Related papers: A three-scale model of spatio-temporal bursting
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
In the paper, we study spatially distributed particle systems whose time evolution is governed by vanishing diffusion in space $\mathbb{R}^d$, $d\ge 1$, and by size-continuous fragmentation and coagulation processes with unbounded rates. We…
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis in the right-hand side. The input of hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic…
We investigate a novel bursting state in inclined layer thermal convection in which convection rolls exhibit intermittent, localized, transverse bursts. With increasing temperature difference, the bursts increase in duration and number…
Temporal inhomogeneities observed in various natural and social phenomena have often been characterized in terms of scaling behaviors in the autocorrelation function with a decaying exponent $\gamma$, the interevent time distribution with a…
Modeling the intermittent behavior of turbulent energy dissipation processes both in space and time is often a relevant problem when dealing with phenomena occurring in high Reynolds number flows, especially in astrophysical and space…
A time-space fractional reaction-diffusion equation in a bounded domain is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time. However, for realistic initial conditions,…
The electric field distributions and space-time singularity curves are computed for ultrashort pulsed Laguerre-Gaussian laser beams having spatial chirp. Due to the breaking of cylindrical symmetry by the spatial chirp, the singularities…
Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity…
Chemically fueled supramolecular systems can exhibit complex, time-dependent behaviors reminiscent of living matter when maintained far from equilibrium by continuous energy or fuel consumption. Here, we introduce a minimal…
This paper compares theory and experiment for the kinetics of time-dependent sedimentation. We discuss non-interacting suspensions and colloids which may exhibit behavior similar to the one-dimensional motion of compressible gas. The…
In this paper we study a three dimensional thermocline planetary geostrophic ``horizontal" hyper--diffusion model of the gyre-scale midlatitude ocean. We show the global existence and uniqueness of the weak and strong solutions to this…
In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…
Spatio-temporal hierarchical modeling is an extremely attractive way to model the spread of crime or terrorism data over a given region, especially when the observations are counts and must be modeled discretely. The spatio-temporal…
The intermittent dynamics of the turbulent GOY shell-model is characterised by a single type of burst-like structure, which moves through the shells like a front. This temporal structure is described by the dynamics of the instantaneous…
Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of…
We present a dynamical log-stable process for the spatio-temporal evolution of the energy-dissipation field in fully developed turbulence. The process is constructed from multifractal scaling relations required for two-point correlators of…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…