Showing papers in "Physica D: Nonlinear Phenomena in 2021"

TL;DR: In this article, the authors provide an extensive survey of the applications and examples where hydrodynamic instabilities play a central role, including solar prominences, ionospheric flows in space, supernovae, inertial fusion and pulsed-power experiments, pulsed detonation engines and Scramjets.

TL;DR: This work develops a new data-driven approach to extract stochastic dynamical systems with non-Gaussian symmetric Levy noise, as well as Gaussian noise from noisy data sets, and designs a numerical algorithm to compute the drift, diffusion coefficient and jump measure, and thus extract a governing Stochastic differential equation with Gaussian and non-GAussian noise.

TL;DR: In this paper, the root structures of the Yablonskii-Vorob'ev polynomial hierarchy of the rogue wave are determined by the root structure of the polynomials, and their orientations are controlled by the phase of the large parameter.

TL;DR: In this paper, an analytical approach for providing an explicit formula associated with a straightforward computation of peak time of outbreak is proposed, where the time scale from the relevant autonomous SIR epidemic model is formulated analytically via an integral based on the fractions of susceptible and infected compartments.

TL;DR: In this article, a family of eigenfunction solutions of the Lax pair of the Kadomtsev-Petviashvili 1 (KP1) equation is constructed in terms of the Taylor coefficients of a fundamental exponential function associated with the lax pair.

TL;DR: Variants of cross-validation and its variants based on Maximum Mean Discrepancy and Lyapunov exponents are presented as simple approaches for learning the kernel used in these emulators.

TL;DR: In this paper, it was shown that an ESN trained on a sequence of observations from an ergodic dynamical system (with invariant measure μ ) using Tikhonov least squares regression against a set of targets, will approximate the target function in the L 2 (μ ) norm.

TL;DR: In this paper, a synthesis of recent work by the authors and others on the formation of localised patterns, isolated spots, or sharp fronts in models of natural processes governed by reaction-diffusion equations is presented.

TL;DR: In this article, it is shown that Shannon entropy is an efficient dynamical indicator that provides a direct measure of the diffusion rate and thus a time-scale for the instabilities arising when dealing with chaos.

TL;DR: In this paper, the authors combine the physics-agnostic data-driven approach of random feature maps as a forecast model within an ensemble Kalman filter data assimilation procedure, which is learned sequentially by incorporating incoming noisy observations.

TL;DR: In this article, the impact of COVID-19 on the populations and equity markets of 92 countries was analyzed, and it was shown that there is no relationship between countries' equity market performance and their success in managing the pandemic.

TL;DR: In this paper, the authors present results from Direct Numerical Simulations (DNS) of Rayleigh-Taylor instability at Atwood numbers up to 0.9, where the velocity changes sign multiple times and the buoyancy term in the turbulent kinetic energy transport equation changes its role back and forth from production to destruction.

TL;DR: In this paper, the transition and mechanism of nonlinear waves in the (2+1)-dimensional Sawada-Kotera (2DSK) equation are studied by means of characteristic line and phase shift analysis, and the dynamic behavior of various nonlinear transformed waves is analyzed.

TL;DR: In this article, the authors considered C 1 dynamical systems having an attracting hyperbolic fixed point or periodic orbit and proved existence and uniqueness results for C k (actually C loc k, α ) linearizing semiconjugacies defined on the entire basin of attraction.

TL;DR: In this article, the authors introduced new methods to study the changing dynamics of COVID-19 cases and deaths among the 50 worst-affected countries throughout 2020, including Pakistan, United States and United Arab Emirates.

TL;DR: In this article, a SEAIR model with an external source of infection and a suitable loss function was used to evaluate sustainable school opening plans for the current pandemic. But, due to the length of the incubation period of Covid-19, full opening of schools in the Fall of 2020 seems to be impractical unless the spread of the virus is completely under control in the surrounding region (e.g. with fewer than 5 active cases every million people).

TL;DR: In this paper, the authors considered the N -person stag hunt game in finite well-mixed populations and obtained the dynamical equation for weak selection to depict the evolutionary dynamics of cooperation in structured populations and found that there still exists the case in which there is only one interior unstable equilibrium.

TL;DR: In this paper, a Gaussian Process Regression (GPR) based interpolation algorithm is proposed for non-intrusive reduced-order models (ROMs) for advection-dominated systems.

TL;DR: In this paper, a modified nonlinear Schrodinger (NLS) equation was proposed to describe the nonlinear propagation of the Alfven waves and the femtosecond optical pulses in a nonlinear single-mode optical fiber.

TL;DR: In this article, it was shown that universal rogue wave patterns exist in integrable systems and that these patterns are determined by the root structures of the Yablonskii-Vorob'ev polynomial hierarchy through a linear transformation.

TL;DR: Numerically, it is shown that the proposed smoother is more accurate than EnKF and 4Dvar in de-noising signals corrupted by independent (but not necessarily identically distributed) noise, even if the smoother is constructed using a data set corrupted by white noise.

TL;DR: The proposed loss function (defined as a nonlinear functional of the empirical distribution) effectively trains the underlying kernel defined by the CNN beyond regressing the data with that kernel.

TL;DR: In this article, the authors studied the subtle mechanism that converts the breathing state into the solitary and periodic ones, through which they obtained various stationary nonlinear excitations such as the multi-peak solitons, (quasi) periodic waves, anti-dark solITons, W-shaped soliton and M-shaped Solitons which exhibit stationary feature.

TL;DR: In this paper, the authors apply the multi-layer physics-informed neural networks (PINNs) deep learning to successfully study the data-driven peakon and periodic peakon solutions of some well-known nonlinear dispersion equations with initial-boundary value conditions.

TL;DR: Schlickeiser and Kroger as mentioned in this paper compare the four expressions for any choice of SIR model parameters and find that SK-I, SK-II and CG are more accurate than MT as long as the amount of population to which the SIR was applied exceeds hundred by far (countries, ss, cities).

TL;DR: In this article, a relativistic version of the Cucker-Smale (RCS) model on Riemannian manifolds is proposed and its collective behavior is studied.

TL;DR: In this paper, the existence and spectral stability of multi-pulse solitary wave solutions to a nonlinear Schrodinger equation with both fourth and second-order dispersion terms were investigated.

TL;DR: In this paper, the authors developed a I¸ -SEIHQRD model, which may be the simplest one satisfying the mentioned requirements for arbitrary territories and can be simplified in particular cases.

TL;DR: In this paper, a class of hyperbolic reaction-diffusion models with crossdiffusion is derived within the context of Extended Thermodynamics, and linear stability analysis on the uniform steady states is performed to derive the conditions for the occurrence of Hopf, Turing and wave instabilities.

TL;DR: In this paper, the authors investigated reactive- versus hydrodynamic-breakup processes of ejecta, where the reactive metal is cerium (Ce) and the non-reactive metal is tin (Sn), the nonreactive gas is helium (He), and the reactive gas is deuterium (D 2 ) or hydrogen (H 2 ).