Relaxing the parity conditions of asymptotically flat gravity
Compère, Geoffrey; Dehouck, François
2011-12-01
Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counterterm which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincaré transformations as well as supertranslations and logarithmic translations are associated with finite and conserved charges which represent the asymptotic symmetry group. Lorentz charges as well as logarithmic translations transform anomalously under a change of regulator. Lorentz charges are generally nonlinear functionals of the asymptotic fields but reduce to well-known linear expressions when parity conditions hold. We also define a covariant phase space of asymptotically flat spacetimes with parity conditions but without restrictions on the Weyl tensor. In this phase space, the anomaly plays classically no dynamical role. Supertranslations are pure gauge and the asymptotic symmetry group is the expected Poincaré group.
Relaxing the Parity Conditions of Asymptotically Flat Gravity
Compère, Geoffrey; Dehouck, François
2011-01-01
Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counter-term which breaks asymptotic translation, supertranslation and logarithmic translation invariance. Poincar\\'e transformations as well as supertranslations and logarithmic translations are associated wi...
Relaxing the parity conditions of asymptotically flat gravity
Compère, G.; Dehouck, F.
2011-01-01
Four-dimensional asymptotically flat spacetimes at spatial infinity are defined from first principles without imposing parity conditions or restrictions on the Weyl tensor. The Einstein-Hilbert action is shown to be a correct variational principle when it is supplemented by an anomalous counterterm
Asymptotic representation of relaxation oscillations in lasers
Grigorieva, Elena V
2017-01-01
In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.
Qiong Wu
2015-01-01
Full Text Available Mild solutions generated by a a, k-regularized family to fractional stochastic relaxation equations are studied. The main objective is to establish the existence and uniqueness of square-mean asymptotically almost automorphic mild solutions to linear and semilinear case of these equations. Under different hypotheses, some new theorems concerning the main objective are derived.
More relaxed conditions for model predictive control with guaranteed stability
Bin LIU; Yugeng XI
2005-01-01
For the model predictive controller,terminal state satisfying a certain inequality can guarantee the stability but it is somewhat conservative.In this paper,we give a more relaxed stability condition by considering the effect of the initial state.Based on that we propose an algorithm to guarantee that the closed loop system is asymptotically stable.Finally,the conclusions are verified by a simulation.
Optimal homotopy asymptotic method for solving fractional relaxation-oscillation equation
Mohammad Hamarsheh
2015-11-01
Full Text Available In this paper, an approximate analytical solution of linear fractional relaxation-oscillation equations in which the fractional derivatives are given in the Caputo sense, is obtained by the optimal homotopy asymptotic method (OHAM. The studied OHAM is based on minimizing the residual error. The results given by OHAM are compared with the exact solutions and the solutions obtained by generalized Taylor matrix method. The reliability and efficiency of the proposed approach are demonstrated in three examples with the aid of the symbolic algebra program Maple.
Asymptotic conditions of motion for radiating charged particles
Anderson, James L.
1997-10-01
Approximate asymptotic conditions on the motion of compact, electrically charged particles are derived within the framework of general relativity using the Einstein-Infeld-Hoffmann (EIH) surface integral method. While superficially similar to the Abraham-Lorentz and Lorentz-Dirac equations, these conditions differ from them in several fundamental ways. They are not equations of motion in the usual sense but rather a set of conditions which these motions must obey asymptotically in the future of an initial starting time. And furthermore, they do not admit the runaway solutions of these other equations. As in the original EIH work, they are integrability conditions gotten from integrating the empty-space (i.e., sourceless) Einstein-Maxwell equations of general relativity over closed two-surfaces surrounding the sources of the fields appearing in these equations. No additional ad hoc assumptions, such as the form of a force law or the introduction of inertial reaction terms, are required for this purpose, nor is there a need for any infinite mass renormalizations such as are required in other derivations since all integrals are over surfaces and thus finite. In addition to being asymptotic, the conditions of motion derived here are also approximate and apply, as do the original EIH equations, only to slowly moving systems. A ``slowness'' parameter ɛ is identified as the ratio of the light travel time across the system divided by a characteristic time, e.g., a period. Use is made of both the method of matched asymptotic expansions and the method of multiple time scales to obtain an asymptotic expansion in ɛ and the expansion is carried to sufficiently high order ɛ7 to obtain the lowest-order radiation reaction terms. The resulting conditions of motion are shown to not allow runaway motions.
Langer, S F J; Habazettl, H; Kuebler, W M; Pries, A R
2005-01-01
The left ventricular isovolumic pressure decay, obtained by cardiac catheterization, is widely characterized by the time constant tau of the exponential regression p(t)=Pomega+(P0-Pomega)exp(-t/tau). However, several authors prefer to prefix Pomega=0 instead of coestimating the pressure asymptote empirically; others present tau values estimated by both methods that often lead to discordant results and interpretation of lusitropic changes. The present study aims to clarify the relations between the tau estimates from both methods and to decide for the more reliable estimate. The effect of presetting a zero asymptote on the tau estimate was investigated mathematically and empirically, based on left ventricular pressure decay data from isolated ejecting rat and guinea pig hearts at different preload and during spontaneous decrease of cardiac function. Estimating tau with preset Pomega=0 always yields smaller values than the regression with empirically estimated asymptote if the latter is negative and vice versa. The sequences of tau estimates from both methods can therefore proceed in reverse direction if tau and Pomega change in opposite directions between the measurements. This is exemplified by data obtained during an increasing preload in spontaneously depressed isolated hearts. The estimation of the time constant of isovolumic pressure fall with a preset zero asymptote is heavily biased and cannot be used for comparing the lusitropic state of the heart in hemodynamic conditions with considerably altered pressure asymptotes.
GLOBAL ASYMPTOTIC STABILITY CONDITIONS OF DELAYED NEURAL NETWORKS
ZHOU Dong-ming; CAO Jin-de; ZHANG Li-ming
2005-01-01
Utilizing the Liapunov functional method and combining the inequality of matrices technique to analyze the existence of a unique equilibrium point and the global asymptotic stability for delayed cellular neural networks (DCNNs), a new sufficient criterion ensuring the global stability of DCNNs is obtained. Our criteria provide some parameters to appropriately compensate for the tradeoff between the matrix definite condition on feedback matrix and delayed feedback matrix. The criteria can easily be used to design and verify globally stable networks. Furthermore, the condition presented here is independent of the delay parameter and is less restrictive than that given in the references.
Schlüter, Steffen [School of Chemical, Biological and Environmental Engineering, Oregon State University, Corvallis Oregon USA; Department Soil Physics, Helmholtz-Centre for Environmental Research-UFZ, Halle Germany; Berg, Steffen [Shell Global Solutions International B.V., Rijswijk Netherlands; Li, Tianyi [School of Chemical, Biological and Environmental Engineering, Oregon State University, Corvallis Oregon USA; Vogel, Hans-Jörg [Department Soil Physics, Helmholtz-Centre for Environmental Research-UFZ, Halle Germany; Institut für Agrar- und Ernährungswissenschaften, Martin-Luther-Universität Halle-Wittenberg, Halle Germany; Wildenschild, Dorthe [School of Chemical, Biological and Environmental Engineering, Oregon State University, Corvallis Oregon USA
2017-06-01
The relaxation dynamics toward a hydrostatic equilibrium after a change in phase saturation in porous media is governed by fluid reconfiguration at the pore scale. Little is known whether a hydrostatic equilibrium in which all interfaces come to rest is ever reached and which microscopic processes govern the time scales of relaxation. Here we apply fast synchrotron-based X-ray tomography (X-ray CT) to measure the slow relaxation dynamics of fluid interfaces in a glass bead pack after fast drainage of the sample. The relaxation of interfaces triggers internal redistribution of fluids, reduces the surface energy stored in the fluid interfaces, and relaxes the contact angle toward the equilibrium value while the fluid topology remains unchanged. The equilibration of capillary pressures occurs in two stages: (i) a quick relaxation within seconds in which most of the pressure drop that built up during drainage is dissipated, a process that is to fast to be captured with fast X-ray CT, and (ii) a slow relaxation with characteristic time scales of 1–4 h which manifests itself as a spontaneous imbibition process that is well described by the Washburn equation for capillary rise in porous media. The slow relaxation implies that a hydrostatic equilibrium is hardly ever attained in practice when conducting two-phase experiments in which a flux boundary condition is changed from flow to no-flow. Implications for experiments with pressure boundary conditions are discussed.
Ørregård Nielsen, Morten
2015-01-01
This article proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time-series models. The model is parametric and quite general and, in particular, encompasses...
Ørregård Nielsen, Morten
This paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time series models. The model is parametric and quite general, and, in particular, encompasses...
Conditions of asymptotic stability for linear homogeneous switched systems
Ivanov, Gennady; Alferov, Gennady; Sharlay, Artem; Efimova, Polina
2017-07-01
In this article the authors prove the theorems giving the necessary and sufficient conditions for stability of robotic and mechatronic systems motion in terms of Lyapunov functions theory with the use of set-theoretic approach.
Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions
Briant, Marc; Guo, Yan
2016-12-01
In a general C1 domain, we study the perturbative Cauchy theory for the Boltzmann equation with Maxwell boundary conditions with an accommodation coefficient α in (√{ 2 / 3 } , 1 ], and discuss this threshold. We consider polynomial or stretched exponential weights m (v) and prove existence, uniqueness and exponential trend to equilibrium around a global Maxwellian in Lx,v∞ (m). Of important note is the fact that the methods do not involve contradiction arguments.
Ploberger, W.; Bierens, H.J.
1995-01-01
In this paper we study further the asymptotic power properties of the integrated conditional moment (ICM) test of Bierens (1982) and Bierens and Ploberger (1994). First, we establish the relation between consistency against global alternatives and nontrivial local power, using the concept of
Prescribing Transient and Asymptotic Behaviour of LTI Systems with Stochastic Initial Conditions
Dresscher, Martijn; Jayawardhana, Bayu
2017-01-01
This paper considers two different control problems for deterministic systems with stochastic initial conditions where, in addition to the usual asymptotic behavior requirement, we are interested in the transient behavior of the state distribution evolution. For the first one, we study control desig
Gerbi, Stéphane
2011-12-01
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.
Asymptotic forms for hard and soft edge general β conditional gap probabilities
Forrester, Peter J.; Witte, Nicholas S.
2012-06-01
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix β-ensembles. The conditioning is that there are n eigenvalues in the gap, with n≪|t|, t denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consist with known asymptotic expansions in the case n=0. With this modification made for general n, the derived expansions — which are for the logarithm of the gap probabilities — are conjectured to be correct up to and including terms O(log|t|). They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating β to 4/β.
Asymptotic forms for hard and soft edge general {beta} conditional gap probabilities
Forrester, Peter J., E-mail: p.forrester@ms.unimelb.edu.au [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia); Witte, Nicholas S., E-mail: nsw@ms.unimelb.edu.au [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia)
2012-06-21
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix {beta}-ensembles. The conditioning is that there are n eigenvalues in the gap, with n Much-Less-Than |t|, t denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consist with known asymptotic expansions in the case n=0. With this modification made for general n, the derived expansions - which are for the logarithm of the gap probabilities - are conjectured to be correct up to and including terms O(log|t|). They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating {beta} to 4/{beta}.
Asymptotic forms for hard and soft edge general $\\beta$ conditional gap probabilities
Forrester, Peter J
2011-01-01
An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix $\\beta$-ensembles. The conditioning is that there are $n$ eigenvalues in the gap, with $n \\ll |t|$, $t$ denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consistent with known asymptotic expansions in the case $n=0$. With this modification made for general $n$, the derived expansions - which are for the logarithm of the gap probabilities - are conjectured to be correct up to and including terms O$(\\log|t|)$. They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating $\\beta$ to $4/\\beta$.
Araneda, Bernardo
2016-01-01
The static region outside the event horizon of an asymptotically anti de Sitter black hole has a conformal timelike boundary $\\mathscr{I}$, the evolution from initial data of linear fields satisfying hyperbolic equations is a well posed problem only after imposing boundary conditions at $\\mathscr{I}$. Boundary conditions preserving the action of the background isometry group on the solution space are limited to the homogeneous Dirichlet, Neumann or Robin types. We study, scalar and Maxwell fields and gravitational perturbations on asymptotically AdS black holes arising in Einstein and Lovelock theories. A decomposition in modes transforms the field equations into a set of wave equations with time independent potentials for auxiliary fields in the $x<0$ half of 1+1 Minkowski spacetime. We study systematically these equations for the case of potentials not diverging at the boundary and prove that there is always an instability if Robin boundary conditions with large $\\gamma$ (the quotient between the derivat...
Laplace asymptotic expansions of conditional Wiener integrals and generalized Mehler kernel formulas
Davies, Ian; Truman, Aubrey
1982-11-01
Imitating Schilder's results for Wiener integrals rigorous Laplace asymptotic expansions are proven for conditional Wiener integrals. Applications are given for deriving generalized Mehler kernel formulas, up to arbitrarily high orders in powers of ℏ, for exp{-TH(ℏ)/ℏ}(x, y), T>0 where H(ℏ)=[(-ℏ2/2)Δ1+V], Δ1 being the one-dimensional Laplacian, V being a real-valued potential V∈C∞(R), bounded below, together with its second derivative.
Wang Kaiyong; Wang Yuebao; Yin Chuancun
2011-01-01
This article gives the equivalent conditions of the local asymptotics for the overshoot of a random walk with heavy-tailed increments, from which we find that the above asymptotics are different from the local asymptoties for the supremum of the random walk. To do this, the article first extends and improves some existing results about the solutions of renewal equations.
A Formulation of Asymptotic and Exact Boundary Conditions Using Local Operators
Hagstrom, T.; Hariharan, S. I.
1998-01-01
In this paper we describe a systematic approach for constructing asymptotic boundary conditions for isotropic wave-like equations using local operators. The conditions take a recursive form with increasing order of accuracy. In three dimensions the recursion terminates and the resulting conditions are exact for solutions which are described by finite combinations of angular spherical harmonics. First, we develop the expansion for the two-dimensional wave equation and construct a sequence of easily implementable boundary conditions. We show that in three dimensions and analogous conditions are again easily implementable in addition to being exact. Also, we provide extensions of these ideas to hyperbolic systems. Namely, Maxwell's equations for TM waves are used to demonstrate the construction. Finally, we provide numerical examples to demonstrate the effectiveness of these conditions for a model problem governed by the wave equation.
The application of polymethylene waxes as conditioning agent in hair relaxers.
Vermeulen, Shani; Van Rensburg, Audrey Jansen; Van Der Merwe, Belinda; Shalvoy, Richard; Willford, Suzanne
2004-01-01
Hair relaxers are harsh chemical treatments that leave the hair dull, dry and limp. There is a constant need for improvement of these products to make them milder and incorporate conditioning properties. Because of the high pH of relaxer or hair straightening systems, most quaternized (conditioning) ingredients are unstable and slowly break down to release ammonia over time, having no conditioning effects by the time the consumers use them. This paper discusses the partial substitution of the fatty alcohols that are traditionally used in relaxer systems with polymethylene wax and the benefits derived from using them. The study included the investigation of synergies among the ingredients, the stabilities of the various systems and comparisons with commercially available systems. The polymethylene wax, used in combination with the mineral oil gel and phosphate salt, coats the hair during the relaxing process, leaving it shiny, soft and conditioned as opposed to the poor condition of the hair relaxed by traditional, commercially available NaOH and LiOH relaxers. An additional benefit of using polymethylene wax in relaxer systems is that the conditioning agents that are normally added to the neutralizing shampoo to repair or mask the damage as a result of the relaxing process can be omitted.
Influence of the storage conditions on prestressing steel relaxation losses
Suárez, F.
2012-12-01
Full Text Available Stress relaxation losses on active reinforcement have significant impact on prestressed concrete structures. This is why relaxation tests are carried out on prestressing steel wires and strands after being manufactured. Then, these materials are coiled and stored for a long-term period, sometimes in excess of one year. The influence of these operations, carried out after manufacturing, is usually neglected. Nevertheless, some manufacturers and contractors have noticed that, sometimes, when relaxation tests are carried out after a long-term storage, the relaxation losses found are higher than those measured immediately after manufacturing. In this work, lab tests are performed to check the influence of the coiling radius and the period of storage on the relaxation test. In addition to this, an analytical model is presented to predict the results of a relaxation test carried out on a wire coiled and stored for a long-term period. This model explains the evolution on the cross-sectional stress profile along the coiling-storing-uncoiling process, as well as the influence of the residual stresses on it.
La pérdida de tensión por relajación en las armaduras activas afecta de forma importante a las estructuras de hormigón pretensado. Por ello se realizan ensayos de relajación de los alambres y cordones de pretensado tras su fabricación. Después, el material es enrollado y almacenado durante periodos que en ocasiones pueden superar el año de duración. Generalmente se desprecia la influencia que estas operaciones posteriores a la fabricación pueden tener sobre el material. Sin embargo, diversos fabricantes y suministradores han constatado experimentalmente que, en ocasiones, el material almacenado durante un periodo prolongado presenta pérdidas de relajación mayores que inmediatamente tras su fabricación. En este trabajo se realizan ensayos de laboratorio para comprobar la influencia que el radio de enrollamiento y el periodo de
Sohel Rana
2014-01-01
Full Text Available Non-Fourier heat conduction model with dual phase lag wave-diffusion model was analyzed by using well-conditioned asymptotic wave evaluation (WCAWE and finite element method (FEM. The non-Fourier heat conduction has been investigated where the maximum likelihood (ML and Tikhonov regularization technique were used successfully to predict the accurate and stable temperature responses without the loss of initial nonlinear/high frequency response. To reduce the increased computational time by Tikhonov WCAWE using ML (TWCAWE-ML, another well-conditioned scheme, called mass effect (ME T-WCAWE, is introduced. TWCAWE with ME (TWCAWE-ME showed more stable and accurate temperature spectrum in comparison to asymptotic wave evaluation (AWE and also partial Pade AWE without sacrificing the computational time. However, the TWCAWE-ML remains as the most stable and hence accurate model to analyze the fast transient thermal analysis of non-Fourier heat conduction model.
马西奎; 韩社教
2002-01-01
Based on the multipole expansion theory of the potential, a satisfactory interpretation is put forward of the exact nature of the approximations of asymptotic boundary condition (called the ABC) techniques for the numerical solutions of open-boundary static electromagnetic-field problems, and a definite physical meaning is bestowed on ABC, which provide a powerful theoretical background for laying down the operating rules and the key to the derivation of asymptotic boundary conditions. This paper is also intended to reveal the shortcomings of the conventional higher-order ABC, and at the same time to give the concept of a new type of higher-order ABC, and to present a somewhat different formulation of the new nth-order ABC. In order to test its feasibility, several simple problems of electrostatic potentials are analyzed. The results are found to be much better than those of conventional higher-order ABCs.
2013-01-01
The main contribution of this paper is to present a new sufficient condition for the subexponential asymptotics of the stationary distribution of a GI/GI/1-type Markov chain without jumps from level "infinity" to level zero. For simplicity, we call such Markov chains {\\it GI/GI/1-type Markov chains without disasters} because they are often used to analyze semi-Markovian queues without "disasters", which are negative customers who remove all the customers in the system (including themselves) o...
Vardanyan S. A.
2007-09-01
Full Text Available In the framework of the asymmetrical momental micropolar theory in the present work the boundary value problem of thermal stresses in a three-dimensional thin plate with independent fields of displacements and rotations is studied on the basis of asymptotic method. Depending on the values of physical dimensionless constants of the material three applied two-dimensional theories of thermoelasticity of micropolar thin plate are constructed (theories with independent rotations, with constrained rotations and with small shift rigidity.
On the Conditions for the Orbitally Asymptotical Stability of the Almost
无
2000-01-01
@@This paper studies the behaviors of the solutions in the vicinity of a givenalmost periodic solution of the autonomous system x′=f(x), x Rn , (1) where f C1 (Rn ,Rn ). Since the periodic solutions of the autonomous system are not Liapunov asymptotic stable, we consider the weak orbitally stability. For the planar autonomous systems (n=2), the classical result of orbitally stability about its periodic solution with period w belongs to Poincare, i.e.
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
Calkins, Michael A; Julien, Keith; Nieves, David; Driggs, Derek; Marti, Philippe
2015-01-01
The influence of fixed temperature and fixed heat flux thermal boundary conditions on rapidly rotating convection in the plane layer geometry is investigated for the case of stress-free mechanical boundary conditions. It is shown that whereas the leading order system satisfies fixed temperature boundary conditions implicitly, a double boundary layer structure is necessary to satisfy the fixed heat flux thermal boundary conditions. The boundary layers consist of a classical Ekman layer adjacent to the solid boundaries that adjust viscous stresses to zero, and a layer in thermal wind balance just outside the Ekman layers adjusts the temperature such that the fixed heat flux thermal boundary conditions are satisfied. The influence of these boundary layers on the interior geostrophically balanced convection is shown to be asymptotically weak, however. Upon defining a simple rescaling of the thermal variables, the leading order reduced system of governing equations are therefore equivalent for both boundary condit...
A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks
Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui;
2016-01-01
This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed...... sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal...... solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks....
A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks
Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui
2016-01-01
This paper proposes a sufficient condition for the convex relaxation of AC Optimal Power Flow (OPF) in radial distribution networks as a second order cone program (SOCP) to be exact. The condition requires that the allowed reverse power flow is only reactive or active, or none. Under the proposed...... sufficient condition, the feasible sub-injection region (power injections of nodes excluding the root node) of the AC OPF is convex. The exactness of the convex relaxation under the proposed condition is proved through constructing a group of monotonic series with limits, which ensures that the optimal...... solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks....
Behzadan, A
2015-01-01
In this article we consider the conformal decomposition of Einstein's constraint equations introduced by Lichnerowicz, Choquet-Bruhat, and York, on asymptotically flat (AF) manifolds. Using the non-CMC fixed-point framework developed in 2009 by Holst, Nagy, and Tsogtgerel and by Maxwell, we establish existence of coupled non-CMC weak solutions for AF manifolds. As is the case for the analogous existence results for non-CMC solutions on closed manifolds and compact manifolds with boundary, our results here avoid the near-CMC assumption by assuming that the freely specifiable part of the data given by the traceless-transverse part of the rescaled extrinsic curvature and the matter fields are sufficiently small. The non-CMC rough solutions results here for AF manifolds may be viewed as extending to AF manifolds the 2009 and 2014 results on rough far-from-CMC positive Yamabe solutions for closed and compact manifolds with boundary. Similarly, our results may be viewed as extending the recent 2014 results for AF m...
Carro, Adrian; Miguel, Maxi San
2012-01-01
We study a model for continuous-opinion dynamics under bounded confidence. In particular, we analyze the importance of the initial distribution of opinions in determining the asymptotic configuration. Thus, we sketch the structure of attractors of the dynamical system, by means of the numerical computation of the time evolution of the agents density. We show that, for a given bound of confidence, a consensus can be encouraged or prevented by certain initial conditions. Furthermore, a noisy perturbation is added to the system with the purpose of modeling the free will of the agents. As a consequence, the importance of the initial condition is partially replaced by that of the statistical distribution of the noise. Nevertheless, we still find evidence of the influence of the initial state upon the final configuration for a short range of the bound of confidence parameter.
Lemos, José P S; Minamitsuji, Masato
2015-01-01
A rotating thin shell in a (2+1)-dimensional asymptotically AdS spacetime is studied. The spacetime exterior to the shell is the rotating BTZ spacetime and the interior is the empty spacetime with a cosmological constant. Through the Einstein equation in (2+1)-dimensions and the corresponding junction conditions we calculate the dynamical relevant quantities, namely, the rest energy-density, the pressure, and the angular momentum flux density. We also analyze the matter in a frame where its energy-momentum tensor has a perfect fluid form. In addition, we show that Machian effects, such as the dragging of inertial frames, also occur in rotating (2+1)-dimensional spacetimes. The weak and the dominant energy condition for these shells are discussed.
Verma, Ram U; Seol, Youngsoo
2016-01-01
First a new notion of the random exponential Hanson-Antczak type [Formula: see text]-V-invexity is introduced, which generalizes most of the existing notions in the literature, second a random function [Formula: see text] of the second order is defined, and finally a class of asymptotically sufficient efficiency conditions in semi-infinite multi-objective fractional programming is established. Furthermore, several sets of asymptotic sufficiency results in which various generalized exponential type [Formula: see text]-V-invexity assumptions are imposed on certain vector functions whose components are the individual as well as some combinations of the problem functions are examined and proved. To the best of our knowledge, all the established results on the semi-infinite aspects of the multi-objective fractional programming are new, which is a significantly new emerging field of the interdisciplinary research in nature. We also observed that the investigated results can be modified and applied to several special classes of nonlinear programming problems.
Zhu, Weiping; Xu, Peng; Xu, Dong; Zhang, Meimei; Liu, Huiming; Gong, Linghui; Lu, Junfeng
2014-05-01
To study the effects of the thermal relaxation, the blood perfusion and the oscillating of ambient heat flux on the living tissue temperature in detail, we analytically investigated the one-dimensional CV model, a thermal wave model presented by Cattaneo and Vernott, for Pennes' bio-heat transfer equation under oscillating second-kind boundary condition. The results showed that the blood perfusion has the effect of maintaining the tissue's temperature. The heat propagation velocity decreases with the thermal relaxation time, while the absolute value of tissue's mean excess temperature at steady state increases with the thermal relaxation time. When the ambient heat flux oscillates, the tissue's temperature oscillates in the same period with a lag time. The results obtained in this paper are valuable for the research reference on the topic of tumor hyperthermia, heat injury, etc.
Asymptotics of Random Contractions
Hashorva, Enkelejd; Tang, Qihe
2010-01-01
In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an extreme value distribution and the distribution function of $S$ satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.
Asymptotic 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.
G.V. Bezprozvannych
2016-05-01
Full Text Available Introduction. The presence of free moisture in power cables leading to the formation of tree structures - water treeing, which originate in the amorphous phase polyethylene and are a major cause of degradation of the polymer insulation. They represent the damage of the polymer size from several microns to 1 mm, developing technology for insulation defects under the combined action of the electric field and the moisture diffusing from the environment. Water treeing destroys the polymer chain, resulting in the formation of microcavities filled with moisture. The dynamics of water treeing and subtle properties largely depend on the composition, morphology of the polymer insulation, chemical nature of the defect, in which they originate. Due to the force of gravity in the water formed typical only for her region with locally ordered structure - clusters, which cause loss of relaxation. Purpose. Features presence of relaxation losses in high-frequency range in polyethylene insulation during aging in high humidity conditions of samples power and RF cables. Methodology. Samples of the power cable for the voltage of 35 kV with a cross-linked polyethylene insulation radial water-blocking protection from moisture and radio-frequency coaxial cable with thermoplastic insulation for 1440 hours in a humidity of 100%. The dielectric loss tangent measured resonance method before and after aging. Originality. Experimentally found evidence of the existence in the polymer cable insulation free water in the form of areas with locally ordered structure - clusters. It is found that the solid polyethylene insulation in the frequency dependence of dielectric loss tangent maximum relaxation shown one at 10 MHz in the initial state, and there are two additional frequency range 500 kHz - 5 MHz after moistening. For cross-linked polyethylene insulation characteristic of large width Δf of the frequency spectrum in which the observed relaxation losses. It is obvious that
Asymptotic structure of the Einstein-Maxwell theory on AdS$_{3}$
Perez, Alfredo; Tempo, David; Troncoso, Ricardo
2015-01-01
The asymptotic structure of AdS spacetimes in the context of General Relativity coupled to the Maxwell field in three spacetime dimensions is analyzed. Although the fall-off of the fields is relaxed with respect to that of Brown and Henneaux, the variation of the canonical generators associated to the asymptotic Killing vectors can be shown to be finite once required to span the Lie derivative of the fields. The corresponding surface integrals then acquire explicit contributions from the electromagnetic field, and become well-defined provided they fulfill suitable integrability conditions, implying that the leading terms of the asymptotic form of the electromagnetic field are functionally related. Consequently, for a generic choice of boundary conditions, the asymptotic symmetries are broken down to $\\mathbb{R}\\otimes U\\left(1\\right)\\otimes U\\left(1\\right)$. Nonetheless, requiring compatibility of the boundary conditions with one of the asymptotic Virasoro symmetries, singles out the set to be characterized b...
Greene, Patrick; Schofield, Sam; Nourgaliev, Robert
2016-11-01
A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin (DG) projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. The method retains the excellent smoothing capabilities of condition number relaxation, while providing a method for clustering mesh cells near regions of interest. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Existence and asymptotic behavior of the wave equation with dynamic boundary conditions
Graber, Philip Jameson
2012-03-07
The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.
Existence and Asymptotic Behavior of the Wave Equation with Dynamic Boundary Conditions
Graber, Philip Jameson, E-mail: pjg9g@virginia.edu [University of Virginia, Department of Mathematics (United States); Said-Houari, Belkacem, E-mail: belkacem.saidhouari@kaust.edu.sa [King Abdullah University of Science and Technology (KAUST), Division of Mathematical and Computer Sciences and Engineering (Saudi Arabia)
2012-08-15
The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time.
Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert
2017-04-01
A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.
The relaxation of initial condition in systems with infinitely many absorbing states
Ódor, G; Dos Santos, M A; Marques, M C; Odor, Geza
1998-01-01
We have investigated the effect of the initial condition on the spreading exponents of the one-dimensional pair contact process (PCP) and threshold transfer process (TTP).The non-order field was found to exhibit critical fluctuations, relaxing to its natural value with the same power-law as the order parameter field. We argue that this slow relaxation, which was not taken into account in earlier studies of these models, is responsible for the continuously changing survival probability exponent. High precision numerical simulations show evidence of a(slight) dependence of the location of the transition point on the initial concentration, in the case of PCP. The damage spreading (DS) point and the spreading exponents coincide with those of the ordinary critical point in both cases.
CHEN Jun; CUI Bao-Tong; GAO Ming
2008-01-01
The global asymptotic stability of delayed Cohen-Grossberg neural networks with impulses is investigated. Based on the new suitable Lyapunov functions and the Jacobsthal inequality, a set of novel sufficient criteria are derived for the global asymptotic stability of Cohen-Grossberg neural networks with time-varying delays and impulses.An illustrative example with its numerical simulations is given to demonstrate the effectiveness of the obtained results.
E. M. E. ZAYED
2003-01-01
The asymptotic expansions of the trace of the heat kernel Θ(t) = ∑∞ν=1 exp(-tλν) for smallpositive t, where {λν} are the eigenvalues of the negative Laplacian -△n = - ∑n i=1 ( / xi )2 in Rn(n= 2or 3), are studied for a general annular bounded domain Ω with a smooth inner boundary (e)Ω1 and asmooth outer boundary (e)Ω2, where a finite number of piecewise smooth Robin boundary conditions((e)/(e)nj+rj)φ=0 on the components γj(j = 1, ..., k)of (e)Ω1 and on teh components γj(j = 1, ..., m) of (e)Ω2 are considered such that( (e)Ω1+ukj=1 Fj and (e)Ω2=Umj=k+1Fj )and where the coefficients (rj(j=1，…，m))are piecewise smooth positive functions. Some applications of Θ(t) for an ideal gasenclosed in the general annular bounded domain Ω are given. Further results are also obtained.
Zhang Jin-Lu; Wang Li-Na; Zhao Xing-Yu; Zhang Li-Li; Zhou Heng-Wei; Wei Lai; Huang Yi-Neng
2011-01-01
The string model for the glass transition can quantitatively describe the universal α-relaxation in glassformers. The string relaxation equation (SRE) of the model simplifies the well-known Debye and Rouse-Zimm relaxation equations at high and low enough temperatures, respectively. However, its initial condition, necessary to the further model predictions of glassy dynamics, has not been solved. In this paper, the general initial condition of the SRE for stochastically spatially configurative strings is solved exactly based on the obtained special initial condition of the SRE for straight strings in a previous paper (J. L. Zhang et al. 2010 Chin. Phya. B 19, 056403).
Scalerandi, M; Johnson, P A
2003-01-01
Local interaction simulation approach simulations of the ultrasonic wave propagation in multi-grained materials have succeeded in reproducing most of the recently observed nonclassical nonlinear effects, such as stress-strain hysteresis and discrete memory in quasi-static experiments and a downwards shift of the resonance frequency and the generation of odd harmonics at specific amplitude rates in dynamics experiments. By including a simple mechanism of thermally activated random transitions, we can predict the occurrence of experimentally observed effects, such as the conditioning and relaxation of the specimen. Experiments are also suggested for a quantitative assessment of the validity of the model.
A Stabilized Incompressible SPH Method by Relaxing the Density Invariance Condition
Mitsuteru Asai
2012-01-01
Full Text Available A stabilized Incompressible Smoothed Particle Hydrodynamics (ISPH is proposed to simulate free surface flow problems. In the ISPH, pressure is evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection method. Even if the pressure is evaluated implicitly, the unrealistic pressure fluctuations cannot be eliminated. In order to overcome this problem, there are several improvements. One is small compressibility approach, and the other is introduction of two kinds of pressure Poisson equation related to velocity divergence-free and density invariance conditions, respectively. In this paper, a stabilized formulation, which was originally proposed in the framework of Moving Particle Semi-implicit (MPS method, is applied to ISPH in order to relax the density invariance condition. This formulation leads to a new pressure Poisson equation with a relaxation coefficient, which can be estimated by a preanalysis calculation. The efficiency of the proposed formulation is tested by a couple of numerical examples of dam-breaking problem, and its effects are discussed by using several resolution models with different particle initial distances. Also, the effect of eddy viscosity is briefly discussed in this paper.
Asymptotic Symmetries from finite boxes
Andrade, Tomas
2015-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincar\\'e asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Le Thi Phuong Ngoc
2016-01-01
Full Text Available This paper is devoted to the study of a nonlinear Carrier wave equation in an annular membrane associated with Robin-Dirichlet conditions. Existence and uniqueness of a weak solution are proved by using the linearization method for nonlinear terms combined with the Faedo-Galerkin method and the weak compact method. Furthermore, an asymptotic expansion of a weak solution of high order in a small parameter is established.
Niu, Xiao-Dong; Hyodo, Shi-Aki; Munekata, Toshihisa; Suga, Kazuhiko
2007-09-01
It is well known that the Navier-Stokes equations cannot adequately describe gas flows in the transition and free-molecular regimes. In these regimes, the Boltzmann equation (BE) of kinetic theory is invoked to govern the flows. However, this equation cannot be solved easily, either by analytical techniques or by numerical methods. Hence, in order to efficiently maneuver around this equation for modeling microscale gas flows, a kinetic lattice Boltzmann method (LBM) has been introduced in recent years. This method is regarded as a numerical approach for solving the BE in discrete velocity space with Gauss-Hermite quadrature. In this paper, a systematic description of the kinetic LBM, including the lattice Boltzmann equation, the diffuse-scattering boundary condition for gas-surface interactions, and definition of the relaxation time, is provided. To capture the nonlinear effects due to the high-order moments and wall boundaries, an effective relaxation time and a modified regularization procedure of the nonequilibrium part of the distribution function are further presented based on previous work [Guo et al., J. Appl. Phys. 99, 074903 (2006); Shan et al., J. Fluid Mech. 550, 413 (2006)]. The capability of the kinetic LBM of simulating microscale gas flows is illustrated based on the numerical investigations of micro Couette and force-driven Poiseuille flows.
Yang, Haiqing; Liu, Junfeng; Zhou, Xiaoping
2017-05-01
The relaxation behavior plays an important role in evaluating the long-term safety of the surrounding rock mass. Normally, the characters of the stress relaxation behavior of a rock mass can be described as the time-dependent rheological crack propagation features. Based on the subcritical crack growth parameters obtained in the double-torsion experiment, the stress relaxation behavior of pre-cracked granite column specimens is presented. The results of the stress relaxation tests indicate that for a certain confining pressure level, the increase in the uniaxial strain contributes to the propagation of the rheological cracks. For stress relaxation tests conducted under different confining pressure conditions, the propagation of the rheological cracks depends mainly on the D value of the axial and confining pressures. Specifically, the rheological cracks tend to propagate more sufficiently with a higher D value. The experimental results are in good agreement with the analytical solution, in accordance with the Burgers model. Furthermore, the results of the stress relaxation tests conducted under different unloading rates show that the relaxation behavior of the studied material tends to be more obvious for a relatively lower unloading rate of the confining pressure. Finally, the failure patterns obtained under stress relaxation and traditional tests are compared. In detail, for the specimens in the traditional triaxial compression test, the fracture is caused by the abrupt coalescence of the wing cracks and the failure is tensile-shear mixed mode, whereas during the stress relaxation test, the failure is transformed into the smooth coalescence of the tensile rheological cracks. The present research can increase the understanding of the relaxation behavior of hard rock under different engineering environments.
Greene, Patrick T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Schofield, Samuel P. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nourgaliev, Robert [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-06-21
A new mesh smoothing method designed to cluster mesh cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered elds, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness to arbitrary Lagrangian Eulerian (ALE) methods.
Asymptotic structure of the Einstein-Maxwell theory on AdS{sub 3}
Pérez, Alfredo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Riquelme, Miguel [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Departamento de Física, Universidad de Concepción,Casilla 160-C, Concepción (Chile); Tempo, David [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes,Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Troncoso, Ricardo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile)
2016-02-02
The asymptotic structure of AdS spacetimes in the context of General Relativity coupled to the Maxwell field in three spacetime dimensions is analyzed. Although the fall-off of the fields is relaxed with respect to that of Brown and Henneaux, the variation of the canonical generators associated to the asymptotic Killing vectors can be shown to be finite once required to span the Lie derivative of the fields. The corresponding surface integrals then acquire explicit contributions from the electromagnetic field, and become well-defined provided they fulfill suitable integrability conditions, implying that the leading terms of the asymptotic form of the electromagnetic field are functionally related. Consequently, for a generic choice of boundary conditions, the asymptotic symmetries are broken down to ℝ⊗U(1)⊗U(1). Nonetheless, requiring compatibility of the boundary conditions with one of the asymptotic Virasoro symmetries, singles out the set to be characterized by an arbitrary function of a single variable, whose precise form depends on the choice of the chiral copy. Remarkably, requiring the asymptotic symmetries to contain the full conformal group selects a very special set of boundary conditions that is labeled by a unique constant parameter, so that the algebra of the canonical generators is given by the direct sum of two copies of the Virasoro algebra with the standard central extension and U(1). This special set of boundary conditions makes the energy spectrum of electrically charged rotating black holes to be well-behaved.
A Note on Asymptotic Contractions
Marina Arav
2006-12-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space X to converge to its unique fixed point, uniformly on each bounded subset of X.
A Note on Asymptotic Contractions
Castillo Santos Francisco Eduardo
2007-01-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space to converge to its unique fixed point, uniformly on each bounded subset of .
Orozco-Davila, Dina; Hernandez, Refugio; Solis, Eduardo; Quintero, J. Luis; Dominguez, Julio, E-mail: dorozco1@prodigy.net.m [United States Department of Agriculture, Gainesville, FL (United States). Agricultural Research Service. Center for Medical, Agricultural, and Veterinary Entomology; Sigma Space Corporation, MD(United States); Programa Moscamed Moscafrut-Desarrollo de Metodos, Chiapas (Mexico)
2006-07-01
Several studies have suggested that maintaining a line of insects under laboratory conditions reduces their biological attributes. With this principle in mind, the mass production of Anastrepha ludens originating from a colony raised under relaxed rearing conditions was evaluated over a period of three years. The results of the evaluation indicated that insects kept under these conditions reached their larval maturity in 10 days, and attained a greater weight, which has a direct influence on pupal quality. In adult cages having a fly density of 70,000 individuals, there was a lower level of stress which favored fecundity. Fertility was apparently not affected by the cage density. These results suggest that keeping a production line under relaxed conditions optimizes insect production and promotes higher quality. (author)
Ndetan, Harrison; Evans, Marion Willard; Williams, Ronald D; Woolsey, Conrad; Swartz, Julie H
2014-01-01
Use of complementary and alternative medicine (CAM) by children under 18 y of age in the United States is becoming more prevalent. According to an analysis of procedures in chiropractic practices in 2010, more than 96% of chiropractors in the United States recommended use of movement therapies (MT) and relaxation techniques (RT) to their patients. The extent of use of these methods as treatment options for specific health conditions in children, however, has been underexplored in the United States. The current study assessed use of MT and RT in children for treatment of various health conditions, as reported in the 2007 National Health Interview Survey (NHIS), and also examined variations in use across various sociodemographic categories. Secondary data from the 2007 National Health Interview Survey (NHIS) Child Alternative Medicine file were analyzed, and the research team generated weighted frequencies and inferential statistics. Odds ratios (OR) and 95% confidence intervals (CI) were computed through binary logistic regression to assess use of MT and RT as functions of various sociodemographic variables. Within the 12 mo prior to the survey, MT and RT use was reported by 2.5% and 2.9% of respondents, respectively. MT, primarily yoga, was used for the control and reduction of anxiety and stress (31.4%), asthma (16.2%), and back/neck pain (15.3%). Alternatively, RT, such as controlled breathing exercises (2.1%) and meditation (2.3%), was used for anxiety and stress (41.4%) and attention-deficit disorders (ADDs) (16.0%). Although data screening did not produce obvious predictors for RT use, age, gender, race/ethnicity, and parents' education levels were potential predictors of MT use. For example, respondents aged 10 y (OR = 0.4; 95% CI, 0.3-0.6), and males reported lower MT use than females (OR = 0.5; 95% CI, 0.3-0.7). MT and RT are used by several million children in the United States each year. The current research suggests that early training on MT and RT can
Kirillova, S.I.; Primachenko, V.E.; Snitko, O.V.
1985-04-16
The nonequilibrium depletion relaxation processes at real, clean, thermally oxidized, and Au and Zn doped n- and p-type Si surfaces are studied. A strong acceleration of the relaxation process with field increase is observed. This is explained by the Frenkel and Franz-Keldysh effect during the transition of majority charge carriers from the surface states into an allowed band. The acceleration is also believed to be due to a tunnel-activation mechanism of majority carriers from surface layer traps into an allowed band. The parameters of the surface states taking part in the relaxation of nonequilibrium depletion (the electron-phonon interaction parameter sigma, being very sensitive to the state of the Si surface, for example) are determined.
E.M.E. ZAYED
2004-01-01
The asymptotic expansion of the heat kernel Θ(t)(∞∑=(i=0))exp (-λi) where({λi}∞i=1) Are the eigen-values of negative Laplacian( -△n=-n∑k=1(θ/θxk)2)in Rn(n=2 or 3) is studied for short-time t for a general bounded domainθΩwith a smooth boundary θΩ.In this paper, we consider the case of a finite number of the Dirichlet conditions φ=0 on Γi (i = J +1,….,J)and the Neumann conditions and (θφ/θ vi) = 0 on Γi (i = J+1,…,k) and the Robin condition (θφ/θ vi+γi) θ=(I=k+1,… m) where γi are piecewise smooth positive impedancem(θφ=mUi=1Γi. )We construct the required asymptotics in the form of a power series over t. The senior coe.cients inthis series are speci.ed as functionals of the geometric shape of the domain Ω.This result is applied to calculatethe one-particle partition function of a "special ideal gas", i.e., the set of non-interacting particles set up in abox with Dirichlet, Neumann and Robin boundary conditions for the appropriate wave function. Calculationof the thermodynamic quantities for the ideal gas such as the internal energy, pressure and speci.c heat revealsthat these quantities alone are incapable of distinguishing between two di.erent shapes of the domain. Thisconclusion seems to be intuitively clear because it is based on a limited information given by a one-particlepartition function; nevertheless, its formal theoretical motivation is of some interest.
A Sufficient Condition on Convex Relaxation of AC Optimal Power Flow in Distribution Networks
Huang, Shaojun; Wu, Qiuwei; Wang, Jianhui;
2016-01-01
solution of the SOCP can be converted to an optimal solution of the original AC OPF. The efficacy of the convex relaxation to solve the AC OPF is demonstrated by case studies of an optimal multi-period planning problem of electric vehicles (EVs) in distribution networks....
O. H. Kapitonov
2010-05-01
Full Text Available A mathematical model of coulostatic relaxation of the potential for solid metallic electrode was presented. The solution in the case of limiting diffusion current was obtained. On the basis of this model the technique of concentration measurements for heavy metal ions in diluted solutions was suggested. The model adequacy was proved by experimental data.
Asymptotically hyperbolic connections
Fine, Joel; Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos
2016-09-01
General relativity in four-dimensions can be equivalently described as a dynamical theory of {SO}(3)˜ {SU}(2)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analogue of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising ‘evolution’ equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the unconstrained by Einstein equations ‘stress-energy tensor’ appears at third order in the expansion. Another interesting feature of the connection formulation is that the ‘counter terms’ required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-defined requires the cosmological constant to be quantised. Finally, in the connection setting one can deform the 4D Einstein condition in an interesting way, and we show that asymptotically hyperbolic connection expansion is universal and valid for any of the deformed theories.
Kiselev, O M
1999-01-01
The asymptotic solution for the Painleve-2 equation with small parameter is considered. The solution has algebraic behavior before point $t_*$ and fast oscillating behavior after the point $t_*$. In the transition layer the behavior of the asymptotic solution is more complicated. The leading term of the asymptotics satisfies the Painleve-1 equation and some elliptic equation with constant coefficients, where the solution of the Painleve-1 equation has poles. The uniform smooth asymptotics are constructed in the interval, containing the critical point $t_*$.
Strings from 3D gravity: asymptotic dynamics of AdS$_3$ gravity with free boundary conditions
Apolo, Luis
2015-01-01
Pure three-dimensional gravity in anti-de Sitter space can be formulated as an SL(2,R) $\\times$ SL(2,R) Chern-Simons theory, and the latter can be reduced to a WZW theory at the boundary. In this paper we show that AdS$_3$ gravity with free boundary conditions is described by a string theory at the boundary whose target spacetime is also AdS$_3$. While boundary conditions in the standard construction of Coussaert, Henneaux, and van Driel are enforced through constraints on the WZW currents, we find that free boundary conditions are partially enforced through the string Virasoro constraints.
Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship
王启华; 荆炳义
2000-01-01
Here we study the problems of local asymptotic normality of the parametric family of distri-butions and asymptotic minimax efficient estimators when the observations are subject to right censor-ing. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and fur-thermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship
无
2000-01-01
Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and furthermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
Vogel, Edgar H
2012-01-01
The purpose of this study was to examine whether the progressive disappearance of short-latency conditioned responses, or inhibition of delay, observed in Pavlovian conditioning with long inter-stimulus intervals, could be reverted by the presentation of a novel stimulus. In one experiment, two groups of rabbits received extensive training with a short (250 ms) or a long (1500 ms) tone that overlapped and terminated with a periorbital shock unconditioned stimulus. After training, the presentation of an extraneous stimulus prior to tone onset produced a reinstatement of short latency CRs in the group trained with the long CS, but did not affect CR latency in the group trained with the short CS. This finding is consistent with Pavlov's (1927) view that conditioning with long conditioned stimuli involves the acquisition of response tendencies in the early portion of the stimulus that are subsequently suppressed by the development of an inhibitory process.
Yijin Zhang
2013-01-01
Full Text Available This work is concerned with the random dynamics of two-dimensional stochastic Boussinesq system with dynamical boundary condition. The white noises affect the system through a dynamical boundary condition. Using a method based on the theory of omega-limit compactness of a random dynamical system, we prove that the L2-random attractor for the generated random dynamical system is exactly the H1-random attractor. This improves a recent conclusion derived by Brune et al. on the existence of the L2-random attractor for the same system.
J.F. Kiviet; J. Niemczyk
2012-01-01
In designing Monte Carlo simulation studies for analyzing finite sample properties of econometric inference methods, one can use either IID drawings in each replication for any series of exogenous explanatory variables or condition on just one realization of these. The results will usually differ, a
Asymptotically locally flat spacetimes and dynamical black flowers in three dimensions
Barnich, Glenn; Tempo, David; Troncoso, Ricardo
2015-01-01
The theory of massive gravity proposed by Bergshoeff, Hohm and Townsend is considered in the special case of the pure irreducibly fourth order quadratic Lagrangian. It is shown that the asymptotically locally flat black holes of this theory can be consistently deformed to "black flowers" that are no longer spherically symmetric. Moreover, we construct radiating spacetimes settling down to these black flowers in the far future. The generic case can be shown to fit within a relaxed set of asymptotic conditions as compared to the ones of general relativity at null infinity, while the asymptotic symmetries remain the same. Conserved charges as surface integrals at null infinity are constructed following a covariant approach, and their algebra represents BMS$_{3}$, but without central extensions. For solutions possessing an event horizon, we derive the first law of thermodynamics from these surface integrals.
Relaxing Tight Frame Condition in Parallel Proximal Methods for Signal Restoration
Pustelnik, Nelly; Chaux, Caroline
2011-01-01
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have become popular optimization techniques to approximate iteratively the desired solution. Until now, in most of these methods, either Lipschitz differentiability properties or tight frame representations were assumed. In this paper, it is shown that it is possible to relax these assumptions by considering a class of non necessarily tight frame representations, thus offering the possibility of addressing a broader class of signal restoration problems. In particular, it is possible to use non necessarily maximally decimated filter banks with perfect reconstruction, which are common tools in digital signal processing. The proposed approach allows us to solve both frame analysis and frame synthesis problems for various noise distributions. In our simulations, it is applied to th...
Porta, G. M.; Ceriotti, G.; Thovert, J.-F.
2016-02-01
We compare the ability of various continuum-scale models to reproduce the key features of a transport setting associated with a bimolecular reaction taking place in the fluid phase and numerically simulated at the pore-scale level in a disordered porous medium. We start by considering a continuum-scale formulation which results from formal upscaling of this reactive transport process by means of volume averaging. The resulting (upscaled) continuum-scale system of equations includes nonlocal integro-differential terms and the effective parameters embedded in the model are quantified directly through computed pore-scale fluid velocity and pore space geometry attributes. The results obtained through this predictive model formulation are then compared against those provided by available effective continuum models which require calibration through parameter estimation. Our analysis considers two models recently proposed in the literature which are designed to embed incomplete mixing arising from the presence of fast reactions under advection-dominated transport conditions. We show that best estimates of the parameters of these two models heavily depend on the type of data employed for model calibration. Our upscaled nonlocal formulation enables us to reproduce most of the critical features observed through pore-scale simulation without any model calibration. As such, our results clearly show that embedding into a continuum-scale model the information content associated with pore-scale geometrical features and fluid velocity yields improved interpretation of typically available continuum-scale transport observations.
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....
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....
Asymptotic Rayleigh instantaneous unit hydrograph
Troutman, B.M.; Karlinger, M.R.
1988-01-01
The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude, N, tends asymptotically, as N grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, {Mathematical expression}, where ?? is a mean link wave travel time. ?? 1988 Springer-Verlag.
Asymptotic Normality of Quadratic Estimators.
Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad
2016-12-01
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.
Schweitzer, S.; Schinagl, C.; Djuras, G.; Frühwirth, M.; Hoschopf, H.; Wagner, F.; Schulz, B.; Nemitz, W.; Grote, V.; Reidl, S.; Pritz, P.; Moser, M.; Wenzl, F. P.
2016-09-01
In recent years, LED lighting became an indispensable alternative to conventional lighting systems. Sophisticated solutions offer not only comfortable white light with a good color rendering. They also provide the possibility of changing illuminance and color temperature. Some systems even simulate daylight over the entire day, some including natural variations as due to clouds. Such systems are supposed to support the chronobiological needs of human and to have a positive effect on well-being, performance, sleep-quality and health. Lighting can also be used to support specific aims in a situation, like to improve productivity in activation or to support recreation in relaxation. Research regarding suitable light-settings for such situations and superordinate questions like their influence on well-being and health is still incomplete. We investigated the subjective preferences of men and women regarding light-settings for activation and relaxation. We supplied two rooms and four cubes with light sources that provide the possibility of tuning illuminance, color temperature and deviation from Plackian locus. More than 80 individuals - belonging to four groups differing in gender and age - were asked to imagine activating and recovering situations for which they should adjust suitable and pleasant lighting by tuning the above mentioned light properties. It was shown that there are clear differences in the lighting conditions preferred for these two situations. Also some combined gender- and age-specific differences became apparent.
Kobayashi, M; Irisawa, H
1961-10-27
The latent period of relaxation of molluscan myocardium due to anodal current is much longer than that of contraction. Although the rate and the grade of relaxation are intimately related to both the stimulus condition and the muscle tension, the latent period of relaxation remains constant, except when the temperature of the bathing fluid is changed.
Mickley, G. Andrew; DiSorbo, Anthony; Wilson, Gina N.; Huffman, Jennifer; Bacik, Stephanie; Hoxha, Zana; Biada, Jaclyn M.; Kim, Ye-Hyun
2009-01-01
Conditioned taste aversions (CTAs) may be acquired when an animal consumes a novel taste (CS) and then experiences the symptoms of poisoning (US). This aversion may be extinguished by repeated exposure to the CS alone. However, following a latency period in which the CS is not presented, the CTA will spontaneously recover (SR). In the current…
More relaxed condition for dynamics of discrete time delayed Hopfield neural networks
Zhang Qiang
2008-01-01
The dynamics of discrete time delayed Hopfield neural networks is investigated.By using a difference inequality combining with the linear matrix inequality,a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found.The result obtained holds not only for constant delay but also for time-varying delays.
Conflict between fastest relaxation of a Markov process and detailed balance condition.
Takahashi, Kazutaka; Ohzeki, Masayuki
2016-01-01
We consider the optimization of Markovian dynamics to pursue the fastest convergence to the stationary state. The brachistochrone method is applied to the continuous-time master equation for finite-size systems. The principle of least action leads to a brachistochrone equation for the transition-rate matrix. Three-state systems are explicitly analyzed, and we find that the solution violates the detailed balance condition. The properties of the solution are studied in detail to observe the optimality of the solution. We also discuss the counterdiabatic driving for the Markovian dynamics. The transition-rate matrix is then divided into two parts, and the state is given by an eigenstate of the first part. The second part violates the detailed balance condition and plays the role of a counterdiabatic term.
Penrose type inequalities for asymptotically hyperbolic graphs
Dahl, Mattias; Sakovich, Anna
2013-01-01
In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\\bH^n$. The graphs are considered as subsets of $\\bH^{n+1}$ and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the integrand for the asymptotically hyperbolic mass. Integrating this divergence we estimate the mass by an integral over an inner boundary. In case the inner boundary satisfies a convexity condition this can in turn be estimated in terms of the area of the inner boundary. The resulting estimates are similar to the conjectured Penrose inequality for asymptotically hyperbolic manifolds. The work presented here is inspired by Lam's article concerning the asymptotically Euclidean case.
Dutt, G. B.; Sachdeva, A.
2003-05-01
Rotational relaxation of three organic solutes, coumarin 6 (C6), 2,5-dimethyl-1, 4-dioxo3,6-diphenylpyrrolo[3,4-c]pyrrole (DMDPP), and nile red (NR), that are similar in size but distinct in shape has been studied in a nonpolar solvent, squalane as a function of temperature to find out how the mechanical friction experienced by the solute molecule is influenced by its shape. It has been observed that C6 rotates slowest followed by NR and DMDPP. The results are analyzed using Stokes-Einstein-Debye (SED) hydrodynamic theory and also quasihydrodynamic theories of Gierer and Wirtz, and Dote, Kivelson, and Schwartz. Analysis of the data using the SED theory reveals that the measured reorientation times of C6 and DMDPP follow subslip behavior whereas those of NR are found to match slip predictions. While no single model could mimic the observed trend even in a qualitative manner, the reorientation times of C6 and DMDPP when normalized by their respective shape factors and boundary-condition parameters can be scaled on a common curve over the entire range of temperature studied. The probable reasons for the distinctive rotational behavior of NR as compared to C6 and DMDPP are explained in terms of its molecular shape and how this in turn influences the boundary-condition parameter are discussed.
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.
Weakly asymptotically hyperbolic manifolds
Allen, Paul T; Lee, John M; Allen, Iva Stavrov
2015-01-01
We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature invariants decay at infinity, identifying a conformally invariant tensor which serves as an obstruction to "higher order decay" of the Riemann curvature operator. Finally, we establish Fredholm results for geometric elliptic operators, extending the work of Rafe Mazzeo and John M. Lee to this setting. As an application, we show that any weakly asymptotically hyperbolic metric is conformally related to a weakly asymptotically hyperbolic metric of constant negative curvature.
ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
SHEN Yi; JIANG Ming-hui; LIAO Xiao-xin
2006-01-01
Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of t he solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.
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...
Coarse-grained model for N2-N relaxation in hypersonic shock conditions using two-dimensional bins
Zhu, Tong; Li, Zheng; Levin, Deborah A.
2016-11-01
A high fidelity internal energy relaxation model for N2-N suitable for use in direct simulation Monte Carlo (DSMC) modeling of chemically reacting flows is proposed. A novel two-dimensional binning approach with variable bin energy resolutions in the rotational and vibrational modes is developed for treating the internal mode of N2. Both bin-to-bin and state-specific relaxation cross sections are obtained using the molecular dynamics/quasi-classical trajectory (MD/QCT) method with two potential energy surfaces as well as the state-specific database of Jaffe et al. The 99 bin model is used in homogeneous DSMC relaxation simulations and is found to be able to recover the state-specific master equation results of Panesi et al. when the Jaffe state-specific cross sections are used. Rotational relaxation energy profiles and relaxation times obtained using the ReaxFF and Jaffe potential energy surfaces (PESs) are in general agreement but there are larger differences between the vibrational relaxation times. These differences become smaller as the translational temperature increases because the difference in the PES energy barrier becomes less important.
Development of a two-dimensional binning model for N2-N relaxation in hypersonic shock conditions
Zhu, Tong; Li, Zheng; Levin, Deborah A.
2016-08-01
A high fidelity internal energy relaxation model for N2-N suitable for use in direct simulation Monte Carlo (DSMC) modeling of chemically reacting flows is proposed. A novel two-dimensional binning approach with variable bin energy resolutions in the rotational and vibrational modes is developed for treating the internal mode of N2. Both bin-to-bin and state-specific relaxation cross sections are obtained using the molecular dynamics/quasi-classical trajectory (MD/QCT) method with two potential energy surfaces as well as the state-specific database of Jaffe et al. The MD/QCT simulations of inelastic energy exchange between N2 and N show that there is a strong forward-preferential scattering behavior at high collision velocities. The 99 bin model is used in homogeneous DSMC relaxation simulations and is found to be able to recover the state-specific master equation results of Panesi et al. when the Jaffe state-specific cross sections are used. Rotational relaxation energy profiles and relaxation times obtained using the ReaxFF and Jaffe potential energy surfaces (PESs) are in general agreement but there are larger differences between the vibrational relaxation times. These differences become smaller as the translational temperature increases because the difference in the PES energy barrier becomes less important.
Ramnath, Rudrapatna V
2012-01-01
This book addresses the task of computation from the standpoint of asymptotic analysis and multiple scales that may be inherent in the system dynamics being studied. This is in contrast to the usual methods of numerical analysis and computation. The technical literature is replete with numerical methods such as Runge-Kutta approach and its variations, finite element methods, and so on. However, not much attention has been given to asymptotic methods for computation, although such approaches have been widely applied with great success in the analysis of dynamic systems. The presence of differen
Yurasov, D. V., E-mail: Inquisitor@ipm.sci-nnov.ru [Russian Academy of Sciences, Institute for Physics of Microstructures (Russian Federation); Bobrov, A. I. [Lobachevsky State University of Nizhny Novgorod (Russian Federation); Daniltsev, V. M.; Novikov, A. V. [Russian Academy of Sciences, Institute for Physics of Microstructures (Russian Federation); Pavlov, D. A. [Lobachevsky State University of Nizhny Novgorod (Russian Federation); Skorokhodov, E. V.; Shaleev, M. V.; Yunin, P. A. [Russian Academy of Sciences, Institute for Physics of Microstructures (Russian Federation)
2015-11-15
Influence of the Ge layer thickness and annealing conditions on the parameters of relaxed Ge/Si(001) layers grown by molecular beam epitaxy via two-stage growth is investigated. The dependences of the threading dislocation density and surface roughness on the Ge layer thickness, annealing temperature and time, and the presence of a hydrogen atmosphere are obtained. As a result of optimization of the growth and annealing conditions, relaxed Ge/Si(001) layers which are thinner than 1 μm with a low threading dislocation density on the order of 10{sup 7} cm{sup –2} and a root mean square roughness of less than 1 nm are obtained.
Asymptotic freedom, asymptotic flatness and cosmology
Kiritsis, Elias
2013-01-01
Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free $\\beta$-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability and other problems of such inflationary models.
Asymptotic symmetry algebra of conformal gravity
Irakleidou, M
2016-01-01
We compute asymptotic symmetry algebras of conformal gravity. Due to more general boundary conditions allowed in conformal gravity in comparison to those in Einstein gravity, we can classify the corresponding algebras. The highest algebra for non-trivial boundary conditions is five dimensional and it leads to global geon solution with non-vanishing charges.
On the Asymptotic Distribution of Signal Fraction
Volobouev, Igor
2016-01-01
Condition of the asymptotic normality of the signal fraction estimate by maximum likelihood is derived under the null hypothesis of no signal. Consequences of this condition for determination of signal significance taking in to account the look elsewhere effect are discussed.
On an asymptotically linear elliptic Dirichlet problem
Zhitao Zhang
2002-01-01
Full Text Available Under very simple conditions, we prove the existence of one positive and one negative solution of an asymptotically linear elliptic boundary value problem. Even for the resonant case at infinity, we do not need to assume any more conditions to ensure the boundness of the (PS sequence of the corresponding functional. Moreover, the proof is very simple.
Mikolasek, Michael; Berg, Jonas; Witt, Claudia M; Barth, Jürgen
2017-07-27
This systematic review aims to summarize eHealth studies with mindfulness- and relaxation-based interventions for medical conditions and to determine whether eHealth interventions have positive effects on health. A comprehensive search of five databases was conducted for all available studies from 1990 to 2015. Studies were included if the intervention was mainly technology delivered and included a mindfulness- or relaxation-based intervention strategy and if patients with a medical condition were treated. Treatment effects were summarized for different outcomes. A total of 2383 records were identified, of which 17 studies with 1855 patients were included in this systematic review. These studies were conducted in patients with irritable bowel syndrome, chronic fatigue syndrome, cancer, chronic pain, surgery, and hypertension. All but one study were delivered online through a web-based platform; one study delivered the intervention with iPods. The studies indicate that mindfulness- and relaxation-based eHealth interventions can have positive effects on patients' general health and psychological well-being. No effects were found for stress or mindfulness. Only five studies reported economic analyses of eHealth interventions without any clear conclusion. There is some evidence that mindfulness- and relaxation-based eHealth interventions for medical conditions can have positive effects on health outcomes. Therefore, such interventions might be a useful addition to standard medical care. No app studies were retrieved, even though a vast number of smartphone apps exist which aim at increasing users' health. Therefore, more studies investigating those health apps are needed.
Liapunov structure and asymptotic expressions of linear differential systems
高维新
1996-01-01
With a view to the researches on asymptotic properties for linear differential systems,the characteristic number is transformed into functional dass which can indicate the change trend of the norm for solution,so the invariant structure is given under Liapunov changes and feasible computational method of asymptotic expressions for linear differential systems with variant coefficients,and various asymptotic conclusions induding the necessary and sufllcient conditions of stability are got.
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...
Litim, Daniel F.; Sannino, Francesco
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet ...... fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.......We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet...
Litim, Daniel F
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.
Composite asymptotic expansions
Fruchard, Augustin
2013-01-01
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance pro...
Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes
M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractThe paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical
Matsubara, Eri; Fukagawa, Mio; Okamoto, Tsuyoshi; Ohnuki, Koichiro; Shimizu, Kuniyoshi; Kondo, Ryuichiro
2011-04-01
(-)-Bornyl acetate is the main volatile constituent in numerous conifer oils and has a camphoraceous, pine-needle-like odor. It is frequently used as the conifer needle composition in soap, bath products, room sprays, and pharmaceutical products. However, the psychophysiological effects of (-)-bornyl acetate remained unclear. We investigated the effects of breathing air mixed with (-)-bornyl acetate at different doses (low-dose and high-dose conditions) on the individuals during and after VDT (visual display terminal) work using a visual discrimination task. The amounts of (-)-bornyl acetate through our odorant delivery system for 40 min were 279.4 µg in the low-dose and 716.3 µg in the high-dose (-)-bornyl acetate condition. (-)-Bornyl acetate induced changes of autonomic nervous system for relaxation and reduced arousal level after VDT work without any influences of task performance in low-dose condition, but not in high-dose condition.
Error estimates in horocycle averages asymptotics: challenges from string theory
Cardella, M.A.
2010-01-01
For modular functions of rapid decay, a classical result connects the error estimate in their long horocycle average asymptotic to the Riemann hypothesis. We study similar asymptotics, for modular functions with not that mild growing conditions, such as of polynomial growth and of exponential growth
Asymptotic Behavior of Solutions to a Linear Volterra Integrodifferential System
Yue-Wen Cheng
2013-01-01
Full Text Available We investigate the asymptotic behavior of solutions to a linear Volterra integrodifferential system , We show that under some suitable conditions, there exists a solution for the above integrodifferential system, which is asymptotically equivalent to some given functions. Two examples are given to illustrate our theorem.
Asymptotic symmetries of de Sitter space-time
Chrusciel, P.T. (Polska Akademia Nauk, Warsaw. Inst. Fizyki)
1981-01-01
The general form of the metric of an axially-symmetrical asymptotically de Sitter space-time fulfilling a radiation condition was found. Using the Bondi-Metzner method, the group of asymptotic symmetries of de Sitter space-time was found. The results obtained in this work agree only partially with Penrose's theory.
Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations
Sachdev, PL
2010-01-01
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/boundary conditions. This title presents the constructive mathematical techniques. It deals with the asymptotic methods which include self-similarity, balancing argument, and matched asymptotic expansions
Rohollah Soleimani
2012-07-01
Full Text Available In this study, Mn-ferrite has been prepared with nominal formula of MnFe2O4, using the dry conventional ceramic method. The raw materials were Mobarakeh steel company modified domestic iron oxide and Merckmanganese oxide. XRD patterns of the prepared samples show that they are single phase. Magnetic measurements have been performed on the toroidal samples sintered in different temperatures, using ahystograph unit MPG100D model. The results of measurements show that optimum formation pressures to obtain maximum relative magnetic permeability and hystersis. The Mn55 nuclear spin- lattice relaxation, and the ferromagnetic resonance linewidth have been studied in the same single crystal of ferromagnetic as a function ofthe temperature.
Ho, Pei-Ming
2017-04-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Ho, Pei-Ming
2016-01-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Confinement versus asymptotic freedom
Dubin, A Yu
2002-01-01
I put forward the low-energy confining asymptote of the solution $$ (valid for large macroscopic contours C of the size $>>1/\\Lambda_{QCD}$) to the large N Loop equation in the D=4 U(N) Yang-Mills theory with the asymptotic freedom in the ultraviolet domain. Adapting the multiscale decomposition characteristic of the Wilsonean renormgroup, the proposed Ansatz for the loop-average is composed in order to sew, along the lines of the bootstrap approach, the large N weak-coupling series for high-momentum modes with the $N\\to{\\infty}$ limit of the recently suggested stringy representation of the 1/N strong-coupling expansion Dub4 applied to low-momentum excitations. The resulting low-energy stringy theory can be described through such superrenormalizable deformation of the noncritical Liouville string that, being devoid of ultraviolet divergences, does not possess propagating degrees of freedom at short-distance scales $<<1/{\\sqrt{\\sigma_{ph}}}$, where $\\sigma_{ph}\\sim{(\\Lambda_{QCD})^{2}}$ is the physical s...
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Asymptotically safe grand unification
Bajc, Borut; Sannino, Francesco
2016-12-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
Asymptotically Safe Grand Unification
Bajc, Borut
2016-01-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
On the asymptotics of the α-Farey transfer operator
Kautzsch, J.; Kesseböhmer, M.; Samuel, T.; Stratmann, B. O.
2015-01-01
We study the asymptotics of iterates of the transfer operator for non-uniformly hyperbolic α-Farey maps. We provide a family of observables which are Riemann integrable, locally constant and of bounded variation, and for which the iterates of the transfer operator, when applied to one of these observables, is not asymptotic to a constant times the wandering rate on the first element of the partition α. Subsequently, sufficient conditions on observables are given under which this expected asymptotic holds. In particular, we obtain an extension theorem which establishes that, if the asymptotic behaviour of iterates of the transfer operator is known on the first element of the partition α, then the same asymptotic holds on any compact set bounded away from the indifferent fixed point.
Asymptotic admissibility of priors and elliptic differential equations
Hartigan, J A
2010-01-01
We evaluate priors by the second order asymptotic behavior of the corresponding estimators.Under certain regularity conditions, the risk differences between efficient estimators of parameters taking values in a domain D, an open connected subset of R^d, are asymptotically expressed as elliptic differential forms depending on the asymptotic covariance matrix V. Each efficient estimator has the same asymptotic risk as a 'local Bayes' estimate corresponding to a prior density p. The asymptotic decision theory of the estimators identifies the smooth prior densities as admissible or inadmissible, according to the existence of solutions to certain elliptic differential equations. The prior p is admissible if the quantity pV is sufficiently small near the boundary of D. We exhibit the unique admissible invariant prior for V=I,D=R^d-{0). A detailed example is given for a normal mixture model.
Asymptotic stability properties of θ-methods for delay differential equations
无
2001-01-01
Deals with the asymptotic stability properties of θ- methods for the pantograph equation and the linear delay differential-algebraic equation with emphasis on the linear θ- methods with variable stepsize schemes for the pantograph equation, proves that asymptotic stability is obtained if and only if θ ＞ 1/2, and studies further the one-leg θ- method for the linear delay differential-algebraic equation and establishes the sufficient asymptotic-ally differential-algebraic stable condition θ = 1.
Asymptotical Properties for Parabolic Systems of Neutral Type
CUI Bao-tong; HAN Mao-an
2005-01-01
Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis. The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.
Asymptotic Extension of Nonlinear Models with Bayesian Conditions%Bayes条件下非线性模型参数估计的渐近展开
吴一凡
2012-01-01
给出了在Bayes条件下非线性回归模型的参数估计，建立了非线性回归模型的几何结构，推广了Bates和Wates关于非线性回归模型的几何框架，用几何方法求出参数估计的随机展开，并讨论了若干与统计曲率相关的渐近性质，给出了该模型的极大似然估计的方差和偏差的近似表示．%In this paper, we propose a differential geometric framework for nonlinear model under Bayesian conditions. Our framework may be regarded as an extension of that presented by Bates & watts for nonlinear regression models. We use this geometric framework to discuss the parameter stochastic expansion by using the curvature in the nonlinear model. Some statistical properties of parameter are studied from the geometric point of view.
Nuclear relaxation via paramagnetic impurities
Dzheparov, F S; Jacquinot, J F
2002-01-01
First part of the work contains a calculation of the kinetics of nuclear relaxation via paramagnetic impurities for systems with arbitrary (including fractal) space dimension d basing on ideas, which run current for 3d objects now. A new mean-field-type theory is constructed in the second part of the work. It reproduces all results of the first part for integer d and gives a possibility to describe the process for longer time, when a crossover to Balagurov-Waks asymptotics starts to develop. Solutions of the equations of the new theory are constructed for integer d. To obtain the solutions a method of calculation of the low-energy and long-wave asymptotics for T matrix of potential scattering out of the mass shell for singular repulsive potentials is developed
Xionghua Wu
2012-01-01
Full Text Available Let {}⊂(0,1 be such that →1 as →∞, let and be two positive numbers such that +=1, and let be a contraction. If be a continuous asymptotically pseudocontractive self-mapping of a nonempty bounded closed convex subset of a real reflexive Banach space with a uniformly Gateaux differentiable norm, under suitable conditions on the sequence {}, we show the existence of a sequence {} satisfying the relation =(1−/(+(/ and prove that {} converges strongly to the fixed point of , which solves some variational inequality provided is uniformly asymptotically regular. As an application, if be an asymptotically nonexpansive self-mapping of a nonempty bounded closed convex subset of a real Banach space with a uniformly Gateaux differentiable norm and which possesses uniform normal structure, we prove that the iterative process defined by 0∈,+1=(1−/(+(/+(/ converges strongly to the fixed point of .
Asymptotic Existence of Nearly Kirkman Systems
沈灏; 储文松
1994-01-01
It is proved in this paper that,for any given positive integer k≥2,there exists a constant v0=v0(k) such that for v≥v0,the necessary condition v=0 (mod k(k-)) for the existence of a nearly Kirkman system NKS (2,k,v) is also sufficient.Thus we have completely determined the asymptotic existence of NKS.
Theorems for Asymptotic Safety of Gauge Theories
Bond, Andrew D
2016-01-01
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasized. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.
Theorems for asymptotic safety of gauge theories
Bond, Andrew D.; Litim, Daniel F. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)
2017-06-15
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated. (orig.)
ASYMPTOTICS OF MEAN TRANSFORMATION ESTIMATORS WITH ERRORS IN VARIABLES MODEL
CUI Hengjian
2005-01-01
This paper addresses estimation and its asymptotics of mean transformation θ = E[h(X)] of a random variable X based on n iid. Observations from errors-in-variables model Y = X + v, where v is a measurement error with a known distribution and h(.) is a known smooth function. The asymptotics of deconvolution kernel estimator for ordinary smooth error distribution and expectation extrapolation estimator are given for normal error distribution respectively. Under some mild regularity conditions, the consistency and asymptotically normality are obtained for both type of estimators. Simulations show they have good performance.
Rupp, Wolf; Simon, Karl-Heinz; Bohnert, Michael
2009-01-01
Complete relaxation can be achieved by floating in a darkened, sound-proof relaxation tank filled with salinated water kept at body temperature. Under these conditions, meditation exercises up to self-hypnosis may lead to deep relaxation with physical and mental revitalization. A user manipulated his tank, presumably to completely cut off all optical and acoustic stimuli and accidentally also covered the ventilation hole. The man was found dead in his relaxation tank. The findings suggested lack of oxygen as the cause of death.
Esmaeili, Shadi; Pleimling, Michel
We study the responses of predator-prey systems to temporary changes in environmental conditions. Such changes can cause a variation in species' predatory preferences which in our model appears as a perturbation in a many-species system. The type of perturbation that we consider in this study is a sudden change in the interaction scheme. We focus on systems evolving on a two-dimensional lattice and discuss the way the systems transition from one steady state to another. Using Monte Carlo simulations we monitor these transitions via the space-time correlation function and the derived correlation length. This work is supported by the US National Science Foundation through Grant DMR-1205309.
Zhang, Baoyong; Lam, James; Xu, Shengyuan
2015-07-01
This paper revisits the problem of asymptotic stability analysis for neural networks with distributed delays. The distributed delays are assumed to be constant and prescribed. Since a positive-definite quadratic functional does not necessarily require all the involved symmetric matrices to be positive definite, it is important for constructing relaxed Lyapunov-Krasovskii functionals, which generally lead to less conservative stability criteria. Based on this fact and using two kinds of integral inequalities, a new delay-dependent condition is obtained, which ensures that the distributed delay neural network under consideration is globally asymptotically stable. This stability criterion is then improved by applying the delay partitioning technique. Two numerical examples are provided to demonstrate the advantage of the presented stability criteria.
Black hole thermodynamics from a variational principle: Asymptotically conical backgrounds
An, Ok Song; Papadimitriou, Ioannis
2016-01-01
The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for $\\mathcal{N}=2$ STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called `subtracted geometries'. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associat...
Semilocal density functional theory with correct surface asymptotics
Constantin, Lucian A.; Fabiano, Eduardo; Pitarke, J. M.; Della Sala, Fabio
2016-03-01
Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the nonlocality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the imagelike surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to those at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.
Fan, Zhengfeng; Liu, Jie
2016-10-01
We present an ion-electron non-equilibrium model, in which the hot-spot ion temperature is higher than its electron temperature so that the hot-spot nuclear reactions are enhanced while energy leaks are considerably reduced. Theoretical analysis shows that the ignition region would be significantly enlarged in the hot-spot rhoR-T space as compared with the commonly used equilibrium model. Simulations show that shocks could be utilized to create and maintain non-equilibrium conditions within the hot spot, and the hot-spot rhoR requirement is remarkably reduced for achieving self-heating. In NIF high-foot implosions, it is observed that the x-ray enhancement factors are less than unity, which is not self-consistent and is caused by assuming Te =Ti. And from this non-consistency, we could infer that ion-electron non-equilibrium exists in the high-foot implosions and the ion temperature could be 9% larger than the equilibrium temperature.
Asymptotic Dynamics of Monopole Walls
Cross, R
2015-01-01
We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs curve using the Newton polytope and amoeba. In particular, we show that the monopole wall splits into subwalls when any of its moduli become large. The long-distance gauge and Higgs field interactions of these subwalls are abelian, allowing us to derive an asymptotic metric for the monopole wall moduli space.
Nakano, Hiroyuki; Tanaka, Takahiro; Nakamura, Takashi
2016-01-01
The Sasaki-Nakamura transformation gives a short-ranged potential and a convergent source term for the master equation of perturbations in the Kerr space-time. In this paper, we study the asymptotic behavior of the transformation, and present a new relaxed necessary and sufficient condition of the transformation to obtain the short-ranged potential in the assumption that the transformation converges in the far distance. Also, we discuss quasinormal mode frequencies which are determined by the information around the peak of the potential in the WKB analysis. Finally, in the extreme Kerr limit, $a/M \\to 1$, where $M$ and $a$ denote the mass and spin parameter of a Kerr black hole, respectively, we find the peak location of the potential, $r_p/M \\lesssim 1 + 1.8 \\,(1-a/M)^{1/2}$ by using the new transformation. The uncertainty of the location is as large as that expected from the equivalence principle.
Asymptotic dynamics of three-dimensional gravity
Donnay, Laura
2016-01-01
These are the lectures notes of the course given at the Eleventh Modave Summer School in Mathematical Physics, 2015, aimed at PhD candidates and junior researchers in theoretical physics. We review in details the result of Coussaert-Henneaux-van Driel showing that the asymptotic dynamics of $(2+1)$- dimensional gravity with negative cosmological constant is described at the classical level by Liouville theory. Boundary conditions implement the asymptotic reduction in two steps: the first set reduces the $SL(2,\\mathbb R)\\times SL(2,\\mathbb R)$ Chern-Simons action, equivalent to the Einstein action, to a non-chiral $SL(2,\\mathbb R)$ Wess-Zumino-Witten model, while the second set imposes constraints on the WZW currents that reduce further the action to Liouville theory. We discuss the issues of considering the latter as an effective description of the dual conformal field theory describing AdS$_3$ gravity beyond the semi-classical regime.
Asymptotic Markov inequality on Jordan arcs
Totik, V.
2017-03-01
Markov's inequality for the derivative of algebraic polynomials is considered on C^2-smooth Jordan arcs. The asymptotically best estimate is given for the kth derivative for all k=1,2,\\dots . The best constant is related to the behaviour around the endpoints of the arc of the normal derivative of the Green's function of the complementary domain. The result is deduced from the asymptotically sharp Bernstein inequality for the kth derivative at inner points of a Jordan arc, which is derived from a recent result of Kalmykov and Nagy on the Bernstein inequality on analytic arcs. In the course of the proof we shall also need to reduce the analyticity condition in this last result to C^2-smoothness. Bibliography: 21 titles.
On asymptotic flatness and Lorentz charges
Compere, Geoffrey [KdV Institute for Mathematics, Universiteit van Amsterdam (Netherlands); Dehouck, Francois; Virmani, Amitabh, E-mail: gcompere@uva.nl, E-mail: fdehouck@ulb.ac.be, E-mail: avirmani@ulb.ac.be [Physique Theorique et Mathematique, Universite Libre de Bruxelles, Bruxelles (Belgium)
2011-07-21
In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence-free tensors that we construct from the equations of motion. Second, we show that the integrability of Einstein's equations in the asymptotic expansion is sufficient to establish the equivalence between counter-term charges defined from the variational principle and charges defined by Ashtekar and Hansen. These results clarify earlier constructions of conserved charges in the hyperboloid representation of spatial infinity. In showing this, the parity condition on the mass aspect is not needed. Along the way in establishing these results, we prove two lemmas on tensor fields on three-dimensional de Sitter spacetime stated by Ashtekar-Hansen and Beig-Schmidt and state and prove three additional lemmas.
Asymptotic Stability of Uniformly Bounded Nonlinear Switched Systems
Jouan, Philippe; Naciri, Said
2012-01-01
We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of inputs with dwell-time, and the class of general ones. For each of them we provide some sufficient conditions for asymptotic stability in terms of the geometry of certain sets. The results, which extend those of Balde, Jouan about linear systems, are illustrated...
Norris, G; McConnell, G
2010-03-01
A novel bi-directional pump geometry that nonlinearly increases the nonlinear optical conversion efficiency of a synchronously pumped optical parametric oscillator (OPO) is reported. This bi-directional pumping method synchronizes the circulating signal pulse with two counter-propagating pump pulses within a linear OPO resonator. Through this pump scheme, an increase in nonlinear optical conversion efficiency of 22% was achieved at the signal wavelength, corresponding to a 95% overall increase in average power. Given an almost unchanged measured pulse duration of 260 fs under optimal performance conditions, this related to a signal wavelength peak power output of 18.8 kW, compared with 10 kW using the traditional single-pass geometry. In this study, a total effective peak intensity pump-field of 7.11 GW/cm(2) (corresponding to 3.55 GW/cm(2) from each pump beam) was applied to a 3 mm long periodically poled lithium niobate crystal, which had a damage threshold intensity of 4 GW/cm(2), without impairing crystal integrity. We therefore prove the application of this novel pump geometry provides opportunities for power-scaling of synchronously pumped OPO systems together with enhanced nonlinear conversion efficiency through relaxed damage threshold intensity conditions.
WIERDA, JMKH; VANDENBROEK, L; PROOST, JH; VERBAAN, BW; HENNIS, PJ
1993-01-01
In a randomized study, we evaluated lag time (time from the end of injection of muscle relaxant until the first depression of the train-of-four response [TOF]), onset time (time from the end of injection of muscle relaxant until the maximum depression of the first twitch of the TOF [T1]), neuromuscu
Polynomial Asymptotes of the Second Kind
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
New asymptotically flat phantom wormhole solutions
Lobo, Francisco S N; Riazi, Nematollah
2012-01-01
A possible cause of the late-time cosmic acceleration is an exotic fluid with an equation of state lying within the phantom regime, i.e., $w=p/\\rho 0. Thus, there is no need to surgically paste the interior wormhole geometry to an exterior vacuum spacetime. We also consider the "volume integral quantifier", which provides useful information regarding the total amount of energy condition violating matter, and show that, in principle, it is possible to construct asymptotically flat wormhole solutions with an arbitrary small amount of energy condition violating matter.
Liu, Q
2016-01-01
In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for convection heat transfer in porous media under local thermal non-equilibrium (LTNE) condition. The model is constructed within the framework of the three-distribution-function approach: two temperature-based MRT-LB equations are proposed for the temperature fields of fluid and solid phases in addition to the MRT-LB equation of a density distribution function for the velocity field described by the generalized non-Darcy model. The thermal non-equilibrium effects are incorporated into the model by adding source terms into the temperature-based MRT-LB equations. Moreover, the discrete lattice effects are considered in the introduction of source terms into the temperature-based MRT-LB equations. The source terms accounting for the thermal non-equilibrium effects are simple and the model retains the inherent features of the standard LB method. Numerical results demonstrate that the proposed model can be served as an accura...
Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle
Salazar, Domingos S. P.; Lira, Sérgio A.
2016-11-01
In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from the stochastic differential equation of our system’s energy in the underdamped regime. By utilizing this stochastic thermodynamics approach, we are able to completely describe the heat exchange process between the nanoparticle and the surrounding environment. As an important consequence of our results, we observe the validity of the heat exchange fluctuation theorem in our setup, which holds for systems arbitrarily far from equilibrium conditions. By extending our results for the case of N noninterating nanoparticles, we perform analytical asymptotic limits and direct numerical simulations that corroborate our analytical predictions.
Dimension reduction for systems with slow relaxation
Venkataramani, Shankar C; Restrepo, Juan M
2016-01-01
We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal' model reductions. We discuss how our methods apply to the practically important problem of modeling oil spills.
Asymptotics of trimmed CUSUM statistics
Berkes, István; Schauer, Johannes; 10.3150/10-BEJ318
2012-01-01
There is a wide literature on change point tests, but the case of variables with infinite variances is essentially unexplored. In this paper we address this problem by studying the asymptotic behavior of trimmed CUSUM statistics. We show that in a location model with i.i.d. errors in the domain of attraction of a stable law of parameter $0<\\alpha <2$, the appropriately trimmed CUSUM process converges weakly to a Brownian bridge. Thus, after moderate trimming, the classical method for detecting change points remains valid also for populations with infinite variance. We note that according to the classical theory, the partial sums of trimmed variables are generally not asymptotically normal and using random centering in the test statistics is crucial in the infinite variance case. We also show that the partial sums of truncated and trimmed random variables have different asymptotic behavior. Finally, we discuss resampling procedures which enable one to determine critical values in the case of small and mo...
Asymptotic aspects of Cayley graphs
Dejter, Italo J
2011-01-01
Arising from complete Cayley graphs $\\Gamma_n$ of odd cyclic groups $\\Z_n$, an asymptotic approach is presented on connected labeled graphs whose vertices are labeled via equally-multicolored copies of $K_4$ in $\\Gamma_n$ with adjacency of any two such vertices whenever they are represented by copies of $K_4$ in $\\Gamma_n$ sharing two equally-multicolored triangles. In fact, these connected labeled graphs are shown to form a family of graphs of largest degree 6 and diameter asymptotically of order $|V|^{1/3}$, properties shared by the initial member of a collection of families of Cayley graphs of degree $2m\\geq 6$ with diameter asymptotically of order $|V|^{1/m}$, where $3\\leq m\\in\\Z$.
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...
Asymptotic vacua with higher derivatives
Spiros Cotsakis
2016-04-01
Full Text Available We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Asymptotic vacua with higher derivatives
Cotsakis, Spiros, E-mail: skot@aegean.gr [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kadry, Seifedine, E-mail: Seifedine.Kadry@aum.edu.kw [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kolionis, Georgios, E-mail: gkolionis@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece); Tsokaros, Antonios, E-mail: atsok@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece)
2016-04-10
We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Expansions and Asymptotics for Statistics
Small, Christopher G
2010-01-01
Providing a broad toolkit of analytical methods, this book shows how asymptotics, when coupled with numerical methods, becomes a powerful way to acquire a deeper understanding of the techniques used in probability and statistics. It describes core ideas in statistical asymptotics; covers Laplace approximation, the saddle-point method, and summation of series; and, includes vignettes of various people from statistics and mathematics whose ideas have been instrumental in the development of the subject. The author also supplements some topics with relevant Maplea commands and provides a list of c
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Higher dimensional nonclassical eigenvalue asymptotics
Camus, Brice; Rautenberg, Nils
2015-02-01
In this article, we extend Simon's construction and results [B. Simon, J. Funct. Anal. 53(1), 84-98 (1983)] for leading order eigenvalue asymptotics to n-dimensional Schrödinger operators with non-confining potentials given by Hn α = - Δ + ∏ i = 1 n |x i| α i on ℝn (n > 2), α ≔ ( α 1 , … , α n ) ∈ ( R+ ∗ ) n . We apply the results to also derive the leading order spectral asymptotics in the case of the Dirichlet Laplacian -ΔD on domains Ωn α = { x ∈ R n : ∏ j = 1 n }x j| /α j α n < 1 } .
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
Relaxation and self-sustained oscillations in the time elapsed neuron network model
Pakdaman, Khashayar; Salort, Delphine
2011-01-01
The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons structured by this time. In an earlier work, based on generalized relative entropy methods, it is proved that for highly or weakly connected networks the model exhibits relaxation to the steady state and for moderately connected networks it is obtained numerical evidence of appearance of self-sustained periodic solutions. Here, we go further and, using the particular form of the model, we quantify the regime where relaxation to a stationary state occurs in terms of the network connectivity. To introduce our methodology, we first consider the case where the neurons are not connected and we give a new statement showing that total asynchronous firing of neurons appears asymptotically. In a second step, we consider the case with connections and give a low connectivity condition that...
Marzola, Luca; Raidal, Martti
2016-11-01
Motivated by natural inflation, we propose a relaxation mechanism consistent with inflationary cosmology that explains the hierarchy between the electroweak scale and Planck scale. This scenario is based on a selection mechanism that identifies the low-scale dynamics as the one that is screened from UV physics. The scenario also predicts the near-criticality and metastability of the Standard Model (SM) vacuum state, explaining the Higgs boson mass observed at the Large Hadron Collider (LHC). Once Majorana right-handed neutrinos are introduced to provide a viable reheating channel, our framework yields a corresponding mass scale that allows for the seesaw mechanism as well as for standard thermal leptogenesis. We argue that considering singlet scalar dark matter extensions of the proposed scenario could solve the vacuum stability problem and discuss how the cosmological constant problem is possibly addressed.
Asymptotic curved interface models in piezoelectric composites
Serpilli, Michele
2016-10-01
We study the electromechanical behavior of a thin interphase, constituted by a piezoelectric anisotropic shell-like thin layer, embedded between two generic three-dimensional piezoelectric bodies by means of the asymptotic analysis in a general curvilinear framework. After defining a small real dimensionless parameter ε, which will tend to zero, we characterize two different limit models and their associated limit problems, the so-called weak and strong piezoelectric curved interface models, respectively. Moreover, we identify the non-classical electromechanical transmission conditions at the interface between the two three-dimensional bodies.
BIHARMONIC EQUATIONS WITH ASYMPTOTICALLY LINEAR NONLINEARITIES
Liu Yue; Wang Zhengping
2007-01-01
This article considers the equation △2u = f(x, u)with boundary conditions either u|(a)Ω = (a)u/(a)n|(a)Ω = 0 or u|(a)Ω = △u|(a)Ω = 0, where f(x,t) is asymptotically linear with respect to t at infinity, and Ω is a smooth bounded domain in RN, N ＞ 4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x, t).
Asymptotics of the QMLE for General ARCH(q) Models
Kristensen, Dennis; Rahbek, Anders Christian
2009-01-01
Asymptotics of the QMLE for Non-Linear ARCH Models Dennis Kristensen, Columbia University Anders Rahbek, University of Copenhagen Abstract Asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for non-linear ARCH(q) models -- including for example Asymmetric Power ARCH and log......-ARCH -- are derived. Strong consistency is established under the assumptions that the ARCH process is geometrically ergodic, the conditional variance function has a finite log-moment, and finite second moment of the rescaled error. Asymptotic normality of the estimator is established under the additional assumption...... that certain ratios involving the conditional variance function are suitably bounded, and that the rescaled errors have little more than fourth moment. We verify our general conditions, including identification, for a wide range of leading specific ARCH models....
Dipolar relaxation of cold sodium atoms in a magnetic field
Zygelman, B
2002-01-01
A quantum mechanical close coupling theory of spin relaxation in the stretched hyperfine level of sodium is presented. We calculate the dipolar relaxation rate of magnetically trapped cold sodium atoms in the magnetic field. The influence of shape resonances and the anisotropy of the dipolar interaction on the collision dynamics are explored. We examine the sensitivity of the calculated cross sections on the choice of asymptotic atomic state basis.
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.
Ruin problems and tail asymptotics
Rønn-Nielsen, Anders
The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived...
Inaccurate usage of asymptotic formulas
Maj, R; Maj, Radoslaw; Mrowczynski, Stanislaw
2004-01-01
The asymptotic form of the plane-wave decomposition into spherical waves, which is often used, in particular, to express the scattering amplitude through the phase shifts, is incorrect. We precisely explain why it is incorrect and show how to circumvent mathematical inconsistency.
Thermodynamics of asymptotically safe theories
Rischke, Dirk H.; Sannino, Francesco
2015-01-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
2011-01-01
This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
MULTIPLE SOLUTIONS TO AN ASYMPTOTICALLY LINEAR ROBIN BOUNDARY VALUE PROBLEM
无
2012-01-01
Under some weaker conditions,we prove the existence of at least two solutions to an asymptotically linear elliptic problem with Robin boundary value condition,using truncation arguments.Our results are also valid for the case of the so-called resonance at infinity.
M-Estimation for Discrete Data. Asymptotic Distribution Theory and Implications.
1985-10-01
DATA: ASYMPTOTIC DISTRIBUTION THEORY AND IMPLICATIONS by 1 Douglas G. Simpson Departr.ient of Statistics University of Illinois Urbana, Illinois...asymptotic distribution theory of M-estimators especially relevant to discrete data, although Theorem 1 is somewhat broader in scope’. The main results are...The version (2.5) c (X9 / - ), where s(a)=9 / + (c) is defined by (2.3), is slightly more convenient. 3. Extended asymptotic distribution theory Conditions
LI Hong; L(U) Shu; ZHONG Shou-ming
2005-01-01
The global uniform asymptotic stability of competitive neural networks with different time scales and delay is investigated. By the method of variation of parameters and the method of inequality analysis, the condition for global uniformly asymptotically stable are given. A strict Lyapunov function for the flow of a competitive neural system with different time scales and delay is presented. Based on the function, the global uniform asymptotic stability of the equilibrium point can be proved.
On transfinite extension of asymptotic dimension
Radul, Taras
2006-01-01
We prove that a transfinite extension of asymptotic dimension asind is trivial. We introduce a transfinite extension of asymptotic dimension asdim and give an example of metric proper space which has transfinite infinite dimension.
Liu, Jing; Wu, Wei-Min; Che, Juan-Juan; Zhang, Jun; Wang, Rui
2006-01-01
Rings of rabbit aorta that were both incubated in a high concentration of D-glucose and contracted submaximally by phenylephrine showed significantly decreased endothelium-dependent relaxations induced by acetylcholine. The cGMP production of aorta rings was also reduced. Treatment with endomorphins (1-1000 nmol/L) restored acetylcholine-induced relaxations of aorta rings incubated in high glucose concentrations and increased the cGMP synthesis. Moreover, this effect of endomorphins on endothelium was antagonized by naloxone, and the increase in the production of cGMP was also blocked.
Nonabelian Higgs models: paving the way for asymptotic freedom
Gies, Holger
2016-01-01
Asymptotically free renormalization group trajectories can be constructed in nonabelian Higgs models with the aid of generalized boundary conditions imposed on the renormalized action. We detail this construction within the languages of simple low-order perturbation theory, effective field theory, as well as modern functional renormalization group equations. We construct a family of explicit scaling solutions using a controlled weak-coupling expansion in the ultraviolet, and obtain a standard Wilsonian RG relevance classification of perturbations about scaling solutions. We obtain global information about the quasi-fixed function for the scalar potential by means of analytic asymptotic expansions and numerical shooting methods. Further analytical evidence for such asymptotically free theories is provided in the large-N limit. We estimate the long-range properties of these theories, and identify initial/boundary conditions giving rise to a conventional Higgs phase.
Black hole thermodynamics from a variational principle: asymptotically conical backgrounds
An, Ok Song; Cvetič, Mirjam; Papadimitriou, Ioannis
2016-03-01
The variational problem of gravity theories is directly related to black hole thermodynamics. For asymptotically locally AdS backgrounds it is known that holographic renormalization results in a variational principle in terms of equivalence classes of boundary data under the local asymptotic symmetries of the theory, which automatically leads to finite conserved charges satisfying the first law of thermodynamics. We show that this connection holds well beyond asymptotically AdS black holes. In particular, we formulate the variational problem for {N}=2 STU supergravity in four dimensions with boundary conditions corresponding to those obeyed by the so called `subtracted geometries'. We show that such boundary conditions can be imposed covariantly in terms of a set of asymptotic second class constraints, and we derive the appropriate boundary terms that render the variational problem well posed in two different duality frames of the STU model. This allows us to define finite conserved charges associated with any asymptotic Killing vector and to demonstrate that these charges satisfy the Smarr formula and the first law of thermodynamics. Moreover, by uplifting the theory to five dimensions and then reducing on a 2-sphere, we provide a precise map between the thermodynamic observables of the subtracted geometries and those of the BTZ black hole. Surface terms play a crucial role in this identification.
A generalized Cauchy process and its application to relaxation phenomena
Lim, S C [Faculty of Engineering, Multimedia University, 63100 Cyberjaya, Selangor (Malaysia); Li Ming [School of Information Science and Technology, East China Normal University, Shanghai 200026 (China)
2006-03-24
We study some of the basic properties of a generalized Cauchy process indexed by two parameters. The application of the Lamperti transformation to the generalized Cauchy process leads to a self-similar process which preserves the long-range dependence. The asymptotic properties of spectral density of the process are derived. Possible application of this process to model relaxation phenomena is considered.
Lezhnin Sergey
2017-01-01
Full Text Available The two-temperature model of the outflow from a vessel with initial supercritical parameters of medium has been realized. The model uses thermodynamic non-equilibrium relaxation approach to describe phase transitions. Based on a new asymptotic model for computing the relaxation time, the outflow of water with supercritical initial pressure and super- and subcritical temperatures has been calculated.
Composite Operators in Asymptotic Safety
Pagani, Carlo
2016-01-01
We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dimensional quantum gravity. Finally, we briefly argue that our construction paves the way to approach observables in the Asymptotic Safety program.
Remarks on asymptotically safe inflation
Tye, S.-H. Henry; Xu, Jiajun
2010-12-01
We comment on Weinberg’s interesting analysis of asymptotically safe inflation [S. Weinberg, Phys. Rev. DPRVDAQ1550-7998 81, 083535 (2010).10.1103/PhysRevD.81.083535]. We find that even if the gravity theory exhibits an ultraviolet fixed point, the energy scale during inflation is way too low to drive the theory close to the fixed point value. We choose the specific renormalization group flow away from the fixed point towards the infrared region that reproduces the Newton’s constant and today’s cosmological constant. We follow this renormalization group flow path to scales below the Planck scale to study the stability of the inflationary scenario. Again, we find that some fine-tuning is necessary to get enough e folds of inflation in the asymptotically safe inflationary scenario.
Asymptotic safety goes on shell
Benedetti, Dario
2012-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.
Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras
LI Jin-xiu; WANG Qin
2006-01-01
We introduce in this note the notions of asymptotic excision of proper metric spaces and asymptotic equivalence relation for subspaces of metric spaces, which are relevant in characterizing spatial ideals of the asymptotic coarse Roe algebras. We show that the lattice of the asymptotic equivalence classes of the subspaces of a proper metric space is isomorphic to the lattice of the spatial ideals of the asymptotic Roe algebra. For asymptotic excisions of the metric space, we also establish a Mayer-Vietoris sequence in K-theory of the asymptotic coarse Roe algebras.
Boundary Conditions for NHEK through Effective Action Approach
CHEN Bin; NING Bo; ZHANG Jia-Ju
2012-01-01
We study the asymptotic symmetry group (ASG) of the near horizon geometry of extreme Kerr black hole through the effective action approach developed by Porfyriadis and Wilczek (arXiv:1007.1031v1[gr qc]).By requiring a finite boundary effective action,we derive a new set of asymptotic Killing vectors and boundary conditions,which are much more relaxed than the ones proposed by Matsuo Y et al.[Nucl.Phys.B 825 (2010) 231],and still allow a copy of a conformal group as its ASG.In the covariant formalism,the asymptotic charges are finite,with the corresponding central charge vanishing.By using the quasi-local charge and introducing a plausible cut-off,we find that the higher order terms of the asymptotic Killing vectors,which could not be determined through the effective action approach,contribute to the central charge as well.We also show that the boundary conditions suggested by Guica et al.[Phys.Rev.D 80 (2009)124008] lead to a divergent first-order boundary effective action.%We study the asymptotic symmetry group (ASG) of the near horizon geometry of extreme Kerr black hole through the effective action approach developed by Porfyriadis and Wilczek (arXiv:1007.1031vl[gr qc]). By requiring a finite boundary effective action, we derive a new set of asymptotic Killing vectors and boundary conditions, which are much more relaxed than the ones proposed by Matsuo Y et al. [Nucl. Phys. B 825 (2010) 231], and still allow a copy of a conformal group as its ASG. In the covariant formalism, the asymptotic charges are finite, with the corresponding central charge vanishing. By using the quasi-local charge and introducing a plausible cut-off, we find that the higher order terms of the asymptotic Killing vectors, which could not be determined through the effective action approach, contribute to the central charge as well. We also show that the boundary conditions suggested by Guica et al. [Phys. Rev. D 80 (2009) 124008] lead to a divergent first-order boundary effective action.
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of an asymptotically free (perhaps magnetic dual) extension.
Asymptotically thermal responses for smoothly switched detectors
Fewster, Christopher J; Louko, Jorma
2015-01-01
Thermal phenomena in quantum field theory can be detected with the aid of particle detectors coupled to quantum fields along stationary worldlines, by testing whether the response of such a detector satisfies the detailed balance version of the KMS condition at a constant temperature. This relation holds when the interaction between the field and the detector has infinite time duration. Operationally, however, detectors interact with fields for a finite amount of time, controlled by a switching function of compact support, and the KMS detailed balance condition cannot hold exactly for finite time interactions at arbitrarily large detector energy gap. In this large energy gap regime, we show that, for an adiabatically switched Rindler detector, the Unruh temperature emerges asymptotically after the detector and the field have interacted for a time that is polynomially long in the large energy. We comment on the significance of the adiabaticity assumption in this result.
Asymptotic integration of differential and difference equations
Bodine, Sigrun
2015-01-01
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...
Traytak, Sergey D., E-mail: sergtray@mail.ru [Centre de Biophysique Moléculaire, CNRS-UPR4301, Rue C. Sadron, 45071 Orléans (France); Le STUDIUM (Loire Valley Institute for Advanced Studies), 3D av. de la Recherche Scientifique, 45071 Orléans (France); Semenov Institute of Chemical Physics RAS, 4 Kosygina St., 117977 Moscow (Russian Federation)
2014-06-14
The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problem and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.
Traytak, Sergey D
2014-06-14
The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problem and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.
Traytak, Sergey D
2013-01-01
The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudial coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudial diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problem and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.
On a new approach to asymptotic stabilization problems
Ivanchikov, A. A.; Kornev, A. A.; Ozeritskii, A. V.
2009-12-01
A numerical algorithm for solving the asymptotic stabilization problem by the initial data to a fixed hyperbolic point with a given rate is proposed and justified. The stabilization problem is reduced to projecting the resolving operator of the given evolution process on a strongly stable manifold. This approach makes it possible to apply the results to a wide class of semidynamical systems including those corresponding to partial differential equations. By way of example, a numerical solution of the problem of the asymptotic stabilization of unstable trajectories of the two-dimensional Chafee-Infante equation in a circular domain by the boundary conditions is given.
The Asymptotic Limit for the 3D Boussinesq System
LI Lin-rui; WANG Ke; HONG Ming-li
2016-01-01
In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coeﬃcient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosityν=0 or zero diffusivityη=0) in 2D case separately.
Asymptotic distributions for a class of generalized $L$-statistics
Borovskikh, Yuri V; 10.3150/09-BEJ240
2010-01-01
We adapt the techniques in Stigler [Ann. Statist. 1 (1973) 472--477] to obtain a new, general asymptotic result for trimmed $U$-statistics via the generalized $L$-statistic representation introduced by Serfling [Ann. Statist. 12 (1984) 76--86]. Unlike existing results, we do not require continuity of an associated distribution at the truncation points. Our results are quite general and are expressed in terms of the quantile function associated with the distribution of the $U$-statistic summands. This approach leads to improved conditions for the asymptotic normality of these trimmed $U$-statistics.
Asymptotic Bifurcation Solutions for Perturbed Kuramoto-Sivashinsky Equation
HUANG Qiong-Wei; TANG Jia-Shi
2011-01-01
Stability and dynamic bifurcation in the perturbed Kuramoto-Sivashinsky (KS) equation with Dirichlet boundary condition are investigated by using central manifold reduction procedure.The result shows, as the bifurcation parameter crosses a critical value, the system undergoes a pitchfork bifurcation to produce two asymptotically stable solutions.Furthermore, when the distance from bifurcation is of comparable order ∈2 (｜∈｜ (≤) 1), the first two terms in e-expansions for the new asymptotic bifurcation solutions are derived by multiscale expansion method.Such information is useful to the bifurcation control.
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.
Asymptotic Distribution of the Jump Change-Point Estimator
Changchun TAN; Huifang NIU; Baiqi MIAO
2012-01-01
The asymptotic distribution of the change-point estimator in a jump changepoint model is considered.For the jump change-point model Xi =a + θI{[nTo] ＜ i ≤n} + εi,where εi (i =1,…,n) are independent identically distributed random variables with Eεi=0 and Var(εi) ＜ oo,with the help of the slip window method,the asymptotic distribution of the jump change-point estimator (T) is studied under the condition of the local alternative hypothesis.
On an Asymptotic Behavior of Exponential Functional Equation
Soon Mo JUNG
2006-01-01
The stability problems of the exponential (functional) equation on a restricted domain will be investigated, and the results will be applied to the study of an asymptotic property of that equation. More precisely, the following asymptotic property is proved: Let X be a real (or complex)normed space. A mapping f : X → C is exponential if and only if f(x + y) - f(x)f(y) → 0 as ‖x‖ + ‖y‖→∞ under some suitable conditions.
Conformal Phase Diagram of Complete Asymptotically Free Theories
Pica, Claudio; Sannino, Francesco
2016-01-01
We investigate the ultraviolet and infrared fixed point structure of gauge-Yukawa theories featuring a single gauge coupling, Yukawa coupling and scalar self coupling. Our investigations are performed using the two loop gauge beta function, one loop Yukawa beta function and one loop scalar beta function. We provide the general conditions that the beta function coefficients must abide for the theory to be completely asymptotically free while simultaneously possessing an infrared stable fixed point. We also uncover special trajectories in coupling space along which some couplings are both asymptotically safe and infrared conformal.
New explicit global asymptotic stability criteria for higher order difference equations
El-Morshedy, Hassan A.
2007-12-01
New explicit sufficient conditions for the asymptotic stability of the zero solution of higher order difference equations are obtained. These criteria can be applied to autonomous and nonautonomous equations. The celebrated Clark asymptotic stability criterion is improved. Also, applications to models from mathematical biology and macroeconomics are given.
Delay-dependent asymptotic stability for neural networks with time-varying delays
Xiaofeng Liao
2006-01-01
ensure local and global asymptotic stability of the equilibrium of the neural network. Our results are applied to a two-neuron system with delayed connections between neurons, and some novel asymptotic stability criteria are also derived. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature. Some numerical examples are included to demonstrate our results.
Wei-hua Mao; An-hua Wan
2006-01-01
The oscillatory and asymptotic behavior of the solutions for third order nonlinear impulsive delay differential equations are investigated. Some novel criteria for all solutions to be oscillatory or be asymptotic are established. Three illustrative examples are proposed to demonstrate the effectiveness of the conditions.
Jie Li DING; Xi Ru CHEN
2006-01-01
For generalized linear models (GLM), in case the regressors are stochastic and have different distributions, the asymptotic properties of the maximum likelihood estimate (MLE)(β^)n of the parameters are studied. Under reasonable conditions, we prove the weak, strong consistency and asymptotic normality of(β^)n.
Uniformly Asymptotic Stability and Existence of Periodic Solutions and Almost Periodic Solutions
林发兴
1994-01-01
We introduce the concepts of uniformly stable solutions and uniformly-asymptotically stable solutions, and then give the relation between Lyapunov function and those concepts. Furthermore, we establish the theorem that an almost periodic system or periodic system has uniformly-asymptotically stable solutions and Lipschitz’ condition has an almost periodic solution or periodic solution.
Levchenko, E. A.; Trifonov, A. Yu.; Shapovalov, A. V.
2015-11-01
Asymptotic solutions of the multidimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation with an influence function that is invariant with respect to a spatial shift are constructed. The asymptotic solutions are perturbations of a spatially-homogeneous quasistationary exact solution. General expressions are illustrated by the example of a two-dimensional equation with a Gaussian initial condition.
ON ASYMPTOTIC NORMALITY OF PARAMETERS IN MULTIPLE LINEAR ERRORS-IN-VARIABLES MODEL
ZHANG Sanguo; CHEN Xiru
2003-01-01
This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.
Asymptotic behaviour near extinction of continuous-state branching processes
Pardo, Juan Carlos; Berzunza, Gabriel
2016-01-01
In this note, we study the asymptotic behaviour near extinction of (sub-) critical continuous state branching processes. In particular, we establish an analogue of Khintchin's law of the iterated logarithm near extinction time for a continuous state branching process whose branching mechanism satisfies a given condition and its reflected process at its infimum.
Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces
de Lima, Levi Lopes
2012-01-01
We establish versions of the Positive Mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual dominant energy condition, we prove in all dimensions $n\\geq 3$ an optimal Penrose inequality for certain graphs in hyperbolic space $\\mathbb H^{n+1}$ whose boundary has constant mean curvature $n-1$.
On global asymptotic controllability of planar affine nonlinear systems
SUN Yimin; GUO Lei
2005-01-01
In this paper, we present a necessary and sufficient condition for globally asymptotic controllability of the general planar affine nonlinear systems with single-input.This result is obtained by introducing a new method in the analysis, which is based on the use of some basic results in planar topology and in the geometric theory of ordinary differential equations.
Asymptotic stability and stabilizability of nonlinear systems with delay.
Srinivasan, V; Sukavanam, N
2016-11-01
This paper is concerned with asymptotic stability and stabilizability of a class of nonlinear dynamical systems with fixed delay in state variable. New sufficient conditions are established in terms of the system parameters such as the eigenvalues of the linear operator, delay parameter, and bounds on the nonlinear parts. Finally, examples are given to testify the effectiveness of the proposed theory.
Tail asymptotics for dependent subexponential diﬀerences
Albrecher, H; Asmussen, Søren; Kortschak, D.
We study the asymptotic behavior of P(X − Y > u) as u → ∞, where X is subexponential and X, Y are positive random variables that may be dependent. We give criteria under which the subtraction of Y does not change the tail behavior of X. It is also studied under which conditions the comonotonic co...
Journal Afrika Statistika ISSN 0852-0305 Asymptotic Confidence ...
K is a real kernel weight function satisfying the folllowing conditions: K.1 For every x ... Asymptotic Confidence Bands for Density and Regression Functions in the Gaussian Case. 280 .... We quote the cross-validation and the plug-in methods.
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
XUE Hongqi; SONG Lixin
2002-01-01
A grouped data model for Weibull distribution is considered. Under mild con-ditions, the maximum likelihood estimators(MLE) are shown to be identifiable, strongly consistent, asymptotically normal, and satisfy the law of iterated logarithm. Newton iter- ation algorithm is also considered, which converges to the unique solution of the likelihood equation. Moreover, we extend these results to a random case.
Equivariant spectral asymptotics for h-pseudodifferential operators
Weich, Tobias
2014-10-01
We prove equivariant spectral asymptotics for h-pseudodifferential operators for compact orthogonal group actions generalizing results of El Houakmi and Helffer ["Comportement semi-classique en présence de symétries: Action d'un groupe de Lie compact," Asymp. Anal. 5(2), 91-113 (1991)] and Cassanas ["Reduced Gutzwiller formula with symmetry: Case of a Lie group," J. Math. Pures Appl. 85(6), 719-742 (2006)]. Using recent results for certain oscillatory integrals with singular critical sets [P. Ramacher, "Singular equivariant asymptotics and Weyl's law: On the distribution of eigenvalues of an invariant elliptic operator," J. Reine Angew. Math. (Crelles J.) (to be published)], we can deduce a weak equivariant Weyl law. Furthermore, we can prove a complete asymptotic expansion for the Gutzwiller trace formula without any additional condition on the group action by a suitable generalization of the dynamical assumptions on the Hamilton flow.
Fast evaluation of asymptotic waveforms from gravitational perturbations
Benedict, Alex G; Lau, Stephen R
2012-01-01
In the context of blackhole perturbation theory, we describe both exact evaluation of an asymptotic waveform from a time series recorded at a finite radial location and its numerical approximation. From the user's standpoint our technique is easy to implement, affords high accuracy, and works for both axial (Regge-Wheeler) and polar (Zerilli) sectors. Our focus is on the ease of implementation with publicly available numerical tables, either as part of an existing evolution code or a post-processing step. Nevertheless, we also present a thorough theoretical discussion of asymptotic waveform evaluation and radiation boundary conditions, which need not be understood by a user of our methods. In particular, we identify (both in the time and frequency domains) analytical asymptotic waveform evaluation kernels, and describe their approximation by techniques developed by Alpert, Greengard, and Hagstrom. This paper also presents new results on the evaluation of far-field signals for the ordinary (acoustic) wave equa...
Spherical convective dynamos in the rapidly rotating asymptotic regime
Aubert, Julien; Fournier, Alexandre
2016-01-01
Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a unidimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state...
A new class of asymptotically non-chaotic vacuum singularities
Klinger, Paul, E-mail: paul.klinger@univie.ac.at
2015-12-15
The BKL conjecture, stated in the 1960s and early 1970s by Belinski, Khalatnikov and Lifschitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated chaotic behaviour in the generic case, but simpler non-chaotic one in cases with symmetry assumptions or certain kinds of matter fields. Here we construct a new class of four-dimensional vacuum spacetimes containing spacelike singularities which show non-chaotic behaviour. In contrast with previous constructions, no symmetry assumptions are made. Rather, the metric is decomposed in Iwasawa variables and conditions on the asymptotic evolution of some of them are imposed. The constructed solutions contain five free functions of all space coordinates, two of which are constrained by inequalities. We investigate continuous and discrete isometries and compare the solutions to previous constructions. Finally, we give the asymptotic behaviour of the metric components and curvature.
Structure and asymptotic theory for nonlinear models with GARCH errors
Felix Chan
2015-01-01
Full Text Available Nonlinear time series models, especially those with regime-switching and/or conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper, we derive sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is essential, among other reasons, to establish the conditions under which the traditional LM linearity tests based on Taylor expansions are valid. We also provide sufficient conditions for consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors.
Asymptotics for Associated Random Variables
Oliveira, Paulo Eduardo
2012-01-01
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting
Asymptotics of robust utility maximization
Knispel, Thomas
2012-01-01
For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\\lambda\\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.
Asymptotics of Lagged Fibonacci Sequences
Mertens, Stephan
2009-01-01
Consider "lagged" Fibonacci sequences $a(n) = a(n-1)+a(\\lfloor n/k\\rfloor)$ for $k > 1$. We show that $\\lim_{n\\to\\infty} a(kn)/a(n)\\cdot\\ln n/n = k\\ln k$ and we demonstrate the slow numerical convergence to this limit and how to deal with this slow convergence. We also discuss the connection between two classical results of N.G. de Bruijn and K. Mahler on the asymptotics of $a(n)$.
Application of AN Asymptotic Method to Transient Dynamic Problems
Fafard, M.; Henchi, K.; Gendron, G.; Ammar, S.
1997-11-01
A new method to solve linear dynamics problems using an asymptotic method is presented. Asymptotic methods have been efficiently used for many decades to solve non-linear quasistatic structural problems. Generally, structural dynamics problems are solved using finite elements for the discretization of the space domain of the differential equations, and explicit or implicit schemes for the time domain. With the asymptotic method, time schemes are not necessary to solve the discretized (space) equations. Using the analytical solution of a single degree of freedom (DOF) problem, it is demonstrated, that the Dynamic Asymptotic Method (DAM) converges to the exact solution when an infinite series expansion is used. The stability of the method has been studied. DAM is conditionally stable for a finite series expansion and unconditionally stable for an infinite series expansion. This method is similar to the analytical method of undetermined coefficients or to power series method being used to solve ordinary differential equations. For a multi-degree-of-freedom (MDOF) problem with a lumped mass matrix, no factorization or explicit inversion of global matrices is necessary. It is shown that this conditionally stable method is more efficient than other conditionally stable explicit central difference integration techniques. The solution is continuous irrespective of the time segment (step) and the derivatives are continuous up to orderN-1 whereNis the order of the series expansion.
Global Asymptotic Behavior of a Nonautonomous Competitor-Competitor-Mutualist Model
Shengmao Fu
2013-01-01
Full Text Available The global asymptotic behavior of a nonautonomous competitor-competitor-mutualist model is investigated, where all the coefficients are time-dependent and asymptotically approach periodic functions, respectively. Under certain conditions, it is shown that the limit periodic system of this asymptotically periodic model admits two positive periodic solutions (u1T,u2T,u3T, (u1T,u2T,u3T such that uiT≤uiT (i=1,2,3, and the sector {(u1,u2,u3:uiT≤ui≤uiT, i=1,2,3} is a global attractor of the asymptotically periodic model. In particular, we derive sufficient conditions that guarantee the existence of a positive periodic solution which is globally asymptotically stable.
Asymptotically Free Gauge Theories. I
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Asymptotic safety goes on shell
Benedetti, Dario
2011-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge-dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector, and a new cut-off scheme. We find a non-trivial fixed point, with a value of the cosmological constant which is independent of the gauge-fixing parameters.
Kolmogorov turbulence by matched asymptotic expansions
Lundgren, Thomas S.
2003-04-01
The Kolmogorov [Dokl. Akad. Nauk. SSSR 30, 299 (1941), hereafter K41] inertial range theory is derived from first principles by analysis of the Navier-Stokes equation using the method of matched asymptotic expansions without assuming isotropy or homogeneity and the Kolmogorov (K62) [J. Fluid Mech. 13, 82 (1962)] refined theory is analyzed. This paper is an extension of Lundgren [Phys. Fluids 14, 638 (2002)], in which the second- and third-order structure functions were determined from the isotropic Karman-Howarth [Proc. R. Soc. London, Ser. A 164, 192 (1938)] equation. The starting point for the present analysis is an equation for the difference in velocity between two points, one of which is a Lagrangian fluid point and the second, slaved to the first by a fixed separation r, is not Lagrangian. The velocity difference, so defined, satisfies the Navier-Stokes equation with spatial variable r. The analysis is carried out in two parts. In the first part the physical hypothesis is made that the mean dissipation is independent of viscosity as viscosity tends to zero, as assumed in K41. This means that the mean dissipation is finite as Reynolds number tends to infinity and leads to the K41 inertial range results. In the second part this dissipation assumption is relaxed in an attempt to duplicate the K62 theory. While the K62 structure is obtained, there are restrictions, resulting from the analysis which shows that there can be no inertial range intermittency as Reynolds number tends to infinity, and therefore the mean dissipation has to be finite as Reynolds number tends to infinity, as assumed in part one. Reynolds number-dependent corrections to the K41 results are obtained in the form of compensating functions of r/λ, which tend to zero slowly like Rλ-2/3 as Rλ→∞.
Asymptotic properties of the C-Metric
Sladek, Pavel
2010-01-01
The aim of this article is to analyze the asymptotic properties of the C-metric, using a general method specified in work of Tafel and coworkers, [1], [2], [3]. By finding an appropriate conformal factor $\\Omega$, it allows the investigation of the asymptotic properties of a given asymptotically flat spacetime. The news function and Bondi mass aspect are computed, their general properties are analyzed, as well as the small mass, small acceleration, small and large Bondi time limits.
Linearized asymptotic stability for fractional differential equations
Nguyen Cong
2016-06-01
Full Text Available We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector $\\{\\lambda \\in \\mathbb{C} : |\\arg \\lambda| > \\frac{\\alpha \\pi}{2}\\}$ where $\\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable.
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth; Sannino, Francesco
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety...... in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those...
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
Fengrong Zhang
2011-01-01
Full Text Available This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Relaxation Techniques for Health
... R S T U V W X Y Z Relaxation Techniques for Health Share: On This Page What’s the ... Bottom Line? How much do we know about relaxation techniques? A substantial amount of research has been done ...
Involatile nanodroplets: an asymptotic analysis.
Jarymowycz, Lucien B; Ortoleva, Peter J
2006-06-21
The structure of nanometer-scale droplets of weakly volatile liquids arises through the interplay of strong intermolecular attraction, and core intermolecular repulsion, interfacial forces, and the large, negative chemical potential of the low density vapor with which it is in equilibrium. Using a van der Waals equation of state and a mesoscopic multiphase model, the structure of such nanodroplets is determined via an asymptotic analysis in terms of the ambient to critical temperature ratio. The structure of a spherical droplet is obtained as the solution of a simple "shooting" problem. The intradroplet pressure profile and a minimal droplet size are determined. The high pressure in the core of the droplet gives evidence for the preferred melting there for systems like water with a negative volume of melting. Our methodology can be generalized to multiphase droplets, as well as to composite structures wherein viruses or other nanoparticles are embedded.
Asymptotic expansions in nonlinear rotordynamics
Day, William B.
1987-01-01
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
On the moving contact line singularity: Asymptotics of a diffuse-interface model
Sibley, David N; Savva, Nikos; Kalliadasis, Serafim
2013-01-01
The behaviour of a solid-liquid-gas system near the three-phase contact line is considered using a diffuse-interface model with no-slip at the solid and where the fluid phase is specified by a continuous density field. Relaxation of the classical approach of a sharp liquid-gas interface and careful examination of the asymptotic behaviour as the contact line is approached is shown to resolve the stress and pressure singularities associated with the moving contact line problem. Various features of the model are scrutinised, alongside extensions to incorporate slip, finite-time relaxation of the chemical potential, or a precursor film at the wall.
无
2001-01-01
Under certain conditions, the dynamic equatioins of membrane shells and the dynamic equations of flexural shells are obtained from dynamic equations of Koiter shells by the method of asymptotic analysis.
肖黎明
2001-01-01
Under certain conditions, starting from the three-dimensional dynamic equations of elastic shells the author gives the justification of dynamic equations of flexural shells by means of themethod of asymptotic analysis.
The Asymptotic Standard Errors of Some Estimates of Uncertainty in the Two-Way Contingency Table
Brown, Morton B.
1975-01-01
Estimates of conditional uncertainty, contingent uncertainty, and normed modifications of contingent uncertainity have been proposed for the two-way contingency table. The asymptotic standard errors of the estimates are derived. (Author)
On an asymptotic distribution of dependent random variables on a 3-dimensional lattice.
Harvey, Danielle J; Weng, Qian; Beckett, Laurel A
2010-06-15
We define conditions under which sums of dependent spatial data will be approximately normally distributed. A theorem on the asymptotic distribution of a sum of dependent random variables defined on a 3-dimensional lattice is presented. Examples are also presented.
De Mey, S.; Thomas, J. D.; Greenberg, N. L.; Vandervoort, P. M.; Verdonck, P. R.
2001-01-01
The objective of this study was to use high-fidelity animal data and numerical simulations to gain more insight into the reliability of the estimated relaxation constant derived from left ventricular pressure decays, assuming a monoexponential model with either a fixed zero or free moving pressure asymptote. Comparison of the experimental data with the results of the simulations demonstrated a trade off between the fixed zero and the free moving asymptote approach. The latter method more closely fits the pressure curves and has the advantage of producing an extra coefficient with potential diagnostic information. On the other hand, this method suffers from larger standard errors on the estimated coefficients. The method with fixed zero asymptote produces values of the time constant of isovolumetric relaxation (tau) within a narrow confidence interval. However, if the pressure curve is actually decaying to a nonzero pressure asymptote, this method results in an inferior fit of the pressure curve and a biased estimation of tau.
Einstein Constraints on Asymptotically Euclidean Manifolds
Choquet-Bruhat, Y; York, J W; Choquet-Bruhat, Yvonne; Isenberg, James; York, James W.
2000-01-01
We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \\geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of existence. We also treat discontinuous scaled sources. In the last section we obtain new results in the case of non-constant mean curvature.
An asymptotic model of the F layer
Oliver, W. L.
2012-01-01
A model of the F layer of the ionosphere is presented that consists of a bottomside asymptote that ignores transport and a topside asymptote that ignores chemistry. The asymptotes connect at the balance height dividing the chemistry and transport regimes. A combination of these two asymptotes produces a good approximation to the true F layer. Analogously, a model of F layer response to an applied vertical drift is presented that consists of two asymptotic responses, one that ignores transport and one that ignores chemistry. The combination of these asymptotic responses produces a good approximation to the response of the true F layer. This latter response is identical to the “servo” response of Rishbeth et al. (1978), derived from the continuity equation. The asymptotic approach bypasses the continuity equation in favor of “force balance” arguments and so replaces a differential equation with simpler algebraic equations. This new approach provides a convenient and intuitive mean for first-order estimates of the change in F layer peak height and density in terms of changes in neutral density, composition, temperature, winds, and electric fields. It is applicable at midlatitudes and at magnetically quiet times at high latitudes. Forensic inverse relations are possible but are not unique. The validity of the asymptotic relations is shown through numerical simulation.
PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS
FEIGUIHUA; QIUQINGJIU
1997-01-01
The authors establish the existence of nontrival periodic solutions of the asymptotically linear Hamiltomian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.
Term structure modeling and asymptotic long rate
Yao, Y.
1999-01-01
This paper examines the dynamics of the asymptotic long rate in three classes of term structure models. It shows that, in a frictionless and arbitrage-free market, the asymptotic long rate is a non-decreasing process. This gives an alternative proof of the same result of Dybvig et al. (Dybvig, P.H.,
Asymptotic properties of random matrices and pseudomatrices
Lenczewski, Romuald
2010-01-01
We study the asymptotics of sums of matricially free random variables called random pseudomatrices, and we compare it with that of random matrices with block-identical variances. For objects of both types we find the limit joint distributions of blocks and give their Hilbert space realizations, using operators called `matricially free Gaussian operators'. In particular, if the variance matrices are symmetric, the asymptotics of symmetric blocks of random pseudomatrices agrees with that of symmetric random blocks. We also show that blocks of random pseudomatrices are `asymptotically matricially free' whereas the corresponding symmetric random blocks are `asymptotically symmetrically matricially free', where symmetric matricial freeness is obtained from matricial freeness by an operation of symmetrization. Finally, we show that row blocks of square, lower-block-triangular and block-diagonal pseudomatrices are asymptotically free, monotone independent and boolean independent, respectively.
Universal asymptotic umbrella for hydraulic fracture modeling
Linkov, Aleksandr M
2014-01-01
The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.
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.
On the asymptotic behaviour of solutions of an asymptotically Lotka-Volterra model
Attila Dénes
2016-09-01
Full Text Available We make more realistic our model [Nonlinear Anal. 73(2010, 650-659] on the coexistence of fishes and plants in Lake Tanganyika. The new model is an asymptotically autonomous system whose limiting equation is a Lotka-Volterra system. We give conditions for the phenomenon that the trajectory of any solution of the original non-autonomous system "rolls up"' onto a cycle of the limiting Lotka-Volterra equation as $t\\to\\infty$, which means that the limit set of the solution of the non-autonomous system coincides with the cycle. A counterexample is constructed showing that the key integral condition on the coefficient function in the original non-autonomous model cannot be dropped. Computer simulations illustrate the results.
Asymptotic behavior of a delayed wave equation without displacement term
Ammari, Kaïs; Chentouf, Boumediène
2017-10-01
This paper is dedicated to the investigation of the asymptotic behavior of a delayed wave equation without the presence of any displacement term. First, it is shown that the problem is well-posed in the sense of semigroups theory. Thereafter, LaSalle's invariance principle is invoked in order to establish the asymptotic convergence for the solutions of the system to a stationary position which depends on the initial data. More importantly, without any geometric condition such as BLR condition (Bardos et al. in SIAM J Control Optim 30:1024-1064, 1992; Lebeau and Robbiano in Duke Math J 86:465-491, 1997) in the control zone, the logarithmic convergence is proved by using an interpolation inequality combined with a resolvent method.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
C.; W.; LIM
2009-01-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
CHEN LiQun; C.W.LIM; HU QingQuan; DING Hu
2009-01-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach.The asymptotic solution is sought for a beam equation with a nonlinear boundary condition.The steady-state responses are determined in primary resonance and subharmonic resonance.The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition.Multivaluedness occurs in the relations as a consequence of the nonlinearity.The stability of steady-state responses is analyzed by use of the Lyapunov linearized sta-bility theory.The stability analysis predicts the jumping phenomenon for certain parameters.The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales.The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Chen, Liqun; Lim, C. W.; Hu, Qingquan; Ding, Hu
2009-09-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Robin, I C; Aichele, T; Bougerol, C; André, R; Tatarenko, S; Bellet-Amalric, E; Van Daele, B; Van Tendeloo, G
2007-07-01
CdSe/ZnSe quantum dot formation is investigated by studying different steps of the growth. To precisely control the critical thickness of CdSe grown on a ZnSe buffer layer, the CdSe self-regulated growth rate in atomic layer epitaxy growth mode is determined by reflection high-energy electron diffraction (RHEED) measurements for a temperature range between 180 and 280 °C. Then, the two-dimensional-three-dimensional (2D-3D) transition of a strained CdSe layer on (001)-ZnSe induced by the use of amorphous selenium is studied. The formation of CdSe islands is found when 3 monolayers (ML) of CdSe are deposited. When only 2.5 ML of CdSe are deposited, another relaxation mechanism is observed, leading to the appearance of strong undulations on the surface. We also studied the evolution of the surface morphology when 2.7 ML are deposited, to study the boundary between those two phenomena. The influence of capping on quantum dot morphology is investigated. It is found that cadmium is redistributed within the layer during capping. Our results show that the cadmium distribution after capping depends on the capping temperature and on the strain of the CdSe layer. Cadmium incorporation after capping is also studied. It is found that the amount of incorporated cadmium depends on the strain of the CdSe layer before capping.
Robin, I C [CEA-CNRS-UJF ' Nanophysics and Semiconductors' Group Laboratoire de Spectrometrie Physique/CNRS UMR5588, Universite J. Fourier, Grenoble, BP87, 38402 St Martin d' Heres (France); Aichele, T [CEA-CNRS-UJF ' Nanophysics and Semiconductors' Group Laboratoire de Spectrometrie Physique/CNRS UMR5588, Universite J. Fourier, Grenoble, BP87, 38402 St Martin d' Heres (France); Bougerol, C [CEA-CNRS-UJF ' Nanophysics and Semiconductors' Group Laboratoire de Spectrometrie Physique/CNRS UMR5588, Universite J. Fourier, Grenoble, BP87, 38402 St Martin d' Heres (France); Andre, R [CEA-CNRS-UJF ' Nanophysics and Semiconductors' Group Laboratoire de Spectrometrie Physique/CNRS UMR5588, Universite J. Fourier, Grenoble, BP87, 38402 St Martin d' Heres (France); Tatarenko, S [CEA-CNRS-UJF ' Nanophysics and Semiconductors' Group Laboratoire de Spectrometrie Physique/CNRS UMR5588, Universite J. Fourier, Grenoble, BP87, 38402 St Martin d' Heres (France); Bellet-Amalric, E [CEA-CNRS-UJF ' Nanophysics and Semiconductors' Group, Departement de Recherche Fondamentale sur la Matiere Condensee/SP2M CEA Grenoble, 17 rue des Martyrs, 38054 Grenoble cedex 9 (France); Daele, B Van [IMEC, Kapeldreef 75, 3001 Leuven (Belgium); Tendeloo, G van [EMAT University of Antwerp (RUCA), Groenenborgerlaan 171, 2020 Antwerp (Belgium)
2007-07-04
CdSe/ZnSe quantum dot formation is investigated by studying different steps of the growth. To precisely control the critical thickness of CdSe grown on a ZnSe buffer layer, the CdSe self-regulated growth rate in atomic layer epitaxy growth mode is determined by reflection high-energy electron diffraction (RHEED) measurements for a temperature range between 180 and 280 deg. C. Then, the two-dimensional-three-dimensional (2D-3D) transition of a strained CdSe layer on (001)-ZnSe induced by the use of amorphous selenium is studied. The formation of CdSe islands is found when 3 monolayers (ML) of CdSe are deposited. When only 2.5 ML of CdSe are deposited, another relaxation mechanism is observed, leading to the appearance of strong undulations on the surface. We also studied the evolution of the surface morphology when 2.7 ML are deposited, to study the boundary between those two phenomena. The influence of capping on quantum dot morphology is investigated. It is found that cadmium is redistributed within the layer during capping. Our results show that the cadmium distribution after capping depends on the capping temperature and on the strain of the CdSe layer. Cadmium incorporation after capping is also studied. It is found that the amount of incorporated cadmium depends on the strain of the CdSe layer before capping.
Choosing a skeletal muscle relaxant.
See, Sharon; Ginzburg, Regina
2008-08-01
Skeletal muscle relaxants are widely used in treating musculoskeletal conditions. However, evidence of their effectiveness consists mainly of studies with poor methodologic design. In addition, these drugs have not been proven to be superior to acetaminophen or nonsteroidal anti-inflammatory drugs for low back pain. Systematic reviews and meta-analyses support using skeletal muscle relaxants for short-term relief of acute low back pain when nonsteroidal anti-inflammatory drugs or acetaminophen are not effective or tolerated. Comparison studies have not shown one skeletal muscle relaxant to be superior to another. Cyclobenzaprine is the most heavily studied and has been shown to be effective for various musculoskeletal conditions. The sedative properties of tizanidine and cyclobenzaprine may benefit patients with insomnia caused by severe muscle spasms. Methocarbamol and metaxalone are less sedating, although effectiveness evidence is limited. Adverse effects, particularly dizziness and drowsiness, are consistently reported with all skeletal muscle relaxants. The potential adverse effects should be communicated clearly to the patient. Because of limited comparable effectiveness data, choice of agent should be based on side-effect profile, patient preference, abuse potential, and possible drug interactions.
Formulas and Asymptotics for the Asymmetric Simple Exclusion Process
Tracy, Craig A.; Widom, Harold, E-mail: widom@ucsc.edu [University of California, Department of Mathematics (United States)
2011-09-15
This is an expanded version of a series of lectures delivered by the second author in June, 2009. It describes the results of three of the authors' papers on the asymmetric simple exclusion process, from the derivation of exact formulas for configuration probabilities, through Fredholm determinant representation, to asymptotics with step initial condition establishing KPZ universality. Although complete proofs are in general not given, at least the main elements of them are.
Asymptotic Expansions of Transition Densities for Hybrid Jump-Diffusions
Yuan-jin Liu; G.Yin
2004-01-01
A class of hybrid jump diffusions modulated by a Markov chain is considered in this work.The motivation stems from insurance risk models,and emerging applications in production planning and wireless communications.The models are hybrid in that they involve both continuous dynamics and discrete events.Under suitable conditions,asymptotic expansions of the transition densities for the underlying processes are developed.The formal expansions are validated and the error bounds obtained.
Asymptotics of nearly critical Galton-Watson processes with immigration
Kevei, Peter
2011-01-01
We investigate the inhomogeneous Galton--Watson processes with immigration, where $\\rho_n$ the offspring means in the $n^\\textrm{th}$ generation tends to 1. We show that if the second derivatives of the offspring generating functions go to 0 rapidly enough, then the asymptotics are the same as in the INAR(1) case, treated by Gy\\"orfi et al. We also determine the limit if this assumption does not hold showing the optimality of the conditions.
Complementarity between Gauge-Boson Compositeness and Asymptotic Freedom
Akama, K; Akama, Keiichi; Hattori, Takashi
1997-01-01
We derive and solve the compositeness condition for the SU(N_c) gauge boson at the next-to-leading order in 1/N_f (N_f is the number of flavors) to obtain the expression of the gauge coupling constant in terms of the compositeness scale. It turns out that the argument of gauge-boson compositeness is successful only for N_f/N_c>11/2, where the asymptotic freedom fails.
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
XUEHongqi; SONGLixin
2002-01-01
A grouped data model for weibull distribution is considered.Under mild conditions .the maximum likelihood estimators(MLE)are shown to be identifiable,strongly consistent,asymptotically normal,and satisfy the law of iterated logarithm .Newton iteration algorthm is also condsidered,which converges to the unique solution of the likelihood equation.Moreover,we extend these results to a random case.
Asymptotic properties of the inhomogeneous Lotka-Von Foerster system.
Inaba, H
1988-01-01
"In this paper, we investigate an extension of the multistate stable population model, which makes allowances for migration. The model is formulated as an inhomogeneous system of first order partial differential equations with integral boundary conditions. First, we construct its classical solution. Next, we reformulate the system as an abstract inhomogeneous Cauchy problem on a Banach space, and give its mild solution by using the population semigroup. Our main purpose is to investigate the asymptotic behavior of the mild solution." (SUMMARY IN FRE)
Asymptotic analytical methods in fluid mechanics related to drag prediction
Inger, G. R.
1975-01-01
Some recent theoretical work of a purely analytical nature is described which promises to provide engineering predictions for the important drag-related phenomena of flow in the stall regime. This analytical work deals with rigorous asymptotic studies of the complete Navier-Stokes equations that govern the viscous flow around any aerodynamic body under conditions where boundary layer separation takes place from the body surface.
The Asymptotic Mandelbrot Law of Some Evolution Networks
Li, Li
2011-01-01
In this letter, we study some evolution networks that grow with linear preferential attachment. Based upon some recent results on the quotient Gamma function, we give a rigorous proof of the asymptotic Mandelbrot law for the degree distribution $p_k \\propto (k + c)^{-\\gamma}$ in certain conditions. We also analytically derive the best fitting values for the scaling exponent $\\gamma$ and the shifting coefficient $c$.
Asymptotics of thermal spectral functions
Caron-Huot, S
2009-01-01
We use operator product expansion (OPE) techniques to study the spectral functions of currents at finite temperature, in the high-energy time-like region $\\omega\\gg T$. The leading corrections to the spectral function of currents and stress tensors are proportional to $\\sim T^4$ expectation values in general, and the leading corrections $\\sim g^2T^4$ are calculated at weak coupling, up to one undetermined coefficient in the shear viscosity channel. Spectral functions in the asymptotic regime are shown to be infrared safe up to order $g^8T^4$. The convergence of sum rules in the shear and bulk viscosity channels is established in QCD to all orders in perturbation theory, though numerically significant tails $\\sim T^4/(\\log\\omega)^3$ are shown to exist in the bulk viscosity channel and to have an impact on sum rules recently proposed by Kharzeev and Tuchin. We argue that the spectral functions of currents and stress tensors in strongly coupled $\\mathcal{N}=4$ super Yang-Mills do not receive any medium-dependent...
Asymptotics of Simple Branching Populations
Huillet, Thierry; Kłopotowski, Andrzej; Porzio, Anna
1995-09-01
In this paper we study a simple deterministic tree structure: an initial individual generates a finite number of offspring, each of which has given integer valued lifetime, iterating the same procedure when dying. Three asymptotic distributions of this asynchronous deterministic branching procedure are considered: the generation distribution, the ability of individuals to generate offspring and the age distribution. Thermodynamic formalism is then developped to reveal the multifractal nature of the mass splitting associated to our process. On considère l'itération d'une structure déterministe arborescente selon laquelle un ancêtre engendre un nombre fini de descendants dont la durée de vie (à valeurs entières) est donnée. Dans un premier temps on s'intéresse aux trois distributions asymptotiques suivantes : répartition des générations, aptitude à engendrer des descendants et répartition selon l'âge. Ensuite nous développons le formalisme thermodynamique pour mettre en évidence le caractère multifractal de la scission d'une masse unitaire associée à cette arborescence.
Ultraviolet asymptotics of glueball propagators
Bochicchio, M
2013-01-01
We point out that perturbation theory in conjunction with the renormalization group (RG) puts a severe constraint on the structure of the large-N non-perturbative glueball propagators in SU(N) pure YM, in QCD and in n=1 SUSY QCD with massless quarks, or in any confining asymptotically-free gauge theory massless in perturbation theory. For the scalar and pseudoscalar glueball propagators in pure YM and QCD with massless quarks we check in detail the RG-improved estimate to the order of the leading and next-to-leading logarithms by means of a remarkable three-loop computation by Chetyrkin et al. We investigate as to whether the aforementioned constraint is satisfied by any of the scalar or pseudoscalar glueball propagators computed in the framework of the AdS String/ large-N Gauge Theory correspondence and of a recent proposal based on a Topological Field Theory underlying the large-N limit of YM. We find that none of the proposals for the scalar or the pseudoscalar glueball propagators based on the AdS String/...
Extended Analytic Device Optimization Employing Asymptotic Expansion
Mackey, Jonathan; Sehirlioglu, Alp; Dynsys, Fred
2013-01-01
Analytic optimization of a thermoelectric junction often introduces several simplifying assumptionsincluding constant material properties, fixed known hot and cold shoe temperatures, and thermallyinsulated leg sides. In fact all of these simplifications will have an effect on device performance,ranging from negligible to significant depending on conditions. Numerical methods, such as FiniteElement Analysis or iterative techniques, are often used to perform more detailed analysis andaccount for these simplifications. While numerical methods may stand as a suitable solution scheme,they are weak in gaining physical understanding and only serve to optimize through iterativesearching techniques. Analytic and asymptotic expansion techniques can be used to solve thegoverning system of thermoelectric differential equations with fewer or less severe assumptionsthan the classic case. Analytic methods can provide meaningful closed form solutions and generatebetter physical understanding of the conditions for when simplifying assumptions may be valid.In obtaining the analytic solutions a set of dimensionless parameters, which characterize allthermoelectric couples, is formulated and provide the limiting cases for validating assumptions.Presentation includes optimization of both classic rectangular couples as well as practically andtheoretically interesting cylindrical couples using optimization parameters physically meaningful toa cylindrical couple. Solutions incorporate the physical behavior for i) thermal resistance of hot andcold shoes, ii) variable material properties with temperature, and iii) lateral heat transfer through legsides.
Power-law relaxation in human violent conflicts
Picoli, Sergio; Antonio, Fernando J.; Itami, Andreia S.; Mendes, Renio S.
2017-08-01
We study relaxation patterns of violent conflicts after bursts of activity. Data were obtained from available catalogs on the conflicts in Iraq, Afghanistan and Northern Ireland. We find several examples in each catalog for which the observed relaxation curves can be well described by an asymptotic power-law decay (the analog of the Omori's law in geophysics). The power-law exponents are robust, nearly independent of the conflict. We also discuss the exogenous or endogenous nature of the shocks. Our results suggest that violent conflicts share with earthquakes and other natural and social phenomena a common feature in the dynamics of aftershocks.
Asymptotic Safety, Emergence and Minimal Length
Percacci, R
2010-01-01
There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that 1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and 2) there is a precise sense in which asymptotic safety implies a minimal length. In so doing we also discuss possible signatures of asymptotic safety in scattering experiments.
Global asymptotic stability for Hopfield-type neural networks with diffusion effects
YAN Xiang-ping; LI Wan-tong
2007-01-01
The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique.
WANG XIONG-RUI; Ji You-qing
2011-01-01
In this paper,the iteration xn+1 =any + (1 - αn)Tk(n)i(n)xn for a family of asymptotically nonexpansive mappings T1,T2,...,TN is originally introduced in an uniformly convex Banach space.Motivated by recent papers,we prove that under suitable conditions the iteration scheme converges strongly to the nearest common fixed point of the family of asymptotically nonexpansive mappings.The results presented in this paper expand and improve correponding ones from Hilbert spaces to uniformly convex Banach spaces,or from nonexpansive mappings to asymptotically nonexpansive mappings.
Regular black hole metrics and the weak energy condition
Balart, Leonardo, E-mail: leonardo.balart@ufrontera.cl [I.C.B. – Institut Carnot de Bourgogne, UMR 5209, CNRS, Faculté des Sciences Mirande, Université de Bourgogne, 9 Avenue Alain Savary, BP 47870, 21078 Dijon Cedex (France); Departamento de Ciencias Físicas, Facultad de Ingeniería y Ciencias, Universidad de La Frontera, Casilla 54-D, Temuco (Chile); Vagenas, Elias C., E-mail: elias.vagenas@ku.edu.kw [Theoretical Physics Group, Department of Physics, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)
2014-03-07
In this work we construct a family of spherically symmetric, static, charged regular black hole metrics in the context of Einstein-nonlinear electrodynamics theory. The construction of the charged regular black hole metrics is based on three requirements: (a) the weak energy condition should be satisfied, (b) the energy–momentum tensor should have the symmetry T{sub 0}{sup 0}=T{sub 1}{sup 1}, and (c) these metrics have to asymptotically behave as the Reissner–Nordström black hole metric. In addition, these charged regular black hole metrics depend on two parameters which for specific values yield regular black hole metrics that already exist in the literature. Furthermore, by relaxing the third requirement, we construct more general regular black hole metrics which do not behave asymptotically as a Reissner–Nordström black hole metric.
On the Asymptotic Limit of Flows Past a Ribbed Boundary
Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka
2008-11-01
We consider a stationary Navier-Stokes flow in a bounded domain supplemented with the complete slip boundary conditions. Assuming the boundary of the domain is formed by a family of unidirectional asperities, whose amplitude as well as frequency is proportional to a small parameter ɛ, we shall show that in the asymptotic limit the motion of the fluid is governed by the same system of the Navier-Stokes equations, however, the limit boundary conditions are different. Specifically, the resulting boundary conditions prevent the fluid from slipping in the direction of asperities, while the motion in the orthogonal direction is allowed without any constraint.
New tuning conditions for a class of nonlinear PID global regulators of robot manipulators
Orrante-Sakanassi, Jorge; Santibánez, Victor; Hernández-Guzmán, Victor M.
2014-04-01
Several nonlinear proportional-integral-derivative (PID) controllers for robot manipulators that ensure global asymptotic stability have been proposed in the literature. However, the tuning criteria obtained are expressed in terms of conditions so restrictive that they have avoided, until now, carrying out experimental tests with such controllers. Tuning criteria of some PID controllers for robot manipulators with conditions more relaxed than those presented previously in the literature have been proposed in two recent works by the authors. This was achieved by setting the tuning conditions individually for each joint instead of general conditions for the whole robot. In this paper we extend these results to a class of nonlinear PID global regulators for robot manipulators. The obtained tuning criteria are given in terms of conditions so relaxed that they have allowed to carry out, for the first time, experimental essays with these controllers. Such experiments are presented in this paper using a two-degrees-of-freedom robot manipulator.
Asymptotic Behavior of Solutions to the Generalized BBM-Burgers Equation
Mi-na Jiang; Yan-ling Xu
2005-01-01
We investigate the asymptotic behavior of solutions of the initial-boundary value problem for the generalized BBM-Burgers equation ut + f(u)x = uxx +uxxt on the half line with the conditions u(0, t) =u-, u(∞, t) = u+ and u- ＜ u+, where the corresponding Cauchy problem admits the rarefaction wave as an asymptotic states. In the present problem, because of the Dirichlet boundary, the asymptotic states are divided into five cases depending on the signs of the characteristic speeds f′(u±) of boundary state u- = u(0) and the far fields states u+ = u(∞). In all cases both global existence of the solution and asymptotic behavior are shown under the smallness conditions.
Lehrer, Paul M.
1978-01-01
Compared physiological effects of progressive relaxation, alpha feedback, and a no-treatment condition. Nonpatients showed more psychophysiological habituation than patients in response to hearing very loud tones and to reaction time tasks. Patients showed greater physiological response to relaxation than nonpatients. After relaxation, autonomic…
Asymptotic silence in loop quantum cosmology
Mielczarek, Jakub
2012-01-01
The state of asymptotic silence, characterized by causal disconnection of the space points, emerges from various approaches aiming to describe gravitational phenomena in the limit of large curvatures. In particular, such behavior was anticipated by Belinsky, Khalatnikov and Lifshitz (BKL) in their famous conjecture put forward in the early seventies of the last century. While the BKL conjecture is based on purely classical considerations, one can expect that asymptotic silence should have its quantum counterpart at the level of a more fundamental theory of quantum gravity, which is the relevant description of gravitational phenomena in the limit of large energy densities. Here, we summarize some recent results which give support to such a possibility. More precisely, we discuss occurrence of the asymptotic silence due to polymerization of space at the Planck scale, in the framework of loop quantum cosmology. In the discussed model, the state of asymptotic silence is realized at the energy density $\\rho = \\rho...
Nonsymmetric gravity does have acceptable global asymptotics
Cornish, N J
1994-01-01
"Reports of my death are greatly exaggerated" - Mark Twain. We consider the claim by Damour, Deser and McCarthy that nonsymmetric gravity theory has unacceptable global asymptotics. We explain why this claim is incorrect.
Asymptotic Evolution of Random Unitary Operations
Novotny, J; Jex, I
2009-01-01
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.
The Lorentzian proper vertex amplitude: Asymptotics
Engle, Jonathan; Zipfel, Antonia
2015-01-01
In previous work, the Lorentzian proper vertex amplitude for a spin-foam model of quantum gravity was derived. In the present work, the asymptotics of this amplitude are studied in the semi-classical limit. The starting point of the analysis is an expression for the amplitude as an action integral with action differing from that in the EPRL case by an extra `projector' term which scales linearly with spins only in the asymptotic limit. New tools are introduced to generalize stationary phase methods to this case. For the case of boundary data which can be glued to a non-degenerate Lorentzian 4-simplex, the asymptotic limit of the amplitude is shown to equal the single Feynman term, showing that the extra term in the asymptotics of the EPRL amplitude has been eliminated.
Hermite polynomials and quasi-classical asymptotics
Ali, S. Twareque, E-mail: twareque.ali@concordia.ca [Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada); Engliš, Miroslav, E-mail: englis@math.cas.cz [Mathematics Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic and Mathematics Institute, Žitná 25, 11567 Prague 1 (Czech Republic)
2014-04-15
We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated quasi-classical asymptotics.
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...
The trouble with asymptotically safe inflation
Fang, Chao
2013-01-01
In this paper we investigate the perturbation theory of the asymptotically safe inflation and we find that all modes of gravitational waves perturbation become ghosts in order to achieve a large enough number of e-folds. Formally we can calculate the power spectrum of gravitational waves perturbation, but we find that it is negative. It indicates that there is serious trouble with the asymptotically safe inflation.
A Shortcut to LAD Estimator Asymptotics
1990-01-01
Using generalized functions of random variables and generalized Taylor series expansions, we provide almost trivial demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, autoregressions and autoregressions with in...
An asymptotic model of unsteady airway reopening.
Naire, S; Jensen, O E
2003-12-01
We consider a simple physical model for the reopening of a collapsed lung airway involving the unsteady propagation of a long bubble of air, driven at a prescribed flow-rate, into a liquid-filled channel formed by two flexible membranes that are held under large longitudinal tension and are confined between two parallel rigid plates. This system is described theoretically using an asymptotic approximation, valid for uniformly small membrane slopes, which reduces to a fourth-order nonlinear evolution equation for the channel width ahead of the bubble tip, from which the time-evolution of the bubble pressure pb* and bubble speed may be determined. The model shows that there can be a substantial delay between the time at which the bubble starts to grow in volume and the time at which its tip starts to move. Under certain conditions, the start of the bubble's motion is accompanied by a transient overshoot in pb*, as seen previously in experiment; the model predicts that the overshoot is greatest in narrow channels when the bubble is driven with a large volume flux. It is also shown how the threshold pressure for steady bubble propagation in wide channels has distinct contributions from the capillary pressure drop across the bubble tip and viscous dissipation in the channel ahead of the bubble.
Asymptotic behavior of singular solutions to semilinear fractional elliptic equations
Guowei Lin
2014-02-01
Full Text Available In this article we study the asymptotic behavior of positive singular solutions to the equation $$ (-\\Delta^{\\alpha} u+u^p=0\\quad\\text{in } \\Omega\\setminus\\{0\\}, $$ subject to the conditions $u=0$ in $\\Omega^c$ and $\\lim_{x\\to0}u(x=\\infty$, where $p\\geq1$, $\\Omega$ is an open bounded regular domain in $\\mathbb{R}^N$ ($N\\ge2$ containing the origin, and $(-\\Delta^\\alpha$ with $\\alpha\\in(0,1$ denotes the fractional Laplacian. We show that the asymptotic behavior of positive singular solutions is controlled by a radially symmetric solution with $\\Omega$ being a ball.
A Framework for Non-Asymptotic Quantum Information Theory
Tomamichel, Marco
2012-01-01
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\\'enyi entropies. We introduce the purified distance, a novel metric for unnormalized quantum states and use it to define smooth entropies as optimizations of the min- and max-entropies over a ball of close states. We explore various properties of these entropies, including data-processing inequalities, chain rules and their classical limits. The most important property is an entropic formulation of the asymptotic equipartition property, which implies that the smooth entropies converge to the von Neumann entropy in the limit of many independent copies. The smooth entropies also satisfy duality and entropic uncertainty relations that provide limits on the power of two different observers to predict the outcome of a measurement on a quantum system. Finally, we discuss three example...
Asymptotically flat black holes with scalar hair: a review
Herdeiro, Carlos A R
2015-01-01
We consider the status of black hole solutions with non-trivial scalar fields but no gauge fields, in four dimensional asymptotically flat space-times, reviewing both classical results and recent developments. We start by providing a simple illustration on the physical difference between black holes in electro-vacuum and scalar-vacuum. Next, we review no-scalar-hair theorems. In particular, we detail an influential theorem by Bekenstein and stress three key assumptions: 1) the type of scalar field equation; 2) the spacetime symmetry inheritance by the scalar field; 3) an energy condition. Then, we list regular (on and outside the horizon), asymptotically flat BH solutions with scalar hair, organizing them by the assumption which is violated in each case and distinguishing primary from secondary hair. We provide a table summary of the state of the art.
Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems
Ewelina Seroka
2015-01-01
Full Text Available The problem of the asymptotic stabilizability in probability of a class of stochastic nonlinear control hybrid systems (with a linear dependence of the control with state dependent, Markovian, and any switching rule is considered in the paper. To solve the issue, the Lyapunov technique, including a common, single, and multiple Lyapunov function, the hybrid control theory, and some results for stochastic nonhybrid systems are used. Sufficient conditions for the asymptotic stabilizability in probability for a considered class of hybrid systems are formulated. Also the stabilizing control in a feedback form is considered. Furthermore, in the case of hybrid systems with the state dependent switching rule, a method for a construction of stabilizing switching rules is proposed. Obtained results are illustrated by examples and numerical simulations.
Asymptotic Analysis of Mixed Modes in Red Giant Stars
Jiang, C
2014-01-01
High precision space observations, such as made by the kepler and corot missions, allow us to detect mixed modes for $l = 1$ modes in their high signal-to-noise photometry data. By means of asteroseismology, the inner structure of red giant (RG) stars is revealed the first time with the help of mixed modes. We analyse these mixed modes of a 1.3 $M_{sun}$ RG model theoretically from the approximate asymptotic descriptions of oscillations. While fitting observed frequencies with the eigenvalue condition for mixed modes, a good estimate of period spacing and coupling strength is also acquired for more evolved models. We show that the behaviour of the mode inertia in a given mode varies dramatically when the coupling is strong. An approximation of period spacings is also obtained from the asymptotic dispersion relation, which provides a good estimate of the coupling strength as well as period spacing when g-mode-like mixed modes are sufficiently dense.
M-Estimation for Discrete Data: Asymptotic Distribution Theory and Implications.
1985-11-01
n 860 0029 M-ESTIMATION FOR DISCRETE DATA: ASYMPTOTIC DISTRIBUTION THEORY AND IMPLICATIONS by Douglas G. Simpson 1 Departraent of Statistics... distribution theory of M-estimators especially relevant to discrete data, although Theorem 1 is somewhat broader in scope’. The main results are given in...Extended asymptotic distribution theory Conditions for consistency of an M-estimator can be found in Huber (1964, 1967, 1981). Since the smoothness plays
Short time kernel asymptotics for Young SDE by means of Watanabe distribution theory
Inahama, Yuzuru
2011-01-01
In this paper we study short time asymptotics of a density function of the solution of a stochastic differential equation driven by fractional Brownian motion with Hurst parameter $H \\in (1/2, 1)$ when the coefficient vector fields satisfy an ellipticity condition at the starting point. We prove both on-diagonal and off-diagonal asymptotics under mild additional assumptions. Our main tool is Malliavin calculus, in particular, Watanabe's theory of generalized Wiener functionals.
On the asymptotic limit of the Navier-Stokes system on domains with rough boundaries
Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka; Wolf, Joerg
We study the asymptotic behavior of solutions to the incompressible Navier-Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter. Imposing the complete slip boundary conditions we show that in the asymptotic limit the fluid sticks completely to the boundary provided the oscillations are non-degenerate, meaning not oriented in a single direction.
Lenart, Łukasz
2011-01-01
The aim of this article is to establish asymptotic distributions and consistency of subsampling for spectral density and for magnitude of coherence for non-stationary, almost periodically correlated time series. We show the asymptotic normality of the spectral density estimator and the limiting distribution of a magnitude of coherence statistic for all points from the bifrequency square. The theoretical results hold under $\\alpha$-mixing and moment conditions.
李大鸣; 张红萍; 高永祥
2002-01-01
A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
ASYMPTOTIC NORMALITY OF QUASI MAXIMUM LIKELIHOOD ESTIMATE IN GENERALIZED LINEAR MODELS
YUE LI; CHEN XIRU
2005-01-01
For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.
PERMANENCE OF ASYMPTOTICALLY PERIODIC MULTISPECIES LOTKA-VOLTERRA COMPETITION PREDATOR-PREY SYSTEM
无
2006-01-01
In this paper, we consider the permanence of asymptotically periodic mul-tispecies Lotka-Volterra competition predator-prey system. By means of the standard comparison theorem, we improve or extend the corresponding results given by Peng and Chen [1], Teng and Li [2], Zhao and Chen [3]. Also, we obtain the conditions which ensure the permanence and global attractivity of asymptotically periodic multispecies competition predator-prey system.
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.
Xueling Jiang
2014-01-01
Full Text Available The problem of adaptive asymptotical synchronization is discussed for the stochastic complex dynamical networks with time-delay and Markovian switching. By applying the stochastic analysis approach and the M-matrix method for stochastic complex networks, several sufficient conditions to ensure adaptive asymptotical synchronization for stochastic complex networks are derived. Through the adaptive feedback control techniques, some suitable parameters update laws are obtained. Simulation result is provided to substantiate the effectiveness and characteristics of the proposed approach.
Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering
Xiu Kan
2012-01-01
Full Text Available The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameter θ:dXt=(θα(t+β(tXtdt+σ(tdWt. Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameter θ based on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.
Relaxation of 2+1 dimensional classical O(2) symmetric scalar fields
Borsanyi, S; Borsanyi, Sz.; Szep, Zs.
2001-01-01
Real time thermalization and relaxation phenomena are studied in the low energy density phase of the 2+1 dimensional classical O(2) symmetric scalar theory by solving numerically its dynamics. The near-equilibrium decay rate of on-shell waves and the power law governing the large time asymptotics of the off-shell relaxation agree with the analytic results based on linear response theory. The realisation of the Mermin-Wagner theorem is also studied in the final equilibrium ensemble.
Charnotskii, Mikhail; Baker, Gary J.
2011-06-01
Asymptotic theory of the finite beam scintillations (Charnotskii, WRM, 1994, JOSA A, 2010) provides an exhaustive description of the dependence of the beam scintillation index on the propagation conditions, beam size and focusing. However the complexity of the asymptotic configuration makes it difficult to apply these results for the practical calculations of the scintillation index (SI). We propose an estimation technique and demonstrate some examples of the calculations of the scintillation index dependence on the propagation path length, initial beam size, wavelength and turbulence strength for the beam geometries and propagation scenarios that are typical for applications. We suggest simple analytic bridging approximations that connect the specific asymptotes with the accuracy sufficient for the engineering estimates. Proposed technique covers propagation of the wide, narrow, collimated and focused beams under the weak and strong scintillation conditions. Direct numeric simulation of the beam waves propagation through turbulence expediently complements the asymptotic theory being most efficient when the governing scales difference is not very large. We performed numerical simulations of the beam wave propagation through turbulence for conditions that partially overlap with the major parameter space domains of the asymptotic theory. The results of the numeric simulation are used to confirm the asymptotic theory and estimate the accuracy of the bridging approximations.
Asymptotic and numerical studies of a differential-delay system
Semak, Matthew Richard
A singularly-perturbed differential-delay equation is studied the form of which is seen in various fields. Relaxation effects are combined with nonlinear driving from the past in this system. Having an infinite dimensional phase space, this flow is capable of very interesting behavior. Among the rich aspects of the dynamics of such a relation, period doubling can be observed as parameters are varied. Rigorous proofs concerning the existence of such periodic solutions can be found in the literature. Attention is given to the (first) Hopf bifurcation as the periodic structure is born. Key questions concern the limit of fast relaxation. In this limit, one can analytically understand the development of the periodic solution in the neighborhood of the bifurcation along with the frequency shift which is encountered. This limit also reveals the underlying mapping structure present. In the model studied, this is the logistic map the behavior of which is well-known. Convergence of periodic solutions to the mapping's square wave involves central issues in this work. An analogue to Gibb's phenomenon presents itself as the mapping structure is approached for a certain range of parameters. Transition layers also exist and, together with the latter, present a challenge to various computational approaches. A highly accurate and efficient spectral numerical technique is introduced to properly resolve such behavior in the limit studied. This scheme is used to measure the period's dependence on the relaxation rate in this region of parameter space. Also, numerically assisted asymptotic analysis develops relations for the layers. Moreover, regimes of parameter values have been identified for which there exist extremely long-lived transient states of arbitrarily complex form. Finally, initial interval states are designed which lead to specific long-lived multi-layer patterns of significant complexity. Layer-layer interactions are considered concerning the formation and lifetime of
Canonical charges and asymptotic symmetry algebra of conformal gravity
Irakleidou, Maria; Preis, Florian
2014-01-01
We study canonical conformal gravity in four dimensions and construct the gauge generators and the associated charges. Using slightly generalized boundary conditions compared to those in \\cite{Grumiller:2013mxa} we find that the charges associated with space-time diffeomorphisms are finite and conserved in time. They are also shown to agree with the Noether charges found in \\cite{Grumiller:2013mxa}. However, there exists no charge associated with Weyl transformations. Consequently the asymptotic symmetry algebra is isomorphic to the Lie algebra of the boundary condition preserving diffeomorphisms. For illustrative purposes we apply the results to the Mannheim--Kazanas--Riegert solution of conformal gravity.
Higher Spin Black Holes in Three Dimensions: Comments on Asymptotics and Regularity
Banados, M; Theisen, S
2016-01-01
In the context of (2+1)--dimensional SL(N,R)\\times SL(N,R) Chern-Simons theory we explore issues related to regularity and asymptotics on the solid torus, for stationary and circularly symmetric solutions. We display and solve all necessary conditions to ensure a regular metric and metric-like higher spin fields. We prove that holonomy conditions are necessary but not sufficient conditions to ensure regularity, and that Hawking conditions do not necessarily follow from them. Finally we give a general proof that once the chemical potentials are turn on -- as demanded by regularity -- the asymptotics cannot be that of Brown-Henneaux.
Higher spin black holes in three dimensions: Remarks on asymptotics and regularity
Bañados, Máximo; Canto, Rodrigo; Theisen, Stefan
2016-07-01
In the context of (2 +1 )-dimensional S L (N ,R )×S L (N ,R ) Chern-Simons theory we explore issues related to regularity and asymptotics on the solid torus, for stationary and circularly symmetric solutions. We display and solve all necessary conditions to ensure a regular metric and metriclike higher spin fields. We prove that holonomy conditions are necessary but not sufficient conditions to ensure regularity, and that Hawking conditions do not necessarily follow from them. Finally we give a general proof that once the chemical potentials are turned on—as demanded by regularity—the asymptotics cannot be that of Brown-Henneaux.
Enhanced Asymptotic Symmetry Algebra of 2+1 Dimensional Flat Space
Detournay, Stéphane
2016-01-01
In this paper we present a new set of asymptotic boundary conditions for Einstein gravity in 2+1 dimensions with vanishing cosmological constant that are a generalization of the Barnich-Comp{\\`e}re boundary conditions gr-qc/0610130. These new boundary conditions lead to an asymptotic symmetry algebra that is generated by a $\\mathfrak{bms}_3$ algebra and two affine $\\hat{\\mathfrak{u}}(1)$ current algebras. We then apply these boundary conditions to Topologically Massive Gravity (TMG) and determine how the presence of the gravitational Chern-Simons term affects the central extensions of the asymptotic symmetry algebra. We furthermore determine the thermal entropy of solutions obeying our new boundary conditions for both Einstein gravity and TMG.
A note on asymptotic expansions for Markov chains using operator theory
Jensen, J.L.
1987-01-01
We consider asymptotic expansions for sums Sn on the form Sn = fhook0(X0) + fhook(X1, X0) + ... + fhook(Xn, Xn-1), where Xi is a Markov chain. Under different ergodicity conditions on the Markov chain and certain conditional moment conditions on fhook(Xi, Xi-1), a simple representation...
Bashir Ali
2012-01-01
Full Text Available Let be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let ={(∶≥0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of , with functions ,∶[0,∞→[0,∞. Let ∶=(=∩≥0((≠∅ and ∶→ be a weakly contractive map. For some positive real numbers and satisfying +>1, let ∶→ be a -strongly accretive and -strictly pseudocontractive map. Let {} be an increasing sequence in [0,∞ with lim→∞=∞, and let {} and {} be sequences in (0,1] satisfying some conditions. Strong convergence of a viscosity iterative sequence to common fixed points of the family of uniformly asymptotically regular asymptotically nonexpansive semigroup, which also solves the variational inequality ⟨(−,(−⟩≤0, for all ∈, is proved in a framework of a real Banach space.
Stellmach, S; Julien, K; Vasil, G; Cheng, J S; Ribeiro, A; King, E M; Aurnou, J M
2014-01-01
Rapidly rotating Rayleigh-B\\'enard convection is studied by combining results from direct numerical simulations (DNS), laboratory experiments and asymptotic modeling. The asymptotic theory is shown to provide a good description of the bulk dynamics at low, but finite Rossby number. However, large deviations from the asymptotically predicted heat transfer scaling are found, with laboratory experiments and DNS consistently yielding much larger Nusselt numbers than expected. These deviations are traced down to dynamically active Ekman boundary layers, which are shown to play an integral part in controlling heat transfer even for Ekman numbers as small as $10^{-7}$. By adding an analytical parameterization of the Ekman transport to simulations using stress-free boundary conditions, we demonstrate that the heat transfer jumps from values broadly compatible with the asymptotic theory to states of strongly increased heat transfer, in good quantitative agreement with no-slip DNS and compatible with the experimental d...
Asymptotically flat structure of hypergravity in three spacetime dimensions
Fuentealba, Oscar; Troncoso, Ricardo
2015-01-01
The asymptotic structure of three-dimensional hypergravity without cosmological constant is analyzed. In the case of gravity minimally coupled to a spin-$5/2$ field, a consistent set of boundary conditions is proposed, being wide enough so as to accommodate a generic choice of chemical potentials associated to the global charges. The algebra of the canonical generators of the asymptotic symmetries is given by a hypersymmetric nonlinear extension of BMS$_{3}$. It is shown that the asymptotic symmetry algebra can be recovered from a subset of a suitable limit of the direct sum of the W$_{\\left(2,4\\right)}$ algebra with its hypersymmetric extension. The presence of hypersymmetry generators allows to construct bounds for the energy, which turn out to be nonlinear and saturate for spacetimes that admit globally-defined "Killing vector-spinors". The null orbifold or Minkowski spacetime can then be seen as the corresponding ground state in the case of fermions that fulfill periodic or anti-periodic boundary conditio...
Plasma Relaxation in Hall Magnetohydrodynamics
Shivamoggi, B K
2011-01-01
Parker's formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD. The torsion coefficient alpha in the Hall MHD Beltrami condition turns out now to be proportional to the "potential vorticity." The Hall MHD Beltrami condition becomes equivalent to the "potential vorticity" conservation equation in two-dimensional hydrodynamics if the Hall MHD Lagrange multiplier beta is taken to be proportional to the "potential vorticity" as well. The winding pattern of the magnetic field lines in Hall MHD then appears to evolve in the same way as "potential vorticity" lines in 2D hydrodynamics.
Stress retardation versus stress relaxation in linear viscoelasticity
Christov, Ivan C
2016-01-01
We present a preliminary examination of a new approach to a long-standing problem in non-Newtonian fluid mechanics. First, we summarize how a general implicit functional relation between stress and rate of strain of a continuum with memory is reduced to the well-known linear differential constitutive relations that account for "relaxation" and "retardation." Then, we show that relaxation and retardation are asymptotically equivalent for small Deborah numbers, whence causal pure relaxation models necessarily correspond to ill-posed pure retardation models. We suggest that this dichotomy could be a possible way to reconcile the discrepancy between the theory of and certain experiments on viscoelastic liquids that are conjectured to exhibit only stress retardation.
Asymptotic normality of recursive algorithms via martingale difference arrays
Werner Schachinger
2001-12-01
Full Text Available We propose martingale central limit theorems as an tool to prove asymptotic normality of the costs of certain recursive algorithms which are subjected to random input data. The recursive algorithms that we have in mind are such that if input data of size N produce random costs L N, then L N = D L n + L N-n +R N for N ≥ n 0 ≥2, where n follows a certain distribution P N on the integers {0, … ,N} and L k = D L k for k≥0. L n, L N-n and R N are independent, conditional on n, and R N are random variables, which may also depend on n, corresponding to the cost of splitting the input data of size N (into subsets of size n and N-n and combining the results of the recursive calls to yield the overall result. We construct a martingale difference array with rows converging to Z N:= [L N- EL N ] / [√ Var L N ]. Under certain compatibility assumptions on the sequence (P N N≥0 we show that a pair of sufficient conditions (of Lyapunov type for Z N → D N(0,1 can be restated as a pair of conditions regarding asymptotic relations between three sequences. All these sequences satisfy the same type of linear equation, that is also the defining equation for the sequence (EL N N≥0 and thus very likely a well studied object. In the case that the P N are binomial distributions with the same parameter p, and for deterministic R N, we demonstrate the power of this approach. We derive very general sufficient conditions in terms of the sequence (R N N≥0 (and for the scale R N =N α a characterization of those α leading to asymptotic normality of Z N.
Parallelism, Uniqueness, and Large-Sample Asymptotics for the Dantzig Selector
Dicker, Lee
2012-01-01
The Dantzig selector (Candes and Tao, 2007) is a popular l1-regularization method for variable selection and estimation in linear regression. We present a very weak geometric condition on the observed predictors which is related to parallelism and, when satisfied, ensures the uniqueness of Dantzig selector estimators. The condition holds with probability 1, if the predictors are drawn from a continuous distribution. We discuss the necessity of this condition for uniqueness and also provide a closely related condition which ensures uniqueness of lasso estimators (Tibshirani, 1996). Large sample asymptotics for the Dantzig selector, i.e. almost sure convergence and the asymptotic distribution, follow directly from our uniqueness results and a continuity argument. The limiting distribution of the Dantzig selector is generally non-normal. Though our asymptotic results require that the number of predictors is fixed (similar to (Knight and Fu, 2000)), our uniqueness results are valid for an arbitrary number of pred...
The optimal homotopy asymptotic method engineering applications
Marinca, Vasile
2015-01-01
This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011, and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five application...
Lectures on renormalization and asymptotic safety
Nagy, Sandor
2012-01-01
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross-Neveu model, the nonlinear $\\sigma$ model, the sine-Gordon model, and the model of quantum Einstein gravity. We also give a detailed analysis of infrared behavior of the models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure ...
Asymptotic analysis of outwardly propagating spherical flames
Yun-Chao Wu; Zheng Chen
2012-01-01
Asymptotic analysis is conducted for outwardly propagating spherical flames with large activation energy.The spherical flame structure consists of the preheat zone,reaction zone,and equilibrium zone.Analytical solutions are separately obtained in these three zones and then asymptotically matched.In the asymptotic analysis,we derive a correlation describing the spherical flame temperature and propagation speed changing with the flame radius.This correlation is compared with previous results derived in the limit of infinite value of activation energy.Based on this correlation,the properties of spherical flame propagation are investigated and the effects of Lewis number on spherical flame propagation speed and extinction stretch rate are assessed.Moreover,the accuracy and performance of different models used in the spherical flame method are examined.It is found that in order to get accurate laminar flame speed and Markstein length,non-linear models should be used.
Nanofluid surface wettability through asymptotic contact angle.
Vafaei, Saeid; Wen, Dongsheng; Borca-Tasciuc, Theodorian
2011-03-15
This investigation introduces the asymptotic contact angle as a criterion to quantify the surface wettability of nanofluids and determines the variation of solid surface tensions with nanofluid concentration and nanoparticle size. The asymptotic contact angle, which is only a function of gas-liquid-solid physical properties, is independent of droplet size for ideal surfaces and can be obtained by equating the normal component of interfacial force on an axisymmetric droplet to that of a spherical droplet. The technique is illustrated for a series of bismuth telluride nanofluids where the variation of surface wettability is measured and evaluated by asymptotic contact angles as a function of nanoparticle size, concentration, and substrate material. It is found that the variation of nanofluid concentration, nanoparticle size, and substrate modifies both the gas-liquid and solid surface tensions, which consequently affects the force balance at the triple line, the contact angle, and surface wettability.
Relations between asymptotic and Fredholm representations
Manuilov, V M
1997-01-01
We prove that for matrix algebras $M_n$ there exists a monomorphism $(\\prod_n M_n/\\oplus_n M_n)\\otimes C(S^1) \\to {\\cal Q} $ into the Calkin algebra which induces an isomorphism of the $K_1$-groups. As a consequence we show that every vector bundle over a classifying space $B\\pi$ which can be obtained from an asymptotic representation of a discrete group $\\pi$ can be obtained also from a representation of the group $\\pi\\times Z$ into the Calkin algebra. We give also a generalization of the notion of Fredholm representation and show that asymptotic representations can be viewed as asymptotic Fredholm representations.
On generalized Nariai solutions and their asymptotics
Beyer, Florian
2009-01-01
In this paper, we consider the class of generalized Nariai solutions of Einstein's field equations in vacuum with a positive cosmological constant. According to the cosmic no-hair conjecture, generic expanding solutions isotropize and approach the de-Sitter solution asymptotically, at least locally in space. The generalized Nariai solutions, however, show quite unusual asymptotics and hence should be non-generic in some sense. In the first part of the paper, we list the necessary facts and characterize the asymptotic behavior geometrically. In the second part, we study the question of non-genericity, which we are able to confirm within the class of spatially homogeneous solutions. It turns out that perturbations of the three isometry classes of generalized Nariai solutions are related to different mass regimes of Schwarzschild de-Sitter solutions. In subsequent papers, we will continue this research in more general classes of solutions.
Relaxation of a 1-D gravitational system
Valageas, P
2006-01-01
We study the relaxation towards thermodynamical equilibrium of a 1-D gravitational system. This OSC model shows a series of critical energies $E_{cn}$ where new equilibria appear and we focus on the homogeneous ($n=0$), one-peak ($n=\\pm 1$) and two-peak ($n=2$) states. Using numerical simulations we investigate the relaxation to the stable equilibrium $n=\\pm 1$ of this $N-$body system starting from initial conditions defined by equilibria $n=0$ and $n=2$. We find that in a fashion similar to other long-range systems the relaxation involves a fast violent relaxation phase followed by a slow collisional phase as the system goes through a series of quasi-stationary states. Moreover, in cases where this slow second stage leads to a dynamically unstable configuration (two peaks with a high mass ratio) it is followed by a new sequence ``violent relaxation/slow collisional relaxation''. We obtain an analytical estimate of the relaxation time $t_{2\\to \\pm 1}$ through the mean escape time of a particle from its potent...
Indentation load relaxation test
Hannula, S.P.; Stone, D.; Li, C.Y. (Cornell Univ., Ithaca, NY (USA))
Most of the models that are used to describe the nonelastic behavior of materials utilize stress-strain rate relations which can be obtained by a load relaxation test. The conventional load relaxation test, however, cannot be performed if the volume of the material to be tested is very small. For such applications the indentation type of test offers an attractive means of obtaining data necessary for materials characterization. In this work the feasibility of the indentation load relaxation test is studied. Experimental techniques are described together with results on Al, Cu and 316 SS. These results are compared to those of conventional uniaxial load relaxation tests, and the conversion of the load-indentation rate data into the stress-strain rate data is discussed.
Relaxation techniques for stress
... problems such as high blood pressure, stomachaches, headaches, anxiety, and depression. Using relaxation techniques can help you feel calm. These exercises can also help you manage stress and ease the effects of stress on your body.
Perturbations and quantum relaxation
Kandhadai, Adithya
2016-01-01
We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding space. We assume an initial wave function with small perturbations to the ground state. We present evidence that the trajectories are highly confined so as to preclude relaxation to equilibrium even over very long timescales. Cosmological implications are briefly discussed.
de Reyna, Juan Arias
2012-01-01
A new derivation of the classic asymptotic expansion of the n-th prime is presented. A fast algorithm for the computation of its terms is also given, which will be an improvement of that by Salvy (1994). Realistic bounds for the error with $\\li^{-1}(n)$, after having retained the first m terms, for $1\\le m\\le 11$, are given. Finally, assuming the Riemann Hypothesis, we give estimations of the best possible $r_3$ such that, for $n\\ge r_3$, we have $p_n> s_3(n)$ where $s_3(n)$ is the sum of the first four terms of the asymptotic expansion.
Asymptotics of a horizontal liquid bridge
Haynes, M.; O'Brien, S. B. G.; Benilov, E. S.
2016-04-01
This paper uses asymptotic techniques to find the shape of a two dimensional liquid bridge suspended between two vertical walls. We model the equilibrium bridge shape using the Laplace-Young equation. We use the Bond number as a small parameter to deduce an asymptotic solution which is then compared with numerical solutions. The perturbation approach demonstrates that equilibrium is only possible if the contact angle lies within a hysteresis interval and the analysis relates the width of this interval to the Bond number. This result is verified by comparison with a global force balance. In addition, we examine the quasi-static evolution of such a two dimensional bridge.
Semiclassical Asymptotics on Manifolds with Boundary
Koldan, Nilufer; Shubin, Mikhail
2008-01-01
We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by Kordyukov, Mathai and Shubin (2005), with a more extended use of quadratic forms instead of the operators. We also utilize some important ideas and technical elements from Helffer and Nier (2006), who were the first to supply a complete proof of the full semi-classical asymptotic expansions for the eigenvalues with fixed numbers.
Asymptotic Methods for Solitary Solutions and Compactons
Ji-Huan He
2012-01-01
Full Text Available This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.
Asymptotic expansions for the Gaussian unitary ensemble
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian...... Unitary Ensemble (GUE). Using an analytical approach, we provide in the present paper an alternative proof of this asymptotic expansion in the GUE case. Specifically we derive for a random matrix Xn that where k is an arbitrary positive integer. Considered as mappings of g, we determine the coefficients...
Asymptotic stability of singularly perturbed differential equations
Artstein, Zvi
2017-02-01
Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.
Asymptotic behavior of asynchronous stochasticapproximation
方海涛; 陈翰馥
2001-01-01
The pathwise convergence of a distributed, asynchronous stochastic approximation (SA) scheme is analyzed. The conditions imposed on the step size and noise are the weakest in comparison with the existing ones. The step sizes in different processors are allowed to be different, and the time_delays between processors are also allowed to be different and even time_varying.
On the Rate of Relaxation for the Landau Kinetic Equation and Related Models
Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong
2017-08-01
We study the rate of relaxation to equilibrium for Landau kinetic equation and some related models by considering the relatively simple case of radial solutions of the linear Landau-type equations. The well-known difficulty is that the evolution operator has no spectral gap, i.e. its spectrum is not separated from zero. Hence we do not expect purely exponential relaxation for large values of time t>0. One of the main goals of our work is to numerically identify the large time asymptotics for the relaxation to equilibrium. We recall the work of Strain and Guo (Arch Rat Mech Anal 187:287-339 2008, Commun Partial Differ Equ 31:17-429 2006), who rigorously show that the expected law of relaxation is \\exp (-ct^{2/3}) with some c > 0. In this manuscript, we find an heuristic way, performed by asymptotic methods, that finds this "law of two thirds", and then study this question numerically. More specifically, the linear Landau equation is approximated by a set of ODEs based on expansions in generalized Laguerre polynomials. We analyze the corresponding quadratic form and the solution of these ODEs in detail. It is shown that the solution has two different asymptotic stages for large values of time t and maximal order of polynomials N: the first one focus on intermediate asymptotics which agrees with the "law of two thirds" for moderately large values of time t and then the second one on absolute, purely exponential asymptotics for very large t, as expected for linear ODEs. We believe that appearance of intermediate asymptotics in finite dimensional approximations must be a generic behavior for different classes of equations in functional spaces (some PDEs, Boltzmann equations for soft potentials, etc.) and that our methods can be applied to related problems.
Non-asymptotic Equipartition Properties for Independent and Identically Distributed Sources
Yang, En-Hui
2012-01-01
Given an independent and identically distributed source $X = \\{X_i \\}_{i=1}^{\\infty}$ with finite Shannon entropy or differential entropy (as the case may be) $H(X)$, the non-asymptotic equipartition property (NEP) with respect to $H(X)$ is established, which characterizes, for any finite block length $n$, how close $-{1\\over n} \\ln p(X_1 X_2...X_n)$ is to $H(X)$ by determining the information spectrum of $X_1 X_2...X_n $, i.e., the distribution of $-{1\\over n} \\ln p(X_1 X_2...X_n)$. Non-asymptotic equipartition properties (with respect to conditional entropy, mutual information, and relative entropy) in a similar nature are also established. These non-asymptotic equipartition properties are instrumental to the development of non-asymptotic coding (including both source and channel coding) results in information theory in the same way as the asymptotic equipartition property to all asymptotic coding theorems established so far in information theory. As an example, the NEP with respect to $H(X)$ is used to est...
Asymptotic Limits for Transport in Binary Stochastic Mixtures
Prinja, A. K. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-05-01
The Karhunen-Loeve stochastic spectral expansion of a random binary mixture of immiscible fluids in planar geometry is used to explore asymptotic limits of radiation transport in such mixtures. Under appropriate scalings of mixing parameters - correlation length, volume fraction, and material cross sections - and employing multiple- scale expansion of the angular flux, previously established atomic mix and diffusion limits are reproduced. When applied to highly contrasting material properties in the small cor- relation length limit, the methodology yields a nonstandard reflective medium transport equation that merits further investigation. Finally, a hybrid closure is proposed that produces both small and large correlation length limits of the closure condition for the material averaged equations.
Precise Asymptotics of Error Variance Estimator in Partially Linear Models
Shao-jun Guo; Min Chen; Feng Liu
2008-01-01
In this paper, we focus our attention on the precise asymptoties of error variance estimator in partially linear regression models, yi = xTi β + g(ti) +εi, 1 ≤i≤n, {εi,i = 1,... ,n } are i.i.d random errors with mean 0 and positive finite variance q2. Following the ideas of Allan Gut and Aurel Spataru[7,8] and Zhang[21],on precise asymptotics in the Baum-Katz and Davis laws of large numbers and precise rate in laws of the iterated logarithm, respectively, and subject to some regular conditions, we obtain the corresponding results in partially linear regression models.
Further evidence for asymptotic safety of quantum gravity
Falls, Kevin; Nikolakopoulos, Konstantinos; Rahmede, Christoph
2014-01-01
The asymptotic safety conjecture is examined for quantum gravity in four dimensions. Using the renormalisation group, we find evidence for an interacting UV fixed point for polynomial actions up to the 34th power in the Ricci scalar. The extrapolation to infinite polynomial order is given, and the self-consistency of the fixed point is established using a bootstrap test. All details of our analysis are provided. We also clarify further aspects such as stability, convergence, the role of boundary conditions, and a partial degeneracy of eigenvalues. Within this setting we find strong support for the conjecture.
无
2001-01-01
Under certain conditions, starting from the three-dimensional dynamic equations of elastic shells the author gives the justification of dynamic equations of flexural shells by means of the method of asymptotic analysis.
Asymptotic Distributions for Tests of Combined Significance.
Becker, Betsy Jane
This paper discusses distribution theory and power computations for four common "tests of combined significance." These tests are calculated using one-sided sample probabilities or p values from independent studies (or hypothesis tests), and provide an overall significance level for the series of results. Noncentral asymptotic sampling…
Breaking a magnetic zero locus: asymptotic analysis
Raymond, Nicolas
2014-01-01
25 pages; This paper deals with the spectral analysis of the Laplacian in presence of a magnetic field vanishing along a broken line. Denoting by $\\theta$ the breaking angle, we prove complete asymptotic expansions of all the lowest eigenpairs when $\\theta$ goes to $0$. The investigation deeply uses a coherent states decomposition and a microlocal analysis of the eigenfunctions.
Asymptotic iteration approach to supersymmetric bistable potentials
H. Ciftci; O. ozer; P. Roy
2012-01-01
We examine quasi exactly solvable bistable potentials and their supersymmetric partners within the framework of the asymptotic iteration method (AIM).It is shown that the AIM produces excellent approximate spectra and that sometimes it is found to be more useful to use the partner potential for computation. We also discuss the direct application of the AIM to the Fokker-Planck equation.
The conformal approach to asymptotic analysis
Nicolas, Jean-Philippe
2015-01-01
This essay was written as an extended version of a talk given at a conference in Strasbourg on "Riemann, Einstein and geometry", organized by Athanase Papadopoulos in September 2014. Its aim is to present Roger Penrose's approach to asymptotic analysis in general relativity, which is based on conformal geometric techniques, focusing on historical and recent aspects of two specialized topics~: conformal scattering and peeling.
An asymptotically optimal nonparametric adaptive controller
郭雷; 谢亮亮
2000-01-01
For discrete-time nonlinear stochastic systems with unknown nonparametric structure, a kernel estimation-based nonparametric adaptive controller is constructed based on truncated certainty equivalence principle. Global stability and asymptotic optimality of the closed-loop systems are established without resorting to any external excitations.
Large degree asymptotics of generalized Bessel polynomials
J.L. López; N.M. Temme (Nico)
2011-01-01
textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the
THE COMPLETE ASYMPTOTIC EXPANSION FOR BASKAKOV OPERATORS
Chungou Zhang; Quane Wang
2007-01-01
In this paper, we derive the complete asymptotic expansion of classical Baskakov itly in terms of Stirling number of the first and second kind and another number G(I, p). As a corollary, we also get the Voronovskaja-type result for the operators.
Fixed Point Theorems for Asymptotically Contractive Multimappings
M. Djedidi
2012-01-01
Full Text Available We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. Some existence results of coincidence points and eigenvalues for multimappings are given.
Couplings and Asymptotic Exponentiality of Exit Times
Brassesco, S.; Olivieri, E.; Vares, M. E.
1998-10-01
The goal of this note is simply to call attention to the resulting simplification in the proof of asymptotic exponentiality of exit times in the Freidlin-Wentzell regime (as proved by F. Martinelli et al.) by using the coupling proposed by T. Lindvall and C. Rogers.
Toeplitz Quantization and Asymptotic Expansions: Geometric Construction
Miroslav Englis
2009-02-01
Full Text Available For a real symmetric domain G_R/K_R, with complexification G_C/K_C, we introduce the concept of ''star-restriction'' (a real analogue of the ''star-products'' for quantization of Kähler manifolds and give a geometric construction of the G_R-invariant differential operators yielding its asymptotic expansion.
On iterative procedures of asymptotic inference
K.O. Dzhaparidze (Kacha)
1983-01-01
textabstractAbstract An informal discussion is given on performing an unconstrained maximization or solving non‐linear equations of statistics by iterative methods with the quadratic termination property. It is shown that if a miximized function, e.g. likelihood, is asymptotically quadratic, then f
Asymptotically periodic solutions of Volterra integral equations
Muhammad N. Islam
2016-03-01
Full Text Available We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.
Asymptotic estimates for generalized Stirling numbers
Chelluri, R.; Richmond, L.B.; Temme, N.M.
1999-01-01
Uniform asymptotic expansions are given for the Stirling numbers of the first kind for integral arguments and for the second kind as defined for real arguments by Flajolet and Prodinger. The logconcavity of the resulting real valued function of Flajolet and Prodinger is established for a range inclu
Discrete Energy Asymptotics on a Riemannian circle
Brauchart, J S; Saff, E B
2009-01-01
We derive the complete asymptotic expansion in terms of powers of $N$ for the geodesic $f$-energy of $N$ equally spaced points on a rectifiable simple closed curve $\\Gamma$ in ${\\mathbb R}^p$, $p\\geq2$, as $N \\to \\infty$. For $f$ decreasing and convex, such a point configuration minimizes the $f$-energy $\\sum_{j\
Asymptotic inversion of the Erlang B formula
J. van Leeuwaarden; N.M. Temme (Nico)
2009-01-01
textabstractThe Erlang B formula represents the steady-state blocking probability in the Erlang loss model or $M/M/s/s$ queue. We derive asymptotic expansions for the offered load that matches, for a given number of servers, a certain blocking probability. In addressing this inversion problem we mak
Resonance asymptotics in the generalized Winter model
Exner, P; Exner, Pavel; Fraas, Martin
2006-01-01
We consider a modification of the Winter model describing a quantum particle in presence of a spherical barrier given by a fixed generalized point interaction. It is shown that the three classes of such interactions correspond to three different types of asymptotic behaviour of resonances of the model at high energies.
Asymptotic and Oscillatory Behavior of Solutions of First Order Neutral Differential Equations
王其如; 李黎
1993-01-01
This paper has made researches on first order neutral differential equations with varia-ble coefficients and several deviations.The asymptotic behavior of nonoscillatory solutions of the equations are discussed.Necessary and sufficient conditions and several sufficient conditions for the oscillations of the equations are obtained.The relevent results in [1-3] are improved and genera-lized.
Multiple Solutions for a Fourth-order Asymptotically Linear Elliptic Problem
Ai Xia QIAN; Shu Jie LI
2006-01-01
Under simple conditions, we prove the existence of three solutions for a fourth-order asymptotically linear elliptic boundary value problem. For the resonance case at infinity, we do not need to assume any more conditions to ensure the boundedness of the (PS) sequence of the corresponding functional.
Scattering by a topological defect connecting two asymptotically Minkowski spacetimes
Pitelli, J P M
2015-01-01
We study the stability and the scattering properties of a spacetime with a topological defect along a spherical bubble. This bubble connects two flat spacetimes which are asymptotically Minkowski, so that the resulting universe may be regarded as containing a wormhole. Its distinguished feature is the absence of exotic matter, i.e., its matter content respects all the energy conditions. Although this wormhole is nontraversable, waves and quantum particles can tunnel between both universes. Interestingly enough, the wave equation alone does not uniquely determine the evolution of scalar waves on this background, and the theory of self-adjoint extensions of symmetric operators is required to find the relevant boundary conditions in this context. Here we show that, for a particular boundary condition, this spacetime is stable and gives rise to a scattering pattern which is identical to the more usual thin-shell wormhole composed of exotic matter. Other boundary conditions of interest are also analyzed, including...
Global dynamics of a Yang-Mills field on an asymptotically hyperbolic space
Bizoń, Piotr
2014-01-01
We consider a spherically symmetric (purely magnetic) SU(2) Yang-Mills field propagating on an ultrastatic spacetime with two asymptotically hyperbolic regions connected by a throat of radius $\\alpha$. Static solutions in this model are shown to exhibit an interesting bifurcation pattern in the parameter $\\alpha$. We relate this pattern to the Morse index of the static solution with maximal energy. Using a hyperboloidal approach to the initial value problem, we describe the relaxation to the ground state solution for generic initial data and unstable static solutions for initial data of codimension one, two, and three.
Wong NC
2006-01-01
Full Text Available We study an implicit predictor-corrector iteration process for finitely many asymptotically quasi-nonexpansive self-mappings on a nonempty closed convex subset of a Banach space . We derive a necessary and sufficient condition for the strong convergence of this iteration process to a common fixed point of these mappings. In the case is a uniformly convex Banach space and the mappings are asymptotically nonexpansive, we verify the weak (resp., strong convergence of this iteration process to a common fixed point of these mappings if Opial's condition is satisfied (resp., one of these mappings is semicompact. Our results improve and extend earlier and recent ones in the literature.
Asymptotic property of solutions to the random cauchy problem for wave equations
Dôku, Isamu
1986-01-01
Based on the existence and uniqueness theorem for random wave equations, we consider asymptotic behaviors of solutions to the random initial value problem. We describe conditions for the equipartition of stochastic energy (or SE for short) by making use of the random spectral theory and, according to Goldstein's semigroup method, we prove the asymptotically equipartitioned SE theorem and the so-called virial theorem of classical mechanics, and also study the probabilistic characterization of the conditions for equipartition. In addition, we show at last the equipartition of SE from a finite time onwards.
Asymptotic expansion of the wavelet transform with error term
Pathak, R.S.; Pathak, Ashish
2014-01-01
UsingWong's technique asymptotic expansion for the wavelet transform is derived and thereby asymptotic expansions for Morlet wavelet transform, Mexican Hat wavelet transform and Haar wavelet transform are obtained.
Molecular Relaxation in Liquids
Bagchi, Biman
2012-01-01
This book brings together many different relaxation phenomena in liquids under a common umbrella and provides a unified view of apparently diverse phenomena. It aligns recent experimental results obtained with modern techniques with recent theoretical developments. Such close interaction between experiment and theory in this area goes back to the works of Einstein, Smoluchowski, Kramers' and de Gennes. Development of ultrafast laser spectroscopy recently allowed study of various relaxation processes directly in the time domain, with time scales going down to picosecond (ps) and femtosecond (fs
Matulich, Javier; Tempo, David; Troncoso, Ricardo
2014-01-01
A generalized set of asymptotic conditions for higher spin gravity without cosmological constant in three spacetime dimensions is constructed. They include the most general temporal components of the gauge fields that manifestly preserve the original asymptotic higher spin extension of the BMS$_{3}$ algebra, with the same central charge. By virtue of a suitable permissible gauge choice, it is shown that this set can be directly recovered as a limit of the boundary conditions that have been recently constructed in the case of negative cosmological constant, whose asymptotic symmetries are spanned by two copies of the centrally-extended W$_{3}$ algebra. Since the generalized asymptotic conditions allow to incorporate chemical potentials conjugated to the higher spin charges, a higher spin extension of locally flat cosmological spacetimes becomes naturally included within the set. It is shown that their thermodynamic properties can be successfully obtained exclusively in terms of gauge fields and the topology of...
Stress relaxation in viscous soft spheres.
Boschan, Julia; Vasudevan, Siddarth A; Boukany, Pouyan E; Somfai, Ellák; Tighe, Brian P
2017-09-27
We report the results of molecular dynamics simulations of stress relaxation tests in athermal viscous soft sphere packings close to their unjamming transition. By systematically and simultaneously varying both the amplitude of the applied strain step and the pressure of the initial condition, we access both linear and nonlinear response regimes and control the distance to jamming. Stress relaxation in viscoelastic solids is characterized by a relaxation time τ* that separates short time scales, where viscous loss is substantial, from long time scales, where elastic storage dominates and the response is essentially quasistatic. We identify two distinct plateaus in the strain dependence of the relaxation time, one each in the linear and nonlinear regimes. The height of both plateaus scales as an inverse power law with the distance to jamming. By probing the time evolution of particle velocities during relaxation, we further identify a correlation between mechanical relaxation in the bulk and the degree of non-affinity in the particle velocities on the micro scale.
Low-frequency asymptotic analysis of seismic reflection from afluid-saturated medium
Silin, D.B.; Korneev, V.A.; Goloshubin, G.M.; Patzek, T.W.
2004-04-14
Reflection of a seismic wave from a plane interface betweentwo elastic media does not depend on the frequency. If one of the mediais poroelastic and fluid-saturated, then the reflection becomesfrequency-dependent. This paper presents a low-frequency asymptoticformula for the reflection of seismic plane p-wave from a fluid-saturatedporous medium. The obtained asymptotic scaling of the frequency-dependentcomponent of the reflection coefficient shows that it is asymptoticallyproportional to the square root of the product of the reservoir fluidmobility and the frequency of the signal. The dependence of this scalingon the dynamic Darcy's law relaxation time is investigated as well.Derivation of the main equations of the theory of poroelasticity from thedynamic filtration theory reveals that this relaxation time isproportional to Biot's tortuosity parameter.
Estimation and asymptotic inference in the first order AR-ARCH model
Lange, Theis; Rahbek, Anders; Jensen, Søren Tolver
2011-01-01
This article studies asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for the parameters in the autoregressive (AR) model with autoregressive conditional heteroskedastic (ARCH) errors. A modified QMLE (MQMLE) is also studied. This estimator is based on truncation of individual...... terms of the likelihood function and is related to the recent so-called self-weighted QMLE in Ling (2007b). We show that the MQMLE is asymptotically normal irrespectively of the existence of finite moments, as geometric ergodicity alone suffice. Moreover, our included simulations show that the MQMLE...... for the QMLE to be asymptotically normal. Finally, geometric ergodicity for AR-ARCH processes is shown to hold under mild and classic conditions on the AR and ARCH processes....
Locally Asymptotic-norming Property and Kadec Property
王建华
2002-01-01
In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property κ, κ=Ⅰ,Ⅱ,Ⅲ,and discuss the relationship between the locally asymptotic-norming property and the Kadec Property.
Preheating in an asymptotically safe quantum field theory
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-01-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, ...
Hyperbolic positive mass theorem under modified energy condition
XIE NaQing
2008-01-01
We provide two new positive mass theorems under respective modified energy conditions allowing Too negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang's previous result for modified asymptotically fiat initial data sets.
Asymptotic Value Distribution for Solutions of the Schroedinger Equation
Breimesser, S. V., E-mail: s.v.breimesser@maths.hull.ac.uk; Pearson, D. B. [University of Hull, Department of Mathematics (United Kingdom)], E-mail: d.b.pearson@maths.hull.ac.uk
2000-12-15
We consider the Dirichlet Schroedinger operator T=-(d{sup 2}/d x{sup 2})+V, acting in L{sup 2}(0,{infinity}), where Vis an arbitrary locally integrable potential which gives rise to absolutely continuous spectrum. Without any other restrictive assumptions on the potential V, the description of asymptotics for solutions of the Schroedinger equation is carried out within the context of the theory of value distribution for boundary values of analytic functions. The large x asymptotic behaviour of the solution v(x,{lambda}) of the equation Tf(x,{lambda})={lambda}f(x,{lambda}), for {lambda} in the support of the absolutely continuous part {mu}{sub a.c.} of the spectral measure {mu}, is linked to the spectral properties of this measure which are determined by the boundary value of the Weyl-Titchmarsh m-function. Our main result (Theorem 1) shows that the value distribution for v'(N,{lambda})/v(N,{lambda}) approaches the associated value distribution of the Herglotz function m{sup N}(z) in the limit N{sup {yields}}{infinity}, where m{sup N}(z) is the Weyl-Titchmarsh m-function for the Schroedinger operator -(d{sup 2}/d x{sup 2})+Vacting in L{sup 2}(N,{infinity}), with Dirichlet boundary condition at x=N. We will relate the analysis of spectral asymptotics for the absolutely continuous component of Schroedinger operators to geometrical properties of the upper half-plane, viewed as a hyperbolic space.
Black holes and asymptotically safe gravity
Falls, Kevin; Raghuraman, Aarti
2010-01-01
Quantum gravitational corrections to black holes are studied in four and higher dimensions using a renormalisation group improvement of the metric. The quantum effects are worked out in detail for asymptotically safe gravity, where the short distance physics is characterized by a non-trivial fixed point of the gravitational coupling. We find that a weakening of gravity implies a decrease of the event horizon, and the existence of a Planck-size black hole remnant with vanishing temperature and vanishing heat capacity. The absence of curvature singularities is generic and discussed together with the conformal structure and the Penrose diagram of asymptotically safe black holes. The production cross section of mini-black holes in energetic particle collisions, such as those at the Large Hadron Collider, is analysed within low-scale quantum gravity models. Quantum gravity corrections imply that cross sections display a threshold, are suppressed in the Planckian, and reproduce the semi-classical result in the deep...
Brane model with two asymptotic regions
Lubo, Musongela
2005-02-01
Some brane models rely on a generalization of the Melvin magnetic universe including a complex scalar field among the sources. We argue that the geometric interpretation of Kip. S. Thorne of this geometry restricts the kind of potential a complex scalar field can display to keep the same asymptotic behavior. While a finite energy is not obtained for a Mexican hat potential in this interpretation, this is the case for a potential displaying a broken phase and an unbroken one. We use for technical simplicity and illustrative purposes an ad hoc potential which however shares some features with those obtained in some supergravity models. We construct a sixth dimensional cylindrically symmetric solution which has two asymptotic regions: the Melvin-like metric on one side and a flat space displaying a conical singularity on the other. The causal structure of the configuration is discussed. Unfortunately, gravity is not localized on the brane.
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.
M. De la Sen
2013-01-01
Full Text Available This paper is focused on the study of the important property of the asymptotic hyperstability of a class of continuous-time dynamic systems. The presence of a parallel connection of a strictly stable subsystem to an asymptotically hyperstable one in the feed-forward loop is allowed while it has also admitted the generation of a finite or infinite number of impulsive control actions which can be combined with a general form of nonimpulsive controls. The asymptotic hyperstability property is guaranteed under a set of sufficiency-type conditions for the impulsive controls.
Li, Yongfeng; Cui, Jingan; Song, Xinyu
2009-01-01
In this paper, the nonautonomous competing two-species Lotka-Volterra models with impulsive effect are considered, where all the parameters are time-dependent and asymptotically approach the corresponding periodic functions. Under some conditions, it is shown that the semi-trivial positive solutions of the models asymptotically approach the semi-trivial positive periodic solutions of the corresponding periodic system. It is also shown that the positive solution of the models asymptotically approach the positive periodic solution of the corresponding periodic system.
Optimization of Parameters of Asymptotically Stable Systems
Anna Guerman
2011-01-01
Full Text Available This work deals with numerical methods of parameter optimization for asymptotically stable systems. We formulate a special mathematical programming problem that allows us to determine optimal parameters of a stabilizer. This problem involves solutions to a differential equation. We show how to chose the mesh in order to obtain discrete problem guaranteeing the necessary accuracy. The developed methodology is illustrated by an example concerning optimization of parameters for a satellite stabilization system.
Asymptotics of high order noise corrections
Sondergaard, N; Pálla, G; Voros, A; Sondergaard, Niels; Vattay, Gabor; Palla, Gergely; Voros, Andre
1999-01-01
We consider an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and noise with finite moments. Using a perturbative expansion of the evolution operator we calculate high order corrections to its trace in the case of a quartic map and Gaussian noise. The leading contributions come from the period one orbits of the map. The asymptotic behaviour is investigated and is found to be independent up to a multiplicative constant of the distribution of noise.
Asymptotic Behaviour Near a Nonlinear Sink
Calder, Matt S
2010-01-01
In this paper, we will explore an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Moreover, we will address the writing of one component in terms of the other in the case of a planar system. Examples will be given, notably the Michaelis-Menten mechanism of enzyme kinetics.
Asymptotic analysis of the Forward Search
Johansen, Søren; Nielsen, Bent
The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made....... The argument involves theory for a new class of weighted and marked empirical processes, quantile process theory, and a fixed point argument to describe the iterative element of the procedure....
Asymptotic modal analysis and statistical energy analysis
Dowell, Earl H.
1988-07-01
Statistical Energy Analysis (SEA) is defined by considering the asymptotic limit of Classical Modal Analysis, an approach called Asymptotic Modal Analysis (AMA). The general approach is described for both structural and acoustical systems. The theoretical foundation is presented for structural systems, and experimental verification is presented for a structural plate responding to a random force. Work accomplished subsequent to the grant initiation focusses on the acoustic response of an interior cavity (i.e., an aircraft or spacecraft fuselage) with a portion of the wall vibrating in a large number of structural modes. First results were presented at the ASME Winter Annual Meeting in December, 1987, and accepted for publication in the Journal of Vibration, Acoustics, Stress and Reliability in Design. It is shown that asymptotically as the number of acoustic modes excited becomes large, the pressure level in the cavity becomes uniform except at the cavity boundaries. However, the mean square pressure at the cavity corner, edge and wall is, respectively, 8, 4, and 2 times the value in the cavity interior. Also it is shown that when the portion of the wall which is vibrating is near a cavity corner or edge, the response is significantly higher.
Asymptotic Enumeration of RNA Structures with Pseudoknots
Jin, Emma Y
2007-01-01
In this paper we present the asymptotic enumeration of RNA structures with pseudoknots. We develop a general framework for the computation of exponential growth rate and the sub exponential factors for $k$-noncrossing RNA structures. Our results are based on the generating function for the number of $k$-noncrossing RNA pseudoknot structures, ${\\sf S}_k(n)$, derived in \\cite{Reidys:07pseu}, where $k-1$ denotes the maximal size of sets of mutually intersecting bonds. We prove a functional equation for the generating function $\\sum_{n\\ge 0}{\\sf S}_k(n)z^n$ and obtain for $k=2$ and $k=3$ the analytic continuation and singular expansions, respectively. It is implicit in our results that for arbitrary $k$ singular expansions exist and via transfer theorems of analytic combinatorics we obtain asymptotic expression for the coefficients. We explicitly derive the asymptotic expressions for 2- and 3-noncrossing RNA structures. Our main result is the derivation of the formula ${\\sf S}_3(n) \\sim \\frac{10.4724\\cdot 4!}{n(n...
Asymptotically flat space-times: an enigma
Newman, Ezra T.
2016-07-01
We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory—absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) asymptotically flat space-times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of Newman-Unti (NU) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-space that has no immediate relationship with space-time. In fact these relations appear in two such spaces, H-space and its dual space \\bar{H}.
M. Venkatesulu
1996-01-01
Full Text Available Solutions of initial value problems associated with a pair of ordinary differential systems (L1,L2 defined on two adjacent intervals I1 and I2 and satisfying certain interface-spatial conditions at the common end (interface point are studied.
Automatically Discovering Relaxed Lyapunov Functions for Polynomial Dynamical Systems
Liu, Jiang; Zhao, Hengjun
2011-01-01
The notion of Lyapunov function plays a key role in design and verification of dynamical systems, as well as hybrid and cyber-physical systems. In this paper, to analyze the asymptotic stability of a dynamical system, we generalize standard Lyapunov functions to relaxed Lyapunov functions (RLFs), by considering higher order Lie derivatives of certain functions along the system's vector field. Furthermore, we present a complete method to automatically discovering polynomial RLFs for polynomial dynamical systems (PDSs). Our method is complete in the sense that it is able to discover all polynomial RLFs by enumerating all polynomial templates for any PDS.
Compaction and relaxation of biofilms
Valladares Linares, R.
2015-06-18
Operation of membrane systems for water treatment can be seriously hampered by biofouling. A better characterization of biofilms in membrane systems and their impact on membrane performance may help to develop effective biofouling control strategies. The objective of this study was to determine the occurrence, extent and timescale of biofilm compaction and relaxation (decompaction), caused by permeate flux variations. The impact of permeate flux changes on biofilm thickness, structure and stiffness was investigated in situ and non-destructively with optical coherence tomography using membrane fouling monitors operated at a constant crossflow velocity of 0.1 m s−1 with permeate production. The permeate flux was varied sequentially from 20 to 60 and back to 20 L m−2 h−1. The study showed that the average biofilm thickness on the membrane decreased after elevating the permeate flux from 20 to 60 L m−2 h−1 while the biofilm thickness increased again after restoring the original flux of 20 L m−2 h−1, indicating the occurrence of biofilm compaction and relaxation. Within a few seconds after the flux change, the biofilm thickness was changed and stabilized, biofilm compaction occurred faster than the relaxation after restoring the original permeate flux. The initial biofilm parameters were not fully reinstated: the biofilm thickness was reduced by 21%, biofilm stiffness had increased and the hydraulic biofilm resistance was elevated by 16%. Biofilm thickness was related to the hydraulic biofilm resistance. Membrane performance losses are related to the biofilm thickness, density and morphology, which are influenced by (variations in) hydraulic conditions. A (temporarily) permeate flux increase caused biofilm compaction, together with membrane performance losses. The impact of biofilms on membrane performance can be influenced (increased and reduced) by operational parameters. The article shows that a (temporary) pressure increase leads to more
asymptoticMK: A Web-Based Tool for the Asymptotic McDonald-Kreitman Test.
Haller, Benjamin C; Messer, Philipp W
2017-03-24
The McDonald-Kreitman (MK) test is a widely used method for quantifying the role of positive selection in molecular evolution. One key shortcoming of this test lies in its sensitivity to the presence of slightly deleterious mutations, which can severely bias its estimates. An asymptotic version of the MK test was recently introduced that addresses this problem by evaluating polymorphism levels for different mutation frequencies separately, and then extrapolating a function fitted to that data. Here we present asymptoticMK, a web-based implementation of this asymptotic McDonald-Kreitman test. Our web service provides a simple R-based interface into which the user can upload the required data (polymorphism and divergence data for the genomic test region and a neutrally evolving reference region). The web service then analyzes the data and provides plots of the test results. This service is free to use, open-source, and available at http://benhaller.com/messerlab/asymptoticMK.html. We provide results from simulations to illustrate the performance and robustness of the asymptoticMK test under a wide range of model parameters.
Adaptive Molecular Resolution Approach in Hamiltonian Form: An Asymptotic Analysis
Zhu, Jinglong; Site, Luigi Delle
2016-01-01
Adaptive Molecular Resolution approaches in Molecular Dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in the way the change of molecular resolution is made in a buffer/transition region. In particular a central question concerns the possibility of the existence of a global Hamiltonian which, by describing the change of resolution, is at the same time physically consistent, mathematically well defined and numerically accurate. In this paper we present an asymptotic analysis of the adaptive process complemented by numerical results and show that under certain mathematical conditions a Hamiltonian, which is physically consistent and numerically accurate, may exist. \\blue{Such conditions show that molecular simulations in the current computational implementation require systems of large size and thus a Hamiltonian approach as the one proposed, at this stage, would not be practica...
... For Consumers Consumer Information by Audience For Women Hair Dye and Hair Relaxers Share Tweet Linkedin Pin it More sharing ... products. If you have a bad reaction to hair dyes and relaxers, you should: Stop using the ...
Relaxation Treatment for Insomnia: A Component Analysis.
Woolfolk, Robert L.; McNulty, Terrence F.
1983-01-01
Compared four relaxation treatments for sleep onset insomnia with a waiting-list control. Treatments varied in presence or absence of muscular tension-release instructions and in foci of attention. Results showed all treatment conditions reduced latency of sleep onset and fatigue; visual focusing best reduced the number of nocturnal awakenings.…
Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence
Zhang Tailei [College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046 (China)], E-mail: t.l.zhang@126.com; Teng Zhidong [College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046 (China)
2008-09-15
In this paper, the asymptotic behavior of solutions of an autonomous SEIRS epidemic model with the saturation incidence is studied. Using the method of Liapunov-LaSalle invariance principle, we obtain the disease-free equilibrium is globally stable if the basic reproduction number is not greater than one. Moreover, we show that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions of locally and globally asymptotically stable convergence to an endemic equilibrium are obtained base on the permanence.
Asymptotic Expansion of the Solutions to Time-Space Fractional Kuramoto-Sivashinsky Equations
Weishi Yin
2016-01-01
Full Text Available This paper is devoted to finding the asymptotic expansion of solutions to fractional partial differential equations with initial conditions. A new method, the residual power series method, is proposed for time-space fractional partial differential equations, where the fractional integral and derivative are described in the sense of Riemann-Liouville integral and Caputo derivative. We apply the method to the linear and nonlinear time-space fractional Kuramoto-Sivashinsky equation with initial value and obtain asymptotic expansion of the solutions, which demonstrates the accuracy and efficiency of the method.
State Estimation for a Biological Phosphorus Removal Process using an Asymptotic Observer
Larose, Claude Alain; Jørgensen, Sten Bay
2001-01-01
This study investigated the use of an asymptotic observer for state estimation in a continuous biological phosphorus removal process. The estimated states are the concentration of heterotrophic, autotrophic, and phosphorus accumulating organisms, polyphosphate, glycogen and PHA. The reaction scheme...... if the convergence, driven by the dilution rate, was slow (from 15 to 60 days). The propagation of the measurement noise and a bias in the estimation of glycogen and PHA could be the result of the high condition number of one of the matrices used in the algorithm of the asymptotic observer for the aerated tanks....
Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps
Xinhong Zhang
2013-07-01
Full Text Available This article concerns the study of stochastic Gilpin-Ayala mutualism models with white noise and Poisson jumps. Firstly, an explicit solution for one-dimensional Gilpin-Ayala mutualism model with jumps is obtained and the asymptotic pathwise behavior is analyzed. Then, sufficient conditions for the existence of global positive solutions, stochastically ultimate boundedness and stochastic permanence are established for the n-dimensional model. Asymptotic pathwise behavior of n-dimensional Gilpin-Ayala mutualism model with jumps is also discussed. Finally numerical examples are introduced to illustrate the results developed.
Hai Zhang
2014-01-01
Full Text Available We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.
Xia ZHOU; Shou Ming ZHONG
2011-01-01
In this paper the asymptotical stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan's results.
Ömer Kavaklıoğlu
2011-01-01
Full Text Available We have presented a derivation of the asymptotic equations for transverse magnetic multiple scattering coefficients of an infinite grating of penetrable circular cylinders for obliquely incident plane electromagnetic waves. We have first deducted an “Ansatz” delineating the asymptotic behavior of the transverse magnetic multiple scattering coefficients associated with the most generalized condition of oblique incidence (Kavaklıoğlu, 2000 by exploiting Schlömilch series corresponding to the special circumstance that the grating spacing is much smaller than the wavelength of the incident electromagnetic radiation. The validity of the asymptotic equations for the aforementioned scattering coefficients has been verified by collating them with the Twersky's asymptotic equations at normal incidence. Besides, we have deduced the consequences that the asymptotic forms of the equations at oblique incidence acquired in this paper reduce to Twersky's asymptotic forms at normal incidence by expanding the generalized scattering coefficients at oblique incidence into an asymptotic series as a function of the ratio of the cylinder radius to the grating spacing.
Zhanhua Yu
2011-01-01
convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results.
Asymptotic Behavior of Equilibrium Point for a Class of Nonlinear Difference Equation
Gong Fei
2009-01-01
Full Text Available We study the asymptotic behavior of the solutions for the following nonlinear difference equation where the initial conditions are arbitrary nonnegative real numbers, are nonnegative integers, , and are positive constants. Moreover, some numerical simulations to the equation are given to illustrate our results.
Uniform Asymptotic Normality of the Matrix-variate Beta-distribution
Kai Can LI; He TANG
2012-01-01
With the upper bound of Kullback-Leibler distance between a matrix variate Beta-distribution and a normal distribution,this paper gives the conditions under which a matrix-variate Betadistribution will approach uniformly and asymptotically a normal distribution.
ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION ON TIME SCALES
无
2011-01-01
In this paper,we investigate a second order impulsive differential equation on time scales.Sufficient conditions are given to guarantee that the solutions tend to zero.The notable effect of impulse upon the asymptotic behavior of solutions is stressed in this paper.At last,we illustrate our results with two examples.
A Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems
Stojanović Sreten B.
2007-01-01
Full Text Available This paper presents a Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems. Based on the methods, delay-independent stability condition is derived. A numerical example has been working out to show the applicability of results derived.
Sinharay, Sandip
2015-01-01
The maximum likelihood estimate (MLE) of the ability parameter of an item response theory model with known item parameters was proved to be asymptotically normally distributed under a set of regularity conditions for tests involving dichotomous items and a unidimensional ability parameter (Klauer, 1990; Lord, 1983). This article first considers…
ASYMPTOTIC STABILITY OF A CLASS OF NONLINEAR NEUTRAL-TYPE SYSTEMS
无
2009-01-01
By Lyapunov functional method, sufficient conditions for the asymptotic stability of a class of neutral-type systems are discussed in this paper. This work extends some results on the stability of neutral-type systems in the previous papers. Several numerical examples are listed in the end of this paper to confirm our results.
S-asymptotically periodic solutions for partial differential equations with finite delay
William Dimbour
2011-09-01
Full Text Available In this article, we give some sufficient conditions for the existence and uniqueness of S-asymptotically periodic (mild solutions for some partial functional differential equations. To illustrate our main result, we study a diffusion equation with delay.
Asymptotic solutions for laminar flow in a channel with uniformly accelerating rigid porous walls
无
2007-01-01
A theoretical investigation was done for the generalized Berman problem, which arises in steady laminar flow of an incompressible viscous fluid along a channel with accelerating rigid porous walls. The existence of multiple solutions and its conditions were established by taking into account exponentially small terms in matched asymptotic expansion. The correctness of the analytical predictions was verified by numerical results.
王金良; 周笠
2003-01-01
In this paper,our main aim is to study the existence and uniqueness of the periodic solution of delayed Logistic equation and its asymptotic behavior.In case the coefficients are periodic,we give some sufficient conditions for the existence and uniqueness of periodic solution.Furthermore,we also study the effect of time-delay on the solution.
Asymptotic theory for weakly non-linear wave equations in semi-infinite domains
Chirakkal V. Easwaran
2004-01-01
Full Text Available We prove the existence and uniqueness of solutions of a class of weakly non-linear wave equations in a semi-infinite region $0le x$, $t< L/sqrt{|epsilon|}$ under arbitrary initial and boundary conditions. We also establish the asymptotic validity of formal perturbation approximations of the solutions in this region.
ASYMPTOTICS OF INITIAL BOUNDARY VALUE PROBLEMS OF BIPOLAR HYDRODYNAMIC MODEL FOR SEMICONDUCTORS
Ju Qiangchang
2004-01-01
In this paper, we study the asymptotic behavior of the solutions to the bipolar hydrodynamic model with Dirichlet boundary conditions. It is shown that the initial boundary problem of the model admits a global smooth solution which decays to the steady state exponentially fast.
On an asymptotic distribution of dependent random variables on a 3-dimensional lattice✩
Harvey, Danielle J.; Weng, Qian; Beckett, Laurel A.
2010-01-01
We define conditions under which sums of dependent spatial data will be approximately normally distributed. A theorem on the asymptotic distribution of a sum of dependent random variables defined on a 3-dimensional lattice is presented. Examples are also presented. PMID:20436940
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
Leonid Berezansky
2005-04-01
Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.
Relaxation Training and Expectation in the Treatment of Postpartum Distress.
Halonen, Jane S.; Passman, Richard H.
1985-01-01
Examined the effectiveness of relaxation training in reducing postpartum distress for 48 first-time mothers-to-be via a treatment-component strategy. Compared with nonrelaxation conditions, relaxation treatments reduced reported postpartal distress. Expectations about treatment effectiveness were not significant factors in treatment outcome.…
Kinetic Actviation Relaxation Technique
Béland, Laurent Karim; El-Mellouhi, Fedwa; Joly, Jean-François; Mousseau, Normand
2011-01-01
We present a detailed description of the kinetic Activation-Relaxation Technique (k-ART), an off-lattice, self-learning kinetic Monte Carlo algorithm with on-the-fly event search. Combining a topological classification for local environments and event generation with ART nouveau, an efficient unbiased sampling method for finding transition states, k-ART can be applied to complex materials with atoms in off-lattice positions or with elastic deformations that cannot be handled with standard KMC approaches. In addition to presenting the various elements of the algorithm, we demonstrate the general character of k-ART by applying the algorithm to three challenging systems: self-defect annihilation in c-Si, self-interstitial diffusion in Fe and structural relaxation in amorphous silicon.
Global asymptotic stabilisation in probability of nonlinear stochastic systems via passivity
Florchinger, Patrick
2016-07-01
The purpose of this paper is to develop a systematic method for global asymptotic stabilisation in probability of nonlinear control stochastic systems with stable in probability unforced dynamics. The method is based on the theory of passivity for nonaffine stochastic differential systems combined with the technique of Lyapunov asymptotic stability in probability for stochastic differential equations. In particular, we prove that a nonlinear stochastic differential system whose unforced dynamics are Lyapunov stable in probability is globally asymptotically stabilisable in probability provided some rank conditions involving the affine part of the system coefficients are satisfied. In this framework, we show that a stabilising smooth state feedback law can be designed explicitly. A dynamic output feedback compensator for a class of nonaffine stochastic systems is constructed as an application of our analysis.
Nonlinear mechanics of thin-walled structures asymptotics, direct approach and numerical analysis
Vetyukov, Yury
2014-01-01
This book presents a hybrid approach to the mechanics of thin bodies. Classical theories of rods, plates and shells with constrained shear are based on asymptotic splitting of the equations and boundary conditions of three-dimensional elasticity. The asymptotic solutions become accurate as the thickness decreases, and the three-dimensional fields of stresses and displacements can be determined. The analysis includes practically important effects of electromechanical coupling and material inhomogeneity. The extension to the geometrically nonlinear range uses the direct approach based on the principle of virtual work. Vibrations and buckling of pre-stressed structures are studied with the help of linearized incremental formulations, and direct tensor calculus rounds out the list of analytical techniques used throughout the book. A novel theory of thin-walled rods of open profile is subsequently developed from the models of rods and shells, and traditionally applied equations are proven to be asymptotically exa...
Nonlinear fractional relaxation
A Tofighi
2012-04-01
We deﬁne a nonlinear model for fractional relaxation phenomena. We use -expansion method to analyse this model. By studying the fundamental solutions of this model we ﬁnd that when → 0 the model exhibits a fast decay rate and when → ∞ the model exhibits a power-law decay. By analysing the frequency response we ﬁnd a logarithmic enhancement for the relative ratio of susceptibility.
Interactive Image Enhancement by Fuzzy Relaxation
Shang-Ming Zhou; John Q.Can; Li-Da Xu; Robert John
2007-01-01
In this paper, an interactive image enhancement (HE) technique based on fuzzy relaxation is presented, which allows the user to select different intensity levels for enhancement and intermit the enhancement process according to his/her preference in applications. First, based on an analysis of the convergence of a fuzzy relaxation algorithm for image contrast enhancement, an improved version of this algorithm, which is called FuzzIIE Method 1, is suggested by deriving a relationship between the convergence regions and the parameters in the transformations defined in the algorithm. Then a method called FuzzIIE Method 2 is introduced by using a different fuzzy relaxation function, in which there is no need to re-select the parameter values for interactive image enhancement. Experimental results are presented demonstrating the enhancement capabilities of the proposed methods under different conditions.
Longo, David J.
A within-subjects, three condition design was employed to examine the effects of three relaxation techniques on blood pressures, pulse rates, and self-report measures of relaxation for 12 college students. Respiratory Manipulation Training incorporated instructions to exhale and not to inhale for as long as possible. When breathing could no longer…
Asymptotic problems for stochastic partial differential equations
Salins, Michael
Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.
Asymptotics for a generalization of Hermite polynomials
Alfaro, M; Peña, A; Rezola, M L
2009-01-01
We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties. Thus, our aim is to study the asymptotics of this sequence of nonstandard orthogonal polynomials. In fact, we obtain Mehler--Heine type formulas for these polynomials and, as a consequence, we prove that there exists an acceleration of the convergence of the smallest positive zeros of these generalized Hermite polynomials towards the origin.
Lectures on the asymptotic theory of ideals
Rees, D
1988-01-01
In this book Professor Rees introduces and proves some of the main results of the asymptotic theory of ideals. The author's aim is to prove his Valuation Theorem, Strong Valuation Theorem, and Degree Formula, and to develop their consequences. The last part of the book is devoted to mixed multiplicities. Here the author develops his theory of general elements of ideals and gives a proof of a generalised degree formula. The reader is assumed to be familiar with basic commutative algebra, as covered in the standard texts, but the presentation is suitable for advanced graduate students. The work
The ADM mass of asymptotically flat hypersurfaces
de Lima, Levi Lopes
2011-01-01
We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of infinity, thus extending Lam's recent results on Euclidean graphs to this broader context. As applications we exhibit, in any dimension, new classes of manifolds for which versions of the Positive Mass and Riemannian Penrose inequalities hold and discuss a notion of quasi-local mass in this setting. The proof explores a novel connection between the co-vector defining the ADM mass of a hypersurface as above and the Newton tensor associated to its shape operator, which takes place in the presence of an ambient Killing field.
Taming perturbative divergences in asymptotically safe gravity
Benedetti, Dario, E-mail: dbenedetti@perimeterinstitute.c [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, N2L 2Y5, Waterloo ON (Canada); Machado, Pedro F., E-mail: p.f.machado@uu.n [Institute for Theoretical Physics, Utrecht University, 3508 TD Utrecht (Netherlands); Saueressig, Frank, E-mail: Frank.Saueressig@cea.f [Institut de Physique Theorique, CEA Saclay, F-91191 Gif-Sur-Yvette Cedex (France); CNRS URA 2306, F-91191 Gif-Sur-Yvette Cedex (France)
2010-01-01
We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may possess a non-trivial renormalization group fixed point controlling its UV behavior. We show that such a fixed point indeed exists within the truncations considered, lending strong support to the conjectured asymptotic safety of the theory. In particular, we demonstrate that the counterterms responsible for its perturbative non-renormalizability have no qualitative effect on this feature.
Homogenization and asymptotics for small transaction costs
Soner, H Mete
2012-01-01
We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic control problem which can be solved in closed form in the one-dimensional case. Unlike the existing literature, we consider a general utility function and general dynamics for the underlying assets. Our arguments are based on ideas from the homogenization theory and use the convergence tools from the theory of viscosity solutions. The multidimensional case is studied in our accompanying paper using the same approach.
Vacuum Potential and its Asymptotic Variation
Dahal, Pravin
2016-09-01
The possible form of existence of dark energy is explained and the relation for its asymptotic variation is given. This has two huge implications in the understanding of the Universe. The first is that the theory predicts that the Universe should be in negative pressure state in the very early period as required for inflation and spontaneous symmetry breaking. The second is that the theory gives the reasonable answer to the astrophysical evidence of dark energy dominating the Universe. The author is presenting his research in the nature of dark energy. Some of the work is submitted for publication in the journal and is currently under review.
Singular asymptotic expansions in nonlinear rotordynamics
Day, W. B.
1985-01-01
During hot firing ground testing of the Space shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.
p-q growth via relaxation methods
Irene Benedetti
2004-01-01
Full Text Available Local Lipschitz continuity of local minimizers of vectorial integrals ∫Ω f(x,Dudx is proved when f satisfies p-q growth condition and ξ↦f(x,ξ is not convex. The uniform convexity and the radial structure condition with respect to the last variable are assumed only at infinity. In the proof, we use semicontinuity and relaxation results for functionals with nonstandard growth.
Global Existence and Asymptotic Behavior of Affine Motion of 3D Ideal Fluids Surrounded by Vacuum
Sideris, Thomas C.
2017-07-01
The 3D compressible and incompressible Euler equations with a physical vacuum free boundary condition and affine initial conditions reduce to a globally solvable Hamiltonian system of ordinary differential equations for the deformation gradient in {GL^+(3, R)}. The evolution of the fluid domain is described by a family of ellipsoids whose diameter grows at a rate proportional to time. Upon rescaling to a fixed diameter, the asymptotic limit of the fluid ellipsoid is determined by a positive semi-definite quadratic form of rank r = 1, 2, or 3, corresponding to the asymptotic degeneration of the ellipsoid along 3- r of its principal axes. In the compressible case, the asymptotic limit has rank r = 3, and asymptotic completeness holds, when the adiabatic index {γ} satisfies {4/3 adiabatic index {γ}. In the incompressible case, affine motion reduces to geodesic flow in {SL(3, R)} with the Euclidean metric. For incompressible affine swirling flow, there is a structural instability. Generically, when the vorticity is nonzero, the domains degenerate along only one axis, but the physical vacuum boundary condition fails over a finite time interval. The rescaled fluid domains of irrotational motion can collapse along two axes.
Some improvements in the theory of plasma relaxation
Hameiri, Eliezer, E-mail: hameiri@cims.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2014-04-15
Taylor's relaxation theory is extended to plasmas with mass flow by using the cross helicity as a conserved quantity, similar to the magnetic helicity. Indeed, it is shown that the conservation of the cross helicity in magnetohydrodynamics is the result of the conservation of two magnetic-like helicities in two-fluid plasmas. In addition, the usually ignored toroidal flux is also held to be conserved. We also view plasma relaxation as attaining a maximum entropy state rather than Taylor's minimum energy state, but prove that maximizing the entropy subject to a given amount of energy is equivalent to minimizing the energy subject to a given amount of entropy. The resulting relaxed state is similar to the one discussed by Finn and Antonsen [Phys. Fluids 26, 3540 (1983)], and involves flow parallel to the magnetic field and constant temperature, but non-constant pressure. We show how to construct an asymptotic solution to the relaxed state based on the smallness of the Alfven Mach number of the flow.
Quasi-static relaxation of arbitrarily shaped sessile drops
Iliev, S; Nikolayev, Vadim
2016-01-01
We study a spontaneous relaxation dynamics of arbitrarily shaped liquid drops on solid surfaces in the partial wetting regime. It is assumed that the energy dissipated near the contact line is much larger than that in the bulk of the fluid. We have shown rigorously in the case of quasi-static relaxation using the standard mechanical description of dissipative system dynamics that the introduction of a dissipation term proportional to the contact line length leads to the well known local relation between the contact line velocity and the dynamic contact angle at every point of an arbitrary contact line shape. A numerical code is developed for 3D drops to study the dependence of the relaxation dynamics on the initial drop shape. The available asymptotic solutions are tested against the obtained numerical data. We show how the relaxation at a given point of the contact line is influenced by the dynamics of the whole drop which is a manifestation of the non-local
WOLF, RFE; DENBUTTER, G; KAMMAN, RL; DEKETH, HP; SLUTTER, WJ; SLOOFF, MJH
1994-01-01
To determine the relation between tissue hydration state-as indicated by tissue proton magnetic resonance relaxation times-in UW-preserved human donor livers and viability parameters of the donor and early graft function, ''ex vivo'' magnetic resonance relaxometry was performed with a clinical MR im
WOLF, RFE; DENBUTTER, G; KAMMAN, RL; DEKETH, HP; SLUTTER, WJ; SLOOFF, MJH
1994-01-01
To determine the relation between tissue hydration state-as indicated by tissue proton magnetic resonance relaxation times-in UW-preserved human donor livers and viability parameters of the donor and early graft function, ''ex vivo'' magnetic resonance relaxometry was performed with a clinical MR
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.
Wei-Cheng Wang
2002-06-01
Full Text Available We study the asymptotic equivalence of the Jin-Xin relaxation model and its formal limit for genuinely nonlinear $2imes 2$ conservation laws. The initial data is allowed to have jump discontinuities corresponding to centered rarefaction waves, which includes Riemann data connected by rarefaction curves. We show that, as long as the initial data is a small perturbation of a constant state, the solution for the relaxation system exists globally in time and converges, in the zero relaxation limit, to the solution of the corresponding conservation law uniformly except for an initial layer.
Numerical and asymptotic studies of delay differential equations
Adhikari, Mohit Hemchandra
Two classes of differential delay equations exhibiting diverse phenomena are studied. The first one is a singularly perturbed delay differential equation which is used to model selected physical systems involving feedback where relaxation effects are combined with nonlinear driving from the past. In the limit of fast relaxation, the differential equation reduces to a difference equation or a map, due to the presence of the delay. A basic question in this field is how the behavior of the map is reflected in the behavior of the solutions of the delay differential equation. In this work, a generic logistic form is used for the underlying map and the above question is studied in the first period-doubling regime of the map. Using an efficient numerical algorithm, the shape and the period of the corresponding asymptotically stable periodic solution is studied first, for various values of the delay. In the limit of large delay, these solutions resemble square-waves of period close to twice the value of the delay, with sharp transition layers joining flat plateau-like regions. A Poincare-Lindstedt method involving a two-parameter perturbation expansion is applied to solve equations representing these layers and accurate expressions for the shape and the period of these solutions, in terms of Jacobi elliptic functions, are obtained. A similar approach is used to obtain leading order expressions for sub-harmonic solutions of shorter periods, but it is shown that while they are extremely long-lived for large values of delay, they eventually decay to the fundamental solutions mentioned above. The spectral algorithm used for the numerical integration is tested by comparing its accuracy and efficiency in obtaining stiff solutions of linear delay equations, with that of a current state-of-the-art time-stepping algorithm for integrating delay equations. Effect of delay on the synchronization of two nerve impulses traveling along two parallel nerve fibers, is the second question
Frenod, Emmanuel
2013-01-01
In this note, a classification of Homogenization-Based Numerical Methods and (in particular) of Numerical Methods that are based on the Two-Scale Convergence is done. In this classification stand: Direct Homogenization-Based Numerical Methods; H-Measure-Based Numerical Methods; Two-Scale Numerical Methods and TSAPS: Two-Scale Asymptotic Preserving Schemes.
ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS
Zeng Luchuan
2006-01-01
This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Ban ach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.
Asymptotic Behavior of an Elastic Satellite with Internal Friction
Haus, E., E-mail: emanuele.haus@unina.it [Università di Napoli Federico II Via Cintia, Dipartimento di Matematica e Applicazioni R. Caccioppoli (Italy); Bambusi, D., E-mail: dario.bambusi@unimi.it [Università degli Studi di Milano, DIpartimento di Matematica F. Enriques (Italy)
2015-12-15
We study the dynamics of an elastic body whose shape and position evolve due to the gravitational forces exerted by a pointlike planet. The main result is that, if all the deformations of the satellite dissipate some energy, then under a suitable nondegeneracy condition there are only three possible outcomes for the dynamics: (i) the orbit of the satellite is unbounded, (ii) the satellite falls on the planet, (iii) the satellite is captured in synchronous resonance i.e. its orbit is asymptotic to a motion in which the barycenter moves on a circular orbit, and the satellite moves rigidly, always showing the same face to the planet. The result is obtained by making use of LaSalle’s invariance principle and by a careful kinematic analysis showing that energy stops dissipating only on synchronous orbits. We also use in quite an extensive way the fact that conservative elastodynamics is a Hamiltonian system invariant under the action of the rotation group.
Asymptotic Behavior of an Elastic Satellite with Internal Friction
Haus, E.; Bambusi, D.
2015-12-01
We study the dynamics of an elastic body whose shape and position evolve due to the gravitational forces exerted by a pointlike planet. The main result is that, if all the deformations of the satellite dissipate some energy, then under a suitable nondegeneracy condition there are only three possible outcomes for the dynamics: (i) the orbit of the satellite is unbounded, (ii) the satellite falls on the planet, (iii) the satellite is captured in synchronous resonance i.e. its orbit is asymptotic to a motion in which the barycenter moves on a circular orbit, and the satellite moves rigidly, always showing the same face to the planet. The result is obtained by making use of LaSalle's invariance principle and by a careful kinematic analysis showing that energy stops dissipating only on synchronous orbits. We also use in quite an extensive way the fact that conservative elastodynamics is a Hamiltonian system invariant under the action of the rotation group.
Asymptotic behaviour of the Weyl tensor in higher dimensions
Ortaggio, Marcello
2014-01-01
We determine the leading order fall-off behaviour of the Weyl tensor in higher dimensional Einstein spacetimes (with and without a cosmological constant) as one approaches infinity along a congruence of null geodesics. The null congruence is assumed to "expand" in all directions near infinity (but it is otherwise generic), which includes in particular asymptotically flat spacetimes. In contrast to the well-known four-dimensional peeling property, the fall-off rate of various Weyl components depends substantially on the chosen boundary conditions, and is also influenced by the presence of a cosmological constant. The leading component is always algebraically special, but in various cases it can be of type N, III or II.
Asymptotic behaviour of Maxwell fields in higher dimensions
Ortaggio, Marcello
2014-01-01
We study the fall-off behaviour of test electromagnetic fields in higher dimensions as one approaches infinity along a congruence of "expanding" null geodesics. The considered backgrounds are Einstein spacetimes including, in particular, (asymptotically) flat and (anti-)de Sitter spacetimes. Various possible boundary conditions result in different characteristic fall-offs, in which the leading component can be of any algebraic type (N, II or G). In particular, the peeling-off of radiative fields F=Nr^{1-n/2}+Gr^{-n/2}+... differs from the standard four-dimensional one (instead it qualitatively resembles the recently determined behaviour of the Weyl tensor in higher dimensions). General p-form fields are also briefly discussed. In even n dimensions, the special case p=n/2 displays unique properties and peels off in the "standard way" as F=Nr^{1-n/2}+IIr^{-n/2}+.... A few explicit examples are mentioned.
Asymptotic Stability of Neutral Differential Equations with Unbounded Delay
YE Hai-ping; GAO Guo-zhu
2002-01-01
Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt [x(t)- P(t)x(h(t))] + Q(t)x(q(t)) -R(t)x(r(t))= 0, t ≥ t0,where P(t)∈ C([t0, ∞), R), Q(t), R(t) ∈ C([t0,∞ ), R+ ), and h, q, r: [ t0, ∞ ) → R are continuously differentiable and strictly increasing, h( t) ＜ t, q( t) ＜t, r(t) ＜ t for all t ≥ t0. In this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable.
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
Asymptotically AdS spacetimes with a timelike Kasner singularity
Ren, Jie [Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2016-07-21
Exact solutions to Einstein’s equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution’s appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The entanglement entropy and Wilson loops are discussed. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimensional reduction.
Asymptotically AdS spacetimes with a timelike Kasner singularity
Ren, Jie
2016-07-01
Exact solutions to Einstein's equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution's appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The entanglement entropy and Wilson loops are discussed. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimensional reduction.
Asymptotic analysis of downlink MISO systems over Rician fading channels
Falconet, Hugo
2016-06-24
In this work, we focus on the ergodic sum rate in the downlink of a single-cell large-scale multi-user MIMO system in which the base station employs N antennas to communicate with K single-antenna user equipments. A regularized zero-forcing (RZF) scheme is used for precoding under the assumption that each link forms a spatially correlated MIMO Rician fading channel. The analysis is conducted assuming N and K grow large with a non trivial ratio and perfect channel state information is available at the base station. Recent results from random matrix theory and large system analysis are used to compute an asymptotic expression of the signal-to-interference-plus-noise ratio as a function of the system parameters, the spatial correlation matrix and the Rician factor. Numerical results are used to evaluate the performance gap in the finite system regime under different operating conditions. © 2016 IEEE.
Asymptotic behaviour of electro-$\\Lambda$ spacetimes
Saw, Vee-Liem
2016-01-01
We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $\\Lambda$ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with $\\Lambda=0$. Using these asymptotic solutions, we discuss the mass-loss of an isolated electro-gravitating system with cosmological constant. In a universe with $\\Lambda>0$, the physics of electromagnetic (EM) radiation is relatively straightforward compared to those of gravitational radiation: 1) It is clear that outgoing EM radiation results in a decrease to the Bondi mass of the isolated system. 2) It is also perspicuous that if any incoming EM radiation from elsewhere is present, those beyond the isolated system's cosmological horizon would eventually arrive at the spacelike $\\mathcal{I}$ and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with the Bondi mass-loss formula in any un...
Vacuum polarization in asymptotically Lifshitz black holes
Quinta, Gonçalo M; Lemos, José P S
2016-01-01
There has been considerable interest in applying the gauge/gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed aiming at incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes, and to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, non-minimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti de Sitter black holes. The basics are similar to previous calculations, however in the Lifshitz case one needs to extend previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulae are shown to reduce to the AdS case studied before once the value of the dynamical exponent is set to...
Vacuum polarization in asymptotically Lifshitz black holes
Quinta, Gonçalo M.; Flachi, Antonino; Lemos, José P. S.
2016-06-01
There has been considerable interest in applying the gauge-gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed, focused on incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes and, to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, nonminimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti-de Sitter black holes. The basics are similar to previous calculations; however, in the Lifshitz case, one needs to extend the previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulas are shown to reduce to the anti-de Sitter (AdS) case studied before once the value of the dynamical exponent is set to unity and the metric functions are accordingly chosen. The analytical results we present are general and can be applied to a variety of cases, in fact, to all spherically symmetric Lifshitz black hole solutions. We also implement the numerical analysis choosing some known Lifshitz black hole solutions as illustration.
Lattice Quantum Gravity and Asymptotic Safety
Laiho, J; Coumbe, D; Du, D; Neelakanta, J T
2016-01-01
We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we identify the target symmetry as the Hamiltonian canonical symmetry, which is closely related to, but not identical to, four-dimensional diffeomorphism invariance. After introducing and fine-tuning a non-trivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with 3/2, a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue tha...
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.
ASYMPTOTIC EXPANSION AND ESTIMATE OF THE LANDAU CONSTANT
A.Eisinberg; G.Franzè; N.Salerno
2001-01-01
Properties of Landau constant are investigated in this note.A new representation in terms of a hypergeometric function 3F2 is given and a property defining the family of asymptotic sequences of Landau constant is formalized.Moreover,we give an other asymptotic expansion of Landau constant by using asymptotic expansion of the ratio of gamma functions in the sense of Poincaré due to Tricomi and Erdélyi.
Coulomb string tension, asymptotic string tension, and the gluon chain
Greensite, Jeff; Szczepaniak, Adam P.
2015-02-01
We compute, via numerical simulations, the nonperturbative Coulomb potential of pure SU(3) gauge theory in Coulomb gauge. We find that the Coulomb potential scales nicely in accordance with asymptotic freedom, that the Coulomb potential is linear in the infrared, and that the Coulomb string tension is about four times larger than the asymptotic string tension. We explain how it is possible that the asymptotic string tension can be lower than the Coulomb string tension by a factor of four.
Relaxation of vacuum energy in q-theory
Klinkhamer, F R; Volovik, G E
2016-01-01
The $q$-theory formalism aims to describe the thermodynamics and dynamics of the deep quantum vacuum. The thermodynamics leads to an exact cancellation of the quantum-field zero-point-energies in equilibrium, which partly solves the main cosmological constant problem. But, with reversible dynamics, the spatially-flat Friedmann-Robertson-Walker universe asymptotically approaches the Minkowski vacuum only if the Big Bang already started out in an initial equilibrium state. Here, we extend $q$-theory by introducing dissipation from irreversible processes. Neglecting the possible instability of a de-Sitter vacuum, we obtain different scenarios with either a de-Sitter asymptote or collapse to a final singularity. The Minkowski asymptote still requires fine-tuning of the initial conditions.
Blue Sky Catastrophe in Systems with Non-classical Relaxation Oscillations
S. D. Glyzin
2015-01-01
Full Text Available The feasibility of a known blue-sky bifurcation in a class of three-dimensional singularly perturbed systems of ordinary differential equations with one fast and two slow variables is studied. A characteristic property of the considered systems is that they permit so-called nonclassic relaxation oscillations, that is, oscillations with slow components asymptotically close to time-discontinuous functions and a δ-like fast component. Cases when blue-sky bifurcation leads to a relaxation cycle or stable two-dimensional torus are analyzed. Also the question of homoclinic structure emergence is considered.
ASYMPTOTIC EXPANSIONS OF ZEROS FOR KRAWTCHOUK POLYNOMIALS WITH ERROR BOUNDS
ZHU Xiao-feng; LI Xiu-chun
2006-01-01
Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds are discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.
Asymptotic variance of grey-scale surface area estimators
Svane, Anne Marie
Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in isotropic and sufficiently smooth settings, resulting...... in a general asymptotic bound. For compact convex sets with nowhere vanishing Gaussian curvature, the asymptotics can be described more explicitly. As in the case of volume estimators, the variance is decomposed into a lattice sum and an oscillating term of at most the same magnitude....
Asymptotic behavior of marginally trapped tubes in spherically symmetric black hole spacetimes
Williams, Catherine M.
We begin by reviewing some fundamental features of general relativity, then outline the mathematical definitions of black holes, trapped surfaces, and marginally trapped tubes, first in general terms, then rigorously in the context of spherical symmetry. We describe explicitly the reduction of Einstein's equation on a spherically symmetric 4-dimensional Lorentzian manifold to a system of partial differential equations on a subset of 2-dimensional Minkowski space. We discuss the asymptotic behavior of marginally trapped tubes in the Schwarzschild, Vaidya, and Reisner-Nordstrom solutions to Einstein's equations in spherical symmetry, as well as in Einstein-Maxwell-scalar field black hole spacetimes generated by evolving certain classes of asymptotically flat initial data. Our first main result gives conditions on a general stress-energy tensor Talphabeta in a spherically symmetric black hole spacetime that are sufficient to guarantee that the black hole will contain a marginally trapped tube which is eventually achronal, connected, and asymptotic to the event horizon. Here "general" means that the matter model is arbitrary, subject only to a certain positive energy condition. A certain matter field decay rate, known as Price law decay in the literature, is not required per se for this asymptotic result, but such decay does imply that the marginally trapped tube has finite length with respect to the induced metric. In our second main result, we give two separate applications of the first theorem to self-gravitating Higgs field spacetimes, one using weak Price law decay, the other certain strong smallness and monotonicity assumptions.
Asymptotics of orthogonal polynomials and point perturbation on the unit circle
Wong, Manwah Lilian
2010-01-01
In the first five sections, we deal with the class of probability measures with asymptotically periodic Verblunsky coefficients of p-type bounded variation. The goal is to investigate the perturbation of the Verblunsky coefficients when we add a pure point to a gap of the essential spectrum. For the asymptotically constant case, we give an asymptotic formula for the orthonormal polynomials in the gap, prove that the perturbation term converges and show the limit explicitly. Furthermore, we prove that the perturbation is of bounded variation. Then we generalize the method to the asymptotically periodic case and prove similar results. In the last two sections, we show that the bounded variation condition can be removed if a certain symmetry condition is satisfied. Finally, we consider the special case when the Verblunsky coefficients are real with the rate of convergence being c_n . We prove that the rate of convergence of the perturbation is in fact O(c_n). In particular, the special case c_n = 1/n will serve ...
Grueneisen relaxation photoacoustic microscopy
Wang, Lidai; Zhang, Chi; Wang, Lihong V.
2014-01-01
The temperature-dependent property of the Grueneisen parameter has been employed in photoacoustic imaging mainly to measure tissue temperature. Here we explore this property using a different approach and develop Grueneisen-relaxation photoacoustic microscopy (GR-PAM), a technique that images non-radiative absorption with confocal optical resolution. GR-PAM sequentially delivers two identical laser pulses with a micro-second-scale time delay. The first laser pulse generates a photoacoustic signal and thermally tags the in-focus absorbers. Owing to the temperature dependence of the Grueneisen parameter, when the second laser pulse excites the tagged absorbers within the thermal relaxation time, a photoacoustic signal stronger than the first one is produced. GR-PAM detects the amplitude difference between the two co-located photoacoustic signals, confocally imaging the non-radiative absorption. We greatly improved axial resolution from 45 µm to 2.3 µm and at the same time slightly improved lateral resolution from 0.63 µm to 0.41 µm. In addition, the optical sectioning capability facilitates the measurement of the absolute absorption coefficient without fluence calibration. PMID:25379919
YIN; Changming; ZHAO; Lincheng; WEI; Chengdong
2006-01-01
In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=1 ZiZ'i, the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.
Asymptotic behavior of a stochastic non-autonomous predator-prey model with impulsive perturbations
Wu, Ruihua; Zou, Xiaoling; Wang, Ke
2015-03-01
This paper is concerned with a stochastic non-autonomous Lotka-Volterra predator-prey model with impulsive effects. The asymptotic properties are examined. Sufficient conditions for persistence and extinction are obtained, our results demonstrate that the impulse has important effects on the persistence and extinction of the species. We also show that the solution is stochastically ultimate bounded under some conditions. Finally, several simulation figures are introduced to confirm our main results.
Home Relaxation Practice in Hypertension Treatment: Objective Assessment and Compliance Induction.
Hoelscher, Timothy J.; And Others
1986-01-01
Evaluated compliance with individualized relaxation, group relaxation, group relaxation plus contingency contracting for home practice, or a waiting list in hypertension treatment. All conditions showed significantly greater reductions in blood pressure than waiting list controls but did not differ from each other. Self-reports exceeded monitored…
Magnetoviscosity and relaxation in ferrofluids
Felderhof
2000-09-01
The increase in viscosity of a ferrofluid due to an applied magnetic field is discussed on the basis of a phenomenological relaxation equation for the magnetization. The relaxation equation was derived earlier from irreversible thermodynamics, and differs from that postulated by Shliomis. The two relaxation equations lead to a different dependence of viscosity on magnetic field, unless the relaxation rates are related in a specific field-dependent way. Both planar Couette flow and Poiseuille pipe flow in parallel and perpendicular magnetic field are discussed. The entropy production for these situations is calculated and related to the magnetoviscosity.
Asymptotic analysis of ultra-relativistic charge
Burton, D A; Tucker, R W; Burton, David A.; Gratus, Jonathan; Tucker, Robin W.
2006-01-01
This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneo...
Asymptotic charged BTZ black hole solutions
Hendi, S. H.
2012-03-01
The well-known (2 + 1)-dimensional Reissner-Nordström (BTZ) black hole can be generalized to three dimensional Einstein-nonlinear electromagnetic field, motivated from obtaining a finite value for the self-energy of a pointlike charge. Considering three types of nonlinear electromagnetic fields coupled with Einstein gravity, we derive three kinds of black hole solutions which their asymptotic properties are the same as charged BTZ solution. In addition, we calculate conserved and thermodynamic quantities of the solutions and show that they satisfy the first law of thermodynamics. Finally, we perform a stability analysis in the canonical ensemble and show that the black holes are stable in the whole phase space.
Modeling of nanoplastic by asymptotic homogenization method
张为民; 何伟; 李亚; 张平; 张淳源
2008-01-01
The so-called nanoplastic is a new simple name for the polymer/layered silicate nanocomposite,which possesses excellent properties.The asymptotic homogenization method(AHM) was applied to determine numerically the effective elastic modulus of a two-phase nanoplastic with different particle aspect ratios,different ratios of elastic modulus of the effective particle to that of the matrix and different volume fractions.A simple representative volume element was proposed,which is assumed that the effective particles are uniform well-aligned and perfectly bonded in an isotropic matrix and have periodic structure.Some different theoretical models and the experimental results were compared.The numerical results are good in agreement with the experimental results.
Chiral fermions in asymptotically safe quantum gravity
Meibohm, J. [Gothenburg University, Department of Physics, Goeteborg (Sweden); Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); Pawlowski, J.M. [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung mbH, ExtreMe Matter Institute EMMI, Darmstadt (Germany)
2016-05-15
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works (Christiansen et al., Phys Rev D 92:121501, 2015; Meibohm et al., Phys Rev D 93:084035, 2016), concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models. We find strong evidence that this feature is independent of the number of fermion fields. This finding suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions. (orig.)
Asymptotic Sharpness of Bounds on Hypertrees
Lin Yi
2017-08-01
Full Text Available The hypertree can be defined in many different ways. Katona and Szabó introduced a new, natural definition of hypertrees in uniform hypergraphs and investigated bounds on the number of edges of the hypertrees. They showed that a k-uniform hypertree on n vertices has at most (nk−1$\\left( {\\matrix{n \\cr {k - 1} } } \\right$ edges and they conjectured that the upper bound is asymptotically sharp. Recently, Szabó verified that the conjecture holds by recursively constructing an infinite sequence of k-uniform hypertrees and making complicated analyses for it. In this note we give a short proof of the conjecture by directly constructing a sequence of k-uniform k-hypertrees.
Motion Parallax is Asymptotic to Binocular Disparity
Stroyan, Keith
2010-01-01
Researchers especially beginning with (Rogers & Graham, 1982) have noticed important psychophysical and experimental similarities between the neurologically different motion parallax and stereopsis cues. Their quantitative analysis relied primarily on the "disparity equivalence" approximation. In this article we show that retinal motion from lateral translation satisfies a strong ("asymptotic") approximation to binocular disparity. This precise mathematical similarity is also practical in the sense that it applies at normal viewing distances. The approximation is an extension to peripheral vision of (Cormac & Fox's 1985) well-known non-trig central vision approximation for binocular disparity. We hope our simple algebraic formula will be useful in analyzing experiments outside central vision where less precise approximations have led to a number of quantitative errors in the vision literature.
Asymptotic methods in mechanics of solids
Bauer, Svetlana M; Smirnov, Andrei L; Tovstik, Petr E; Vaillancourt, Rémi
2015-01-01
The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russi...
Asymptotic sampling formulae for Lambda-coalescents
Berestycki, Julien; Limic, Vlada
2012-01-01
We present a robust method which translates information on the speed of coming down from infinity of a genealogical tree into sampling formulae for the underlying population. We apply these results to population dynamics where the genealogy is given by a Lambda-coalescent. This allows us to derive an exact formula for the asymptotic behavior of the site and allele frequency spectrum and the number of segregating sites, as the sample size tends to infinity. Some of our results hold in the case of a general Lambda-coalescent that comes down from infinity, but we obtain more precise information under a regular variation assumption. In this case, we obtain results of independent interest for the time at which a mutation uniformly chosen at random was generated. This exhibits a phase transition at \\alpha=3/2, where \\alpha \\in(1,2) is the exponent of regular variation.
Universality and asymptotic scaling in drilling percolation
Grassberger, Peter
2017-01-01
We present simulations of a three-dimensional percolation model studied recently by K. J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016), 10.1103/PhysRevLett.116.055701], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems and higher statistics used in the present Rapid Communication, but we also find indications that the results do not yet represent the true asymptotic behavior. The model is obtained by replacing the isotropic holes in ordinary Bernoulli percolation by randomly placed and oriented cylinders, with the constraint that the cylinders are parallel to one of the three coordinate axes. We also speculate on possible generalizations.
Dimensionally reduced gravity theories are asymptotically safe
Niedermaier, Max E-mail: max@phys.univ-tours.fr
2003-11-24
4D Einstein gravity coupled to scalars and abelian gauge fields in its 2-Killing vector reduction is shown to be quasi-renormalizable to all loop orders at the expense of introducing infinitely many essential couplings. The latter can be combined into one or two functions of the 'area radius' associated with the two Killing vectors. The renormalization flow of these couplings is governed by beta functionals expressible in closed form in terms of the (one coupling) beta function of a symmetric space sigma-model. Generically the matter coupled systems are asymptotically safe, that is the flow possesses a non-trivial UV stable fixed point at which the trace anomaly vanishes. The main exception is a minimal coupling of 4D Einstein gravity to massless free scalars, in which case the scalars decouple from gravity at the fixed point.
Holographic Renormalization of Asymptotically Flat Gravity
Park, Miok
2012-01-01
We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotic flat and static spacetime for cylindrical boundary surface as $r \\rightarrow \\infty$, and find that the form of the boundary stress tensor is the same as the hyperbolic boundary case in 4 dimensions, but has additional terms in higher than 4 dimensions. We find that these additional terms are impotent and do not contribute to conserved charges. We also check the conservation of the boundary stress tensor in a sense that $\\mathcal{D}^a T_{ab} = 0$, and apply our result to the ($n+3$)-dimensional static black hole solution. As a result, we show that the stress boundary tensor with Mann-Marolf counterterm works well in standard boundary surfaces.
Chiral fermions in asymptotically safe quantum gravity
Meibohm, Jan
2016-01-01
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck-scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works \\cite{Christiansen:2015rva, Meibohm:2015twa}, concludes that gravity-induced chiral symmetry breaking at the Planck scale is avoided for a general class of NJL-type models, regardless of the number of fermion flavours. This suggests that the phase diagram for these models is topologically stable under the influence of gravitational interactions.
Grassmann scalar fields and asymptotic freedom
Palumbo, F. [INFN, Laboratori Nazionali di Frascati, Rome (Italy)
1996-03-01
The authors extend previous results about scalar fields whose Fourier components are even elements of a Grassmann algebra with given index of nilpotency. Their main interest in particle physics is related to the possibility that they describe fermionic composites analogous to the Copper pairs of superconductivity. The authors evaluate the free propagators for arbitrary index of nilpotency and they investigate a {phi}{sup 4} model to one loop. Due to the nature of the integral over even Grassmann fields such as a model exists for repulsive as well as attractive self interaction. In the first case the {beta}-function is equal to that of the ordinary theory, while in the second one the model is asymptotically free. The bare mass has a peculiar dependence on the cutoff, being quadratically decreasing/increasing for attractive/repulsive self interaction.
Asymptotic stability of steady compressible fluids
Padula, Mariarosaria
2011-01-01
This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory. The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems: (i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous. (ii) An isothermal viscous gas in a domain with free boundaries. (iii) A h...
Asymptotic properties of restricted naming games
Bhattacherjee, Biplab; Datta, Amitava; Manna, S. S.
2017-07-01
Asymptotic properties of the symmetric and asymmetric naming games have been studied under some restrictions in a community of agents. In one version, the vocabulary sizes of the agents are restricted to finite capacities. In this case, compared to the original naming games, the dynamics takes much longer time for achieving the consensus. In the second version, the symmetric game starts with a limited number of distinct names distributed among the agents. Three different quantities are measured for a quantitative comparison, namely, the maximum value of the total number of names in the community, the time at which the community attains the maximal number of names, and the global convergence time. Using an extensive numerical study, the entire set of three power law exponents characterizing these quantities are estimated for both the versions which are observed to be distinctly different from their counter parts of the original naming games.
The asymptotic safety scenario in quantum gravity
Saueressig, Frank [Institute of Physics, University of Mainz, D-55099 Mainz (Germany)
2011-07-01
Asymptotic safety offers the possibility that gravity constitutes a consistent and predictive quantum field theory within Wilsons generalized framework of renormalization. The key ingredient of this scenario is a non-trivial fixed point of the gravitational renormalization group flow which governs the UV behavior of the theory. The fixed point itself thereby guarantees the absence of unphysical UV divergences while its associated finite-dimensional UV-critical surface ensures the predictivity of the resulting quantum theory. This talk summarizes the evidence for the existence of such a fixed point, which emerged from the flow equation for the effective average action, the gravitational beta-functions in 2+{epsilon} dimensions, the 2-Killing vector reduction of the gravitational path-integral and lattice simulations. Possible phenomenological consequences are discussed in detail.
Asymptotic theory of weakly dependent random processes
Rio, Emmanuel
2017-01-01
Presenting tools to aid understanding of asymptotic theory and weakly dependent processes, this book is devoted to inequalities and limit theorems for sequences of random variables that are strongly mixing in the sense of Rosenblatt, or absolutely regular. The first chapter introduces covariance inequalities under strong mixing or absolute regularity. These covariance inequalities are applied in Chapters 2, 3 and 4 to moment inequalities, rates of convergence in the strong law, and central limit theorems. Chapter 5 concerns coupling. In Chapter 6 new deviation inequalities and new moment inequalities for partial sums via the coupling lemmas of Chapter 5 are derived and applied to the bounded law of the iterated logarithm. Chapters 7 and 8 deal with the theory of empirical processes under weak dependence. Lastly, Chapter 9 describes links between ergodicity, return times and rates of mixing in the case of irreducible Markov chains. Each chapter ends with a set of exercises. The book is an updated and extended ...
Hydrodynamics, resurgence and trans-asymptotics
Basar, Gokce
2015-01-01
The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exponentially suppressed at late times, analogous to the quasi-normal-modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semi-classical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these non-hydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with init...
Asymptotic Linear Stability of Solitary Water Waves
Pego, Robert L.; Sun, Shu-Ming
2016-12-01
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (that is, symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.
Entropy Production during Asymptotically Safe Inflation
Martin Reuter
2011-01-01
Full Text Available The Asymptotic Safety scenario predicts that the deep ultraviolet of Quantum Einstein Gravity is governed by a nontrivial renormalization group fixed point. Analyzing its implications for cosmology using renormalization group improved Einstein equations, we find that it can give rise to a phase of inflationary expansion in the early Universe. Inflation is a pure quantum effect here and requires no inflaton field. It is driven by the cosmological constant and ends automatically when the renormalization group evolution has reduced the vacuum energy to the level of the matter energy density. The quantum gravity effects also provide a natural mechanism for the generation of entropy. It could easily account for the entire entropy of the present Universe in the massless sector.
Asymptotic Behavior of Excitable Cellular Automata
Durrett, R; Durrett, Richard; Griffeath, David
1993-01-01
Abstract: We study two families of excitable cellular automata known as the Greenberg-Hastings Model (GHM) and the Cyclic Cellular Automaton (CCA). Each family consists of local deterministic oscillating lattice dynamics, with parallel discrete-time updating, parametrized by the range of interaction, the "shape" of its neighbor set, threshold value for contact updating, and number of possible states per site. GHM and CCA are mathematically tractable prototypes for the spatially distributed periodic wave activity of so-called excitable media observed in diverse disciplines of experimental science. Earlier work by Fisch, Gravner, and Griffeath studied the ergodic behavior of these excitable cellular automata on Z^2, and identified two distinct (but closely-related) elaborate phase portraits as the parameters vary. In particular, they noted the emergence of asymptotic phase diagrams (and Euclidean dynamics) in a well-defined threshold-range scaling limit. In this study we present several rigorous results and som...
Introduction to Asymptotic Giant Branch Stars
El Eid, Mounib F.
2016-04-01
A brief introduction on the main characteristics of the asymptotic giant branch stars (briefly: AGB) is presented. We describe a link to observations and outline basic features of theoretical modeling of these important evolutionary phases of stars. The most important aspects of the AGB stars is not only because they are the progenitors of white dwarfs, but also they represent the site of almost half of the heavy element formation beyond iron in the galaxy. These elements and their isotopes are produced by the s-process nucleosynthesis, which is a neutron capture process competing with the β- radioactive decay. The neutron source is mainly due to the reaction 13C(α,n)16O reaction. It is still a challenging problem to obtain the right amount of 13 C that can lead to s-process abundances compatible with observation. Some ideas are presented in this context.
Load Relaxation of Olivine Single Crystals
Cooper, R. F.; Stone, D. S.; Plookphol, T.
2016-12-01
Single crystals of ferromagnesian olivine (San Carlos, AZ, peridot; Fo90-92) have been deformed in both uniaxial creep and load relaxation under conditions of ambient pressure, T = 1500ºC and pO2 = 10-10 atm; creep stresses were in the range 40 ≤ σ1 (MPa) ≤ 220. The crystals were oriented such that the applied stress was parallel to [011]c, which promotes single slip on the slowest slip system in olivine, (010)[001]. The creep rates at steady state match well the results of earlier investigators, as does the stress sensitivity (a power-law exponent of n = 3.6). Dislocation microstructures, including spatial distribution of low-angle (subgrain) boundaries, additionally confirm previous investigations. Inverted primary creep (an accelerating strain rate with an increase in stress) was observed. Load-relaxation, however, produced a singular response—a single hardness curve—regardless of the magnitude of creep stress or total accumulated strain preceding relaxation. The log-stress v. log-strain rate data from load-relaxation and creep experiments overlap to within experimental error. The load-relaxation behavior is distinctly different that that described for other crystalline solids, where the flow stress is affected strongly by work hardening such that a family of distinct hardness curves is generated, which are related by a scaling function. The response of olivine for the conditions studied, thus, indicates flow that is rate-limited by dislocation glide, reflecting specifically a high intrinsic lattice resistance (Peierls stress).
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.
Relaxing Behavioural Inheritance
Nuno Amálio
2013-05-01
Full Text Available Object-oriented (OO inheritance allows the definition of families of classes in a hierarchical way. In behavioural inheritance, a strong version, it should be possible to substitute an object of a subclass for an object of its superclass without any observable effect on the system. Behavioural inheritance is related to formal refinement, but, as observed in the literature, the refinement constraints are too restrictive, ruling out many useful OO subclassings. This paper studies behavioural inheritance in the context of ZOO, an object-oriented style for Z. To overcome refinement's restrictions, this paper proposes relaxations to the behavioural inheritance refinement rules. The work is presented for Z, but the results are applicable to any OO language that supports design-by-contract.
离散时延双神经元网络的渐近稳定性%Asymptotic Stability Criteria for a Two-Neuron Network with Different Time Delays
李绍文; 李绍荣; 廖晓峰
2003-01-01
New sufficient conditions for the asymptotic stability of a two-neuron network with different time delays are derived. These conditions lead to delay-dependent and delay-independent asymptotic stability. Our results are shown to be less conservative and restrictive than those reported in the literature. Some examples are given to illustrate the correctness of our results.
An asymptotic solution of large-$N$ $QCD$
Bochicchio, Marco
2014-01-01
We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-$N$ $QCD$, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-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 $LSZ$ 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 strin...
Echoes of asymptotic silence in causal set quantum gravity
Eichhorn, Astrid; Mizera, Sebastian; Surya, Sumati
2017-08-01
We explore the idea of asymptotic silence in causal set theory and find that causal sets approximated by continuum spacetimes exhibit behavior akin to asymptotic silence. We make use of an intrinsic definition of spatial distance between causal set elements in the discrete analogue of a spatial hypersurface. Using numerical simulations for causal sets approximated by \
Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices
Cha, Ye Sle; Sakovich, Anna
2016-01-01
We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case in the asymptotically flat setting, whenever a geometrically motivated system of elliptic equations admits a solution.
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.
Small-x asymptotics of structure function $g_2$
Ermolaev, B I
1997-01-01
Nonsinglet structure function g_2(x) for deep inelastic scattering of a lepton on a constituent quark is calculated in the double logarithmic approximation at x<<1. Small-x asymptotics of g_2 is shown to have the same singular behaviour as asymptotics of the nonsinglet structure function g_1.
Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings
Wei Shi-long; Guo Wei-ping
2015-01-01
The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.
Asymptotic Hyperstability of Dynamic Systems with Point Delays
M. De la Sen
2005-01-01
Full Text Available It is proved that a linear time-invariant system with internal point delays is asymptotically hyperstable independent of the delays if an associate delay-free system is asymptotically hyperstable and the delayed dynamics are sufficiently small.
The asymptotic variance of departures in critically loaded queues
A. Al Hanbali; M.R.H. Mandjes (Michel); Y. Nazarathy (Yoni); W. Whitt
2010-01-01
htmlabstractWe consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time t. We focus on the case that the system load rho equals 1, and prove that the asymptotic variance rate satisfies lim_t Var D(t)/t = lambda
Asymptotic expansions for high-contrast linear elasticity
Poveda, Leonardo A.
2015-03-01
We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.
Numerical and asymptotic aspects of parabolic cylinder functions
Temme, N.M.
2000-01-01
Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic expansions given earlier by F.W.J. Olver. Some of his results are
Global asymptotic stability of cellular neural networks with multiple delays
无
2006-01-01
Global asymptotic stability (GAS) is discussed for cellular neural networks (CNN) with multiple time delays. Several criteria are proposed to ascertain the uniqueness and global asymptotic stability of the equilibrium point for the CNN with delays. These criteria can eliminate the difference between the neuronal excitatory and inhibitory effects. Two examples are presented to demonstrate the effectiveness of the criteria.