Search results for " Nonlinear"
showing 10 items of 1224 documents
Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters
2020
[EN] In spite of its simple formulation via a nonlinear differential equation, the Gompertz model has been widely applied to describe the dynamics of biological and biophysical parts of complex systems (growth of living organisms, number of bacteria, volume of infected cells, etc.). Its parameters or coefficients and the initial condition represent biological quantities (usually, rates and number of individual/particles, respectively) whose nature is random rather than deterministic. In this paper, we present a complete uncertainty quantification analysis of the randomized Gomperz model via the computation of an explicit expression to the first probability density function of its solution s…
Regular and singular pulse and front solutions and possible isochronous behavior in the Extended-Reduced Ostrovsky Equation: Phase-plane, multi-infin…
2016
In this paper we employ three recent analytical approaches to investigate several classes of traveling wave solutions of the so-called extended-reduced Ostrovsky Equation (exROE). A recent extension of phase-plane analysis is first employed to show the existence of breaking kink wave solutions and smooth periodic wave (compacton) solutions. Next, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of the traveling-wave equations for the exROE equation. These correspond to pulse solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddl…
Stochastic linearization critically re-examined
1997
Abstract The stochastic linearization technique, widely used for the analysis of nonlinear dynamic systems subjected to random excitations, is revisited. It is shown that the standard procedure universally adopted for determining the so-called effective stiffness of the equivalent linear system is erroneous in all previous publications. Two error-free stochastic linearization techniques are elucidated, namely those based on (1) the force linearization and (2) energy linearization.
A constructive theory of shape
2021
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of qualitatively similar shapes are constructed giving as input a finite ordered set of characteristic points (landmarks) and the value of a continuous parameter $\kappa \in (0,\infty)$. We prove that all shapes belonging to the same family are located within the convex hull of the landmarks. The theory is constructive in the sense that it provides a systematic means to build a mathematical model for any shape taken from the physical world. We illustrate this with a va…
A note on correlation and local dimensions
2015
Abstract Under very mild assumptions, we give formulas for the correlation and local dimensions of measures on the limit set of a Moran construction by means of the data used to construct the set.
Surface-directed spinodal decomposition in a thin-film geometry: A computer simulation
1994
The phase separation kinetics of a two-dimensional binary mixture at critical composition confined between (one-dimensional) straight walls which preferentially attract one component of the mixture is studied for a wide range of distancesD between the walls. Following earlier related work on semiinfinite systems, two choices of surface forces at the walls are considered, one corresponding to an incompletely wet state of the walls, the other to a completely wet state (forD→∞). The nonlinear Cahn-Hilliard-type equation, supplemented with appropriate boundary conditions which account for the presence of surfaces, is replaced by a discrete equivalent and integrated numerically. Starting from a …
Energy landscape properties studied using symbolic sequences
2006
We investigate a classical lattice system with $N$ particles. The potential energy $V$ of the scalar displacements is chosen as a $\phi ^4$ on-site potential plus interactions. Its stationary points are solutions of a coupled set of nonlinear equations. Starting with Aubry's anti-continuum limit it is easy to establish a one-to-one correspondence between the stationary points of $V$ and symbolic sequences $\bm{\sigma} = (\sigma_1,...,\sigma_N)$ with $\sigma_n=+,0,-$. We prove that this correspondence remains valid for interactions with a coupling constant $\epsilon$ below a critical value $\epsilon_c$ and that it allows the use of a ''thermodynamic'' formalism to calculate statistical prope…
HIGH-PRECISION MONTE CARLO DETERMINATION OF α/ν IN THE 3D CLASSICAL HEISENBERG MODEL
1994
To study the role of topological defects in the three-dimensional classical Heisenberg model we have simulated this model on simple cubic lattices of size up to 803, using the single-cluster Monte Carlo update. Analysing the specific-heat data of these simulations, we obtain a very accurate estimate for the ratio of the specific-heat exponent with the correlation-length exponent, α/ν, from a usual finite-size scaling analysis at the critical coupling Kc. Moreover, by fitting the energy at Kc, we reduce the error estimates by another factor of two, and get a value of α/ν, which is comparable in accuracy to best field theoretic estimates.
Variable kinematics models and finite elements for nonlinear analysis of multilayered smart plates
2015
Abstract A variable kinematics approach for moderately large deflection analysis of smart magneto-electro-elastic multilayered plates is presented. The approach is based on the condensation of the electro-magnetic state into the plate kinematics, whose nonlinear strain–displacement relationships are expressed in the von Karman sense. This leads to models resulting in an effective mechanical plate, which takes the multifield coupling effects into account by the plate stiffness, inertia and loading characteristics, consistently defined as combinations of the layers material properties. By a unified approach, both equivalent single layer and layerwise models are developed formulating the assoc…
Nonlinear pulse deceleration using photorefractive four-wave mixing
2009
We investigate the possibilities of the backward four-wave coupling based on the nonlocal photorefractive response for the nonlinear deceleration of light pulses. The presence of an additional external variable parameter—the pump intensity ratio—allows to improve the output characteristics of the decelerated pulses compared to those typical of the two-wave coupling. In particular, large delay times of the output pulses can be achieved without their strong amplification. This positive distinctive feature of the pulse deceleration occurs far from threshold of the mirrorless optical oscillation.