Related papers: Capturing rogue waves by multi-point statistics
We consider the statistics of extreme ship motions in a nonlinear irregular wave field. While an accurate computation is possible by using a full Monte-Carlo method to cover all individual wave conditions, the computational cost may become…
Stochastic acceleration of charged particles due to interactions with magnetohydrodynamic (MHD) plasma waves is the dominant process leading to the formation of the high-energy electron and ion distributions in a variety of astrophysical…
Several environmental phenomena can be described by different correlated variables that must be considered jointly in order to be more representative of the nature of these phenomena. For such events, identification of extremes is…
In this work, we report the emergence of extreme events in a damped and driven velocity-dependent mechanical system. We observe that the extreme events emerge at multiple points. We further notice that the extreme events occur symmetrically…
We investigate the rogue wave dynamics of the dissipative Kundu-Eckhaus equation. With this motivation, we propose a split-step Fourier scheme for its numerical solution. After testing the accuracy and stability of the scheme using an…
Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely…
The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
General higher order rogue waves of a vector nonlinear Schrodinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational solutions containing 3N free…
We present an approximate analytical expression for the escape rate of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrate-and-fire model for neural spiking. The novel approximation is…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
Extreme events are emergent phenomena in multi-particle transport processes on complex networks. In practice, such events could range from power blackouts to call drops in cellular networks to traffic congestion on roads. All the earlier…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
When modelling turbulent flows, it is often the case that information on the forcing terms or the boundary conditions is either not available or overly complicated and expensive to implement. Instead, some flow features, such as the mean…
We present new stochastic geometry theorems that give bounds on the probability that $m$ random data classes all contain a point in common in their convex hulls. We apply these stochastic separation theorems to obtain bounds on the…
Among the most relevant processes in the Earth system for human habitability are quasi-periodic, ocean-driven multi-year events whose dynamics are currently incompletely characterized by physical models, and hence poorly predictable. This…
A Fokker-Planck equation approach for the treatment of non-Markovian stochastic processes is proposed. The approach is based on the introduction of fictitious trajectories sharing with the real ones their local structure and initial…
A leading goal for climate science and weather risk management is to accurately model both the physics and statistics of extreme events. These two goals are fundamentally at odds: the higher a computational model's resolution, the more…
We study the Floating Offshore Wind Turbine (FOWT) dynamic response to high wind velocity scenarios utilizing an extensive Markov Chain Monte Carlo simulation involving 10,000 trials of a reduced model from \cite{betti_development_2014}…
Some multidimensional generalizations of the Fokker-Planck equation used by R. Friedrich and J. Peinke for the description of a turbulent cascade as a stochastic process of Markovian type, are considered. The exact solutions of the Cauchy…
We perform statistical analysis on discrete nonlinear waves generated though modulational instability in the context of the Salerno model that interpolates between the intergable Ablowitz-Ladik (AL) equation and the nonintegrable discrete…