Search results for "Exponential function"
showing 10 items of 173 documents
Numerical simulation of resonant activation in a fluctuating metastable model system
1998
We study the escape time from a metastable overdamped model system in the presence of two noise sources: a white noise and a random telegraph noise. The random telegraph noise controls the height of the potential barrier of the metastable system while the white noise mimics the presence of a given temperature. We report on numerical simulations about: (i) the average residence time of the system in the metastable state; (ii) the probability density function (PDF) of the residence time at various values of the correlation time T c of the random telegraph noise. Resonant activation is observed in the dynamics of the investigated system. The PDF shows different shapes for different values of τ…
Luminescence of localized states in silicon dioxide glass. A short review
2011
Abstract The target is the description of the properties of localized states in silica glass, which relate to aspects of short-to-intermediate-range order. It has been observed that laser light interaction with localized states of silica glass leads to the creation of luminescence centers. Created luminescence centers, excited with laser light, provide intra-center luminescence of oxygen deficient centers (ODC) comprising a blue band at 2.7 eV and a UV band at 4.4 eV. Structurally, these ODCs are understood to comprise twofold-coordinated silicons that are commonly part of some larger local structure, and their luminescence bands can be suppressed by reaction with chlorine or hydrogen. Besi…
Dynamic anomaly in the glass transition region of orthoterphenyl
1991
We report on incoherent and coherent neutron scattering results in the supercooled liquid and the glassy regime of the van der Waals fluido-terphenyl using the backscattering and spin echo technique, respectively. A critical comparison of both techniques is presented. The data are analysed in the time domain assuming that microscopic correlation times (τ) scale with the viscosity η according to τ(T)∼η(T)/T. With this assumption we obtain an agreement with several predictions of mode coupling theory: the existence of a critical temperatureT c is shown, independently for both incoherent and coherent data, by a cusp in the temperature dependence of the Debye-Waller factorf Q (T). BelowT c fQ(T…
Annihilation Operators for Exponential Spaces in Subdivision
2022
We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperbolic functions. Although exponential functions appear in a variety of contexts, the motivation behind this work comes from considering subdivision schemes with the capability of preserving those exponential functions required for an exact description of surfaces parametrized in terms of trigonometric and hyperbolic functions.
Aging effects in simple models for glassy relaxation
2006
Aging effects in the two-time correlation function and the response function after a quench from a high temperature to some low temperature are considered for a simple kinetic random energy model exhibiting stretched exponential relaxation. Because the system reaches thermal equilibrium for long times after the quench, all aging effect are of a transient nature. In particular, the violations of the fluctuation-dissipation theorem are considered and it is found that the relation between the response and the two-time correlation function depends on another function, the so-called asymmetry. This asymmetry vanishes in equilibrium but cannot be neglected in the aging regime. It is found that pl…
Notice of Violation of IEEE Publication Principles: New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With M…
2010
This paper establishes an exponential H infin synchronization method for a class of uncertain master and slave neural networks (MSNNs) with mixed time delays, where the mixed delays comprise different neutral, discrete, and distributed time delays. The polytopic and the norm-bounded uncertainties are separately taken into consideration. An appropriate discretized Lyapunov-Krasovskii functional and some free-weighting matrices are utilized to establish some delay-dependent sufficient conditions for designing delayed state-feedback control as a synchronization law in terms of linear matrix inequalities under less restrictive conditions. The controller guarantees the exponential H infin synchr…
Non-periodic Discrete-Spline Wavelets
2015
This chapter describes wavelet analysis in the spaces of discrete splines whose spans are powers of 2. This wavelet analysis is similar to wavelet analysis in the polynomial-spline spaces. The transforms are based on relations between exponential discrete splines from different resolution scales. Generators of discrete-spline wavelet spaces are described. The discrete-spline wavelet transforms generate wavelet transforms in signal space. Practically, wavelet transforms of signals are implemented by multirate filtering of signals by two-channel filter banks with the downsampling factor 2 (critically sampled filter banks). The filtering implementation is accelerated by switching to the polyph…
Performance of polarization-consistent vs. correlation-consistent basis sets for CCSD(T) prediction of water dimer interaction energy
2019
Abstract Detailed study of Jensen’s polarization-consistent vs. Dunning’s correlation-consistent basis set families performance on the extrapolation of raw and counterpoise-corrected interaction energies of water dimer using coupled cluster with single, double, and perturbative correction for connected triple excitations (CCSD(T)) in the complete basis set (CBS) limit are reported. Both 3-parameter exponential and 2-parameter inverse-power fits vs. the cardinal number of basis set, as well as the number of basis functions were analyzed and compared with one of the most extensive CCSD(T) results reported recently. The obtained results for both Jensen- and Dunning-type basis sets underestimat…
Modified Gaussian models applied to the description and deconvolution of peaks in chiral liquid chromatography.
2020
Abstract The description of the profiles of chromatographic peaks has been studied extensively, with a large number of proposed mathematical functions. Among them, the accuracy achieved with modified Gaussian models that describe the deviation of an ideal Gaussian peak as a change in the peak variance or standard deviation over time, has been highlighted. These models are, in fact, a family of functions of different complexity with great flexibility to adjust chromatographic peaks over a wide range of asymmetries and shapes. However, an uncontrolled behaviour of the signal may occur outside the region being fitted, forcing the use of different strategies to overcome this problem. In this wo…
Application of cohesive-zone models to delamination behaviour of composite material
2012
International audience; The parameters of cohesive elements have to be chosen correctly in the simulation of composite delamination by finite element method: such as interface strength, interface stiffness and shape of cohesive law. The purpose of this work is to investigate their influence on the accuracy of the results obtained. A three-dimensional cohesive-zone model has been established using Ls-dyna to simulate Double-Cantilever-Beam mode I (DCB) and Edge-Notched-Flexure mode II (ENF) tests. The influence of these parameters of cohesive element on the maximum load and the slope of load-displacement curve have been discussed by comparing experimental and numerical results. Four traction…