Search results for " Nonlinear"
showing 10 items of 1224 documents
Spatial beam cleaning in quadratic nonlinear medium
2018
We show experimentally that a laser beam scrambled by propagation in a short segment of multimode fiber may be cleaned by the nonlinear propagation in KTP cristal with type-II second-harmonic generation.
Inferring causal relations from observational long-term carbon and water fluxes records
2022
AbstractLand, atmosphere and climate interact constantly and at different spatial and temporal scales. In this paper we rely on causal discovery methods to infer spatial patterns of causal relations between several key variables of the carbon and water cycles: gross primary productivity, latent heat energy flux for evaporation, surface air temperature, precipitation, soil moisture and radiation. We introduce a methodology based on the convergent cross-mapping (CCM) technique. Despite its good performance in general, CCM is sensitive to (even moderate) noise levels and hyper-parameter selection. We present a robust CCM (RCCM) that relies on temporal bootstrapping decision scores and the deri…
On the multifractal analysis of measures
1992
On Discovering Low Order Models in Biochemical Reaction Kinetics
2007
We develop a method by which a large number of differential equations representing biochemical reaction kinetics may be represented by a smaller number of differential equations. The basis of our technique is a conjecture that the high dimension equations of biochemical kinetics, which involve reaction terms of specific forms, are actually implementing a low dimension system whose behavior requires right hand sides that can not be biochemically implemented. For systems that satisfy this conjecture, we develop a simple approximation scheme based on multilinear algebra that extracts the low dimensional system from simulations of the high dimension system. We demonstrate this technique on a st…
FINITE-SIZE CORRECTIONS TO CORRELATION FUNCTION AND SUSCEPTIBILITY IN 2D ISING MODEL
2006
Transfer matrix calculations of the critical two-point correlation function in 2D Ising model on a finite-size [Formula: see text] lattice with periodic boundaries along 〈11〉 direction are extended to L = 21. A refined analysis of the correlation function in 〈10〉 crystallographic direction at the distance r = L indicates the existence of a nontrivial finite-size correction of a very small amplitude with correction-to-scaling exponent ω < 2 in agreement with our foregoing study for L ≤ 20. Here we provide an additional evidence and show that amplitude a of the multiplicative correction term 1 + aL-ωis about -3.5·10-8if ω = 1/4 (the expected value). We calculate also the susceptibility for…
HHT-α and TR-BDF2 schemes for dynamic contact problems
2023
This work focuses on the numerical performance of HHT-α and TR-BDF2 schemes for dynamic frictionless unilateral contact problems between an elastic body and a rigid obstacle. Nitsche's method, the penalty method, and the augmented Lagrangian method are considered to handle unilateral contact conditions. Analysis of the convergence of an opposed value of the parameter α for the HHT-α method is achieved. The mass redistribution method has also been tested and compared with the standard mass matrix. Numerical results for 1D and 3D benchmarks show the functionality of the combinations of schemes and methods used.
Role of noise in a market model with stochastic volatility
2006
We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES ef…
Memristors and nonequilibrium stochastic multistable systems
2022
The main aim of this special issue is to report the recent advances and new trends in memristors and nonequilibrium stochastic multistable systems, both theoretically and experimentally, within an interdisci-plinary context. In particular, memristors are multistable systems whose switching dynamics is a stochastic process, which can be controlled by internal and external noise sources, unveiling the constructive role of random fluctuations. Furthermore, the use of memristors as memory elements in neuromorphic systems with noise-assisted persistence of memory states, chaotic dynamics, metastable chaos and chaos synchronization, new stochastic nonlinear models, noise-induced phenomena such as…
On the modeling of nonlinear interactions in large complex systems
2010
Abstract This work deals with the modeling of large systems of interacting entities in the framework of the mathematical kinetic theory for active particles. The contents are specifically focused on the modeling of nonlinear interactions which is one of the most important issues in the mathematical approach to modeling and simulating complex systems, and which includes a learning–hiding dynamics. Applications are focused on the modeling of complex biological systems and on immune competition.
The Heat Content for Nonlocal Diffusion with Non-singular Kernels
2017
Abstract We study the behavior of the heat content for a nonlocal evolution problem.We obtain an asymptotic expansion for the heat content of a set D, defined as ℍ D J ( t ) := ∫ D u ( x , t ) 𝑑 x ${\mathbb{H}_{D}^{J}(t):=\int_{D}u(x,t)\,dx}$ , with u being the solution to u t = J ∗ u - u ${u_{t}=J\ast u-u}$ withinitial condition u 0 = χ D ${u_{0}=\chi_{D}}$ . This expansion is given in terms of geometric values of D. As a consequence, we obtain that ℍ D J ( t ) = | D | - P J ( D ) t + o ( t ) ${\mathbb{H}^{J}_{D}(t)=\lvert D\rvert-P_{J}(D)t+o(t)}$ as t ↓ 0 ${t\downarrow 0}$ .We also recover the usual heat content for the heat equation when we rescale the kernel J in an appro…