Search results for "piecewise linear"
showing 10 items of 31 documents
Subsignal-based denoising from piecewise linear or constant signal
2011
15 pages; International audience; n the present work, a novel signal denoising technique for piecewise constant or linear signals is presented termed as "signal split." The proposed method separates the sharp edges or transitions from the noise elements by splitting the signal into different parts. Unlike many noise removal techniques, the method works only in the nonorthogonal domain. The new method utilizes Stein unbiased risk estimate (SURE) to split the signal, Lipschitz exponents to identify noise elements, and a polynomial fitting approach for the sub signal reconstruction. At the final stage, merging of all parts yield in the fully denoised signal at a very low computational cost. St…
Open and Discrete Maps with Piecewise Linear Branch Set Images are Piecewise Linear Maps
2018
The image of the branch set of a piecewise linear (PL)‐branched cover between PL 𝑛n‐manifolds is a simplicial (𝑛−2)(n−2)‐complex. We demonstrate that the reverse implication also holds: an open and discrete map 𝑓:𝕊𝑛→𝕊𝑛f:Sn→Sn with the image of the branch set contained in a simplicial (𝑛−2)(n−2)‐complex is equivalent up to homeomorphism to a PL‐branched cover. peerReviewed
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.
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…
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.
A unified approach to quasi-static shakedown problems for elastic-plastic solids with piecewise linear yield surface
1978
The paper concerns shakedown analysis of elastic-plastic bodies subjected to quasi-statically varying loads within a given domain. Using a perturbation method, a general inequality is given, from which, by simply specializing the perturbing terms, the generalized Melan theorem as well as bounds on various deformation parameters (such as displacements or plastic strain intensities) are derived. The solution of the «perturbed» shakedown problem in finite or holonimic terms permits the bound to be the most stringent and expressible in «local» terms instead of integral terms. A simple application concludes the paper.
Shakedown of Structures Subjected to Dynamic External Actions and Related Bounding Techniques
2002
The shakedown theory for dynamic external actions is expounded considering elastic-plastic internal-variable material models endowed with hardening saturation surface and assuming small displacements and strains as long with negligible effects of temperature variations on material data. Two sorts of dynamic shakedown theories are presented, i.e.: i) Unrestricted dynamic shakedown, in which the structure is subjected to (unknown) sequences of short-duration excitations belonging to a known excitation domain, with no-load no-motion time periods in between and for which a unified framework with quasi-static shakedown is presented; and ii) Restricted dynamic shakedown, in which the structure is…
Efficient full decay inversion of MRS data with a stretched-exponential approximation of the distribution
2012
SUMMARY We present a new, efficient and accurate forward modelling and inversion scheme for magnetic resonance sounding (MRS) data. MRS, also called surface-nuclear magnetic resonance (surface-NMR), is the only non-invasive geophysical technique that directly detects free water in the subsurface. Based on the physical principle of NMR, protons of the water molecules in the subsurface are excited at a specific frequency, and the superposition of signals from all protons within the excited earth volume is measured to estimate the subsurface water content and other hydrological parameters. In this paper, a new inversion scheme is presented in which the entire data set is used, and multi-expone…
A Lagrange Multiplier Based Domain Decomposition Method for the Solution of a Wave Problem with Discontinuous Coefficients
2008
In this paper we consider the numerical solution of a linear wave equation with discontinuous coefficients. We divide the computational domain into two subdomains and use explicit time difference scheme along with piecewise linear finite element approximations on semimatching grids. We apply boundary supported Lagrange multiplier method to match the solution on the interface between subdomains. The resulting system of linear equations of the “saddle-point” type is solved efficiently by a conjugate gradient method.