Search results for "Piecewise"
showing 10 items of 108 documents
Edge detection insensitive to changes of illumination in the image
2010
In this paper we present new edge detection algorithms which are motivated by recent developments on edge-adapted reconstruction techniques [F. Arandiga, A. Cohen, R. Donat, N. Dyn, B. Matei, Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques, Appl. Comput. Harmon. Anal. 24 (2) (2008) 225-250]. They are based on comparing local quantities rather than on filtering and thresholding. This comparison process is invariant under certain transformations that model light changes in the image, hence we obtain edge detection algorithms which are insensitive to changes in illumination.
Step-by-step integration for fractional operators
2018
Abstract In this paper, an approach based on the definition of the Riemann–Liouville fractional operators is proposed in order to provide a different discretisation technique as alternative to the Grunwald–Letnikov operators. The proposed Riemann–Liouville discretisation consists of performing step-by-step integration based upon the discretisation of the function f(t). It has been shown that, as f(t) is discretised as stepwise or piecewise function, the Riemann–Liouville fractional integral and derivative are governing by operators very similar to the Grunwald–Letnikov operators. In order to show the accuracy and capabilities of the proposed Riemann–Liouville discretisation technique and th…
Eventually periodic solutions of single neuron model
2020
In this paper, we consider a nonautonomous piecewise linear difference equation that describes a discrete version of a single neuron model with a periodic (period two and period three) internal decay rate. We investigated the periodic behavior of solutions relative to the periodic internal decay rate in our previous papers. Our goal is to prove that this model contains a large quantity of initial conditions that generate eventually periodic solutions. We will show that only periodic solutions and eventually periodic solutions exist in several cases.
Fluctuation dissipation ratio in an aging Lennard-Jones glass
1998
By using extensive Molecular Dynamics simulations, we have determined the violation of the fluctuation-dissipation theorem in a Lennard-Jones liquid quenched to low temperatures. For this we have calculated $X(C)$, the ratio between a one particle time-correlation function $C$ and the associated response function. Our results are best fitted by assuming that $X(C)$ is a discontinuous, piecewise constant function. This is similar to what is found in spin systems with one step replica symmetry breaking. This strengthen the conjecture of a similarity between the phase space structure of structural glasses and such spin systems.
Number of metastable states of a chain with competing and anharmonicΦ4−like interactions
1993
We investigate the number of metastable configurations of a Φ 4 -like model with competing and anharmonic interactions as a function of an effective coupling constant η. The model has piecewise harmonic nearest-neighbor and harmonic next-nearerst-neighbor interactions. The number M of metastable states in the configuration space increases exponentially with the number N of particles: M∞exp(vN). It is shown numerically that, outside the previously considered range |η|<1/3, v is approximately linearly decreasing with η for |η|<1 and that v=0 for η≥1. These findings can be understood by describing the metastable configurations as an arrangement of kink solitons whose width creases with η
Numerical viscosity in simulations of the two-dimensional Kelvin-Helmholtz instability
2020
The Kelvin-Helmholtz instability serves as a simple, well-defined setup for assessing the accuracy of different numerical methods for solving the equations of hydrodynamics. We use it to extend our previous analysis of the convergence and the numerical dissipation in models of the propagation of waves and in the tearing-mode instability in magnetohydrodynamic models. To this end, we perform two-dimensional simulations with and without explicit physical viscosity at different resolutions. A comparison of the growth of the modes excited by our initial perturbations allows us to estimate the effective numerical viscosity of two spatial reconstruction schemes (fifth-order monotonicity preservin…
Piecewise static Hamiltonian for an atom in strong laser field
2009
We show that it is possible to use a piecewise constant Hamiltonian to describe the main features of the dynamics of an atom interacting with a laser field. In particular we show that using this approximation we are able to give a good description of the ionization signal, of the HHG spectra and of the attosecond pulses generated by the radiating electron. Finally, we give an explicit formula to evaluate the ionization rate in the time dependent laser field. This formula, which is a generalization of the Landau formula for the ionization rate of an atom in a static electric field, fairly well reproduces the numerical ionization rates for a broad range of laser frequency and intensity. The m…
Two-Dimensional Boundary Layer Equations: High Resolution Capturing Methods
1993
In this paper we apply the piecewise hyperbolic and parabolic essentially non-oscillatory (ENO) capturing schemes (see [2] and [4]) to approximate the solution to the boundary layer equations for two-dimensional incompressible flow. We have tested several numerical examples analyzing their resolutive power and efficiency with respect to small values of the kinematic viscosity of the flow.
Periodic orbits of a neuron model with periodic internal decay rate
2015
In this paper we will study a non-autonomous piecewise linear difference equation which describes a discrete version of a single neuron model with a periodic internal decay rate. We will investigate the periodic behavior of solutions relative to the periodic internal decay rate. Furthermore, we will show that only periodic orbits of even periods can exist and show their stability character.
Superconvergence phenomenon in the finite element method arising from averaging gradients
1984
We study a superconvergence phenomenon which can be obtained when solving a 2nd order elliptic problem by the usual linear elements. The averaged gradient is a piecewise linear continuous vector field, the value of which at any nodal point is an average of gradients of linear elements on triangles incident with this nodal point. The convergence rate of the averaged gradient to an exact gradient in theL 2-norm can locally be higher even by one than that of the original piecewise constant discrete gradient.