor. In this phase space, the anomaly plays classically no dynamical role. Supertranslations are pure gauge and the asymptotic symmetry group is the expected Poincaré group.
Asymptotic behavior of marginally trapped tubes in spherically symmetric black hole spacetimes
Williams, Catherine M.
We begin by reviewing some fundamental features of general relativity, then outline the mathematical definitions of black holes, trapped surfaces, and marginally trapped tubes, first in general terms, then rigorously in the context of spherical symmetry. We describe explicitly the reduction of Einstein's equation on a spherically symmetric 4-dimensional Lorentzian manifold to a system of partial differential equations on a subset of 2-dimensional Minkowski space. We discuss the asymptotic behavior of marginally trapped tubes in the Schwarzschild, Vaidya, and Reisner-Nordstrom solutions to Einstein's equations in spherical symmetry, as well as in Einstein-Maxwell-scalar field black hole spacetimes generated by evolving certain classes of asymptotically flat initial data. Our first main result gives conditions on a general stress-energy tensor Talphabeta in a spherically symmetric black hole spacetime that are sufficient to guarantee that the black hole will contain a marginally trapped tube which is eventually achronal, connected, and asymptotic to the event horizon. Here "general" means that the matter model is arbitrary, subject only to a certain positive energy condition. A certain matter field decay rate, known as Price law decay in the literature, is not required per se for this asymptotic result, but such decay does imply that the marginally trapped tube has finite length with respect to the induced metric. In our second main result, we give two separate applications of the first theorem to self-gravitating Higgs field spacetimes, one using weak Price law decay, the other certain strong smallness and monotonicity assumptions.
Asymptotic and stable proper ties of general stochastic functional differential equations
Institute of Scientific and Technical Information of China (English)
Xiaojing Zhong; Feiqi Deng
2014-01-01
The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.
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...
Shock solution for quasilinear singularly perturbed Robin problem
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The shock solution for the quasilinear singularly perturbed Robin problem is considered. Under suitable conditions and using the theory of differential inequalities the existence and asymptotic behavior of the shock solution for the original boundary value problems are studied.
ASYMPTOTIC EXPANSION AND ESTIMATE OF THE LANDAU CONSTANT
Institute of Scientific and Technical Information of China (English)
A.Eisinberg; G.Franzè; N.Salerno
2001-01-01
Properties of Landau constant are investigated in this note.A new representation in terms of a hypergeometric function 3F2 is given and a property defining the family of asymptotic sequences of Landau constant is formalized.Moreover,we give an other asymptotic expansion of Landau constant by using asymptotic expansion of the ratio of gamma functions in the sense of Poincaré due to Tricomi and Erdélyi.
Coulomb string tension, asymptotic string tension, and the gluon chain
Greensite, Jeff; Szczepaniak, Adam P.
2015-02-01
We compute, via numerical simulations, the nonperturbative Coulomb potential of pure SU(3) gauge theory in Coulomb gauge. We find that the Coulomb potential scales nicely in accordance with asymptotic freedom, that the Coulomb potential is linear in the infrared, and that the Coulomb string tension is about four times larger than the asymptotic string tension. We explain how it is possible that the asymptotic string tension can be lower than the Coulomb string tension by a factor of four.
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....
ASYMPTOTIC EXPANSIONS OF ZEROS FOR KRAWTCHOUK POLYNOMIALS WITH ERROR BOUNDS
Institute of Scientific and Technical Information of China (English)
ZHU Xiao-feng; LI Xiu-chun
2006-01-01
Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds are discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.
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.
Directory of Open Access Journals (Sweden)
Masato Shinjo
2015-12-01
Full Text Available The Hankel determinant appears in representations of solutions to several integrable systems. An asymptotic expansion of the Hankel determinant thus plays a key role in the investigation of asymptotic analysis of such integrable systems. This paper presents an asymptotic expansion formula of a certain Casorati determinant as an extension of the Hankel case. This Casorati determinant is then shown to be associated with the solution to the discrete hungry Lotka–Volterra (dhLV system, which is an integrable variant of the famous prey–predator model in mathematical biology. Finally, the asymptotic behavior of the dhLV system is clarified using the expansion formula for the Casorati determinant.
Modeling quasi-static poroelastic propagation using an asymptotic approach
Energy Technology Data Exchange (ETDEWEB)
Vasco, D.W.
2007-11-01
solution. Unfortunately, analytic solutions are only available for highly idealized conditions, such as a uniform (Rudnicki(1986)) or one-dimensional (Simon et al.(1984)Simon, Zienkiewicz, & Paul; Gajo & Mongiovi(1995); Wang & Kumpel(2003)) medium. In this paper I derive an asymptotic, semi-analytic solution for coupled deformation and flow. The approach is similar to trajectory- or ray-based methods used to model elastic and electromagnetic wave propagation (Aki & Richards(1980); Kline & Kay(1979); Kravtsov & Orlov(1990); Keller & Lewis(1995)) and, more recently, diffusive propagation (Virieux et al.(1994)Virieux, Flores-Luna, & Gibert; Vasco et al.(2000)Vasco, Karasaki, & Keers; Shapiro et al.(2002)Shapiro, Rothert, Rath, & Rindschwentner; Vasco(2007)). The asymptotic solution is valid in the presence of smoothly-varying, heterogeneous flow properties. The situation I am modeling is that of a formation with heterogeneous flow properties and uniform mechanical properties. The boundaries of the layer may vary arbitrary and can define discontinuities in both flow and mechanical properties. Thus, using the techniques presented here, it is possible to model a stack of irregular layers with differing mechanical properties. Within each layer the hydraulic conductivity and porosity can vary smoothly but with an arbitrarily large magnitude. The advantages of this approach are that it produces explicit, semi-analytic expressions for the arrival time and amplitude of the Biot slow and fast waves, expressions which are valid in a medium with heterogeneous properties. As shown here, the semi-analytic expressions provide insight into the nature of pressure and deformation signals recorded at an observation point. Finally, the technique requires considerably fewer computer resources than does a fully numerical treatment.
Introduction to Asymptotic Giant Branch Stars
El Eid, Mounib F.
2016-04-01
A brief introduction on the main characteristics of the asymptotic giant branch stars (briefly: AGB) is presented. We describe a link to observations and outline basic features of theoretical modeling of these important evolutionary phases of stars. The most important aspects of the AGB stars is not only because they are the progenitors of white dwarfs, but also they represent the site of almost half of the heavy element formation beyond iron in the galaxy. These elements and their isotopes are produced by the s-process nucleosynthesis, which is a neutron capture process competing with the β- radioactive decay. The neutron source is mainly due to the reaction 13C(α,n)16O reaction. It is still a challenging problem to obtain the right amount of 13 C that can lead to s-process abundances compatible with observation. Some ideas are presented in this context.
Dimensionally reduced gravity theories are asymptotically safe
Energy Technology Data Exchange (ETDEWEB)
Niedermaier, Max E-mail: max@phys.univ-tours.fr
2003-11-24
4D Einstein gravity coupled to scalars and abelian gauge fields in its 2-Killing vector reduction is shown to be quasi-renormalizable to all loop orders at the expense of introducing infinitely many essential couplings. The latter can be combined into one or two functions of the 'area radius' associated with the two Killing vectors. The renormalization flow of these couplings is governed by beta functionals expressible in closed form in terms of the (one coupling) beta function of a symmetric space sigma-model. Generically the matter coupled systems are asymptotically safe, that is the flow possesses a non-trivial UV stable fixed point at which the trace anomaly vanishes. The main exception is a minimal coupling of 4D Einstein gravity to massless free scalars, in which case the scalars decouple from gravity at the fixed point.
Entropy Production during Asymptotically Safe Inflation
Directory of Open Access Journals (Sweden)
Martin Reuter
2011-01-01
Full Text Available The Asymptotic Safety scenario predicts that the deep ultraviolet of Quantum Einstein Gravity is governed by a nontrivial renormalization group fixed point. Analyzing its implications for cosmology using renormalization group improved Einstein equations, we find that it can give rise to a phase of inflationary expansion in the early Universe. Inflation is a pure quantum effect here and requires no inflaton field. It is driven by the cosmological constant and ends automatically when the renormalization group evolution has reduced the vacuum energy to the level of the matter energy density. The quantum gravity effects also provide a natural mechanism for the generation of entropy. It could easily account for the entire entropy of the present Universe in the massless sector.
Asymptotic sampling formulae for Lambda-coalescents
Berestycki, Julien; Limic, Vlada
2012-01-01
We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy is given by a Lambda-coalescent. This allows us to derive an exact formula for the asymptotic behavior of the site and allele frequency spectrum and the number of segregating sites, as the sample size tends to infinity. Some of our results hold in the case of a general Lambda-coalescent that comes down from infinity, but we obtain more precise information under a regular variation assumption. In this case, we obtain results of independent interest for the time at which a mutation uniformly chosen at random was generated. This exhibits a phase transition at \\alpha=3/2, where \\alpha \\in(1,2) is the exponent of regular variation.
Universality and asymptotic scaling in drilling percolation
Grassberger, Peter
2017-01-01
We present simulations of a three-dimensional percolation model studied recently by K. J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016), 10.1103/PhysRevLett.116.055701], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems and higher statistics used in the present Rapid Communication, but we also find indications that the results do not yet represent the true asymptotic behavior. The model is obtained by replacing the isotropic holes in ordinary Bernoulli percolation by randomly placed and oriented cylinders, with the constraint that the cylinders are parallel to one of the three coordinate axes. We also speculate on possible generalizations.
Asymptotic Behavior of Excitable Cellular Automata
Durrett, R; Durrett, Richard; Griffeath, David
1993-01-01
Abstract: We study two families of excitable cellular automata known as the Greenberg-Hastings Model (GHM) and the Cyclic Cellular Automaton (CCA). Each family consists of local deterministic oscillating lattice dynamics, with parallel discrete-time updating, parametrized by the range of interaction, the "shape" of its neighbor set, threshold value for contact updating, and number of possible states per site. GHM and CCA are mathematically tractable prototypes for the spatially distributed periodic wave activity of so-called excitable media observed in diverse disciplines of experimental science. Earlier work by Fisch, Gravner, and Griffeath studied the ergodic behavior of these excitable cellular automata on Z^2, and identified two distinct (but closely-related) elaborate phase portraits as the parameters vary. In particular, they noted the emergence of asymptotic phase diagrams (and Euclidean dynamics) in a well-defined threshold-range scaling limit. In this study we present several rigorous results and som...
The asymptotic safety scenario in quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Saueressig, Frank [Institute of Physics, University of Mainz, D-55099 Mainz (Germany)
2011-07-01
Asymptotic safety offers the possibility that gravity constitutes a consistent and predictive quantum field theory within Wilsons generalized framework of renormalization. The key ingredient of this scenario is a non-trivial fixed point of the gravitational renormalization group flow which governs the UV behavior of the theory. The fixed point itself thereby guarantees the absence of unphysical UV divergences while its associated finite-dimensional UV-critical surface ensures the predictivity of the resulting quantum theory. This talk summarizes the evidence for the existence of such a fixed point, which emerged from the flow equation for the effective average action, the gravitational beta-functions in 2+{epsilon} dimensions, the 2-Killing vector reduction of the gravitational path-integral and lattice simulations. Possible phenomenological consequences are discussed in detail.
Hydrodynamics, resurgence and trans-asymptotics
Basar, Gokce
2015-01-01
The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exponentially suppressed at late times, analogous to the quasi-normal-modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semi-classical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these non-hydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with init...
Grassmann scalar fields and asymptotic freedom
Energy Technology Data Exchange (ETDEWEB)
Palumbo, F. [INFN, Laboratori Nazionali di Frascati, Rome (Italy)
1996-03-01
The authors extend previous results about scalar fields whose Fourier components are even elements of a Grassmann algebra with given index of nilpotency. Their main interest in particle physics is related to the possibility that they describe fermionic composites analogous to the Copper pairs of superconductivity. The authors evaluate the free propagators for arbitrary index of nilpotency and they investigate a {phi}{sup 4} model to one loop. Due to the nature of the integral over even Grassmann fields such as a model exists for repulsive as well as attractive self interaction. In the first case the {beta}-function is equal to that of the ordinary theory, while in the second one the model is asymptotically free. The bare mass has a peculiar dependence on the cutoff, being quadratically decreasing/increasing for attractive/repulsive self interaction.
Modeling of nanoplastic by asymptotic homogenization method
Institute of Scientific and Technical Information of China (English)
张为民; 何伟; 李亚; 张平; 张淳源
2008-01-01
The so-called nanoplastic is a new simple name for the polymer/layered silicate nanocomposite,which possesses excellent properties.The asymptotic homogenization method(AHM) was applied to determine numerically the effective elastic modulus of a two-phase nanoplastic with different particle aspect ratios,different ratios of elastic modulus of the effective particle to that of the matrix and different volume fractions.A simple representative volume element was proposed,which is assumed that the effective particles are uniform well-aligned and perfectly bonded in an isotropic matrix and have periodic structure.Some different theoretical models and the experimental results were compared.The numerical results are good in agreement with the experimental results.
Chiral fermions in asymptotically safe quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Meibohm, J. [Gothenburg University, Department of Physics, Goeteborg (Sweden); Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); Pawlowski, J.M. [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung mbH, ExtreMe Matter Institute EMMI, Darmstadt (Germany)
2016-05-15
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions. (orig.)
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.
Chiral fermions in asymptotically safe quantum gravity
Meibohm, Jan
2016-01-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck-scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works \\cite{Christiansen:2015rva, Meibohm:2015twa}, concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models, regardless of the number of fermion flavours. This suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Asymptotically thermal responses for smoothly switched detectors
Fewster, Christopher J; Louko, Jorma
2015-01-01
Thermal phenomena in quantum field theory can be detected with the aid of particle detectors coupled to quantum fields along stationary worldlines, by testing whether the response of such a detector satisfies the detailed balance version of the KMS condition at a constant temperature. This relation holds when the interaction between the field and the detector has infinite time duration. Operationally, however, detectors interact with fields for a finite amount of time, controlled by a switching function of compact support, and the KMS detailed balance condition cannot hold exactly for finite time interactions at arbitrarily large detector energy gap. In this large energy gap regime, we show that, for an adiabatically switched Rindler detector, the Unruh temperature emerges asymptotically after the detector and the field have interacted for a time that is polynomially long in the large energy. We comment on the significance of the adiabaticity assumption in this result.
The perturbed solution of sea-air oscillator for ENSO model
Institute of Scientific and Technical Information of China (English)
MO Jiaqi; LIN Wantao; ZHU Jiang
2004-01-01
A class of delayed oscillators and coupled systems to oscillation of El Nino-Southern Oscillation (ENSO) models are considered. Using the perturbed theory and other methods, the exact solution or asymptotic expansions of the solution for ENSO models is obtained and the asymptotic behavior of solution of corresponding problem is studied.
PERTURBED SOLUTION OF SEA-AIR OSCILLATOR FOR THE EL NI(N)O/LA NI(N)O-SOUTHERN OSCILLATION MECHANISM
Institute of Scientific and Technical Information of China (English)
Mo Jiaqi; Wang Hui; Lin Wantao
2005-01-01
A class of coupled system to oscillate of the El Nino/La Nino-Southern Oscillation (ENSO) mechanism is studied. Using the perturbed theory, the asymptotic expansions and asymptotic behavior of the solution for an ENSO model are obtained.
Radially Symmetric Solutions of
Directory of Open Access Journals (Sweden)
William C. Troy
2012-01-01
Full Text Available We investigate solutions of and focus on the regime and . Our advance is to develop a technique to efficiently classify the behavior of solutions on , their maximal positive interval of existence. Our approach is to transform the nonautonomous equation into an autonomous ODE. This reduces the problem to analyzing the phase plane of the autonomous equation. We prove the existence of new families of solutions of the equation and describe their asymptotic behavior. In the subcritical case there is a well-known closed-form singular solution, , such that as and as . Our advance is to prove the existence of a family of solutions of the subcritical case which satisfies for infinitely many values . At the critical value there is a continuum of positive singular solutions, and a continuum of sign changing singular solutions. In the supercritical regime we prove the existence of a family of “super singular” sign changing singular solutions.
Asymptotic symmetries of de Sitter space-time
Energy Technology Data Exchange (ETDEWEB)
Chrusciel, P.T. (Polska Akademia Nauk, Warsaw. Inst. Fizyki)
1981-01-01
The general form of the metric of an axially-symmetrical asymptotically de Sitter space-time fulfilling a radiation condition was found. Using the Bondi-Metzner method, the group of asymptotic symmetries of de Sitter space-time was found. The results obtained in this work agree only partially with Penrose's theory.
Numerical and asymptotic aspects of parabolic cylinder functions
Temme, N.M.
2000-01-01
Several 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 results are
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.
Asymptotic Hyperstability of Dynamic Systems with Point Delays
Directory of Open Access Journals (Sweden)
M. De la Sen
2005-01-01
Full Text Available It is proved that a linear time-invariant system with internal point delays is asymptotically hyperstable independent of the delays if an associate delay-free system is asymptotically hyperstable and the delayed dynamics are sufficiently small.
Error estimates in horocycle averages asymptotics: challenges from string theory
Cardella, M.A.
2010-01-01
For modular functions of rapid decay, a classical result connects the error estimate in their long horocycle average asymptotic to the Riemann hypothesis. We study similar asymptotics, for modular functions with not that mild growing conditions, such as of polynomial growth and of exponential growth
Small-x asymptotics of structure function $g_2$
Ermolaev, B I
1997-01-01
Nonsinglet structure function g_2(x) for deep inelastic scattering of a lepton on a constituent quark is calculated in the double logarithmic approximation at x<<1. Small-x asymptotics of g_2 is shown to have the same singular behaviour as asymptotics of the nonsinglet structure function g_1.
Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings
Institute of Scientific and Technical Information of China (English)
Wei Shi-long; Guo Wei-ping
2015-01-01
The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.
Global asymptotic stability of cellular neural networks with multiple delays
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Global asymptotic stability (GAS) is discussed for cellular neural networks (CNN) with multiple time delays. Several criteria are proposed to ascertain the uniqueness and global asymptotic stability of the equilibrium point for the CNN with delays. These criteria can eliminate the difference between the neuronal excitatory and inhibitory effects. Two examples are presented to demonstrate the effectiveness of the criteria.
LONG-TIME ASYMPTOTIC FOR THE DAMPED BOUSSINESQ EQUATION IN A CIRCLE
Institute of Scientific and Technical Information of China (English)
Zhang Yi; Lin Qun; Lai Shaoyong
2005-01-01
The first initial-boundary value problem for the following equation utt - a△utt - 2b△ut = α△3u - β△2u + △u + γ△(u2) in a unit circle is considered. The existence of strong solution is established in the space Co([0, ∞), HST(0, 1)), s ＜ 7/2, and the solutions are constructed in the form of series in the small parameter present in the initial conditions. For 5/2 ＜ s ＜ 7/2, the uniqueness is proved. The long-time asymptotics is obtained in the explicit form.
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.
2017-02-01
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 behavior of stochastic multi-group epidemic models with distributed delays
Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed
2017-02-01
In this paper, we introduce stochasticity into multi-group epidemic models with distributed delays and general kernel functions. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by using the method of stochastic Lyapunov functions, we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the stochastic system oscillates around the disease-free equilibrium E0, while if R0 > 1, the solution of the stochastic model fluctuates around the endemic equilibrium E∗. Moreover, we also establish sufficient conditions of these results.
Asymptotic analysis of a semilinear elliptic equation in highly oscillating thin domains
Pereira, Marcone Corrêa
2016-10-01
In this work we are interested in the asymptotic behavior of a family of solutions of a semilinear elliptic problem with homogeneous Neumann boundary condition defined in a two-dimensional bounded set which degenerates to the unit interval as a positive parameter {ɛ} goes to zero. Here we also allow that upper and lower boundaries from this singular region present highly oscillatory behavior with different orders and variable profile. Combining results from linear homogenization theory and nonlinear analyzes we get the limit problem showing upper and lower semicontinuity of the solutions at {ɛ=0}.