Search results for "nonlinear"

Probabilistic solution of a homogeneous linear second-order differential equation with randomized complex coefficients

2022

In this paper, an exact expression for the first probability density function of the solution stochastic process to a randomized homogeneous linear second-order complex differential equation is determined. To complete the probabilistic analysis, the first probability density functions of the real and complex contributions of the solution stochastic process are also calculated. To compute the densities, the random variable transformation method is applied under general hypothesis, all coefficients and initial conditions are absolutely continuous complex random variables. The capability of the theoretical results established is demonstrated by several numerical examples. Finally, we show the …

Kernel image similarity criterion

2011

This paper presents a family of metrics for assessing image similarity. The methods use the Hilbert-Schmidt Independence Criterion (HSIC) to estimate nonlinear statistical dependence between multidimensional images. The proposed methods have very good theoretical and practical properties. We illustrate the performance in evaluating the quality of natural photographic images, hyperspectral images under different noise levels, in synthetic multiresolution problems, and real pansharpening products.

A Computational Two-Scale Approach to Nonlinear Analysis of Etherogeneous Composite Structures

2010

An application of the arithmetic euler function to the construction of nonclassical states of a quantum harmonic oscillator

2001

Abstract All quantum superpositions of two equal intensity coherent states exhibiting infinitely many zeros in their Fock distributions are explicitly constructed and studied. Our approach is based on results from number theory and, in particular, on the properties of arithmetic Euler function. The nonclassical nature of these states is briefly pointed out. Some interesting properties are brought to light.

Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral

2014

A novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators endowed with fractional derivatives elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes which rely on a discrete version of the…

A New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal

1999

In this paper we summarize the main features of a new time dependent model to approximate the solution to the nonlinear total variation optimization problem for deblurring and noise removal introduced by Rudin, Osher and Fatemi. Our model is based on level set motion whose steady state is quickly reached by means of an explicit procedure based on an ENO Hamilton-Jacobi version of Roe's scheme. We show numerical evidence of the speed, resolution and stability of this simple explicit procedure in two representative 1D and 2D numerical examples.

Optical Dark Rogue Wave

2016

AbstractPhotonics enables to develop simple lab experiments that mimic water rogue wave generation phenomena, as well as relativistic gravitational effects such as event horizons, gravitational lensing and Hawking radiation. The basis for analog gravity experiments is light propagation through an effective moving medium obtained via the nonlinear response of the material. So far, analogue gravity kinematics was reproduced in scalar optical wave propagation test models. Multimode and spatiotemporal nonlinear interactions exhibit a rich spectrum of excitations, which may substantially expand the range of rogue wave phenomena and lead to novel space-time analogies, for example with multi-parti…

INTERFACE TENSION AND CORRELATION LENGTH OF 2D POTTS MODELS: NUMERICAL VERSUS EXACT RESULTS

1994

I briefly review new analytical formulas for the correlation length and interface tension of two-dimensional q-state Potts models and compare them with numerical results from recent Monte Carlo simulation studies.

Magnetic field dynamos and magnetically triggered flow instabilities

2017

The project A2 of the LIMTECH Alliance aimed at a better understanding of those magnetohydrodynamic instabilities that are relevant for the generation and the action of cosmic magnetic fields. These comprise the hydromagnetic dynamo effect and various magnetically triggered flow instabilities, such as the magnetorotational instability and the Tayler instability. The project was intended to support the experimental capabilities to become available in the framework of the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN). An associated starting grant was focused on the dimensioning of a liquid metal experiment on the newly found magnetic destabilization of rotating flow…

A 2D-FEM Model of Nonlinear Ultrasound Propagation in Trans-cranial MRgFUS Technique

2022

Magnetic Resonance guided Focused Ultrasound (MRgFUS) is a non-invasive technique based on the thermal ablation of a target using high intensity focused ultrasound. MRgFUS treatment applied to brain is challenging due to the skull presence that attenuates ultrasound, leading to heating effects in bone region. In this study, we simulate trans-cranial nonlinear ultrasound propagation considering the detailed structure of bone tissue. We developed a 2D Finite Element (FE) model that mimics the propagation of focused ultrasound through skin, skull and brain tissue. The skull is represented as a three-layered system with two cortical tables packing a layer of trabecular bone. We assume that the …