Related papers: Stochastic Rotating Waves
We study nonlinear wave equations perturbed by transport noise acting either on the displacement or on the velocity. Such noise models random advection and, under suitable scaling of space covariance, may generate an effective dissipative…
Presented is a data-driven Machine Learning (ML) framework for the identification and modeling of traveling wave spatiotemporal dynamics. The presented framework is based on the steadily-propagating traveling wave ansatz, $u(x,t) = U(\xi=x…
This study examines the challenges of modeling complex and noisy data related to socioeconomic factors over time, with a focus on data from various districts in Odisha, India. Traditional time-series models struggle to capture both trends…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
We consider propagating, spatially localised waves in a class of equations that contain variational and non-variational terms. The dynamics of the waves is analysed through a collective coordinate approach. Motivated by the variational…
Periodic water waves of permanent form traveling at constant speed, the so-called Stokes waves, are studied in water of fixed finite depth using methods previously used in water of infinite depth. We apply our methods to waves of varying…
Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…
Traditional models of wormlike chains in shear flows at finite temperature approximate the equation of motion via finite difference discretization (bead and rod models). We introduce here a new method based on a spectral representation in…
Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are…
Re-entrant spiral waves are observed in many different situations in nature, perhaps most importantly in excitable electrophysiological tissue where they are believed to be responsible for pathological conditions such as cardiac…
We introduce a new model equation for Stokes gravity waves based on conformal transformations of Euler's equations. The local version of the model equation is relevant for dynamics of shallow water waves. It allows us to characterize the…
This paper is concerned with the global stability of non-critical/critical traveling waves with oscillations for time-delayed nonlocal dispersion equations. We first theoretically prove that all traveling waves, especially the critical…
We study strictly parabolic stochastic partial differential equations on $\R^d$, $d\ge 1$, driven by a Gaussian noise white in time and coloured in space. Assuming that the coefficients of the differential operator are random, we give…
Stop-and-go waves are commonly observed in traffic and pedestrian flows. In most traffic models they occur through a phase transition after fine tuning of parameters when the model has unstable homogeneous solutions. Inertia effects are…
We introduce a variational method for analyzing limit cycle oscillators in $\mathbb{R}^d$ driven by Gaussian noise. This allows us to derive exact stochastic differential equations (SDEs) for the amplitude and phase of the solution, which…
The rotating shallow water model is a simplification of oceanic and atmospheric general circulation models that are used in many applications such as surge prediction, tsunami tracking and ocean modelling. In this paper we introduce a class…
We study the stability of Stokes waves on a free surface of an ideal fluid of infinite depth. For small steepness the modulational instability dominates the dynamics, but its growth rate is vastly surpassed for steeper waves by an…
Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative…
In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can…