Related papers: Equivalent linearization finds nonzero frequency c…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
We analyze a semi-explicit time discretization scheme of first order for poro\-elasticity with nonlinear permeability provided that the elasticity model and the flow equation are only weakly coupled. The approach leads to a decoupling of…
We subject the stationary solutions of inviscid and axially symmetric rotational accretion to a time-dependent radial perturbation, which includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of…
We construct an analytical theory of interplay between synchronizing effects by common noise and by global coupling for a general class of smooth limit-cycle oscillators. Both the cases of attractive and repulsive coupling are considered.…
Oscillators - dynamical systems with stable periodic orbits - arise in many systems of physical, technological, and biological interest. The standard phase reduction, a model reduction technique based on isochrons, can be unsuitable for…
In this paper we firstly review how to \textit{explicitly} solve a system of $3$ \textit{first-order linear recursions }and outline the main properties of these solutions. Next, via a change of variables, we identify a class of systems of…
A real-space renormalization transformation is constructed for lattices of non-identical oscillators with dynamics of the general form $d\phi_{k}/dt=\omega_{k}+g\sum_{l}f_{lk}(\phi_{l},\phi_{k})$. The transformation acts on ensembles of…
We implement nonlinear anharmonic interaction in the coupled van der Pol oscillators to investigate the quantum synchronization behaviour of the systems. We study the quantum synchronization in two oscillator models, coupled quantum van der…
We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which…
The set of world lines for the non-relativistic quartic oscillator satisfying Newton's equation of motion for all space and time in 1-1 dimensions with no constraints other than the "spring" restoring force is shown to be equivalent…
Higher order corrections (up to n-th order) are obtained for the perihelion precession in binary systems like OJ287 using the Schwarzschild metric and complex integration. The corrections are performed considering the third root of the…
Several scenarios have been proposed in which the orbits of binary black holes enter the band of a gravitational wave detector with significant eccentricity. To avoid missing these signals or biasing parameter estimation it is important…
This paper proposes a novel method to achieve and preserve synchronization for a set of connected heterogeneous Van der Pol oscillators. Unlike the state-of-the-art synchronization methods, in which a large coupling gain is applied to…
We consider first-order linear systems of ordinary differential equations with periodic coefficients. Supposing that right-hand sides of equations are not known and subjected to some quadratic restrictions, we obtain optimal, in certain…
In this paper, we propose two novel fourth-order integrators that exhibit uniformly high accuracy and long-term near conservations for solving the nonlinear Dirac equation (NLDE) in the nonrelativistic regime. In this regime, the solution…
An inexact framework for high-order adaptive regularization methods is presented, in which approximations may be used for the $p$th-order tensor, based on lower-order derivatives. Between each recalculation of the $p$th-order derivative…
We present in this work the first experimental observation of oscillations in Parity-Time symmetric ZRC dimers. The system obtained is of first order ordinary differential equation due to the use of imaginary resistors. The coupled cells…
This article is concerned with uniform $C^{1,\alpha}$ and $C^{1,1}$ estimates in periodic homogenization of fully nonlinear elliptic equations. The analysis is based on the compactness method, which involves linearization of the operator at…
Li\'enard-type nonlinear one-dimensional oscillator is quantized using van Roos symmetric ordering recipe for the kinetic-like part of the new derived Hamiltonian. The corresponding Schr\"odinger equation is exactly solved in momuntum space…
We study the nonlinear behaviors of mass-spring systems damped by dry friction using simulation by a nonlinear LC circuit damped by anti-parallel diodes. We show that the differential equation for the electric oscillator is equivalent to…