Related papers: Transitions in Stochastic Non-equilibrium Systems:…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
While equilibrium phase transitions are well described by a free-energy landscape, there are few tools to describe general features of their non-equilibrium counterparts. On the other hand, near-equilibrium free-energies are easily…
Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales…
Spontaneous transitions between non-equilibrium patterns are characterised by hydrodynamic calculations of ideal straight roll steady state heat convection. The calculations are tested quantitatively against existing experimental data. It…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
Most of the turbulent flows appearing in nature (e.g. geophysical and astrophysical flows) are subjected to strong rotation and stratification. These effects break the symmetries of classical, homogenous isotropic turbulence. In doing so,…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
We consider the relation for the stochastic equilibrium states between the reduced system on a random slow manifold and the original system. This provides a theoretical basis for the reduction about sophisti- cated detailed models by the…
We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing perturbations. The proposed modeling framework extends the…
Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less well studied and is an important one. A…
Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
The influence of dissipation on the fluctuation statistics of the total energy is investigated through both a phenomenological and a stochastic model for dissipative energy-transfer through a cascade of states. In equilibrium the states…
The paper assesses stationary probability distributions in out of equilibrium systems. In the phenomenology proposed, no free energy can be well defined. Fluctuations of Landau free energy couplings arise when the intrinsic chemical…
Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…
Can far-from-equilibrium material response under arbitrary loading be inferred from equilibrium data and vice versa? Can the effect of element transmutation on mechanical behavior be predicted? Remarkably, such extrapolations are possible…
The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…
This paper introduces a method for predicting the likely behaviors of continuous nonlinear systems in equilibrium in which the input values can vary. The method uses a parameterized equation model and a lower bound on the input joint…
Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these…
Although the roll/streak structure is ubiquitous in pre-transitional wall-bounded shear flow, this structure is linearly stable if the idealization of laminar flow is made. Lacking an instability, the large transient growth of the…