相关论文: Symbolic Computations for Nonlinear Resonances

We propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The model describes an array of linearly…

The design of structures submitted to aerodynamic loads usually requires the development of specific computational models considering fluid-structure interactions. Models using structural frame elements are developed in several relevant…

We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…

A new non-perturbative method of solution of the nonlinear Heisenberg equations in the finite-dimensional subspace is illustrated. The method, being a counterpart of the traditional Schrodinger picture method, is based on a finite operator…

Nonlinear mixed effects modeling is a powerful tool when analyzing data from several entities in an experiment. In this paper, we present NLMEModeling, a package for mixed effects modeling in Wolfram Mathematica. NLMEModeling supports mixed…

Nonlinear string vibration, in particular the case of nonplanar motion, has been an area of intense study for many years. Numerical simulation methods, essential for the comparison between measured data and theory, have received somewhat…

In an effort to provide an alternative method to represent a quantum spin, a precise nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a multi-body,…

In this paper we discuss the dynamics of the cosmological Bartnick-McKinnon analogue with $n=1$ and $\Lambda=\Lambda_{reg}(n)$ . We derive boundary conditions from energy considerations. Numerical simulations are carried out to show the…

We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…

Real-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the…

We present a new technique for verifying nonlinear and hybrid models with inputs. We observe that once an input signal is fixed, the sensitivity analysis of the model can be computed much more precisely. Based on this result, we propose a…

Parametric representations of various functions are fundamental tools in science and engineering. This paper introduces a fixed-initial-state constant-input dynamical system (FISCIDS) representation, which provides an exact and parametric…

We consider a broad class of systems of nonlinear integro-differential equations posed on the real line that arise as Euler-Lagrange equations to energies involving nonlinear nonlocal interactions. Although these equations are not readily…

The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

A closed-form analytical solution is found for the nonlinear dynamics of isolated, near-threshold waves in the presence of strong scattering. The proposed solution can be useful in verifying codes across several disciplines, including…

This paper presents a fast and effective computer algebraic method for analyzing and verifying non-linear integer arithmetic circuits using a novel algebraic spectral model. It introduces a concept of algebraic spectrum, a numerical form of…

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…

The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…

In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…