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The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomised alternating sine flow…
Using the non-canonical model of scalar field, the cosmological consequences of a pervasive, self-interacting, homogeneous and rolling scalar field are studied. In this model, the scalar field potential is nonlinear and decreases in…
It is shown that homogeneous Rayleigh-Benard flow, i.e., Rayleigh-Benard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient, has a family of exact, exponentially…
In the recent literature dealing with spatial extensions of the continuous Ramsey model, the capital accumulation process via time and space is modeled as a linear parabolic partial differential equation. The process of capital movement…
In this work, we discuss how the linear and non-linear advection terms modify the scaling behavior of the continuous symmetry breaking and stabilize the long-range order, even in $d=2$ far from equilibrium, by means of simple scaling…
Aims: To quantify the transient growth of nonaxisymmetric perturbations in unstratified magnetized and stratified non-magnetized rotating linear shear flows in the shearing sheet approximation of accretion disc flows. Method: The Rayleigh…
Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced.…
In densely-packed two-dimensional systems of growing cells, such as rod-shaped bacteria, a number of experimental and numerical studies report distinct patterns of nematic orientational order in the presence of confinement. So far, these…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
In the conceptual framework of phase ordering after temperature quenches below transition, we consider the underdamped Bales-Gooding-type 'momentum conserving' dynamics of a 2D martensitic structural transition from a square-to-rectangle…
The kinetics of encounter-controlled processes in growing domains is markedly different from that in a static domain. Here, we consider the specific example of diffusion limited coalescence and annihilation reactions in one-dimensional…
In this work, we investigate the dynamics of a non-local model describing spontaneous cell polarisation. It consists in a drift-diffusion equation set in the half-space, with the coupling involving the trace value on the boundary. We…
The theory of phase ordering dynamics -- the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase -- is reviewed, with the emphasis on recent developments. Interest will…
We investigate the stability and dynamics of natural convection in two dimensions, subject to inhomogeneous boundary conditions. In particular, we consider a Rayleigh-B\`enard (RB) cell, where the horizontal top boundary contains a periodic…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
In context of the Wolfram Physics Project, a certain class of abstract rewrite systems known as "multiway systems" have played an important role in discrete models of spacetime and quantum mechanics. However, as abstract mathematical…
We present a model for the kinetics of spontaneous membrane domain (raft) assembly that includes the effect of membrane recycling ubiquitous in living cells. We show that the domains have a broad power-law distribution with an average…
We investigate the laws of coarsening of a two-dimensional system of Ising spins evolving under single-spin-flip irreversible dynamics at low temperature from a disordered initial condition. The irreversibility of the dynamics comes from…
We study the coarsening of strongly microphase separated membrane domains in the presence of recycling of material. We study the dynamics of the domain size distribution under both scale-free and size-dependent recycling. Closed form…
An interesting feature in dissipative nonlinear systems is the emergence of characteristic domains in parameter space that exhibit periodic temporal evolution, known as shrimp-shaped domains. We investigate the parameter space of the…