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Artigos de revistas sobre o tema "Exponential decay of correlation functions"

Autor: Grafiati

Publicado: 4 de junho de 2021

Última modificação: 3 de fevereiro de 2022

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1

Poghosyan, H. R., H. M. Babujian e G. K. Savvidy. "Artin Billiard: Exponential Decay of Correlation Functions". Theoretical and Mathematical Physics 197, n.º 2 (novembro de 2018): 1592–610. http://dx.doi.org/10.1134/s004057791811003x.

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2

Kashima, Yohei. "Exponential decay of correlation functions in many-electron systems". Journal of Mathematical Physics 51, n.º 6 (junho de 2010): 063521. http://dx.doi.org/10.1063/1.3409395.

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3

COURBAGE, M., e D. HAMDAN. "Decay of correlations and mixing properties in a dynamical system with zero K–S entropy". Ergodic Theory and Dynamical Systems 17, n.º 1 (fevereiro de 1997): 87–103. http://dx.doi.org/10.1017/s0143385797061051.

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We consider the ergodic skew product of translations on the torus ${\Bbb T}^{2}$. We characterize a class of smooth functions with exponential correlation decay rate and a class of subsets with an exponential rate of mixing. We show that the class of functions with sub-exponential correlation decay rate is generic. We also characterize another class of subsets with mixing rate of the order of $1/t$.

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4

OKABE, Yasunori, e Akihiko INOUE. "On the exponential decay of the correlation functions for KMO-Langevin equations". Japanese journal of mathematics. New series 18, n.º 1 (1992): 13–24. http://dx.doi.org/10.4099/math1924.18.13.

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5

FINE, BORIS V. "LONG-TIME RELAXATION ON SPIN LATTICE AS A MANIFESTATION OF CHAOTIC DYNAMICS". International Journal of Modern Physics B 18, n.º 08 (30 de março de 2004): 1119–59. http://dx.doi.org/10.1142/s0217979204024689.

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The long-time behavior of the infinite temperature spin correlation functions describing the free induction decay in nuclear magnetic resonance and intermediate structure factors in inelastic neutron scattering is considered. These correlation functions are defined for one-, two- and three-dimensional infinite lattices of interacting spins, both classical and quantum. It is shown that, even though the characteristic time-scale of the long-time decay of the correlation functions considered is non-Markovian, the generic functional form of this decay is either simple exponential or exponential multiplied by cosine. This work contains (i) the summary of the existing experimental and numerical evidence of the above asymptotic behavior; (ii) theoretical explanation of this behavior; and (iii) semi-empirical analysis of various factors discriminating between the monotonic and the oscillatory long-time decays. The theory is based on a fairly strong conjecture that, as a result of chaos generated by spin dynamics, a Brownian-like Markovian description can be applied to the long-time properties of ensemble average quantities on a non-Markovian time-scale. The formalism resulting from that conjecture can be described as "correlated diffusion in finite volumes."

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6

Braga, Gastão A., Paulo C. Lima e Michael L. O'Carroll. "Exponential Decay of Truncated Correlation Functions Via the Generating Function: A Direct Method". Reviews in Mathematical Physics 10, n.º 04 (maio de 1998): 429–38. http://dx.doi.org/10.1142/s0129055x98000136.

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We consider statistical mechanics lattice models where the external field dependent partition function can be represented as a standard polymer system. Using this polymer representation and elementary complex analytic arguments, we obtain upper bounds and give a simple proof on the uniform (in n) exponential decay of the n-point truncated correlation function. We illustrate the method by applying it to the high and low temperature Ising model and to contour models.

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7

MARINO, E. C. "A NEW QUANTUM VORTEX OPERATOR AND ITS CORRELATION FUNCTIONS". International Journal of Modern Physics A 10, n.º 30 (10 de dezembro de 1995): 4311–24. http://dx.doi.org/10.1142/s0217751x95001996.

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A new local and gauge-invariant quantum vortex operator is constructed in three-dimensional gauge field theories. The correlation functions of this operator are evaluated exactly in pure Maxwell theory and by means of an expansion around a constant absolute value of the Higgs field in the Abelian Higgs model. In the broken symmetry phase of the latter an explicit expression for the mass of the quantum vortices is obtained from the long distance exponential decay of the two-point function.

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8

Göhmann, F., A. G. Izergin, V. E. Korepin e A. G. Pronko. "Time and Temperature Dependent Correlation Functions of the One-Dimensional Impenetrable Electron Gas". International Journal of Modern Physics B 12, n.º 23 (20 de setembro de 1998): 2409–33. http://dx.doi.org/10.1142/s0217979298001411.

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We consider the one-dimensional delta-interacting electron gas in the case of infinite repulsion. We use determinant representations to study the long time, large distance asymptotics of correlation functions of local fields in the gas phase. We derive differential equations which drive the correlation functions. Using a related Riemann–Hilbert problem we obtain formulae for the asymptotics of the correlation functions, which are valid at all finite temperatures. At low temperatures these formulae lead to explicit asymptotic expressions for the correlation functions, which describe power law behavior and exponential decay as functions of temperature, magnetic field and chemical potential.

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9

Savvidy, George, e Konstantin Savvidy. "Exponential decay of correlations functions in MIXMAX generator of pseudorandom numbers". Chaos, Solitons & Fractals 107 (fevereiro de 2018): 244–50. http://dx.doi.org/10.1016/j.chaos.2018.01.007.

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10

Stolze, Joachim, Angela Nöppert e Gerhard Müller. "Gaussian, exponential, and power-law decay of time-dependent correlation functions in quantum spin chains". Physical Review B 52, n.º 6 (1 de agosto de 1995): 4319–26. http://dx.doi.org/10.1103/physrevb.52.4319.

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11

Lo, Assane. "On the exponential decay of the n-point correlation functions and the analyticity of the pressure". Journal of Mathematical Physics 48, n.º 12 (dezembro de 2007): 123506. http://dx.doi.org/10.1063/1.2819601.

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12

Babujian, Hrachya, Rubik Poghossian e George Savvidy. "Correlation Functions of Quantum Artin System". Universe 6, n.º 7 (30 de junho de 2020): 91. http://dx.doi.org/10.3390/universe6070091.

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It was conjectured by Maldacena, Shenker and Stanford that the classical chaos can be diagnosed in thermal quantum systems by using an out-of-time-order correlation function. The Artin dynamical system defined on the fundamental region of the modular group SL(2,Z) represents a well defined example of a highly chaotic dynamical system in its classical regime. We investigated the influence of the classical chaotic behaviour on the quantum–mechanical properties of the Artin system calculating the corresponding out-of-time-order thermal quantum–mechanical correlation functions. We demonstrated that the two- and four-point correlation functions of the Liouiville-like operators decay exponentially with temperature dependent exponents and that the square of the commutator of the Liouiville-like operators separated in time grows exponentially.

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13

BURIONI, RAFFAELLA, e DAVIDE CASSI. "ABSENCE OF PHASE TRANSITIONS ON TREE STRUCTURES". Modern Physics Letters B 07, n.º 29n30 (30 de dezembro de 1993): 1947–50. http://dx.doi.org/10.1142/s0217984993001971.

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We rigorously prove that the correlation functions of any statistical model having a compact transitive symmetry group and nearest-neighbor interactions on any tree structure are equal to the corresponding ones on a linear chain. The exponential decay of the latter implies the absence of long-range order on any tree. On the other hand, for trees with exponential growth such as Bethe lattices, one can show the existence of a particular kind of mean field phase transition without long-range order.

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14

Ngo Ngoc, Hoa, Thu Le Minh, Trang Nguyen Huyen e Tuong Le Cong. "DETERMINATION OF THE MASS DIFFUSION COEFFICIENT OF H2O DILUTED IN N2 USING CLASSICAL MOLECULAR DYNAMIC SIMULATION". Journal of Science Natural Science 65, n.º 6 (junho de 2020): 75–81. http://dx.doi.org/10.18173/2354-1059.2020-0031.

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In this work, the auto-correlation function of the center of mass velocity has been used to deduce the mass diffusion coefficient (D) of water diluted in nitrogen using the Classical Molecular Dynamics Simulations (CMDS). The calculations have been performed at room temperature (296 K) for different mixtures of H2O in N2 and 2.107 molecules from a five-sites potential. The results show that the auto-correlation functions expected exponential decay behavior [i.e. v v t exp( ) τ      ] and from the decay times τv , the mass diffusion coefficient and the velocity changing collisions frequency have been determined. The comparison between the CMDS results and experimental results are presented and discussed.

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15

Omari, Rami, e Gilbert Ayuk. "A study of Supported Poly (n-butyl methacrylate) (PBMA) Thin Polymer Films Near the Glass Transition Temperature". Material Science Research India 14, n.º 1 (25 de abril de 2017): 31–36. http://dx.doi.org/10.13005/msri/140105.

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The glass transition temperature and the surface dynamics of poly (butyl methacrylate) (PBMA) films have been studied using a phase-modulated ellipsometer equipped with a home-built sample cell with temperature controller. Experiments were performed for a range of temperatures, both above and below the glass transition temperature (Tg). In our study the glass transition temperature was obtained by plotting the ellipticity, as a function of temperature using the data from the ellipsometric cooling scan. the correlation functions governing the fluctuations were calculated at each temperature from the time-dependent fluctuations in film thickness as a function of temperature using ellipsometry data collected at 50 Hz frequency. The results indicate that at temperatures well above Tg, the correlation functions obey a simple exponential decay. However, as Tg is approached, the correlation functions are best fitted with a stretched exponential relation, indicating a broad distribution of relaxation times. In addition, the temperature dependence of surface relaxation process has been found to be much weaker compared to the bulk relaxation.

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16

TSVELIK, A. M. "TWO WEAKLY COUPLED HEISENBERG CHAINS—SOLUTION IN CONTINUOUS LIMIT". Modern Physics Letters B 05, n.º 30 (30 de dezembro de 1991): 1973–79. http://dx.doi.org/10.1142/s0217984991002379.

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Using the bosonization procedure proposed for the spin-1/2 Heisenberg chain in Ref. 8 we obtain the effective Hamiltonian for the system of two weakly coupled Heisenberg chains with the XXZ anisotropy as the sum of two sine-Gordon Hamiltonians. It appears that this simple system reveals a rather rich variety of properties in different regions of anisotropy. We calculate the spin-spin correlation functions; two-spin correlation functions decay exponentially but there are regions where the four-spin correlation functions decay as a power law. In particular, if both the inter- and intrachain exchange interactions are isotropic and the interchain exchange is ferromagnetic correlations of the chirality field χ= S 1× S 2 (the indexes 1 and 2 numerate the chains) are enhanced and their correlation functions follow a power law. In this case coupling between pairs of chains can lead to chiral ordering in three dimensions.

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17

Kashima, Yohei. "Exponential Decay of Equal-Time Four-Point Correlation Functions in the Hubbard Model on the Copper-Oxide Lattice". Annales Henri Poincaré 15, n.º 8 (30 de julho de 2013): 1453–522. http://dx.doi.org/10.1007/s00023-013-0278-0.

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18

TSENG, HSEN-CHE, e HUNG-JUNG CHEN. "CORRELATIONS IN THE DIFFUSIVE MAPS WITH QUENCHED DISORDER". International Journal of Modern Physics B 14, n.º 06 (10 de março de 2000): 643–53. http://dx.doi.org/10.1142/s0217979200000583.

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It was shown by G. Radons1 that, for a large class of one-dimensional maps, diffusion is suppressed by the presence of quenched disorder. Focusing on simple diffusive maps with discrete disorder, we investigate the behavior of the correlation functions χ1 (τ; t) and χ01 (τ; t), which arise naturally from the random walks induced by disorder of the system. Our numerical simulations show that both χ1 (τ; t) and χ01 (τ; t) decay with τ more slowly than the exponential decay, and both scale linearly with t; i.e. χ1 (τ; t) = tϕ1 (τ) and χ01 (τ; t) = tϕ01 (τ). Interestingly, we have also found that both [Formula: see text] and [Formula: see text] are mainly independent of the disorder configurations of the system.

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19

Andrews, Ross N., Suresh Narayanan, Fan Zhang, Ivan Kuzmenko e Jan Ilavsky. "Inverse transformation: unleashing spatially heterogeneous dynamics with an alternative approach to XPCS data analysis". Journal of Applied Crystallography 51, n.º 1 (1 de fevereiro de 2018): 35–46. http://dx.doi.org/10.1107/s1600576717015795.

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X-ray photon correlation spectroscopy (XPCS), an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering-vector-dependent sample dynamics at length scales smaller than DLS. The penetrating power of X-rays enables XPCS to probe the dynamics in a broad array of materials, including polymers, glasses and metal alloys, where attempts to describe the dynamics with a simple exponential fit usually fail. In these cases, the prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions (Kohlrausch functions), which implicitly assume homogeneous dynamics. This paper proposes an alternative analysis scheme based upon inverse Laplace or Gaussian transformation for elucidating heterogeneous distributions of dynamic time scales in XPCS, an approach analogous to theCONTINalgorithm widely accepted in the analysis of DLS from polydisperse and multimodal systems. Using XPCS data measured from colloidal gels, it is demonstrated that the inverse transform approach reveals hidden multimodal dynamics in materials, unleashing the full potential of XPCS.

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20

GURUSWAMY, S., e P. VITALE. "CORRELATION FUNCTIONS OF A CONFORMAL FIELD THEORY IN THREE DIMENSIONS". Modern Physics Letters A 11, n.º 13 (30 de abril de 1996): 1047–59. http://dx.doi.org/10.1142/s0217732396001089.

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We derive explicit forms of the two-point correlation functions of the O(N) nonlinear sigma model at the critical point, in the large-N limit, on various three-dimensional manifolds of constant curvature. The two-point correlation function, G(x, y), is the only n-point correlation function which survives in this limit. We analyze the short distance and long distance behaviors of G(x, y). It is shown that G(x, y) decays exponentially with the Riemannian distance on the spaces R2×S1, S1×S1×R, S2×R, H2×R. The decay on R3 is of course a power law. We show that the scale for the correlation length is given by the geometry of the space and therefore the long distance behavior of the critical correlation function is not necessarily a power law even though the manifold is of infinite extent in all directions; this is the case of the hyperbolic space where the radius of curvature plays the role of a scale parameter. We also verify that the scalar field in this theory is a primary field with weight [Formula: see text]; we illustrate this using the example of the manifold S2×R whose metric is conformally equivalent to that of R3–{0} up to a reparametrization.

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21

Beneš, Viktor, Christoph Hofer-Temmel, Günter Last e Jakub Večeřa. "Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics". Journal of Applied Probability 57, n.º 3 (setembro de 2020): 928–55. http://dx.doi.org/10.1017/jpr.2020.51.

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AbstractWe study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of an activity parameter and non-negative interaction potentials of finite range. Using disagreement percolation, we prove exponential decay of the correlation functions, provided a dominating Boolean model is subcritical. We also prove this property for the weighted moments of a U-statistic of the process. Under the assumption of a suitable lower bound on the variance, this implies a central limit theorem for such U-statistics of the Gibbs particle process. A by-product of our approach is a new uniqueness result for Gibbs particle processes.

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22

Choudhury, Sayantan. ":THE COSMOLOGICAL OTOC: Formulating New Cosmological Micro-Canonical Correlation Functions for Random Chaotic Fluctuations in Out-Of-Equilibrium Quantum Statistical Field Theory". Symmetry 12, n.º 9 (16 de setembro de 2020): 1527. http://dx.doi.org/10.3390/sym12091527.

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The out-of-time-ordered correlation (OTOC) function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. In this paper, using for the first time the slogan “Cosmology meets Condensed Matter Physics”, we demonstrate a formalism to compute the Cosmological OTOC during the stochastic particle production during inflation and reheating following the canonical quantization technique. In this computation, two dynamical time scales are involved—out of them, at one time scale, the cosmological perturbation variable, and for the other, the canonically conjugate momentum, is defined, which is the strict requirement to define the time scale-separated quantum operators for OTOC and is perfectly consistent with the general definition of OTOC. Most importantly, using the present formalism, not only one can study the quantum correlation during stochastic inflation and reheating, but can also study quantum correlation for any random events in Cosmology. Next, using the late time exponential decay of cosmological OTOC with respect to the dynamical time scale of our universe which is associated with the canonically conjugate momentum operator in this formalism, we study the phenomenon of quantum chaos by computing the expression for the Lyapunov spectrum. Furthermore, using the well known Maldacena Shenker Stanford (MSS) bound on the Lyapunov exponent, λ≤2π/β, we propose a lower bound on the equilibrium temperature, T=1/β, at the very late time scale of the universe. On the other hand, with respect to the other time scale with which the perturbation variable is associated, we find decreasing, but not exponentially decaying, behaviour, which quantifies the random quantum correlation function out-of-equilibrium. We have also studied the classical limit of the OTOC and checked the consistency with the large time limiting behaviour of the correlation. Finally, we prove that the normalized version of OTOC is completely independent of the choice of the preferred definition of the cosmological perturbation variable.

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23

PEREIRA, RODRIGO G. "LONG TIME CORRELATIONS OF NONLINEAR LUTTINGER LIQUIDS". International Journal of Modern Physics B 26, n.º 22 (26 de julho de 2012): 1244008. http://dx.doi.org/10.1142/s0217979212440080.

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An overview is given of the limitations of Luttinger liquid theory in describing the real time equilibrium dynamics of critical one-dimensional systems with nonlinear dispersion relation. After exposing the singularities of perturbation theory in band curvature effects that break the Lorentz invariance of the Tomonaga–Luttinger model, the origin of high frequency oscillations in the long time behaviour of correlation functions is discussed. The notion that correlations decay exponentially at finite temperature is challenged by the effects of diffusion in the density–density correlation due to umklapp scattering in lattice models.

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24

Meisinger, Peter N., e Michael C. Ogilvie. "PT symmetry in classical and quantum statistical mechanics". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, n.º 1989 (28 de abril de 2013): 20120058. http://dx.doi.org/10.1098/rsta.2012.0058.

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-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside the conventional equilibrium statistical mechanics of Hermitian systems. -symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviours than Hermitian systems, displaying sinusoidally modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with -symmetry include Z( N ) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbour Ising model. Quantum many-body problems with a non-zero chemical potential have a natural -symmetric representation related to the sign problem. Two-dimensional quantum chromodynamics with heavy quarks at non-zero chemical potential can be solved by diagonalizing an appropriate -symmetric Hamiltonian.

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25

Huttunen, J., A. Arola, G. Myhre, A. V. Lindfors, T. Mielonen, S. Mikkonen, J. Schafer et al. "Effect of water vapour on the determination of Aerosol Direct Radiative Effect based on the AERONET fluxes". Atmospheric Chemistry and Physics Discussions 14, n.º 1 (10 de janeiro de 2014): 751–67. http://dx.doi.org/10.5194/acpd-14-751-2014.

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Abstract. The Aerosol Direct Radiative Effect (ADRE) is defined as the change in the solar radiation flux, F, due to aerosol scattering and absorption. The difficulty in determining ADRE stems mainly from the need to estimate F without aerosols, F0, with either radiative transfer modelling and knowledge of the atmospheric state, or regression analysis of radiation data down to zero aerosol optical depth (AOD), if only F and AOD are observed. This paper examines the regression analysis method by using modeled surface data products provided by the AErosol RObotic NETwork (AERONET). We extrapolated F0 by two functions: a straight linear line and an exponential nonlinear decay. The exponential decay regression is expected to give a better estimation of ADRE with a few percents larger extrapolated F0 than the linear regression. We found that, contrary to the expectation, in most cases the linear regression gives better results than the nonlinear. In such cases the extrapolated F0 represents an unrealistically low WVC, resulting in underestimation of attenuation caused by the water vapour, and hence too large F0 and overestimation of the magnitude of ADRE. The nonlinear ADRE is generally 40–50% larger in magnitude than the linear ADRE due to the extrapolated F0 difference. Since for a majority of locations, AOD and water vapour column (WVC) have a positive correlation, the extrapolated F0 with the nonlinear regression fit represents an unrealistically low WVC, and hence too large F0. The systematic underestimation of F0 with the linear regression is compensated by the positive correlation between AOD and water vapour, providing the better result.

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26

Huttunen, J., A. Arola, G. Myhre, A. V. Lindfors, T. Mielonen, S. Mikkonen, J. S. Schafer et al. "Effect of water vapor on the determination of aerosol direct radiative effect based on the AERONET fluxes". Atmospheric Chemistry and Physics 14, n.º 12 (20 de junho de 2014): 6103–10. http://dx.doi.org/10.5194/acp-14-6103-2014.

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Abstract. The aerosol direct radiative effect (ADRE) is defined as the change in the solar radiation flux, F, due to aerosol scattering and absorption. The difficulty in determining ADRE stems mainly from the need to estimate F without aerosols, F0, with either radiative transfer modeling and knowledge of the atmospheric state, or regression analysis of radiation data down to zero aerosol optical depth (AOD), if only F and AOD are observed. This paper examines the regression analysis method by using modeled surface data products provided by the Aerosol Robotic Network (AERONET). We extrapolated F0 by two functions: a straight linear line and an exponential nonlinear decay. The exponential decay regression is expected to give a better estimation of ADRE with a few percent larger extrapolated F0 than the linear regression. We found that, contrary to the expectation, in most cases the linear regression gives better results than the nonlinear. In such cases the extrapolated F0 represents an unrealistically low water vapor column (WVC), resulting in underestimation of attenuation caused by the water vapor, and hence too large F0 and overestimation of the magnitude of ADRE. The nonlinear ADRE is generally 40–50% larger in magnitude than the linear ADRE due to the extrapolated F0 difference. Since for a majority of locations, AOD and WVC have a positive correlation, the extrapolated F0 with the nonlinear regression fit represents an unrealistically low WVC, and hence too large F0. The systematic underestimation of F0 with the linear regression is compensated by the positive correlation between AOD and water vapor, providing the better result.

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27

Ramakrishnan, N., Y. Wang, D. M. Eckmann, P. S. Ayyaswamy e R. Radhakrishnan. "Motion of a nano-spheroid in a cylindrical vessel flow: Brownian and hydrodynamic interactions". Journal of Fluid Mechanics 821 (18 de maio de 2017): 117–52. http://dx.doi.org/10.1017/jfm.2017.182.

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We study the motion of a buoyant or a nearly neutrally buoyant nano-sized spheroid in a fluid filled tube without or with an imposed pressure gradient (weak Poiseuille flow). The fluctuating hydrodynamics approach and the deterministic method are both employed. We ensure that the fluctuation–dissipation relation and the principle of thermal equipartition of energy are both satisfied. The major focus is on the effect of the confining boundary. Results for the velocity and the angular velocity autocorrelations (VACF and AVACF), the diffusivities and the drag and the lift forces as functions of the shape, the aspect ratio, the inclination angle and the proximity to the wall are presented. For the parameters considered, the boundary modifies the VACF and AVACF such that three distinct regimes are discernible – an initial exponential decay followed by an algebraic decay culminating in a second exponential decay. The first is due to the thermal noise, the algebraic regime is due both to the thermal noise and the hydrodynamic correlations, while the second exponential decay shows the effect of momentum reflection from the confining wall. Our predictions display excellent comparison with published results for the algebraic regime (the only regime for which earlier results exist). We also discuss the role of the off-diagonal elements of the mobility and the diffusivity tensors that enable the quantifications of the degree of lift and margination of the nanocarrier. Our study covers a range of parameters that are of wide applicability in nanotechnology, microrheology and in targeted drug delivery.

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GUPTA, BHASKAR SEN, e SHANKAR P. DAS. "TESTING POWER-LAW RELAXATION SCENARIOS IN A METASTABLE LIQUID". International Journal of Modern Physics B 26, n.º 29 (27 de setembro de 2012): 1250146. http://dx.doi.org/10.1142/s0217979212501469.

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The renormalized dynamics described by the equations of nonlinear fluctuating hydrodynamics (NFH) treated at one loop order gives rise to the basic model of the mode coupling theory (MCT). We investigate here by analyzing the density correlation function, a crucial prediction of ideal MCT, namely the validity of the multi step relaxation scenario. The equilibrium density correlation function is calculated here from the direct solutions of NFH equations for a hard sphere system. We make first detailed investigation for the robustness of the correlation functions obtained from the numerical solutions by varying the size of the grid. For an optimum choice of grid size we analyze the decay of the density correlation function to identify the multi-step relaxation process. Weak signatures of two step power law relaxation is seen with exponents which do not match predictions from the one loop MCT. For the final relaxation stretched exponential (KWW) behavior is seen and the relaxation time grows with increase of density. But apparent power law divergences indicate a critical packing fraction much higher than the corresponding MCT predictions for a hard sphere fluid.

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29

Ainbinder, N. E., G. B. Furman, G. E. Kibrik, A. Yu Poljakov e I. G. Shaposhnikov. "Relaxation Processes in NQR Multiple-Pulse Spin-Locking". Zeitschrift für Naturforschung A 41, n.º 1-2 (1 de fevereiro de 1986): 366–69. http://dx.doi.org/10.1515/zna-1986-1-269.

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A theory of the spin-lattice and spin-spin relaxation processes in quadrupole spin systems with I > 1/2 in the situation of the multiple-pulse NQR spin locking is proposed for the pulse sequence MW-4. The theory is based on the assumption that for t ≳ T2 the change of the spin system is a quasi-equilibrium process. Rate equations for inverse generalized temperatures are obtained and the kinetic coefficients calculated for the case o f exponential correlation functions. The above assumption was confirmed for some substances containing the 35Cl and 123Sb, and the time constant T1e characterizing the spin echo signal decay was investigated and compared with the time constant T1q, in the case of continuous spin locking.

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30

Cè, Marco, Leonardo Giusti e Stefan Schaefer. "Local multiboson factorization of the quark determinant". EPJ Web of Conferences 175 (2018): 11005. http://dx.doi.org/10.1051/epjconf/201817511005.

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We discuss the recently proposed multiboson domain-decomposed factorization of the gauge-field dependence of the fermion determinant in lattice QCD. In particular, we focus on the case of a lattice divided in an arbitrary number of thick time slices. As a consequence, multiple space-time regions can be updated independently. This allows to address the exponential degradation of the signal-to-noise ration of correlation functions with multilevel Monte Carlo sampling. We show numerical evidence of the effectiveness of a two-level integration for pseudoscalar propagators with momentum and for vector propagators, in a two active regions setup. These results are relevant to lattice computation of the hadronic contributions to the anomalous magnetic moment of the muon and to heavy meson decay form factors.

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MALLAMACE, F., S. H. CHEN, P. GAMBADAURO, D. LOMBARDO, A. FARAONE e P. TARTAGLIA. "PERCOLATION AND CRITICAL PHENOMENA OF AN ATTRACTIVE MICELLAR SYSTEM". Fractals 11, supp01 (fevereiro de 2003): 37–52. http://dx.doi.org/10.1142/s0218348x03001707.

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In this work we study an attractive micellar system for which the percolation curve terminates near the critical point. We have studied such an intriguing situation by means of scattering (elastic and dynamical) and viscoelasticity experiments. Obtained data are accounted by considering in a proper way the fractal clustering processes typical of percolating systems and the related scaling concepts. We observe that the main role in the system structure and dynamics it is played by the cluster's partial screening of hydrodynamic interaction. This behaves on approaching the percolation threshold dramatic effects on the system rheological properties and on the density decay relaxations. The measured correlation functions assume a stretched exponential form and the system becomes strongly viscoelastic. The overall behavior of the measured dynamical and structural parameters indicates, that in the present micellar system, the clustering process originates dilute, polydisperse and swelling structures. Finally, this originates an interesting situation observed in the present experiment. As it has been previously, proposed by A. Coniglio et al., percolation clusters can be considered to be "Ising clusters" with the same properties as the Fisher's critical droplets. Therefore at the critical point the percolation connectedness length (ξp) can be assumed as the diverging correlation length (ξp ≡ ξ) and the mean cluster size diverges as the susceptibility.

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Zhang, Wei, Jian Zhou, Xuejie Zhang, Yan Zhang e Kun Liu. "Quantitative investigation on force chain lengths during high velocity compaction of ferrous powder". Modern Physics Letters B 33, n.º 10 (10 de abril de 2019): 1950113. http://dx.doi.org/10.1142/s0217984919501136.

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Force chains play an important role in linking the macro- and micro-mechanisms of powder in high velocity compaction (HVC). Force chain lengths, as an important quantitative characteristic, can describe the geometry of force chains. In this study, force chain lengths and their relation to other force chain characteristics in HVC were investigated by discrete element method. Results revealed that force chain length decreased and it can be related to the densification process of ferrous powder in HVC. Moreover, long force chains extended from top to bottom and may play a major role in supporting load, although the percentage of long force chains was low. Probability density functions of force chain lengths further showed the exponential decay. The proportion of short force chains increased and the proportion of long force chains decreased. Long force chains had high strength and can be aligned to the direction of the external load, but force chain lengths did not have clear relation to straightness. These relations were confirmed by Pearson correlation coefficients.

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Williams, S. H., e D. Johnston. "Kinetic properties of two anatomically distinct excitatory synapses in hippocampal CA3 pyramidal neurons". Journal of Neurophysiology 66, n.º 3 (1 de setembro de 1991): 1010–20. http://dx.doi.org/10.1152/jn.1991.66.3.1010.

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1. We have investigated the kinetic properties of pharmacologically isolated excitatory synaptic currents in hippocampal CA3 neurons. Two distinct anatomic pathways, the commissural/associational (C/A) and the mossy fiber inputs, were compared to test the hypothesis derived from cable theory that distal inputs have slower kinetics than proximal inputs when measured at the soma. 2. Intracellular recordings were made from adult rat hippocampal slices using a single-electrode voltage clamp and low-resistance microelectrodes. A mixture of 10 microM picrotoxin and 10 microM bicuculine was used to block completely fast GABAergic inhibition. The slow inhibitory input was blocked by intracellular cesium. 3. The mean reversal potential of mossy fiber synaptic currents, -2.8 mV, was not significantly different from that of the C/A synaptic current, -1.4 mV. The mean 10-90% rise time of the mossy-fiber synaptic current [1.7 +/- 0.08 (SE) ms], however, was significantly faster than the C/A synaptic current (3.2 +/- 0.16 ms). Both mossy fiber and C/A synaptic-current decays were fit with a single exponential. The decay time constant of mossy fiber synaptic currents was also faster than that of the C/A excitatory postsynaptic current, 6.5 +/- 0.4 versus 10.1 +/- 0.8 ms. The mossy fiber synaptic current decay time constant showed little voltage dependence. 4. A modified shape index plot of synaptic current rise time versus decay time constant, normalized to membrane time constant, yielded a good linear relation for C/A synapses. A poorer correlation was observed for mossy fiber synapses. 5. Both synaptic currents could be fit by alpha functions. A representative value of alpha for the mossy fiber synapse was 295/s, and for the C/A was 172/s. 6. The rise time of the mossy fiber synaptic potential was significantly faster (5.3 ms) than the C/A (7.5 ms). The decay of both mossy fiber and C/A synaptic potentials was slower than the membrane time constant, suggesting that active currents may contribute to their falling phases. This prolongation was voltage dependent but insensitive to 2-amino-5-phosphonovaleric acid. 7. Our data provide a quantitative comparison of a proximal and a more distal synaptic input to CA3 hippocampal neurons. Distal inputs show slower kinetics than proximal synapses, as predicted. However, the voltage dependence of synaptic potential decays suggests that synaptic integration may be affected by active dendritic conductances.

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Ni, Rui, Shi-Di Huang e Ke-Qing Xia. "Lagrangian acceleration measurements in convective thermal turbulence". Journal of Fluid Mechanics 692 (6 de janeiro de 2012): 395–419. http://dx.doi.org/10.1017/jfm.2011.520.

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AbstractWe report the first experimental study of Lagrangian acceleration in turbulent Rayleigh–Bénard convection, using particle tracking velocimetry. A method has been developed to quantitatively evaluate and eliminate the uncertainties induced by temperature and refraction index fluctuations caused by the thermal plumes. It is found that the acceleration p.d.f. exhibits a stretched exponential form and that the probability for large magnitude of acceleration in the lateral direction is higher than those in the vertical directions, which can be attributed to the vortical motion of the thermal plumes. The local acceleration variance $\langle {a}^{2} \rangle $ was obtained for various values of the three control parameters: the Rayleigh number $\mathit{Ra}$ ($6\ensuremath{\times} 1{0}^{8} \leq \mathit{Ra}\leq 1\ensuremath{\times} 1{0}^{11} $), the Prandtl number $\mathit{Pr}$ ($\mathit{Pr}= 4. 4, 5. 5$ and 6.1) and the system size $L~(L= 19. 2\text{~and~} 48. 6~\mathrm{cm} )$. These were then compared with the theoretically predicted dependence on these parameters for buoyancy-dominated turbulent flows and for homogeneous and isotropic turbulence, respectively. It is found that $\langle {a}^{2} \rangle $ in the central region is dominated by contributions from the turbulent background rather than from the buoyancy force, and the Heisenberg–Yaglom relation holds in this region. From this, we obtain the first experimental results of the constant ${a}_{0} $ of the acceleration variance in the micro-scale Reynolds number range $20\leq {R}_{\lambda } \leq 120$, which fills a gap in this constant in the lower ${R}_{\lambda } $ end from the experimental side, and provides possible constraints for its high ${R}_{\lambda } $ behaviour if a certain fitting function is attempted. In addition, acceleration correlation functions were obtained for different $\mathit{Ra}$. It is found that the zero crossing time of acceleration correlation functions is at $\tau \approx 2. 2{\tau }_{\eta } $ (${\tau }_{\eta } $ is the Kolmogorov time scale) over the range of $\mathit{Ra}({R}_{\lambda } )$ spanned in our experiments, which is the same as the simulation results in isotropic turbulence, and the exponential decay time ${\tau }_{1/ e} = (1. 12\pm 0. 05){\tau }_{\eta } $, which is larger than $(0. 73\ensuremath{\sim} 0. 80){\tau }_{\eta } $ found experimentally for other types of turbulent flows with larger ${R}_{\lambda } $.

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Zhou, Fu-Ming, e John J. Hablitz. "Rapid Kinetics and Inward Rectification of Miniature EPSCs in Layer I Neurons of Rat Neocortex". Journal of Neurophysiology 77, n.º 5 (1 de maio de 1997): 2416–26. http://dx.doi.org/10.1152/jn.1997.77.5.2416.

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Zhou, Fu-Ming and John J. Hablitz. Rapid kinetics and inward rectification of miniature EPSCs in layer I neurons of rat neocortex. J. Neurophysiol. 77: 2416–2426, 1997. With the use of the whole cell patch-clamp technique combined with visualization of neurons in brain slices, we studied the properties of miniature excitatory postsynaptic currents (mEPSCs) in rat neocortical layer I neurons. At holding potentials (−50 to −70 mV) near the resting membrane potential (RMP), mEPSCs had amplitudes of 5–100 pA and were mediated mostly by α-amino-3-hydroxy-5-methyl-4-isoxazoleproprionate (AMPA) receptors. Amplitude histograms were skewed toward large events. An N-methyl-d-aspartate (NMDA) component was revealed by depolarization to −30 mV or by the use of a Mg2+-free bathing solution. At RMP, averaged AMPA mEPSCs had a 10–90% rise time of ∼0.3 ms (uncorrected for instrument filtering). The decay of averaged mEPSCs was best fit by double-exponential functions in most cases. The fast, dominating component had a decay time constant of ∼1.2 ms and comprised ∼80% of the total amplitude. A small slow component had a decay time constant of ∼4 ms. Positive correlations were found between rise and decay times of both individual and averaged mEPSCs, indicative of dendritic filtering. Some large-amplitude mEPSCs and spontaneous EPSCs (recorded in the absence of tetrodotoxin) had slower kinetics, suggesting a role of asynchronous transmitter release in shaping EPSCs. The amplitudes of mEPSCs were much smaller at +60 mV than at −60 mV, indicating that synaptic AMPA-receptor-mediated currents were inwardly rectifying. These results suggest that neocortical layer I neurons receive both NMDA- and AMPA-receptor-mediated synaptic inputs. The rapid decay of EPSCs appears to be largely determined by AMPA receptor deactivation. The observed rectification of synaptic responses suggests that synaptic AMPA receptors in layer I neurons may lack GluR-2 subunits and may be Ca2+ permeable.

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BRUIN, HENK, MARK DEMERS e IAN MELBOURNE. "Existence and convergence properties of physical measures for certain dynamical systems with holes". Ergodic Theory and Dynamical Systems 30, n.º 3 (24 de novembro de 2009): 687–728. http://dx.doi.org/10.1017/s0143385709000200.

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AbstractWe study two classes of dynamical systems with holes: expanding maps of the interval and Collet–Eckmann maps with singularities. In both cases, we prove that there is a natural absolutely continuous conditionally invariant measure μ (a.c.c.i.m.) with the physical property that strictly positive Hölder continuous functions converge to the density of μ under the renormalized dynamics of the system. In addition, we construct an invariant measure ν, supported on the Cantor set of points that never escape from the system, that is ergodic and enjoys exponential decay of correlations for Hölder observables. We show that ν satisfies an equilibrium principle which implies that the escape rate formula, familiar to the thermodynamic formalism, holds outside the usual setting. In particular, it holds for Collet–Eckmann maps with holes, which are not uniformly hyperbolic and do not admit a finite Markov partition. We use a general framework of Young towers with holes and first prove results about the a.c.c.i.m. and the invariant measure on the tower. Then we show how to transfer results to the original dynamical system. This approach can be expected to generalize to other dynamical systems than the two above classes.

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37

MYDLARSKI, L. "Mixed velocity–passive scalar statistics in high-Reynolds-number turbulence". Journal of Fluid Mechanics 475 (25 de janeiro de 2003): 173–203. http://dx.doi.org/10.1017/s0022112002002756.

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Statistics of the mixed velocity–passive scalar field and its Reynolds number dependence are studied in quasi-isotropic decaying grid turbulence with an imposed mean temperature gradient. The turbulent Reynolds number (using the Taylor microscale as the length scale), Rλ, is varied over the range 85 [les ] Rλ [les ] 582. The passive scalar under consideration is temperature in air. The turbulence is generated by means of an active grid and the temperature fluctuations result from the action of the turbulence on the mean temperature gradient. The latter is created by differentially heating elements at the entrance to the wind tunnel plenum chamber. The mixed velocity–passive scalar field evolves slowly with Reynolds number. Inertial-range scaling exponents of the co-spectra of transverse velocity and temperature, Evθ(k1), and its real-space analogue, the ‘heat flux structure function,’ 〈Δv(r)Δθ(r)〉, show a slow evolution towards their theoretical predictions of −7/3 and 4/3, respectively. The sixth-order longitudinal mixed structure functions, 〈(Δu(r))2(Δθ(r))4〉, exhibit inertial-range structure function exponents of 1.36–1.52. However, discrepancies still exist with respect to the various methods used to estimate the scaling exponents, the value of the scalar intermittency exponent, μθ, and the effects of large-scale phenomena (namely shear, decay and turbulent production of 〈θ2〉) on 〈(Δu(r))2(Δθ(r))4〉. All the measured fine-scale statistics required to be zero in a locally isotropic flow are, or tend towards, zero in the limit of large Reynolds numbers. The probability density functions (PDFs) of Δv(r)Δθ(r) exhibit roughly exponential tails for large separations and super-exponential tails for small separations, thus displaying the effects of internal intermittency. As the Reynolds number increases, the PDFs become symmetric at the smallest scales – in accordance with local isotropy. The expectation of the transverse velocity fluctuation conditioned on the scalar fluctuation is linear for all Reynolds numbers, with slope equal to the correlation coefficient between v and θ. The expectation of (a surrogate of) the Laplacian of the scalar reveals a Reynolds number dependence when conditioned on the transverse velocity fluctuation (but displays no such dependence when conditioned on the scalar fluctuation). This former Reynolds number dependence is consistent with Taylor’s diffusivity independence hypothesis. Lastly, for the statistics measured, no violations of local isotropy were observed.

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Chen, Xiang, e Pengfei Jia. "A systematic evaluation of accessibility measures by the two-step floating catchment area (2SFCA) method". Abstracts of the ICA 1 (15 de julho de 2019): 1–2. http://dx.doi.org/10.5194/ica-abs-1-41-2019.

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<p><strong>Abstract.</strong> Accessibility, as an important theme in geospatial science, measures the potential of interaction between geographic entities. Originated in Hansen’s (1959) empirical model for land use planning, place-based accessibility becomes an integrated assessment of urban settlements in relation to social services and opportunities, such as employment, education, and entertainment. Traditional place-based accessibility models, such as the integral measure or the cumulative-opportunity measure (Kwan, 1998), are primarily dependent on the assessment of the supply (e.g., stores, restaurants), evaluating if goods or services could be delivered or reached at an acceptable cost (e.g., distance, time). This assessment overlooks the complex spatial interactions between the supply and demand, referred to as the “complementarity” (Haynes & Fotheringham, 1984). Recent development of the place-based accessibility theory revolves around the two-step floating catchment area (2SFCA) method (Luo & Wang, 2003). The model evaluates if the capacity of service facilities can cater to nearby demand in a two-step search process. Initially serving for the assessment of health care facilities, the model has been further modified to accommodate various urban planning scenarios (Chen, 2017).</p><p> One compartment of the model in need of further evaluation is the distance decay. Although the 2SFCA model and its extensions have involved different distance decay functions, such as the Gaussian form and the kernel density form, there is a limited scope of work systematically comparing the performance and limitations of different 2SFCA models. In this study, we have proposed an analytic framework that includes six distance decay functions: the rectangular cumulative-opportunity (CUMR), negative-linear cumulative-opportunity (CUML), inverse-power gravity-type (POW), exponential gravity-type (EXP), and Gaussian gravity-type (GAUSS), and kernel density (KD) models. Examples of these distance decay functions are shown in Figure 1. Each model further consists of four variable scenarios, generating a total of twenty-four 2SFCA measures for comparison in a systematic manner.</p><p> Using the datasets of point-based food stores (i.e., the supply) and population (i.e., the demand) in the state of Arkansas, the United States, three sets of sensitivity analyses have been conducted to compare the results derived from these twenty-four models. These analyses include (1) Pearson’s correlation between models, (2) assessment by urban-rural status, and (3) variability analysis of the catchment size. Observations about the sensitivity of the 2SFCA models to the distance decay function and the catchment size are drawn from the analyses, providing valuable information for better understanding the intricacy of the model compartments. For example, we have employed the coefficient of variation (<i>C</i><sub>V</sub>), defined as the division of the standard deviation to the mean, to examine the spatial inequity of different 2SFCA models as a function of the catchment size (<i>d</i><sub>0</sub>, in miles). As shown in Figure 2, all models have a large degree of variability with a small <i>d</i><sub>0</sub>; when <i>d</i><sub>0</sub> increases to a certain threshold, <i>C</i><sub>V</sub> becomes relatively convergent (<i>d</i><sub>0</sub>&thinsp;&geq;&thinsp;9.5). It is also observed that POW20 has a higher level of variability than other models. In this respect, POW20 should be avoided in future model implementation as it derives a different spatial inequity pattern than other models.</p><p> In addition to revealing the applicability of the models, the paper further draws two important conclusions. First, on a small analysis scale (e.g., community), the catchment size is the most important modeling variable. In this scenario, variation in the catchment size can cause a high degree of measurement uncertainties. Thus, it is a necessity to examine and justify the choice of the catchment size when applying the 2SFCA model to a small-scale analysis. Second, on a large analysis scale (e.g., state, province), the distance decay function is of critical importance. In this scenario, using the 2SFCA model without the distance decay will likely overestimate the supply-demand interaction and thus obfuscate the inequity pattern. In sum, the comparison and the sensitivity analysis outline the potential applicability and limitations of different 2SFCA models. It provides the theoretical rapport necessary to future applications of the model for various urban planning, service delivery, and spatial equity problems.</p>

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39

Bryan, Joel A. "Using Radioactive Decay to Investigate Exponential Functions". Mathematics Teacher 106, n.º 1 (agosto de 2012): 52–58. http://dx.doi.org/10.5951/mathteacher.106.1.0052.

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During the thirteen years that I taught high school physics and mathematics, I found that my physics students typically came to class excited to learn. As in all science classes, they interacted with fellow classmates while performing laboratory investigations and other group activities requiring higher-order thinking skills. To create a similar experience for my mathematics students, I developed a laboratory investigation for my precalculus class. These students responded just as favorably as my physics students to hands-on data collection activities.

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40

Bach, Volker, e Jacob Schach Møller. "Correlation at low temperature: I. Exponential decay". Journal of Functional Analysis 203, n.º 1 (setembro de 2003): 93–148. http://dx.doi.org/10.1016/s0022-1236(03)00046-6.

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Skibsted, Erik. "Truncated Gamow functions, ?-decay and the exponential law". Communications in Mathematical Physics 104, n.º 4 (dezembro de 1986): 591–604. http://dx.doi.org/10.1007/bf01211067.

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42

Chen, Reuven, e P. L. Leung. "The decay of OSL signals as stretched-exponential functions". Radiation Measurements 37, n.º 4-5 (agosto de 2003): 519–26. http://dx.doi.org/10.1016/s1350-4487(03)00007-6.

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43

He, Lixin, e David Vanderbilt. "Exponential Decay Properties of Wannier Functions and Related Quantities". Physical Review Letters 86, n.º 23 (4 de junho de 2001): 5341–44. http://dx.doi.org/10.1103/physrevlett.86.5341.

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Bradie, Brian. "Activities: Rate of Change of Exponential Functions: A Precalculus Perspective". Mathematics Teacher 91, n.º 3 (março de 1998): 224–26. http://dx.doi.org/10.5951/mt.91.3.0224.

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I have never been satisfied with the applications of exponential functions that are presented in precalculus courses. That coverage consists primarily of supplying the requisite formula for, say, the growth of a bacterial colony or the decay of some radioactive substance, without explaining or deriving the reasons that the exponential function appears in the formula. The students are more than willing to accept the formulas and crunch through the numbers. However, unless I present a mathematical explanation describing the reasons that the exponential function appears in the formulas governing population growth and radioactive decay, I have not fostered my students' ability to recognize other phenomena, either in mathematics or in other disciplines, that use exponential functions.

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45

Martynov, G. A. "Power and exponential asymptotic forms of correlation functions". Theoretical and Mathematical Physics 156, n.º 3 (setembro de 2008): 1356–64. http://dx.doi.org/10.1007/s11232-008-0112-x.

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46

Jia, Rong-Qing, e Song Li. "Refinable Functions with Exponential Decay: An Approach via Cascade Algorithms". Journal of Fourier Analysis and Applications 17, n.º 5 (22 de janeiro de 2011): 1008–34. http://dx.doi.org/10.1007/s00041-011-9170-9.

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Dorlas, T. C., A. L. Rebenko e B. Savoie. "Correlation of clusters: Partially truncated correlation functions and their decay". Journal of Mathematical Physics 61, n.º 3 (1 de março de 2020): 033303. http://dx.doi.org/10.1063/1.5092615.

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Kim, Sunghu, Byung-Kuk Yoo, Yuri Choi, Byeong-Su Kim e Oh-Hoon Kwon. "Time-resolved spectroscopy of the ensembled photoluminescence of nitrogen- and boron/nitrogen-doped carbon dots". Physical Chemistry Chemical Physics 20, n.º 17 (2018): 11673–81. http://dx.doi.org/10.1039/c8cp01619d.

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Baladi, Viviane, Michael Benedicks e Véronique Maume-Deschamps. "Decay of random correlation functions for unimodal maps". Reports on Mathematical Physics 46, n.º 1-2 (agosto de 2000): 15–26. http://dx.doi.org/10.1016/s0034-4877(01)80004-5.

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Mall, Alison L., e Mike Risinger. "The Back Page: My Favorite Lesson: Modeling Exponential Decay". Mathematics Teacher 107, n.º 5 (dezembro de 2013): 400. http://dx.doi.org/10.5951/mathteacher.107.5.0400.

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Our favorite lesson, an interactive experiment that models exponential decay, launches with a loud dice roll. This exploration engages students in lively data collection that motivates interest in key components of the Common Core State Standards for Mathematics: functions, modeling, and statistics and probability (CCSSI 2010).

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