Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations

KAUST Repository

Figalli, Alessio; Gomes, Diogo A.; Marcon, Diego

2016-01-01

Here, we extend the weak KAM and Aubry–Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton–Jacobi equations, and the long-time behavior of time-dependent systems. We prove the existence and regularity of action minimizers, obtain necessary conditions for minimality, extend Fathi’s weak KAM theorem, and describe the asymptotic limit of the generalized Lax–Oleinik semigroup. © 2016, Springer-Verlag Berlin Heidelberg.

Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations

KAUST Repository

Figalli, Alessio

2016-06-23

Here, we extend the weak KAM and Aubry–Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton–Jacobi equations, and the long-time behavior of time-dependent systems. We prove the existence and regularity of action minimizers, obtain necessary conditions for minimality, extend Fathi’s weak KAM theorem, and describe the asymptotic limit of the generalized Lax–Oleinik semigroup. © 2016, Springer-Verlag Berlin Heidelberg.

Application of the weak-field asymptotic theory to the analysis of tunneling ionization of linear molecules

DEFF Research Database (Denmark)

Madsen, Lars Bojer; Tolstikhin, Oleg I.; Morishita, Toru

2012-01-01

The recently developed weak-field asymptotic theory [ Phys. Rev. A 84 053423 (2011)] is applied to the analysis of tunneling ionization of a molecular ion (H2+), several homonuclear (H2, N2, O2) and heteronuclear (CO, HF) diatomic molecules, and a linear triatomic molecule (CO2) in a static...... electric field. The dependence of the ionization rate on the angle between the molecular axis and the field is determined by a structure factor for the highest occupied molecular orbital. This factor is calculated using a virtually exact discrete variable representation wave function for H2+, very accurate...... Hartree-Fock wave functions for the diatomics, and a Hartree-Fock quantum chemistry wave function for CO2. The structure factors are expanded in terms of standard functions and the associated structure coefficients, allowing the determination of the ionization rate for any orientation of the molecule...

Microcavity polariton linewidths in the weak-disorder regime

DEFF Research Database (Denmark)

Borri, Paola; Langbein, Wolfgang Werner; Woggon, U.

2000-01-01

Polariton linewidths have been measured in a series of high-quality microcavities with different excitonic inhomogeneous broadening in the weak-disorder regime. We show experimentally that the influence of the disorder on the polariton linewidths is canceled when the polariton energies are far in...... in the tail of the excitonic absorption. The measured linewidths are quantitatively compared with an estimation using the measured excitonic absorption spectrum of the bare quantum wells, and good agreement is found....

Directions for model building from asymptotic safety

Science.gov (United States)

Bond, Andrew D.; Hiller, Gudrun; Kowalska, Kamila; Litim, Daniel F.

2017-08-01

Building on recent advances in the understanding of gauge-Yukawa theories we explore possibilities to UV-complete the Standard Model in an asymptotically safe manner. Minimal extensions are based on a large flavor sector of additional fermions coupled to a scalar singlet matrix field. We find that asymptotic safety requires fermions in higher representations of SU(3) C × SU(2) L . Possible signatures at colliders are worked out and include R-hadron searches, diboson signatures and the evolution of the strong and weak coupling constants.

Bound states in weakly disordered spin ladders

Energy Technology Data Exchange (ETDEWEB)

Arlego, M. [Departamento de Fisica, Universidad Nacional de La Plata, CC 67 (1900) La Plata (Argentina)]. E-mail: arlego@venus.fisica.unlp.edu.ar; Brenig, W. [Institut fuer Theoretische Physik, Technische Universitaet Braunschweig (Germany); Cabra, D.C. [Laboratoire de Physique Theorique, Universite Louis Pasteur Strasbourg (France); Heidrich-Meisner, F. [Institut fuer Theoretische Physik, Technische Universitaet Braunschweig (Germany); Honecker, A. [Institut fuer Theoretische Physik, Technische Universitaet Braunschweig (Germany); Rossini, G. [Departamento de Fisica, Universidad Nacional de La Plata, CC 67 (1900) La Plata (Argentina)

2005-04-30

We study the appearance of bound states in the spin gap of spin-12 ladders induced by weak bond disorder. Starting from the strong-coupling limit, i.e., the limit of weakly coupled dimers, we perform a projection on the single-triplet subspace and derive the position of bound states for the single impurity problem of one modified coupling as well as for small impurity clusters. The case of a finite concentration of impurities is treated with the coherent-potential approximation (CPA) in the strong-coupling limit and compared with numerical results. Further, we analyze the details in the structure of the density of states and relate their origin to the influence of impurity clusters.

An asymptotic safety scenario for gauged chiral Higgs-Yukawa models

International Nuclear Information System (INIS)

Gies, Holger; Rechenberger, Stefan; Scherer, Michael M.; Zambelli, Luca

2013-01-01

We investigate chiral Higgs-Yukawa models with a non-abelian gauged left-handed sector reminiscent to a sub-sector of the standard model. We discover a new weak-coupling fixed-point behavior that allows for ultraviolet complete RG trajectories which can be connected with a conventional long-range infrared behavior in the Higgs phase. This non-trivial ultraviolet behavior is characterized by asymptotic freedom in all interaction couplings, but a quasi conformal behavior in all mass-like parameters. The stable microscopic scalar potential asymptotically approaches flatness in the ultraviolet, however, with a non-vanishing minimum increasing inversely proportional to the asymptotically free gauge coupling. This gives rise to non-perturbative - though weak-coupling - threshold effects which induce ultraviolet stability along a line of fixed points. Despite the weak-coupling properties, the system exhibits non-Gaussian features which are distinctly different from its standard perturbative counterpart: e.g., on a branch of the line of fixed points, we find linear instead of quadratically running renormalization constants. Whereas the Fermi constant and the top mass are naturally of the same order of magnitude, our model generically allows for light Higgs boson masses. Realistic mass ratios are related to particular RG trajectories with a ''walking'' mid-momentum regime. (orig.)

An asymptotic safety scenario for gauged chiral Higgs-Yukawa models

Science.gov (United States)

Gies, Holger; Rechenberger, Stefan; Scherer, Michael M.; Zambelli, Luca

2013-12-01

We investigate chiral Higgs-Yukawa models with a non-abelian gauged left-handed sector reminiscent to a sub-sector of the standard model. We discover a new weak-coupling fixed-point behavior that allows for ultraviolet complete RG trajectories which can be connected with a conventional long-range infrared behavior in the Higgs phase. This non-trivial ultraviolet behavior is characterized by asymptotic freedom in all interaction couplings, but a quasi conformal behavior in all mass-like parameters. The stable microscopic scalar potential asymptotically approaches flatness in the ultraviolet, however, with a non-vanishing minimum increasing inversely proportional to the asymptotically free gauge coupling. This gives rise to non-perturbative—though weak-coupling—threshold effects which induce ultraviolet stability along a line of fixed points. Despite the weak-coupling properties, the system exhibits non-Gaußian features which are distinctly different from its standard perturbative counterpart: e.g., on a branch of the line of fixed points, we find linear instead of quadratically running renormalization constants. Whereas the Fermi constant and the top mass are naturally of the same order of magnitude, our model generically allows for light Higgs boson masses. Realistic mass ratios are related to particular RG trajectories with a "walking" mid-momentum regime.

Asymptotic series and functional integrals in quantum field theory

International Nuclear Information System (INIS)

Shirkov, D.V.

1979-01-01

Investigations of the methods for analyzing ultra-violet and infrared asymptotics in the quantum field theory (QFT) have been reviewed. A powerful method of the QFT analysis connected with the group property of renormalized transformations has been created at the first stage. The result of the studies of the second period is the constructive solution of the problem of outgoing the framework of weak coupling. At the third stage of studies essential are the asymptotic series and functional integrals in the QFT, which are used for obtaining the asymptotic type of the power expansion coefficients in the coupling constant at high values of the exponents for a number of simple models. Further advance to higher values of the coupling constant requires surmounting the difficulties resulting from the asymptotic character of expansions and a constructive application in the region of strong coupling (g >> 1)

Weak interactions

International Nuclear Information System (INIS)

Bjorken, J.D.

1978-01-01

Weak interactions are studied from a phenomenological point of view, by using a minimal number of theoretical hypotheses. Charged-current phenomenology, and then neutral-current phenomenology are discussed. This all is described in terms of a global SU(2) symmetry plus an electromagnetic correction. The intermediate-boson hypothesis is introduced and lower bounds on the range of the weak force are inferred. This phenomenology does not yet reconstruct all the predictions of the conventional SU(2)xU(1) gauge theory. To do that requires an additional assumption of restoration of SU(2) symmetry at asymptotic energies

Robust methods and asymptotic theory in nonlinear econometrics

CERN Document Server

Bierens, Herman J

1981-01-01

This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non­ linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...

q Breathers in Finite Lattices: Nonlinearity and Weak Disorder

Science.gov (United States)

Ivanchenko, M. V.

2009-05-01

Nonlinearity and disorder are the recognized ingredients of the lattice vibrational dynamics, the factors that could be diminished, but never excluded. We generalize the concept of q breathers—periodic orbits in nonlinear lattices, exponentially localized in the linear mode space—to the case of weak disorder, taking the Fermi-Pasta-Ulan chain as an example. We show that these nonlinear vibrational modes remain exponentially localized near the central mode and stable, provided the disorder is sufficiently small. The instability threshold depends sensitively on a particular realization of disorder and can be modified by specifically designed impurities. Based on this sensitivity, an approach to controlling the energy flow between the modes is proposed. The relevance to other model lattices and experimental miniature arrays is discussed.

Superdiffusive transport and energy localization in disordered granular crystals

International Nuclear Information System (INIS)

Martinez, Alejandro J.; Kevrekidis, Panagiotis G.; Porter, Mason A.

2016-01-01

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition. Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m ~ 2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder

Luttinger liquid behavior of weakly disordered quantum wires

International Nuclear Information System (INIS)

Palevski, A.; Levy, E.; Karpovski, M.; Tsukernik, A.; Dwir, B.; Kapon, E.

2005-01-01

Full Text:The talk will be devoted to the electronic transport in quantum nano wires. The temperature dependence of the conductance in long V-groove quantum wires fabricated in GaAs/AlGaAs heterostructures is consistent with recent theories given within the framework of the Luttinger liquid model, in the limit of weakly disordered wires. We show that for the relatively small amount of disorder in our quantum wires, the value of the interaction parameter g is g=0.66, which is the expected value for GaAs. However, samples with a higher level of disorder show conductance with stronger temperature dependence, which exceeds the range of validity of a perturbation theory. Trying to fit such data with perturbation-theory models leads inevitably to wrong (lower) values of g

Asymptotically Almost Periodic Solutions of Evolution Equations in Banach Spaces

Science.gov (United States)

Ruess, W. M.; Phong, V. Q.

Tile linear abstract evolution equation (∗) u'( t) = Au( t) + ƒ( t), t ∈ R, is considered, where A: D( A) ⊂ E → E is the generator of a strongly continuous semigroup of operators in the Banach space E. Starting from analogs of Kadets' and Loomis' Theorems for vector valued almost periodic Functions, we show that if σ( A) ∩ iR is countable and ƒ: R → E is [asymptotically] almost periodic, then every bounded and uniformly continuous solution u to (∗) is [asymptotically] almost periodic, provided e-λ tu( t) has uniformly convergent means for all λ ∈ σ( A) ∩ iR. Related results on Eberlein-weakly asymptotically almost periodic, periodic, asymptotically periodic and C 0-solutions of (∗), as well as on the discrete case of solutions of difference equations are included.

Weak point disorder in strongly fluctuating flux-line liquids

Indian Academy of Sciences (India)

We consider the effect of weak uncorrelated quenched disorder (point defects) on a strongly fluctuating flux-line liquid. We use a hydrodynamic model which is based on mapping the flux-line system onto a quantum liquid of relativistic charged bosons in 2 + 1 dimensions [P Benetatos and M C Marchetti, Phys. Rev. B64 ...

Asymptotic numbers, asymptotic functions and distributions

International Nuclear Information System (INIS)

Todorov, T.D.

1979-07-01

The asymptotic functions are a new type of generalized functions. But they are not functionals on some space of test-functions as the distributions of Schwartz. They are mappings of the set denoted by A into A, where A is the set of the asymptotic numbers introduced by Christov. On its part A is a totally-ordered set of generalized numbers including the system of real numbers R as well as infinitesimals and infinitely large numbers. Every two asymptotic functions can be multiplied. On the other hand, the distributions have realizations as asymptotic functions in a certain sense. (author)

Efficient bootstrap with weakly dependent processes

NARCIS (Netherlands)

Bravo, Francesco; Crudu, Federico

The efficient bootstrap methodology is developed for overidentified moment conditions models with weakly dependent observation. The resulting bootstrap procedure is shown to be asymptotically valid and can be used to approximate the distributions of t-statistics, the J-statistic for overidentifying

The Q{sup p}{sub Weak} experiment

Energy Technology Data Exchange (ETDEWEB)

Androic, D. [University of Zagreb (Croatia); Armstrong, D. S. [The College of William and Mary (United States); Asaturyan, A. [Yerevan Physics Institute (Armenia); Averett, T. [The College of William and Mary (United States); Balewski, J. [Massachusetts Institute of Technology (United States); Beaufait, J. [Thomas Jefferson National Accelerator Facility (United States); Beminiwattha, R. S. [Ohio University (United States); Benesch, J. [Thomas Jefferson National Accelerator Facility (United States); Benmokhtar, F. [Duquesne University (United States); Birchall, J. [University of Manitoba (Canada); Carlini, R. D.; Cornejo, J. C. [The College of William and Mary (United States); Covrig, S. [Thomas Jefferson National Accelerator Facility (United States); Dalton, M. M. [University of Virginia (United States); Davis, C. A. [TRIUMF (United States); Deconinck, W. [The College of William and Mary (United States); Diefenbach, J. [Hampton University (United States); Dow, K. [Massachusetts Institute of Technology (United States); Dowd, J. F. [The College of William and Mary (United States); Dunne, J. A. [Mississippi State University (United States); and others

2013-03-15

In May 2012, the Q{sup p}{sub Weak} collaboration completed a two year measurement program to determine the weak charge of the proton Q{sub W}{sup p} = ( 1 - 4sin{sup 2}{theta}{sub W}) at the Thomas Jefferson National Accelerator Facility (TJNAF). The experiment was designed to produce a 4.0 % measurement of the weak charge, via a 2.5 % measurement of the parity violating asymmetry in the number of elastically scattered 1.165 GeV electrons from protons, at forward angles. At the proposed precision, the experiment would produce a 0.3 % measurement of the weak mixing angle at a momentum transfer of Q{sup 2} = 0.026 GeV{sup 2}, making it the most precise stand alone measurement of the weak mixing angle at low momentum transfer. In combination with other parity measurements, Q{sup p}{sub Weak} will also provide a high precision determination of the weak charges of the up and down quarks. At the proposed precision, a significant deviation from the Standard Model prediction could be a signal of new physics at mass scales up to Asymptotically-Equal-To 6 TeV, whereas agreement would place new and significant constraints on possible Standard Model extensions at mass scales up to Asymptotically-Equal-To 2 TeV. This paper provides an overview of the physics and the experiment, as well as a brief look at some preliminary diagnostic and analysis data.

Asymptotic behaviour of a rescattering series for nonlinear reggeons

International Nuclear Information System (INIS)

Akkelin, S.V.; Martynov, E.S.

1990-01-01

A series of elastic re-scattering (both quasi-eikonal and U-matrix ones) for reggeons with nonlinear trajectories are estimated asymptotically. The calculations are performed for models of supercritical and dipole pomerons. A weak dependence of the series of re-scattering on reggeon trajectory nonlinearity is revealed. 13 refs.; 3 figs

Quantum mechanical calculations on weakly interacting complexes

NARCIS (Netherlands)

Heijmen, T.G.A.

1998-01-01

Symmetry-adapted perturbation theory (SAPT) has been applied to compute the intermolecular potential energy surfaces and the interaction-induced electrical properties of weakly interacting complexes. Asymptotic (large R) expressions have been derived for the contributions to the collision-induced

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

International Nuclear Information System (INIS)

Harada, Tomohiro; Maeda, Hideki; Carr, B. J.

2008-01-01

Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid with equation of state p=(γ-1)μ with 0 1). However, in the latter case there is an additional parameter associated with the weak discontinuity at the sonic point and the solutions are only asymptotically 'quasi-Friedmann', in the sense that they exhibit an angle deficit at large distances. In the 0<γ<2/3 case, there is no sonic point and there exists a one-parameter family of solutions which are genuinely asymptotically Friedmann at large distances. We find eight classes of asymptotic behavior: Friedmann or quasi-Friedmann or quasistatic or constant-velocity at large distances, quasi-Friedmann or positive-mass singular or negative-mass singular at small distances, and quasi-Kantowski-Sachs at intermediate distances. The self-similar asymptotically quasistatic and quasi-Kantowski-Sachs solutions are analytically extendible and of great cosmological interest. We also investigate their conformal diagrams. The results of the present analysis are utilized in an accompanying paper to obtain and physically interpret numerical solutions

Analyticity in a phenomenology of electro-weak structure of hadrons

International Nuclear Information System (INIS)

Dubnicka, S.; Dubnickova, A. Z.

2010-01-01

The utility of an application of the analyticity in a phenomenology of electro-weak structure of hadrons is demonstrated in a number of obtained new and experimentally verifiable results. With this aim first the problem of an inconsistency of the asymptotic behavior of vector-meson-dominance model with the asymptotic behavior of form factors of baryons and nuclei is solved generally and a general approach for determination of the lowest normal and anomalous singularities of form factors from the corresponding Feynman diagrams is reviewed. Then many useful applications by making use of the analytic properties of electro-weak form factors and amplitudes of various electromagnetic processes of hadrons are carried out. (Author)

Theory of weakly nonlinear self-sustained detonations

KAUST Repository

Faria, Luiz; Kasimov, Aslan R.; Rosales, Rodolfo R.

2015-01-01

We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced

Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights

Science.gov (United States)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2009-12-01

We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form , with [gamma]>0, which include as particular cases the counterparts of the so-called Freud (i.e., when [phi] has a polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived.

Asymptotic stability of linearly evolving non-stationary modes in a ...

Indian Academy of Sciences (India)

attention and it is believed to shed important light on the unresolved .... number assumption and is termed as the triple-deck theory. Having ... to analyse asymptotically the linear and weakly non-linear stability features of the station- ..... A numerical integration of equations (7–9) was implemented first to obtain the basic flow.

Derivation of asymptotic Vertical BarΔIVertical Bar = 1/2 rule

International Nuclear Information System (INIS)

Terasaki, K.; Oneda, S.

1982-01-01

It is argued that the origin of the observed approximate Vertical BarΔIVertical Bar = 1/2 rule is the presence of an asymptotic Vertical BarΔIVertical Bar = 1/2 rule which exists among certain two-body hadronic weak matrix elements, involving especially the ground-state hadrons

Statistics of resonances in a one-dimensional chain: a weak disorder limit

International Nuclear Information System (INIS)

Vinayak

2012-01-01

We study statistics of resonances in a one-dimensional disordered chain coupled to an outer world simulated by a perfect lead. We consider a limiting case for weak disorder and derive some results which are new in these studies. The main focus of this study is to describe the statistics of the scattered complex energies. We derive compact analytic statistical results for long chains. A comparison of these results has been found to be in good agreement with numerical simulations. (paper)

Current flow in random resistor networks: the role of percolation in weak and strong disorder.

Science.gov (United States)

Wu, Zhenhua; López, Eduardo; Buldyrev, Sergey V; Braunstein, Lidia A; Havlin, Shlomo; Stanley, H Eugene

2005-04-01

We study the current flow paths between two edges in a random resistor network on a L X L square lattice. Each resistor has resistance e(ax) , where x is a uniformly distributed random variable and a controls the broadness of the distribution. We find that: (a) The scaled variable u identical with u congruent to L/a(nu) , where nu is the percolation connectedness exponent, fully determines the distribution of the current path length l for all values of u . For u > 1, the behavior corresponds to the weak disorder limit and l scales as l approximately L, while for u < 1 , the behavior corresponds to the strong disorder limit with l approximately L(d(opt) ), where d(opt) =1.22+/-0.01 is the optimal path exponent. (b) In the weak disorder regime, there is a length scale xi approximately a(nu), below which strong disorder and critical percolation characterize the current path.

Theorems for asymptotic safety of gauge theories

Energy Technology Data Exchange (ETDEWEB)

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.)

Black holes and the weak cosmic censorship

International Nuclear Information System (INIS)

Krolak, A.

1984-01-01

A theory of black holes is developed under the assumption of the weak cosmic censorship. It includes Hawking's theory of black holes in the future asymptotically predictable space-times as a special case but it also applies to the cosmological situations including models with nonzero cosmological constant of both signs. (author)

The Weak Coherence Account: Detail-Focused Cognitive Style in Autism Spectrum Disorders

Science.gov (United States)

Happe, Francesca; Frith, Uta

2006-01-01

"Weak central coherence" refers to the detail-focused processing style proposed to characterise autism spectrum disorders (ASD). The original suggestion of a core deficit in central processing resulting in failure to extract global form/meaning, has been challenged in three ways. First, it may represent an outcome of superiority in local…

Thermodynamics of a Bose-Einstein condensate with weak disorder

International Nuclear Information System (INIS)

Falco, G. M.; Pelster, A.; Graham, R.

2007-01-01

We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an external random δ-correlated potential by means of a Bogoliubov transformation. We extend this approach to finite temperature by combining the Popov and the many-body T-matrix approximations. This approach permits us to include the quasiparticle interactions within this temperature range. We derive the disorder-induced shifts of the Bose-Einstein critical temperature and of the temperature for the onset of superfluidity by approaching the transition points from below, i.e., from the superfluid phase. Our results lead to a phase diagram consistent with that of the finite-temperature theory of Lopatin and Vinokur which was based on the replica method, and in which the transition points were approached from above

Asymptotic Distribution of Eigenvalues of Weakly Dilute Wishart Matrices

Energy Technology Data Exchange (ETDEWEB)

Khorunzhy, A. [Institute for Low Temperature Physics (Ukraine)], E-mail: khorunjy@ilt.kharkov.ua; Rodgers, G. J. [Brunel University, Uxbridge, Department of Mathematics and Statistics (United Kingdom)], E-mail: g.j.rodgers@brunel.ac.uk

2000-03-15

We study the eigenvalue distribution of large random matrices that are randomly diluted. We consider two random matrix ensembles that in the pure (nondilute) case have a limiting eigenvalue distribution with a singular component at the origin. These include the Wishart random matrix ensemble and Gaussian random matrices with correlated entries. Our results show that the singularity in the eigenvalue distribution is rather unstable under dilution and that even weak dilution destroys it.

Quasi-extended asymptotic functions

International Nuclear Information System (INIS)

Todorov, T.D.

1979-01-01

The class F of ''quasi-extended asymptotic functions'' is introduced. It contains all extended asymptotic functions as well as some new asymptotic functions very similar to the Schwartz distributions. On the other hand, every two quasiextended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square delta 2 of an asymptotic function delta similar to Dirac's delta-function, is constructed as an example

On the Convergence of Implicit Iterative Processes for Asymptotically Pseudocontractive Mappings in the Intermediate Sense

Directory of Open Access Journals (Sweden)

Xiaolong Qin

2011-01-01

Full Text Available An implicit iterative process is considered. Strong and weak convergence theorems of common fixed points of a finite family of asymptotically pseudocontractive mappings in the intermediate sense are established in a real Hilbert space.

Correlation function of weakly interacting bosons in a disordered lattice

Energy Technology Data Exchange (ETDEWEB)

Deissler, B; Lucioni, E; Modugno, M; Roati, G; Tanzi, L; Zaccanti, M; Inguscio, M; Modugno, G, E-mail: deissler@lens.unifi.it, E-mail: modugno@lens.unifi.it [LENS and Dipartimento di Fisica e Astronomia, Universita di Firenze, 50019 Sesto Fiorentino (Italy)

2011-02-15

One of the most important issues in disordered systems is the interplay of the disorder and repulsive interactions. Several recent experimental advances on this topic have been made with ultracold atoms, in particular the observation of Anderson localization and the realization of the disordered Bose-Hubbard model. There are, however, still questions as to how to differentiate the complex insulating phases resulting from this interplay, and how to measure the size of the superfluid fragments that these phases entail. It has been suggested that the correlation function of such a system can give new insights, but so far very little experimental investigation has been performed. Here, we show the first experimental analysis of the correlation function for a weakly interacting, bosonic system in a quasiperiodic lattice. We observe an increase in the correlation length as well as a change in the shape of the correlation function in the delocalization crossover from Anderson glass to coherent, extended state. In between, the experiment indicates the formation of progressively larger coherent fragments, consistent with a fragmented BEC, or Bose glass.

Correlation function of weakly interacting bosons in a disordered lattice

International Nuclear Information System (INIS)

Deissler, B; Lucioni, E; Modugno, M; Roati, G; Tanzi, L; Zaccanti, M; Inguscio, M; Modugno, G

2011-01-01

One of the most important issues in disordered systems is the interplay of the disorder and repulsive interactions. Several recent experimental advances on this topic have been made with ultracold atoms, in particular the observation of Anderson localization and the realization of the disordered Bose-Hubbard model. There are, however, still questions as to how to differentiate the complex insulating phases resulting from this interplay, and how to measure the size of the superfluid fragments that these phases entail. It has been suggested that the correlation function of such a system can give new insights, but so far very little experimental investigation has been performed. Here, we show the first experimental analysis of the correlation function for a weakly interacting, bosonic system in a quasiperiodic lattice. We observe an increase in the correlation length as well as a change in the shape of the correlation function in the delocalization crossover from Anderson glass to coherent, extended state. In between, the experiment indicates the formation of progressively larger coherent fragments, consistent with a fragmented BEC, or Bose glass.

Asymptotic equivalence of neutron diffusion and transport in time-independent reactor systems

International Nuclear Information System (INIS)

Borysiewicz, M.; Mika, J.; Spiga, G.

1982-01-01

Presented in this paper is the asymptotic analysis of the time-independent neutron transport equation in the second-order variational formulation. The small parameter introduced into the equation is an estimate of the ratio of absorption and leakage to scattering in the system considered. When the ratio tends to zero, the weak solution to the transport problem tends to the weak solution of the diffusion problem, including properly defined boundary conditions. A formula for the diffusion coefficient different from that based on averaging the transport mean-free-path is derived

Weak interaction models with spontaneously broken left-right symmetry

International Nuclear Information System (INIS)

Mohapatra, R.H.

1978-01-01

The present status of weak interaction models with spontaneously broken left-right symmetry is reviewed. The theoretical basis for asymptotic parity conservation, manifest left-right symmetry in charged current weak interactions, natural parity conservation in neutral currents and CP-violation in the context of SU(2)/sub L/ circled x SU (2)/sub R/ circled x U(1) models are outlined in detail. Various directions for further research in the theoretical and experimental side are indicated

The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces

Directory of Open Access Journals (Sweden)

Rabian Wangkeeree

2012-01-01

Full Text Available We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.

Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings

Directory of Open Access Journals (Sweden)

Watcharaporn Cholamjiak

2009-01-01

Full Text Available We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006 and Nakajo and Takahashi (2003.

Elephants in Pyjamas: Testing the Weak Central Coherence Account of Autism Spectrum Disorders Using a Syntactic Disambiguation Task

Science.gov (United States)

Riches, N. G.; Loucas, T.; Baird, G.; Charman, T.; Simonoff, E.

2016-01-01

According to the weak central coherence (CC) account individuals with autism spectrum disorders (ASD) exhibit enhanced local processing and weak part-whole integration. CC was investigated in the verbal domain. Adolescents, recruited using a 2 (ASD status) by 2 (language impairment status) design, completed an aural forced choice comprehension…

The disordered Bose condensate in two dimensions: application to high-Tc superconductors

International Nuclear Information System (INIS)

Gold, A.

1992-01-01

We calculate the dynamical conductivity for a weakly disordered Bose condensate in two dimensions. The disorder is due to neutral impurities. We compare the asymptotic laws (for small and large frequencies) for neutral impurities with the ones for charged impurities. Universal functions for the dynamical transport properties are derived. The plasmon density of states shows a linear increase with energy for intermediate energies and a peak structure at larger energies. Our theoretical results are compared with experimental results (far-infrared, electron-energy-loss and Raman spectroscopy) found in the high-Tc superconductor YBa 2 Cu 3 O 7-δ . The occurrence of a quasi-gap in a disordered Bose condensate is described and discussed in connection with experiments on high-Tc superconductors. (orig.)

Asymptotics and Borel summability

CERN Document Server

Costin, Ovidiu

2008-01-01

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

Asymptotically Safe Dark Matter

DEFF Research Database (Denmark)

Sannino, Francesco; Shoemaker, Ian M.

2015-01-01

We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....

More asymptotic safety guaranteed

Science.gov (United States)

Bond, Andrew D.; Litim, Daniel F.

2018-04-01

We study interacting fixed points and phase diagrams of simple and semisimple quantum field theories in four dimensions involving non-Abelian gauge fields, fermions and scalars in the Veneziano limit. Particular emphasis is put on new phenomena which arise due to the semisimple nature of the theory. Using matter field multiplicities as free parameters, we find a large variety of interacting conformal fixed points with stable vacua and crossovers inbetween. Highlights include semisimple gauge theories with exact asymptotic safety, theories with one or several interacting fixed points in the IR, theories where one of the gauge sectors is both UV free and IR free, and theories with weakly interacting fixed points in the UV and the IR limits. The phase diagrams for various simple and semisimple settings are also given. Further aspects such as perturbativity beyond the Veneziano limit, conformal windows, and implications for model building are discussed.

Asymptotic Eigenstructures

Science.gov (United States)

Thompson, P. M.; Stein, G.

1980-01-01

The behavior of the closed loop eigenstructure of a linear system with output feedback is analyzed as a single parameter multiplying the feedback gain is varied. An algorithm is presented that computes the asymptotically infinite eigenstructure, and it is shown how a system with high gain, feedback decouples into single input, single output systems. Then a synthesis algorithm is presented which uses full state feedback to achieve a desired asymptotic eigenstructure.

Extended asymptotic functions - some examples

International Nuclear Information System (INIS)

Todorov, T.D.

1981-01-01

Several examples of extended asymptotic functions of two variables are given. This type of asymptotic functions has been introduced as an extension of continuous ordinary functions. The presented examples are realizations of some Schwartz distributions delta(x), THETA(x), P(1/xsup(n)) and can be multiplied in the class of the asymptotic functions as opposed to the theory of Schwartz distributions. The examples illustrate the method of construction of extended asymptotic functions similar to the distributions. The set formed by the extended asymptotic functions is also considered. It is shown, that this set is not closed with respect to addition and multiplication

Dephasing in coherent communication with weak signal states

International Nuclear Information System (INIS)

Jarzyna, Marcin; Banaszek, Konrad; Demkowicz-Dobrzański, Rafał

2014-01-01

We analyse the ultimate quantum limit on the accessible information for an optical communication scheme when time bins carry coherent light pulses prepared in one of several orthogonal modes and the phase undergoes diffusion after each channel use. This scheme, an example of a quantum memory channel, can be viewed as noisy pulse position modulation (PPM) keying with phase fluctuations occurring between consecutive PPM symbols. We derive a general expression for the output states in the Fock basis and implement a numerical procedure to calculate the Holevo quantity. Using asymptotic properties of Toeplitz matrices, we also present an analytic expression for the Holevo quantity valid for very weak signals and sufficiently strong dephasing when the dominant contribution comes from the single-photon sector in the Hilbert space of signal states. Based on numerical results we conjecture an inequality for contributions to the Holevo quantity from multiphoton sectors which implies that in the asymptotic limit of weak signals, for arbitrarily small dephasing the accessible information scales linearly with the average number of photons contained in the pulse. Such behaviour presents a qualitative departure from the fully coherent case. (paper)

Asymptotics of relativistic spin networks

International Nuclear Information System (INIS)

Barrett, John W; Steele, Christopher M

2003-01-01

The stationary phase technique is used to calculate asymptotic formulae for SO(4) relativistic spin networks. For the tetrahedral spin network this gives the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j-symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the spin network evaluation. Finally, we discuss the asymptotics of the SO(3, 1) 10j-symbol

On hierarchy in asymptotic reconstruction of spontaneously broken isotopic symmetry

International Nuclear Information System (INIS)

Ermolaev, B.I.

1978-01-01

The isotopic features of the effective current-current lagrangian of the Lsub(eff) electromagnetic-weak interaction between elementary particles are treated at large momentum transfers using the Weinberg-Salam model. Transition to other models may be made by analogy. It is shown that when the collision energies of elementary particles exceed 90 GeV one may expect the hierarchy in the asymptotic reconstruction of the isotopic symmetry. Such hierarchy could be observed, in particular, in experiments on elastic leptonic collisions at high energies

Global asymptotic stability of bistable traveling fronts in reaction-diffusion systems and their applications to biological models

International Nuclear Information System (INIS)

Wu Shiliang; Li Wantong

2009-01-01

This paper deals with the global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts in a class of reaction-diffusion systems. The known results do not apply in solving these problems because the reaction terms do not satisfy the required monotone condition. To overcome the difficulty, a weak monotone condition is proposed for the reaction terms, which is called interval monotone condition. Under such a weak monotone condition, the existence and comparison theorem of solutions is first established for reaction-diffusion systems on R by appealing to the theory of abstract differential equations. The global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts are then proved by the elementary super- and sub-solution comparison and squeezing methods for nonlinear evolution equations. Finally, these abstract results are applied to a two species competition-diffusion model and a system modeling man-environment-man epidemics.

Asymptotic and geometrical quantization

International Nuclear Information System (INIS)

Karasev, M.V.; Maslov, V.P.

1984-01-01

The main ideas of geometric-, deformation- and asymptotic quantizations are compared. It is shown that, on the one hand, the asymptotic approach is a direct generalization of exact geometric quantization, on the other hand, it generates deformation in multiplication of symbols and Poisson brackets. Besides investigating the general quantization diagram, its applications to the calculation of asymptotics of a series of eigenvalues of operators possessing symmetry groups are considered

Variationally Asymptotically Stable Difference Systems

Directory of Open Access Journals (Sweden)

Goo YoonHoe

2007-01-01

Full Text Available We characterize the h-stability in variation and asymptotic equilibrium in variation for nonlinear difference systems via n∞-summable similarity and comparison principle. Furthermore we study the asymptotic equivalence between nonlinear difference systems and their variational difference systems by means of asymptotic equilibria of two systems.

Thermodynamical fluctuations and critical behavior in weakly disordered YBCO thin and ultra-thin films

International Nuclear Information System (INIS)

Lesueur, J.; Aprili, M.; Degoy, S.; Chambonnet, D.; Keller, D.

1996-01-01

The specific role of disorder in the transport properties of YBCO has been investigated, using both light-ion irradiation of thin films to finely tune the amount of atomic disorder, and ultra-thin films grown to study possible dimensional effects. For weak disorder, the samples display a resistive transition typical of the mean-field paraconductive regime of a homogeneous media, well described by the Lawrence and Doniach model for layered superconductors. As the disorder increases, two effects take place. First, the c-axis coherence length becomes shorter, leading to a more anisotropic material, as shown by the excess conductivity above T c . Second, an incipient granularity is revealed, leading to a less sharper transition, which is analyzed within the random 3D XY critical model for the paracoherence transition. Two main results are derived: an experimental test of the Ginzburg criteria for the paracoherence transition, and a new fluctuation regime in nanometric grain size superconductors

Semiclassical Weyl Formula for a Class of Weakly Regular Elliptic Operators

Energy Technology Data Exchange (ETDEWEB)

Zielinski, Lech [Universite du Littoral, LMPA, Centre Mi-Voix (France)], E-mail: Lech.Zielinski@lmpa.univ-littoral.fr

2006-02-15

We investigate the semiclassical Weyl formula describing the asymptotic behaviour of the counting function for the number of eigenvalues in the case of self-adjoint elliptic differential operators satisfying weak regularity hypotheses. We consider symbols with possible critical points and with coefficients which have Hoelder continuous derivatives of first order.

Semiclassical Weyl Formula for a Class of Weakly Regular Elliptic Operators

International Nuclear Information System (INIS)

Zielinski, Lech

2006-01-01

We investigate the semiclassical Weyl formula describing the asymptotic behaviour of the counting function for the number of eigenvalues in the case of self-adjoint elliptic differential operators satisfying weak regularity hypotheses. We consider symbols with possible critical points and with coefficients which have Hoelder continuous derivatives of first order

Polynomial Asymptotes of the Second Kind

Science.gov (United States)

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…

Analytical solutions of weakly coupled map lattices using recurrence relations

Energy Technology Data Exchange (ETDEWEB)

Sotelo Herrera, Dolores, E-mail: dsh@dfmf.uned.e [Applied Maths, EUITI, UPM, Ronda de Valencia, 3-28012 Madrid (Spain); San Martin, Jesus [Applied Maths, EUITI, UPM, Ronda de Valencia, 3-28012 Madrid (Spain); Dep. Fisica Matematica y de Fluidos, UNED, Senda del Rey 9-28040 Madrid (Spain)

2009-07-20

By using asymptotic methods recurrence relations are found that rule weakly CML evolution, with both global and diffusive coupling. The solutions obtained from these relations are very general because they do not hold restrictions about boundary conditions, initial conditions and number of oscilators in the CML. Furthermore, oscillators are ruled by an arbitraty C{sup 2} function.

Facial-muscle weakness, speech disorders and dysphagia are common in patients with classic infantile Pompe disease treated with enzyme therapy.

Science.gov (United States)

van Gelder, C M; van Capelle, C I; Ebbink, B J; Moor-van Nugteren, I; van den Hout, J M P; Hakkesteegt, M M; van Doorn, P A; de Coo, I F M; Reuser, A J J; de Gier, H H W; van der Ploeg, A T

2012-05-01

Classic infantile Pompe disease is an inherited generalized glycogen storage disorder caused by deficiency of lysosomal acid α-glucosidase. If left untreated, patients die before one year of age. Although enzyme-replacement therapy (ERT) has significantly prolonged lifespan, it has also revealed new aspects of the disease. For up to 11 years, we investigated the frequency and consequences of facial-muscle weakness, speech disorders and dysphagia in long-term survivors. Sequential photographs were used to determine the timing and severity of facial-muscle weakness. Using standardized articulation tests and fibreoptic endoscopic evaluation of swallowing, we investigated speech and swallowing function in a subset of patients. This study included 11 patients with classic infantile Pompe disease. Median age at the start of ERT was 2.4 months (range 0.1-8.3 months), and median age at the end of the study was 4.3 years (range 7.7 months -12.2 years). All patients developed facial-muscle weakness before the age of 15 months. Speech was studied in four patients. Articulation was disordered, with hypernasal resonance and reduced speech intelligibility in all four. Swallowing function was studied in six patients, the most important findings being ineffective swallowing with residues of food (5/6), penetration or aspiration (3/6), and reduced pharyngeal and/or laryngeal sensibility (2/6). We conclude that facial-muscle weakness, speech disorders and dysphagia are common in long-term survivors receiving ERT for classic infantile Pompe disease. To improve speech and reduce the risk for aspiration, early treatment by a speech therapist and regular swallowing assessments are recommended.

Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality

Science.gov (United States)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2008-10-01

We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same nth root asymptotic behavior as the weighted norms of certain extremal polynomials. This result is applied to obtain the (contracted) weak zero distribution for orthogonal polynomials with respect to a Sobolev inner product with exponential weights of the form e-[phi](x), giving a unified treatment for the so-called Freud (i.e., when [phi] has polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) cases. In addition, we provide a new proof for the bound of the distance of the zeros to the convex hull of the support for these Sobolev orthogonal polynomials.

Gossip and Distributed Kalman Filtering: Weak Consensus Under Weak Detectability

Science.gov (United States)

Kar, Soummya; Moura, José M. F.

2011-04-01

The paper presents the gossip interactive Kalman filter (GIKF) for distributed Kalman filtering for networked systems and sensor networks, where inter-sensor communication and observations occur at the same time-scale. The communication among sensors is random; each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link. We show that under a weak distributed detectability condition: 1. the GIKF error process remains stochastically bounded, irrespective of the instability properties of the random process dynamics; and 2. the network achieves \\emph{weak consensus}, i.e., the conditional estimation error covariance at a (uniformly) randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semi-definite matrices (independent of the initial state.) To prove these results, we interpret the filtered states (estimates and error covariances) at each node in the GIKF as stochastic particles with local interactions. We analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched (random) Riccati equation, the switching being dictated by a non-stationary Markov chain on the network graph.

Asymptotic numbers: Pt.1

International Nuclear Information System (INIS)

Todorov, T.D.

1980-01-01

The set of asymptotic numbers A as a system of generalized numbers including the system of real numbers R, as well as infinitely small (infinitesimals) and infinitely large numbers, is introduced. The detailed algebraic properties of A, which are unusual as compared with the known algebraic structures, are studied. It is proved that the set of asymptotic numbers A cannot be isomorphically embedded as a subspace in any group, ring or field, but some particular subsets of asymptotic numbers are shown to be groups, rings, and fields. The algebraic operation, additive and multiplicative forms, and the algebraic properties are constructed in an appropriate way. It is shown that the asymptotic numbers give rise to a new type of generalized functions quite analogous to the distributions of Schwartz allowing, however, the operation multiplication. A possible application of these functions to quantum theory is discussed

Asymptotic Safety Guaranteed in Supersymmetry

Science.gov (United States)

Bond, Andrew D.; Litim, Daniel F.

2017-11-01

We explain how asymptotic safety arises in four-dimensional supersymmetric gauge theories. We provide asymptotically safe supersymmetric gauge theories together with their superconformal fixed points, R charges, phase diagrams, and UV-IR connecting trajectories. Strict perturbative control is achieved in a Veneziano limit. Consistency with unitarity and the a theorem is established. We find that supersymmetry enhances the predictivity of asymptotically safe theories.

On the theory of weak turbulence for the nonlinear Schrödinger equation

CERN Document Server

Escobedo, M

2015-01-01

The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.

Kasner asymptotics of mixmaster Horava-Witten and pre-big-bang cosmologies

International Nuclear Information System (INIS)

Dabrowski, Mariusz P.

2001-01-01

We discuss various superstring effective actions and, in particular, their common sector which leads to the so-called pre-big-bang cosmology (cosmology in a weak coupling limit of heterotic superstring theory. Using the conformal relationship between these two theories we present Kasner asymptotic solutions of Bianchi type IX geometries within these theories and make predictions about possible emergence of chaos. Finally, we present a possible method of generating Horava-Witten cosmological solutions out of the well-known general relativistic or pre-big-bang solutions

An asymptotically consistent approximant for the equatorial bending angle of light due to Kerr black holes

Science.gov (United States)

Barlow, Nathaniel S.; Weinstein, Steven J.; Faber, Joshua A.

2017-07-01

An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary spin. This expression is constructed by assuring that the weak- and strong-deflection limits are explicitly satisfied while maintaining accuracy at intermediate values of impact parameter via the method of asymptotic approximants (Barlow et al 2017 Q. J. Mech. Appl. Math. 70 21-48). To this end, the strong deflection limit for a prograde orbit around an extremal black hole is examined, and the full non-vanishing asymptotic behavior is determined. The derived approximant may be an attractive alternative to computationally expensive elliptical integrals used in black hole simulations.

An asymptotic solution of large-N QCD

Directory of Open Access Journals (Sweden)

Bochicchio Marco

2014-01-01

Full Text Available We find an asymptotic solution for two-, three- and multi-point correlators of local gauge-invariant operators, in a lower-spin sector of massless large-N QCD, in terms of glueball and meson propagators, in such a way that the solution is asymptotic in the ultraviolet to renormalization-group improved perturbation theory, by means of a new purely field-theoretical technique that we call the asymptotically-free bootstrap, based on a recently-proved asymptotic structure theorem for two-point correlators. The asymptotically-free bootstrap provides as well asymptotic S-matrix amplitudes in terms of glueball and meson propagators. Remarkably, the asymptotic S-matrix depends only on the unknown particle spectrum, but not on the anomalous dimensions, as a consequence of the LS Z reduction formulae. Very many physics consequences follow, both practically and theoretically. In fact, the asymptotic solution sets the strongest constraints on any actual solution of large-N QCD, and in particular on any string solution.

Asymptotic structure of isolated systems

International Nuclear Information System (INIS)

Schmidt, B.G.

1979-01-01

The main methods to formulate asymptotic flatness conditions are introduced and motivation and basic ideas are emphasized. Any asymptotic flatness condition proposed up to now describes space-times which behave somehow like Minkowski space, and a very explicit exposition of the structure at infinity of Minkowski space is given. This structure is used to describe the asymptotic behaviour of fields on Minkowski space in a frame-dependent way. The definition of null infinity for curved space-time according to Penrose is given and attempts to define spacelike infinity are outlined. The conformal bundle approach to the formulation of asymptotic behaviour is described and its relation to null and spacelike infinity is given, as far as known. (Auth.)

On extracting physical content from asymptotically flat spacetime metrics

International Nuclear Information System (INIS)

Kozameh, C; Newman, E T; Silva-Ortigoza, G

2008-01-01

A major issue in general relativity, from its earliest days to the present, is how to extract physical information from any solution or class of solutions to the Einstein equations. Though certain information can be obtained for arbitrary solutions, e.g., via geodesic deviation, in general, because of the coordinate freedom, it is often hard or impossible to do. Most of the time information is found from special conditions, e.g. degenerate principle null vectors, weak fields close to Minkowski space (using coordinates close to Minkowski coordinates), or from solutions that have symmetries or approximate symmetries. In the present work, we will be concerned with asymptotically flat spacetimes where the approximate symmetry is the Bondi-Metzner-Sachs group. For these spaces the Bondi 4-momentum vector and its evolution, found from the Weyl tensor at infinity, describes the total energy-momentum of the interior source and the energy-momentum radiated. By generalizing the structures (shear-free null geodesic congruences) associated with the algebraically special metrics to asymptotically shear-free null geodesic congruences, which are available in all asymptotically flat spacetimes, we give kinematic meaning to the Bondi 4-momentum. In other words, we describe the Bondi vector and its evolution in terms of a center of mass position vector, its velocity and a spin vector, all having clear geometric meaning. Among other items, from dynamic arguments, we define a unique (at our level of approximation) total angular momentum and extract its evolution equation in the form of a conservation law with an angular momentum flux

Generating asymptotically plane wave spacetimes

International Nuclear Information System (INIS)

Hubeny, Veronika E.; Rangamani, Mukund

2003-01-01

In an attempt to study asymptotically plane wave spacetimes which admit an event horizon, we find solutions to vacuum Einstein's equations in arbitrary dimension which have a globally null Killing field and rotational symmetry. We show that while such solutions can be deformed to include ones which are asymptotically plane wave, they do not posses a regular event horizon. If we allow for additional matter, such as in supergravity theories, we show that it is possible to have extremal solutions with globally null Killing field, a regular horizon, and which, in addition, are asymptotically plane wave. In particular, we deform the extremal M2-brane solution in 11-dimensional supergravity so that it behaves asymptotically as a 10-dimensional vacuum plane wave times a real line. (author)

Asymptotic twistor theory and the Kerr theorem

International Nuclear Information System (INIS)

Newman, Ezra T

2006-01-01

We first review asymptotic twistor theory with its real subspace of null asymptotic twistors: a five-dimensional CR manifold. This is followed by a description of the Kerr theorem (the identification of shear-free null congruences, in Minkowski space, with the zeros of holomorphic functions of three variables) and an asymptotic version of the Kerr theorem that produces regular asymptotically shear-free null geodesic congruences in arbitrary asymptotically flat Einstein or Einstein-Maxwell spacetimes. A surprising aspect of this work is the role played by analytic curves in H-space, each curve generating an asymptotically flat null geodesic congruence. Also there is a discussion of the physical space realizations of the two associated five- and three-dimensional CR manifolds

Asymptotic integration of differential and difference equations

CERN Document Server

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...

Landau-Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols

Science.gov (United States)

Novelli, Anna; Belzig, Wolfgang; Nitzan, Abraham

2015-01-01

The time evolution and the asymptotic outcome of a Landau-Zener-Stueckelberg-Majorana (LZ) process under continuous weak non-selective measurement is analyzed. We compare two measurement protocols in which the populations of either the adiabatic or the non-adiabatic levels are (continuously and weakly) monitored. The weak measurement formalism, described using a Gaussian Kraus operator, leads to a time evolution characterized by a Markovian dephasing process, which, in the non-adiabatic measurement protocol is similar to earlier studies of LZ dynamics in a dephasing environment. Casting the problem in the language of measurement theory makes it possible for us to compare diabatic and adiabatic measurement scenarios, to consider engineered dephasing as a control device and to examine the manifestation of the Zeno effect under the different measurement protocols. In particular, under measurement of the non-adiabatic populations, the Zeno effect is manifested not as a freezing of the measured system in its initial state, but rather as an approach to equal asymptotic populations of the two diabatic states. This behavior can be traced to the way by which the weak measurement formalism behaves in the strong measurement limit, with a built-in relationship between measurement time and strength.

Asymptotic behaviour of Feynman integrals

International Nuclear Information System (INIS)

Bergere, M.C.

1980-01-01

In these lecture notes, we describe how to obtain the asymptotic behaviour of Feynman amplitudes; this technique has been already applied in several cases, but the general solution for any kind of asymptotic behaviour has not yet been found. From the mathematical point of view, the problem to solve is close to the following problem: find the asymptotic expansion at large lambda of the integral ∫...∫ [dx] esup(-LambdaP[x]) where P[x] is a polynomial of several variables. (orig.)

Nonminimal hints for asymptotic safety

Science.gov (United States)

Eichhorn, Astrid; Lippoldt, Stefan; Skrinjar, Vedran

2018-01-01

In the asymptotic-safety scenario for gravity, nonzero interactions are present in the ultraviolet. This property should also percolate into the matter sector. Symmetry-based arguments suggest that nonminimal derivative interactions of scalars with curvature tensors should therefore be present in the ultraviolet regime. We perform a nonminimal test of the viability of the asymptotic-safety scenario by working in a truncation of the renormalization group flow, where we discover the existence of an interacting fixed point for a corresponding nonminimal coupling. The back-coupling of such nonminimal interactions could in turn destroy the asymptotically safe fixed point in the gravity sector. As a key finding, we observe nontrivial indications of stability of the fixed-point properties under the impact of nonminimal derivative interactions, further strengthening the case for asymptotic safety in gravity-matter systems.

Site-disorder driven superconductor–insulator transition: a dynamical mean field study

International Nuclear Information System (INIS)

Kamar, Naushad Ahmad; Vidhyadhiraja, N S

2014-01-01

We investigate the effect of site disorder on the superconducting state in the attractive Hubbard model within the framework of dynamical mean field theory. For a fixed interaction strength (U), the superconducting order parameter decreases monotonically with increasing disorder (x), while the single-particle spectral gap decreases for small x, reaches a minimum and keeps increasing for larger x. Thus, the system remains gapped beyond the destruction of the superconducting state, indicating a disorder-driven superconductor–insulator transition. We investigate this transition in depth considering the effects of weak and strong disorder for a range of interaction strengths. In the clean case, the order parameter is known to increase monotonically with increasing interaction, saturating at a finite value asymptotically for U→∞. The presence of disorder results in destruction of superconductivity at large U, thus drastically modifying the clean case behaviour. A physical understanding of our findings is obtained by invoking particle–hole asymmetry and the probability distributions of the order parameter and spectral gap. (paper)

Asymptotic functions and multiplication of distributions

International Nuclear Information System (INIS)

Todorov, T.D.

1979-01-01

Considered is a new type of generalized asymptotic functions, which are not functionals on some space of test functions as the Schwartz distributions. The definition of the generalized asymptotic functions is given. It is pointed out that in future the particular asymptotic functions will be used for solving some topics of quantum mechanics and quantum theory

An asymptotically consistent approximant for the equatorial bending angle of light due to Kerr black holes

International Nuclear Information System (INIS)

Barlow, Nathaniel S; Faber, Joshua A; Weinstein, Steven J

2017-01-01

An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary spin. This expression is constructed by assuring that the weak- and strong-deflection limits are explicitly satisfied while maintaining accuracy at intermediate values of impact parameter via the method of asymptotic approximants (Barlow et al 2017 Q. J. Mech. Appl. Math . 70 21–48). To this end, the strong deflection limit for a prograde orbit around an extremal black hole is examined, and the full non-vanishing asymptotic behavior is determined. The derived approximant may be an attractive alternative to computationally expensive elliptical integrals used in black hole simulations. (paper)

Weak disorder asymptotics in the stochastic mean-field model of distance

NARCIS (Netherlands)

Bhamidi, S.; Hofstad, van der R.W.

2010-01-01

In the recent past, there has been a concerted effort to develop mathematical models for real-world networks and analyze various dynamics on these models. One particular problem of significant importance is to understand the effect of random edge lengths or costs on the geometry and flow

Weak disorder asymptotics in the stochastic mean-field model of distance

NARCIS (Netherlands)

Bhamidi, S.; Hofstad, van der R.W.

2012-01-01

In the recent past, there has been a concerted effort to develop mathematical models for real-world networks and to analyze various dynamics on these models. One particular problem of significant importance is to understand the effect of random edge lengths or costs on the geometry and flow

Superdiffusive transport and energy localization in disordered granular crystals

Science.gov (United States)

Martínez, Alejandro J.; Kevrekidis, P. G.; Porter, Mason A.

2016-02-01

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to differ fundamentally from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder—an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements)—and for two types of initial conditions (displacement excitations and velocity excitations). We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics depend strongly on the type of initial condition. In particular, for displacement excitations, the long-time asymptotic behavior of the second moment m˜2 of the energy has oscillations that depend on the type of disorder, with a complex trend that differs markedly from a power law and which is particularly evident for an Anderson-like disorder. By contrast, for velocity excitations, we find that a standard scaling m˜2˜tγ (for some constant γ ) applies for all three types of disorder. For weakly precompressed (i.e., strongly nonlinear) chains, m˜2 and the inverse participation ratio P-1 satisfy scaling relations m˜2˜tγ and P-1˜t-η , and the dynamics is superdiffusive for all of the cases that we consider. Additionally, when precompression is strong, the inverse participation ratio decreases slowly (with η disorder, and the dynamics leads to a partial localization around the core and the leading edge of a propagating wave packet. For an Anderson-like disorder, displacement perturbations lead to localization of energy primarily in the core, and velocity perturbations cause the energy to be divided between the core and the leading edge. This localization phenomenon does not occur in the sonic-vacuum regime, which yields the surprising result that the energy is no longer

A ferromagnetic chain in a random weak field

Science.gov (United States)

Avgin, I.

1996-10-01

The harmonic magnon modes in a Heisenberg ferromagnetic chain in a random weak field are studied. The Lyapunov exponent for the uniform ( k = 0) mode is computed using the coherent potential approximation (CPA) in the weak-disorder limit. The CPA results are compared with the numerical and weak-disorder expansions of various random systems. We have found that the inverse localization length and the integrated density of states have anomalous power law behaviour as reported earlier. The CPA also reproduces the dispersion law for the same system, calculated by Pimentel and Stinchcombe using the real space renormalization scaling technique. A brief comment is also made for the uniform weak-field case.

Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces

Directory of Open Access Journals (Sweden)

Juguo Su

2012-01-01

Full Text Available The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.

Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex Nonlinearity

Directory of Open Access Journals (Sweden)

Antonio Olivas Martinez

2009-01-01

Full Text Available We consider the Riemann problem for the Hopf equation with concave-convex flux functions. Applying the weak asymptotics method we construct a uniform in time description for the Cauchy data evolution and show that the use of this method implies automatically the appearance of the Oleinik E-condition.

Scaling versus asymptotic scaling in the non-linear σ-model in 2D. Continuum version

International Nuclear Information System (INIS)

Flyvbjerg, H.

1990-01-01

The two-point function of the O(N)-symmetric non-linear σ-model in two dimensions is large-N expanded and renormalized, neglecting terms of O(1/N 2 ). At finite cut-off, universal, analytical expressions relate the magnetic susceptibility and the dressed mass to the bare coupling. Removing the cut-off, a similar relation gives the renormalized coupling as a function of the mass gap. In the weak-coupling limit these relations reproduce the results of renormalization group improved weak-coupling perturbation theory to two-loop order. The constant left unknown, when the renormalization group is integrated, is determined here. The approach to asymptotic scaling is studied for various values of N. (orig.)

Weak chaos in the disordered nonlinear Schroedinger chain: Destruction of Anderson localization by Arnold diffusion

International Nuclear Information System (INIS)

Basko, D.M.

2011-01-01

Research highlights: → In a one-dimensional disordered chain of oscillators all normal modes are localized. → Nonlinearity leads to chaotic dynamics. → Chaos is concentrated on rare chaotic spots. → Chaotic spots drive energy exchange between oscillators. → Macroscopic transport coefficients are obtained. - Abstract: The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of equilibration at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The corresponding macroscopic transport equations are obtained.

Landau–Zener evolution under weak measurement: manifestation of the Zeno effect under diabatic and adiabatic measurement protocols

International Nuclear Information System (INIS)

Novelli, Anna; Belzig, Wolfgang; Nitzan, Abraham

2015-01-01

The time evolution and the asymptotic outcome of a Landau–Zener–Stueckelberg–Majorana (LZ) process under continuous weak non-selective measurement is analyzed. We compare two measurement protocols in which the populations of either the adiabatic or the non-adiabatic levels are (continuously and weakly) monitored. The weak measurement formalism, described using a Gaussian Kraus operator, leads to a time evolution characterized by a Markovian dephasing process, which, in the non-adiabatic measurement protocol is similar to earlier studies of LZ dynamics in a dephasing environment. Casting the problem in the language of measurement theory makes it possible for us to compare diabatic and adiabatic measurement scenarios, to consider engineered dephasing as a control device and to examine the manifestation of the Zeno effect under the different measurement protocols. In particular, under measurement of the non-adiabatic populations, the Zeno effect is manifested not as a freezing of the measured system in its initial state, but rather as an approach to equal asymptotic populations of the two diabatic states. This behavior can be traced to the way by which the weak measurement formalism behaves in the strong measurement limit, with a built-in relationship between measurement time and strength. (paper)

Turbulence of Weak Gravitational Waves in the Early Universe.

Science.gov (United States)

Galtier, Sébastien; Nazarenko, Sergey V

2017-12-01

We study the statistical properties of an ensemble of weak gravitational waves interacting nonlinearly in a flat space-time. We show that the resonant three-wave interactions are absent and develop a theory for four-wave interactions in the reduced case of a 2.5+1 diagonal metric tensor. In this limit, where only plus-polarized gravitational waves are present, we derive the interaction Hamiltonian and consider the asymptotic regime of weak gravitational wave turbulence. Both direct and inverse cascades are found for the energy and the wave action, respectively, and the corresponding wave spectra are derived. The inverse cascade is characterized by a finite-time propagation of the metric excitations-a process similar to an explosive nonequilibrium Bose-Einstein condensation, which provides an efficient mechanism to ironing out small-scale inhomogeneities. The direct cascade leads to an accumulation of the radiation energy in the system. These processes might be important for understanding the early Universe where a background of weak nonlinear gravitational waves is expected.

Peripheral facial weakness (Bell's palsy).

Science.gov (United States)

Basić-Kes, Vanja; Dobrota, Vesna Dermanović; Cesarik, Marijan; Matovina, Lucija Zadro; Madzar, Zrinko; Zavoreo, Iris; Demarin, Vida

2013-06-01

Peripheral facial weakness is a facial nerve damage that results in muscle weakness on one side of the face. It may be idiopathic (Bell's palsy) or may have a detectable cause. Almost 80% of peripheral facial weakness cases are primary and the rest of them are secondary. The most frequent causes of secondary peripheral facial weakness are systemic viral infections, trauma, surgery, diabetes, local infections, tumor, immune disorders, drugs, degenerative diseases of the central nervous system, etc. The diagnosis relies upon the presence of typical signs and symptoms, blood chemistry tests, cerebrospinal fluid investigations, nerve conduction studies and neuroimaging methods (cerebral MRI, x-ray of the skull and mastoid). Treatment of secondary peripheral facial weakness is based on therapy for the underlying disorder, unlike the treatment of Bell's palsy that is controversial due to the lack of large, randomized, controlled, prospective studies. There are some indications that steroids or antiviral agents are beneficial but there are also studies that show no beneficial effect. Additional treatments include eye protection, physiotherapy, acupuncture, botulinum toxin, or surgery. Bell's palsy has a benign prognosis with complete recovery in about 80% of patients, 15% experience some mode of permanent nerve damage and severe consequences remain in 5% of patients.

Chiral symmetry breaking in asymptotically free and non-asymptotically free gauge theories

International Nuclear Information System (INIS)

Gusynin, V.P.; Miranskij, V.A.

1986-01-01

An essential distinction in the realization of the PCAC-dynamics in vector-like asymptotically free and non-asymptotically free (with a non-trival ultraviolet stable fixed point) gauge theories is revealed. For the latter theories an analytical expression for the condensate is obtained in the two-loop approximation and the arguments in support of a soft behaviour at small distances of composite operators are given. The problem of factorizing the low-energy region for the Wess-Zumino-Witten action is discussed

Weak Localisation in Clean and Highly Disordered Graphene

International Nuclear Information System (INIS)

Hilke, Michael; Massicotte, Mathieu; Whiteway, Eric; Yu, Victor

2013-01-01

We look at the magnetic field induced weak localisation peak of graphene samples with different mobilities. At very low temperatures, low mobility samples exhibit a very broad peak as a function of the magnetic field, in contrast to higher mobility samples, where the weak localisation peak is very sharp. We analyze the experimental data in the context of the localisation length, which allows us to extract, both the localisation length and the phase coherence length of the samples, regardless of their mobilities. This analysis is made possible by the observation that the localisation length undergoes a generic weak localisation dependence with striking universal properties

Journal Afrika Statistika ISSN 0852-0305 Asymptotic representation ...

African Journals Online (AJOL)

Asymptotic representation theorems for poverty indices ... Statistical asymptotic laws for these indices, particularly asymptotic normality, on which statistical inference on the ... population of individuals, each of which having a random income or ...

Asymptotic safety, emergence and minimal length

International Nuclear Information System (INIS)

Percacci, Roberto; Vacca, Gian Paolo

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 sense in which asymptotic safety implies a minimal length. In doing so we also discuss possible signatures of asymptotic safety in scattering experiments.

Perils of Asymptotics

International Nuclear Information System (INIS)

Dewar, R. L.

1995-01-01

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

Asymptotic Poincare lemma and its applications

International Nuclear Information System (INIS)

Ziolkowski, R.W.; Deschamps, G.A.

1984-01-01

An asymptotic version of Poincare's lemma is defined and solutions are obtained with the calculus of exterior differential forms. They are used to construct the asymptotic approximations of multidimensional oscillatory integrals whose forms are commonly encountered, for example, in electromagnetic problems. In particular, the boundary and stationary point evaluations of these integrals are considered. The former is applied to the Kirchhoff representation of a scalar field diffracted through an aperture and simply recovers the Maggi-Rubinowicz-Miyamoto-Wolf results. Asymptotic approximations in the presence of other (standard) critical points are also discussed. Techniques developed for the asymptotic Poincare lemma are used to generate a general representation of the Leray form. All of the (differential form) expressions presented are generalizations of known (vector calculus) results. 14 references, 4 figures

Renormalization group and asymptotic freedom

International Nuclear Information System (INIS)

Morris, J.R.

1978-01-01

Several field theoretic models are presented which allow exact expressions of the renormalization constants and renormalized coupling constants. These models are analyzed as to their content of asymptotic free field behavior through the use of the Callan-Symanzik renormalization group equation. It is found that none of these models possesses asymptotic freedom in four dimensions

Weak disorder expansion of the invariant measure for the one-dimensional Anderson model

International Nuclear Information System (INIS)

Bovier, A.; Klein, A.

1988-01-01

We show that the formal perturbation expansion of the invariant measure for the Anderson model in one dimension has singularities at all energies E 0 = 2 cos π(p/q); we derive a modified expansion near these energies that we show to have finite coefficients to all orders. Moreover, we show that the first q - 3 of them coincide with those of the naive expansion, while there is an anomaly in the (q - 2)th term. This also gives a weak disorder expansion for the Liapunov exponent and for the density of states. This generalizes previous results of Kappus and Wegner and of Derrida and Gardner

Conductivity of Weakly Disordered Metals Close to a "Ferromagnetic" Quantum Critical Point

Science.gov (United States)

Kastrinakis, George

2018-05-01

We calculate analytically the conductivity of weakly disordered metals close to a "ferromagnetic" quantum critical point in the low-temperature regime. Ferromagnetic in the sense that the effective carrier potential V(q,ω ), due to critical fluctuations, is peaked at zero momentum q=0. Vertex corrections, due to both critical fluctuations and impurity scattering, are explicitly considered. We find that only the vertex corrections due to impurity scattering, combined with the self-energy, generate appreciable effects as a function of the temperature T and the control parameter a, which measures the proximity to the critical point. Our results are consistent with resistivity experiments in several materials displaying typical Fermi liquid behaviour, but with a diverging prefactor of the T^2 term for small a.

Asymptotics of Laplace-Dirichlet integrals

International Nuclear Information System (INIS)

Kozlov, S.M.

1990-01-01

Here we consider the problem of the asymptotic expansion of the Laplace-Dirichlet integral. In homogenization theory such an integral represents the energy, and in general depends on the cohomology class. Here the asymptotic behaviour of this integral is found. The full text will appear in Functional Analysis and Applications, 1990, No.2. (author). 3 refs

Time-asymptotic interaction of flocking particles and an incompressible viscous fluid

International Nuclear Information System (INIS)

Bae, Hyeong-Ohk; Choi, Young-Pil; Ha, Seung-Yeal; Kang, Moon-Jin

2012-01-01

We present a new coupled kinetic-fluid model for the interactions between Cucker–Smale (C–S) flocking particles and incompressible fluid on the periodic spatial domain T d . Our coupled system consists of the kinetic C–S equation and the incompressible Navier–Stokes equations, and these two systems are coupled through the drag force. For the proposed model, we provide a global existence of weak solutions and a priori time-asymptotic exponential flocking estimates for any smooth flow, when the kinematic viscosity of the fluid is sufficiently large. The velocity of individual C–S particles and fluid velocity tend to the averaged time-dependent particle velocities exponentially fast

Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions

International Nuclear Information System (INIS)

Huveneers, François

2013-01-01

We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter ϵ > 0. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in ϵ as ϵ → 0. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz (2008 Phys. Rev. Lett. 100 134301), and to a classic spin chain recently investigated by Oganesyan, Pal and Huse (2009 Phys. Rev. B 80 115104). (paper)

Asymptotic conditions and conserved quantities

International Nuclear Information System (INIS)

Koul, R.K.

1990-01-01

Two problems have been investigated in this dissertation. The first one deals with the relationship between stationary space-times which are flat at null infinity and stationary space-times which are asymptotic flat at space-like infinity. It is shown that the stationary space-times which are asymptotically flat, in the Penrose sense, at null infinity, are asymptotically flat at space-like infinity in the Geroch sense and metric at space like infinity is at least C 1 . In the converse it is shown that the stationary space-times which are asymptotically flat at space like infinity, in the Beig sense, are asymptotically flat at null infinity in the Penrose sense. The second problem addressed deals with the theories of arbitrary dimensions. The theories treated are the ones which have fiber bundle structure, outside some compact region. For these theories the criterion for the choice of the background metric is specified, and the boundary condition for the initial data set (q ab , P ab ) is given in terms of the background metric. Having these boundary conditions it is shown that the symplectic structure and the constraint functionals are well defined. The conserved quantities associated with internal Killing vector fields are specified. Lastly the energy relative to a fixed background and the total energy of the theory have been given. It is also shown that the total energy of the theory is independent of the choice of the background

Trinucleon asymptotic normalization constants including Coulomb effects

International Nuclear Information System (INIS)

Friar, J.L.; Gibson, B.F.; Lehman, D.R.; Payne, G.L.

1982-01-01

Exact theoretical expressions for calculating the trinucleon S- and D-wave asymptotic normalization constants, with and without Coulomb effects, are presented. Coordinate-space Faddeev-type equations are used to generate the trinucleon wave functions, and integral relations for the asymptotic norms are derived within this framework. The definition of the asymptotic norms in the presence of the Coulomb interaction is emphasized. Numerical calculations are carried out for the s-wave NN interaction models of Malfliet and Tjon and the tensor force model of Reid. Comparison with previously published results is made. The first estimate of Coulomb effects for the D-wave asymptotic norm is given. All theoretical values are carefully compared with experiment and suggestions are made for improving the experimental situation. We find that Coulomb effects increase the 3 He S-wave asymptotic norm by less than 1% relative to that of 3 H, that Coulomb effects decrease the 3 He D-wave asymptotic norm by approximately 8% relative to that of 3 H, and that the distorted-wave Born approximation D-state parameter, D 2 , is only 1% smaller in magnitude for 3 He than for 3 H due to compensating Coulomb effects

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

Directory of Open Access Journals (Sweden)

G. M. N’Guérékata

2018-01-01

Full Text Available The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.

The limits of weak selection and large population size in evolutionary game theory.

Science.gov (United States)

Sample, Christine; Allen, Benjamin

2017-11-01

Evolutionary game theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two limits are both mathematically convenient and biologically relevant: weak selection and large population size. These limits can be combined in different ways, leading to potentially different results. We consider two orderings: the [Formula: see text] limit, in which weak selection is applied before the large population limit, and the [Formula: see text] limit, in which the order is reversed. Formal mathematical definitions of the [Formula: see text] and [Formula: see text] limits are provided. Applying these definitions to the Moran process of evolutionary game theory, we obtain asymptotic expressions for fixation probability and conditions for success in these limits. We find that the asymptotic expressions for fixation probability, and the conditions for a strategy to be favored over a neutral mutation, are different in the [Formula: see text] and [Formula: see text] limits. However, the ordering of limits does not affect the conditions for one strategy to be favored over another.

On maximal surfaces in asymptotically flat space-times

International Nuclear Information System (INIS)

Bartnik, R.; Chrusciel, P.T.; O Murchadha, N.

1990-01-01

Existence of maximal and 'almost maximal' hypersurfaces in asymptotically flat space-times is established under boundary conditions weaker than those considered previously. We show in particular that every vacuum evolution of asymptotically flat data for Einstein equations can be foliated by slices maximal outside a spatially compact set and that every (strictly) stationary asymptotically flat space-time can be foliated by maximal hypersurfaces. Amongst other uniqueness results, we show that maximal hypersurface can be used to 'partially fix' an asymptotic Poincare group. (orig.)

On asymptotic continuity of functions of quantum states

International Nuclear Information System (INIS)

Synak-Radtke, Barbara; Horodecki, Michal

2006-01-01

A useful kind of continuity of quantum states functions in asymptotic regime is so-called asymptotic continuity. In this letter, we provide general tools for checking if a function possesses this property. First we prove equivalence of asymptotic continuity with so-called robustness under admixture. This allows us to show that relative entropy distance from a convex set including a maximally mixed state is asymptotically continuous. Subsequently, we consider arrowing-a way of building a new function out of a given one. The procedure originates from constructions of intrinsic information and entanglement of formation. We show that arrowing preserves asymptotic continuity for a class of functions (so-called subextensive ones). The result is illustrated by means of several examples. (letter to the editor)

Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

Science.gov (United States)

Böttcher, A.; Bogoya, J. M.; Grudsky, S. M.; Maximenko, E. A.

2017-11-01

Analysis of the asymptotic behaviour of the spectral characteristics of Toeplitz matrices as the dimension of the matrix tends to infinity has a history of over 100 years. For instance, quite a number of versions of Szegő's theorem on the asymptotic behaviour of eigenvalues and of the so-called strong Szegő theorem on the asymptotic behaviour of the determinants of Toeplitz matrices are known. Starting in the 1950s, the asymptotics of the maximum and minimum eigenvalues were actively investigated. However, investigation of the individual asymptotics of all the eigenvalues and eigenvectors of Toeplitz matrices started only quite recently: the first papers on this subject were published in 2009-2010. A survey of this new field is presented here. Bibliography: 55 titles.

Qualitative and Asymptotic Theory of Detonations

KAUST Repository

Faria, Luiz

2014-11-09

Shock waves in reactive media possess very rich dynamics: from formation of cells in multiple dimensions to oscillating shock fronts in one-dimension. Because of the extreme complexity of the equations of combustion theory, most of the current understanding of unstable detonation waves relies on extensive numerical simulations of the reactive compressible Euler/Navier-Stokes equations. Attempts at a simplified theory have been made in the past, most of which are very successful in describing steady detonation waves. In this work we focus on obtaining simplified theories capable of capturing not only the steady, but also the unsteady behavior of detonation waves. The first part of this thesis is focused on qualitative theories of detonation, where ad hoc models are proposed and analyzed. We show that equations as simple as a forced Burgers equation can capture most of the complex phenomena observed in detonations. In the second part of this thesis we focus on rational theories, and derive a weakly nonlinear model of multi-dimensional detonations. We also show, by analysis and numerical simulations, that the asymptotic equations provide good quantitative predictions.

Asymptotic variance of grey-scale surface area estimators

DEFF Research Database (Denmark)

Svane, Anne Marie

Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in isotropic and sufficiently smooth settings, resulting...... in a general asymptotic bound. For compact convex sets with nowhere vanishing Gaussian curvature, the asymptotics can be described more explicitly. As in the case of volume estimators, the variance is decomposed into a lattice sum and an oscillating term of at most the same magnitude....

On the asymptotic ergodic capacity of FSO links with generalized pointing error model

KAUST Repository

Al-Quwaiee, Hessa

2015-09-11

Free-space optical (FSO) communication systems are negatively affected by two physical phenomenon, namely, scintillation due to atmospheric turbulence and pointing errors. To quantize the effect of these two factors on FSO system performance, we need an effective mathematical model for them. Scintillations are typically modeled by the log-normal and Gamma-Gamma distributions for weak and strong turbulence conditions, respectively. In this paper, we propose and study a generalized pointing error model based on the Beckmann distribution. We then derive the asymptotic ergodic capacity of FSO systems under the joint impact of turbulence and generalized pointing error impairments. © 2015 IEEE.

Critical Correlation Functions for the 4-Dimensional Weakly Self-Avoiding Walk and n-Component {|\\varphi|^4} Model

Science.gov (United States)

Slade, Gordon; Tomberg, Alexandre

2016-03-01

We extend and apply a rigorous renormalisation group method to study critical correlation functions, on the 4-dimensional lattice Z4, for the weakly coupled n-component {|\\varphi|4} spin model for all {n ≥ 1}, and for the continuous-time weakly self-avoiding walk. For the {|\\varphi|4} model, we prove that the critical two-point function has | x|-2 (Gaussian) decay asymptotically, for {n ≥ 1}. We also determine the asymptotic decay of the critical correlations of the squares of components of {\\varphi}, including the logarithmic corrections to Gaussian scaling, for {n ≥ 1}. The above extends previously known results for n = 1 to all {n ≥ 1}, and also observes new phenomena for n > 1, all with a new method of proof. For the continuous-time weakly self-avoiding walk, we determine the decay of the critical generating function for the "watermelon" network consisting of p weakly mutually- and self-avoiding walks, for all {p ≥ 1}, including the logarithmic corrections. This extends a previously known result for p = 1, for which there is no logarithmic correction, to a much more general setting. In addition, for both models, we study the approach to the critical point and prove the existence of logarithmic corrections to scaling for certain correlation functions. Our method gives a rigorous analysis of the weakly self-avoiding walk as the n = 0 case of the {|\\varphi|4} model, and provides a unified treatment of both models, and of all the above results.

Inhomogeneous quasi-adiabatic driving of quantum critical dynamics in weakly disordered spin chains

International Nuclear Information System (INIS)

Rams, Marek M; Mohseni, Masoud; Campo, Adolfo del

2016-01-01

We introduce an inhomogeneous protocol to drive a weakly disordered quantum spin chain quasi-adiabatically across a quantum phase transition and minimize the residual energy of the final state. The number of spins that simultaneously reach the critical point is controlled by the length scale in which the magnetic field is modulated, introducing an effective size that favors adiabatic dynamics. The dependence of the residual energy on this length scale and the velocity at which the magnetic field sweeps out the chain is shown to be nonmonotonic. We determine the conditions for an optimal suppression of the residual energy of the final state and show that inhomogeneous driving can outperform conventional adiabatic schemes based on homogeneous control fields by several orders of magnitude. (paper)

Asymptotic Conservation Laws in Classical Field Theory

International Nuclear Information System (INIS)

Anderson, I.M.; Torre, C.G.

1996-01-01

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity. copyright 1996 The American Physical Society

Asymptotic symmetries, holography and topological hair

Science.gov (United States)

Mishra, Rashmish K.; Sundrum, Raman

2018-01-01

Asymptotic symmetries of AdS4 quantum gravity and gauge theory are derived by coupling the holographically dual CFT3 to Chern-Simons gauge theory and 3D gravity in a "probe" (large-level) limit. Despite the fact that the three-dimensional AdS4 boundary as a whole is consistent with only finite-dimensional asymptotic symmetries, given by AdS isometries, infinite-dimensional symmetries are shown to arise in circumstances where one is restricted to boundary subspaces with effectively two-dimensional geometry. A canonical example of such a restriction occurs within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS4 quantum gravity. An AdS4 analog of Minkowski "super-rotation" asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT2 structure (in a large central charge limit), via AdS3 foliation of AdS4 and the AdS3/CFT2 correspondence. The maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D gravities have Chern-Simons formulation, manifesting their topological character. Chern-Simons structure is also shown to be emergent in the Poincare patch of AdS4, as soft/boundary limits of 4D gauge theory, rather than "put in by hand" as an external probe. This results in a finite effective Chern-Simons level. Several of the considerations of asymptotic symmetry structure are found to be simpler for AdS4 than for Mink4, such as non-zero 4D particle masses, 4D non-perturbative "hard" effects, and consistency with unitarity. The last of these in particular is greatly simplified because in some set-ups the time dimension is explicitly shared by each level of description: Lorentzian AdS4, CFT3 and CFT2. Relatedly, the CFT2 structure clarifies the sense in which the infinite asymptotic charges constitute a useful form of "hair" for black holes and other complex 4D states. An AdS4 analog of Minkowski "memory" effects is derived, but with late-time memory of earlier events being replaced by (holographic) "shadow" effects. Lessons

ASYMPTOTICS OF a PARTICLES TRANSPORT PROBLEM

Directory of Open Access Journals (Sweden)

Kuzmina Ludmila Ivanovna

2017-11-01

Full Text Available Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.

Asymptotic work distributions in driven bistable systems

International Nuclear Information System (INIS)

Nickelsen, D; Engel, A

2012-01-01

The asymptotic tails of the probability distributions of thermodynamic quantities convey important information about the physics of nanoscopic systems driven out of equilibrium. We apply a recently proposed method to analytically determine the asymptotics of work distributions in Langevin systems to an one-dimensional model of single-molecule force spectroscopy. The results are in excellent agreement with numerical simulations, even in the centre of the distributions. We compare our findings with a recent proposal for an universal form of the asymptotics of work distributions in single-molecule experiments.

Large gauge symmetries and asymptotic states in QED

Energy Technology Data Exchange (ETDEWEB)

Gabai, Barak; Sever, Amit [School of Physics and Astronomy, Tel Aviv University,Ramat Aviv 69978 (Israel)

2016-12-19

Large Gauge Transformations (LGT) are gauge transformations that do not vanish at infinity. Instead, they asymptotically approach arbitrary functions on the conformal sphere at infinity. Recently, it was argued that the LGT should be treated as an infinite set of global symmetries which are spontaneously broken by the vacuum. It was established that in QED, the Ward identities of their induced symmetries are equivalent to the Soft Photon Theorem. In this paper we study the implications of LGT on the S-matrix between physical asymptotic states in massive QED. In appose to the naively free scattering states, physical asymptotic states incorporate the long range electric field between asymptotic charged particles and were already constructed in 1970 by Kulish and Faddeev. We find that the LGT charge is independent of the particles’ momenta and may be associated to the vacuum. The soft theorem’s manifestation as a Ward identity turns out to be an outcome of not working with the physical asymptotic states.

Asymptotic analysis and boundary layers

CERN Document Server

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 results for the semi-Markovian random walk with delay

International Nuclear Information System (INIS)

Khaniyev, T.A.; Aliyev, R.T.

2006-12-01

In this study, the semi-Markovian random walk with a discrete interference of chance (X(t) ) is considered and under some weak assumptions the ergodicity of this process is discussed. Characteristic function of the ergodic distribution of X(t) is expressed by means of the probability characteristics of the boundary functionals (N,S N ). Some exact formulas for first and second moments of ergodic distribution of the process X(t) are obtained when the random variable ζ 1 - s, which is describing a discrete interference of chance, has Gamma distribution on the interval [0, ∞) with parameter (α,λ) . Based on these results, the asymptotic expansions with three terms for the first two moments of the ergodic distribution of the process X(t) are obtained, as λ → 0. (author)

Asymptotic theory for regressions with smoothly changing parameters

DEFF Research Database (Denmark)

Hillebrand, Eric; Medeiros, Marcelo; Xu, Junyue

2013-01-01

We derive asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual pT-rate and has...... an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data....

Large Deviations and Asymptotic Methods in Finance

CERN Document Server

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...

A quantum kinematics for asymptotically flat gravity

Science.gov (United States)

Campiglia, Miguel; Varadarajan, Madhavan

2015-07-01

We construct a quantum kinematics for asymptotically flat gravity based on the Koslowski-Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying loop quantum gravity (LQG) which supports, in addition to the usual LQG operators, the action of ‘background exponential operators’, which are connection dependent operators labelled by ‘background’ su(2) electric fields. KS states have, in addition to the LQG state label corresponding to one dimensional excitations of the triad, a label corresponding to a ‘background’ electric field that describes three dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields that label the states and the background electric fields that label the operators. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We show that KS states can be realised as wave functions on a quantum configuration space of generalized connections and that the asymptotic behaviour of each such generalized connection is determined by that of the background electric fields which label the background exponential operators. Similar to the spatially compact case, the Gauss law and diffeomorphism constraints are then imposed through group averaging techniques to obtain a large sector of gauge invariant states. It is shown that this sector supports a unitary action of the group of asymptotic rotations and translations and that, as anticipated by Friedman and Sorkin, for appropriate spatial topology, this sector contains states that display fermionic behaviour under 2π rotations.

Asymptotic evolution of quantum Markov chains

Energy Technology Data Exchange (ETDEWEB)

Novotny, Jaroslav [FNSPE, CTU in Prague, 115 19 Praha 1 - Stare Mesto (Czech Republic); Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)

2012-07-01

The iterated quantum operations, so called quantum Markov chains, play an important role in various branches of physics. They constitute basis for many discrete models capable to explore fundamental physical problems, such as the approach to thermal equilibrium, or the asymptotic dynamics of macroscopic physical systems far from thermal equilibrium. On the other hand, in the more applied area of quantum technology they also describe general characteristic properties of quantum networks or they can describe different quantum protocols in the presence of decoherence. A particularly, an interesting aspect of these quantum Markov chains is their asymptotic dynamics and its characteristic features. We demonstrate there is always a vector subspace (typically low-dimensional) of so-called attractors on which the resulting superoperator governing the iterative time evolution of quantum states can be diagonalized and in which the asymptotic quantum dynamics takes place. As the main result interesting algebraic relations are presented for this set of attractors which allow to specify their dual basis and to determine them in a convenient way. Based on this general theory we show some generalizations concerning the theory of fixed points or asymptotic evolution of random quantum operations.

Criteria for exponential asymptotic stability in the large of ...

African Journals Online (AJOL)

The purpose of this study is to provide necessary and sufficient conditions for exponential asymptotic stability in the large and uniform asymptotic stability of perturbations of linear systems with unbounded delays. A strong relationship is established between the two types of asymptotic stability. It is found that if the ...

Asymptotic Theory for Regressions with Smoothly Changing Parameters

DEFF Research Database (Denmark)

Hillebrand, Eric Tobias; Medeiros, Marcelo C.; Xu, Junyue

We derive asymptotic properties of the quasi maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual square-root-of-T rate...... and has an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data....

Asymptotic expansion of the Keesom integral

International Nuclear Information System (INIS)

Abbott, Paul C

2007-01-01

The asymptotic evaluation and expansion of the Keesom integral, K(a), is discussed at some length in Battezzati and Magnasco (2004 J. Phys. A: Math. Gen. 37 9677; 2005 J. Phys. A: Math. Gen. 38 6715). Here, using standard identities, it is shown that this triple integral can be reduced to a single integral from which the asymptotic behaviour is readily obtained using Laplace's method. (comment)

AGB [asymptotic giant branch]: Star evolution

International Nuclear Information System (INIS)

Becker, S.A.

1987-01-01

Asymptotic giant branch stars are red supergiant stars of low-to-intermediate mass. This class of stars is of particular interest because many of these stars can have nuclear processed material brought up repeatedly from the deep interior to the surface where it can be observed. A review of recent theoretical and observational work on stars undergoing the asymptotic giant branch phase is presented. 41 refs

Wijsman Orlicz Asymptotically Ideal -Statistical Equivalent Sequences

Directory of Open Access Journals (Sweden)

Bipan Hazarika

2013-01-01

in Wijsman sense and present some definitions which are the natural combination of the definition of asymptotic equivalence, statistical equivalent, -statistical equivalent sequences in Wijsman sense. Finally, we introduce the notion of Cesaro Orlicz asymptotically -equivalent sequences in Wijsman sense and establish their relationship with other classes.

Asymptotic geometric analysis, part I

CERN Document Server

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

Interplay between short-range correlated disorder and Coulomb interaction in nodal-line semimetals

Science.gov (United States)

Wang, Yuxuan; Nandkishore, Rahul M.

2017-09-01

In nodal-line semimetals, Coulomb interactions and short-range correlated disorder are both marginal perturbations to the clean noninteracting Hamiltonian. We analyze their interplay using a weak-coupling renormalization group approach. In the clean case, the Coulomb interaction has been found to be marginally irrelevant, leading to Fermi liquid behavior. We extend the analysis to incorporate the effects of disorder. The nodal line structure gives rise to kinematical constraints similar to that for a two-dimensional Fermi surface, which plays a crucial role in the one-loop renormalization of the disorder couplings. For a twofold degenerate nodal loop (Weyl loop), we show that disorder flows to strong coupling along a unique fixed trajectory in the space of symmetry inequivalent disorder couplings. Along this fixed trajectory, all symmetry inequivalent disorder strengths become equal. For a fourfold degenerate nodal loop (Dirac loop), disorder also flows to strong coupling, however, the strengths of symmetry inequivalent disorder couplings remain different. We show that feedback from disorder reverses the sign of the beta function for the Coulomb interaction, causing the Coulomb interaction to flow to strong coupling as well. However, the Coulomb interaction flows to strong coupling asymptotically more slowly than disorder. Extrapolating our results to strong coupling, we conjecture that at low energies nodal line semimetals should be described by a noninteracting nonlinear sigma model. We discuss the relation of our results with possible many-body localization at zero temperatures in such materials.

Approximate |ΔI| = 1/2 rule in K → ππ decays from asymptotic quark-line diagram approach

International Nuclear Information System (INIS)

Terasaki, K.; Oneda, S.

1989-07-01

A general method which copes with both the long and short distance physics aspects of nonleptonic weak interactions in presented. First, the four-point decay amplitude can be expressed in terms of the three-point asymptotic matrix elements of the effective weak Hamiltonian H w , taken between the on-mass-shell single-hadron states with infinite momenta. The study of these matrix elements in terms of the quark-lines in the infinite momentum frame reveals that, for the K → ππ decays, those involving only the ordinary (QQ-bar) mesons do satisfy the strict |ΔI| = 1/2 rule. However, the contribution of the (QQ) (Q-barQ-bar) type exotic mesons leads explicitly to a small violation of the selection rule. (author)

Asymptotic safety guaranteed

DEFF Research Database (Denmark)

Litim, Daniel F.; Sannino, Francesco

2014-01-01

We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet ...

Asymptotics of bivariate generating functions with algebraic singularities

Science.gov (United States)

Greenwood, Torin

Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.

Asymptotic expansions for high-contrast linear elasticity

KAUST Repository

Poveda, Leonardo A.; Huepo, Sebastian; Calo, Victor M.; Galvis, Juan

2015-01-01

We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm. © 2015 Elsevier B.V.

Asymptotic expansions for high-contrast linear elasticity

KAUST Repository

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.

On asymptotic analysis of spectral problems in elasticity

Directory of Open Access Journals (Sweden)

S.A. Nazarov

Full Text Available The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies and the corresponding elastic eigenmodes are constructed and justified. New technicalities of the asymptotic analysis are related to variable coefficients of differential operators, vectorial setting of the problem, and usage of intrinsic integral characteristics of defects. The asymptotic formulae are developed in a form convenient for application in shape optimization and inverse problems.

Theory of weakly nonlinear self-sustained detonations

KAUST Repository

Faria, Luiz

2015-11-03

We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced unsteady small-disturbance transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multidimensional detonations.

Analytical solution for a coaxial plasma gun: Weak coupling limit

International Nuclear Information System (INIS)

Dietz, D.

1987-01-01

The analytical solution of the system of coupled ODE's which describes the time evolution of an ideal (i.e., zero resistance) coaxial plasma gun operating in the snowplow mode is obtained in the weak coupling limit, i.e, when the gun is fully influenced by the driving (RLC) circuit in which it resides but the circuit is negligibly influenced by the gun. Criteria for the validity of this limit are derived and numerical examples are presented. Although others have obtained approximate, asymptotic and numerical solutions of the equations, the present analytical results seem not to have appeared previously in the literature

Asymptotically free SU(5) models

International Nuclear Information System (INIS)

Kogan, Ya.I.; Ter-Martirosyan, K.A.; Zhelonkin, A.V.

1981-01-01

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

8. Asymptotically Flat and Regular Cauchy Data

Science.gov (United States)

Dain, Sergio

I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.

An order-by-disorder process in the cyclic phase of spin-2 condensate with a weak magnetic field

International Nuclear Information System (INIS)

Zheng, Gong-Ping; Xu, Lei-Kuan; Qin, Shuai-Feng; Jian, Wen-Tian; Liang, J.-Q.

2013-01-01

We present in this paper a model study on the “order-by-disorder” process in the cyclic phase of spin-2 condensate, which forms a family of incommensurable, spiral degenerate ground states. On the basis of the ordering mechanism of entropic splitting, it is demonstrated that the energy corrections resulting from quantum fluctuations of disorder lift the accidental degeneracy of the cyclic configurations and thus lead to an eventual spiral order called the cyclic order. The order-by-disorder phenomenon is then realized even if the magnetic field exists. Finally, we show that our theoretic observations can be verified experimentally by direct detection of the cyclic order in the 87 Rb condensate of a spin-2 manifold with a weak magnetic field. -- Highlights: •A model for the order-by-disorder process in the cyclic phase of spin-2 condensate is presented. •The second-order quantum fluctuations of the mean-field states are studied. •The energy corrections lift the accidental degeneracy of the cyclic configurations. •The order-by-disorder phenomenon is realized even if a magnetic field exists. •The theoretic observations can be verified experimentally for 87 Rb condensate

Asymptotics for the Kummer function of Bose plasmas

International Nuclear Information System (INIS)

Kowalenko, V.; Frankel, N.E.

1993-01-01

The asymptotic expansions for the Kummer function obtained in the study of the linear response of magnetised Bose plasmas at T = 0 K are presented for large and small values of its parameter, thereby displaying the function's asymptotic non-uniformity. The large parameter expansion plays a determining role in the behaviour of these Bose systems in the limit that the external magnetic field B →0. This particular expansion is generalised herein and its validity tested by determining the asymptotic expansion for the Hurwitz zeta function. 18 refs., 1 tab., 2 figs

Impact of weak excitatory synapses on chaotic transients in a diffusively coupled Morris-Lecar neuronal network

Energy Technology Data Exchange (ETDEWEB)

Lafranceschina, Jacopo, E-mail: jlafranceschina@alaska.edu; Wackerbauer, Renate, E-mail: rawackerbauer@alaska.edu [Department of Physics, University of Alaska, Fairbanks, Alaska 99775-5920 (United States)

2015-01-15

Spatiotemporal chaos collapses to either a rest state or a propagating pulse solution in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Weak excitatory synapses can increase the Lyapunov exponent, expedite the collapse, and promote the collapse to the rest state rather than the pulse state. A single traveling pulse solution may no longer be asymptotic for certain combinations of network topology and (weak) coupling strengths, and initiate spatiotemporal chaos. Multiple pulses can cause chaos initiation due to diffusive and synaptic pulse-pulse interaction. In the presence of chaos initiation, intermittent spatiotemporal chaos exists until typically a collapse to the rest state.

Impact of weak excitatory synapses on chaotic transients in a diffusively coupled Morris-Lecar neuronal network

International Nuclear Information System (INIS)

Lafranceschina, Jacopo; Wackerbauer, Renate

2015-01-01

Spatiotemporal chaos collapses to either a rest state or a propagating pulse solution in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Weak excitatory synapses can increase the Lyapunov exponent, expedite the collapse, and promote the collapse to the rest state rather than the pulse state. A single traveling pulse solution may no longer be asymptotic for certain combinations of network topology and (weak) coupling strengths, and initiate spatiotemporal chaos. Multiple pulses can cause chaos initiation due to diffusive and synaptic pulse-pulse interaction. In the presence of chaos initiation, intermittent spatiotemporal chaos exists until typically a collapse to the rest state

The symptom of functional weakness: a controlled study of 107 patients.

Science.gov (United States)

Stone, Jon; Warlow, Charles; Sharpe, Michael

2010-05-01

Functional weakness describes weakness which is both internally inconsistent and incongruent with any recognizable neurological disease. It may be diagnosed as a manifestation of conversion disorder or dissociative motor disorder. Other names include psychogenic or 'non-organic' paralysis. We aimed to describe the incidence, demographic and clinical characteristics of cases with functional weakness of less than 2 years duration, and to compare these with controls with weakness attributable to neurological disease. Both cases and controls were recruited from consultant neurologists in South East Scotland. Participating patients underwent detailed assessments which included: physical examination, structured psychiatric interview (Structured Clinical Interview for the Diagnostic and Statistical Manual of Mental Disorders), measures of symptoms, disability and distress [Short Form (36) Health Survey, Hospital and Anxiety Depression Scale], and assessment of their illness beliefs using an augmented version of the Illness Perception Questionnaire. In total, 107 cases (79% female, mean age 39 years, median duration of illness 9 months) were recruited. This number suggests a minimum annual incidence of 3.9/100 000. Forty-six controls (83% female, median age 39 years, duration 11 months) were also recruited. Compared to controls, cases had similar levels of disability but more physical symptoms, especially pain. They had a higher frequency of psychiatric disorders, especially current major depression (32 versus 7%, P anxiety disorder (21 versus 2%, P disorder (36 versus 13%, P disorder (27 versus 0%, P anxiety and depression scores. Paradoxically, they were less likely than controls to agree that stress was a possible cause of their illness (24 versus 56%, P anxiety diagnoses and the patient's willingness to accept these as potentially relevant to their symptoms. We discuss the theoretical and practical implications of these findings for the concept of conversion disorder.

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

KAUST Repository

Aguareles, M.

2014-06-01

In this paper we consider an oscillatory medium whose dynamics are modeled by the complex Ginzburg-Landau equation. In particular, we focus on n-armed spiral wave solutions of the complex Ginzburg-Landau equation in a disk of radius d with homogeneous Neumann boundary conditions. It is well-known that such solutions exist for small enough values of the twist parameter q and large enough values of d. We investigate the effect of boundaries on the rotational frequency of the spirals, which is an unknown of the problem uniquely determined by the parameters d and q. We show that there is a threshold in the parameter space where the effect of the boundary on the rotational frequency switches from being algebraic to exponentially weak. We use the method of matched asymptotic expansions to obtain explicit expressions for the asymptotic wavenumber as a function of the twist parameter and the domain size for small values of q. © 2014 Elsevier B.V. All rights reserved.

Komar integrals in asymptotically anti-de Sitter space-times

International Nuclear Information System (INIS)

Magnon, A.

1985-01-01

Recently, boundary conditions governing the asymptotic behavior of the gravitational field in the presence of a negative cosmological constant have been introduced using Penrose's conformal techniques. The subsequent analysis has led to expressions of conserved quantities (associated with asymptotic symmetries) involving asymptotic Weyl curvature. On the other hand, if the underlying space-time is equipped with isometries, a generalization of the Komar integral which incorporates the cosmological constant is also available. Thus, in the presence of an isometry, one is faced with two apparently unrelated definitions. It is shown that these definitions agree. This coherence supports the choice of boundary conditions for asymptotically anti-de Sitter space-times and reinforces the definitions of conserved quantities

A weak scientific basis for gaming disorder

DEFF Research Database (Denmark)

van Rooij, Antonius; Ferguson, Chris; Nielsen, Rune Kristian Lundedal

2018-01-01

We greatly appreciate the care and thought that is evident in the 10 commentaries that discuss our debate paper, the majority of which argued in favor of a formalized ICD-11 gaming disorder. We agree that there are some people whose play of video games is related to life problems. We believe...... that understanding this population and the nature and severity of the problems they experience should be a focus area for future research. However, moving from research construct to formal disorder requires a much stronger evidence base than we currently have. The burden of evidence and the clinical utility should...... general behavioral addictions concept, the exploration of non-addiction approaches, and the unbiased exploration of clinical approaches that treat potentially underlying issues, such as depressive mood or social anxiety first. We acknowledge there could be benefits to formalizing gaming disorder, many...

Preheating in an asymptotically safe quantum field theory

DEFF Research Database (Denmark)

Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert

2016-01-01

. High Energy Phys. 01 (2016) 081]. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. Since the models contain many scalar fields which are intrinsically coupled to the inflaton there is the possibility of parametric resonance...... fluctuations induced by the parametrically amplified entropy modes do not exceed the upper observational bounds puts a lower bound on the number of fields which the model followed in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F......We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J...

A method for summing nonalternating asymptotic series

International Nuclear Information System (INIS)

Kazakov, D.I.

1980-01-01

A method for reconstructing a function from its nonalternating asymptotic series is proposed. It can also be applied when only a limited number of coefficients and their high order asymptotic behaviour are known. The method is illustrated by examples of the ordinary simple integral simulating a functional integral in a theory with degenerate minimum and of the double-well unharmonic oscillator

Asymptotic Analysis in MIMO MRT/MRC Systems

Directory of Open Access Journals (Sweden)

Zhou Quan

2006-01-01

Full Text Available Through the analysis of the probability density function of the squared largest singular value of a complex Gaussian matrix at the origin and tail, we obtain two asymptotic results related to the multi-input multi-output (MIMO maximum-ratio-transmission/maximum-ratio-combining (MRT/MRC systems. One is the asymptotic error performance (in terms of SNR in a single-user system, and the other is the asymptotic system capacity (in terms of the number of users in the multiuser scenario when multiuser diversity is exploited. Similar results are also obtained for two other MIMO diversity schemes, space-time block coding and selection combining. Our results reveal a simple connection with system parameters, providing good insights for the design of MIMO diversity systems.

End Point of Black Ring Instabilities and the Weak Cosmic Censorship Conjecture.

Science.gov (United States)

Figueras, Pau; Kunesch, Markus; Tunyasuvunakool, Saran

2016-02-19

We produce the first concrete evidence that violation of the weak cosmic censorship conjecture can occur in asymptotically flat spaces of five dimensions by numerically evolving perturbed black rings. For certain thin rings, we identify a new, elastic-type instability dominating the evolution, causing the system to settle to a spherical black hole. However, for sufficiently thin rings the Gregory-Laflamme mode is dominant, and the instability unfolds similarly to that of black strings, where the horizon develops a structure of bulges connected by necks which become ever thinner over time.

Asymptotic failure rate of a continuously monitored system

International Nuclear Information System (INIS)

Grall, A.; Dieulle, L.; Berenguer, C.; Roussignol, M.

2006-01-01

This paper deals with a perfectly continuously monitored system which gradually and stochastically deteriorates. The system is renewed by a delayed maintenance operation, which is triggered when the measured deterioration level exceeds an alarm threshold. A mathematical model is developed to study the asymptotic behavior of the reliability function. A procedure is proposed which allows us to identify the asymptotic failure rate of the maintained system. Numerical experiments illustrate the efficiency of the proposed procedure and emphasize the relevance of the asymptotic failure rate as an interesting indicator for the evaluation of the control-limit preventive replacement policy

Asymptotic failure rate of a continuously monitored system

Energy Technology Data Exchange (ETDEWEB)

Grall, A. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: antoine.grall@utt.fr; Dieulle, L. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: laurence.dieulle@utt.fr; Berenguer, C. [Institut des Sciences et Technologies de l' Information de Troyes (CNRS-FRE 2732), Equipe de Modelisation et de Surete des Systemes, Universite de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010 Troyes Cedex (France)]. E-mail: christophe.berenguer@utt.fr; Roussignol, M. [Laboratoire d' Analyse et de Mathematiques Appliquees, Universite de Marne la Vallee, 5 bd Descartes, Champs sur Marne, 77454 Marne la Vallee, Cedex 2 (France)]. E-mail: michel.roussignol@univ-mlv.fr

2006-02-01

This paper deals with a perfectly continuously monitored system which gradually and stochastically deteriorates. The system is renewed by a delayed maintenance operation, which is triggered when the measured deterioration level exceeds an alarm threshold. A mathematical model is developed to study the asymptotic behavior of the reliability function. A procedure is proposed which allows us to identify the asymptotic failure rate of the maintained system. Numerical experiments illustrate the efficiency of the proposed procedure and emphasize the relevance of the asymptotic failure rate as an interesting indicator for the evaluation of the control-limit preventive replacement policy.

Comment on 'Asymptotic form of the Kohn-Sham correlation potential'

International Nuclear Information System (INIS)

Holas, A.

2008-01-01

For finite systems that have the energetically highest-occupied molecular orbital (HOMO) with an asymptotic nodal surface, Joubert demonstrated recently [Phys. Rev. A 76, 012501 (2007)] strongly anisotropic behavior (in the asymptotic large-r region) of the exact correlation potential of density-functional theory. As is shown by us, this result is a direct and simple consequence of the strong anisotropy of the exact exchange potential obtained by Della Sala and Goerling [Phys. Rev. Lett. 89, 033003 (2002); Della Sala and GoerlingJ. Chem. Phys. 116, 5374 (2002)] and the assumption about the asymptotic isotropy of the Kohn-Sham (KS) potential (based on the investigation of Almbladh and von Barth [Phys. Rev. B 31, 3231 (1985)] for atoms). Joubert's result remains a hypothesis only, because the last assumption is in contradiction with the asymptotic strong anisotropy of the KS potential for systems with asymptotic nodal surface of the HOMO, demonstrated by Wu, Ayers, and Yang [J. Chem. Phys. 119, 2978 (2003)]. The correlation potential in the asymptotic region, stemming from their results, is given

Pseudo-random number generator based on asymptotic deterministic randomness

Science.gov (United States)

Wang, Kai; Pei, Wenjiang; Xia, Haishan; Cheung, Yiu-ming

2008-06-01

A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks.

Pseudo-random number generator based on asymptotic deterministic randomness

International Nuclear Information System (INIS)

Wang Kai; Pei Wenjiang; Xia Haishan; Cheung Yiuming

2008-01-01

A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks

Numerical algorithms for uniform Airy-type asymptotic expansions

NARCIS (Netherlands)

N.M. Temme (Nico)

1997-01-01

textabstractAiry-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing

H. David Politzer, Asymptotic Freedom, and Strong Interaction

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dropdown arrow Site Map A-Z Index Menu Synopsis H. David Politzer, Asymptotic Freedom, and Strong Interaction Resources with Additional Information H. David Politzer Photo Credit: California Institute of Technology H. David Politzer has won the 2004 Nobel Prize in Physics 'for the discovery of asymptotic freedom

Stark resonances: asymptotics and distributional Borel sum

International Nuclear Information System (INIS)

Caliceti, E.; Grecchi, V.; Maioli, M.

1993-01-01

We prove that the Stark effect perturbation theory of a class of bound states uniquely determines the position and the width of the resonances by Distributional Borel Sum. In particular the small field asymptotics of the width is uniquely related to the large order asymptotics of the perturbation coefficients. Similar results apply to all the ''resonances'' of the anharmonic and double well oscillators. (orig.)

Numerical simulations of generalized Langevin equations with deeply asymptotic parameters

International Nuclear Information System (INIS)

Bao Jingdong; Li Rongwu; Wu Wei

2004-01-01

A unified algorithm for solving Langevin equations with deeply asymptotic parameters is proposed and tested. The method consists of identifying solvable linear friction and implementing the force evaluations by use of the Runge-Kutta method. We apply the present scheme to the periodic motion of an overdamped particle subjected to a multiplicative white noise. The accurate calculations for the temporal velocity of the particle and its correlation function can be realized by introducing an inertial term. It is shown that the fluctuation around the steady quantity increases with decreasing time step in the overdamped white-noise algorithm, however, a massive white-noise technique greatly reduces this spurious drift, and the result can converge to the correct value if the added inertia approaches zero. The other application is the simulation of generalized Langevin equation with an exponential memory friction, this allows us to treat a weak non-Markovian process

Asymptotic freedom without guilt

International Nuclear Information System (INIS)

Ma, E.

1979-01-01

The notion of asymptotic freedom in quantum chromodynamics is explained on general physical grounds, without invoking the formal arguments of renormalizable quantum field theory. The related concept of quark confinement is also discussed along the same line. 5 references

Conformal Phase Diagram of Complete Asymptotically Free Theories

DEFF Research Database (Denmark)

Pica, Claudio; Ryttov, Thomas A.; Sannino, Francesco

2017-01-01

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....

Asymptotic representation theorems for poverty indices | Lo | Afrika ...

African Journals Online (AJOL)

Abstract. We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotic of the bulk of poverty indices and issues in poverty ...

Behavior of asymptotically electro-Λ spacetimes

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Saw, Vee-Liem

2017-04-01

We present the asymptotic solutions for spacetimes with nonzero cosmological constant Λ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with Λ ≠0 . The results are given in two different null tetrads: the Newman-Unti and Szabados-Tod null tetrads, where the peeling property is exhibited in the former but not the latter. Using these asymptotic solutions, we discuss the mass loss of an isolated electrogravitating system with cosmological constant. In a universe with Λ >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 I and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with Λ in the Bondi mass-loss formula in an unusual manner, unlike the gravitational counterpart where outgoing gravitational radiation induces nonconformal flatness of I . These asymptotic solutions to the Einstein-Maxwell-de Sitter equations presented here may be used to extend a raft of existing results based on Newman-Unti's asymptotic solutions to the Einstein-Maxwell equations where Λ =0 , to now incorporate the cosmological constant Λ .

Numerical integration of asymptotic solutions of ordinary differential equations

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Thurston, Gaylen A.

1989-01-01

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

Exact asymptotic expansions for solutions of multi-dimensional renewal equations

International Nuclear Information System (INIS)

Sgibnev, M S

2006-01-01

We derive expansions with exact asymptotic expressions for the remainders for solutions of multi-dimensional renewal equations. The effect of the roots of the characteristic equation on the asymptotic representation of solutions is taken into account. The resulting formulae are used to investigate the asymptotic behaviour of the average number of particles in age-dependent branching processes having several types of particles

Asymptotic stability of a catalyst particle

DEFF Research Database (Denmark)

Wedel, Stig; Michelsen, Michael L.; Villadsen, John

1977-01-01

The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0. These a......The catalyst asymptotic stability problem is studied by means of several new methods that allow accurate solutions to be calculated where other methods have given qualitatively erroneous results. The underlying eigenvalue problem is considered in three limiting situations Le = ∞, 1 and 0...

Thermal boundary conditions for electrons in a weakly ionized gas near a catalytic wall

International Nuclear Information System (INIS)

Chekmarev, I.

1981-01-01

A technique of matched asymptotic expansions is used to examine the derivation of hydrodynamic transport equations for the external region of a weakly ionized multitemperature gas near an absorbing and conducting wall. An approximate moment solution is constructed for the Knudsen boundary layer. The conditions for the matching of the external and internal expansions lead to a new form of the hydrodynamic boundary conditions, from which the singular behavior of the energy equation for electrons near the wall has been eliminated

Non-Asymptotic Confidence Sets for Circular Means

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Thomas Hotz

2016-10-01

Full Text Available The mean of data on the unit circle is defined as the minimizer of the average squared Euclidean distance to the data. Based on Hoeffding’s mass concentration inequalities, non-asymptotic confidence sets for circular means are constructed which are universal in the sense that they require no distributional assumptions. These are then compared with asymptotic confidence sets in simulations and for a real data set.

Asymptotic freedom

International Nuclear Information System (INIS)

Meyer, P.

1978-01-01

After having established the renormalization group equations and the possibilities of fixed points for the effective coupling constants the non abelian gauge theories are shown to have the property of asymptotic freedom. These results are applied to the colour gauge group of the strong interactions of quarks and gluons. The behavior of the moments of the structure functions of the deep inelastic scattering of leptons on nucleons (scaling and its logarithmic violations) is then deduced with using the Wilson's operator product expansion [fr

Cookbook asymptotics for spiral and scroll waves in excitable media.

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Margerit, Daniel; Barkley, Dwight

2002-09-01

Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion. (c) 2002 American Institute of Physics.

Asymptotic propagators and trajectories in plasma turbulence theory. The importance of irreversibility, asymptoticity and non-Markovian terms

International Nuclear Information System (INIS)

Misguich, J.H.

1978-09-01

The physical meaning of perturbed trajectories in turbulent fields is analysed. Special care is devoted to the asymptotic description of average trajectories for long time intervals, as occuring in many recent plasma turbulence theories. Equivalence is proved between asymptotic average trajectories described as well (i) by the propagators V(t,t-tau) for retrodiction and Wsub(J)(t,t+tau) for prediction, and (ii) by the long time secular behavior of the solution of the equations of motion. This confirms the equivalence between perturbed orbit theories and renormalized theories, including non-Markovian contributions

An asymptotical machine

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Cristallini, Achille

2016-07-01

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

Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos.

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Basko, D M

2014-02-01

We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.

Linearly resummed hydrodynamics in a weakly curved spacetime

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Bu, Yanyan; Lublinsky, Michael

2015-04-01

We extend our study of all-order linearly resummed hydrodynamics in a flat space [1, 2] to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically locally AdS5 geometry to relativistic conformal fluids in a weakly curved 4D background. To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid's energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders. We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations. In addition to two viscosity functions discussed at length in refs. [1, 2], we find four curvature induced structures coupled to the fluid via new transport coefficient functions. In ref. [3], the latter were referred to as gravitational susceptibilities of the fluid. We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.

Asymptotically anti-de Sitter spacetimes in topologically massive gravity

International Nuclear Information System (INIS)

Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo

2009-01-01

We consider asymptotically anti-de Sitter spacetimes in three-dimensional topologically massive gravity with a negative cosmological constant, for all values of the mass parameter μ (μ≠0). We provide consistent boundary conditions that accommodate the recent solutions considered in the literature, which may have a slower falloff than the one relevant for general relativity. These conditions are such that the asymptotic symmetry is in all cases the conformal group, in the sense that they are invariant under asymptotic conformal transformations and that the corresponding Virasoro generators are finite. It is found that, at the chiral point |μl|=1 (where l is the anti-de Sitter radius), allowing for logarithmic terms (absent for general relativity) in the asymptotic behavior of the metric makes both sets of Virasoro generators nonzero even though one of the central charges vanishes.

Quantum Butterfly Effect in Weakly Interacting Diffusive Metals

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Aavishkar A. Patel

2017-09-01

Full Text Available We study scrambling, an avatar of chaos, in a weakly interacting metal in the presence of random potential disorder. It is well known that charge and heat spread via diffusion in such an interacting disordered metal. In contrast, we show within perturbation theory that chaos spreads in a ballistic fashion. The squared anticommutator of the electron-field operators inherits a light-cone-like growth, arising from an interplay of a growth (Lyapunov exponent that scales as the inelastic electron scattering rate and a diffusive piece due to the presence of disorder. In two spatial dimensions, the Lyapunov exponent is universally related at weak coupling to the sheet resistivity. We are able to define an effective temperature-dependent butterfly velocity, a speed limit for the propagation of quantum information that is much slower than microscopic velocities such as the Fermi velocity and that is qualitatively similar to that of a quantum critical system with a dynamical critical exponent z>1.

Asymptotically shear-free and twist-free null geodesic congruences

International Nuclear Information System (INIS)

Kozameh, Carlos; Newman, Ezra T

2007-01-01

The Robinson-Trautman spacetime is a special case of asymptotically flat spacetimes that possess asymptotically shear-free and twist-free (surface forming) null geodesic congruences. In this paper we show that, although they are rare, a larger class of asymptotically flat spacetimes with this property does exist. In particular, we display the class of spacetimes that possess this dual property and demonstrate how these congruences can be found. In addition, we show that in each case the congruence is isolated in the sense that there are no other neighbouring congruences with this dual property

Heat Kernel Asymptotics of Zaremba Boundary Value Problem

Energy Technology Data Exchange (ETDEWEB)

Avramidi, Ivan G. [Department of Mathematics, New Mexico Institute of Mining and Technology (United States)], E-mail: iavramid@nmt.edu

2004-03-15

The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections of a vector bundle over a smooth compact Riemannian manifold with smooth boundary but with discontinuous boundary conditions, which include Dirichlet boundary conditions on one part of the boundary and Neumann boundary conditions on another part of the boundary. We study the heat kernel asymptotics of Zaremba boundary value problem. The construction of the asymptotic solution of the heat equation is described in detail and the heat kernel is computed explicitly in the leading approximation. Some of the first nontrivial coefficients of the heat kernel asymptotic expansion are computed explicitly.

Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation

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Timothy M. Adamo

2009-09-01

Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in complex Minkowski space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi’s integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum–conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation

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Timothy M. Adamo

2012-01-01

Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, H-space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi's integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum--conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation.

Science.gov (United States)

Adamo, Timothy M; Newman, Ezra T; Kozameh, Carlos

2012-01-01

A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, [Formula: see text]-space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell) field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi's) integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum-conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

Szegö Kernels and Asymptotic Expansions for Legendre Polynomials

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Roberto Paoletti

2017-01-01

Full Text Available We present a geometric approach to the asymptotics of the Legendre polynomials Pk,n+1, based on the Szegö kernel of the Fermat quadric hypersurface, leading to complete asymptotic expansions holding on expanding subintervals of [-1,1].

Time-asymptotic interactions of two ensembles of Cucker-Smale flocking particles

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Ha, Seung-Yeal; Ko, Dongnam; Zhang, Xiongtao; Zhang, Yinglong

2017-07-01

We study the time-asymptotic interactions of two ensembles of Cucker-Smale flocking particles. For this, we use a coupled hydrodynamic Cucker-Smale system and discuss two frameworks, leading to mono-cluster and bi-cluster flockings asymptotically depending on initial configurations, coupling strengths, and the far-field decay property of communication weights. Under the proposed two frameworks, we show that mono-cluster and bi-cluster flockings emerge asymptotically exponentially fast and algebraically slow, respectively. Our asymptotic analysis uses the Lyapunov functional approach and a Lagrangian formulation of the coupled system.

Asymptotically Safe Standard Model Extensions arXiv

CERN Document Server

Pelaggi, Giulio Maria; Salvio, Alberto; Sannino, Francesco; Smirnov, Juri; Strumia, Alessandro

We consider theories with a large number NF of charged fermions and compute the renormalisation group equations for the gauge, Yukawa and quartic couplings resummed at leading order in NF. We construct extensions of the Standard Model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.

Composite asymptotic expansions and scaling wall turbulence.

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Panton, Ronald L

2007-03-15

In this article, the assumptions and reasoning that yield composite asymptotic expansions for wall turbulence are discussed. Particular attention is paid to the scaling quantities that are used to render the variables non-dimensional and of order one. An asymptotic expansion is proposed for the streamwise Reynolds stress that accounts for the active and inactive turbulence by using different scalings. The idea is tested with the data from the channel flows and appears to have merit.

arXiv Asymptotically Safe Standard Model Extensions?

CERN Document Server

Pelaggi, Giulio Maria; Salvio, Alberto; Sannino, Francesco; Smirnov, Juri; Strumia, Alessandro

2018-05-15

We consider theories with a large number NF of charged fermions and compute the renormalization group equations for the gauge, Yukawa and quartic couplings resummed at leading order in 1/NF. We construct extensions of the standard model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.

Asymptotic time dependent neutron transport in multidimensional systems

International Nuclear Information System (INIS)

Nagy, M.E.; Sawan, M.E.; Wassef, W.A.; El-Gueraly, L.A.

1983-01-01

A model which predicts the asymptotic time behavior of the neutron distribution in multi-dimensional systems is presented. The model is based on the kernel factorization method used for stationary neutron transport in a rectangular parallelepiped. The accuracy of diffusion theory in predicting the asymptotic time dependence is assessed. The use of neutron pulse experiments for predicting the diffusion parameters is also investigated

Some asymptotic properties of functions holomorphic in tubular domains

International Nuclear Information System (INIS)

Zavialov, B.I.

1988-10-01

For the function holomorphic in curved tubular domain the connection between asymptotic behaviour of real part of its boundary value at a given point of base manifold and asymptotic behaviour of the whole function from the inside of this domain is studied. (author). 3 refs

Asymptotically double lacunry equivalent sequences defined by Orlicz functions

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Ayhan Esi

2014-04-01

Full Text Available This paper presents the following definition which is natural combition of the definition for asymptotically equivalent and Orlicz function. The two nonnegative double sequences x=(x_{k,l} and y=(y_{k,l} are said to be M-asymptotically double equivalent to multiple L provided that for every ε>0, P-lim_{k,l}M(((|((x_{k,l}/(y_{k,l}-L|/ρ=0, for some ρ>0, (denoted by x∽y and simply M-asymptotically double equivalent if L=1. Also we give some new concepts related to this definition and some inclusion theorems.

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

KAUST Repository

Abdulle, Assyr

2013-01-01

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.

Coulomb string tension, asymptotic string tension, and the gluon chain

OpenAIRE

Greensite, Jeff; Szczepaniak, Adam P.

2014-01-01

We compute, via numerical simulations, the non-perturbative Coulomb potential of pure SU(3) gauge theory in Coulomb gauge. We find that 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.

Global asymptotic stability of density dependent integral population projection models.

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Rebarber, Richard; Tenhumberg, Brigitte; Townley, Stuart

2012-02-01

Many stage-structured density dependent populations with a continuum of stages can be naturally modeled using nonlinear integral projection models. In this paper, we study a trichotomy of global stability result for a class of density dependent systems which include a Platte thistle model. Specifically, we identify those systems parameters for which zero is globally asymptotically stable, parameters for which there is a positive asymptotically stable equilibrium, and parameters for which there is no asymptotically stable equilibrium. Copyright © 2011 Elsevier Inc. All rights reserved.

Asymptotic Expansions for Higher-Order Scalar Difference Equations

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Pituk Mihály

2007-01-01

Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

Asymptotic structure of isolated systems

International Nuclear Information System (INIS)

Beig, R.

1988-01-01

I discuss the general ideas underlying the subject of ''asymptotics'' in general relativity and describe the current status of the concepts resulting from these ideas. My main concern will be the problem of consistency. By this I mean the question as to whether the geometric assumptions inherent in these concepts are compatible with the dynamics of the theory, as determined by Einstein's equations. This rather strong bias forces me to leave untouched several issues related to asymptotics, discussed in the recent literature, some of which are perhaps thought equally, or more important, by other workers in the field. In addition I shall, for coherence of presentation, mainly consider Einstein's equations in vacuo. When attention is confined to small neighbourhoods of null and spacelike infinity, this restriction is not important, but is surely relevant for more global issues. (author)

Regge asymptotics of scattering with flavour exchange in QCD

International Nuclear Information System (INIS)

Kirschner, R.

1994-06-01

The contribution to the perturbative Regge asymptotics of the exchange of two reggeized fermions with opposite helicity is investigated. The methods of conformal symmetry known for the case of gluon exchange are extended to this case where double-logarithmic contributions dominate the asymptotics. The Regge trajectories at large momentum transfer are calculated. (orig.)

On the asymptotics of dimers on tori

OpenAIRE

Kenyon, Richard W.; Sun, Nike; Wilson, David B.

2013-01-01

We study asymptotics of the dimer model on large toric graphs. Let $\\mathbb L$ be a weighted $\\mathbb{Z}^2$-periodic planar graph, and let $\\mathbb{Z}^2 E$ be a large-index sublattice of $\\mathbb{Z}^2$. For $\\mathbb L$ bipartite we show that the dimer partition function on the quotient $\\mathbb{L}/(\\mathbb{Z}^2 E)$ has the asymptotic expansion $\\exp[A f_0 + \\text{fsc} + o(1)]$, where $A$ is the area of $\\mathbb{L}/(\\mathbb{Z}^2 E)$, $f_0$ is the free energy density in the bulk, and $\\text{fsc...

Crossover to Fermi-liquid behavior for weakly-coupled Luttinger liquids in the anisotropic large-dimension limit

OpenAIRE

Arrigoni, E.

1999-01-01

We study the problem of the crossover from one- to higher-dimensional metals by considering an array of Luttinger liquids (one-dimensional chains) coupled by a weak interchain hopping {\\tp.} We evaluate the exact asymptotic low-energy behavior of the self-energy in the anisotropic infinite-dimension limit. This limit extends the dinamical mean field concept to the case of a chain embedded in a self-consistent medium. The system flows to a Fermi-liquid fixed point for energies below the dimens...

Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size

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King, Richard B.

2016-01-01

Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females) and annual growth increments of individuals of unknown age (1,152 males, 730 females). We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631–820 mm snout-vent length in males and from 835–1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further investigation. PMID

Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size.

Directory of Open Access Journals (Sweden)

Richard B King

Full Text Available Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females and annual growth increments of individuals of unknown age (1,152 males, 730 females. We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631-820 mm snout-vent length in males and from 835-1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further

Deep learning ensemble with asymptotic techniques for oscillometric blood pressure estimation.

Science.gov (United States)

Lee, Soojeong; Chang, Joon-Hyuk

2017-11-01

This paper proposes a deep learning based ensemble regression estimator with asymptotic techniques, and offers a method that can decrease uncertainty for oscillometric blood pressure (BP) measurements using the bootstrap and Monte-Carlo approach. While the former is used to estimate SBP and DBP, the latter attempts to determine confidence intervals (CIs) for SBP and DBP based on oscillometric BP measurements. This work originally employs deep belief networks (DBN)-deep neural networks (DNN) to effectively estimate BPs based on oscillometric measurements. However, there are some inherent problems with these methods. First, it is not easy to determine the best DBN-DNN estimator, and worthy information might be omitted when selecting one DBN-DNN estimator and discarding the others. Additionally, our input feature vectors, obtained from only five measurements per subject, represent a very small sample size; this is a critical weakness when using the DBN-DNN technique and can cause overfitting or underfitting, depending on the structure of the algorithm. To address these problems, an ensemble with an asymptotic approach (based on combining the bootstrap with the DBN-DNN technique) is utilized to generate the pseudo features needed to estimate the SBP and DBP. In the first stage, the bootstrap-aggregation technique is used to create ensemble parameters. Afterward, the AdaBoost approach is employed for the second-stage SBP and DBP estimation. We then use the bootstrap and Monte-Carlo techniques in order to determine the CIs based on the target BP estimated using the DBN-DNN ensemble regression estimator with the asymptotic technique in the third stage. The proposed method can mitigate the estimation uncertainty such as large the standard deviation of error (SDE) on comparing the proposed DBN-DNN ensemble regression estimator with the DBN-DNN single regression estimator, we identify that the SDEs of the SBP and DBP are reduced by 0.58 and 0.57  mmHg, respectively. These

An asymptotic formula of the divergent bilateral basic hypergeometric series

OpenAIRE

Morita, Takeshi

2012-01-01

We show an asymptotic formula of the divergent bilateral basic hypergeometric series ${}_1\\psi_0 (a;-;q,\\cdot)$ with using the $q$-Borel-Laplace method. We also give the limit $q\\to 1-0$ of our asymptotic formula.

Survival and weak chaos.

Science.gov (United States)

Nee, Sean

2018-05-01

Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as 'infant mortality'. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality- sensu engineering-without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy.

Caustics, counting maps and semi-classical asymptotics

Science.gov (United States)

Ercolani, N. M.

2011-02-01

This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function, also known as the genus expansion (and its derivatives), are generating functions for a variety of graphical enumeration problems. The main results are to prove that these generating functions are, in fact, specific rational functions of a distinguished irrational (algebraic) function, z0(t). This distinguished function is itself the generating function for the Catalan numbers (or generalized Catalan numbers, depending on the choice of weight of the parameter t). It is also a solution of the inviscid Burgers equation for certain initial data. The shock formation, or caustic, of the Burgers characteristic solution is directly related to the poles of the rational forms of the generating functions. As an intriguing application, one gains new insights into the relation between certain derivatives of the genus expansion, in a double-scaling limit, and the asymptotic expansion of the first Painlevé transcendent. This provides a precise expression of the Painlevé asymptotic coefficients directly in terms of the coefficients of the partial fractions expansion of the rational form of the generating functions established in this paper. Moreover, these insights point towards a more general program relating the first Painlevé hierarchy to the higher order structure of the double-scaling limit through the specific rational structure of generating functions in the genus expansion. The paper closes with a discussion of the relation of this work to recent developments in understanding the asymptotics of graphical enumeration. As a by-product, these results also yield new information about the asymptotics of recurrence coefficients for orthogonal polynomials with respect to exponential weights, the calculation of correlation functions for certain

Caustics, counting maps and semi-classical asymptotics

International Nuclear Information System (INIS)

Ercolani, N M

2011-01-01

This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function, also known as the genus expansion (and its derivatives), are generating functions for a variety of graphical enumeration problems. The main results are to prove that these generating functions are, in fact, specific rational functions of a distinguished irrational (algebraic) function, z 0 (t). This distinguished function is itself the generating function for the Catalan numbers (or generalized Catalan numbers, depending on the choice of weight of the parameter t). It is also a solution of the inviscid Burgers equation for certain initial data. The shock formation, or caustic, of the Burgers characteristic solution is directly related to the poles of the rational forms of the generating functions. As an intriguing application, one gains new insights into the relation between certain derivatives of the genus expansion, in a double-scaling limit, and the asymptotic expansion of the first Painlevé transcendent. This provides a precise expression of the Painlevé asymptotic coefficients directly in terms of the coefficients of the partial fractions expansion of the rational form of the generating functions established in this paper. Moreover, these insights point towards a more general program relating the first Painlevé hierarchy to the higher order structure of the double-scaling limit through the specific rational structure of generating functions in the genus expansion. The paper closes with a discussion of the relation of this work to recent developments in understanding the asymptotics of graphical enumeration. As a by-product, these results also yield new information about the asymptotics of recurrence coefficients for orthogonal polynomials with respect to exponential weights, the calculation of correlation functions for certain

Asymptotics for a special solution to the second member of the Painleve I hierarchy

International Nuclear Information System (INIS)

Claeys, T

2010-01-01

We study the asymptotic behavior of a special smooth solution y(x, t) to the second member of the Painleve I hierarchy. This solution arises in random matrix theory and in the study of the Hamiltonian perturbations of hyperbolic equations. The asymptotic behavior of y(x, t) if x → ±∞ (for fixed t) is known and relatively simple, but it turns out to be more subtle when x and t tend to infinity simultaneously. We distinguish a region of algebraic asymptotic behavior and a region of elliptic asymptotic behavior, and we obtain rigorous asymptotics in both regions. We also discuss two critical transitional asymptotic regimes.

Watermelon configurations with wall interaction: exact and asymptotic results

Energy Technology Data Exchange (ETDEWEB)

Krattenthaler, C [Institut Camille Jordan, Universite Claude Bernard Lyon-I, 21, avenue Claude Bernard, F-69622 Villeurbanne Cedex (France)

2006-06-15

We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.

Watermelon configurations with wall interaction: exact and asymptotic results

International Nuclear Information System (INIS)

Krattenthaler, C

2006-01-01

We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature

Watermelon configurations with wall interaction: exact and asymptotic results

Science.gov (United States)

Krattenthaler, C.

2006-06-01

We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.

Asymptotic Expansions for Higher-Order Scalar Difference Equations

Directory of Open Access Journals (Sweden)

Ravi P. Agarwal

2007-04-01

Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

Microscopic universality of complex matrix model correlation functions at weak non-Hermiticity

International Nuclear Information System (INIS)

Akemann, G.

2002-01-01

The microscopic correlation functions of non-chiral random matrix models with complex eigenvalues are analyzed for a wide class of non-Gaussian measures. In the large-N limit of weak non-Hermiticity, where N is the size of the complex matrices, we can prove that all k-point correlation functions including an arbitrary number of Dirac mass terms are universal close to the origin. To this aim we establish the universality of the asymptotics of orthogonal polynomials in the complex plane. The universality of the correlation functions then follows from that of the kernel of orthogonal polynomials and a mapping of massive to massless correlators

Numerical Asymptotic Solutions Of Differential Equations

Science.gov (United States)

Thurston, Gaylen A.

1992-01-01

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

Convergence theorems for mappings which are asymptotically nonexpansive in the intermediate sense

International Nuclear Information System (INIS)

Chidume, C.E.; Shahzad, Naseer; Zegeye, Habtu

2003-08-01

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K → E be a non-self mapping which is asymptotically nonexpansive in the intermediate sense with F(T) := {x is an element of K : Tx x} ≠ 0. A demiclosed principle for T is proved. Moreover, if T is completely continuous, an iterative sequence {x n } is constructed which converges strongly to some x* is an element of F(T). If T is not assumed to be completely continuous but the dual E* of E is assumed to have the Kadec-Klee property, then {x n } converges weakly to some x* is an element of F(T). The operator P which plays a central role in our proofs is, in this case, the Banach space analogue of the proximity map in Hilbert spaces. (author)

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

International Nuclear Information System (INIS)

Cui, Xia; Yuan, Guang-wei; Shen, Zhi-jun

2016-01-01

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-order accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.

Event schemas in autism spectrum disorders: the role of theory of mind and weak central coherence.

Science.gov (United States)

Loth, Eva; Gómez, Juan Carlos; Happé, Francesca

2008-03-01

Event schemas (generalized knowledge of what happens at common real-life events, e.g., a birthday party) are an important cognitive tool for social understanding: They provide structure for social experiences while accounting for many variable aspects. Using an event narratives task, this study tested the hypotheses that theory of mind (ToM) deficits and weak central coherence (WCC, a local processing bias) undermine different aspects of event knowledge in people with autism spectrum disorder (ASD). Event narratives of ASD ToM-failers were overall significantly impaired. ASD ToM-passers showed more specific abnormalities relating to variable activities, and some of these were significantly associated to WCC. Abnormalities in event knowledge might help linking ASD-typical social deficits in real-life situations and the adherence to inflexible routines.

Spectral asymptotics of a strong δ′ interaction supported by a surface

International Nuclear Information System (INIS)

Exner, Pavel; Jex, Michal

2014-01-01

Highlights: • Attractive δ ′ interactions supported by a smooth surface are considered. • Surfaces can be either infinite and asymptotically planar, or compact and closed. • Spectral asymptotics is determined by the geometry of the interaction support. - Abstract: We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive δ ′ interaction supported by a smooth surface in R 3 , either infinite and asymptotically planar, or compact and closed. Its second term is found to be determined by a Schrödinger type operator with an effective potential expressed in terms of the interaction support curvatures

Error estimates in horocycle averages asymptotics: challenges from string theory

NARCIS (Netherlands)

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 chaos expansions in finance theory and practice

CERN Document Server

Nicolay, David

2014-01-01

Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (suc...

Contact mechanics of articular cartilage layers asymptotic models

CERN Document Server

Argatov, Ivan

2015-01-01

This book presents a comprehensive and unifying approach to articular contact mechanics with an emphasis on frictionless contact interaction of thin cartilage layers. The first part of the book (Chapters 1–4) reviews the results of asymptotic analysis of the deformational behavior of thin elastic and viscoelastic layers. A comprehensive review of the literature is combined with the authors’ original contributions. The compressible and incompressible cases are treated separately with a focus on exact solutions for asymptotic models of frictionless contact for thin transversely isotropic layers bonded to rigid substrates shaped like elliptic paraboloids. The second part (Chapters 5, 6, and 7) deals with the non-axisymmetric contact of thin transversely isotropic biphasic layers and presents the asymptotic modelling methodology for tibio-femoral contact. The third part of the book consists of Chapter 8, which covers contact problems for thin bonded inhomogeneous transversely isotropic elastic layers, and Cha...

The unusual asymptotics of three-sided prudent polygons

International Nuclear Information System (INIS)

Beaton, Nicholas R; Guttmann, Anthony J; Flajolet, Philippe

2010-01-01

We have studied the area-generating function of prudent polygons on the square lattice. Exact solutions are obtained for the generating function of two-sided and three-sided prudent polygons, and a functional equation is found for four-sided prudent polygons. This is used to generate series coefficients in polynomial time, and these are analysed to determine the asymptotics numerically. A careful asymptotic analysis of the three-sided polygons produces a most surprising result. A transcendental critical exponent is found, and the leading amplitude is not quite a constant, but is a constant plus a small oscillatory component with an amplitude approximately 10 -8 times that of the leading amplitude. This effect cannot be seen by any standard numerical analysis, but it may be present in other models. If so, it changes our whole view of the asymptotic behaviour of lattice models. (fast track communication)

Conductivity of weakly disordered strange metals: From conformal to hyperscaling-violating regimes

Directory of Open Access Journals (Sweden)

Andrew Lucas

2015-03-01

Full Text Available We present a semi-analytic method for constructing holographic black holes that interpolate from anti-de Sitter space to hyperscaling-violating geometries. These are holographic duals of conformal field theories in the presence of an applied chemical potential, μ, at a non-zero temperature, T, and allow us to describe the crossover from ‘strange metal’ physics at T≪μ, to conformal physics at T≫μ. Our holographic technique adds an extra gauge field and exploits structure of the Einstein–Maxwell system to manifestly find 1-parameter families of solutions of the Einstein-matter system in terms of a small family of functions, obeying a nested set of differential equations. Using these interpolating geometries, we re-consider holographically some recent questions of interest about hyperscaling-violating field theories. Our focus is a more detailed holographic computation of the conductivity of strange metals, weakly perturbed by disorder coupled to scalar operators, including both the average conductivity as well as sample-to-sample fluctuations. Our findings are consistent with previous scaling arguments, though we point out logarithmic corrections in some special (holographic cases. We also discuss the nature of superconducting instabilities in hyperscaling-violating geometries with appropriate choices of scalar couplings.

Asymptotic Solution of the Theory of Shells Boundary Value Problem

Directory of Open Access Journals (Sweden)

I. V. Andrianov

2007-01-01

Full Text Available This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i it is devoted to the fundamental principles of asymptotic approaches, and (ii it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.

Asymptotics for the ratio and the zeros of multiple Charlier polynomials

OpenAIRE

Ndayiragije, François; Van Assche, Walter

2011-01-01

We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the asymptotic distribution of the zeros, which is uniform on an interval. We also deal with the case where one of the parameters of the various Poisson distributions depend on the degree of the polynomial, in which case we obtain another asymptotic distributio...

Asymptotic strength of thermal pulses in the helium shell burning

Energy Technology Data Exchange (ETDEWEB)

Fujimoto, M Y [Niigata Univ. (Japan); Sugimoto, D

1979-03-01

Secular growth in the strength of the recurrent thermal pulses of helium shell burning is discussed for the purpose of determining its asymptotic strength. It is shown that the pulse grows stronger if the helium zone has been cooled more before the initiation of the pulse. The secular growth of the pulse is related with the increasing degree of cooling. Thermal pulses are computed for an initial model corresponding to the maximum possible cooling, i.e., for a model in which the steady-state entropy distribution was realized in the helium zone. Such thermal pulses are shown to give an upper bound to the asymptotic strength, which is close enough to the asymptotic strength itself for relatively large core masses. Numerical results are given for the core mass of 1.07 M sub(sun), for which the asymptotic strength is found to be 9 x 10/sup 6/ L sub(sun). Thermal pulses are also computed for an initial model which has been cooled artificially more than the steady-state model. The first pulse results in a much greater strength than in the normal model, but a later pulse approaches the normal asymptotic value. Such models are also discussed in relation to the shell flashes on accreting white dwarfs.

Left--right symmetric gauge theories of weak and electromagnetic interactions

International Nuclear Information System (INIS)

Sidhu, D.P.

1978-01-01

We review the recent progress in spontaneously broken left-right symmetric gauge theories of weak and electromagnetic interactions. Recently gauge theories based on the group SU(2)/Sub L/ x SU(2)/sub R/ x U(1) have been proposed as serious candidates for a unified description of the weak and electromagnetic interactions. Such theories have a number of attractive features which are not shared by the standard SU(2) x U(1) theories. Parity violation as well as CP-violation are spontaneous in origin and, therefore, theories are parity conserving before spontaneous breakdown of the symmetry and also afterwards at asymptotic energies. The asymmetry in low energy charged current weak interaction, i.e., predominance of left-handed charged current interactions over the right-handed ones, is a consequence of the symmetry breaking thus leading to a conceptually different picture of weak interaction at low energies. Another appealing feature of these theories is the beauty and richness of the structure of weak neutral current interactions. One can have a parity conserving structure of the neutral currents (one neutral boson (Z/sub V/) has pure vector and the other (Z/sub A/) pure axial vector coupling to quarks and leptons) which is natural in the technical sense of the word. Models of this type provide the most elegant explanation of the failure to find parity violation in atoms at the level predicted on the basis of the Weinberg-Salam model. In spite of manifestly parity conserving neutral current interactions, ν/sub μ/N and anti ν/sub μ/N (also ν/sub μ/e and anti ν/sub μ/e) neutral current cross-sections have to be unequal in these theories because of the definite parity and charge conjugation of the Z-bosons

Diagnosis of functional (psychogenic paresis and weakness

Directory of Open Access Journals (Sweden)

Savkov V.S.

2018-03-01

Full Text Available Functional (conversion neurological symptoms represent one of the most common situations faced by neurologists in their everyday practice. Among them, acute or subacute functional weakness may mimic very prevalent conditions such as stroke or traumatic injury. In the diagnosis of functional weakness, although elements of the history are helpful, physical signs are often of crucial importance in the diagnosis and positive signs are as important as absence of signs of disease. Hence, accurate and reliable positive signs of functional weakness are valuable for obtaining timely diagnosis and treatment, making it possible to avoid unnecessary or invasive tests and procedures up to thrombolysis. Functional weakness commonly presents as weakness of an entire limb, paraparesis, or hemiparesis, with observable or demonstrable inconsistencies and non-anatomic accompaniments. Documentation of limb movements during sleep, the arm drop test, the Babinski’s trunk-thigh test, Hoover tests, the Sonoo abductor test, and various dynamometer tests can provide useful bedside diagnostic information on functional weakness. We therefore present here a brief overview of the positive neurological signs of functional weakness available, both in the lower and in the upper limbs; but none should be used in isolation and must be interpreted in the overall context of the presentation. It should be borne in mind that a patient may have both a functional and an organic disorder.

Ruin problems and tail asymptotics

DEFF Research Database (Denmark)

Rønn-Nielsen, Anders

The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived...

Global asymptotic stability of delayed Cohen-Grossberg neural networks

International Nuclear Information System (INIS)

Wu Wei; Cui Baotong; Huang Min

2007-01-01

In this letter, the global asymptotic stability of a class of Cohen-Grossberg neural networks with time-varying delays is discussed. A new set of sufficient conditions for the neural networks are proposed to guarantee the global asymptotic convergence. Our criteria represent an extension of the existing results in literatures. An example is also presented to compare our results with the previous results

The asymptotic variance of departures in critically loaded queues

NARCIS (Netherlands)

Al Hanbali, Ahmad; Mandjes, M.R.H.; Nazarathy, Y.; Whitt, W.

2011-01-01

We 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 where the system load ϱ equals 1, and prove that the asymptotic variance rate satisfies limt→∞varD(t) / t = λ(1 - 2 / π)(ca2 +

Asymptotic symmetries of Rindler space at the horizon and null infinity

International Nuclear Information System (INIS)

Chung, Hyeyoun

2010-01-01

We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler space at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.

Large time asymptotics of solutions of the equations of principal chiral field

International Nuclear Information System (INIS)

Sukhanov, V.V.

1990-01-01

Asymptotic behaviour of solutions of the equations of principal chiral field when one of the arguments tends to infinity is investigated. Asymptotics of solutions of the corresponding spectral problem is investigated as well. explicit formulas are constructed which connect the coefficients of the asymptotic decomposition of the potential with the data of the corresponding inverse problem by means of a birational transformation

On asymptotics and resurgent structures of enumerative Gromov-Witten invariants

International Nuclear Information System (INIS)

Couso-Santamaria, Ricardo; Schiappa, Ricardo; Geneve Univ.; Vaz, Ricardo; DESY Hamburg

2016-05-01

Making use of large-order techniques in asymptotics and resurgent analysis, this work addresses the growth of enumerative Gromov-Witten invariants - in their dependence upon genus and degree of the embedded curve - for several different threefold Calabi-Yau toric-varieties. In particular, while the leading asymptotics of these invariants at large genus or at large degree is exponential, at combined large genus and degree it turns out to be factorial. This factorial growth has a resurgent nature, originating via mirror symmetry from the resurgent-transseries description of the B-model free energy. This implies the existence of nonperturbative sectors controlling the asymptotics of the Gromov-Witten invariants, which could themselves have an enumerative-geometry interpretation. The examples addressed include: the resolved conifold; the local surfaces local P 2 and local P 1 x P 1 ; the local curves and Hurwitz theory; and the compact quintic. All examples suggest very rich interplays between resurgent asymptotics and enumerative problems in algebraic geometry.

On asymptotics and resurgent structures of enumerative Gromov-Witten invariants

Energy Technology Data Exchange (ETDEWEB)

Couso-Santamaria, Ricardo [Lisboa Univ. (Portugal). Inst. Superior Tecnico (IST); Schiappa, Ricardo [Lisboa Univ. (Portugal). Inst. Superior Tecnico (IST); Geneve Univ. (Switzerland). Dept. de Physique Theoretique et Section de Mathematiques; Vaz, Ricardo [Lisboa Univ. (Portugal). Inst. Superior Tecnico (IST); DESY Hamburg (Germany). Theory Group

2016-05-15

Making use of large-order techniques in asymptotics and resurgent analysis, this work addresses the growth of enumerative Gromov-Witten invariants - in their dependence upon genus and degree of the embedded curve - for several different threefold Calabi-Yau toric-varieties. In particular, while the leading asymptotics of these invariants at large genus or at large degree is exponential, at combined large genus and degree it turns out to be factorial. This factorial growth has a resurgent nature, originating via mirror symmetry from the resurgent-transseries description of the B-model free energy. This implies the existence of nonperturbative sectors controlling the asymptotics of the Gromov-Witten invariants, which could themselves have an enumerative-geometry interpretation. The examples addressed include: the resolved conifold; the local surfaces local P{sup 2} and local P{sup 1} x P{sup 1}; the local curves and Hurwitz theory; and the compact quintic. All examples suggest very rich interplays between resurgent asymptotics and enumerative problems in algebraic geometry.

The PN theory as an asymptotic limit of transport theory in planar geometry. 1

International Nuclear Information System (INIS)

Larsen, E.W.; Pomraning, G.C.

1991-01-01

In this paper the P N theory is shown to be an asymptotic limit of transport theory for an optically thick planar-geometry system with small absorption and highly anisotropic scattering. The asymptotic analysis shows that the solution in the interior of the system is described by the standard P N equations for which initial, boundary, and interface conditions are determined by asymptotic initial, boundary layer, and interface layer calculations. The asymptotic initial, (reflecting) boundary, and interface conditions for the P N equations agree with conventional formulations. However, at a boundary having a prescribed incident flux, the asymptotic boundary layer analysis yields P N boundary conditions that differ from previous formulations. Numerical transport and P N results are presented to substantiate this asymptotic theory

ADM Mass for Asymptotically de Sitter Space-Time

International Nuclear Information System (INIS)

Huang Shiming; Yue Ruihong; Jia Dongyan

2010-01-01

In this paper, an ADM mass formula for asymptotically de Sitter(dS) space-time is derived from the energy-momentum tensor. We take the vacuum dS space as the background and investigate the ADM mass of the (d + 3)-dimensional sphere-symmetric space with a positive cosmological constant, and find that the ADM mass of asymptotically dS space is based on the ADM mass of Schwarzschild field and the cosmological background brings some small mass contribution as well. (general)

Gravitational charges of transverse asymptotically AdS spacetimes

International Nuclear Information System (INIS)

Cebeci, Hakan; Sarioglu, Oezguer; Tekin, Bayram

2006-01-01

Using Killing-Yano symmetries, we construct conserved charges of spacetimes that asymptotically approach to the flat or anti-de Sitter spaces only in certain directions. In D dimensions, this allows one to define gravitational charges (such as mass and angular momenta densities) of p-dimensional branes/solitons or any other extended objects that curve the transverse space into an asymptotically flat or AdS one. Our construction answers the question of what kind of charges the antisymmetric Killing-Yano tensors lead to

Thermodynamics of asymptotically safe theories

DEFF Research Database (Denmark)

Rischke, Dirk H.; Sannino, Francesco

2015-01-01

We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...

Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review

Directory of Open Access Journals (Sweden)

Mahmoud Bayat

Full Text Available This review features a survey of some recent developments in asymptotic techniques and new developments, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the achieved approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to over-come the shortcomings.In this review we have applied different powerful analytical methods to solve high nonlinear problems in engineering vibrations. Some patterns are given to illustrate the effectiveness and convenience of the methodologies.

Numerical relativity and asymptotic flatness

International Nuclear Information System (INIS)

Deadman, E; Stewart, J M

2009-01-01

It is highly plausible that the region of spacetime far from an isolated gravitating body is, in some sense, asymptotically Minkowskian. However theoretical studies of the full nonlinear theory, initiated by Bondi et al (1962 Proc. R. Soc. A 269 21-51), Sachs (1962 Proc. R. Soc. A 270 103-26) and Newman and Unti (1962 J. Math. Phys. 3 891-901), rely on careful, clever, a priori choices of a chart (and tetrad) and so are not readily accessible to the numerical relativist, who chooses her/his chart on the basis of quite different grounds. This paper seeks to close this gap. Starting from data available in a typical numerical evolution, we construct a chart and tetrad which are, asymptotically, sufficiently close to the theoretical ones, so that the key concepts of the Bondi news function, Bondi mass and its rate of decrease can be estimated. In particular, these estimates can be expressed in the numerical relativist's chart as numerical relativity recipes.

Ratio asymptotics of Hermite-Pade polynomials for Nikishin systems

International Nuclear Information System (INIS)

Aptekarev, A I; Lopez, Guillermo L; Rocha, I A

2005-01-01

The existence of ratio asymptotics is proved for a sequence of multiple orthogonal polynomials with orthogonality relations distributed among a system of m finite Borel measures with support on a bounded interval of the real line which form a so-called Nikishin system. For m=1 this result reduces to Rakhmanov's celebrated theorem on the ratio asymptotics for orthogonal polynomials on the real line.

Asymptotic density and effective negligibility

Science.gov (United States)

Astor, Eric P.

In this thesis, we join the study of asymptotic computability, a project attempting to capture the idea that an algorithm might work correctly in all but a vanishing fraction of cases. In collaboration with Hirschfeldt and Jockusch, broadening the original investigation of Jockusch and Schupp, we introduce dense computation, the weakest notion of asymptotic computability (requiring only that the correct answer is produced on a set of density 1), and effective dense computation, where every computation halts with either the correct answer or (on a set of density 0) a symbol denoting uncertainty. A few results make more precise the relationship between these notions and work already done with Jockusch and Schupp's original definitions of coarse and generic computability. For all four types of asymptotic computation, including generic computation, we demonstrate that non-trivial upper cones have measure 0, building on recent work of Hirschfeldt, Jockusch, Kuyper, and Schupp in which they establish this for coarse computation. Their result transfers to yield a minimal pair for relative coarse computation; we generalize their method and extract a similar result for relative dense computation (and thus for its corresponding reducibility). However, all of these notions of near-computation treat a set as negligible iff it has asymptotic density 0. Noting that this definition is not computably invariant, this produces some failures of intuition and a break with standard expectations in computability theory. For instance, as shown by Hamkins and Miasnikov, the halting problem is (in some formulations) effectively densely computable, even in polynomial time---yet this result appears fragile, as indicated by Rybalov. In independent work, we respond to this by strengthening the approach of Jockusch and Schupp to avoid such phenomena; specifically, we introduce a new notion of intrinsic asymptotic density, invariant under computable permutation, with rich relations to both

On calculating double logarithmical asymptotics of vertex functions defined on the mass shell

International Nuclear Information System (INIS)

Belokurov, V.V.; Usyukina, N.I.

1981-01-01

The essence of the calculation method of double logarithmical asymptotics of vertex functions defined on the mass shell is presented. Using the method the asymptotics of the form-factor of electron is calculated. The ladder and cross-ladder diagrams are asymptotically considerable in every order of the perturbation theory. The way in which the asymptotics of the 4-order diagrams is calculated has been shown. The diagrams of this order and reduction procedures for them are given in a graphic form. The photon mass μ 2 not equal to 0 plays the role of a regulator, removing infrared divergencies. The double logarithmical asymptotics of the form-factor of electron on the mass shell is calculated rigorously in an arbitrary order of the perturbation theory [ru

Scalar hairy black holes and solitons in asymptotically flat spacetimes

International Nuclear Information System (INIS)

Nucamendi, Ulises; Salgado, Marcelo

2003-01-01

A numerical analysis shows that the Einstein field equations allow static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. When regularity at the origin is imposed (i.e., in the absence of a horizon) globally regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential V(φ) of the theory is not positive semidefinite and such that its local minimum is also a zero of the potential, the scalar field settling asymptotically at that minimum. The configurations, although unstable under spherically symmetric linear perturbations, are regular and thus can serve as counterexamples to the no-scalar-hair conjecture

Non-Weyl asymptotics for quantum graphs with general coupling conditions

International Nuclear Information System (INIS)

Davies, E Brian; Exner, Pavel; Lipovsky, JirI

2010-01-01

Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in the case of Kirchhoff or anti-Kirchhoff conditions. While for graphs without permutation symmetry numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight into what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with unequal edge weights.

Inverted hierarchy and asymptotic freedom in grand unified supersymmetric theories

International Nuclear Information System (INIS)

Aratyn, H.

1983-01-01

The interrelation between an inverted hierarchy mechanism and asymptotic freedom in supersymmetric theories is analyzed in two models for which we performed a detailed analysis of the effective potentials and effective couplings. We find it difficult to accommodate an inverted hierarchy together with asymptotic freedom for the matter-Yukawa couplings. (orig.)

Effective action for composite operators and chiral symmetry breakdown in asymptotically free and non-asymptotically free gauge theories

International Nuclear Information System (INIS)

Gusynin, V.P.; Miranskij, V.A.

1987-01-01

An essential distinction in the relaization of the PCAC dynamics in asymptotically free and non-asymptotically free (with a non-trivial ultraviolet-stable fixed point) gauge theories is revealed. For the latter theories an analytical expressions for the condensate is obtained in the two-loop approximation and arguments of support of a soft behaviour at small distances of composite operators are given. The problem of factorizing the low-energy region for the Wess-Zumino-Witten action is discussed. Besides, the mass relations for pseudoscalar mesons in arbitrary Θ-sector are obtained in the first order in fermion bare masses and the impossibility for spontaneous P and CP-symmetries breaking in vector-like gauge theories at Θ=0 is shown

Weakly sheared active suspensions: hydrodynamics, stability, and rheology.

Science.gov (United States)

Cui, Zhenlu

2011-03-01

We present a kinetic model for flowing active suspensions and analyze the behavior of a suspension subjected to a weak steady shear. Asymptotic solutions are sought in Deborah number expansions. At the leading order, we explore the steady states and perform their stability analysis. We predict the rheology of active systems including an activity thickening or thinning behavior of the apparent viscosity and a negative apparent viscosity depending on the particle type, flow alignment, and the anchoring conditions, which can be tested on bacterial suspensions. We find remarkable dualities that show that flow-aligning rodlike contractile (extensile) particles are dynamically and rheologically equivalent to flow-aligning discoid extensile (contractile) particles for both tangential and homeotropic anchoring conditions. Another key prediction of this work is the role of the concentration of active suspensions in controlling the rheological behavior: the apparent viscosity may decrease with the increase of the concentration.

Non-pionic effects in deuteron asymptotic observables

International Nuclear Information System (INIS)

Ballot, J.L.; Robilotta, M.R.

1991-01-01

It is well known that pion dynamics dominates deuteron asymptotic observables, especially η, the D/S ratio and Q, the quadrupole moment. A procedure has been discussed earlier that allows the unambiguous determination of the pion contribution to these observables as function of the pion-nucleon coupling constant. This problem is discussed in the framework of a specific model for the nucleon-nucleon interaction, namely the potential developed by the Tourreil, Rouben and Sprung. The contribution of non-pionic dynamics to deuteron asymptotic observables is investigated. It is shown that effects due to ρ and ω exchanges are negligible. (K.A.) 8 refs., 1 fig., 1 tab

New rigorous asymptotic theorems for inverse scattering amplitudes

International Nuclear Information System (INIS)

Lomsadze, Sh.Yu.; Lomsadze, Yu.M.

1984-01-01

The rigorous asymptotic theorems both of integral and local types obtained earlier and establishing logarithmic and in some cases even power correlations aetdeen the real and imaginary parts of scattering amplitudes Fsub(+-) are extended to the inverse amplitudes 1/Fsub(+-). One also succeeds in establishing power correlations of a new type between the real and imaginary parts, both for the amplitudes themselves and for the inverse ones. All the obtained assertions are convenient to be tested in high energy experiments when the amplitudes show asymptotic behaviour

Vacuum energy in asymptotically flat 2 + 1 gravity

Energy Technology Data Exchange (ETDEWEB)

Miskovic, Olivera, E-mail: olivera.miskovic@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Olea, Rodrigo, E-mail: rodrigo.olea@unab.cl [Departamento de Ciencias Físicas, Universidad Andres Bello, Sazié 2212, Piso 7, Santiago (Chile); Roy, Debraj, E-mail: roy.debraj@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile)

2017-04-10

We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern–Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein–Hilbert term in the bulk plus half of the Gibbons–Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.

Vacuum energy in asymptotically flat 2 + 1 gravity

International Nuclear Information System (INIS)

Miskovic, Olivera; Olea, Rodrigo; Roy, Debraj

2017-01-01

We compute the vacuum energy of three-dimensional asymptotically flat space based on a Chern–Simons formulation for the Poincaré group. The equivalent action is nothing but the Einstein–Hilbert term in the bulk plus half of the Gibbons–Hawking term at the boundary. The derivation is based on the evaluation of the Noether charges in the vacuum. We obtain that the vacuum energy of this space has the same value as the one of the asymptotically flat limit of three-dimensional anti-de Sitter space.

Black hole thermodynamics from a variational principle: asymptotically conical backgrounds

Energy Technology Data Exchange (ETDEWEB)

An, Ok Song [SISSA and INFN, Sezione di Trieste,Via Bonomea 265, 34136 Trieste (Italy); Department of Physics, Kim Il Sung University,Ryongnam Dong, TaeSong District, Pyongyang, D.P.R. (Korea, Republic of); ICTP,Strada Costiera 11, 34014 Trieste (Italy); Cvetič, Mirjam [Department of Physics and Astronomy, University of Pennsylvania,209 S 33rd St, Philadelphia, PA 19104 (United States); Center for Applied Mathematics and Theoretical Physics, University of Maribor,Mladinska 3, SI2000 Maribor (Slovenia); Papadimitriou, Ioannis [SISSA and INFN, Sezione di Trieste,Via Bonomea 265, 34136 Trieste (Italy)

2016-03-14

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.

More on asymptotically anti-de Sitter spaces in topologically massive gravity

International Nuclear Information System (INIS)

Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo

2010-01-01

Recently, the asymptotic behavior of three-dimensional anti-de Sitter (AdS) gravity with a topological mass term was investigated. Boundary conditions were given that were asymptotically invariant under the two dimensional conformal group and that included a falloff of the metric sufficiently slow to consistently allow pp-wave type of solutions. Now, pp waves can have two different chiralities. Above the chiral point and at the chiral point, however, only one chirality can be considered, namely, the chirality that has the milder behavior at infinity. The other chirality blows up faster than AdS and does not define an asymptotically AdS spacetime. By contrast, both chiralities are subdominant with respect to the asymptotic behavior of AdS spacetime below the chiral point. Nevertheless, the boundary conditions given in the earlier treatment only included one of the two chiralities (which could be either one) at a time. We investigate in this paper whether one can generalize these boundary conditions in order to consider simultaneously both chiralities below the chiral point. We show that this is not possible if one wants to keep the two-dimensional conformal group as asymptotic symmetry group. Hence, the boundary conditions given in the earlier treatment appear to be the best possible ones compatible with conformal symmetry. In the course of our investigations, we provide general formulas controlling the asymptotic charges for all values of the topological mass (not just below the chiral point).

Asymptotic stability of a genetic network under impulsive control

International Nuclear Information System (INIS)

Li Fangfei; Sun Jitao

2010-01-01

The study of the stability of genetic network is an important motif for the understanding of the living organism at both molecular and cellular levels. In this Letter, we provide a theoretical method for analyzing the asymptotic stability of a genetic network under impulsive control. And the sufficient conditions of its asymptotic stability under impulsive control are obtained. Finally, an example is given to illustrate the effectiveness of the obtained method.

Asymptotic freedom and the symplectic and G2 groups

International Nuclear Information System (INIS)

Chaichian, M; Kolmakov, Yu. N.; Nelipa, N. F.

1978-01-01

It is shown that the symplectic Sp(4), Sp(6) and the exceptional G 2 gauge field theories with complete Spontaneous symmetry breaking through the Higgs mechanism are not asymptotically free. This, together with earlier results for other groups, hints at the existence of a general theorem according to which it would no longer be possible for asymptotic freedom to coexist with the absence of infrared divergences. (author)

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

Science.gov (United States)

Clark, S. E.; Oishi, Jeffrey S.

2017-05-01

The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg-Landau equation. We further find that the Ginzburg-Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

Energy Technology Data Exchange (ETDEWEB)

Clark, S. E. [Department of Astronomy, Columbia University, New York, NY 10027 (United States); Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu [Department of Physics and Astronomy, Bates College, Lewiston, ME 04240 (United States)

2017-05-20

The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg–Landau equation. We further find that the Ginzburg–Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg–Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.

On Asymptotically Lacunary Statistical Equivalent Sequences of Order α in Probability

Directory of Open Access Journals (Sweden)

Işık Mahmut

2017-01-01

Full Text Available In this study, we introduce and examine the concepts of asymptotically lacunary statistical equivalent of order α in probability and strong asymptotically lacunary equivalent of order α in probability. We give some relations connected to these concepts.

On the Construction and Properties of Weak Solutions Describing Dynamic Cavitation

KAUST Repository

Miroshnikov, Alexey

2014-08-21

We consider the problem of dynamic cavity formation in isotropic compressible nonlinear elastic media. For the equations of radial elasticity we construct self-similar weak solutions that describe a cavity emanating from a state of uniform deformation. For dimensions d=2,3 we show that cavity formation is necessarily associated with a unique precursor shock. We also study the bifurcation diagram and do a detailed analysis of the singular asymptotics associated to cavity initiation as a function of the cavity speed of the self-similar profiles. We show that for stress free cavities the critical stretching associated with dynamically cavitating solutions coincides with the critical stretching in the bifurcation diagram of equilibrium elasticity. Our analysis treats both stress-free cavities and cavities with contents.

On the asymptotic stability of nonlinear mechanical switched systems

Science.gov (United States)

Platonov, A. V.

2018-05-01

Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.

Polymers and Random graphs: Asymptotic equivalence to branching processes

International Nuclear Information System (INIS)

Spouge, J.L.

1985-01-01

In 1974, Falk and Thomas did a computer simulation of Flory's Equireactive RA/sub f/ Polymer model, rings forbidden and rings allowed. Asymptotically, the Rings Forbidden model tended to Stockmayer's RA/sub f/ distribution (in which the sol distribution ''sticks'' after gelation), while the Rings Allowed model tended to the Flory version of the RA/sub f/ distribution. In 1965, Whittle introduced the Tree and Pseudomultigraph models. We show that these random graphs generalize the Falk and Thomas models by incorporating first-shell substitution effects. Moreover, asymptotically the Tree model displays postgelation ''sticking.'' Hence this phenomenon results from the absence of rings and occurs independently of equireactivity. We also show that the Pseudomultigraph model is asymptotically identical to the Branching Process model introduced by Gordon in 1962. This provides a possible basis for the Branching Process model in standard statistical mechanics

Systematic assignment of Feshbach resonances via an asymptotic bound state model

NARCIS (Netherlands)

Goosen, M.; Kokkelmans, SJ.J.M.F.

2008-01-01

We present an Asymptotic Bound state Model (ABM), which is useful to predict Feshbach resonances. The model utilizes asymptotic properties of the interaction potentials to represent coupled molecular wavefunctions. The bound states of this system give rise to Feshbach resonances, localized at the

Asymptotic solving method for sea-air coupled oscillator ENSO model

International Nuclear Information System (INIS)

Zhou Xian-Chun; Yao Jing-Sun; Mo Jia-Qi

2012-01-01

The ENSO is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interaction. In this article, we create an asymptotic solving method for the nonlinear system of the ENSO model. The asymptotic solution is obtained. And then we can furnish weather forecasts theoretically and other behaviors and rules for the atmosphere-ocean oscillator of the ENSO. (general)

A multigroup flux-limited asymptotic diffusion Fokker-Planck equation

International Nuclear Information System (INIS)

Liu Chengan

1987-01-01

A more perfrect flux-limited method is applied to combine with asymptotic diffusion theory of the radiation transpore, and the high peaked component in the scattering angle is treated with Fokker-Planck methods, thus the flux-limited asymptotic diffusion Fokker-Planck equation has been founded. Since the equation is of diffusion form, it retains the simplity and the convenience of the classical diffusion theory, and improves precision in describing radiation transport problems

Asymptotic normalization coefficients and astrophysical factors

International Nuclear Information System (INIS)

Mukhamedzhanov, A.M.; Azhari, A.; Clark, H.L.; Gagliardi, C.A.; Lui, Y.-W.; Sattarov, A.; Trache, L.; Tribble, R.E.; Burjan, V.; Kroha, V.; Carstoiu, F.

2000-01-01

The S factor for the direct capture reaction 7 Be(p,γ) 8 B can be found at astrophysical energies from the asymptotic normalization coefficients (ANC's) which provide the normalization of the tails of the overlap functions for 8 B → 7 Be + p. Peripheral transfer reactions offer a technique to determine these ANC's. Using this technique, the 10 B( 7 Be, 8 B) 9 Be and 14 N( 7 Be, 8 B) 13 C reactions have been used to measure the asymptotic normalization coefficient for 7 Be(p, γ) 8 B. These results provide an indirect determination of S 17 (0). Analysis of the existing 9 Be(p, γ) 10 B experimental data within the framework of the R-matrix method demonstrates that experimentally measured ANC's can provide a reasonable determination of direct radiative capture rates. (author)

Asymptotic properties of a simple random motion

International Nuclear Information System (INIS)

Ravishankar, K.

1988-01-01

A random walker in R/sup N/ is considered. At each step the walker picks a point in R/sup N/ from a fixed finite set of destination points. Having chosen the point, the walker moves a fraction r (r < 1) of the distance toward the point along a straight line. Assuming that the successive destination points are chosen independently, it is shown that the asymptotic distribution of the walker's position has the same mean as the destination point distribution. An estimate is obtained for the fraction of time the walker stays within a ball centered at the mean value for almost every destination sequence. Examples show that the asymptotic distribution could have intricate structure

Callan-Symanzik equation and asymptotic freedom in the Marr-Shimamoto model

International Nuclear Information System (INIS)

Scarfone, Leonard M.

2010-01-01

The exactly soluble nonrelativistic Marr-Shimamoto model was introduced in 1964 as an example of the Lee model with a propagator and a nontrivial vertex function. An exactly soluble relativistic version of this model, known as the Zachariasen model, has been found to be asymptotically free in terms of coupling constant renormalization at an arbitrary spacelike momentum and on the basis of exact solutions of the Gell-Mann-Low equations. This is accomplished with conventional cut-off regularization by setting up the Yukawa and Fermi coupling constants at Euclidean momenta in terms of on mass-shell couplings and then taking the asymptotic limit. In view of this background, it may be expected that an investigation of the nonrelativistic Marr-Shimamoto theory may also exhibit asymptotic freedom in view of its manifest mathematical similarity to that of the Zachariasen model. To prove this point, the present paper prefers to examine asymptotic freedom in the nonrelativistic Marr-Shimamoto theory using the powerful concepts of the renormalization group and the Callan-Symanzik equation, in conjunction with the specificity of dimensional regularization and on-shell renormalization. This approach is based on calculations of the Callan-Symanzik coefficients and determinations of the effective coupling constants. It is shown that the Marr-Shimamoto theory is asymptotically free for dimensions D 3 occurring in periodic intervals over the range of 0< D<27 of particular interest. This differs from the original Lee model which has been shown by several authors, using these same concepts, to be asymptotically free only for D<4.

The importance and use of asymptotic freedom beyond the leading order

International Nuclear Information System (INIS)

Duke, D.W.

1979-05-01

The theoretical and phenomenological importance of asymptotic freedom beyond the leading order is discussed. The two main topics are (1) the determination of the fundamental scale Λ, and (2) ambiguities in parton model definitions when using the higher order effects of asymptotic freedom. (author)

Modeling broadband poroelastic propagation using an asymptotic approach

Energy Technology Data Exchange (ETDEWEB)

Vasco, Donald W.

2009-05-01

An asymptotic method, valid in the presence of smoothly-varying heterogeneity, is used to derive a semi-analytic solution to the equations for fluid and solid displacements in a poroelastic medium. The solution is defined along trajectories through the porous medium model, in the manner of ray theory. The lowest order expression in the asymptotic expansion provides an eikonal equation for the phase. There are three modes of propagation, two modes of longitudinal displacement and a single mode of transverse displacement. The two longitudinal modes define the Biot fast and slow waves which have very different propagation characteristics. In the limit of low frequency, the Biot slow wave propagates as a diffusive disturbance, in essence a transient pressure pulse. Conversely, at low frequencies the Biot fast wave and the transverse mode are modified elastic waves. At intermediate frequencies the wave characteristics of the longitudinal modes are mixed. A comparison of the asymptotic solution with analytic and numerical solutions shows reasonably good agreement for both homogeneous and heterogeneous Earth models.

Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations

International Nuclear Information System (INIS)

Kaikina, Elena I; Naumkin, Pavel I; Shishmarev, Il'ya A

2009-01-01

The large-time asymptotic behaviour of solutions of the Cauchy problem is investigated for a non-linear Sobolev-type equation with dissipation. For small initial data the approach taken is based on a detailed analysis of the Green's function of the linear problem and the use of the contraction mapping method. The case of large initial data is also closely considered. In the supercritical case the asymptotic formulae are quasi-linear. The asymptotic behaviour of solutions of a non-linear Sobolev-type equation with a critical non-linearity of the non-convective kind differs by a logarithmic correction term from the behaviour of solutions of the corresponding linear equation. For a critical convective non-linearity, as well as for a subcritical non-convective non-linearity it is proved that the leading term of the asymptotic expression for large times is a self-similar solution. For Sobolev equations with convective non-linearity the asymptotic behaviour of solutions in the subcritical case is the product of a rarefaction wave and a shock wave. Bibliography: 84 titles.

Naturalness of asymptotically safe Higgs

DEFF Research Database (Denmark)

Pelaggi, Giulio M.; Sannino, Francesco; Strumia, Alessandro

2017-01-01

that the scalars can be lighter than Λ. Although we do not have an answer to whether the Standard Model hypercharge coupling growth toward a Landau pole at around Λ ~ 1040GeV can be tamed by non-perturbative asymptotic safety, our results indicate that such a possibility is worth exploring. In fact, if successful...

Derivative analyticity relations and asymptotic energies

International Nuclear Information System (INIS)

Fischer, J.

1976-01-01

On the basis of general principles of the S-matrix theory theorems are derived showing that derivative analyticity relations analogous to those of Bronzen, Kane and Sukhatme hold at asymptotic energies if the high-energy limits of certain physical quantities exist

Asymptotical behaviour of pion electromagnetic form factor in QCD

International Nuclear Information System (INIS)

Efremov, A.V.; Radyushkin, A.V.

1978-01-01

In the framework of the renormalizable quantum field theory a new approach is developed to the investigation of asymptotical behaviour of two-particle bound state electromagnetic form factor. It is shown that the behaviour of the pion EM form factor in quantum chromodynamics at sufficiently large momentum transfers is controlled by the short-distance dynamics only. The formula is obtained which expresses the asymptotical behaviour of the pion form factor in terms of the fundamental constants of the theory

Inelastic multiple scattering of interacting bosons in weak random potentials

International Nuclear Information System (INIS)

Geiger, Tobias

2013-01-01

Within the present thesis we develop a diagrammatic scattering theory for interacting bosons in a three-dimensional, weakly disordered potential. Based on a microscopic N-body scattering theory, we identify the relevant diagrams including elastic and inelastic collision processes that are sufficient to describe quantum transport in the regime of weak disorder. By taking advantage of the statistical properties of the weak disorder potential, we demonstrate how the N-body dynamics can be reduced to a nonlinear integral equation of Boltzmann type for the single-particle diffusive flux. A presently available alternative description - based on the Gross-Pitaevskii equation - only includes elastic collisions. In contrast, we show that far from equilibrium the presence of inelastic collisions - even for weak interaction strength - must be accounted for and can induce the full thermalization of the single-particle current. In addition, we also determine the coherent corrections to the incoherent transport, leading to the effect of coherent backscattering. For the first time, we are able to analyze the influence of inelastic collisions on the coherent backscattering signal, which lead to an enhancement of the backscattered cone in a narrow spectral window, even for increasing non-linearity. With a short recollection of the presently available experimental techniques we furthermore show how an immediate implementation of our suggested setup with confined Bose-Einstein condensates can be accomplished. Thereby, the emergence of collective and/or thermodynamic behavior from fundamental, microscopic constituents can also be assessed experimentally. In a second part of this thesis, we present first results for light scattering off strongly interacting Rydberg atoms trapped in a one-dimensional, chain-like configuration. In order to monitor the time-dependence of this interacting many-body system, we devise a weak measurement scenario for which we derive a master equation for the

Asymptotic Expansions - Methods and Applications

International Nuclear Information System (INIS)

Harlander, R.

1999-01-01

Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta. Several recent applications also for other limiting cases are touched upon. Finally, the pros and cons of the different approaches are briefly discussed. (author)

Centrally extended symmetry algebra of asymptotically Goedel spacetimes

International Nuclear Information System (INIS)

Compere, Geoffrey; Detournay, Stephane

2007-01-01

We define an asymptotic symmetry algebra for three-dimensional Goedel spacetimes supported by a gauge field which turns out to be the semi-direct sum of the diffeomorphisms on the circle with two loop algebras. A class of fields admitting this asymptotic symmetry algebra and leading to well-defined conserved charges is found. The covariant Poisson bracket of the conserved charges is then shown to be centrally extended to the semi-direct sum of a Virasoro algebra and two affine algebras. The subsequent analysis of three-dimensional Goedel black holes indicates that the Virasoro central charge is negative

Deep inelastic scattering in an asymptotically free gauge theory

International Nuclear Information System (INIS)

Fujiwara, Tsutomu

1977-01-01

This paper reviews the success of the asymptotically free gauge theory which describes the deep inelastic lepton-hadron scattering. The asymptotically free gauge theory was discussed as well as the reason why the parton has the nature like free particles by the aid of the field theory. The asymptotically free gauge theory (AFGT) gives the prediction that the Bjorken scaling gives rise to logarithmic violation. The theory was applied to the exchange processes of single photon and two photons. First, this paper describes the approaches to the Bjorken scaling. The approaches are the discussion of the scaling law dependent on the model and the discussion of the scaling law independent of the model. The field theoretical treatment in described. This is called the method of the renormalization group introduced by Wilson. The asymptotically free gauge theory was formed on the basis of the Callan-Symanzik equation (CSE) and of the Weinberg's power counting theorem. The exact Bjorken scaling does not hold in the quantum field theory, at least there must be logarithmic violation. The pattern of the scaling violation cannot be clarified by the present data. Discussions concerning two gamma process are presented. The measurement of the photon-photon scattering process will give the judgement whether the prediction of the AFGT is correct or not. (Kato, T.)

On iterative procedures of asymptotic inference

NARCIS (Netherlands)

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

First-passage time asymptotics over moving boundaries for random walk bridges

NARCIS (Netherlands)

Sloothaak, F.; Zwart, B.; Wachtel, V.

2017-01-01

We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with

Equations of motion according to the asymptotic post-Newtonian scheme for general relativity in the harmonic gauge

Science.gov (United States)

Arminjon, Mayeul

2005-10-01

The asymptotic scheme of post-Newtonian approximation defined for general relativity in the harmonic gauge by Futamase & Schutz (1983) is based on a family of initial data for the matter fields of a perfect fluid and for the initial metric, defining a family of weakly self-gravitating systems. We show that Weinberg’s (1972) expansion of the metric and his general expansion of the energy-momentum tensor T, as well as his expanded equations for the gravitational field and his general form of the expanded dynamical equations, apply naturally to this family. Then, following the asymptotic scheme, we derive the explicit form of the expansion of T for a perfect fluid, and the expanded fluid-dynamical equations. (These differ from those written by Weinberg.) By integrating these equations in the domain occupied by a body, we obtain a general form of the translational equations of motion for a 1PN perfect-fluid system in general relativity. To put them into a tractable form, we use an asymptotic framework for the separation parameter η, by defining a family of well-separated 1PN systems. We calculate all terms in the equations of motion up to the order η3 included. To calculate the 1PN correction part, we assume that the Newtonian motion of each body is a rigid one, and that the family is quasispherical, in the sense that in all bodies the inertia tensor comes close to being spherical as η→0. Apart from corrections that cancel for exact spherical symmetry, there is in the final equations of motion one additional term, as compared with the Lorentz-Droste (Einstein-Infeld-Hoffmann) acceleration. This term depends on the spin of the body and on its internal structure.

Asymptotic dynamics for the Cucker-Smale-type model with the Rayleigh friction

International Nuclear Information System (INIS)

Ha, Seung-Yeal; Ha, Taeyoung; Kim, Jong-Ho

2010-01-01

We study the asymptotic flocking dynamics for the Cucker-Smale-type second-order continuous-time dynamical system with the Rayleigh friction. For mean-field communications with a positive lower bound, we show that an asymptotic flocking occurs for any compactly supported initial configuration in a large coupling regime. In contrast, in a small coupling regime, an asymptotic flocking is possible for a restricted class of initial configurations near complete flocking states. We also present several numerical simulations and compare them with our analytical results.

Asymptotic dynamics for the Cucker-Smale-type model with the Rayleigh friction

Energy Technology Data Exchange (ETDEWEB)

Ha, Seung-Yeal [Department of Mathematical Sciences, Seoul National University, Seoul 151-747 (Korea, Republic of); Ha, Taeyoung; Kim, Jong-Ho, E-mail: syha@snu.ac.k, E-mail: tha@nims.re.k, E-mail: jhkim@nims.re.k [National Institute for Mathematical Sciences, 385-16, 3F Tower Koreana, Doryong-dong, Yuseong-gu, Daejeon, 305-340 (Korea, Republic of)

2010-08-06

We study the asymptotic flocking dynamics for the Cucker-Smale-type second-order continuous-time dynamical system with the Rayleigh friction. For mean-field communications with a positive lower bound, we show that an asymptotic flocking occurs for any compactly supported initial configuration in a large coupling regime. In contrast, in a small coupling regime, an asymptotic flocking is possible for a restricted class of initial configurations near complete flocking states. We also present several numerical simulations and compare them with our analytical results.

Asymptotic formulae for solutions of the two-group integral neutron-transport equation

International Nuclear Information System (INIS)

Duracz, T.

1976-01-01

The steady-state, two-group integral neutron-transport equation is considered for two cases. First, for plane geometry, formulae for the asymptotic flux are obtained, under assumptions of homogeneous medium with isotropic scattering, extended to infinity (whole space and half-space), with sources vanishing at infinity as 0(esup(-IXI)). Next, for spherical geometry, the Milne problem is considered and formulae for the asymptotic flux are obtained. These formulae have the form of asymptotic expansions for small and large radii of the black sphere. (orig.) [de

The Asymptotic Safety Scenario in Quantum Gravity.

Science.gov (United States)

Niedermaier, Max; Reuter, Martin

2006-01-01

The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.

Self similar asymptotics of the drift ion acoustic waves

International Nuclear Information System (INIS)

Taranov, V.B.

2004-01-01

A 3D model for the coupled drift and ion acoustic waves is considered. It is shown that self-similar solutions can exist due to the symmetry extension in asymptotic regimes. The form of these solutions is determined in the presence of the magnetic shear as well as in the shear less case. Some of the most symmetric exact solutions are obtained explicitly. In particular, solutions describing asymptotics of zonal flow interaction with monochromatic waves are presented and corresponding frequency shifts are determined

Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations

Directory of Open Access Journals (Sweden)

Zhinan Xia

2014-01-01

Full Text Available We define the concept of discrete weighted pseudo-S-asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo-S-asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem.

Perturbed asymptotically linear problems

OpenAIRE

Bartolo, R.; Candela, A. M.; Salvatore, A.

2012-01-01

The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which is just continuous. Also in the case when the problem has not a variational structure, suitable procedures and estimates allow us to prove that the number of distinct crtitical levels of the functional associated to the unperturbed problem is "stable" unde...

Global asymptotic behavior in a Lotka–Volterra competition system with spatio-temporal delays

International Nuclear Information System (INIS)

Zhang, Jia-Fang; Chen, Heshan

2014-01-01

This paper is concerned with a Lotka–Volterra competition system with spatio-temporal delays. By using the linearization method, we show the local asymptotic behavior of the nonnegative steady-state solutions. Especially, the global asymptotic stability of the positive steady-state solution is investigated by the method of upper and lower solutions. The result of global asymptotic stability implies that the system has no nonconstant positive steady-state solution

Holography in asymptotically flat spacetimes and the BMS group

International Nuclear Information System (INIS)

Arcioni, Giovanni; Dappiaggi, Claudio

2004-01-01

In a previous paper (Arcioni G and Dappiaggi C 2003 Preprint hep-th/0306142) we have started to explore the holographic principle in the case of asymptotically flat spacetimes and analysed, in particular, different aspects of the Bondi-Metzner-Sachs (BMS) group, namely the asymptotic symmetry group of any asymptotically flat spacetime. We continue this investigation in this paper. Having in mind an S-matrix approach with future and past null infinity playing the role of holographic screens on which the BMS group acts, we connect the IR sectors of the gravitational field with the representation theory of the BMS group. We analyse the (complicated) mapping between bulk and boundary symmetries pointing out differences with respect to the anti-de Sitter (AdS)/CFT set up. Finally, we construct a BMS phase space and a free Hamiltonian for fields transforming with respect to BMS representations. The last step is supposed to be an explorative investigation of the boundary data living on the degenerate null manifold at infinity

Asymptotic analysis of the Forward Search

DEFF Research Database (Denmark)

Johansen, Søren; Nielsen, Bent

The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data. This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000). An asymptotic analysis of the Forward Search is made...

An asymptotic problem in renewal theory

NARCIS (Netherlands)

Klamkin, M.S.; van Lint, J.H.

1972-01-01

A special problem in renewal theory is considered. The asymptotic behavior of the renewal function was studied by W. L. Smith. Here we show that his result with an exponentially small remainder term follows from a theorem of De Bruijn on Volterra integral equations.

Asymptotic structure of the Einstein-Maxwell theory on AdS{sub 3}

Energy Technology Data Exchange (ETDEWEB)

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.

Reconstructing weak values without weak measurements

International Nuclear Information System (INIS)

Johansen, Lars M.

2007-01-01

I propose a scheme for reconstructing the weak value of an observable without the need for weak measurements. The post-selection in weak measurements is replaced by an initial projector measurement. The observable can be measured using any form of interaction, including projective measurements. The reconstruction is effected by measuring the change in the expectation value of the observable due to the projector measurement. The weak value may take nonclassical values if the projector measurement disturbs the expectation value of the observable

High-frequency asymptotics of the local vertex function. Algorithmic implementations

Energy Technology Data Exchange (ETDEWEB)

Tagliavini, Agnese; Wentzell, Nils [Institut fuer Theoretische Physik, Eberhard Karls Universitaet, 72076 Tuebingen (Germany); Institute for Solid State Physics, Vienna University of Technology, 1040 Vienna (Austria); Li, Gang; Rohringer, Georg; Held, Karsten; Toschi, Alessandro [Institute for Solid State Physics, Vienna University of Technology, 1040 Vienna (Austria); Taranto, Ciro [Institute for Solid State Physics, Vienna University of Technology, 1040 Vienna (Austria); Max Planck Institute for Solid State Research, D-70569 Stuttgart (Germany); Andergassen, Sabine [Institut fuer Theoretische Physik, Eberhard Karls Universitaet, 72076 Tuebingen (Germany)

2016-07-01

Local vertex functions are a crucial ingredient of several forefront many-body algorithms in condensed matter physics. However, the full treatment of their frequency dependence poses a huge limitation to the numerical performance. A significant advancement requires an efficient treatment of the high-frequency asymptotic behavior of the vertex functions. We here provide a detailed diagrammatic analysis of the high-frequency asymptotic structures and their physical interpretation. Based on these insights, we propose a frequency parametrization, which captures the whole high-frequency asymptotics for arbitrary values of the local Coulomb interaction and electronic density. We present its algorithmic implementation in many-body solvers based on parquet-equations as well as functional renormalization group schemes and assess its validity by comparing our results for the single impurity Anderson model with exact diagonalization calculations.

Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks.

Science.gov (United States)

Chen, Boshan; Chen, Jiejie

2015-08-01

We study the global asymptotic ω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ω-periodic or autonomous fractional-order neural networks cannot generate exactly ω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymptotically converge to the same nonconstant ω-periodic function that may be not a solution. Copyright © 2015 Elsevier Ltd. All rights reserved.

Asymptotic symmetries on the Kerr-Newman horizon without the anomaly of diffeomorphism invariance

International Nuclear Information System (INIS)

Koga, Jun-ichirou

2008-01-01

We analyze asymptotic symmetries on the Killing horizon of the four-dimensional Kerr-Newman black hole. We first derive the asymptotic Killing vectors on the Killing horizon, which describe the asymptotic symmetries, and find that the general form of these asymptotic Killing vectors is the universal one possessed by arbitrary Killing horizons. We then construct the phase space associated with the asymptotic symmetries. It is shown that the phase space of an extreme black hole either has the size comparable with a non-extreme black hole, or is small enough to exclude degeneracy, depending on whether or not the global structure of a Killing horizon particular to an extreme black hole is respected. We also show that the classical central charge in the Poisson brackets algebra of these asymptotic symmetries vanishes, which implies that there is not an anomaly of diffeomorphism invariance. By taking into account other results in the literature, we argue that the vanishing central charge on a black hole horizon, in an effective theory, looks consistent with the thermal feature of a black hole. We furthermore argue that the vanishing central charge implies that there are sufficiently many classical configurations that constitute a single macroscopic state, while these configurations are distinguished physically

ESR study of weakly irradiated organic conductors: TMTSF-DMTCNQ and (TMTSF)2PF6

International Nuclear Information System (INIS)

Forro, L.; Beuneu, F.

1982-01-01

ESR experiments are presented on irradiated TMTSF-DMTCNQ and (TMTSF) 2 PF 6 . They suggest that a weak disorder extends the metallic phases to low temperatures. Surprisingly, disorder has no effect on the ESR linewidth of (TMTSF) 2 PF 6 between 20 and 30 K, where the d.c. conductivity changes a lot with disorder. (author)

Gravitational perturbation of the BTZ black hole induced by test particles and weak cosmic censorship in AdS spacetime

International Nuclear Information System (INIS)

Rocha, Jorge V.; Cardoso, Vitor

2011-01-01

We analyze the gravitational perturbations induced by particles falling into a three dimensional, asymptotically AdS black hole geometry. More specifically, we solve the linearized perturbation equations obtained from the geodesic motion of a ringlike distribution of test particles in the BTZ background. This setup ensures that the U(1) symmetry of the background is preserved. The nonasymptotic flatness of the background raises difficulties in attributing the significance of energy and angular momentum to the conserved quantities of the test particles. This issue is well known but, to the best of our knowledge, has never been addressed in the literature. We confirm that the naive expressions for energy and angular momentum are the correct definitions. Finally, we put an asymptotically AdS version of the weak cosmic censorship to a test: by attempting to overspin the BTZ black hole with test particles it is found that the black hole cannot be spun-up past its extremal limit.

Effect of state-dependent delay on a weakly damped nonlinear oscillator.

Science.gov (United States)

Mitchell, Jonathan L; Carr, Thomas W

2011-04-01

We consider a weakly damped nonlinear oscillator with state-dependent delay, which has applications in models for lasers, epidemics, and microparasites. More generally, the delay-differential equations considered are a predator-prey system where the delayed term is linear and represents the proliferation of the predator. We determine the critical value of the delay that causes the steady state to become unstable to periodic oscillations via a Hopf bifurcation. Using asymptotic averaging, we determine how the system's behavior is influenced by the functional form of the state-dependent delay. Specifically, we determine whether the branch of periodic solutions will be either sub- or supercritical as well as an accurate estimation of the amplitude. Finally, we choose a few examples of state-dependent delay to test our analytical results by comparing them to numerical continuation.

Selected asymptotic methods with applications to electromagnetics and antennas

CERN Document Server

Fikioris, George; Bakas, Odysseas N

2013-01-01

This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include som

Asymptotic inverse periods of reflected reactors above prompt critical

International Nuclear Information System (INIS)

Spriggs, G.D.; Busch, R.D.

1995-01-01

It is commonly assumed that the kinetic behavior of reflected and unreflected reactors is identical. In particular, it is often accepted that a given reactivity change in either type of system will result in an identical asymptotic inverse period. This is generally true for reactivities below prompt critical. For reactivities above prompt critical, however, the asymptotic inverse period can vary in a highly nonlinear fashion with system reactivity depending on the reflector return fraction, the neutron lifetime in the core, and the neutron lifetime in the reflector

Asymptotic solution of the non-isothermal Cahn-Hilliard system

International Nuclear Information System (INIS)

Omel'yanov, G.A.

1995-05-01

The non-isothermal Cahn-Hillard questions with a small parameter in the n-dimensional case (n = 2.3) are considered. The small parameter is proportional both to the relaxation time and to the linear scale of transition zone, so the large time process is examined. The asymptotic solution describing the free interface dynamics is constructed. As the small parameter tends to zero, the limiting solution satisfies the modified Stefan problem with corrected Gibbs-Thomson law. The justification of the asymptotic solution is proved. (author). 26 refs

Proximal weakness of lower limbs as the sole presentation of hyperthyroidism: report of one case.

Science.gov (United States)

Chen, Chu-Chin; Chiu, Pao-Chin; Shih, Chen-Houng; Hsieh, Kai-Sheng

2005-01-01

Most children with acute or chronic flaccid limb weakness have a disorder of motor unit. However, it is very important to exclude cerebral or other upper motor neuron disorders before we approach such patients as pure muscle disorders. In general, neuropathy results in distal limb weakness, myopathy manifests with proximal weakness. There are exceptions, however. Accurate diagnosis in this wide array of disorders is dependent on a careful clinical assessment followed by the appropriate investigations. Here we report a 14-year-old girl who presented with progressive difficulty in rising up from the floor for one month. Neurological examination revealed an obese, clumsy but clear girl with stable vital signs. The muscle power of neck and upper limbs was normal. There was positive Gower sign, but the toe and heel gaits were acceptable. The initial blood work and motor/sensory nerve conduction velocity were unremarkable. Further study for thyroid function showed a hyperthyroid state. The proximal myopathy recovered soon after medical treatment. There were no other symptoms, and signs indicating hyperthyroidism and proximal myopathy of lower limbs was the isolated clinical feature. Hyperthyroid myopathy is common in hyperthyroidism, but is unusual as the sole presenting symptom.

Asymptotic solutions of diffusion models for risk reserves

Directory of Open Access Journals (Sweden)

S. Shao

2003-01-01

Full Text Available We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armed with asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate governing the conditional probability of ruin over a finite time in terms of interest rate.

Asymptotic expansion of unsteady gravity flow of a power-law fluid ...

African Journals Online (AJOL)

We present a paper on the asymptotic expansion of unsteady non-linear rheological effects of a power-law fluid under gravity. The fluid flows through a porous medium. The asymptotic expansion is employed to obtain solution of the nonlinear problem. The results show the existence of traveling waves. It is assumed that the ...

Asymptotic adaptive bipartite entanglement-distillation protocol

International Nuclear Information System (INIS)

Hostens, Erik; Dehaene, Jeroen; De Moor, Bart

2006-01-01

We present an asymptotic bipartite entanglement-distillation protocol that outperforms all existing asymptotic schemes. This protocol is based on the breeding protocol with the incorporation of two-way classical communication. Like breeding, the protocol starts with an infinite number of copies of a Bell-diagonal mixed state. Breeding can be carried out as successive stages of partial information extraction, yielding the same result: one bit of information is gained at the cost (measurement) of one pure Bell state pair (ebit). The basic principle of our protocol is at every stage to replace measurements on ebits by measurements on a finite number of copies, whenever there are two equiprobable outcomes. In that case, the entropy of the global state is reduced by more than one bit. Therefore, every such replacement results in an improvement of the protocol. We explain how our protocol is organized as to have as many replacements as possible. The yield is then calculated for Werner states

Integrable theories that are asymptotically CFT

CERN Document Server

Evans, J M; Jonathan M Evans; Timothy J Hollowood

1995-01-01

A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level k. In contrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered here may be termed ``asymptotically CFT''. These theories have previously been conjectured to be quantum integrable; we confirm this by proposing a factorizable S-matrix to describe their infra-red behaviour and then carrying out a stringent test of this proposal. The test involves coupling the theory to a conserved charge and evaluating the response of the free-energy both in perturbation theory to one loop and directly from the S-matrix via the Thermodynamic Bethe Ansatz with a chemical potential at zero temperature. Comparison of these results provides convincing evidence in favour of the proposed S-matrix; it also yields the universal coefficients of the beta-func...

Model Hadron asymptotic behaviour

International Nuclear Information System (INIS)

Kralchevsky, P.; Nikolov, A.

1983-01-01

The work is devoted to the problem of solving a set of asymptotic equations describing the model hardon interaction. More specifically an interactive procedure consisting of two stages is proposed and the first stage is exhaustively studied here. The principle of contracting transformations has been applied for this purpose. Under rather general and natural assumptions, solutions in a series of metric spaces suitable for physical applications have been found. For each of these spaces a solution with unique definiteness is found. (authors)

The BFKL high energy asymptotic in the next-to-leading approximation

International Nuclear Information System (INIS)

Levin, Eugene

1999-01-01

We discuss the high energy asymptotic in the next-to-leading (NLO) BFKL equation. We find a general solution for the Green functions and consider two properties of the NLO BFKL kernel: running QCD coupling and large NLO corrections to the conformal part of the kernel. Both these effects lead to Regge-BFKL asymptotic only in the limited range of energy (y = ln(s/qq 0 ) ≤ (α S ) ((-5)/(3)) ) and change the energy behaviour of the amplitude for higher values of energy. We confirm the oscillation in the total cross section found by D.A. Ross [SHEP-98-06, hep-ph/9804332] in the NLO BFKL asymptotic, which shows that the NLO BFKL has a serious pathology

Asymptotic mass degeneracies in conformal field theories

International Nuclear Information System (INIS)

Kani, I.; Vafa, C.

1990-01-01

By applying a method of Hardy and Ramanujan to characters of rational conformal field theories, we find an asymptotic expansion for degeneracy of states in the limit of large mass which is exact for strings propagating in more than two uncompactified space-time dimensions. Moreover we explore how the rationality of the conformal theory is reflected in the degeneracy of states. We also consider the one loop partition function for strings, restricted to physical states, for arbitrary (irrational) conformal theories, and obtain an asymptotic expansion for it in the limit that the torus degenerates. This expansion depends only on the spectrum of (physical and unphysical) relevant operators in the theory. We see how rationality is consistent with the smoothness of mass degeneracies as a function of moduli. (orig.)

The Asymptotic Safety Scenario in Quantum Gravity

Directory of Open Access Journals (Sweden)

Niedermaier Max

2006-12-01

Full Text Available The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.

Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems

DEFF Research Database (Denmark)

Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian

2011-01-01

The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has consid...... dimensional reliability problems in structural dynamics.......The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high...

Asymptotic near freedom

International Nuclear Information System (INIS)

Bailin, D.

1974-01-01

It is proved that the characteristic power deviations from scaling of the theories which are not asymptotically free should be detectable in the N.A.L. muon experiments. The Yukawa theories here considered have SU(3) non-singlet structure function moments varying as a power of -q 2 , namely (-q 2 ) at power -p. The maximum value of p is determined to be 2/3:SU3 and 1:SU2. The outstanding question is whether the Yukawa theories considered do in fact have fixed points satisfying the inequalities, and thus simultaneous (non-trivial) zeroes of β(g) and β(lambda) have to be found

Supersymmetric asymptotic safety is not guaranteed

DEFF Research Database (Denmark)

Intriligator, Kenneth; Sannino, Francesco

2015-01-01

in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those...

Linearly resummed hydrodynamics in a weakly curved spacetime

International Nuclear Information System (INIS)

Bu, Yanyan; Lublinsky, Michael

2015-01-01

We extend our study of all-order linearly resummed hydrodynamics in a flat space (http://dx.doi.org/10.1103/PhysRevD.90.086003, http://dx.doi.org/10.1007/JHEP11(2014)064) to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature N=4 super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically locally AdS 5 geometry to relativistic conformal fluids in a weakly curved 4D background. To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid’s energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders. We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations. In addition to two viscosity functions discussed at length in refs. (http://dx.doi.org/10.1103/PhysRevD.90.086003, http://dx.doi.org/10.1007/JHEP11(2014)064), we find four curvature induced structures coupled to the fluid via new transport coefficient functions. In ref. (http://dx.doi.org/10.1103/PhysRevD.80.065026), the latter were referred to as gravitational susceptibilities of the fluid. We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.

Linearly resummed hydrodynamics in a weakly curved spacetime

Energy Technology Data Exchange (ETDEWEB)

Bu, Yanyan; Lublinsky, Michael [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel)

2015-04-24

We extend our study of all-order linearly resummed hydrodynamics in a flat space (http://dx.doi.org/10.1103/PhysRevD.90.086003, http://dx.doi.org/10.1007/JHEP11(2014)064) to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature N=4 super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically locally AdS{sub 5} geometry to relativistic conformal fluids in a weakly curved 4D background. To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid’s energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders. We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations. In addition to two viscosity functions discussed at length in refs. (http://dx.doi.org/10.1103/PhysRevD.90.086003, http://dx.doi.org/10.1007/JHEP11(2014)064), we find four curvature induced structures coupled to the fluid via new transport coefficient functions. In ref. (http://dx.doi.org/10.1103/PhysRevD.80.065026), the latter were referred to as gravitational susceptibilities of the fluid. We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.

Generalized heat kernel coefficients for a new asymptotic expansion

International Nuclear Information System (INIS)

Osipov, Alexander A.; Hiller, Brigitte

2003-01-01

The method which allows for asymptotic expansion of the one-loop effective action W = lndetA is formulated. The positively defined elliptic operator A = U + M2 depends on the external classical fields taking values in the Lie algebra of the internal symmetry group G. Unlike the standard method of Schwinger - DeWitt, the more general case with the nongenerate mass matrix M = diag(m1, m2, ...) is considered. The first coefficients of the new asymptotic series are calculated and their relationship with the Seeley - DeWitt coefficients is clarified

Global Asymptotic Stability of Switched Neural Networks with Delays

Directory of Open Access Journals (Sweden)

Zhenyu Lu

2015-01-01

Full Text Available This paper investigates the global asymptotic stability of a class of switched neural networks with delays. Several new criteria ensuring global asymptotic stability in terms of linear matrix inequalities (LMIs are obtained via Lyapunov-Krasovskii functional. And here, we adopt the quadratic convex approach, which is different from the linear and reciprocal convex combinations that are extensively used in recent literature. In addition, the proposed results here are very easy to be verified and complemented. Finally, a numerical example is provided to illustrate the effectiveness of the results.

Asymptotic analysis of spatial discretizations in implicit Monte Carlo

International Nuclear Information System (INIS)

Densmore, Jeffery D.

2009-01-01

We perform an asymptotic analysis of spatial discretizations in Implicit Monte Carlo (IMC). We consider two asymptotic scalings: one that represents a time step that resolves the mean-free time, and one that corresponds to a fixed, optically large time step. We show that only the latter scaling results in a valid spatial discretization of the proper diffusion equation, and thus we conclude that IMC only yields accurate solutions when using optically large spatial cells if time steps are also optically large. We demonstrate the validity of our analysis with a set of numerical examples.

Asymptotic properties of spherically symmetric, regular and static solutions to Yang-Mills equations

International Nuclear Information System (INIS)

Cronstrom, C.

1987-01-01

In this paper the author discusses the asymptotic properties of solutions to Yang-Mills equations with the gauge group SU(2), for spherically symmetric, regular and static potentials. It is known, that the pure Yang-Mills equations cannot have nontrivial regular solutions which vanish rapidly at space infinity (socalled finite energy solutions). So, if regular solutions exist, they must have non-trivial asymptotic properties. However, if the asymptotic behaviour of the solutions is non-trivial, then the fact must be explicitly taken into account in constructing the proper action (and energy) for the theory. The elucidation of the appropriate surface correction to the Yang-Mills action (and hence the energy-momentum tensor density) is one of the main motivations behind the present study. In this paper the author restricts to the asymptotic behaviour of the static solutions. It is shown that this asymptotic behaviour is such that surface corrections (at space-infinity) are needed in order to obtain a well-defined (classical) theory. This is of relevance in formulating a quantum Yang-Mills theory

Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures

KAUST Repository

Huser, Raphaël

2017-06-23

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.

Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures

KAUST Repository

Huser, Raphaë l; Opitz, Thomas; Thibaud, Emeric

2017-01-01

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.

EMC effect: asymptotic freedom with nuclear targets

International Nuclear Information System (INIS)

West, G.B.

1984-01-01

General features of the EMC effect are discussed within the framework of quantum chromodynamics as expressed via the operator product expansion and asymptotic freedom. These techniques are reviewed with emphasis on the target dependence. 22 references

Asymptotic Likelihood Distribution for Correlated & Constrained Systems

CERN Document Server

Agarwal, Ujjwal

2016-01-01

It describes my work as summer student at CERN. The report discusses the asymptotic distribution of the likelihood ratio for total no. of parameters being h and 2 out of these being are constrained and correlated.

Structure of the gravitational field at spatial infinity. II. Asymptotically Minkowskian space--times

International Nuclear Information System (INIS)

Persides, S.

1980-01-01

A new formulation is established for the study of the asymptotic structure at spatial infinity of asymptotically Minkowskian space--times. First, the concept of an asymptotically simple space--time at spatial infinity is defined. This is a (physical) space--time (M,g) which can be imbedded in an unphysical space--time (M,g) with a boundary S, a C/sup infinity/ metric g and a C/sup infinity/ scalar field Ω such that Ω=0 on S, Ω>0 on M-S, and g/sup munu/ + g/sup mulambda/ g/sup nurho/ Ω/sub vertical-barlambda/ Ω/sub vertical-barrho/=Ω -2 g/sup murho/ +Ω -4 g/sup mulambda/ g/sup nurho/ Ω/sub ;/lambda Ω/sub ;/rho on M. Then an almost asymptotically flat space--time (AAFS) is defined as an asymptotically simple space--time for which S is isometric to the unit timelike hyperboloid and g/sup munu/ Ω/sub vertical-barmu/ Ω/sub vertical-barnu/ =Ω -4 g/sup munu/ Ω/sub ;/μΩ/sub ;/ν=-1 on S. Equivalent definitions are given in terms of the existence of coordinate systems in which g/sub munu/ or g/sub munu/ have simple explicitly given forms. The group of asymptotic symmetries of (M,g) is studied and is found to be isomorphic to the Lorentz group. The asymptotic behavior of an AAFS is studied. It is proven that the conformal metric g/sub munu/=Ω 2 g/sub munu/ gives C/sup lambdamurhonu/=0, Ω -1 C/sup lambdamurhonu/ Ω/sub ;/μ =0, Ω -2 C/sup lambdamurhonu/ Ω/sub ;/μ Ω/sub ;/ν=0 on S

Asymptotic analysis for a weakly damped wave equation with application to a problem arising in elasticity

Directory of Open Access Journals (Sweden)

Gabriel Nguetseng

2010-01-01

Full Text Available The present work is devoted to the study of homogenization of the weakly damped wave equation ∫Ωρε∂2uε∂t2(t⋅υdx+2ε2μ∫ΩfεEij(∂uε∂t(tEij(υdx+ε2λ∫Ωfεdiv(∂uε∂t(tdiv υdx+ϑ∫Ωfεdiv(uε(tdivυdx=∫Ωf(t⋅υdx  for all υ=(υ1,υ2,υ3∈Vε(0

Assessing model fit in latent class analysis when asymptotics do not hold

NARCIS (Netherlands)

van Kollenburg, Geert H.; Mulder, Joris; Vermunt, Jeroen K.

2015-01-01

The application of latent class (LC) analysis involves evaluating the LC model using goodness-of-fit statistics. To assess the misfit of a specified model, say with the Pearson chi-squared statistic, a p-value can be obtained using an asymptotic reference distribution. However, asymptotic p-values

Spectral asymptotic in the large coupling limit

CERN Document Server

Bruneau, V

2002-01-01

In this paper, we study a singular perturbation of an eigenvalues problem related to supra-conductor wave guides. Using boundary layer tools we perform a complete asymptotic expansion of the eigenvalues as the conductivity tends to $+\\infty$.

Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces

Directory of Open Access Journals (Sweden)

Anna Kisiolek

2005-10-01

Full Text Available We consider the second-order nonlinear difference equations of the form Δ(rn−1Δxn−1+pnf(xn−k=hn. We show that there exists a solution (xn, which possesses the asymptotic behaviour ‖xn−a∑j=0n−1(1/rj+b‖=o(1, a,b∈ℝ. In this paper, we extend the results of Agarwal (1992, Dawidowski et al. (2001, Drozdowicz and Popenda (1987, M. Migda (2001, and M. Migda and J. Migda (1988. We suppose that f has values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.

Optimal Homotopy Asymptotic Method for Solving System of Fredholm Integral Equations

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Bahman Ghazanfari

2013-08-01

Full Text Available In this paper, optimal homotopy asymptotic method (OHAM is applied to solve system of Fredholm integral equations. The effectiveness of optimal homotopy asymptotic method is presented. This method provides easy tools to control the convergence region of approximating solution series wherever necessary. The results of OHAM are compared with homotopy perturbation method (HPM and Taylor series expansion method (TSEM.

Asymptotic kinetic theory of magnetized plasmas: quasi-particle concept

International Nuclear Information System (INIS)

Sosenko, P.P.; Zagorodny, A.H.

2004-01-01

The asymptotic kinetic theory of magnetized plasmas is elaborated within the context of general statistical approach and asymptotic methods, developed by M. Krylov and M. Bohol'ubov, for linear and non-linear dynamic systems with a rapidly rotating phase. The quasi-particles are introduced already on the microscopic level. Asymptotic expansions enable to close the description for slow processes, and to relate consistently particles and guiding centres to quasi-particles. The kinetic equation for quasi-particles is derived. It makes a basis for the reduced description of slow collective phenomena in the medium. The kinetic equation for quasi-particles takes into account self-consistent interaction fields, quasi-particle collisions and collective-fluctuation-induced relaxation of quasi-particle distribution function. The relationships between the distribution functions for particles, guiding centres and quasi-particles are derived taking into account fluctuations, which can be especially important in turbulent states. In this way macroscopic (statistical) particle properties can be obtained from those of quasi-particles in the general case of non-equilibrium. (authors)

Globally asymptotically stable analysis in a discrete time eco-epidemiological system

International Nuclear Information System (INIS)

Hu, Zengyun; Teng, Zhidong; Zhang, Tailei; Zhou, Qiming; Chen, Xi

2017-01-01

Highlights: • Dynamical behaviors of a discrete time eco-epidemiological system are discussed. • Global asymptotical stability of this system is obtained by an iteration scheme which can be expended to general dimensional discrete system. • More complex dynamical behaviors are obtained by numerical simulations. - Abstract: In this study, the dynamical behaviors of a discrete time eco-epidemiological system are discussed. The local stability, bifurcation and chaos are obtained. Moreover, the global asymptotical stability of this system is explored by an iteration scheme. The numerical simulations illustrate the theoretical results and exhibit the complex dynamical behaviors such as flip bifurcation, Hopf bifurcation and chaotic dynamical behaviors. Our main results provide an efficient method to analyze the global asymptotical stability for general three dimensional discrete systems.

Inverse curvature flows in asymptotically Robertson Walker spaces

Science.gov (United States)

Kröner, Heiko

2018-04-01

In this paper we consider inverse curvature flows in a Lorentzian manifold N which is the topological product of the real numbers with a closed Riemannian manifold and equipped with a Lorentzian metric having a future singularity so that N is asymptotically Robertson Walker. The flow speeds are future directed and given by 1 / F where F is a homogeneous degree one curvature function of class (K*) of the principal curvatures, i.e. the n-th root of the Gauss curvature. We prove longtime existence of these flows and that the flow hypersurfaces converge to smooth functions when they are rescaled with a proper factor which results from the asymptotics of the metric.

Asymptotic boundary conditions for dissipative waves: General theory

Science.gov (United States)

Hagstrom, Thomas

1990-01-01

An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.

Asymptotic boundary conditions for dissipative waves - General theory

Science.gov (United States)

Hagstrom, Thomas

1991-01-01

An outstanding issue in computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.

Strong and Weak Convergence Criteria of Composite Iterative Algorithms for Systems of Generalized Equilibria

Directory of Open Access Journals (Sweden)

Lu-Chuan Ceng

2014-01-01

Full Text Available We first introduce and analyze one iterative algorithm by using the composite shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: a generalized mixed equilibrium problem, finitely many variational inequalities, and the common fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense and infinitely many nonexpansive mappings in a real Hilbert space. We prove a strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions. Our results improve and extend the corresponding results in the earlier and recent literature.

Weakly nonlinear sloshing in a truncated circular conical tank

International Nuclear Information System (INIS)

Gavrilyuk, I P; Hermann, M; Lukovsky, I A; Solodun, O V; Timokha, A N

2013-01-01

Sloshing of an ideal incompressible liquid in a rigid truncated (tapered) conical tank is considered when the tank performs small-magnitude oscillatory motions with the forcing frequency close to the lowest natural sloshing frequency. The multimodal method, the non-conformal mapping technique and the Moiseev type asymptotics are employed to derive a finite-dimensional system of weakly nonlinear ordinary differential (modal) equations. This modal system is a generalization of that by Gavrilyuk et al 2005 Fluid Dyn. Res. 37 399–429. Using the derived modal equations, we classify the resonant steady-state wave regimes occurring due to horizontal harmonic tank excitations. The frequency ranges are detected where the ‘planar’ and/or ‘swirling’ steady-state sloshing are stable as well as a range in which all steady-state wave regimes are not stable and irregular (chaotic) liquid motions occur is established. The results on the frequency ranges are qualitatively supported by experiments by Matta E 2002 PhD Thesis Politecnico di Torino, Torino. (paper)

Nonequilibrium electrophoresis of an ion-selective microgranule for weak and moderate external electric fields

Science.gov (United States)

Frants, E. A.; Ganchenko, G. S.; Shelistov, V. S.; Amiroudine, S.; Demekhin, E. A.

2018-02-01

Electrokinetics and the movement of charge-selective micro-granules in an electrolyte solution under the influence of an external electric field are investigated theoretically. Straightforward perturbation analysis is applied to a thin electric double layer and a weak external field, while a numerical solution is used for moderate electric fields. The asymptotic solution enables the determination of the salt concentration, electric charge distribution, and electro-osmotic velocity fields. It may also be used to obtain a simple analytical formula for the electrophoretic velocity in the case of quasi-equilibrium electrophoresis (electrophoresis of the first kind). This formula differs from the famous Helmholtz-Smoluchowski relation, which applies to dielectric microparticles, but not to ion-selective granules. Numerical calculations are used to validate the derived formula for weak external electric fields, but for moderate fields, nonlinear effects lead to a significant increase in electrophoretic mobility and to a transition from quasi-equilibrium electrophoresis of the first kind to nonequilibrium electrophoresis of the second kind. Theoretical results are successfully compared with experimental data.

Asymptotic theory of two-dimensional trailing-edge flows

Science.gov (United States)

Melnik, R. E.; Chow, R.

1975-01-01

Problems of laminar and turbulent viscous interaction near trailing edges of streamlined bodies are considered. Asymptotic expansions of the Navier-Stokes equations in the limit of large Reynolds numbers are used to describe the local solution near the trailing edge of cusped or nearly cusped airfoils at small angles of attack in compressible flow. A complicated inverse iterative procedure, involving finite-difference solutions of the triple-deck equations coupled with asymptotic solutions of the boundary values, is used to accurately solve the viscous interaction problem. Results are given for the correction to the boundary-layer solution for drag of a finite flat plate at zero angle of attack and for the viscous correction to the lift of an airfoil at incidence. A rational asymptotic theory is developed for treating turbulent interactions near trailing edges and is shown to lead to a multilayer structure of turbulent boundary layers. The flow over most of the boundary layer is described by a Lighthill model of inviscid rotational flow. The main features of the model are discussed and a sample solution for the skin friction is obtained and compared with the data of Schubauer and Klebanoff for a turbulent flow in a moderately large adverse pressure gradient.

Physically asymptotic Hartree-Fock stationary-phase approximant to the many-body S-matrix

International Nuclear Information System (INIS)

Griffin, J.J.; Dworzecka, M.

1982-01-01

The Asymptotic Hartree-Fock Approximant replaces the physically non-asymptotic (and dynamically nontrivial) external translation of the FISP result with the asymptotic and dynamically trivial translational evolution of Dirac-TDHF by adding an explicit restriction upon the acceptable channel states. It is therefore preferable under the principle of commensurability, which judges the expected output of physical descriptions in terms of the physical assumptions they incorporate. Further insight into the relationship between the TDSHF and FISP methods will reward careful comparison of the respective expressions, in specific cases

Asymptotically flat structure of hypergravity in three spacetime dimensions

Energy Technology Data Exchange (ETDEWEB)

Fuentealba, Oscar [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Departamento de Física, Universidad de Concepción,Casilla 160-C, Concepción (Chile); Matulich, Javier; Troncoso, Ricardo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile)

2015-10-02

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{sub 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{sub (2,4)} 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 antiperiodic boundary conditions, respectively. The hypergravity theory is also explicitly extended so as to admit parity-odd terms in the action. It is then shown that the asymptotic symmetry algebra includes an additional central charge, being proportional to the coupling of the Lorentz-Chern-Simons form. The generalization of these results in the case of gravity minimally coupled to arbitrary half-integer spin fields is also carried out. The hypersymmetry bounds are found to be given by a suitable polynomial of degree s+(1/2) in the energy, where s is the spin of the fermionic generators.

Ultraviolet asymptotic behavior of the photon propagator in dimensionally regularized quantum electrodynamics

International Nuclear Information System (INIS)

Krasnikov, N.V.

1991-01-01

Study of the ultraviolet behavior of asymptotically nonfree theories is one of the most important problems of quantum field theory. Unfortunately, not too much is known about the ultraviolet properties in asymptotically nonfree theories; the main obstacle is the growth of the effective coupling constant in the ultraviolet region, which renders perturbation theory inapplicable. It is shown that in quantum electrodynamics in n = 4 + 2 var-epsilon space-time (var-epsilon > 0) the photon propagator has the ultraviolet asymptotic behavior D(k 2 ) ∼ (k 2 ) -1-var-epsilon . In the case var-epsilon R ≤ -3π var-epsilon + O(var-epsilon 2 )

High frequency asymptotic methods

International Nuclear Information System (INIS)

Bouche, D.; Dessarce, R.; Gay, J.; Vermersch, S.

1991-01-01

The asymptotic methods allow us to compute the interaction of high frequency electromagnetic waves with structures. After an outline of their foundations with emphasis on the geometrical theory of diffraction, it is shown how to use these methods to evaluate the radar cross section (RCS) of complex tri-dimensional objects of great size compared to the wave-length. The different stages in simulating phenomena which contribute to the RCS are reviewed: physical theory of diffraction, multiple interactions computed by shooting rays, research for creeping rays. (author). 7 refs., 6 figs., 3 insets

Rapid Linguistic Ambiguity Resolution in Young Children with Autism Spectrum Disorder: Eye Tracking Evidence for the Limits of Weak Central Coherence.

Science.gov (United States)

Hahn, Noemi; Snedeker, Jesse; Rabagliati, Hugh

2015-12-01

Individuals with autism spectrum disorders (ASD) have often been reported to have difficulty integrating information into its broader context, which has motivated the Weak Central Coherence theory of ASD. In the linguistic domain, evidence for this difficulty comes from reports of impaired use of linguistic context to resolve ambiguous words. However, recent work has suggested that impaired use of linguistic context may not be characteristic of ASD, and is instead better explained by co-occurring language impairments. Here, we provide a strong test of these claims, using the visual world eye tracking paradigm to examine the online mechanisms by which children with autism resolve linguistic ambiguity. To address concerns about both language impairments and compensatory strategies, we used a sample whose verbal skills were strong and whose average age (7; 6) was lower than previous work on lexical ambiguity resolution in ASD. Participants (40 with autism and 40 controls) heard sentences with ambiguous words in contexts that either strongly supported one reading or were consistent with both (John fed/saw the bat). We measured activation of the unintended meaning through implicit semantic priming of an associate (looks to a depicted baseball glove). Contrary to the predictions of weak central coherence, children with ASD, like controls, quickly used context to resolve ambiguity, selecting appropriate meanings within a second. We discuss how these results constrain the generality of weak central coherence. © 2015 International Society for Autism Research, Wiley Periodicals, Inc.

Existence and asymptotic behavior of solutions for nonlinear Schrödinger-Poisson systems with steep potential well.

Science.gov (United States)

Du, Miao; Tian, Lixin; Wang, Jun; Zhang, Fubao

2016-03-01

In this paper, we are concerned with a class of Schrödinger-Poisson systems with the asymptotically linear or asymptotically 3-linear nonlinearity. Under some suitable assumptions on V , K , a , and f , we prove the existence, nonexistence, and asymptotic behavior of solutions via variational methods. In particular, the potential V is allowed to be sign-changing for the asymptotically linear case.

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

Directory of Open Access Journals (Sweden)

Yuncheng You

2008-12-01

Full Text Available The asymptotic dynamics of high-order temporal-spatial derivatives of the two-dimensional vorticity and velocity of an incompressible, viscous fluid flow in $mathbb{R}^2$ are studied, which is equivalent to the 2D Navier-Stokes equation. It is known that for any integrable initial vorticity, the 2D vorticity solution converges to the Oseen vortex. In this paper, sharp exterior decay estimates of the temporal-spatial derivatives of the vorticity solution are established. These estimates are then used and combined with similarity and $L^p$ compactness to show the asymptotical attraction rates of temporal-spatial derivatives of generic 2D vorticity and velocity solutions by the Oseen vortices and velocity solutions respectively. The asymptotic estimates and the asymptotic attraction rates of all the derivatives obtained in this paper are independent of low or high Reynolds numbers.

Asymptotic stability of a coupled advection-diffusion-reaction system arising in bioreactor processes

Directory of Open Access Journals (Sweden)

Maria Crespo

2017-08-01

Full Text Available In this work, we present an asymptotic analysis of a coupled system of two advection-diffusion-reaction equations with Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacteria, called biomass, and a diluted organic contaminant (e.g., nitrates, called substrate, in a continuous flow bioreactor. This system exhibits, under suitable conditions, two stable equilibrium states: one steady state in which the biomass becomes extinct and no reaction is produced, called washout, and another steady state, which corresponds to the partial elimination of the substrate. We use the linearization method to give sufficient conditions for the linear asymptotic stability of the two stable equilibrium configurations. Finally, we compare our asymptotic analysis with the usual asymptotic analysis associated to the continuous bioreactor when it is modeled with ordinary differential equations.

Asymptotic Poisson distribution for the number of system failures of a monotone system

International Nuclear Information System (INIS)

Aven, Terje; Haukis, Harald

1997-01-01

It is well known that for highly available monotone systems, the time to the first system failure is approximately exponentially distributed. Various normalising factors can be used as the parameter of the exponential distribution to ensure the asymptotic exponentiality. More generally, it can be shown that the number of system failures is asymptotic Poisson distributed. In this paper we study the performance of some of the normalising factors by using Monte Carlo simulation. The results show that the exponential/Poisson distribution gives in general very good approximations for highly available components. The asymptotic failure rate of the system gives best results when the process is in steady state, whereas other normalising factors seem preferable when the process is not in steady state. From a computational point of view the asymptotic system failure rate is most attractive

On the asymptotics of the Gell-Mann-Low function in quantum field theory

International Nuclear Information System (INIS)

Kazakov, D.I.; Popov, V.S.

2003-01-01

The problem of reconstructing the Gell-Mann-Low function in quantum field theory starting with its asymptotic series with the first terms calculated by perturbation theory is discussed. And though in a strict mathematical sense this is not unambiguously realizable, under reasonable assumptions about the function it appears to be possible to reconstruct it in some finite interval of g. However, any attempts to find its asymptotics as g→∞ from our point of view are not justified. We also present the conditions under which the sum of the asymptotic series may decrease at infinity

Asymptotics of QCD factorization in exclusive hadronic decays of B mesons

International Nuclear Information System (INIS)

Becher, Thomas; Neubert, Matthias; Pecjak, Ben D.

2001-01-01

Using the renormalon calculus, we study the asymptotic behavior of the perturbative expansion of the hard-scattering kernels entering the QCD factorization formula for the nonleptonic weak decays B-bar 0 →D (*)+ M - , where M is a light meson. In the 'large-β 0 limit', the kernels are infrared finite and free of endpoint singularities to all orders of perturbation theory. The leading infrared renormalon singularity corresponding to a power correction of order Λ QCD /m b vanishes if the light meson has a symmetric light-cone distribution amplitude. We calculate the Borel transforms and the corresponding momentum distribution functions of the hard-scattering kernels, and resum the series of O(β 0 n-1 α s n ) corrections to explore the numerical significance of higher-order perturbative and power corrections. We also derive explicit expressions for the O(β 0 α s 2 ) contributions to the kernels, and for the renormalon singularities corresponding to power corrections of order (Λ QCD /m b ) 2 . Finally, we study the limit m c →0 relevant to charmless hadronic decays such as B→ππ

Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes

International Nuclear Information System (INIS)

Bachoc, Francois

2014-01-01

Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar regularity parameter. Consistency and asymptotic normality are proved for the Maximum Likelihood and Cross Validation estimators of the covariance parameters. The asymptotic covariance matrices of the covariance parameter estimators are deterministic functions of the regularity parameter. By means of an exhaustive study of the asymptotic covariance matrices, it is shown that the estimation is improved when the regular grid is strongly perturbed. Hence, an asymptotic confirmation is given to the commonly admitted fact that using groups of observation points with small spacing is beneficial to covariance function estimation. Finally, the prediction error, using a consistent estimator of the covariance parameters, is analyzed in detail. (authors)

Asymptotic behavior of the warm inflation scenario with viscous pressure

International Nuclear Information System (INIS)

Mimoso, Jose P.; Nunes, Ana; Pavon, Diego

2006-01-01

We analyze the dynamics of models of warm inflation with general dissipative effects. We consider phenomenological terms both for the inflaton decay rate and for viscous effects within matter. We provide a classification of the asymptotic behavior of these models and show that the existence of a late-time scaling regime depends not only on an asymptotic behavior of the scalar field potential, but also on an appropriate asymptotic behavior of the inflaton decay rate. There are scaling solutions whenever the latter evolves to become proportional to the Hubble rate of expansion regardless of the steepness of the scalar field exponential potential. We show from thermodynamic arguments that the scaling regime is associated with a power-law dependence of the matter-radiation temperature on the scale factor, which allows a mild variation of the temperature of the matter/radiation fluid. We also show that the late-time contribution of the dissipative terms alleviates the depletion of matter, and increases the duration of inflation

Asymptotic absolute continuity for perturbed time-dependent ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

We study the notion of asymptotic velocity for a class of perturbed time- ... for Mathematical Physics and Stochastics, funded by a grant from the Danish National Research Foun- .... Using (2.4) we can readily continue α(t) to the whole half-axis.

Asymptotically Safe Standard Model via Vectorlike Fermions

Science.gov (United States)

Mann, R. B.; Meffe, J. R.; Sannino, F.; Steele, T. G.; Wang, Z. W.; Zhang, C.

2017-12-01

We construct asymptotically safe extensions of the standard model by adding gauged vectorlike fermions. Using large number-of-flavor techniques we argue that all gauge couplings, including the hypercharge and, under certain conditions, the Higgs coupling, can achieve an interacting ultraviolet fixed point.

Multiple cognitive capabilities/deficits in children with an autism spectrum disorder: "weak" central coherence and its relationship to theory of mind and executive control.

Science.gov (United States)

Pellicano, Elizabeth; Maybery, Murray; Durkin, Kevin; Maley, Alana

2006-01-01

This study examined the validity of "weak" central coherence (CC) in the context of multiple cognitive capabilities/deficits in autism. Children with an autism spectrum disorder (ASD) and matched typically developing children were administered tasks tapping visuospatial coherence, false-belief understanding and aspects of executive control. Significant group differences were found in all three cognitive domains. Evidence of local processing on coherence tasks was widespread in the ASD group, but difficulties in attributing false beliefs and in components of executive functioning were present in fewer of the children with ASD. This cognitive profile was generally similar for younger and older children with ASD. Furthermore, weak CC was unrelated to false-belief understanding, but aspects of coherence (related to integration) were associated with aspects of executive control. Few associations were found between cognitive variables and indices of autistic symptomatology. Implications for CC theory are discussed.

Fast-slow asymptotics for a Markov chain model of fast sodium current

Science.gov (United States)

Starý, Tomáš; Biktashev, Vadim N.

2017-09-01

We explore the feasibility of using fast-slow asymptotics to eliminate the computational stiffness of discrete-state, continuous-time deterministic Markov chain models of ionic channels underlying cardiac excitability. We focus on a Markov chain model of fast sodium current, and investigate its asymptotic behaviour with respect to small parameters identified in different ways.

Asymptotics of pion electromagnetics form factor in scale invariant quark model

International Nuclear Information System (INIS)

Efremov, A.V.; Radyushkin, A.V.

1976-01-01

A consistent relativistic approach is proposed to the investigation of asymptotic behaviour of form factor of a system, composed of two spinor particles, interacting with the vector of (pseudo) scalar neutral field. It is shown that the assumption of finite and small asymptotical value of quark-gluon interaction invariant charge at small distances (g 9 2 9 2 ln(-Q 2 ) 2 values (Q 2 is squared momentum)

Mass loss by stars at the stage of the asymptotic giant branch

International Nuclear Information System (INIS)

Frantsman, Y.L.

1986-01-01

For a given initial stellar mass function, star formation function, and initial chemical composition, distributions have been constructed for stars of the asymptotic giant branch by luminosity, and for white dwarfs by mass, by calculating the approximate evolution of a large number of stars. Variants are calculated with different assumptions about the mass loss in the asymptotic branch. Theory can be reconciled with observation only if it is assumed that at this stage there is also a still large mass loss in addition to the stellar wind and the ejection of a planetary nebula shell. This provides the explanation for the absence in the Magellanic clouds of carbon stars with M /sub bol/ 1.0M /sub ./. The degenerate carbon-oxygen nuclei of stars evolving along the asymptotic giant branch cannot attain the Chandrasekhar limit on account of the great mass loss by the stars. The luminosity of stars of the asymptotic giant branch in the globular clusters of the Magellanic Clouds is a good indicator of the age of the clusters

Asymptotic sequences over ideals and projectively equivalent ideals with respect to modules

International Nuclear Information System (INIS)

Naghipour, R.; Sedghi, M.

2007-09-01

Let R be a commutative Noetherian ring, and let N be a non-zero finitely generated R-module. The purpose of this paper is to show that if I and J are projectively equivalent ideals w.r.t. N, then a sequence x := x 1 , . . . , x n of elements of R is an asymptotic sequence over I w.r.t. N if and only if it is an asymptotic sequence over J w.r.t. N. Also, it is shown that if R is local, then the lengths of all maximal asymptotic sequences over an ideal I w.r.t. N are the same. As a consequence we derive a generalization of Rees' theorem. (author)

Asymptotic behavior of quark masses induced by instantons

International Nuclear Information System (INIS)

Carneiro, C.E.I.; Frenkel, J.

1984-02-01

A simple argument which shows that the dynamical mass induced by interactions of massless quarks with pseudo-particle configurations, behaves like p -6 for asymptotically large quark momenta is presented. (Author) [pt

Non-linear and signal energy optimal asymptotic filter design

Directory of Open Access Journals (Sweden)

Josef Hrusak

2003-10-01

Full Text Available The paper studies some connections between the main results of the well known Wiener-Kalman-Bucy stochastic approach to filtering problems based mainly on the linear stochastic estimation theory and emphasizing the optimality aspects of the achieved results and the classical deterministic frequency domain linear filters such as Chebyshev, Butterworth, Bessel, etc. A new non-stochastic but not necessarily deterministic (possibly non-linear alternative approach called asymptotic filtering based mainly on the concepts of signal power, signal energy and a system equivalence relation plays an important role in the presentation. Filtering error invariance and convergence aspects are emphasized in the approach. It is shown that introducing the signal power as the quantitative measure of energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. The property of structural energy dissipativeness is one of the most important and fundamental features of resulting filters. Therefore, it is natural to call them asymptotic filters. The notion of the asymptotic filter is carried in the paper as a proper tool in order to unify stochastic and non-stochastic, linear and nonlinear approaches to signal filtering.

Asymptotics for the minimum covariance determinant estimator

NARCIS (Netherlands)

Butler, R.W.; Davies, P.L.; Jhun, M.

1993-01-01

Consistency is shown for the minimum covariance determinant (MCD) estimators of multivariate location and scale and asymptotic normality is shown for the former. The proofs are made possible by showing a separating ellipsoid property for the MCD subset of observations. An analogous property is shown

The positive action conjecture and asymptotically euclidean metrics in quantum gravity

International Nuclear Information System (INIS)

Gibbons, G.W.; Pope, C.N.

1979-01-01

The positive action conjecture requires that the action of any asymptotically Euclidean 4-dimensional Riemannian metric be positive, vanishing if and only if the space is flat. Because any Ricci flat, asymptotically Euclidean metric has zero action and is local extremum of the action which is a local minimum at flat space, the conjecture requires that there are no Ricci flat asymptotically Euclidean metrics other than flat space, which would establish that flat space is the only local minimum. We prove this for metrics on R 4 and a large class of more complicated topologies and for self-dual metrics. We show that if Rsupμsubμ >= 0 there are no bound states of the Dirac equation and discuss the relevance to possible baryon non-conserving processes mediated by gravitational instantons. We conclude that these are forbidden in the lowest stationary phase approximation. We give a detailed discussion of instantons invariant under an SU(2) or SO(3) isometry group. We find all regular solutions, none of which is asymptotically Euclidean and all of which possess a further Killing vector. In an appendix we construct an approximate self-dual metric on K3 - the only simply connected compact manifold which admits a self-dual metric. (orig.) [de

Asymptotic expansion and statistical description of turbulent systems

International Nuclear Information System (INIS)

Hagan, W.K. III.

1986-01-01

A new approach to studying turbulent systems is presented in which an asymptotic expansion of the general dynamical equations is performed prior to the application of statistical methods for describing the evolution of the system. This approach has been applied to two specific systems: anomalous drift wave turbulence in plasmas and homogeneous, isotropic turbulence in fluids. For the plasma case, the time and length scales of the turbulent state result in the asymptotic expansion of the Vlasov/Poisson equations taking the form of nonlinear gyrokinetic theory. Questions regarding this theory and modern Hamiltonian perturbation methods are discussed and resolved. A new alternative Hamiltonian method is described. The Eulerian Direct Interaction Approximation (EDIA) is slightly reformulated and applied to the equations of nonlinear gyrokinetic theory. Using a similarity transformation technique, expressions for the thermal diffusivity are derived from the EDIA equations for various geometries, including a tokamak. In particular, the unique result for generalized geometry may be of use in evaluating fusion reactor designs and theories of anomalous thermal transport in tokamaks. Finally, a new and useful property of the EDIA is pointed out. For the fluid case, an asymptotic expansion is applied to the Navier-Stokes equation and the results lead to the speculation that such an approach may resolve the problem of predicting the Kolmogorov inertial range energy spectrum for homogeneous, isotropic turbulence. 45 refs., 3 figs

Induction motor IFOC based speed-controlled drive with asymptotic disturbance compensation

Directory of Open Access Journals (Sweden)

Stojić Đorđe M.

2012-01-01

Full Text Available This paper presents the design of digitally controlled speed electrical drive, with the asymptotic compensation of external disturbances, implemented by using the IFOC (Indirect Field Oriented Control torque controlled induction motor. The asymptotic disturbance compensation is achieved by using the DOB (Disturbance Observer with the IMP (Internal Model Principle. When compared to the existing IMP-based DOB solutions, in this paper the robust stability and disturbance compensation are improved by implementing the minimal order DOB filter. Also, the IMP-based DOB design is improved by employing the asymptotic compensation of all elemental or more complex external disturbances. The dynamic model of the IFOC torque electrical drive is, also, included in the speed-controller and DOB section design. The simulation and experimental measurements presented in the paper illustrate the effectiveness and robustness of the proposed control scheme.

Nonlinear adaptive control system design with asymptotically stable parameter estimation error

Science.gov (United States)

Mishkov, Rumen; Darmonski, Stanislav

2018-01-01

The paper presents a new general method for nonlinear adaptive system design with asymptotic stability of the parameter estimation error. The advantages of the approach include asymptotic unknown parameter estimation without persistent excitation and capability to directly control the estimates transient response time. The method proposed modifies the basic parameter estimation dynamics designed via a known nonlinear adaptive control approach. The modification is based on the generalised prediction error, a priori constraints with a hierarchical parameter projection algorithm, and the stable data accumulation concepts. The data accumulation principle is the main tool for achieving asymptotic unknown parameter estimation. It relies on the parametric identifiability system property introduced. Necessary and sufficient conditions for exponential stability of the data accumulation dynamics are derived. The approach is applied in a nonlinear adaptive speed tracking vector control of a three-phase induction motor.

Methods and Algorithms for Approximating the Gamma Function and Related Functions. A survey. Part I: Asymptotic Series

Directory of Open Access Journals (Sweden)

Cristinel Mortici

2015-01-01

Full Text Available In this survey we present our recent results on analysis of gamma function and related functions. The results obtained are in the theory of asymptotic analysis, approximation of gamma and polygamma functions, or in the theory of completely monotonic functions. The motivation of this first part is the work of C. Mortici [Product Approximations via Asymptotic Integration Amer. Math. Monthly 117 (2010 434-441] where a simple strategy for constructing asymptotic series is presented. The classical asymptotic series associated to Stirling, Wallis, Glaisher-Kinkelin are rediscovered. In the second section we discuss some new inequalities related to Landau constants and we establish some asymptotic formulas.

The Comorbidity between Attention-Deficit/Hyperactivity Disorder (ADHD) in Children and Arabic Speech Sound Disorder

Science.gov (United States)

Hariri, Ruaa Osama

2016-01-01

Children with Attention-Deficiency/Hyperactive Disorder (ADHD) often have co-existing learning disabilities and developmental weaknesses or delays in some areas including speech (Rief, 2005). Seeing that phonological disorders include articulation errors and other forms of speech disorders, studies pertaining to children with ADHD symptoms who…

Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups

International Nuclear Information System (INIS)

Drozhzhinov, Yurii N; Zav'yalov, Boris I

2012-01-01

We give a complete description of distributions that are asymptotically homogeneous (including the case of critical index of the asymptotic scale) along the trajectories determined by continuous multiplicative one-parameter transformation groups such that the real parts of all eigenvalues of the infinitesimal matrix are positive. To do this, we introduce and study special spaces of distributions. As an application of our results, we describe distributions that are homogeneous along such groups.

What can asymptotic expansions tell us about large-scale quasi-geostrophic anticyclonic vortices?

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A. Stegner

1995-01-01

Full Text Available The problem of the large-scale quasi-geostrophic anticyclonic vortices is studied in the framework of the baratropic rotating shallow- water equations on the β-plane. A systematic approach based on the multiplescale asymptotic expansions is used leading to a hierarchy of governing equations for the large-scale vortices depending on their characteristic size, velocity and a free surface elevation. Among them are the Charney-Obukhov equation, the intermediate geostrophic model equation, the frontal dynamics equation and some new nonlinear quasi-geostrophic equation. We are looking for steady-drifting axisymmetric anticyclonic solutions and find them in a consistent way only in this last equation. These solutions are soliton-like in the sense that the effects of weak non-linearity and dispersion balance each other. The same regimes on the paraboloidal β-plane are studied, all giving a negative result in what concerns the axisymmetric steady solutions, except for a strong elevation case where any circular profile is found to be steadily propagating within the accuracy of the approximation.

Ghost anomalous dimension in asymptotically safe quantum gravity

International Nuclear Information System (INIS)

Eichhorn, Astrid; Gies, Holger

2010-01-01

We compute the ghost anomalous dimension within the asymptotic-safety scenario for quantum gravity. For a class of covariant gauge fixings and using a functional renormalization group scheme, the anomalous dimension η c is negative, implying an improved UV behavior of ghost fluctuations. At the non-Gaussian UV fixed point, we observe a maximum value of η c ≅-0.78 for the Landau-deWitt gauge within the given scheme and truncation. Most importantly, the backreaction of the ghost flow onto the Einstein-Hilbert sector preserves the non-Gaussian fixed point with only mild modifications of the fixed-point values for the gravitational coupling and cosmological constant and the associated critical exponents; also their gauge dependence is slightly reduced. Our results provide further evidence for the asymptotic-safety scenario of quantum gravity.

Hadronic Form Factors in Asymptotically Free Field Theories

Science.gov (United States)

Gross, D. J.; Treiman, S. B.

1974-01-01

The breakdown of Bjorken scaling in asymptotically free gauge theories of the strong interactions is explored for its implications on the large q{sup 2} behavior of nucleon form factors. Duality arguments of Bloom and Gilman suggest a connection between the form factors and the threshold properties of the deep inelastic structure functions. The latter are addressed directly in an analysis of asymptotically free theories; and through the duality connection we are then led to statements about the form factors. For very large q{sup 2} the form factors are predicted to fall faster than any inverse power of q{sup 2}. For the more modest range of q{sup 2} reached in existing experiments the agreement with data is fairly good, though this may well be fortuitous. Extrapolations beyond this range are presented.

Molten salt reactor as asymptotic safety nuclear system

International Nuclear Information System (INIS)

Novikov, V.M.; Ignatyev, V.V.

1989-01-01

Safety is becoming the main and priority problem of the nuclear power development. An increase of the active safety measures could hardly be considered as the proper way to achieve the asymptotically high level of nuclear safety. It seem that the more realistic way to achieve such a goal is to minimize risk factors and to maximize the use of inherent and passive safety properties. The passive inherent safety features of the liquid fuel molten salt reactor (MSR) technology are making it attractive for future energy generation. The achievement of the asymptotic safety in MSR is being connected with the minimization of such risk factors as a reactivity excess, radioactivity stored, decay heat, non nuclear energy stored in core. In this paper safety peculiarities of the different MSR concepts are discussed

Asymptotic matching of the solar-system gravitational yields

International Nuclear Information System (INIS)

Kopejkin, S.M.

1989-01-01

In the framework of the general relativity, the structure of the Solar-system gravitational fields is investigated and the relativistic formulae of transformation between nonrotating in the dynamical sense harmonic reference systems - barycentric, planetocentric and topocentric (satelite) ones - are derived by the method of the asymptotic mathing of components of the metric tensor. The derived formulae generalize the linear Poincare transformation in the case of curved space-time. With the help of the asymptotic matching formulae, the relationships between relativistic time scales inside the Solar system have been established, the equations of relativistic precession of the space axis of one reference system with respect to another one have been derived, the equations of translational motion of the center-of-mass of planets (the Sun) and their satellites have been obtained

The Barrett–Crane model: asymptotic measure factor

International Nuclear Information System (INIS)

Kamiński, Wojciech; Steinhaus, Sebastian

2014-01-01

The original spin foam model construction for 4D gravity by Barrett and Crane suffers from a few troubling issues. In the simple examples of the vertex amplitude they can be summarized as the existence of contributions to the asymptotics from non-geometric configurations. Even restricted to geometric contributions the amplitude is not completely worked out. While the phase is known to be the Regge action, the so-called measure factor has remained mysterious for a decade. In the toy model case of the 6j symbol this measure factor has a nice geometric interpretation of V −1/2 leading to speculations that a similar interpretation should be possible also in the 4D case. In this paper we provide the first geometric interpretation of the geometric part of the asymptotic for the spin foam consisting of two glued 4-simplices (decomposition of the 4-sphere) in the Barrett–Crane model in the large internal spin regime. (paper)

The Barrett-Crane model: asymptotic measure factor

Science.gov (United States)

Kamiński, Wojciech; Steinhaus, Sebastian

2014-04-01

The original spin foam model construction for 4D gravity by Barrett and Crane suffers from a few troubling issues. In the simple examples of the vertex amplitude they can be summarized as the existence of contributions to the asymptotics from non-geometric configurations. Even restricted to geometric contributions the amplitude is not completely worked out. While the phase is known to be the Regge action, the so-called measure factor has remained mysterious for a decade. In the toy model case of the 6j symbol this measure factor has a nice geometric interpretation of V-1/2 leading to speculations that a similar interpretation should be possible also in the 4D case. In this paper we provide the first geometric interpretation of the geometric part of the asymptotic for the spin foam consisting of two glued 4-simplices (decomposition of the 4-sphere) in the Barrett-Crane model in the large internal spin regime.

A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis

Directory of Open Access Journals (Sweden)

R. Fares

2012-01-01

Full Text Available We study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and some a priori estimates, we construct an asymptotic solution. The existence of a junction region between the two rectangles imposes to consider, as part of the asymptotic solution, some boundary layer correctors that correspond to this region. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. By means of the a priori estimates, we justify our asymptotic construction, by obtaining a small error between the exact and the asymptotic solutions.

Extreme-Strike and Small-time Asymptotics for Gaussian Stochastic Volatility Models

OpenAIRE

Zhang, Xin

2016-01-01

Asymptotic behavior of implied volatility is of our interest in this dissertation. For extreme strike, we consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Loève expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we derive asymptotics for the asset price density for large or smal...

Large degree asymptotics of generalized Bessel polynomials

NARCIS (Netherlands)

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

Infrared studies of asymptotic giant branch stars

International Nuclear Information System (INIS)

Willems, F.J.

1987-01-01

In this thesis studies are presented of asymptotic giant branch stars, which are thought to be an important link in the evolution of the galaxy. The studies were performed on the basis of data collected by the IRAS, the infrared astronomical satelite. 233 refs.; 33 figs.; 16 tabs

Infrared divergences in the asymptotically not free Yang-Mills theory

International Nuclear Information System (INIS)

Fajzullaev, B.A.

1979-01-01

Shown is analogy of infrared asymptotics (with the accuracy up to the multiplier in the degree index) of Green fermion functions in quantum electrodynamics as well as in nonabelian asymptotics free and not free models. Infrared asymptotics of Green functions of calibrating boson in accordance with Appelquist and Carazzone theorem does not depend on the present massive fermions. The calculations showed that in the fermion models interacting with nonabelian calibrating fields, infrared divergences in the physical processes are not reduced no matter whether they are free or not free. So, in these models the point αsub(c)=0 will always be infrared-instable no matter whether αsub(c)=0 is ultraviolet-stable or not. This result is in agreement with one of the Appelquist-Carazzone theorem consequences stating that if the calibrating group is divided into direct product of several subgroups and they are connected only by exchange of a heavy particle, then the charge of each subgroup is subjected (within the infrared limit) to its renormgroup equation

Asymptotic freedom and Zweig's rule

International Nuclear Information System (INIS)

Appelquist, Th.

1977-01-01

Some theoretical aspects of applying short distance physics (asymptotic freedom) are discussed to prove the correctness of the quantum chromodynamics. Properties of new particles that depend only on short distance physics can be dealt with perturbatively. The new mesons are assumed to be CantiC bound states, where C is a new heavy quark. With this in mind some comments are made on the calculation of total widths for the direct decay of different CantiC states into ordinary hadrons

Analyticity of event horizons of five-dimensional multi-black holes with nontrivial asymptotic structure

International Nuclear Information System (INIS)

Kimura, Masashi

2008-01-01

We show that there exist five-dimensional multi-black hole solutions which have analytic event horizons when the space-time has nontrivial asymptotic structure, unlike the case of five-dimensional multi-black hole solutions in asymptotically flat space-time.

Mass loss by stars on the asymptotic giant branch

International Nuclear Information System (INIS)

Frantsman, Yu.L.

1986-01-01

The theoretical populations of white dwarfs and carbon stars were generated for Salpeter initial mass function and constant stellar birth rate history. The effect of very strong mass loss on the mass distribution of white dwarfs and luminosity distribution of carbon stars is discussed and the results are compared with observations. This comparison suggested that a signioficant mass loss by stars on the asymptotic giant branch occurs besides stellar wind and planetary nebulae ejection. Thus it is possible to explain the absence of carbon stars with Msub(bol) 1.0 Msub(sun). The luminosity of asymptotic giant branch stars in the globular clusters of the Magellanic Clouds appears to be a very good indicator of the age

Asymptotics of the filtration problem for suspension in porous media

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Kuzmina Ludmila Ivanovna

2015-01-01

Full Text Available The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and are stuck at the inlet of pores that are smaller than the particle size. It is considered that one particle can clog only one small pore and vice versa. The particles stuck in the pores remain motionless and form a deposit. The concentrations of suspended and retained particles satisfy a quasilinear hyperbolic system of partial differential equations of the first order, obtained as a result of macro-averaging of micro-stochastic diffusion equations. Initially the porous media contains no particles and both concentrations are equal to zero; the suspension supplied to the porous media inlet has a constant concentration of suspended particles. The flow of particles moves in the porous media with a constant speed, before the wave front the concentrations of suspended and retained particles are zero. Assuming that the filtration coefficient is small we construct an asymptotic solution of the filtration problem over the concentration front. The terms of the asymptotic expansions satisfy linear partial differential equations of the first order and are determined successively in an explicit form. It is shown that in the simplest case the asymptotics found matches the known asymptotic expansion of the solution near the concentration front.

Asymptotic description of plasma turbulence: Krylov-Bogoliubov methods and quasi-particles

International Nuclear Information System (INIS)

Sosenko, P.P.; Bertrand, P.; Decyk, V.K.

2001-01-01

The asymptotic theory of charged particle motion in electromagnetic fields is developed for the general case of finite Larmor-radius effects by means of Krylov-Bogoliubov averaging method. The correspondence between the general asymptotic methods, elaborated by M. Krylov and M.Bogoliubov, the quasi-particle description and gyrokinetics is established. Such a comparison is used to shed more light on the physical sense of the reduced Poisson equation, introduced in gyrokinetics, and the particle polarization drift. It is shown that the modification of the Poisson equation in the asymptotic theory is due to the non-conservation of the magnetic moment and gyrophase trembling. it is shown that the second-order modification of the adiabatic invariant can determine the conditions of global plasma stability and introduces new nonlinear terms into the reduced Poisson equation. Such a modification is important for several plasma orderings, e.g. NHD type ordering. The feasibility of numerical simulation schemes in which the polarization drift is included into the quasi-particle equations of motion, and the Poisson equation remains unchanged is analyzed. A consistent asymptotic model is proposed in which the polarization drift is included into the quasi-particle equations of motion and the particle and quasi-particle velocities are equal. It is shown that in such models there are additional modifications of the reduced Poisson equation. The latter becomes even more complicated in contrast to earlier suggestions

Weak point disorder in strongly fluctuating flux-line liquids

Indian Academy of Sciences (India)

of intense research activity in the past fifteen odd years [1–5]. Potential ... types of disorder give rise to a variety of phases, thus making vortex matter an ... A powerful method for describing both clean and ..... We have predicted qualitative.

Asymptotics with a positive cosmological constant: I. Basic framework

Science.gov (United States)

Ashtekar, Abhay; Bonga, Béatrice; Kesavan, Aruna

2015-01-01

The asymptotic structure of the gravitational field of isolated systems has been analyzed in great detail in the case when the cosmological constant Λ is zero. The resulting framework lies at the foundation of research in diverse areas in gravitational science. Examples include: (i) positive energy theorems in geometric analysis; (ii) the coordinate invariant characterization of gravitational waves in full, nonlinear general relativity; (iii) computations of the energy-momentum emission in gravitational collapse and binary mergers in numerical relativity and relativistic astrophysics; and (iv) constructions of asymptotic Hilbert spaces to calculate S-matrices and analyze the issue of information loss in the quantum evaporation of black holes. However, by now observations have led to a strong consensus that Λ is positive in our universe. In this paper we show that, unfortunately, the standard framework does not extend from the Λ =0 case to the Λ \\gt 0 case in a physically useful manner. In particular, we do not have positive energy theorems, nor an invariant notion of gravitational waves in the nonlinear regime, nor asymptotic Hilbert spaces in dynamical situations of semi-classical gravity. A suitable framework to address these conceptual issues of direct physical importance is developed in subsequent papers.

The asymptotic expansion method via symbolic computation

OpenAIRE

Navarro, Juan F.

2012-01-01

This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.

Asymptotic inversion of the Erlang B formula

NARCIS (Netherlands)

Leeuwaarden, van J.S.H.; Temme, N.M.

2008-01-01

The 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 make use of

Asymptotic behaviour of firmly non expansive sequences

International Nuclear Information System (INIS)

Rouhani, B.D.

1993-04-01

We introduce the notion of firmly non expansive sequences in a Banach space and present several results concerning their asymptotic behaviour extending previous results and giving an affirmative answer to an open question raised by S. Reich and I. Shafir. Applications to averaged mappings are also given. (author). 16 refs

Asymptotically anti-de Sitter spacetimes and scalar fields with a logarithmic branch

International Nuclear Information System (INIS)

Henneaux, Marc; Martinez, Cristian; Troncoso, Ricardo; Zanelli, Jorge

2004-01-01

We consider a self-interacting scalar field whose mass saturates the Breitenlohner-Freedman bound, minimally coupled to Einstein gravity with a negative cosmological constant in D≥3 dimensions. It is shown that the asymptotic behavior of the metric has a slower fall-off than that of pure gravity with a localized distribution of matter, due to the back-reaction of the scalar field, which has a logarithmic branch decreasing as r -(D-1)/2 ln r for large radius r. We find the asymptotic conditions on the fields which are invariant under the same symmetry group as pure gravity with negative cosmological constant (conformal group in D-1 dimensions). The generators of the asymptotic symmetries are finite even when the logarithmic branch is considered but acquire, however, a contribution from the scalar field

Exact asymptotic relations for the effective response of linear viscoelastic heterogeneous media

Science.gov (United States)

Gallican, Valentin; Brenner, Renald; Suquet, Pierre

2017-11-01

This article addresses the asymptotic response of viscoelastic heterogeneous media in the frequency domain, at high and low frequencies, for different types of elementary linear viscoelastic constituents. By resorting to stationary principles for complex viscoelasticity and adopting a classification of the viscoelastic behaviours based on the nature of their asymptotic regimes, either elastic or viscous, four exact relations are obtained on the overall viscoelastic complex moduli in each case. Two relations are related to the asymptotic uncoupled heterogeneous problems, while the two remaining ones result from the viscoelastic coupling that manifests itself in the transient regime. These results also provide exact conditions on certain integrals in time of the effective relaxation spectrum. This general setting encompasses the results obtained in preceding studies on mixtures of Maxwell constituents [1,2]. xml:lang="fr"

Asymptotically optimal production policies in dynamic stochastic jobshops with limited buffers

Science.gov (United States)

Hou, Yumei; Sethi, Suresh P.; Zhang, Hanqin; Zhang, Qing

2006-05-01

We consider a production planning problem for a jobshop with unreliable machines producing a number of products. There are upper and lower bounds on intermediate parts and an upper bound on finished parts. The machine capacities are modelled as finite state Markov chains. The objective is to choose the rate of production so as to minimize the total discounted cost of inventory and production. Finding an optimal control policy for this problem is difficult. Instead, we derive an asymptotic approximation by letting the rates of change of the machine states approach infinity. The asymptotic analysis leads to a limiting problem in which the stochastic machine capacities are replaced by their equilibrium mean capacities. The value function for the original problem is shown to converge to the value function of the limiting problem. The convergence rate of the value function together with the error estimate for the constructed asymptotic optimal production policies are established.

Weak measurements and quantum weak values for NOON states

Science.gov (United States)

Rosales-Zárate, L.; Opanchuk, B.; Reid, M. D.

2018-03-01

Quantum weak values arise when the mean outcome of a weak measurement made on certain preselected and postselected quantum systems goes beyond the eigenvalue range for a quantum observable. Here, we propose how to determine quantum weak values for superpositions of states with a macroscopically or mesoscopically distinct mode number, that might be realized as two-mode Bose-Einstein condensate or photonic NOON states. Specifically, we give a model for a weak measurement of the Schwinger spin of a two-mode NOON state, for arbitrary N . The weak measurement arises from a nondestructive measurement of the two-mode occupation number difference, which for atomic NOON states might be realized via phase contrast imaging and the ac Stark effect using an optical meter prepared in a coherent state. The meter-system coupling results in an entangled cat-state. By subsequently evolving the system under the action of a nonlinear Josephson Hamiltonian, we show how postselection leads to quantum weak values, for arbitrary N . Since the weak measurement can be shown to be minimally invasive, the weak values provide a useful strategy for a Leggett-Garg test of N -scopic realism.

The Asymptotic Expansion Method via Symbolic Computation

Directory of Open Access Journals (Sweden)

Juan F. Navarro

2012-01-01

Full Text Available This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.

Finger extension weakness and downbeat nystagmus motor neuron disease syndrome: A novel motor neuron disorder?

Science.gov (United States)

Delva, Aline; Thakore, Nimish; Pioro, Erik P; Poesen, Koen; Saunders-Pullman, Rachel; Meijer, Inge A; Rucker, Janet C; Kissel, John T; Van Damme, Philip

2017-12-01

Disturbances of eye movements are infrequently encountered in motor neuron diseases (MNDs) or motor neuropathies, and there is no known syndrome that combines progressive muscle weakness with downbeat nystagmus. To describe the core clinical features of a syndrome of MND associated with downbeat nystagmus, clinical features were collected from 6 patients. All patients had slowly progressive muscle weakness and wasting in combination with downbeat nystagmus, which was clinically most obvious in downward and lateral gaze. Onset was in the second to fourth decade with finger extension weakness, progressing to other distal and sometimes more proximal muscles. Visual complaints were not always present. Electrodiagnostic testing showed signs of regional motor axonal loss in all patients. The etiology of this syndrome remains elusive. Because finger extension weakness and downbeat nystagmus are the discriminating clinical features of this MND, we propose the name FEWDON-MND syndrome. Muscle Nerve 56: 1164-1168, 2017. © 2017 The Authors Muscle & Nerve Published by Wiley Periodicals, Inc.

CROSS-CORRELATION WEAK LENSING OF SDSS GALAXY CLUSTERS. III. MASS-TO-LIGHT RATIOS

International Nuclear Information System (INIS)

Sheldon, Erin S.; Johnston, David E.; Masjedi, Morad; Blanton, Michael R.; McKay, Timothy A.; Scranton, Ryan; Wechsler, Risa H.; Koester, Benjamin P.; Hansen, Sarah M.; Frieman, Joshua A.; Annis, James

2009-01-01

We present measurements of the excess mass-to-light ratio (M/L) measured around MaxBCG galaxy clusters observed in the Sloan Digital Sky Survey. This red-sequence cluster sample includes objects from small groups with M 200 ∼ 5 x 10 12 h -1 M sun to clusters with M 200 ∼ 10 15 h -1 M sun . Using cross-correlation weak lensing, we measure the excess mass density profile above the universal mean Δρ(r)=ρ(r)-ρ-bar for clusters in bins of richness and optical luminosity. We also measure the excess luminosity density Δl(r)=l(r)-l-bar measured in the z = 0.25 i band. For both mass and light, we de-project the profiles to produce three-dimensional mass and light profiles over scales from 25 h -1 kpc to 22 h -1 Mpc. From these profiles we calculate the cumulative excess mass ΔM(r) and excess light ΔL(r) as a function of separation from the BCG. On small scales, where ρ(r)>>ρ-bar, the integrated mass-to-light profile (ΔM/ΔL)(r) may be interpreted as the cluster M/L. We find the (ΔM/ΔL) 200 , the M/L within r 200 , scales with cluster mass as a power law with index 0.33 ± 0.02. On large scales, where ρ(r)∼ρ-bar, the ΔM/ΔL approaches an asymptotic value independent of cluster richness. For small groups, the mean (ΔM/ΔL) 200 is much smaller than the asymptotic value, while for large clusters (ΔM/ΔL) 200 is consistent with the asymptotic value. This asymptotic value should be proportional to the mean M/L of the universe (M/L). We find (M/L)b -2 M/L = 362 ± 54h (statistical). There is additional uncertainty in the overall calibration at the ∼10% level. The parameter b 2 M/L is primarily a function of the bias of the L ∼ * galaxies used as light tracers, and should be of order unity. Multiplying by the luminosity density in the same bandpass we find Ω m b -2 M/L = 0.20 ± 0.03, independent of the Hubble parameter.

Some asymptotic theory for variance function smoothing | Kibua ...

African Journals Online (AJOL)

Simple selection of the smoothing parameter is suggested. Both homoscedastic and heteroscedastic regression models are considered. Keywords: Asymptotic, Smoothing, Kernel, Bandwidth, Bias, Variance, Mean squared error, Homoscedastic, Heteroscedastic. > East African Journal of Statistics Vol. 1 (1) 2005: pp. 9-22 ...

Asymptotically perfect discrimination in the local-operation-and-classical-communication paradigm

International Nuclear Information System (INIS)

Kleinmann, M.; Kampermann, H.; Bruss, D.

2011-01-01

We revisit the problem of discriminating orthogonal quantum states within the local-quantum-operation-and-classical-communication (LOCC) paradigm. Our particular focus is on the asymptotic situation where the parties have infinite resources and the protocol may become arbitrarily long. Our main result is a necessary condition for perfect asymptotic LOCC discrimination. As an application, we prove that for complete product bases, unlimited resources are of no advantage. On the other hand, we identify an example for which it still remains undecided whether unlimited resources are superior.

First-passage time asymptotics over moving boundaries for random walk bridges

OpenAIRE

Sloothaak, F.; Zwart, B.; Wachtel, V.

2017-01-01

We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior may be described through a regularly varying function with exponent -1/2, where the impact of the boundary is captured by the slowly varying function. Yet, the moving boundary may have a stronger effect when the tail is considered at a time close to the re...

Asymptotic elastic energy in simple metals

International Nuclear Information System (INIS)

Khalifeh, J.M.

1983-07-01

The asymptotic form of the elastic binding energy ΔEsup(as)(R) between two Mg atoms in Al is expressed as a product of a lattice Green function and the dipole force tensor P. The quantity P is obtained by a nearly free electron model in which the impurity effect is introduced by a screened Ashcroft pseudopotential characterized by an excess charge ΔZ and a core radius rsub(j). (author)

Asymptotic dynamics in perturbative quantum gravity and BMS supertranslations

Science.gov (United States)

Choi, Sangmin; Kol, Uri; Akhoury, Ratindranath

2018-01-01

Recently it has been shown that infrared divergences in the conventional S-matrix elements of gauge and gravitational theories arise from a violation of the conservation laws associated with large gauge symmetries. These infrared divergences can be cured by using the Faddeev-Kulish (FK) asymptotic states as the basis for S-matrix elements. Motivated by this connection, we study the action of BMS supertranslations on the FK asymptotic states of perturbative quantum gravity. We compute the BMS charge of the FK states and show that it characterizes the superselection sector to which the state belongs. Conservation of the BMS charge then implies that there is no transition between different superselection sectors, hence showing that the FK graviton clouds implement the necessary transition induced by the scattering process.

A mutually profitable alliance - Asymptotic expansions and numerical computations

Science.gov (United States)

Euvrard, D.

Problems including the flow past a wing airfoil at Mach 1, and the two-dimensional flow past a partially immersed body are used to show the advantages of coupling a standard numerical method for the whole domain where everything is of the order of 1, with an appropriate asymptotic expansion in the vicinity of some singular point. Cases more closely linking the two approaches are then considered. In the localized finite element method, the asymptotic expansion at infinity becomes a convergent series and the problem reduces to a variational form. Combined analytical and numerical methods are used in the singularity distribution method and in the various couplings of finite elements and a Green integral representation to design a subroutine to compute the Green function and its derivatives.

Asymptotic problems for stochastic partial differential equations

Science.gov (United States)

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.

Asymptotic freedom in the theory of the strong interaction. Comment on the nobel prize in physics 2004

International Nuclear Information System (INIS)

Zhang Zhaoxi

2005-01-01

The 2004 Nobel Prize in Physics was awarded to David J. Gross, Frank Wilczek and H. David Politzer for their decisive contributions to the theory of the asymptotic freedom of the strong interaction (a fundamental interaction). The fundamental elements of quantum chromodynamics (QCD) and the theory of the strong interaction are briefly reviewed in their historical context. How to achieve asymptotic freedom is introduced and its physical meaning explained. The latest experimental tests of asymptotic freedom are presented, and it is shown that the theoretical prediction agrees excellently with the experimental measurements. Perturbative QCD which is based on the asymptotic freedom is outlined. It is pointed out that the theoretical discovery and experimental proof of the asymptotic freedom are crucial for QCD to be the correct theory of strong interaction. Certain frontier research areas of QCD, such as 'color confinement', are mentioned. The discovery and confirmation of asymptotic freedom has indeed deeply affected particle physics, and has led to QCD becoming a main content of the standard model, and to further development of the so-called grand unification theories of interactions. (author)

Asymptotic analysis of methane-hydrogen-air mixtures

NARCIS (Netherlands)

Hermanns, R.T.E.; Bastiaans, R.J.M.; Goey, de L.P.H.

2005-01-01

In this paper an asymptotic analysis of de Goey et al.concerning premixed stoichiometric methane-hydrogen-air flames is analyzed in depth. The analysis is performed with up to 50 mole percent of hydrogen in the fuel, at gas inlet temperatures ranging from 300 K to 650 K and pressures from 1 to 15

Renormalization and asymptotic freedom in quantum gravity

International Nuclear Information System (INIS)

Tomboulis, E.T.

1984-01-01

The article reviews some recent attempts to construct satisfactory theories of quantum gravity within the framework of local, continuum field theory. Quantum gravity; the renormalization group and its fixed points; fixed points and dimensional continuation in gravity; and quantum gravity at d=4-the 1/N expansion-asymptotic freedom; are all discussed. (U.K.)

On Parametric Gevrey Asymptotics for Some Cauchy Problems in Quasiperiodic Function Spaces

Directory of Open Access Journals (Sweden)

A. Lastra

2014-01-01

Full Text Available We investigate Gevrey asymptotics for solutions to nonlinear parameter depending Cauchy problems with 2π-periodic coefficients, for initial data living in a space of quasiperiodic functions. By means of the Borel-Laplace summation procedure, we construct sectorial holomorphic solutions which are shown to share the same formal power series as asymptotic expansion in the perturbation parameter. We observe a small divisor phenomenon which emerges from the quasiperiodic nature of the solutions space and which is the origin of the Gevrey type divergence of this formal series. Our result rests on the classical Ramis-Sibuya theorem which asks to prove that the difference of any two neighboring constructed solutions satisfies some exponential decay. This is done by an asymptotic study of a Dirichlet-like series whose exponents are positive real numbers which accumulate to the origin.

Asymptotic behavior of second-order impulsive differential equations

Directory of Open Access Journals (Sweden)

Haifeng Liu

2011-02-01

Full Text Available In this article, we study the asymptotic behavior of all solutions of 2-th order nonlinear delay differential equation with impulses. Our main tools are impulsive differential inequalities and the Riccati transformation. We illustrate the results by an example.

Asymptotics for Estimating Equations in Hidden Markov Models

DEFF Research Database (Denmark)

Hansen, Jørgen Vinsløv; Jensen, Jens Ledet

Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...

AdS-like spectrum of the asymptotically Goedel space-times

International Nuclear Information System (INIS)

Konoplya, R. A.; Zhidenko, A.

2011-01-01

A black hole immersed in a rotating universe, described by the Gimon-Hashimoto solution, is tested on stability against scalar field perturbations. Unlike the previous studies on perturbations of this solution, which dealt only with the limit of slow universe rotation j, we managed to separate variables in the perturbation equation for the general case of arbitrary rotation. This leads to qualitatively different dynamics of perturbations, because the exact effective potential does not allow for Schwarzschild-like asymptotic of the wave function in the form of purely outgoing waves. The Dirichlet boundary conditions are allowed instead, which result in a totally different spectrum of asymptotically Goedel black holes: the spectrum of quasinormal frequencies is similar to the one of asymptotically anti-de Sitter black holes. At large and intermediate overtones N, the spectrum is equidistant in N. In the limit of small black holes, quasinormal modes (QNMs) approach the normal modes of the empty Goedel space-time. There is no evidence of instability in the found frequencies, which supports the idea that the existence of closed timelike curves (CTCs) and the onset of instability correlate (if at all) not in a straightforward way.

Higher order corrections to asymptotic-de Sitter inflation

Science.gov (United States)

Mohsenzadeh, M.; Yusofi, E.

2017-08-01

Since trans-Planckian considerations can be associated with the re-definition of the initial vacuum, we investigate further the influence of trans-Planckian physics on the spectra produced by the initial quasi-de Sitter (dS) state during inflation. We use the asymptotic-dS mode to study the trans-Planckian correction of the power spectrum to the quasi-dS inflation. The obtained spectra consist of higher order corrections associated with the type of geometry and harmonic terms sensitive to the fluctuations of space-time (or gravitational waves) during inflation. As an important result, the amplitude of the power spectrum is dependent on the choice of c, i.e. the type of space-time in the period of inflation. Also, the results are always valid for any asymptotic dS space-time and particularly coincide with the conventional results for dS and flat space-time.

Asymptotic SER performance comparison of MPSK and MDPSK in wireless fading channels

KAUST Repository

Song, Xuegui; Yang, Fan; Cheng, Julian; Alouini, Mohamed-Slim

2015-01-01

We propose a general framework to investigate asymptotic relative performance between M-ary phase-shift keying (MPSK) and M-ary differential phase-shift keying (MDPSK) in wireless fading channels. Using this framework, we provide an alternative derivation for the closed-form expression of the asymptotic performance loss of MDPSK w.r.t. MPSK in an additive white Gaussian noise channel. The same performance loss is also shown to be true for the lognormal fading channels.

Asymptotic SER performance comparison of MPSK and MDPSK in wireless fading channels

KAUST Repository

Song, Xuegui

2015-02-01

We propose a general framework to investigate asymptotic relative performance between M-ary phase-shift keying (MPSK) and M-ary differential phase-shift keying (MDPSK) in wireless fading channels. Using this framework, we provide an alternative derivation for the closed-form expression of the asymptotic performance loss of MDPSK w.r.t. MPSK in an additive white Gaussian noise channel. The same performance loss is also shown to be true for the lognormal fading channels.

Asymptotics for Associated Random Variables

CERN Document Server

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

Convergence Theorem for Finite Family of Total Asymptotically Nonexpansive Mappings

Directory of Open Access Journals (Sweden)

E.U. Ofoedu

2015-11-01

Full Text Available In this paper we introduce an explicit iteration process and prove strong convergence of the scheme in a real Hilbert space $H$ to the common fixed point of finite family of total asymptotically nonexpansive mappings which is nearest to the point $u \\in H$.  Our results improve previously known ones obtained for the class of asymptotically nonexpansive mappings. As application, iterative method for: approximation of solution of variational Inequality problem, finite family of continuous pseudocontractive mappings, approximation of solutions of classical equilibrium problems and approximation of solutions of convex minimization problems are proposed. Our theorems unify and complement many recently announced results.

Non-asymptotic fractional order differentiators via an algebraic parametric method

KAUST Repository

Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid

2012-01-01

Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

Non-asymptotic fractional order differentiators via an algebraic parametric method

KAUST Repository

Liu, Dayan

2012-08-01

Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

Asymptotic behavior of Bayes estimators for hidden Markov models with application to ion channels

NARCIS (Netherlands)

de Gunst, M.C.M.; Shcherbakova, O.V.

2008-01-01

In this paper we study the asymptotic behavior of Bayes estimators for hidden Markov models as the number of observations goes to infinity. The theorem that we prove is similar to the Bernstein-von Mises theorem on the asymptotic behavior of the posterior distribution for the case of independent

Neurologic complications of disorders of the adrenal glands.

Science.gov (United States)

Bertorini, Tulio E; Perez, Angel

2014-01-01

Disorders of the adrenal glands frequently have secondary neurological manifestations, while some diseases that involve the central nervous system are accompanied by adrenal gland dysfunction. Excessive corticosteroid secretions in primary or secondary Cushing's syndrome causes muscle weakness and behavioral disturbances, such as emotional lability and sometimes depression, while adrenal insufficiency may cause fatigue, weakness, and depression. Adrenoleukodystrophy and adrenoneuromyelopathy are X-linked recessive disorders of the metabolism of very long chain fatty acids that manifest with white matter abnormalities of the brain, myelopathy and/or neuropathy, as well as adrenal insufficiency. Other disorders of the adrenal glands include hyperaldosteroidism, which may cause weakness from hypokalemia. Dysfunction of the adrenal medulla causes excessive or deficient secretion of catecholamines, primarily causing cardiovascular symptoms. This chapter reviews the clinical manifestations and diagnostic aspects and treatment of the various disorders of the adrenal glands. Some of the congenital adrenal diseases are also discussed. © 2014 Elsevier B.V. All rights reserved.

Laminar flow and convective transport processes scaling principles and asymptotic analysis

CERN Document Server

Brenner, Howard

1992-01-01

Laminar Flow and Convective Transport Processes: Scaling Principles and Asymptotic Analysis presents analytic methods for the solution of fluid mechanics and convective transport processes, all in the laminar flow regime. This book brings together the results of almost 30 years of research on the use of nondimensionalization, scaling principles, and asymptotic analysis into a comprehensive form suitable for presentation in a core graduate-level course on fluid mechanics and the convective transport of heat. A considerable amount of material on viscous-dominated flows is covered.A unique feat

Asymptotic expansions for the Gaussian unitary ensemble

DEFF Research Database (Denmark)

Haagerup, Uffe; Thorbjørnsen, Steen

2012-01-01

Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian U...

Tail asymptotics for dependent subexponential differences

DEFF Research Database (Denmark)

Albrecher, H; Asmussen, Søren; Kortschak, D.

We study the asymptotic behavior of P(X − Y > u) as u → ∞, where X is subexponential and X, Y are positive random variables that may be dependent. We give criteria under which the subtraction of Y does not change the tail behavior of X. It is also studied under which conditions the comonotonic co...

Penrose inequality for asymptotically AdS spaces

International Nuclear Information System (INIS)

Itkin, Igor; Oz, Yaron

2012-01-01

In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by an initial Cauchy data, it suggests a creation of a naked singularity, thus providing means to consider the cosmic censorship hypothesis. We propose a general form of Penrose inequality for asymptotically locally AdS spaces.

Penrose inequality for asymptotically AdS spaces

Energy Technology Data Exchange (ETDEWEB)

Itkin, Igor [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel); Oz, Yaron, E-mail: yaronoz@post.tau.ac.il [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel)

2012-02-28

In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by an initial Cauchy data, it suggests a creation of a naked singularity, thus providing means to consider the cosmic censorship hypothesis. We propose a general form of Penrose inequality for asymptotically locally AdS spaces.

Asymptotic Value Distribution for Solutions of the Schroedinger Equation

International Nuclear Information System (INIS)

Breimesser, S. V.; Pearson, D. B.

2000-01-01

We consider the Dirichlet Schroedinger operator T=-(d 2 /d x 2 )+V, acting in L 2 (0,∞), 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,λ) of the equation Tf(x,λ)=λf(x,λ), for λ in the support of the absolutely continuous part μ a.c. of the spectral measure μ, 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,λ)/v(N,λ) approaches the associated value distribution of the Herglotz function m N (z) in the limit N → ∞, where m N (z) is the Weyl-Titchmarsh m-function for the Schroedinger operator -(d 2 /d x 2 )+Vacting in L 2 (N,∞), 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

Coordinate asymptotics of the (3→3) wave functions for a three charged particle system

International Nuclear Information System (INIS)

Merkur'ev, S.P.

1977-01-01

Coordinate asymptotics of the (3 → 3) wave functions for three particles system with Coulomb interaction in the scattering problem is plotted. (3 → 3) and (3 → 2) process cases are considered, when the particles are not connected at the initial state. For coordinate asymptotics plotting the basis functions are used which meet Schroedinger equation in the eikonal approximation. The wave functions coordinate asymptotics plotting method is described far from special directions. Wave function asymptotical form is studied in the range of special directions and (3 → 3) scattering amplitude singularities are described. All data are given in accordance with the system with 2 charged particles only. The model in question is of special interest because of the described ppn system the studying of which is of great importance in nuclear physics. Final formulae are discussed for the most general case of three charged particles. Boundary problems for Schroedinger equation are shown to give the only way of definition for the (3 → 3) wave functions. It is pointed out that in special directions wave function coordinate asymptotics is presented with accuracy that gives the possibility to set such a boundary problem

Small Bandwidth Asymptotics for Density-Weighted Average Derivatives

DEFF Research Database (Denmark)

Cattaneo, Matias D.; Crump, Richard K.; Jansson, Michael

This paper proposes (apparently) novel standard error formulas for the density-weighted average derivative estimator of Powell, Stock, and Stoker (1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels and the standard errors...

Ergodic Retractions for Families of Asymptotically Nonexpansive Mappings

Directory of Open Access Journals (Sweden)

Saeidi Shahram

2010-01-01

Full Text Available We prove some theorems for the existence of ergodic retractions onto the set of common fixed points of a family of asymptotically nonexpansive mappings. Our results extend corresponding results of Benavides and Ramírez (2001, and Li and Sims (2002.

Asymptotic Behavior of the Stock Price Distribution Density and Implied Volatility in Stochastic Volatility Models

International Nuclear Information System (INIS)

Gulisashvili, Archil; Stein, Elias M.

2010-01-01

We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model. We find explicit formulas for leading terms in asymptotic expansions of these densities and give error estimates. As an application of our results, sharp asymptotic formulas for the implied volatility in the Stein-Stein and the Heston model are obtained.

Asymptotic stability of discrete-time systems with time-varying delay subject to saturation nonlinearities

International Nuclear Information System (INIS)

Chen, S.-F.

2009-01-01

The asymptotic stability problem for discrete-time systems with time-varying delay subject to saturation nonlinearities is addressed in this paper. In terms of linear matrix inequalities (LMIs), a delay-dependent sufficient condition is derived to ensure the asymptotic stability. A numerical example is given to demonstrate the theoretical results.

Asymptotic structure of space-time with a positive cosmological constant

Science.gov (United States)

Kesavan, Aruna

In general relativity a satisfactory framework for describing isolated systems exists when the cosmological constant Lambda is zero. The detailed analysis of the asymptotic structure of the gravitational field, which constitutes the framework of asymptotic flatness, lays the foundation for research in diverse areas in gravitational science. However, the framework is incomplete in two respects. First, asymptotic flatness provides well-defined expressions for physical observables such as energy and momentum as 'charges' of asymptotic symmetries at null infinity, [special character omitted] +. But the asymptotic symmetry group, called the Bondi-Metzner-Sachs group is infinite-dimensional and a tensorial expression for the 'charge' integral of an arbitrary BMS element is missing. We address this issue by providing a charge formula which is a 2-sphere integral over fields local to the 2-sphere and refers to no extraneous structure. The second, and more significant shortcoming is that observations have established that Lambda is not zero but positive in our universe. Can the framework describing isolated systems and their gravitational radiation be extended to incorporate this fact? In this dissertation we show that, unfortunately, the standard framework does not extend from the Lambda = 0 case to the Lambda > 0 case in a physically useful manner. In particular, we do not have an invariant notion of gravitational waves in the non-linear regime, nor an analog of the Bondi 'news tensor', nor positive energy theorems. In addition, we argue that the stronger boundary condition of conformal flatness of intrinsic metric on [special character omitted]+, which reduces the asymptotic symmetry group from Diff([special character omitted]) to the de Sitter group, is insufficient to characterize gravitational fluxes and is physically unreasonable. To obtain guidance for the full non-linear theory with Lambda > 0, linearized gravitational waves in de Sitter space-time are analyzed in

On Small Deviation Asymptotics In L2 of Some Mixed Gaussian Processes

Directory of Open Access Journals (Sweden)

Alexander I. Nazarov

2018-04-01

Full Text Available We study the exact small deviation asymptotics with respect to the Hilbert norm for some mixed Gaussian processes. The simplest example here is the linear combination of the Wiener process and the Brownian bridge. We get the precise final result in this case and in some examples of more complicated processes of similar structure. The proof is based on Karhunen–Loève expansion together with spectral asymptotics of differential operators and complex analysis methods.

Co-activation: its association with weakness and specific neurological pathology

Directory of Open Access Journals (Sweden)

Wiles Charles M

2006-11-01

Full Text Available Abstract Background Net agonist muscle strength is in part determined by the degree of antagonist co-activation. The level of co-activation might vary in different neurological disorders causing weakness or might vary with agonist strength. Aim This study investigated whether antagonist co-activation changed a with the degree of muscle weakness and b with the nature of the neurological lesion causing weakness. Methods Measures of isometric quadriceps and hamstrings strength were obtained. Antagonist (hamstring co-activation during knee extension was calculated as a ratio of hamstrings over quadriceps activity both during an isometric and during a functional sit to stand (STS task (using kinematics in groups of patients with extrapyramidal (n = 15, upper motor neuron (UMN (n = 12, lower motor neuron (LMN with (n = 18 or without (n = 12 sensory loss, primary muscle or neuromuscular junction disorder (n = 17 and in healthy matched controls (n = 32. Independent t-tests or Mann Witney U tests were used to compare between the groups. Correlations between variables were also investigated. Results In healthy subjects mean (SD co-activation of hamstrings during isometric knee extension was 11.8 (6.2% and during STS was 20.5 (12.9%. In patients, co-activation ranged from 7 to 17% during isometric knee extension and 15 to 25% during STS. Only the extrapyramidal group had lower co-activation levels than healthy matched controls (p Conclusion It is concluded that antagonist co-activation does not systematically vary with the site of neurological pathology when compared to healthy matched controls or, in most patient groups, with strength. The lower co-activation levels found in the extrapyramidal group require confirmation and further investigation. Co-activation may be relevant to individuals with muscle weakness. Within patient serial studies in the presence of changing muscle strength may help to understand these relationships more clearly.

Quantum gravity and the functional renormalization group the road towards asymptotic safety

CERN Document Server

Reuter, Martin

2018-01-01

During the past two decades the gravitational asymptotic safety scenario has undergone a major transition from an exotic possibility to a serious contender for a realistic theory of quantum gravity. It aims at a mathematically consistent quantum description of the gravitational interaction and the geometry of spacetime within the realm of quantum field theory, which keeps its predictive power at the highest energies. This volume provides a self-contained pedagogical introduction to asymptotic safety, and introduces the functional renormalization group techniques used in its investigation, along with the requisite computational techniques. The foundational chapters are followed by an accessible summary of the results obtained so far. It is the first detailed exposition of asymptotic safety, providing a unique introduction to quantum gravity and it assumes no previous familiarity with the renormalization group. It serves as an important resource for both practising researchers and graduate students entering thi...

Nonlinear mechanics of thin-walled structures asymptotics, direct approach and numerical analysis

CERN Document Server

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...

Asymptotic Co- and Post-seismic displacements in a homogeneous Maxwell sphere

Science.gov (United States)

Tang, He; Sun, Wenke

2018-05-01

The deformations of the Earth caused by internal and external forces are usually expressed through Green's functions or the superposition of normal modes, i.e. via numerical methods, which are applicable for computing both co- and post-seismic deformations. It is difficult to express these deformations in an analytical form, even for a uniform viscoelastic sphere. In this study, we present a set of asymptotic solutions for computing co- and post-seismic displacements; these solutions can be further applied to solving co- and post-seismic geoid, gravity, and strain changes. Expressions are derived for a uniform Maxwell Earth by combining the reciprocity theorem, which links earthquake, tidal, shear and loading deformations, with the asymptotic solutions of these three external forces (tidal, shear and loading) and analytical inverse Laplace transformation formulae. Since the asymptotic solutions are given in a purely analytical form without series summations or extra convergence skills, they can be practically applied in an efficient way, especially when computing post-seismic deformations and glacial isotactic adjustments of the Earth over long timescales.

Existence and Asymptotic Stability of Periodic Solutions of the Reaction-Diffusion Equations in the Case of a Rapid Reaction

Science.gov (United States)

Nefedov, N. N.; Nikulin, E. I.

2018-01-01

A singularly perturbed periodic in time problem for a parabolic reaction-diffusion equation in a two-dimensional domain is studied. The case of existence of an internal transition layer under the conditions of balanced and unbalanced rapid reaction is considered. An asymptotic expansion of a solution is constructed. To justify the asymptotic expansion thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is investigated.

Asymptotic behavior of tidal damping in alluvial estuaries

NARCIS (Netherlands)

Cai, H.; Savenije, H.H.G.

2013-01-01

Tidal wave propagation can be described analytically by a set of four implicit equations, i.e., the phase lag equation, the scaling equation, the damping equation, and the celerity equation. It is demonstrated that this system of equations has an asymptotic solution for an infinite channel,

Asymptotic behavior of discrete holomorphic maps z^c, log(z) and discrete Painleve transcedents

OpenAIRE

Agafonov, S. I.

2005-01-01

It is shown that discrete analogs of z^c and log(z) have the same asymptotic behavior as their smooth counterparts. These discrete maps are described in terms of special solutions of discrete Painleve-II equations, asymptotics of these solutions providing the behaviour of discrete z^c and log(z) at infinity.

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

Directory of Open Access Journals (Sweden)

Zhanhua Yu

2011-01-01

Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.

Postoperative conversion disorder.

Science.gov (United States)

Afolabi, Kola; Ali, Sameer; Gahtan, Vivian; Gorji, Reza; Li, Fenghua; Nussmeier, Nancy A

2016-05-01

Conversion disorder is a psychiatric disorder in which psychological stress causes neurologic deficits. A 28-year-old female surgical patient had uneventful general anesthesia and emergence but developed conversion disorder 1 hour postoperatively. She reported difficulty speaking, right-hand numbness and weakness, and right-leg paralysis. Neurologic examination and imaging revealed no neuronal damage, herniation, hemorrhage, or stroke. The patient mentioned failing examinations the day before surgery and discontinuing her prescribed antidepressant medication, leading us to diagnose conversion disorder, with eventual confirmation by neuroimaging and follow-up examinations. Copyright © 2016 Elsevier Inc. All rights reserved.

Spectral statistics in chiral-orthogonal disordered systems

International Nuclear Information System (INIS)

Evangelou, S N; Katsanos, D E

2003-01-01

We describe the singularities in the averaged density of states and the corresponding statistics of the energy levels in two- (2D) and three-dimensional (3D) chiral symmetric and time-reversal invariant disordered systems, realized in bipartite lattices with real off-diagonal disorder. For off-diagonal disorder of zero mean, we obtain a singular density of states in 2D which becomes much less pronounced in 3D, while the level-statistics can be described by a semi-Poisson distribution with mostly critical fractal states in 2D and Wigner surmise with mostly delocalized states in 3D. For logarithmic off-diagonal disorder of large strength, we find behaviour indistinguishable from ordinary disorder with strong localization in any dimension but in addition one-dimensional 1/ vertical bar E vertical bar Dyson-like asymptotic spectral singularities. The off-diagonal disorder is also shown to enhance the propagation of two interacting particles similarly to systems with diagonal disorder. Although disordered models with chiral symmetry differ from non-chiral ones due to the presence of spectral singularities, both share the same qualitative localization properties except at the chiral symmetry point E=0 which is critical

Asymptotic behavior for a quadratic nonlinear Schrodinger equation

Directory of Open Access Journals (Sweden)

Pavel I. Naumkin

2008-02-01

Full Text Available We study the initial-value problem for the quadratic nonlinear Schrodinger equation $$displaylines{ iu_{t}+frac{1}{2}u_{xx}=partial _{x}overline{u}^{2},quad xin mathbb{R},; t>1, cr u(1,x=u_{1}(x,quad xin mathbb{R}. }$$ For small initial data $u_{1}in mathbf{H}^{2,2}$ we prove that there exists a unique global solution $uin mathbf{C}([1,infty ;mathbf{H}^{2,2}$ of this Cauchy problem. Moreover we show that the large time asymptotic behavior of the solution is defined in the region $|x|leq Csqrt{t}$ by the self-similar solution $frac{1}{sqrt{t}}MS(frac{x}{sqrt{t}}$ such that the total mass $$ frac{1}{sqrt{t}}int_{mathbb{R}}MS(frac{x}{sqrt{t}} dx=int_{mathbb{R}}u_{1}(xdx, $$ and in the far region $|x|>sqrt{t}$ the asymptotic behavior of solutions has rapidly oscillating structure similar to that of the cubic nonlinear Schrodinger equations.

Asymptotic stabilization of nonlinear systems using state feedback

International Nuclear Information System (INIS)

D'Attellis, Carlos

1990-01-01

This paper studies the design of state-feedback controllers for the stabilization of single-input single-output nonlinear systems x = f(x) + g(x)u, y = h(x). Two approaches for the stabilization problem are given; the asymptotic stability is achieved by means of: a) nonlinear state feedback: two nonlinear feedbacks are used; the first separates the system in a controllable linear part and in the zeros-dynamic part. The second feedback generates an asymptotically stable equilibrium on the manifold where this dynamics evolves; b) nonlinear dynamic feedback: conditions are established under which the system can follow the output of a completely controllable bilinear system which uses bounded controls. This fact enables the system to reach, using bounded controls too, a desired output value in finite time. As this value corresponds to a state that lays in the attraction basin of a stable equilibrium with the same output, the system evolves to that point. The two methods are illustrated by examples. (Author) [es

Fatigue is associated with muscle weakness in Ehlers-Danlos syndrome: an explorative study

NARCIS (Netherlands)

Voermans, N.C.; Knoop, H.; Bleijenberg, G.; Engelen, B.G.M. van

2011-01-01

OBJECTIVES: Ehlers-Danlos syndrome (EDS) is a clinically and genetically heterogeneous group of inherited connective tissue disorders characterised by joint hypermobility, skin hyperextensibility and tissue fragility. It has recently been shown that muscle weakness occurs frequently in EDS, and that

Asymptotic Translation Length in the Curve Complex

OpenAIRE

Valdivia, Aaron D.

2013-01-01

We show that when the genus and punctures of a surface are directly proportional by some rational number the minimal asymptotic translation length in the curve complex has behavior inverse to the square of the Euler characteristic. We also show that when the genus is fixed and the number of punctures varies the behavior is inverse to the Euler characteristic.

To quantum averages through asymptotic expansion of classical averages on infinite-dimensional space

International Nuclear Information System (INIS)

Khrennikov, Andrei

2007-01-01

We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of scaling of the covariation operator of a Gaussian measure and the second (Frechet) derivative of a functional. In this way we couple classical average (given by an infinite-dimensional Gaussian integral) and quantum average (given by the von Neumann trace formula). We can interpret this mathematical construction as a procedure of 'dequantization' of quantum mechanics. We represent quantum mechanics as an asymptotic projection of classical statistical mechanics with infinite-dimensional phase space. This space can be represented as the space of classical fields, so quantum mechanics is represented as a projection of 'prequantum classical statistical field theory'

Asymptotic state discrimination and a strict hierarchy in distinguishability norms

Energy Technology Data Exchange (ETDEWEB)

Chitambar, Eric [Department of Physics and Astronomy, Southern Illinois University, Carbondale, Illinois 62901 (United States); Hsieh, Min-Hsiu [Centre for Quantum Computation and Intelligent Systems (QCIS), Faculty of Engineering and Information Technology (FEIT), University of Technology Sydney - UTS, NSW 2007 (Australia)

2014-11-15

In this paper, we consider the problem of discriminating quantum states by local operations and classical communication (LOCC) when an arbitrarily small amount of error is permitted. This paradigm is known as asymptotic state discrimination, and we derive necessary conditions for when two multipartite states of any size can be discriminated perfectly by asymptotic LOCC. We use this new criterion to prove a gap in the LOCC and separable distinguishability norms. We then turn to the operational advantage of using two-way classical communication over one-way communication in LOCC processing. With a simple two-qubit product state ensemble, we demonstrate a strict majorization of the two-way LOCC norm over the one-way norm.

Asymptotic behaviour of the scattering phase for non-trapping metrics

International Nuclear Information System (INIS)

Popov, G.S.

1982-01-01

The asymptotic behaviour of the scattering phase is considered at infinity for an elliptic, self-adjoint, second order differential operator H, defined either in Rsup(n) or in an unbounded domain Ω contains Rsup(n) with Dirichlet or Neumann boundary conditions. The operator H has the form H=- δsub(g)+hD+V where δsub(g) is the Laplace-Beltrami operator related to a Riemann metric g in anti Ω. Provided a non-trapping hypothesis is fulfilled and H coincides with the Laplace operator δ in a neighbourhood of infinity, an asymptotic development of the scattering phase s(lambda) is obtained for lambda → infinity. The first coefficients in this development are found

Asymptotic Estimates of Gerber-Shiu Functions in the Renewal Risk Model with Exponential Claims

Institute of Scientific and Technical Information of China (English)

Li WEI

2012-01-01

This paper continues to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large.Under the assumption that the claim-size distribution is exponential,we establish an explicit asymptotic formula.Some straightforward consequences of this formula match existing results in the field.

Asymptotic behaviour of unbounded trajectories for some non-autonomous systems in a Hilbert space

International Nuclear Information System (INIS)

Djafari Rouhani, B.

1990-07-01

The asymptotic behaviour of unbounded trajectories for non expansive mappings in a real Hilbert space and the extension to more general Banach spaces and to nonlinear contraction semi-group have been studied by many authors. In this paper we study the asymptotic behaviour of unbounded trajectories for a quasi non-autonomous dissipative systems. 26 refs

Asymptotic distribution of products of sums of independent random ...

Indian Academy of Sciences (India)

integrable random variables (r.v.) are asymptotically log-normal. This fact ... the product of the partial sums of i.i.d. positive random variables as follows. .... Now define ..... by Henan Province Foundation and Frontier Technology Research Plan.

Confinement and asymptotic freedom seen with a golden eye

International Nuclear Information System (INIS)

Elokaby, A.

2009-01-01

The present short note is an attempt to reconcile the current conventional understanding of quarks confinement and asymptotic freedom with the results found by El Naschie using the exact renormalization equation of his quantum golden field theory.

Fisher information and asymptotic normality in system identification for quantum Markov chains

International Nuclear Information System (INIS)

Guta, Madalin

2011-01-01

This paper deals with the problem of estimating the coupling constant θ of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of θ whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolute bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of θ=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.

Asymptotics for the greatest zeros of solutions of a particular O.D.E.

Directory of Open Access Journals (Sweden)

Silvia Noschese

1994-05-01

Full Text Available This paper deals with the Liouville-Stekeloff method for approximating solutions of homogeneous linear ODE and a general result due to Tricomi which provides estimates for the zeros of functions by means of the knowledge of an asymptotic representation. From the classical tools we deduce information about the asymptotics of the greatest zeros of a class of solutions of a particular ODE, including the classical Hermite polynomials.

Two-parameter asymptotics in magnetic Weyl calculus

International Nuclear Information System (INIS)

Lein, Max

2010-01-01

This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter ε, the case of small coupling λ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hoermander class symbols are proven as (i) ε<< 1 and λ<< 1, (ii) ε<< 1 and λ= 1, as well as (iii) ε= 1 and λ<< 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.

TAIL ASYMPTOTICS OF LIGHT-TAILED WEIBULL-LIKE SUMS

DEFF Research Database (Denmark)

Asmussen, Soren; Hashorva, Enkelejd; Laub, Patrick J.

2017-01-01

We consider sums of n i.i.d. random variables with tails close to exp{-x(beta)} for some beta > 1. Asymptotics developed by Rootzen (1987) and Balkema, Kluppelberg, and Resnick (1993) are discussed from the point of view of tails rather than of densities, using a somewhat different angle...

Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence

International Nuclear Information System (INIS)

Zhang Tailei; Teng Zhidong

2008-01-01

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 integration of a linear fourth order differential equation of Poincaré type

Directory of Open Access Journals (Sweden)

Anibal Coronel

2015-11-01

Full Text Available This article deals with the asymptotic behavior of nonoscillatory solutions of fourth order linear differential equation where the coefficients are perturbations of constants. We define a change of variable and deduce that the new variable satisfies a third order nonlinear differential equation. We assume three hypotheses. The first hypothesis is related to the constant coefficients and set up that the characteristic polynomial associated with the fourth order linear equation has simple and real roots. The other two hypotheses are related to the behavior of the perturbation functions and establish asymptotic integral smallness conditions of the perturbations. Under these general hypotheses, we obtain four main results. The first two results are related to the application of a fixed point argument to prove that the nonlinear third order equation has a unique solution. The next result concerns with the asymptotic behavior of the solutions of the nonlinear third order equation. The fourth main theorem is introduced to establish the existence of a fundamental system of solutions and to precise the formulas for the asymptotic behavior of the linear fourth order differential equation. In addition, we present an example to show that the results introduced in this paper can be applied in situations where the assumptions of some classical theorems are not satisfied.

On approach to double asymptotic scaling at low x

International Nuclear Information System (INIS)

Choudhury, D.K.

1994-10-01

We obtain the finite x correlations to the gluon structure function which exhibits double asymptotic scaling at low x. The technique used is the GLAP equation for gluon approximated at low x by a Taylor expansion. (author). 27 refs

On some asymptotic relations in the Boltzmann-Enskog model

International Nuclear Information System (INIS)

Sadovnikov, B.I.; Inozemtseva, N.G.

1977-04-01

The coefficients in the tsup(-3/2) asymptotics of the time autocorrelation functions are successively determined in the framework of the non-linear Boltzmann-Enskog model. The left and right eigenfunction systems are constructed for the Boltzmann-Enskog operator

Models of plastic depinning of driven disordered systems

Indian Academy of Sciences (India)

The second class allows for proliferation of topological defects due to the interplay of strong disorder and drive. In mean field theory both models exhibit a tricritical point as a function of disorder strength. At weak disorder depinning is continuous and the sliding state is unique. At strong disorder depinning is discontinuous ...

High energy asymptotics of the scattering amplitude for the ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

Keywords. Scattering matrix; asymptotic expansion; high energy; diagonal singula- ..... (see subsection 2 of § 3) with functions of the generator of dilations. A = 1. 2 d ..... ness in quantum scattering theory, Ann. Inst. Henri Poincaré, Phys. Théor.

The P(phi)2 Green's functions; asymptotic perturbation expansion

International Nuclear Information System (INIS)

Dimock, J.

1976-01-01

The real time Green's functions in the P(phi) 2 quantum field theory are infinitely differentiable functions of the coupling constant lambda up to and including lamba=0. It follows that the perturbation series are asymptotic as lambda→0 + . (Auth.)

Weak interactions

International Nuclear Information System (INIS)

Ogava, S.; Savada, S.; Nakagava, M.

1983-01-01

The problem of the use of weak interaction laws to study models of elementary particles is discussed. The most typical examples of weak interaction is beta-decay of nucleons and muons. Beta-interaction is presented by quark currents in the form of universal interaction of the V-A type. Universality of weak interactions is well confirmed using as examples e- and μ-channels of pion decay. Hypothesis on partial preservation of axial current is applicable to the analysis of processes with pion participation. In the framework of the model with four flavours lepton decays of hadrons are considered. Weak interaction without lepton participation are also considered. Properties of neutral currents are described briefly

Asymptotic Completeness for a Renormalized Nonrelativistic Hamiltonian in Quantum Field Theory: The Nelson Model

International Nuclear Information System (INIS)

Ammari, Zied

2000-01-01

Scattering theory for the Nelson model is studied. We show Rosen estimates and we prove the existence of a ground state for the Nelson Hamiltonian. Also we prove that it has a locally finite pure point spectrum outside its thresholds. We study the asymptotic fields and the existence of the wave operators. Finally we show asymptotic completeness for the Nelson Hamiltonian

Asymptotic solution for the El Niño time delay sea—air oscillator model

International Nuclear Information System (INIS)

Mo Jia-Qi; Lin Wan-Tao; Lin Yi-Hua

2011-01-01

A sea—air oscillator model is studied using the time delay theory. The aim is to find an asymptotic solving method for the El Niño-southern oscillation (ENSO) model. Employing the perturbed method, an asymptotic solution of the corresponding problem is obtained. Thus we can obtain the prognoses of the sea surface temperature (SST) anomaly and the related physical quantities. (general)

Weakly clopen functions

International Nuclear Information System (INIS)

Son, Mi Jung; Park, Jin Han; Lim, Ki Moon

2007-01-01

We introduce a new class of functions called weakly clopen function which includes the class of almost clopen functions due to Ekici [Ekici E. Generalization of perfectly continuous, regular set-connected and clopen functions. Acta Math Hungar 2005;107:193-206] and is included in the class of weakly continuous functions due to Levine [Levine N. A decomposition of continuity in topological spaces. Am Math Mon 1961;68:44-6]. Some characterizations and several properties concerning weakly clopenness are obtained. Furthermore, relationships among weak clopenness, almost clopenness, clopenness and weak continuity are investigated

Asymptotic analysis for Nakagami-m fading channels with relay selection

KAUST Repository

Zhong, Caijun

2011-06-01

In this paper, we analyze the asymptotic outage probability performance of both decode-and-forward (DF) and amplify-and-forward (AF) relaying systems using partial relay selection and the "best" relay selection schemes for Nakagami-m fading channels. We derive their respective outage probability expressions in the asymptotic high signal-to-noise ratio (SNR) regime, from which the diversity order and coding gain are analyzed. In addition, we investigate the impact of power allocation between the source and relay terminals and derive the diversity-multiplexing tradeoff (DMT) for these relay selection systems. The theoretical findings suggest that partial relay selection can improve the diversity of the system and can achieve the same DMT as the "best" relay selection scheme under certain conditions. © 2011 IEEE.

Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions

Energy Technology Data Exchange (ETDEWEB)

Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)

2010-05-15

In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)

Non-unique turbulent boundary layer flows having a moderately large velocity defect: a rational extension of the classical asymptotic theory

Science.gov (United States)

Scheichl, B.; Kluwick, A.

2013-11-01

The classical analysis of turbulent boundary layers in the limit of large Reynolds number Re is characterised by an asymptotically small velocity defect with respect to the external irrotational flow. As an extension of the classical theory, it is shown in the present work that the defect may become moderately large and, in the most general case, independent of Re but still remain small compared to the external streamwise velocity for non-zero pressure gradient boundary layers. That wake-type flow turns out to be characterised by large values of the Rotta-Clauser parameter, serving as an appropriate measure for the defect and hence as a second perturbation parameter besides Re. Most important, it is demonstrated that also this case can be addressed by rigorous asymptotic analysis, which is essentially independent of the choice of a specific Reynolds stress closure. As a salient result of this procedure, transition from the classical small defect to a pronounced wake flow is found to be accompanied by quasi-equilibrium flow, described by a distinguished limit that involves the wall shear stress. This situation is associated with double-valued solutions of the boundary layer equations and an unconventional weak Re-dependence of the external bulk flow—a phenomenon seen to agree well with previous semi-empirical studies and early experimental observations. Numerical computations of the boundary layer flow for various values of Re reproduce these analytical findings with satisfactory agreement.

Path integral representation of Lorentzian spinfoam model, asymptotics and simplicial geometries

International Nuclear Information System (INIS)

Han, Muxin; Krajewski, Thomas

2014-01-01

A new path integral representation of Lorentzian Engle–Pereira–Rovelli–Livine spinfoam model is derived by employing the theory of unitary representation of SL(2,C). The path integral representation is taken as a starting point of semiclassical analysis. The relation between the spinfoam model and classical simplicial geometry is studied via the large-spin asymptotic expansion of the spinfoam amplitude with all spins uniformly large. More precisely, in the large-spin regime, there is an equivalence between the spinfoam critical configuration (with certain nondegeneracy assumption) and a classical Lorentzian simplicial geometry. Such an equivalence relation allows us to classify the spinfoam critical configurations by their geometrical interpretations, via two types of solution-generating maps. The equivalence between spinfoam critical configuration and simplical geometry also allows us to define the notion of globally oriented and time-oriented spinfoam critical configuration. It is shown that only at the globally oriented and time-oriented spinfoam critical configuration, the leading-order contribution of spinfoam large-spin asymptotics gives precisely an exponential of Lorentzian Regge action of General Relativity. At all other (unphysical) critical configurations, spinfoam large-spin asymptotics modifies the Regge action at the leading-order approximation. (paper)

Organic random lasers in the weak-scattering regime

CERN Document Server

Polson, R C; 10.1103/PhysRevB.71.045205

2005-01-01

We used the ensemble-averaged power Fourier transform (PFT) of random laser emission spectra over the illuminated area to study random lasers with coherent feedback in four different disordered organic gain media in the weak scattering regime, where the light mean free path, l* is much larger than the emission wavelength. The disordered gain media include a pi -conjugated polymer film, an opal photonic crystal infiltrated with a laser dye (rhodamine 6G; R6G) having optical gain in the visible spectral range, a suspension of titania balls in R6G solution, and biological tissues such as chicken breast infiltrated with R6G. We show the existence of universality among the random resonators in each gain medium that we tested, in which at the same excitation intensity a dominant random cavity is excited in different parts of the sample. We show a second universality when scaling the average PFT of the four different media by l*; we found that the dominant cavity in each disordered gain medium scales with l *. The e...

Skeletal muscle weakness in osteogenesis imperfecta mice.

Science.gov (United States)

Gentry, Bettina A; Ferreira, J Andries; McCambridge, Amanda J; Brown, Marybeth; Phillips, Charlotte L

2010-09-01

Exercise intolerance, muscle fatigue and weakness are often-reported, little-investigated concerns of patients with osteogenesis imperfecta (OI). OI is a heritable connective tissue disorder hallmarked by bone fragility resulting primarily from dominant mutations in the proα1(I) or proα2(I) collagen genes and the recently discovered recessive mutations in post-translational modifying proteins of type I collagen. In this study we examined the soleus (S), plantaris (P), gastrocnemius (G), tibialis anterior (TA) and quadriceps (Q) muscles of mice expressing mild (+/oim) and moderately severe (oim/oim) OI for evidence of inherent muscle pathology. In particular, muscle weight, fiber cross-sectional area (CSA), fiber type, fiber histomorphology, fibrillar collagen content, absolute, relative and specific peak tetanic force (P(o), P(o)/mg and P(o)/CSA respectively) of individual muscles were evaluated. Oim/oim mouse muscles were generally smaller, contained less fibrillar collagen, had decreased P(o) and an inability to sustain P(o) for the 300-ms testing duration for specific muscles; +/oim mice had a similar but milder skeletal muscle phenotype. +/oim mice had mild weakness of specific muscles but were less affected than their oim/oim counterparts which demonstrated readily apparent skeletal muscle pathology. Therefore muscle weakness in oim mice reflects inherent skeletal muscle pathology. Copyright © 2010 Elsevier B.V. All rights reserved.