Related papers: Nonlinear Generalization of Den Hartog's Equal-Pea…
In this article, we present a new approach to averaging in non-Hamiltonian systems with periodic forcing. The results here do not depend on the existence of a small parameter. In fact, we show that our averaging method fits into an…
We study dynamics of two coupled periodically driven oscillators. Important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions…
Low-rank adaptation (LoRA) approximates the update of a pretrained weight matrix using the product of two low-rank matrices. However, standard LoRA follows an explicit-rank paradigm, where increasing model capacity requires adding more rows…
A previously proposed variational approach for momentum-conserving systems [J. Liu et.al., Phys. Rev. E 91, 042910 (2015)] is extended to systematically investigate general momentum-nonconserving nonlinear lattices. Two intrinsic identities…
We investigate the potential of adaptive equalization techniques to mitigate inter-channel nonlinear interference noise (NLIN). We derive a lower bound on the mutual information of a system using adaptive equalization, showing that the…
We consider a semiparametric partly linear model identified by instrumental variables. We propose an estimation method that does not smooth on the instruments and we extend the Landweber-Fridman regularization scheme to the estimation of…
We consider the general question of estimating decay of correlations for non-uniformly expanding maps, for classes of observables which are much larger than the usual class of Holder continuous functions. Our results give new estimates for…
The Duffing oscillator is a paradigm of bistable oscillatory motion in physics, engineering, and biology. Time series of such oscillations are often observed experimentally in a nonlinear system excited by a spontaneously fluctuating force.…
We present a systematic approach for the semiclassical treatment of many-body dynamics of interacting, open spin systems. Our approach overcomes some of the shortcomings of the recently developed discrete truncated Wigner approximation…
In this paper, we study two systems with a time-variable coefficient and general time-gradually-degenerate damping. More explicitly, we construct the Riemann solutions to the time-variable coefficient Zeldovich approximation and…
We study acoustic wave propagation in a uniform stationary flow. We develop a method founded on the Lorentz transform and a hypothesis of irrotationality of the acoustic perturbation. After a transformation of the space-time and of the…
The recent classical nonlocal generalization of Einstein's theory of gravitation is presented within the framework of general relativity via the introduction of a preferred frame field. The nonlocal generalization of Einstein's field…
The classical 'time-bandwidth' limit for linear time-invariant (LTI) devices asserts that it is impossible to store broadband waves (large {\Delta}{\omega}'s) for long times (large {\Delta}t's). For standing waves, i.e., vibrations, in…
A bistable nonlinear energy sink conceived to mitigate the vibrations of host structural systems is considered in this paper. The hosting structure consists of two coupled symmetric linear oscillators (LOs) and the nonlinear energy sink…
Nonlinear acceleration methods are powerful techniques to speed up fixed-point iterations. However, many acceleration methods require storing a large number of previous iterates and this can become impractical if computational resources are…
We introduce algorithms for learning nonlinear dynamical systems of the form $x_{t+1}=\sigma(\Theta^{\star}x_t)+\varepsilon_t$, where $\Theta^{\star}$ is a weight matrix, $\sigma$ is a nonlinear link function, and $\varepsilon_t$ is a…
In this study, a novel non-negative tensor factorization (NTF)-based method for vibration-based local damage detection in rolling element bearings is proposed. As the diagnostic signal registered from a faulty machine is non-stationary, the…
Nonlinear absorption in four and five energy level systems have been studied with the aid of steady-state rate equation approach. We report on the tunability of saturable and reverse saturable absorption as a function of spectroscopic…
We develop the generalized rotating-wave approximation (GRWA) approach (Phys. Rev. Lett. 99, 173601 (2007)) to study the single-photon scattering on a two-level system (TLS) with arbitrarily strong coupling to a local mode in a…
This article investigates how a uniform high frequency (HF) drive applied to each site of a weakly-coupled discrete nonlinear resonator array can modulate the onsite natural stiffness and damping and thereby facilitate the active tunability…