Related papers: Conservative Numerical Methods for Nonlinear Strin…
The computation of time dynamics arising in nonlinear time-dependent partial differential equations is an ongoing challenge in numerical analysis, especially once roughness comes into play. Classical numerical schemes in general fail to…
Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $\alpha\in(0,1)$ in time, due to their many successful applications in engineering, physics, biology…
Classical strings coupled to a metric, a dilaton and an axion, as conceived by superstring theory, suffer from ultraviolet divergences due to self-interactions. Consequently, as in the case of radiating charged particles, the corresponding…
We develop expressions for the nonlinear wave damping and frequency correction of a field of random, spatially homogeneous, acoustic waves. The implications for the nature of the equilibrium spectral energy distribution are discussed
In this study a new approach to the problem of transverse vibrations of an ideal string is presented. Unlike previous studies, assumptions such as constant tension, inextensibility, constant crosssectional area, small deformations and…
Conservation laws are of great theoretical and practical interest. We describe a novel approach to machine learning conservation laws of finite-dimensional dynamical systems using trajectory data. It is the first such approach based on…
In this paper we consider unconditionally energy stable numerical schemes for the nonstationary 3D magneto-micropolar equations that describes the microstructure of rigid microelements in electrically conducting fluid flow under some…
The spectrum of oscillating compact objects can be considerably altered in alternative theories of gravity. In particular, it may be enriched by modes with no counterpart in general relativity, tied to the dynamics of additional degrees of…
In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves…
A cantilever beam under axial flow, confined or not, is known to develop self-sustained oscillations at sufficiently large flow velocities. In recent decades, the analysis of this archetypal system has been mostly pursued under linearized…
In this paper we review the simulation method of the non-smooth contact dynamics. This technique was designed to solve the unilateral and frictional contact problem for a large number of rigid bodies and has proved to be especially valuable…
Structural resonance involves the absorption of inertial loads by a tuned structural elasticity: a process playing a key role in a wide range of biological and technological systems, including many biological and bio-inspired locomotion…
The Nystr\"om method is a widely used technique for improving the scalability of kernel-based algorithms, including kernel ridge regression, spectral clustering, and Gaussian processes. Despite its popularity, the numerical stability of the…
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…
Nonlinear acoustic evolution is often discussed in the context of wave-steepening that leads to shock formation, and is of special interest in applications where the shock continues to strengthen due to a narrowing of its channel or the…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
A stochastic model for nondemolition continuous measurement in a quantum system is given. It is shown that the posterior dynamics, including a continuous collapse of the wave function, is described by a nonlinear stochastic wave equation.…
We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time…
Analyzing data from dynamical systems often begins with creating a reconstruction of the trajectory based on one or more variables, but not all variables are suitable for reconstructing the trajectory. The concept of nonlinear observability…
We initiate a search for non-perturbative consistency conditions in M theory. Some non-perturbative conditions are already known in Type I theories; we review these and search for others. We focus principally on possible anomalies in…