#### Sample records for asymptotic solutions

1. Numerical Asymptotic Solutions Of Differential Equations

Thurston, Gaylen A.

1992-01-01

Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

2. Solutions of special asymptotics to the Einstein constraint equations

Huang, Lan-Hsuan

2010-01-01

We construct solutions with prescribed asymptotics to the Einstein constraint equations using a cut-off technique. Moreover, we give various examples of vacuum asymptotically flat manifolds whose center of mass and angular momentum are ill-defined.

3. Numerical integration of asymptotic solutions of ordinary differential equations

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

4. On Approximate Asymptotic Solution of Integral Equations

Jikia, Vagner

2013-01-01

It is well known that multi-particle integral equations of collision theory, in general, are not compact. At the same time it has been shown that the motion of three and four particles is described with consistent integral equations. In particular, by using identical transformations of the kernel of the Lipman-Schwinger equation for certain classes of potentials Faddeev obtained Fredholm type integral equations for three-particle problems $[1]$. The motion of for bodies is described by equations of Yakubovsky and Alt-Grassberger-Sandhas-Khelashvili $[2.3]$, which are obtained as a result of two subsequent transpormations of the kernel of Lipman-Schwinger equation. in the case of $N>4$ the compactness of multi-particle equations has not been proven yet. In turn out that for sufficiently high energies the $N$-particle $\\left( {N \\ge 3} \\right)$ dynamic equations have correct asymptotic solutions satisfying unitary condition $[4]$. In present paper by using the Heitler formalism we obtain the results briefly sum...

5. Asymptotic Solutions of Serial Radial Fuel Shuffling

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.

6. An asymptotic solution of large-N QCD

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.

7. Asymptotic solutions of magnetohydrodynamics equations near the derivatives discontinuity lines

Asymptotic solutions of one-dimensional and scalar magnetohydrodynamics equations near the derivatives discontinuity lines have been discussed. The equations of magnetohydrodynamics for the cases of finite and infinite conductivities are formulated and the problem of eigenvalues and eigenvectors is solved. The so called transport equations which describe the behaviour of derivatives in solutions of the quasilinear equations have been used to find the asymptotic solutions of the magnetohydrodynamics equations. (S.B.)

8. ASYMPTOTIC SOLUTION TO NONLINEAR ECOLOGICAL REACTION DIFFUSION SYSTEM

2010-01-01

Nonlinear ecological species group singularly perturbed initial boundary value problems for reaction diffusion systems are considered. Under suitable conditions, using the theory of differential inequalities, the existence and asymptotic behavior of solution to initial boundary value problems are studied.

9. 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.

10. AN ASYMPTOTIC SOLUTION OF THE NONLINEAR REDUCED WAVE EQUATION

2001-01-01

This paper uses the boundary layer theory to obtain an asymptotic solution of the nonlinear educed wave equation. This solution is valid in the secular region where the geometrical optics result fails. However it agrees with the geometrical optics result when the field is away from the secular region. By using this solution the self-focusing length can also be obtained.

11. On the Number of Solutions to Asymptotic Plateau Problem

Coskunuzer, Baris

2005-01-01

We give a simple topological argument to show that the number of solutions of the asymptotic Plateau problem in hyperbolic space is generically unique. In particular, we show that the space of codimension-1 closed submanifolds of sphere at infinity, which bounds a unique absolutely area minimizing hypersurface in hyperbolic n-space, is dense in the space of all codimension-1 closed submanifolds at infinity. In dimension 3, we also prove that the set of uniqueness curves in asymptotic sphere f...

12. Asymptotic behaviour of solutions of fourth order Dirichlet problems

Dall'Aglio, Paolo

2000-01-01

The asymptotic behaviour of solutions to fourth order Dirichlet elliptic problems, on varying domains, is studied through the decomposition into a system of second order ones, which leads to relaxed formulations with the introduction of measure terms. This allows to salve a shape optimization problem for a simply supported thin plate.

13. Asymptotic behaviour of solutions to cable stayed bridge equations

Malík, Josef

2006-01-01

Roč. 317, - (2006), s. 146-162. ISSN 0022-247X R&D Projects: GA AV ČR(CZ) 1ET400300415 Institutional research plan: CEZ:AV0Z30860518 Keywords : cable stayed bridge * vertical and torsional oscillations * asymptotic behaviour of solutions Subject RIV: BA - General Mathematics Impact factor: 0.758, year: 2006

14. The Asymptotic Behavior for Numerical Solution of a Volterra Equation

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.

15. Solution branches for nonlinear problems with an asymptotic oscillation property

Lin Gong

2015-10-01

Full Text Available In this article we employ an oscillatory condition on the nonlinear term, to prove the existence of a connected component of solutions of a nonlinear problem, which bifurcates from infinity and asymptotically oscillates over an interval of parameter values. An interesting and immediate consequence of such oscillation property of the connected component is the existence of infinitely many solutions to the nonlinear problem for all parameter values in that interval.

16. 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.

17. 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.

18. An Asymptotic Solution for the Navier-Stokes Equation

Casuso Romate E.; Beckman J. E.

2009-01-01

We have used as the velocity field of a fluid the functional form derived in Casuso (2007), obtained by studying the origin of turbulence as a consequence of a new de- scription of the density distribution of matter as a modified discontinuous Dirichlet in- tegral. As an interesting result we have found that this functional form for velocities is a solution to the Navier-Stokes equation when considering asymptotic behaviour, i.e. for large values of time.

19. Asymptotics of Time Harmonic Solutions to a Thin Ferroelectric Model

Naïma Aïssa

2007-01-01

Full Text Available We introduce new model equations to describe the dynamics of the electric polarization in a ferroelectric material. We consider a thin cylinder representing the material with thickness ɛ and discuss the asymptotic behavior of the time harmonic solutions to the model when ɛ tends to 0. We obtain a reduced model settled in the cross-section of the cylinder describing the dynamics of the plane components of the polarization and electric fields.

20. Solute transport through porous media using asymptotic dispersivity

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.

1. Asymptotic shape of solutions to the perturbed simple pendulum problems

Tetsutaro Shibata

2007-05-01

Full Text Available We consider the positive solution of the perturbed simple pendulum problem $$u''(r + frac{N-1}{r}u'(r - g(u(t + lambda sin u(r = 0,$$ with $0 < r < R$, $u'(0 = u(R = 0$. To understand well the shape of the solution $u_lambda$ when $lambda gg 1$, we establish the leading and second terms of $Vert u_lambdaVert_q$ ($1 le q < infty$ with the estimate of third term as $lambda o infty$. We also obtain the asymptotic formula for $u_lambda'(R$ as $lambda o infty$.

2. Stokes Waves Revisited: Exact Solutions in the Asymptotic Limit

Davies, Megan

2016-01-01

Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic secular variation in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long standing theoretical insufficiency by invoking a compact exact $n$-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third ordered perturbative solution, that leads to a seamless extension to higher order (e.g. fifth order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desir...

3. Global, uniform, asymptotic wave-equation solutions for large wavenumbers

Klauder, John R.

1987-11-01

For each of a large class of linear wave equations-relevant, for example, to very general acoustical or optical propagation problems-we develop within a single expression a global, uniform, asymptotic solution for large wavenumbers (small wavelengths) based on coherentstate transformation techniques. Such techniques effectively separate the configuration-space field into its orientational components, and are thus analogous to a phase-space description of rays by their position and direction. The resultant coherent-state approximation offers distinct advantages over more traditional asymptotic approximations based on direct or Fourier transform techniques. In particular, coherent-state methods lead to an everywhere well-defined approximation independent of the complexity of the caustic structure, independent of whether there are a few or a vast number of relevant rays, or even in shadow regions where no conventional rays exist. For propagation in random media it is shown that coherent-state techniques also offer certain advantages. Approximations are developed for wave equations in an arbitrary number of space dimensions for single component fields as well as multicomponent fields that, for example, can account for backscattering. It is noteworthy that the coherentstate asymptotic approximation should lend itself to numerical studies as well.

4. Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case

Zhang JM; Cao LH

2010-01-01

We discuss in detail the error bounds for asymptotic solutions of second-order linear difference equation where and are integers, and have asymptotic expansions of the form , , for large values of , , and .

5. Asymptotic solution for EI Nino-southern oscillation of nonlinear model

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.

6. Asymptotic solution for heat convection-radiation equation

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.

7. Solution of internal erosion equations by asymptotic expansion

Dubujet P.

2012-07-01

Full Text Available One dimensional coupled soil internal erosion and consolidation equations are considered in this work for the special case of well determined sand and clay mixtures with a small proportion of clay phase. An enhanced modelling of the effect of erosion on elastic soil behavior was introduced through damage mechanics concepts. A modified erosion law was proposed. The erosion phenomenon taking place inside the soil was shown to act like a perturbation affecting the classical soil consolidation equation. This interpretation has enabled considering an asymptotic expansion of the coupled erosion consolidation equations in terms of a perturbation parameter linked to the maximum expected internal erosion. A robust analytical solution was obtained via direct integration of equations at order zero and an adequate finite difference scheme that was applied at order one.

8. Ground state solutions for asymptotically periodic Schrodinger equations with critical growth

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.

9. Exact solutions of dilaton gravity with (anti)-de Sitter asymptotics

Mignemi, S.

2009-01-01

We present a technique for obtaining spherically symmetric, asymptotically (anti)-de Sitter, black hole solutions of dilaton gravity with generic coupling to a Maxwell field, starting from exact asymptotically flat solutions and adding a suitable dilaton potential to the action.

10. Existence and Asymptotic Stability of Solutions for Hyperbolic Differential Inclusions with a Source Term

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.

11. Asymptotic Solution of the Theory of Shells Boundary Value Problem

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.

12. THE ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS TO THE MACROSCOPIC MODELS FOR SEMICONDUCTORS

2001-01-01

The authors study the asymptotic behavior of the smooth solutions to the Cauchy problems for two macroscopic models (hydrodynamic and drift-diffusion models) for semiconductors and the related relaxation limit problem. First, it is proved that the solutions to these two systems converge to the unique stationary solution time asymptotically without the smallness assumption on doping profile. Then, very sharp estimates on the smooth solutions, independent of the relaxation time, are obtained and used to establish the zero relaxation limit.

13. Asymptotic Behavior of Periodic Wave Solution to the Hirota-Satsuma Equation

WU Yong-Qi

2011-01-01

The one- and two-periodic wave solutions (or the Hirota-Satsuma (HS) equation are presented by using the Hirota derivative and Riemann theta function. The rigorous proofs on asymptotic behaviors of these two solutions are given such that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.%@@ The one- and two-periodic wave solutions for the Hirota-Satsuma (HS) equation are presented by using the Hirota derivative and Riemann theta function.The rigorous proofs on asymptotic behaviors of these two solutions are g/ven such that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.

14. ASYMPTOTIC SOLUTION OF ACTIVATOR INHIBITOR SYSTEMS FOR NONLINEAR REACTION DIFFUSION EQUATIONS

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.

15. Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations

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.

16. Asymptotic behaviour of the solutions of Schroedinger equation with impulse effect in a Banach space

The present paper studies the asymptotic behaviour of the solutions of linear homogeneous differential Schroedinger equation with impulse effect in a Banach space and finds a dependence between their asymptotic behaviour and the spectrum of the linear Hamiltonian operator. 6 refs

17. Asymptotically free scaling solutions in non-Abelian Higgs models

Gies, Holger; Zambelli, Luca

2015-07-01

We construct asymptotically free renormalization group trajectories for the generic non-Abelian Higgs model in four-dimensional spacetime. These ultraviolet-complete trajectories become visible by generalizing the renormalization/boundary conditions in the definition of the correlation functions of the theory. Though they are accessible in a controlled weak-coupling analysis, these trajectories originate from threshold phenomena which are missed in a conventional perturbative analysis relying on the deep Euclidean region. We identify a candidate three-parameter family of renormalization group trajectories interconnecting the asymptotically free ultraviolet regime with a Higgs phase in the low-energy limit. We provide estimates of their low-energy properties in the light of a possible application to the standard model Higgs sector. Finally, we find a two-parameter subclass of asymptotically free Coleman-Weinberg-type trajectories that do not suffer from a naturalness problem.

18. ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A CLASS OF REACTION DIFFUSION EQUATIONS

MoJiaqi; LinWantao; ZhuJiang

2004-01-01

A class of initial boundary value problems for the reaction diffusion equations are considered. The asymptotic behavior of solution for the problem is obtained using the theory of differential inequality.

19. An asymptotic formula for decreasing solutions to coupled nonlinear differential systems

Matucci, S.; Řehák, Pavel

2012-01-01

Roč. 22, č. 2 (2012), s. 67-75. ISSN 1064-9735 Institutional research plan: CEZ:AV0Z10190503 Keywords : system of quasilinear equation s * strongly decreasing solutions * asymptotic equivalence Subject RIV: BA - General Mathematics

20. Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation

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.

1. Asymptotic behavior of solutions to a class of linear non-autonomous neutral delay differential equations

Guiling Chen

2011-01-01

We study a class of linear non-autonomous neutral delay differential equations, and establish a criterion for the asymptotic behavior of their solutions, by using the corresponding characteristic equation.

2. Asymptotic analysis of fundamental solutions of Dirac operators on even dimensional Euclidean spaces

We analyze the short distance asymptotic behavior of some quantities formed out of fundamental solutions of Dirac operators on even dimensional Euclidean spaces with finite dimensional matrix-valued potentials. (orig.)

3. S-asymptotically -periodic Solutions of R-L Fractional Derivative-Integral Equation

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.

4. Asymptotic Stability and Balanced Growth Solution of the Singular Dynamic Input-Output System＊

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.

5. 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.

6. Self-similar cosmological solutions with dark energy. I. Formulation and asymptotic analysis

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 01). 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

7. EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTION OF DELAYED LOGISTIC EQUATION AND ITS ASYMPTOTIC BEHAVIOR

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.

8. Asymptotic stability of a decaying solution to the Keller-Segel system of degenerate type

Ogawa, Takayoshi

2008-01-01

We discuss the global behavior of the weak solution of the Keller-Segel system of degenerate type. Asymptotic stability of the Barenblatt-Pattle solution and its convergence rate for the decaying weak solution in $L^1({\\mathbb R}^n)$ is shown for the degenerated case $1 9. Non-asymptotically AdS/dS Solutions and Their Higher Dimensional Origins Cai, R G; Cai, Rong-Gen; Wang, Anzhong 2004-01-01 We look for and analyze in some details some exact solutions of Einstein-Maxwell-dilaton gravity with one or two Liouville-type dilaton potential(s) in an arbitrary dimension. Such a theory could be obtained by dimensionally reducing Einstein-Maxwell theory with a cosmological constant to a lower dimension. These (neutral/magnetic/electric charged) solutions can have a (two) black hole horizon(s), cosmological horizon, or a naked singularity. Black hole horizon or cosmological horizon of these solutions can be a hypersurface of positive, zero or negative constant curvature. These exact solutions are neither asymptotically flat, nor asymptotically AdS/dS. But some of them can be uplifted to a higher dimension, and those higher dimensional solutions are either asymptotically flat, or asymptotically AdS/dS with/without a compact constant curvature space. This observation is useful to better understand holographic properties of these non-asymptotically AdS/dS solutions. 10. General asymptotic solutions of the Einstein equations and phase transitions in quantum gravity Podolsky, D. 2007-01-01 We discuss generic properties of classical and quantum theories of gravity with a scalar field which are revealed at the vicinity of the cosmological singularity. When the potential of the scalar field is exponential and unbounded from below, the general solution of the Einstein equations has quasi-isotropic asymptotics near the singularity instead of the usual anisotropic Belinskii - Khalatnikov - Lifshitz (BKL) asymptotics. Depending on the strength of scalar field potential, there exist tw... 11. Asymptotic solution for the El Niño time delay sea—air oscillator model A sea—air oscillator model is studied using the time delay theory. The aim is to find an asymptotic solving method for the El Niño-southern oscillation (ENSO) model. Employing the perturbed method, an asymptotic solution of the corresponding problem is obtained. Thus we can obtain the prognoses of the sea surface temperature (SST) anomaly and the related physical quantities. (general) 12. Asymptotic solution of the non-isothermal Cahn-Hilliard system The non-isothermal Cahn-Hillard questions with a small parameter in the n-dimensional case (n = 2.3) are considered. The small parameter is proportional both to the relaxation time and to the linear scale of transition zone, so the large time process is examined. The asymptotic solution describing the free interface dynamics is constructed. As the small parameter tends to zero, the limiting solution satisfies the modified Stefan problem with corrected Gibbs-Thomson law. The justification of the asymptotic solution is proved. (author). 26 refs 13. THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE NONLINEAR HEAT-CONDUCTION EQUATION AND ITS APPLICATION 陈方年; 段志文 2001-01-01 In this paper the nonlinear heat-conduction equations with Dirichlet boundary condition and the nonlinear boundary condition are studied. The asymptotic behavior of the global of solution are analyzed by using Lyapuunov function.As its application, the approximate solutions are constructed. 14. Asymptotic Solution of Nonlinear Nonlocal Singularly Perturbed Reaction Diffusion Problems with Two Parameters Zai-ying ZHOU; Jia-qi MO 2012-01-01 A class of differential-difference reaction diffusion equations initial boundary problem with a small time delay is considered.Under suitable conditions and by using method of the stretched variable,the formal asymptotic solution is constructed. And then,by using the theory of differential inequalities the uniformly validity of solution is proved. 15. ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR A CLASS OF DELAY DIFFERENCE EQUATION ZhuHuiyan; HuangLihong 2005-01-01 We propose a class of delay difference equation with piecewise constant nonlinearity. Such a delay difference equation can be regarded as the discrete analog of a differential equation. The convergence of solutions and the existence of asymptotically stable periodic solutions are investigated for such a class of difference equation. 16. A class of asymptotic solution for the time delay wind field model of an ocean A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturbation method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-latitude wind field, and the physical meaning of the corresponding solution is also discussed. (general) 17. On Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem Luo, Tao; Xin, Zhouping; Zeng, Huihui 2015-01-01 This paper proves the nonlinear asymptotic stability of the Lane-Emden solutions for spherically symmetric motions of viscous gaseous stars if the adiabatic constant$\\gamma$lies in the stability range$(4/3, 2)$. It is shown that for small perturbations of a Lane-Emden solution with same mass, there exists a unique global (in time) strong solution to the vacuum free boundary problem of the compressible Navier-Stokes-Poisson system with spherical symmetry for viscous stars, and the solution ... 18. Asymptotic properties of solutions of some iterative functional inequalities Dobiesław Brydak; Bogdan Choczewski; Marek Czerni 2008-01-01 Continuous solutions of iterative linear inequalities of the first and second order are considered, belonging to a class \$$\\mathcal{F}_T\$$ of functions behaving at the origin as a prescribed function \$$T\$$. 19. A porous medium equation involving the infinity-Laplacian. Viscosity solutions and asymptotic behaviour Portilheiro, Manuel; Vazquez, Juan Luis 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 equa... 20. An exact, asymptotically flat, vacuum solution of Einstein's equations with closed timelike curves Solutions of Einstein's equations representing spacetimes with closed timelike curves (CTC) are commonly dismissed as unrealistic. Recently I published approximate solutions, containing CTC, which refer to ordinary sources. In this paper I present an exact vacuum solution, asymptotically flat, which contains CTC. It represents a massless rotating rod of finite length, and I give reasons why addition of mass would not abolish the CTC. I suggest that there is now an urgent need for a realistic physical interpretation of CTC in general relativity 1. Solution of the Falkner-Skan wedge flow by a revised optimal homotopy asymptotic method. Madaki, A G; Abdulhameed, M; Ali, M; Roslan, R 2016-01-01 In this paper, a revised optimal homotopy asymptotic method (OHAM) is applied to derive an explicit analytical solution of the Falkner-Skan wedge flow problem. The comparisons between the present study with the numerical solutions using (fourth order Runge-Kutta) scheme and with analytical solution using HPM-Padé of order [4/4] and order [13/13] show that the revised form of OHAM is an extremely effective analytical technique. PMID:27186477 2. Asymptotic behavior of a generalized Burgers' equation solutions on a finite interval The article is concerned with the study of asymptotic behavior of solutions of the Burgers equation and its generalizations with initial value — boundary problem on a finite interval, with constant boundary conditions. Since these equations take a dissipation into account, it is naturally to presuppose that any initial profile will evolve to an invariant time-independent solution with the same boundary values. Yet the answer happens to be slightly more complex. There are three possibilities: the initial profile may regularly decay to an invariant solution; or a Heaviside-type gap develops through a dispersive shock and multi-oscillations; or, exotically, an asymptotic limit is a 'frozen multi-oscillation' piecewise-differentiable solution, composed of different smooth invariant solutions 3. MULTIPLICITY OF SOLUTIONS TO ASYMPTOTICALLY LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL SYSTEM 2011-01-01 In this paper,we consider an asymptotically linear second-order ordinary differential system with Dirchlet boundary value conditions. Under some conditions,we show the multiplicity of solutions to the system by the Morse theory and an index theory. 4. ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS TO THE EULER-POISSON SYSTEM IN SEMICONDUCTORS 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. 5. The exact asymptotic behaviour of the unique solution to a singular Dirichlet problem Yu Jianning; Zhang Zhijun 2006-01-01 By Karamata regular variation theory, we show the existence and exact asymptotic behaviour of the unique classical solution near the boundary to a singular Dirichlet problem , , , , where is a bounded domain with smooth boundary in , , , for each and some ; and for some , which is nonnegative on and may be unbounded or singular on the boundary. 6. Error estimates for asymptotic solutions of dynamic equations on time scales 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]. 7. Symbolic computation of polyhomogeneous asymptotic solutions of Einstein's equations in null characteristic transport form Full text: Calculational methods and Reduce software are described for determining polyhomogeneous asymptotic expansions of solutions of Einstein's equations in null characteristic transport form. As an example, results concerning peeling of gravitational radiation in Null Quasi-Spherical (NQS) spacetimes are presented 8. Existence of radial positive solutions vanishing at infinity for asymptotically homogeneous systems Ali Djellit 2010-04-01 Full Text Available In this article we study elliptic systems called asymptotically homogeneous because their nonlinearities may not have polynomial growth. Using the Gidas-Spruck Blow-up method, we obtain a priori estimates, and then using Leray-Schauder topological degree theory, we obtain radial positive solutions vanishing at infinity. 9. Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations Řehák, Pavel 2013-01-01 Roč. 77, January 12 (2013), s. 45-58. ISSN 0362-546X Institutional support: RVO:67985840 Keywords : oncreasing solution * asymptotic formula * quasilinear system Subject RIV: BA - General Mathematics Impact factor: 1.612, year: 2013 http://www.sciencedirect.com/science/article/pii/S0362546X12003513 10. Asymptotic behavior of solutions to a degenerate quasilinear parabolic equation with a gradient term 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. 11. Asymptotically flat, stable black hole solutions in Einstein-Yang-Mills-Chern-Simons theory. Brihaye, Yves; Radu, Eugen; Tchrakian, D H 2011-02-18 We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein-Yang-Mills-Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations. PMID:21405506 12. TIME-ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR GENERAL NAVIER-STOKES EQUATIONS IN EVEN SPACE-DIMENSION 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. 13. Asymptotic stability of Riemann solutions in BGK approximations to certain multidimensional systems of conservation laws Frid, Hermano; Rendón, Leonardo We prove the asymptotic stability of nonplanar two-states Riemann solutions in BGK approximations of a class of multidimensional systems of conservation laws. The latter consists of systems whose flux-functions in different directions share a common complete system of Riemann invariants, the level surfaces of which are hyperplanes. The asymptotic stability to which the main result refers is in the sense of the convergence as t→∞ in Lloc1 of the space of directions ζ=x/t. That is, the solution z(t,x,ξ) of the perturbed Cauchy problem for the corresponding BGK system satisfies ∫z(t,tζ,ξ) dμ(ξ)→R(ζ) as t→∞, in Lloc1(R), where R(ζ) is the self-similar entropy solution of the two-states nonplanar Riemann problem for the system of conservation laws. 14. FLUID-SOLID COUPLING MATHEMATICAL MODEL OF CONTAMINANT TRANSPORT IN UNSATURATED ZONE AND ITS ASYMPTOTICAL SOLUTION 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. 15. Asymptotic behaviour of solutions for porous medium equation with periodic absorption Wang Yifu 2001-04-01 Full Text Available This paper is concerned with porous medium equation with periodic absorption. We are interested in the discussion of asymptotic behaviour of solutions of the first boundary value problem for the equation. In contrast to the equation without sources, we show that the solutions may not decay but may be Ã‚Â“attractedÃ‚Â” into any small neighborhood of the set of all nontrivial periodic solutions, as time tends to infinity. As a direct consequence, the null periodic solution is Ã‚Â“unstable.Ã‚Â” We have presented an accurate condition on the sources for solutions to have such a property. Whereas in other cases of the sources, the solutions might decay with power speed, which implies that the null periodic solution is Ã‚Â“stable.Ã‚Â” 16. Quasi-Periodic Solutions and Asymptotic Properties for the Isospectral BKP Equation In this paper, based on a Riemann theta function and Hirota's bilinear form, a straightforward way is presented to explicitly construct Riemann theta functions periodic waves solutions of the isospectral BKP equation. Once the bilinear form of an equation obtained, its periodic wave solutions can be directly obtained by means of an unified theta function formula and the way of obtaining the bilinear form is given in this paper. Based on this, the Riemann theta function periodic wave solutions and soliton solutions are presented. The relations between the periodic wave solutions and soliton solutions are strictly established and asymptotic behaviors of the Riemann theta function periodic waves are analyzed by a limiting procedure. The N-soliton solutions of isospectral BKP equation are presented with its detailed proof. (general) 17. Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. 2; Global Asymptotic Behavior of Time Discretizations; 2. Global Asymptotic Behavior of time Discretizations Yee, H. C.; Sweby, P. K. 1995-01-01 The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES. 18. Asymptotics of the nodal lines of solutions of 2-dimensional Schroedinger equations Results on nodal properties of L2 solutions of two-dimensional Schroedinger equations obtained in a previous paper are refined. The generally unbounded nodal set of ψ is investigated for r → ∞ and shown that in this limit the nodal set consists of non-intersecting nodal lines which look asymptotically either like straight lines or like branches of parabolas. (G.Q.) 19. Exact Solutions and Their Asymptotic Behaviors for the Averaged Generalized Fractional Elastic Models The generalized fractional elastic models govern the stochastic motion of several many-body systems, e.g., polymers, membranes, and growing interfaces. This paper focuses on the exact formulations and their asymptotic behaviors of the average of the solutions of the generalized fractional elastic models. So we directly analyze the Cauchy problem of the averaged generalized elastic model involving time fractional derivative and the convolution integral of a radially symmetric friction kernel with space fractional Laplacian. (general) 20. Asymptotic Convergence of the Solutions of a Dynamic Equation on Discrete Time Scales J. Diblík 2012-01-01 Full Text Available The paper investigates a dynamic equation Δy(tn=β(tn[y(tn−j−y(tn−k] for n→∞, where k and j are integers such that k>j≥0, on an arbitrary discrete time scale T:={tn} with tn∈ℝ, n∈ℤn0−k∞={n0−k,n0−k+1,…}, n0∈ℕ, tnasymptotic convergence of all solutions, the existence of an increasing and asymptotically convergent solution is sufficient. Therefore, the main attention is paid to the criteria for the existence of an increasing solution asymptotically convergent for n→∞. The results are presented as inequalities for the function β. Examples demonstrate that the criteria obtained are sharp in a sense. 1. Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments Cristóbal González 2013-01-01 Full Text Available In this paper, we propose the study of an integral equation, with deviating arguments, of the type y(t=ω(t-∫0∞‍f(t,s,y(γ1(s,…,y(γN(sds,t≥0, in the context of Banach spaces, with the intention of giving sufficient conditions that ensure the existence of solutions with the same asymptotic behavior at ∞ as ω(t. A similar equation, but requiring a little less restrictive hypotheses, is y(t=ω(t-∫0∞‍q(t,sF(s,y(γ1(s,…,y(γN(sds,t≥0. In the case of q(t,s=(t-s+, its solutions with asymptotic behavior given by ω(t yield solutions of the second order nonlinear abstract differential equation y''(t-ω''(t+F(t,y(γ1(t,…,y(γN(t=0, with the same asymptotic behavior at ∞ as ω(t. 2. Asymptotic solutions of Hartree equations concentrated near low-dimensional submanifolds. I. The model with logarithmic singularity We consider a two-dimensional model Schroedinger equation with logarithmic integral non-linearity. We find asymptotic expansions for its solutions (Airy polarons) that decay exponentially at the 'semi-infinity' and oscillate along one direction. These solutions may be regarded as new special functions, which are somewhat similar to the Airy function. We use them to construct global asymptotic solutions of Schroedinger equations with a small parameter and with integral non-linearity of Hartree type 3. Remarks on the asymptotically discretely self-similar solutions of the Navier-Stokes and the Euler equations Chae, Dongho 2013-01-01 We study scenarios of self-similar type blow-up for the incompressible Navier-Stokes and the Euler equations. The previous notions of the discretely (backward) self-similar solution and the asymptotically self-similar solution are generalized to the locally asymptotically discretely self-similar solution. We prove that there exists no such locally asymptotically discretely self-similar blow-up for the 3D Navier-Stokes equations if the blow-up profile is a time periodic function belonging to$...

4. A quasilinear delayed hyperbolic Navier-Stokes System : Global solution, asymptotics and relaxation limit

Schöwe, Alexander

2012-01-01

We consider a hyperbolic quasilinear fluid model, that arises from a delayed version for the constitutive law for the deformation tensor in the incompressible Navier-Stokes equation. We prove global existence of small solutions and asymptotic results in $\\R^{3}$ and the half-space with slip boundary conditions. Futhermore we show that this relaxed system is close to the classical Navier-Stokes equation in the sense that for small times $t$ the solutions converge in high Sobolev norms to the s...

5. An invariant asymptotic formula for solutions of second-order linear ODE's

Gingold, H.

1988-01-01

An invariant-matrix technique for the approximate solution of second-order ordinary differential equations (ODEs) of form y-double-prime = phi(x)y is developed analytically and demonstrated. A set of linear transformations for the companion matrix differential system is proposed; the diagonalization procedure employed in the final stage of the asymptotic decomposition is explained; and a scalar formulation of solutions for the ODEs is obtained. Several typical ODEs are analyzed, and it is shown that the Liouville-Green or WKB approximation is a special case of the present formula, which provides an approximation which is valid for the entire interval (0, infinity).

6. Asymptotic Behaviors of the Solutions to Scalar Viscous Conservation Laws on Bounded Interval

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.

7. Numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions

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.

8. Quasi-periodic wave solutions with asymptotic analysis to the Saweda-Kotera-Kadomtsev-Petviashvili equation

Xu, Mei-Juan; Tian, Shou-Fu; Tu, Jian-Min; Ma, Pan-Li; Zhang, Tian-Tian

2015-08-01

In this paper, the (2+1)-dimensional Saweda-Kotera-Kadomtsev-Petviashvili (SK-KP) equation is investigated, which can be used to describe certain situations from the fluid mechanics, ocean dynamics and plasma physics. With the aid of generalized Bell's polynomials, the Hirota's bilinear equation and N-soliton solution are explicitly constructed to the SK-KP equation, respectively. Based on the Riemann theta function, a direct and lucid way is presented to explicitly construct quasi-periodic wave solutions for the SK-KP equation. The two-periodic waves admit two independent spatial periods in two independent horizontal directions, which are a direct generalization of one-periodic waves. Finally, the relationships between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure.

9. Asymptotic Stability of Riemann Solutions for a Class of Multidimensional Systems of Conservation Laws with Viscosity

Frid, Hermano

2006-07-01

We prove the asymptotic stability of two-state nonplanar Riemann solutions for a class of multidimensional hyperbolic systems of conservation laws when the initial data are perturbed and viscosity is added. The class considered here is those systems whose flux functions in different directions share a common complete system of Riemann invariants, the level surfaces of which are hyperplanes. In particular, we obtain the uniqueness of the self-similar L ∞ entropy solution of the two-state nonplanar Riemann problem. The asymptotic stability to which the main result refers is in the sense of the convergence as t→∞ in L loc 1 of the space of directions ξ = x/t. That is, the solution u(t, x) of the perturbed problem satisfies u(t, t ξ)→R(ξ) as t→∞, in L loc 1(ℝ n ), where R(ξ) is the self-similar entropy solution of the corresponding two-state nonplanar Riemann problem.

10. Two reliable approaches involving Haar wavelet method and Optimal Homotopy Asymptotic method for the solution of fractional Fisher type equation

In this article, two reliable techniques, Haar wavelet method and optimal homotopy asymptotic method (OHAM) are presented. Haar wavelet method is an efficient numerical method for the numerical solution of fractional order partial differential equation like Fisher type. The approximate solutions of the fractional Fisher type equation are compared with the optimal homotopy asymptotic method as well as with the exact solutions. Comparisons between the obtained solutions with the exact solutions exhibit that both the featured methods are effective and efficient in solving nonlinear problems. However, the results indicate that OHAM provides more accurate value than Haar wavelet method

11. Heat Conduction in a Functionally Graded Plate Subjected to Finite Cooling/Heating Rates: An Asymptotic Solution

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.

12. Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus

Safa Dridi

2015-01-01

Full Text Available In this paper, we establish existence and asymptotic behavior of a positive classical solution to the following semilinear boundary value problem: \$-\\Delta u=q(xu^{\\sigma }\\;\\text{in}\\;\\Omega,\\quad u_{|\\partial\\Omega}=0.\$ Here \$$\\Omega\\ is an annulus in \\(\\mathbb{R}^{n}\\, \\(n\\geq 3\\, \\(\\sigma \\lt 1\\ and \\(q\\ is a positive function in \\(\\mathcal{C}_{loc}^{\\gamma }(\\Omega \\, \\(0\\lt\\gamma \\lt 1\\, satisfying some appropriate assumptions related to Karamata regular variation theory. Our arguments combine a method of sub- and supersolutions with Karamata regular variation theory. 13. A uniformly valid asymptotic solution of the surface wave problem due to underwater sources The two-dimensional linearized problem of surface waves in water of finite (or infinite) depth due to a stationary periodic source situated at a finite depth below the free surface, is considered. The formal solution of the problem is derived by using Laplace and Fourier transforms. A uniformly valid asymptotic expansion of the wave integral is obtained by using the method of Bleistein in the case of finite depth and that of Vander Waerden in the case of infinite depth. Physical interpretation of the results so derived is given. (author) 14. THE EXISTENCE AND GLOBAL OPTIMAL ASYMPTOTIC BEHAVIOUR OF LARGE SOLUTIONS FOR A SEMILINEAR ELLIPTIC PROBLEM 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. 15. 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. 16. Asymptotic behavior of positive solutions of a semilinear Dirichlet problem outside the unit ball Habib Maagli 2013-04-01 Full Text Available In this article, we are concerned with the existence, uniqueness and asymptotic behavior of a positive classical solution to the semilinear boundary-value problem displaylines{ -Delta u=a(xu^{sigma }quadext{in }D, cr lim _{|x|o 1}u(x= lim_{|x|o infty}u(x =0. } Here D is the complement of the closed unit ball of mathbb{R} ^n (ngeq 3, sigma<1 and the function a is a nonnegative function in C_{m loc}^{gamma}(D, 0 17. Optimal Homotopy Asymptotic Solution for Exothermic Reactions Model with Constant Heat Source in a Porous Medium Fazle Mabood 2015-01-01 Full Text Available The heat flow patterns profiles are required for heat transfer simulation in each type of the thermal insulation. The exothermic reaction models in porous medium can prescribe the problems in the form of nonlinear ordinary differential equations. In this research, the driving force model due to the temperature gradients is considered. A governing equation of the model is restricted into an energy balance equation that provides the temperature profile in conduction state with constant heat source on the steady state. The proposed optimal homotopy asymptotic method (OHAM is used to compute the solutions of the exothermic reactions equation. 18. Stability and Asymptotic Behavior of Periodic Traveling Wave Solutions of Viscous Conservation Laws in Several Dimensions Oh, Myunghyun; Zumbrun, Kevin 2010-04-01 Under natural spectral stability assumptions motivated by previous investigations of the associated spectral stability problem, we determine sharp L p estimates on the linearized solution operator about a multidimensional planar periodic wave of a system of conservation laws with viscosity, yielding linearized L 1 ∩ L p → L p stability for all {p ≥q 2} and dimensions {d ≥q 1} and nonlinear L 1 ∩ H s → L p ∩ H s stability and L 2-asymptotic behavior for {p≥q 2} and {d≥q 3} . The behavior can in general be rather complicated, involving both convective (that is, wave-like) and diffusive effects. 19. Asymptotic solution of a sea-air oscillator for ENSO mechanism Mo Jia-Qi; Lin Wan-Tao; Wang Hui 2007-01-01 The EI Ni(n)o/La Ni(n)a-Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this paper,a class of coupled system of the ENSO mechanism is considered.Based on a class of oscillator of ENSO model,the asymptotic solution of a corresponding problem is studied by employing the approximate method.It is proved from the results that the perturbation method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for the ENSO model. 20. Stability and asymptotic behavior of periodic traveling wave solutions of viscous conservation laws in several dimensions Oh, Myunghyun; Zumbrun, Kevin 2008-01-01 Under natural spectral stability assumptions motivated by previous investigations of the associated spectral stability problem, we determine sharp L^p estimates on the linearized solution operator about a multidimensional planar periodic wave of a system of conservation laws with viscosity, yielding linearized L^1\\cap L^p\\to L^p stability for all p \\ge 2 and dimensions d \\ge 1 and nonlinear L^1\\cap H^s\\to L^p\\cap H^s stability and L^2-asymptotic behavior for p\\ge 2 and d\\ge 3.... 1. Asymptotic solution of light transport problems in optically thick luminescent media We study light transport in optically thick luminescent random media. Using radiative transport theory for luminescent media and applying asymptotic and computational methods, a corrected diffusion approximation is derived with the associated boundary conditions and boundary layer solution. The accuracy of this approach is verified for a plane-parallel slab problem. In particular, the reduced system models accurately the effect of reabsorption. The impacts of varying the Stokes shift and using experimentally measured luminescence data are explored in detail. The results of this study have application to the design of luminescent solar concentrators, fluorescence medical imaging, and optical cooling using anti-Stokes fluorescence 2. Multi-layer asymptotic solution for wetting fronts in porous media with exponential moisture diffusivity 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... 3. Impedance of strip-traveling waves on an elastic half space - Asymptotic solution Crandall, S. H.; Nigam, A. K. 1973-01-01 The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution. 4. Asymptotic solutions for an electrically induced Freedericksz transition in a wedge of smectic C liquid crystal Theoretical work based on the Freedericksz transition in a wedge of smectic C liquid crystal is presented. Continuum theory is employed in order to mathematically model the two-way interaction between the anisotropic fluid and an applied electric field. Asymptotic methods are used to obtain concise and informative explicit solutions for limiting regimes where (a) the applied voltage is just above threshold, and (b) a high voltage is applied. As is anticipated, in the case of a small dielectric anisotropy, the solution reduces to that obtained when the two-way interaction is neglected. Nevertheless, at voltages close to threshold, this interaction can have a significant effect upon the director profile. Realistic material, geometry and field parameters are adopted in order to display these solutions. By comparing them with those obtained using a numerical method, a high degree of accuracy can be found within the above regimes 5. On the asymptotic of solutions of elliptic boundary value problems in domains with edges Solutions of elliptic boundary value problems in three-dimensional domains with edges may exhibit singularities. The usual procedure to study these singularities is by the application of the classical Mellin transformation or continuous Fourier transformation. In this paper, we show how the asymptotic behavior of solutions of elliptic boundary value problems in general three-dimensional domains with straight edges can be investigated by means of discrete Fourier transformation. We apply this approach to time-harmonic Maxwell's equations and prove that the singular solutions can fully be described in terms of Fourier series. The representation here can easily be used to approximate three-dimensional stress intensity factors associated with edge singularities. (author) 6. GLOBAL EXISTENCE AND ASYMPTOTICS BEHAVIOR OF SOLUTIONS FOR A RESONANT KLEIN-GORDON SYSTEM IN TWO SPACE DIMENSIONS XUE RUYING; FANG DAOYUAN 2005-01-01 The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that the asymptotic profile of the solution is quite different from that of the free solution. 7. 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. 8. Analytical Solutions, Moments, and Their Asymptotic Behaviors for the Time-Space Fractional Cable Equation Following the fractional cable equation established in the letter [B.I. Henry, T.A.M. Langlands, and S.L. Wearne, Phys. Rev. Lett. 100 (2008) 128103], we present the time-space fractional cable equation which describes the anomalous transport of electrodiffusion in nerve cells. The derivation is based on the generalized fractional Ohm's law; and the temporal memory effects and spatial-nonlocality are involved in the time-space fractional model. With the help of integral transform method we derive the analytical solutions expressed by the Green's function; the corresponding fractional moments are calculated; and their asymptotic behaviors are discussed. In addition, the explicit solutions of the considered model with two different external current injections are also presented. (general) 9. 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. 10. A third-order asymptotic solution of nonlinear standing water waves in Lagrangian coordinates Chen Yang-Yih; Hsu Hung-Chu 2009-01-01 Asymptotic solutions up to third-order which describe irrotational finite amplitude standing waves are derived in Lagrangian coordinates. The analytical Lagrangian solution that is uniformly valid for large times satisfies the irrotational condition and the pressure p = 0 at the free surface, which is in contrast with the Eulerian solution existing under a residual pressure at the free surface due to Taylor's series expansion. In the third-order Lagrangian approximation, the explicit parametric equation and the Lagrangian wave frequency of water particles could be obtained. In particular, the Lagrangian mean level of a particle motion that is a function of vertical label is found as a part of the solution which is different from that in an Eulerian description. The dynamic properties of nonlinear standing waves in water of a finite depth, including particle trajectory, surface profile and wave pressure are investigated. It is also shown that the Lagrangian solution is superior to an Eulerian solution of the same order for describing the wave shape and the kinematics above the mean water level. 11. On "scattering law" for Kasner parameters appearing in asymptotics of an exact S-brane solution Ivashchuk, V D 2007-01-01 Multidimensional cosmological model with scalar and form fields [1,2,3,4] is studied. An exact S-brane solution (either electric or magnetic one) in a model with l scalar fields and one antisymmetric form of rank m > 1 is considered. This solution is defined on a product manifold containing n Ricci-flat factor spaces M_1, ..., M_n. In the case when the kinetic term for scalar fields is positive definite we singled out a special solution governed by cosh-function. It is shown that this special solution has Kasner-like asymptotics in the limits \\tau \\to + 0 and \\tau \\to + \\infty, where \\tau is a synchronous time variable. A relation between two sets of Kasner parameters \\alpha_{\\infty} and \\alpha_0 is found. This relation, named as scattering law'' (SL) formula, is coinciding with the collision law'' (CL) formula obtained previously in Ref. [5] in a context of a billiard description of S-brane solutions near the singularity. A geometrical sense of SL formula is clarified: it is shown that SL transformation ... 12. Asymptotic behavior of solutions of the radial Schroedinger equation and applications to long-range potential scattering A brief statement of the problem of time-independent scattering theory introduces the notation to be used. Product integration is then used to discover asymptotic forms of solutions of the radial Schroedinger equation. Finally, these solutions are used to demonstrate existence of ordinary and modified Moller wave operators for a wide class of long-range radial potentials 13. Asymptotic solution for a class of sea-air oscillator model for El Nino-southern oscillation The El Nino-Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific Ocean-atmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model 14. Stability and asymptotic behavior of periodic traveling wave solutions of viscous conservation laws in several dimensions Oh, Myunghyun; 10.1007/s00205-009-0229-6 2009-01-01 Under natural spectral stability assumptions motivated by previous investigations of the associated spectral stability problem, we determine sharp L^p estimates on the linearized solution operator about a multidimensional planar periodic wave of a system of conservation laws with viscosity, yielding linearized L^1\\cap L^p\\to L^p stability for all p \\ge 2 and dimensions d \\ge 1 and nonlinear L^1\\cap H^s\\to L^p\\cap H^s stability and L^2-asymptotic behavior for p\\ge 2 and d\\ge 3. The behavior can in general be rather complicated, involving both convective (i.e., wave-like) and diffusive effects. 15. 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. 16. Elliptic boundary value problems on corner domains smoothness and asymptotics of solutions Dauge, Monique 1988-01-01 This research monograph focusses on a large class of variational elliptic problems with mixed boundary conditions on domains with various corner singularities, edges, polyhedral vertices, cracks, slits. In a natural functional framework (ordinary Sobolev Hilbert spaces) Fredholm and semi-Fredholm properties of induced operators are completely characterized. By specially choosing the classes of operators and domains and the functional spaces used, precise and general results may be obtained on the smoothness and asymptotics of solutions. A new type of characteristic condition is introduced which involves the spectrum of associated operator pencils and some ideals of polynomials satisfying some boundary conditions on cones. The methods involve many perturbation arguments and a new use of Mellin transform. Basic knowledge about BVP on smooth domains in Sobolev spaces is the main prerequisite to the understanding of this book. Readers interested in the general theory of corner domains will find here a new basic t... 17. Asymptotic expansion of the solution of the steady Stokes equation with variable viscosity in a two-dimensional tube structure Cardone, G; Panasenko, G P 2012-01-01 The Stokes equation with the varying viscosity is considered in a thin tube structure, i.e. in a connected union of thin rectangles with heights of order \\varepsilon<<1  and with bases of order 1 with smoothened boundary. An asymptotic expansion of the solution is constructed: it contains some Poiseuille type flows in the channels (rectangles) with some boundary layers correctors in the neighborhoods of the bifurcations of the channels. The estimates for the difference of the exact solution and its asymptotic approximation are proved. 18. An asymptotic solution of Large-N QCD, for the glueball and meson spectrum and the collinear S-matrix Bochicchio, Marco 2016-05-01 Employing a new class of string theories we construct a family of S -matrix amplitudes that factorize over linear Regge trajectories, and that are good candidates to be asymptotically free, i.e. to lead to asymptotically-free correlation functions working out the LS Z formulae the other way around. In particular, we propose a candidate for a string solution of QCD with NF massless quarks in the large-N 't Hooft limit, for the glueball and meson spectrum, and for certain S-matrix amplitudes in the collinear limit. The solution extends to massive quarks of equal mass. 19. Generalized linear Boltzmann equation, describing non-classical particle transport, and related asymptotic solutions for small mean free paths Rukolaine, Sergey A. 2016-05-01 In classical kinetic models a particle free path distribution is exponential, but this is more likely to be an exception than a rule. In this paper we derive a generalized linear Boltzmann equation (GLBE) for a general free path distribution in the framework of Alt's model. In the case that the free path distribution has at least first and second finite moments we construct an asymptotic solution to the initial value problem for the GLBE for small mean free paths. In the special case of the one-speed transport problem the asymptotic solution results in a diffusion approximation to the GLBE. 20. Asymptotics of self-similar solutions to coagulation equations with product kernel McLeod, J B; Velázquez, J J L 2011-01-01 We consider mass-conserving self-similar solutions for Smoluchowski's coagulation equation with kernel K(\\xi,\\eta)= (\\xi \\eta)^{\\lambda} with \\lambda \\in (0,1/2). It is known that such self-similar solutions g(x) satisfy that x^{-1+2\\lambda} g(x) is bounded above and below as x \\to 0. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function h(x)=h_{\\lambda} x^{-1+2\\lambda} g(x) in the limit \\lambda \\to 0. It turns out that h \\sim 1+ C x^{\\lambda/2} \\cos(\\sqrt{\\lambda} \\log x) as x \\to 0. As x becomes larger h develops peaks of height 1/\\lambda that are separated by large regions where h is small. Finally, h converges to zero exponentially fast as x \\to \\infty. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE. 1. On parametric domain for asymptotic stability with probability one of zero solution of linear Ito stochastic differential equations We describe a practical implementation for finding parametric domain for asymptotic stability with probability one of zero solution of linear Ito stochastic differential equations based on Korenevskij and Mitropolskij's sufficient condition and our sufficient conditions. Numerical results show that all of these sufficient conditions are crucial in the implementation. (author) 2. Asymptotic expansion of the solution of a Cauchy problem for singularly perturbed differential-operational nonlinear equation A formal asymptotic expansion of a solution of the initial problem for a singularly perturbed differential-operational nonlinear equation in a small parameter has been constructed in the critical case. Splash functions of and boundary functions have been estimated of found and assessment of the residual member of the expansion has been obtained 3. On existence and asymptotic behaviour of solutions of a fractional integral equation with linear modification of the argument Darwish, Mohamed Abdalla 2008-01-01 We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions. 4. Stochastic quasi-steady state approximations for asymptotic solutions of the chemical master equation Alarcón, Tomás [Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra (Barcelona) (Spain); Departament de Matemàtiques, Universitat Atonòma de Barcelona, 08193 Bellaterra (Barcelona) (Spain) 2014-05-14 In this paper, we propose two methods to carry out the quasi-steady state approximation in stochastic models of enzyme catalytic regulation, based on WKB asymptotics of the chemical master equation or of the corresponding partial differential equation for the generating function. The first of the methods we propose involves the development of multiscale generalisation of a WKB approximation of the solution of the master equation, where the separation of time scales is made explicit which allows us to apply the quasi-steady state approximation in a straightforward manner. To the lowest order, the multi-scale WKB method provides a quasi-steady state, Gaussian approximation of the probability distribution. The second method is based on the Hamilton-Jacobi representation of the stochastic process where, as predicted by large deviation theory, the solution of the partial differential equation for the corresponding characteristic function is given in terms of an effective action functional. The optimal transition paths between two states are then given by those paths that maximise the effective action. Such paths are the solutions of the Hamilton equations for the Hamiltonian associated to the effective action functional. The quasi-steady state approximation is applied to the Hamilton equations thus providing an approximation to the optimal transition paths and the transition time between two states. Using this approximation we predict that, unlike the mean-field quasi-steady approximation result, the rate of enzyme catalysis depends explicitly on the initial number of enzyme molecules. The accuracy and validity of our approximated results as well as that of our predictions regarding the behaviour of the stochastic enzyme catalytic models are verified by direct simulation of the stochastic model using Gillespie stochastic simulation algorithm. 5. Asymptotic behavior of solutions to Schr\\"odinger equations near an isolated singularity of the electromagnetic potential Felli, Veronica; Ferrero, Alberto; Terracini, Susanna 2008-01-01 Asymptotics of solutions to Schroedinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order -1. 6. 5D supersymmetric domain wall solution with active hyperscalars and mixed AdS/non-AdS asymptotics BellorIn, Jorge; Colonnello, Claudia, E-mail: jorgebellorin@usb.v, E-mail: ccolonnello@sinata.fis.usb.v [Departamento de Fisica, Universidad Simon BolIvar, Valle de Sartenejas, 1080-A Caracas (Venezuela, Bolivarian Republic of) 2011-05-21 We find a new supersymmetric 5D solution of N= 2 supergravity coupled to one hypermultiplet that depends only on the fifth dimension (the energy scale in a holographic context). In one asymptotic limit the domain wall approaches to the AdS{sub 5} form but in the other one it does not. Similarly, the hyperscalars, which are all proportional between them, go asymptotically to a critical point of the potential only in one direction. The quaternionic Kaehler manifold of the model is the H{sup 4} hyperboloid. We use the standard metric of H{sup 4} in an explicit conformally flat form with several arbitrary parameters. We argue that the holographic dual of the domain wall is a RG flow of a D = 4, N= 1 gauge theory acquiring a conformal supersymmetry at the IR limit, which corresponds to the AdS{sub 5} asymptotic limit. 7. Pressurized Poroelastic Inclusions: Short-term and Long-term Asymptotic Solutions Bedayat, Houman; Dahi Taleghani, Arash 2015-11-01 This paper provides semi-analytical, asymptotic short-term and long-term solutions for the volume change and corresponding leak-off volume of a fluid-saturated, three-dimensional poroelastic inclusion, considering fluid exchange with the surrounding poroelastic medium. Considering possibly different material properties and different fluid pressure of hydrocarbon-bearing formations or proppant-filled fractures in comparison to those of the surrounding geological structures, fractures or whole reservoirs can be regarded as inclusions. The problem-solving approach used in our study is inspired by the theory of inclusions and modal decomposition technique previously developed and used to solve several poroelasticity problems. Previous studies on the topic, however, have not incorporated the hydraulic communication between the inclusion and the surrounding medium; therefore, fluid pressure changes in the surrounding rock due to fluid pressure changes in the inclusion were ignored. An example of this problem would be a pressurized stationary fracture, which, depending on pressure, might have fluid exchange with the surroundings. Numerical examples considering inclusions with different aspect ratios and material properties are provided to better describe the significance of fluid exchange. 8. Asymptotic expansions of the solutions for nonautonomous systems and applications in quantum mechanics 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. 9. Non-CMC Solutions to the Einstein Constraint Equations on Asymptotically Euclidean Manifolds with Apparent Horizon Boundaries 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... 10. On the dynamics of internal waves propagating in stratified media of a variable depth: exact and asymptotic solutions Bulatov, Vitaly V 2012-01-01 The dynamics of internal waves in stratified media, such as the ocean or atmosphere, is highly dependent on the topography of their floor. A closed-form analytical solution can be derived only in cases when the water distribution density and the shape of the floor are modeled with specific functions. In a general case when the characteristics of stratified media and the boundary conditions are arbitrary, the dynamics of internal waves can be only approximated with numerical methods. However, numerical solutions do not describe the wave field qualitatively. At the same time, the need for a qualitative analysis of the far field of internal waves arises in studies applying remote sensing methods in space-based radar applications. In this case, the dynamics of internal waves can be described using asymptotic models. In this paper, we derive asymptotic solutions to the problem of characterizing the far field of internal gravity waves propagating in a stratified medium with a smoothly varying floor. 11. A Semi-Analytical Solution to Classic Yang—Mills Equations with Both Asymptotical Freedom and Confining Features It is well known that confinings and asymptotic freedom are properties of quantum chromo-dynamics (QCD). But hints of these features can also be observed at purely classic levels. For this purpose we need to find solutions to the colorly-sourceful Yang—Mills equations with both confining and asymptotic freedom features. We provide such a solution in this paper which at the near-source region is of serial form, while at the far-away region is approximately expressed through simple elementary functions. From the solution, we derive out a classically non-perturbative beta function describing the running of effective coupling constant, which is linear in the couplings both in the infrared and ultraviolet region. (physics of elementary particles and fields) 12. 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. 13. Asymptotic behaviour of the solution for the singular Lane-Emden-Fowler equation with nonlinear convection terms 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. 14. Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem with Degenerate Density Dependent Viscosities Luo, Tao; Xin, Zhouping; Zeng, Huihui 2015-01-01 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 \\gamma 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, w... 15. On Asymptotic Behavior and Blow-Up of Solutions for a Nonlinear Viscoelastic Petrovsky Equation with Positive Initial Energy Gang Li 2013-01-01 Full Text Available This paper deals with the initial boundary value problem for the nonlinear viscoelastic Petrovsky equation utt+Δ2u−∫0tgt−τΔ2ux,τdτ−Δut−Δutt+utm−1ut=up−1u. Under certain conditions on g and the assumption that masymptotic behavior and blow-up results for solutions with positive initial energy. 16. Asymptotic stability of solutions of nonlinear fractional differential equations of order 1 < α < 2 Ge, Fudong; KOU Chunhai 2015-01-01 This paper is mainly concerned with the asymptotic stability of the solutions of a class of nonlinear fractional differential equations of order 1 < α < 2 in a weighted Banach space. By first converting the nonlinear fractional differential equations to ordinary differential equations with a fractional integral perturbation, our main results are obtained via the Banach contraction mapping principle, which surely provides a new way to the stability analysis of nonlinear fractional differe... 17. Asymptotic solution for a class of sea-air oscillator model for El Ni(n)o-southern oscillation Mo Jia-Qi; Lin Wan-Tao 2008-01-01 The El Ni(n)o-Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions.In this paper,an asymptotic method of solving the nonlinear equation for the ENSO model is used.And based on a class of oscillator of ENSO model,the approximate solution of a corresponding problem is studied by employing the perturbation method.Firstly,an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced,Secondly,by using the perturbed method,the zeroth and first order asymptotic perturbed solutions are constructed.Finally,from the comparison of the values for a figure,it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy.And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model. 18. Percolation induced effects in two-dimensional coined quantum walks: analytic asymptotic solutions Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the long-time behaviour appears untreatable with direct numerical methods. We develop novel analytic methods based on the theory of random unitary operations which help us to determine explicitly the asymptotic dynamics of quantum walks on two-dimensional finite integer lattices with percolation. Based on this theory, we find new unexpected features of percolated walks like asymptotic position inhomogeneity or special directional symmetry breaking. (paper) 19. Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field We propose a general method for solving exactly the static field equations of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field. Our method starts from an ansatz for the scalar field profile, and determines, together with the metric functions, the corresponding form of the scalar self-interaction potential. Using this method we prove a new no-hair theorem about the existence of hairy black-hole and black-brane solutions and derive broad classes of static solutions with radial symmetry of the theory, which may play an important role in applications of the AdS/CFT correspondence to condensed matter and strongly coupled QFTs. These solutions include: (1) four- or generic (d+2)-dimensional solutions with planar, spherical or hyperbolic horizon topology; (2) solutions with anti-de Sitter, domain wall and Lifshitz asymptotics; (3) solutions interpolating between an anti-de Sitter spacetime in the asymptotic region and a domain wall or conformal Lifshitz spacetime in the near-horizon region. 20. Existence and Asymptotic Behavior of Global Solutions for a Class of Nonlinear Higher-Order Wave Equation Yaojun Ye 2010-01-01 Full Text Available The initial boundary value problem for a class of nonlinear higher-order wave equation with damping and source term utt+Au+a|ut|p−1ut=b|u|q−1u in a bounded domain is studied, where A=(−Δm, m≥1 is a nature number, and a,b>0 and p,q>1 are real numbers. The existence of global solutions for this problem is proved by constructing the stable sets and shows the asymptotic stability of the global solutions as time goes to infinity by applying the multiplier method. 1. Long-time asymptotics of solutions of the second initial-boundary value problem for the damped Boussinesq equation 1997-01-01 For the damped Boussinesq equation u_{tt}-2bu_{txx}= -\\alpha u_{xxxx}+ u_{xx}+\\beta(u^2)_{xx},x\\in(0,\\pi),t > 0;\\alpha,b = const > 0,\\beta = const\\in R^1 , the second initial-boundary value problem is considered with small initial data. Its classical solution is constructed in the form of a series in small parameter present in the initial conditions and the uniqueness of solutions is proved. The long-time asymptotics is obtained in the explicit form and the question of the blow up of the so... 2. Quasi-periodic wave solutions and asymptotic properties for a fifth-order Korteweg-de Vries type equation Qin, Chun-Yan; Tian, Shou-Fu; Wang, Xiu-Bin; Zhang, Tian-Tian 2016-07-01 Under investigation in this paper is a fifth-order Korteweg-de Vries type (fKdV-type) equation with time-dependent coefficients, which can be used to describe many nonlinear phenomena in fluid mechanics, ocean dynamics and plasma physics. The binary Bell polynomials are employed to find its Hirota’s bilinear formalism with an extra auxiliary variable, based on which its N-soliton solutions can be also directly derived. Furthermore, by considering multi-dimensional Riemann theta function, a lucid and straightforward generalization of the Hirota-Riemann method is presented to explicitly construct the multiperiodic wave solutions of the equation. Finally, the asymptotic properties of these periodic wave solutions are strictly analyzed to reveal the relationships between periodic wave solutions and soliton solutions. 3. Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations Řehák, Pavel -, - (2011), s. 986343. ISSN 1085-3375 Institutional research plan: CEZ:AV0Z10190503 Keywords : second order q-difference equation * asymptotic behavior * q-regularly varying sequence * Banach fixed point theorem Subject RIV: BA - General Mathematics Impact factor: 1.318, year: 2011 http://www.hindawi.com/journals/aaa/2011/986343/ 4. Integrable nonlinear coupled waves with an exact asymptotic singular solution in the context of laser–plasma interaction Latifi, A. 2016-07-01 A special case of coupled integrable nonlinear equations with a singular dispersion law is derived in the context of the small amplitude limit of general wave equations in a fluid-type warm electrons/cold ions plasma irradiated by a continuous laser beam. This model accounts for a nonlinear mode coupling of the electrostatic wave with the ion sound wave and is shown to be highly unstable. Its instability is understood as a continuous secular transfer of energy from the electrostatic wave to the ion sound wave through the ponderomotive force. The exact asymptotic solution of the system is constructed and shows that the dynamics of the energy transfer results in a singular asymptotic behavior of the ion sound wave, which explains the low penetration of the incident laser beam. 5. 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. 6. Asymptotically AdS_3 Solutions to Topologically Massive Gravity at Special Values of the Coupling Constants 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... 7. THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS OF THE REACTION DIFFUSION EQUATIONS IN A PART OF DOMAIN 刘其林; 莫嘉琪 2001-01-01 A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied. 8. Asymptotic solution of a weak nonlinear model for the mid-latitude stationary wind field of a two-layer barotropic ocean A weak nonlinear model of a two-layer barotropic ocean with Rayleigh dissipation is built. The analytic asymptotic solution is derived in the mid-latitude stationary wind field, and the physical meaning of the corresponding problem is discussed 9. Exact Half-BPS Flux Solutions in M-theory III Existence and rigidity of global solutions asymptotic to AdS4 x S7 D'Hoker, Eric; Gutperle, Michael; Krym, Darya 2009-01-01 The BPS equations in M-theory for solutions with 16 residual supersymmetries, SO(2,2)\\times SO(4)\\times SO(4) symmetry, and AdS_4 \\times S^7 asymptotics, were reduced in [arXiv:0806.0605] to a linear first order partial differential equation on a Riemann surface with boundary, subject to a non-trivial quadratic constraint. In the present paper, suitable regularity and boundary conditions are imposed for the existence of global solutions. We seek regular solutions with multiple distinct asymptotic AdS_4 \\times S^7 regions, but find that, remarkably, such solutions invariably reduce to multiple covers of the M-Janus solution found by the authors in [arXiv:0904.3313], suggesting rigidity of the half-BPS M-Janus solution. In particular, we prove analytically that no other smooth deformations away from the M-Janus solution exist, as such deformations invariably violate the quadratic constraint. These rigidity results are contrasted to the existence of half-BPS solutions with non-trivial 4-form fluxes and cha... 10. Analytical Solutions for the Equilibrium states of a Swollen Hydrogel Shell and an Extended Method of Matched Asymptotics 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... 11. Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method Resita Arum, Sari; A, Suparmi; C, Cari 2016-01-01 The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation, then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function. Project supported by the Higher Education Project (Grant No. 698/UN27.11/PN/2015). 12. Existence and asymptotic behavior of positive continuous solutions for a nonlinear elliptic system in the half space Sameh Turki 2012-01-01 This paper deals with the existence and the asymptotic behavior of positive continuous solutions of the nonlinear elliptic system \\(\\Delta u=p(x)u^{\\alpha}v^r\$$, \$$\\Delta v = q(x)u^s v^{\\beta}\$$, in the half space \$$\\mathbb{R}^n_+ :=\\{x=(x_1,..., x_n)\\in \\mathbb{R}^n : x_n \\gt 0\\}\$$, \$$n \\geq 2\$$, where \$$\\alpha, \\beta \\gt 1\$$ and \$$r, s \\geq 0\$$. The functions \$$p\$$ and \$$q\$$ are required to satisfy some appropriate conditions related to the Kato class \$$K^{\\infty}(\\mathbb{R}^n_+)\$$. Our app...

13. Existence and Asymptotic Behavior of Radially Symmetric Solutions to a Semilinear Hyperbolic System in Odd Space Dimensions

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.

14. Asymptotic solution of the low Reynolds-number flow between two co-axial cones of common apex

Y. K. Gayed

1984-12-01

Full Text Available The paper is concerned with the axi-symmetrlc, incompressible, steady, laminar and Newtonian flow between two, stationary, conical-boundaries, which exhibit a common apex but may include arbitrary angles. The flow pattern and pressure field are obtained by solving the pertinent Navier-Stokes' equations in the spherical coordinate system. The solution is presented in the form of an asymptotic series, which converges towards the creeping flow solution as a cross-sectional Reynolds-number tends to zero. The first term in the series, namely the creeping flow solution, is given in closed form; whereas, higher order terms contain functions which generally could only be expressed in infinite series form, or else evaluated numerically. Some of the results obtained for converging and diverging flows are displayed and they are demonstrated to be plausible and informative.

15. Quasi-periodic wave solutions and asymptotic properties to an extended Korteweg-de Vries equation from fluid dynamics

Xu, Mei-Juan; Tian, Shou-Fu; Tu, Jian-Min; Ma, Pan-Li; Zhang, Tian-Tian

2016-01-01

In this paper, an extended Korteweg-de Vries (eKdV) equation is investigated, which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. With the aid of the generalized Bell’s polynomials, the Hirota’s bilinear equation to the eKdV equation is succinctly constructed. Based on that, its solition solutions are directly obtained. By virtue of the Riemann theta function, a straightforward way is presented to explicitly construct Riemann theta function periodic wave solutions of the eKdV equation. Finally, the asymptotic behaviors of the Riemann theta function periodic waves are presented, which yields a relationship between the periodic waves and solition solutions by considering a limiting procedure.

16. Asymptotic Solutions of Detonation Propagation in a 2D Circular Arc.

Short, Mark; Meyer, Chad; Quirk, James

2015-11-01

The large pressure of the product gas generated by detonating high explosives causes lateral motion of the explosive at the material interface between the explosive and its confinement. In turn, this leads to streamline divergence and curvature of the detonation front (typically in a divergent fashion). The propagation of a detonation front in a given geometry depends on the amount of curvature generated. Here we describe an asymptotic analysis of detonation propagation in a 2D circular arc, examining dependencies of the motion on the size of the inner and outer arc radii, and the relation between the detonation velocity and curvature for different types of explosive.

17. The effect of boundaries on the asymptotic wavenumber of spiral wave solutions of the complex Ginzburg–Landau equation

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.

18. Asymptotics of physical solutions to the Lorentz-Dirac equation for a planar motion in constant electromagnetic fields

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.

19. Asymptotics of physical solutions to the Lorentz-Dirac equation for planar motion in constant electromagnetic fields

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.

20. Asymptotics of physical solutions to the Lorentz-Dirac equation for planar motion in constant electromagnetic fields

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.

1. Asymptotics of physical solutions to the Lorentz-Dirac equation for planar motion in constant electromagnetic fields.

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. PMID:21797506

2. The asymptotic behavior and self-similar solutions for disperse systems with coagulation and fragmentation

The paper analyzes the asymptotic behavior of disperse systems with coagulation and fragmentation of particles. The possible types of self-similarity regimes have been analyzed and conditions required for their existence have been set. The generalized approximation method (GA-method) numerical simulation is used to determine the actual behavior of moments Lα(t). The examples of GA-method application show its suitability for use in research problems. In general, the obtained results show that binary breakage coagulation is a wide and non-trivial scope for investigation. A number of regimes are represented such as steady state, coagulation winning, gelation, collapsing self-similarity and spectrum singularity. The existence of collapsing (accumulating in zero) self-similar spectra is illustrated in terms of a particular example of the coagulation kernel K(g, n) = gn and breakage rate f(g, n) = a. (paper)

3. ASYMPTOTIC METHOD OF TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR REACTION DIFFUSION EQUATION

Mo Jiaqi; Zhang Weijiang; He Ming

2007-01-01

In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.

4. Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions

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.

5. On Constructing the Asymptotic Solutions for Phase Transitions in a Slender Cylinder Composed of a Compressible Hyperelastic Material with Clamped End Conditions

Dai, Hui-Hui; Chen, Zhen

2008-01-01

In this paper, we study phase transitions in a slender circular cylinder composed of a compressible hyperelastic material with a non-convex strain energy function. We aim to construct the asymptotic solutions based on an axisymmetrical three-dimensional setting and use the results to describe the key features (in particular, instability phenomena) observed in the experiments by others. The difficult problem of the solution bifurcations of the governing nonlinear partial differential equations (PDE's) is solved through a novel approach. By using a methodology involving coupled series-asymptotic expansions, we derive the normal form equation of the original complicated system of nonlinear PDE's. By writing the normal form equation into a first-order dynamical system and with a phase-plane analysis, we manage to deduce the global bifurcation properties and to solve the boundary-value problem analytically. The asymptotic solutions (including post-bifurcation solutions) in terms of integrals are obtained. The engi...

6. Asymptotic behavior of solutions to wave equations with a memory condition at the boundary

Mauro de Lima Santos

2001-11-01

Full Text Available In this paper, we study the stability of solutions for wave equations whose boundary condition includes a integral that represents the memory effect. We show that the dissipation is strong enough to produce exponential decay of the solution, provided the relaxation function also decays exponentially. When the relaxation function decays polynomially, we show that the solution decays polynomially and with the same rate.

7. Asymptotic Behavior of Global Entropy Solutions for Nonstrictly Hyperbolic Systems with Linear Damping

Richard Alexander De la Cruz Guerrero

2014-01-01

Full Text Available We investigate the large time behavior of the global weak entropy solutions to the symmetric Keyfitz-Kranzer system with linear damping. It is proved that as t→∞ the entropy solutions tend to zero in the Lp norm.

An asymptotic solution is presented for the singular stress and strain fields near the tip of a steadily growing crack in an elastic-viscoplastic material under Mode III loading. By taking into account the experimental study made by Clark-Duwez in which no further increase of dynamic yield stress was observed when the strain rate exceeded the critical value, an intense strain region which behaves as an elastic-perfectly plastic material is introduced in the vicinity of the crack tip where this region is surrounded by the elastic-viscoplastic material. It is shown that the size of the intense strain region measured along the crack line is proportional to the velocity of the crack growth, and the singularity of the strain distribution near the crack tip is weakened by the intense strain region. (author)

9. Time-convolutionless mode-coupling theory near the glass transition-A recursion formula and its asymptotic solutions

Tokuyama, Michio

2015-07-01

The time-convolutionless mode-coupling theory (TMCT) equation for the intermediate scattering function fα(q , t) derived recently by the present author is analyzed mathematically and numerically, where α = c stands for a collective case and α = s for a self case. All the mathematical formulations discussed by Götze for the MCT equation are then shown to be directly applicable to the TMCT equation. Firstly, it is shown that similarly to MCT, there exists an ergodic to non-ergodic transition at a critical point, above which the long-time solution fα(q , t = ∞) , that is, the so-called Debye-Waller factor fα(q) , reduces to a non-zero value. The critical point is then shown to be definitely different from that of MCT. Secondly, it is also shown that there is a two-step relaxation process in a β stage near the critical point, which is described by the same two different power-law decays as those obtained in MCT. In order to discuss the asymptotic solutions, the TMCT equation is then transformed into a recursion formula for a cumulant function Kα(q , t) (= - ln [fα(q , t) ]) . By employing the same simplified model as that proposed by MCT, the simplified asymptotic recursion formula is then numerically solved for different temperatures under the initial conditions obtained from the simulations. Thus, it is discussed how the TMCT equation can describe the simulation results within the simplified model.

10. Filters and Ultrafilters as Approximate Solutions in the Attainability Problems with Constrains of Asymptotic Character

Chentsov, Alexander G

2010-01-01

Problems about attainability in topological spaces are considered. Some nonsequential version of the Warga approximate solutions is investigated: we use filters and ultrafilters of measurable spaces. Attraction sets are constructed.

11. 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.

12. Asymptotic Behavior of Solutions to the Liquid Crystals System in $\\mathbb{R}^3$

Dai, Mimi; Schonbek, Maria E

2011-01-01

In this paper we study the large time behavior of solutions to a nematic liquid crystals system in the whole space $\\mathbb{R}^3$. The fluid under consideration has constant density and small initial data.

13. On Oscillation and Asymptotic Behaviour of Solutions of Forced First Order Neutral Differential Equations

N Parhi; R N Rath

2001-08-01

In this paper, sufficient conditions have been obtained under which every solution of $[y(t)± y(t-)]'±\\mathcal{Q}(t)G(y(t-)) = f(t),\\quad t≥ 0$, oscillates or tends to zero or to ± ∞ as → ∞. Usually these conditions are stronger than \\begin{equation*}\\int\\limits_0^∞\\mathcal{Q}(t)dt=∞.\\tag{*}\\end{equation*} An example is given to show that the condition $(*)$ is not enough to arrive at the above conclusion. Existence of a positive (or negative) solution of $[y(t)-y(t-)]'+\\mathcal{Q}(t)G(y(t-))=f(t)$ is considered.

14. ASYMPTOTIC PROPERTY OF THE TIME-DEPENDENT SOLUTION OF A RELIABILITY MODEL

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.

15. Asymptotic behaviors of solutions for viscoelastic wave equation with space-time dependent damping term

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.

16. On the Problem of Asymptotic Positivity of Solutions for Dissipative Partial Differential Equations

Bartuccelli, M.V.; Gourley, S.A.

1999-01-01

The objective of this paper aims to prove positivity of solutions for the following semilinear partial differential equationu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $$u_t = - \\alpha u_{xxxx} + (u^2 )_{xx} + u(1 - u^2 )$$ \\end{document}....

17. Asymptotic representations and q-oscillator solutions of the graded Yang–Baxter equation related to Baxter Q-operators

Tsuboi, Zengo, E-mail: ztsuboi@yahoo.co.jp

2014-09-15

We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra U{sub q}(gl{sup ^}(M|N)). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of U{sub 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 also discuss an extension of these representations to the ones for contracted algebras of U{sub q}(gl{sup ^}(M|N)) by considering the action of renormalized generators of the other side of the Borel subalgebra. 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{sub q}(sl{sup ^}(2|1)) case [1] in part, and also give a cue for the operator realization of our Wronskian-like formulas on T- and Q-functions in [2,3].

18. UNIFORMLY VALID ASYMPTOTIC SOLUTIONS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE OF FOUR CLAMPED EDGES WITH VARIABLE THICKNESS

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.

19. 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.

20. A large time asymptotics for the solution of the Cauchy problem for the Novikov-Veselov equation at negative energy with non-singular scattering data

Kazeykina, Anna

2011-01-01

In the present paper we are concerned with the Novikov--Veselov equation at negative energy, i.e. with the $(2 + 1)$--dimensional analog of the KdV equation integrable by the method of inverse scattering for the two--dimensional Schr\\"odinger equation at negative energy. We show that the solution of the Cauchy problem for this equation with non--singular scattering data behaves asymptotically as $\\frac{\\const}{t^{3/4}}$ in the uniform norm at large times $t$. We also present some arguments which indicate that this asymptotics is optimal.

1. 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.

2. Global Well-Posedness and Large Time Asymptotic Behavior of Classical Solutions to the Compressible Navier-Stokes Equations with Vacuum

Li, Jing; Xin, Zhouping

2013-01-01

This paper concerns the global well-posedness and large time asymptotic behavior of strong and classical solutions to the Cauchy problem of the Navier-Stokes equations for viscous compressible barotropic flows in two or three spatial dimensions with vacuum as far field density. For strong and classical solutions, some a priori decay with rates (in large time) for both the pressure and the spatial gradient of the velocity field are obtained provided that the initial total energy is suitably {s...

3. Extending the range of validity of Fourier's law into the kinetic transport regime via asymptotic solution of the phonon Boltzmann transport equation

Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G.

2015-01-01

We derive the continuum equations and boundary conditions governing phonon-mediated heat transfer in the limit of small but finite mean free path from asymptotic solution of the linearized Boltzmann equation in the relaxation time approximation. Our approach uses the ratio of the mean free path to the characteristic system lengthscale, also known as the Knudsen number, as the expansion parameter to study the effects of boundaries on the breakdown of the Fourier descrition. We show that, in th...

4. Approximate solution of two-term fractional-order diffusion, wave-diffusion, and telegraph models arising in mathematical physics using optimal homotopy asymptotic method

Sarwar, S.; Rashidi, M. M.

2016-07-01

This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.

5. On asymptotics for difference equations

Rafei, M.

2012-01-01

In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the

6. Extending the range of validity of Fourier's law into the kinetic transport regime via asymptotic solution of the phonon Boltzmann transport equation

Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G.

2016-01-01

We derive the continuum equations and boundary conditions governing phonon-mediated heat transfer in the limit of a small but finite mean-free path from the asymptotic solution of the linearized Boltzmann equation in the relaxation time approximation. Our approach uses the ratio of the mean-free path to the characteristic system length scale, also known as the Knudsen number, as the expansion parameter to study the effects of boundaries on the breakdown of the Fourier description. We show that, in the bulk, the traditional heat conduction equation using Fourier's law as a constitutive relation is valid at least up to second order in the Knudsen number for steady problems and first order for time-dependent problems. However, this description does not hold within distances on the order of a few mean-free paths from the boundary; this breakdown is a result of kinetic effects that are always present in the boundary vicinity and require solution of a Boltzmann boundary layer problem to be determined. Matching the inner, boundary layer solution to the outer, bulk solution yields boundary conditions for the Fourier description as well as additive corrections in the form of universal kinetic boundary layers; both are found to be proportional to the bulk-solution gradients at the boundary and parametrized by the material model and the phonon-boundary interaction model (Boltzmann boundary condition). Our derivation shows that the traditional no-jump boundary condition for prescribed temperature boundaries and the no-flux boundary condition for diffusely reflecting boundaries are appropriate only to zeroth order in the Knudsen number; at higher order, boundary conditions are of the jump type. We illustrate the utility of the asymptotic solution procedure by demonstrating that it can be used to predict the Kapitza resistance (and temperature jump) associated with an interface between two materials. All results are validated via comparisons with low-variance deviational Monte

7. Perils of Asymptotics

A large part of physics consists of learning which asymptotic methods to apply where, yet physicists are not always taught asymptotics in a systematic way. Asymptotology is given using an example from aerodynamics, and a rent Phys. Rev. Letter Comment is used as a case study of one subtle way things can go wrong. It is shown that the application of local analysis leads to erroneous conclusions regarding the existence of a continuous spectrum in a simple test problem, showing that a global analysis must be used. The final section presents results on a more sophisticated example, namely the WKBJ solution of Mathieu equation. 13 refs., 2 figs

8. Fractal asymptotics

Dettmann, Carl P.

2002-01-01

Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions obtained from integrals and with a previous calculation of the electrostatic potential of exactly selfsimilar fractal charge distributions, suggests a remarkably accurate form for the late terms in the expansion, with parameters determined independently from the...

9. Solution of Augmented Systems from a Mixed-Hybrid Finite Element Discretization of the Potential Fluid Flow Problem: Asymptotic Rates of Convergence

Maryška, Jiří; Rozložník, Miroslav; Tůma, Miroslav

Bratislava : Vydavateĺstvo STU, 2000 - (Handlovičová, A.; Komorníková, M.; Mikula, K.; Ševčovič, D.), s. 100-109 ISBN 80-227-1391-0. [ALGORITMY 2000. Conference on Scientific Computing /15./. Podbanské (SK), 10.09.2000-15.09.2000] R&D Projects: GA ČR GA201/98/P108; GA ČR GA101/00/1035; GA ČR GA201/00/0080 Institutional research plan: AV0Z1030915 Keywords : potential fluid flow problem * mixed-hybrid finite element approximation * symmetric indefinite linear systems * iterative solution * Schur complement system * null-space method * conjugate gradient-type methods * asymptotic rate of convergence Subject RIV: BA - General Mathematics

10. Existence and Global Asymptotic Behavior of Positive Solutions for Nonlinear Fractional Dirichlet Problems on the Half-Line

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→0⁡t2-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.

11. Asymptotically Plane Wave Spacetimes and their Actions

Witt, Julian Le; Ross, Simon F.

2008-01-01

We propose a definition of asymptotically plane wave spacetimes in vacuum gravity in terms of the asymptotic falloff of the metric, and discuss the relation to previously constructed exact solutions. We construct a well-behaved action principle for such spacetimes, using the formalism developed by Mann and Marolf. We show that this action is finite on-shell and that the variational principle is well-defined for solutions of vacuum gravity satisfying our asymptotically plane wave falloff condi...

12. Exponential asymptotic stability for linear volterra equations

John A. D. Appleby

2000-01-01

This note studies the exponential asymptotic stability of the zero solution of the linear Volterra equation x˙ (t) = Ax(t) + t 0 K(t − s)x(s) ds by extending results in the paper of Murakami “Exponential Asymptotic Stability for scalar linear Volterra Equations”, Differential and Integral Equations, 4, 1991. In particular, when K isi ntegrable and has entries which do not change sign, and the equation has a uniformly asymptotically stable solution, exponential asympto...

13. 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...

14. Asymptotic behavior of the solution to the Cauchy problem for the Timoshenko system in thermoelasticity of type III

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).

15. Nontrivial Solutions for Schrodinger-Poisson Equations with Asymptotically Linear Terms%渐近线性薛定谔-泊松方程的非平凡解

刘传庆; 于涛; 栾世霞

2014-01-01

研究以下带有渐近线性薛定谔-泊松方程-Δu＋V（x）u＋（u）＝f（u），x ∈R3，-Δ＝u2， x ∈R3．｛（SP）该方程也被称为薛定谔-麦克斯韦方程的非平凡解的存在性，其中卡氏函数f（u）∈C（R，R）为超线性的．%We consider the existence of solutions of the Schrdinger-Poisson equation with asymptoti-cally linear term-Δu+V(x)u+(u)=f(u),x∈R3 ,-Δ=u2 , x∈R3 ,{(SP) this equation is also called Schrdinger-Maxwell equation,whereV,u∈C(R3 ,R).We also study the exist-ence of nontrivial solutions for Schrodinger-Poisson equation in a concrete condition,using mountain pass theorem and variational method.

16. Global well-posedness and asymptotic behavior of the solutions to non-classical thermo(visco)elastic models

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.

17. Upscaling transport of a reacting solute through a peridocially converging-diverging channel at pre-asymptotic times

Sund, Nicole L.; Bolster, Diogo; Dawson, Clint

2015-11-01

In this study we extend the Spatial Markov model, which has been successfully used to upscale conservative transport across a diverse range of porous media flows, to test if it can accurately upscale reactive transport, defined by a spatially heterogeneous first order degradation rate. We test the model in a well known highly simplified geometry, commonly considered as an idealized pore or fracture structure, a periodic channel with wavy boundaries. The edges of the flow domain have a layer through which there is no flow, but in which diffusion of a solute still occurs. Reactions are confined to this region. We demonstrate that the Spatial Markov model, an upscaled random walk model that enforces correlation between successive jumps, can reproduce breakthrough curves measured from microscale simulations that explicitly resolve all pertinent processes. We also demonstrate that a similar random walk model that does not enforce successive correlations is unable to reproduce all features of the measured breakthrough curves.

18. Asymptotic freedom, asymptotic flatness and cosmology

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 β-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, naturalness and other problems of such inflationary models

19. Existence of bounded uniformly continuous mild solutions on $\\Bbb{R}$ of evolution equations and their asymptotic behaviour

Basit, Bolis

2011-01-01

We prove that $u'= A u + \\phi$ has on $\\Bbb{R}$ a mild solution $u_{\\phi}\\in BUC (\\Bbb{R},X)$ (that is bounded and uniformly continuous), where $A$ is the generator of a $C_0$-semigroup on the Banach space ${X}$ with resolvent satisfying $||R(it,A)||= O(|t|^{-\\theta})$, $|t|\\to \\infty$, with some $\\theta > 1/2$, $\\phi\\in L^{\\infty} (\\Bbb{R},{X})$ and $i\\,sp (\\phi)\\cap \\sigma (A)=\\emptyset$. As a consequence it is shown that if ${\\Cal F}$ is the space of almost periodic, almost automorphic, bounded Levitan almost periodic or certain classes of recurrent functions and $\\phi$ as above is such that $M_h \\phi:=(1/h)\\int_0^h \\phi (\\cdot+s)\\, ds \\in \\Cal {F}$ for each $h >0$, then $u_{\\phi}\\in \\Cal {F}\\cap BUC (\\Bbb{R},X)$. These results seem new and strengthen several recent theorems.

20. Asymptotic perturbation theory of waves

Ostrovsky, Lev

2014-01-01

This book is an introduction to the perturbation theory for linear and nonlinear waves in dispersive and dissipative media. The main focus is on the direct asymptotic method which is based on the asymptotic expansion of the solution in series of one or more small parameters and demanding finiteness of the perturbations; this results in slow variation of the main-order solution. The method, which does not depend on integrability of basic equations, is applied to quasi-harmonic and non-harmonic periodic waves, as well as to localized waves such as solitons, kinks, and autowaves. The basic theor

1. On the Quasi-Periodic Wave Solutions and Asymptotic Analysis to a (3+1)-Dimensional Generalized Kadomtsev—Petviashvili Equation

In this paper, a (3+1)-dimensional generalized Kadomtsev—Petviashvili (GKP) equation is investigated, which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized Bell's polynomials, we succinctly construct the Hirota's bilinear equation to the GKP equation. By virtue of multidimensional Riemann theta functions, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta function periodic waves (quasi-periodic waves) for the (3+1)-dimensional GKP equation. Interestingly, the one-periodic waves are well-known cnoidal waves, which are considered as one-dimensional models of periodic waves. The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional that they have two independent spatial periods in two independent horizontal directions. Finally, we analyze asymptotic behavior of the multiperiodic periodic waves, and rigorously present the relationships between the periodic waves and soliton solutions by a limiting procedure. (general)

2. Asymptotically free SU(5) models

The behaviour of Yukawa and Higgs effective charges of the minimal SU(5) unification model is investigated. The model includes ν=3 (or more, up to ν=7) generations of quarks and leptons and, in addition, the 24-plet of heavy fermions. A number of solutions of the renorm-group equations are found, which reproduce the known data about quarks and leptons and, due to a special choice of the coupling constants at the unification point are asymptotically free in all charges. The requirement of the asymptotical freedom leads to some restrictions on the masses of particles and on their mixing angles

3. 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...

4. Asymptotically Safe Dark Matter

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....

5. Asymptotically hyperbolic black holes in Horava gravity

Janiszewski, Stefan

2014-01-01

Solutions of Hořava gravity that are asymptotically Lifshitz are explored. General near boundary expansions allow the calculation of the mass of these spacetimes via a Hamiltonian method. Both analytic and numeric solutions are studied which exhibit a causal boundary called the universal horizon, and are therefore black holes of the theory. The thermodynamics of an asymptotically Anti-de Sitter Hořava black hole are verified.

6. Asymptotic Behavior of Solutions of Second Order Self-Adjoint Difference Equations With Disturbing Terms%扰动二阶自共轭差分方程解的渐近性质

吴春青

2001-01-01

In this paper,we study the asymptotic properties of the solutions of the following equation (A) △(cn△zn)+anzn+1=f(n,zn,zn+1) and obtain several sufficient conditions which guarantee that (A) has the asymptotic properties limn→∞zn=α or limn→∞(zn)/(Cn)=β,where α,β are real numbers and Cn=nj=1c-1j.%研究了差分方程△(cn△zn)+anzn+1=f(n,zn,zn+1)的系数和扰动项满足的条件，使得方程有解具有性质limn→∞zn=α或limn→∞(zn)/(Cn)=β,这里α，β为实数，Cn=nj=1c-1j.

7. Universal asymptotic umbrella for hydraulic fracture modeling

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.

8. Asymptotic stability of Riemann waves for conservation laws

Chen, G.-Q.; Frid, H.; Marta

We are concerned with the asymptotic behavior of entropy solutions of conservation laws. A new notion about the asymptotic stability of Riemann solutions is introduced, and corresponding analytical frameworks are developed. The correlation between the asymptotic problem and many important topics in conservation laws and nonlinear analysis is recognized and analyzed, such as zero dissipation limits, uniqueness of entropy solutions, entropy analysis, and divergence-measure fields in L∞ . Then this theory is applied to understanding the asymptotic behavior of entropy solutions for many important systems of conservation laws.

9. Asymptotic analysis of mode Ⅰ propagating crack-tip field in a creeping material

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.

10. Asymptotics and Borel summability

Costin, Ovidiu

2008-01-01

Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers.To give a sense of how new methods are us

11. Asymptotics-based CI models for atoms:Properties, exact solution of a minimal model for Li to Ne, and application to atomic spectra

Friesecke, G.; Goddard, B.D.

2009-01-01

Configuration-interaction (CI) models are approximations to the electronic Schrödinger equation which are widely used for numerical electronic structure calculations in quantum chemistry. Based on our recent closed-form asymptotic results for the full atomic Schrödinger equation in the limit of fixed electron number and large nuclear charge [SIAM J. Math. Anal., 41 (2009), pp. 631-664], we introduce a class of CI models for atoms which reproduce, at fixed finite model dimension, the correct S...

12. On asymptotic extension dimension

Repovš, Dušan; Zarichnyi, Mykhailo

2011-01-01

The aim of this paper is to introduce an asymptotic counterpart of the extension dimension defined by Dranishnikov. The main result establishes a relation between the asymptotic extensional dimension of a proper metric space and extension dimension of its Higson corona.

13. ASYMPTOTIC QUANTIZATION OF PROBABILITY DISTRIBUTIONS

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.

14. Asymptotic Resource Usage Bounds

Albert E.; Alonso D.; Arenas P.; Genaim S.; Puebla G.

2009-01-01

When describing the resource usage of a program, it is usual to talk in asymptotic terms, such as the well-known “big O” notation, whereby we focus on the behaviour of the program for large input data and make a rough approximation by considering as equivalent programs whose resource usage grows at the same rate. Motivated by the existence of non-asymptotic resource usage analyzers, in this paper, we develop a novel transformation from a non-asymptotic cost function (which can be produced by ...

15. 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...

16. 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...

17. Asymptotic Entropy Bounds

Bousso, Raphael

2016-01-01

We show that known entropy bounds constrain the information carried off by radiation to null infinity. We consider distant, planar null hypersurfaces in asymptotically flat spacetime. Their focussing and area loss can be computed perturbatively on a Minkowski background, yielding entropy bounds in terms of the energy flux of the outgoing radiation. In the asymptotic limit, we obtain boundary versions of the Quantum Null Energy Condition, of the Generalized Second Law, and of the Quantum Bousso Bound.

18. Asymptotically Safe Dark Matter

Sannino, Francesco

2014-01-01

We introduce a new paradigm for dark matter interactions according to which the interaction strength is asymptotically safe. In models of this type, the interaction strength is small at low energies but increases at higher energies towards a finite constant value of the coupling. The net effect is to partially offset direct detection constraints without affecting thermal freeze-out at higher energies. High-energy collider and indirect annihilation searches are the primary ways to constrain or discover asymptotically safe dark matter.

19. Asymptotic analysis of the Nörlund and Stirling polynomials

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.

20. Quasi-extended asymptotic functions

The class F of ''quasi-extended asymptotic functions'' is introduced. It contains all extended asymptotic functions as well as some new asymptotic functions very similar to the Schwartz distributions. On the other hand, every two quasiextended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square delta2 of an asymptotic function delta similar to Dirac's delta-function, is constructed as an example

1. Asymptotic cyclic cohomology

Puschnigg, Michael

1996-01-01

The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes. The basic example is the approximation of topological K-theory by de Rham cohomology via the classical Chern character. A cyclic cohomology theory for operator algebras is developed in the book, based on Connes' work on noncommutative geometry. Asymptotic cyclic cohomology faithfully reflects the basic properties and features of operator K-theory. It thus becomes a natural target for a Chern character. The central result of the book is a general Grothendieck-Riemann-Roch theorem in noncommutative geometry with values in asymptotic cyclic homology. Besides this, the book contains numerous examples and calculations of asymptotic cyclic cohomology groups.

2. Introduction to asymptotics

Jones, D S

1997-01-01

Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hy

3. Asymptotics for spherical needlets

Baldi, P.; Kerkyacharian, G.; Marinucci, D.; Picard, D.

We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This property is used to derive CLT and functional CLT convergence results for polynomial functionals of the needlet coefficients: here the asymptotic theory is considered in the high-frequency sense. Our proposals emerge from strong empirical motivations, especially in connection with the analysis of cosmological data sets.

4. Asymptotic approaches to marginally stable resonators.

Nagel, J; Rogovin, D; Avizonis, P; Butts, R

1979-09-01

We present analytical solutions valid for large Fresnel number of the Fresnel-Kirchhoff integral equation for marginally stable resonators, for the specific case of flat circular mirrors. The asymptotic approaches used for curved mirrors have been extended to the waveguide region given by m diffraction around the mirror edge. PMID:19687883

5. Eigenvalue asymptotics for Dirac-Bessel operators

Hryniv, Rostyslav O.; Mykytyuk, Yaroslav V.

2016-06-01

In this paper, we establish the eigenvalue asymptotics for non-self-adjoint Dirac-Bessel operators on (0, 1) with arbitrary real angular momenta and square integrable potentials, which gives the first step for solution of the related inverse problem. The approach is based on a careful examination of the corresponding characteristic functions and their zero distribution.

6. Asymptotic safety guaranteed

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 ...

7. An asymptotical machine

Cristallini, Achille

2016-07-01

A new and intriguing machine may be obtained replacing the moving pulley of a gun tackle with a fixed point in the rope. Its most important feature is the asymptotic efficiency. Here we obtain a satisfactory description of this machine by means of vector calculus and elementary trigonometry. The mathematical model has been compared with experimental data and briefly discussed.

8. 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.

9. An Overview of Geometric Asymptotic Analysis of Continuous and Discrete Painlev\\'e Equations

Joshi, Nalini

2013-01-01

The classical Painlev\\'e equations are so well known that it may come as a surprise to learn that the asymptotic description of its solutions remains incomplete. The problem lies mainly with the description of families of solutions in the complex domain. Where asymptotic descriptions are known, they are stated in the literature as valid for large connected domains, which include movable poles of families of solutions. However, asymptotic analysis necessarily assumes that the solutions are bou...

10. Optimistic Agents are Asymptotically Optimal

Sunehag, Peter; Hutter, Marcus

2012-01-01

We use optimism to introduce generic asymptotically optimal reinforcement learning agents. They achieve, with an arbitrary finite or compact class of environments, asymptotically optimal behavior. Furthermore, in the finite deterministic case we provide finite error bounds.

11. The maximum drag reduction asymptote

Choueiri, George H.; Hof, Bjorn

2015-11-01

Addition of long chain polymers is one of the most efficient ways to reduce the drag of turbulent flows. Already very low concentration of polymers can lead to a substantial drag and upon further increase of the concentration the drag reduces until it reaches an empirically found limit, the so called maximum drag reduction (MDR) asymptote, which is independent of the type of polymer used. We here carry out a detailed experimental study of the approach to this asymptote for pipe flow. Particular attention is paid to the recently observed state of elasto-inertial turbulence (EIT) which has been reported to occur in polymer solutions at sufficiently high shear. Our results show that upon the approach to MDR Newtonian turbulence becomes marginalized (hibernation) and eventually completely disappears and is replaced by EIT. In particular, spectra of high Reynolds number MDR flows are compared to flows at high shear rates in small diameter tubes where EIT is found at Re Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n° [291734].

12. Global Existence and Large Time Asymptotic Behavior of Strong Solutions to the Cauchy Problem of 2D Density-Dependent Navier-Stokes Equations with Vacuum

Lv, Boqiang; Shi, Xiaoding; Zhong, Xin

2015-01-01

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D Cauchy problem of the density-dependent Navier-Stokes equations on the whole space $\\mathbb{R}^2$ admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compa...

13. Asymptotic Flatness in Rainbow Gravity

Hackett, Jonathan

2005-01-01

A construction of conformal infinity in null and spatial directions is constructed for the Rainbow-flat space-time corresponding to doubly special relativity. From this construction a definition of asymptotic DSRness is put forward which is compatible with the correspondence principle of Rainbow gravity. Furthermore a result equating asymptotically flat space-times with asymptotically DSR spacetimes is presented.

14. Coarse geometry and asymptotic dimension

Grave, Bernd

2006-01-01

We consider asymptotic dimension of coarse spaces. We analyse coarse structures induced by metrisable compactifications. We calculate asymptotic dimension of coarse cell complexes. We calculate the asymptotic dimension of certain negatively curved spaces, e.g. for complete, simply connected manifolds with bounded, strictly negative sectional curvature.

15. Another Asymptotic Notation : "Almost"

Mondal, Nabarun; Ghosh, Partha P.

2013-01-01

Asymptotic notations are heavily used while analysing runtimes of algorithms. Present paper argues that some of these usages are non trivial, therefore incurring errors in communication of ideas. After careful reconsidera- tion of the various existing notations a new notation is proposed. This notation has similarities with the other heavily used notations like Big-Oh, Big Theta, while being more accurate when describing the order relationship. It has been argued that this notation is more su...

16. Duality and asymptotic geometries

Boonstra, H J; Skenderis, K

1997-01-01

We consider a series of duality transformations that leads to a constant shift in the harmonic functions appearing in the description of a configuration of branes. This way, for several intersections of branes, we can relate the original brane configuration which is asymptotically flat to a geometry of the type $adS_k \\xx E^l \\xx S^m$. The implications of our results for supersymmetry enhancement, M(atrix) theory at finite N, and for supergravity theories in diverse dimensions are discussed.

17. Asymptotically Lifshitz Brane-World Black Holes

Ranjbar, Arash; Shahidi, Shahab

2012-01-01

We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We show that although the Lifshitz space-time cannot be considered as a vacuum solution of the RSII brane-world, the asymptotically Lifshitz solution can. We then study the thermodynamical behavior of such asymptotically Lifshitz black holes. It is shown that the condition on the positivity of entropy imposes an upper bound on the critical exponent $z$. This maximum value of $z$ corresponds to a positive infinite entropy as long as the temperature is kept positive. The stability and phase transition for different spatial topologies are also discussed.

18. Asymptotic linear stability of solitary water waves

Pego, Robert L.; Sun, Shu-Ming

2010-01-01

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 a...

19. Vacuum polarization in asymptotically Lifshitz black holes

Quinta, Gonçalo M.(Centro Multidisciplinar de Astrofísica – CENTRA, Departamento de Física, Instituto Superior Técnico – IST, Universidade de Lisboa – UL, Avenida Rovisco Pais 1, Lisboa, 1049-001, Portugal); Flachi, Antonino; 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 th...

20. Asymptotic Symmetries from finite boxes

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.

1. Asymptotic symmetries from finite boxes

2016-01-01

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 Poincaré 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 AdS3 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.

2. Asymptotic analysis, Working Note No. 1: Basic concepts and definitions

Garbey, M. [Universite Claude Bernard Lyon 1, 69 - Villeurbanne (France). Lab. d`Analyse Numerique; Kaper, H.G. [Argonne National Lab., IL (United States)

1993-07-01

In this note we introduce the basic concepts of asymptotic analysis. After some comments of historical interest we begin by defining the order relations O, o, and O{sup {number_sign}}, which enable us to compare the asymptotic behavior of functions of a small positive parameter {epsilon} as {epsilon} {down_arrow} 0. Next, we introduce order functions, asymptotic sequences of order functions and more general gauge sets of order functions and define the concepts of an asymptotic approximation and an asymptotic expansion with respect to a given gauge set. This string of definitions culminates in the introduction of the concept of a regular asymptotic expansion, also known as a Poincare expansion, of a function f : (0, {epsilon}{sub o}) {yields} X, where X is a normed vector space of functions defined on a domain D {epsilon} R{sup N}. We conclude the note with the asymptotic analysis of an initial value problem whose solution is obtained in the form of a regular asymptotic expansion.

3. Phase Spaces for asymptotically de Sitter Cosmologies

Kelly, William R

2012-01-01

We construct two types of phase spaces for asymptotically de Sitter Einstein-Hilbert gravity in each spacetime dimension $d \\ge 3$. One type contains solutions asymptotic to the expanding spatially-flat ($k=0$) cosmological patch of de Sitter space while the other is asymptotic to the expanding hyperbolic $(k=-1)$ patch. Each phase space has a non-trivial asymptotic symmetry group (ASG) which includes the isometry group of the corresponding de Sitter patch. For $d=3$ and $k=-1$ our ASG also contains additional generators and leads to a Virasoro algebra with vanishing central charge. Furthermore, we identify an interesting algebra (even larger than the ASG) containing two Virasoro algebras related by a reality condition and having imaginary central charges $\\pm i \\frac{3\\ell}{2G}$. On the appropriate phase spaces, our charges agree with those obtained previously using dS/CFT methods. Thus we provide a sense in which (some of) the dS/CFT charges act on a well-defined phase space. Along the way we show that, des...

4. Regular Variation and Smile Asymptotics

Benaim, Shalom; Friz, Peter

2006-01-01

We consider risk-neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated moment formula. The theory of regular variation provides the ideal mathematical framework to formulate and prove such results. The practical value of our formulae comes from the vast literature on tail asymptotics and our conditions are often seen to be true by simple inspection of known results.

5. Asymptotics of the instantons of Painleve I

Garoufalidis, Stavros; Kapaev, Andrei; Marino, Marcos

2010-01-01

The 0-instanton solution of Painlev\\'e I is a sequence $(u_{n,0})$ of complex numbers which appears universally in many enumerative problems in algebraic geometry, graph theory, matrix models and 2-dimensional quantum gravity. The asymptotics of the 0-instanton $(u_{n,0})$ for large $n$ were obtained by the third author using the Riemann-Hilbert approach. For $k=0,1,2,...$, the $k$-instanton solution of Painlev\\'e I is a doubly-indexed sequence $(u_{n,k})$ of complex numbers that satisfies an explicit quadratic non-linear recursion relation. The goal of the paper is three-fold: (a) to compute the asymptotics of the 1-instanton sequence $(u_{n,1})$ to all orders in $1/n$ by using the Riemann-Hilbert method, (b) to present formulas for the asymptotics of $(u_{n,k})$ for fixed $k$ and to all orders in $1/n$ using resurgent analysis, and (c) to confirm numerically the predictions of resurgent analysis. We point out that the instanton solutions display a new type of Stokes behavior, induced from the tritronqu\\'ee ...

6. Extended asymptotic functions - some examples

Several examples of extended asymptotic functions are exposed. These examples will illustrate the notions introduced in another paper but at the same time they have a significance as realizations of some Schwartz disctibutions: delta(x), H(x), P(1/xsup(n)), etc. The important thing is that the asymptotic functions of these examples (which, on their part, are realizations of the above-mentioned distributions) can be multiplied in the class of the asymptotic functions as opposed to the theory of Schwartz distributions. Some properties of the set of all extended asymptotic functions are considered which are essential for the next step of this approach

7. Asymptotic stability of solitons for the Benjamin-Ono equation

Kenig, C. E.; Martel, Y.

2008-01-01

In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of [Martel, Y. and Merle, F.: Asymptotic stability of solitons for subcritical generalized KdV equations. Arch. Ration. Mech. Anal. 157 (2001), 219-254], [Martel, Y. and Merle, F.: Asymptotic stability of solitons of the gKdV equations wit...

8. Research on temperature profiles of honeycomb regenerator with asymptotic analysis

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.

9. Asymptotic properties of difference schemes of maximum odd accuracy

The asymptotic estimates of the difference Green function and difference step function are obtained for difference schemes of maximum odd accuracy (2k-1), k = 0(1nh-1), h is step of the net. The problem is reduced to construction of asymptotic expansion of some integrals. Principal estimates are obtained by application of the saddle point method. The saddle points determining asymptotic expansion are situated near finite radius circle and they become close to each other when h → 0. These asymptotic estimates give that the numerical solution convergences to the solution of the continuous problem with the rate 0(hsup(N+α) 1n1nh-1). The width of zone over which an isolated discontinuity spreads out is proportional to 1nh-1

10. Asymptotic Efficiency in OLEDS

Nelson, Mitchell C

2015-01-01

Asymptotic efficiency (high output without droop) was recently reported for OLEDS in which a thin emitter layer is located at the anti-node in a resonant microcavity. Here we extend our theoretical analysis to treat multi-mode devices with isotropic emitter orientation. We recover our efficiency equations for the limiting cases with an isotropic emitter layer located at the anti-node where output is linear in current, and for an isotropic emitter located at the node where output can exhibit second order losses with an overall efficiency coefficient that depends on loss terms in competition with a cavity factor. Additional scenarios are described where output is driven by spontaneous emission, or mixed spontaneous and stimulated emission, with stimulated emission present in a loss mode, potentially resulting in cavity driven droop or output clamping, and where the emitter layer is a host-guest system.