Search results for "Exponential function"
showing 10 items of 173 documents
2-D mapping of skin chromophores in the spectral range 500 - 700 nm
2009
The multi-spectral imaging technique has been used for distant mapping of in-vivo skin chromophores by analyzing spectral data at each reflected image pixel and constructing 2-D maps of the relative concentrations of oxy-/deoxy-haemoglobin and melanin. Instead of using a broad visible-NIR spectral range, this study focuses on narrowed spectral band 500–700 nm, speeding-up the signal processing procedure. Regression analysis confirmed that superposition of three Gaussians is optimal analytic approximation for the oxy-haemoglobin absorption tabular spectrum in this spectral band, while superposition of two Gaussians fits well for deoxy-haemoglobin absorption and exponential function – for mel…
Iterative approach to the exponential representation of the time–displacement operator
2005
An iterative method due to Voslamber is reconsidered. It provides successive approximations for the logarithm of the time–displacement operator in quantum mechanics. The procedure may be interpreted, a posteriori, as an infinite re-summation of terms in the so-called Magnus expansion. A recursive generator for higher terms is obtained. From two illustrative examples, a detailed comparative study is carried out between the results of the iterative method and those of the Magnus expansion.
Exponential Transients in Continuous-Time Symmetric Hopfield Nets
2001
We establish a fundamental result in the theory of continuous-time neural computation, by showing that so called continuous-time symmetric Hopfield nets, whose asymptotic convergence is always guaranteed by the existence of a Liapunov function may, in the worst case, possess a transient period that is exponential in the network size. The result stands in contrast to e.g. the use of such network models in combinatorial optimization applications. peerReviewed
Lyapunov Functions for Second-Order Differential Inclusions: A Viability Approach
2001
AbstractIn this paper the existence of Lyapunov functions for second-order differential inclusions is analyzed by using the methodology of the Viability Theory. A necessary assumption on the initial states and sufficient conditions for the existence of local and global Lyapunov functions are obtained. An application is also provided.
An LMI Approach to Exponential Stock Level Estimation for Large-Scale Logistics Networks
2013
This article aims to present a convex optimization approach for exponential stock level estimation problem of large-scale logistics networks. The model under consideration presents the dependency and interconnections between the dynamics of each single location. Using a Lyapunov function, new sufficient conditions for exponential estimation of the networks are driven in terms of linear matrix inequalities (LMIs). The explicit expression of the observer gain is parameterized based on the solvability conditions. A numerical example is included to illustrate the applicability of the proposed design method.
Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations
2021
Abstract The generalized Langevin equation is a model for the motion of coarse-grained particles where dissipative forces are represented by a memory term. The numerical realization of such a model requires the implementation of a stochastic delay-differential equation and the estimation of a corresponding memory kernel. Here we develop a new approach for computing a data-driven Markov model for the motion of the particles, given equidistant samples of their velocity autocorrelation function. Our method bypasses the determination of the underlying memory kernel by representing it via up to about twenty auxiliary variables. The algorithm is based on a sophisticated variant of the Prony metho…
Irreversible Multilayer Adsorption
1993
Random sequential adsorption (RSA) models have been studied due to their relevance to deposition processes on surfaces. The depositing particles are represented by hard-core extended objects; they are not allowed to overlap. Numerical Monte Carlo studies and analytical considerations are reported for 1D and 2D models of multilayer adsorption processes. Deposition without screening is investigated, in certain models the density may actually increase away from the substrate. Analytical studies of the late stage coverage behavior show the crossover from exponential time dependence for the lattice case to the power law behavior in the continuum deposition. 2D lattice and continuum simulations r…
Strength distribution in paper
1998
Abstract Tensile strength distributions are studied in four paper samples that exhibit a variety of brittle-to-ductile properties. 1005 tensile specimens were measured in each case. The standard Gumbel and Weibull distributions, and a recently proposed double exponential modification of the former are compared with the observations visually and using chi-squared and Kolmogorov–Smirnov tests. The Gumbel distribution fails to fit the data while the Weibull distribution gives satisfactory agreement. However, the double exponential distribution fits the data best, regardless of the ductility of the material.
Experimental validation of a fractional model for creep/recovery testing of asphalt mixtures
2012
Abstract Prediction of asphalt mixtures’ behavior during their service life is a challenge due to its complexity and sensitivity to environmental and loading conditions. It has been proved that, when subjected to loading conditions comparable with most pavement operating conditions, asphalt mixtures behave as linear visco-elastic (LVE) materials. Traditionally the LVE behavior of bituminous material is modeled via creep/recovery functions. In the past, several rheological models constituted by elastic and viscous elements arranged in series or in parallel (analogical models) have been proposed and specified for both bitumen and asphalt mixtures. The corresponding constitutive laws always in…
Numerical study of blow-up and dispersive shocks in solutions to generalized Korteweg–de Vries equations
2015
Abstract We present a detailed numerical study of solutions to general Korteweg–de Vries equations with critical and supercritical nonlinearity, both in the context of dispersive shocks and blow-up. We study the stability of solitons and show that they are unstable against being radiated away and blow-up. In the L 2 critical case, the blow-up mechanism by Martel, Merle and Raphael can be numerically identified. In the limit of small dispersion, it is shown that a dispersive shock always appears before an eventual blow-up. In the latter case, always the first soliton to appear will blow up. It is shown that the same type of blow-up as for the perturbations of the soliton can be observed whic…