Related papers: Nonreciprocal pattern formation of conserved field…
Oscillatory behavior is ubiquitous in out-of-equilibrium systems showing spatio-temporal pattern formation. Starting from a linear large-scale oscillatory instability -- a conserved-Hopf instability -- that naturally occurs in many active…
We study a minimal model involving two species of particles interacting via quorum-sensing rules. Combining simulations of the microscopic model and linear stability analysis of the associated coarse-grained field theory, we identify a…
In this article, we are interested in the behavior of a fully connected network of $N$ neurons, where $N$ tends to infinity. We assume that the neurons follow the stochastic FitzHugh-Nagumo model, whose specificity is the non-linearity with…
We present the phenomenology of the one dimensional non-reciprocal Cahn Hilliard model for varying non-reciprocity $(\alpha)$ and different boundary conditions. At small $\alpha$, a perturbed uniform state evolves to a defect laden…
This article is concerned with the existence of traveling wave solutions, including standing waves, to some models based on configurational forces, describing respectively the diffusionless phase transformations of solid materials, e.g.,…
Nonreciprocal coupling can alter the transport properties of material media, producing striking phenomena such as unidirectional amplification of waves, boundary modes, or self-assembled pattern formation. It is responsible for nonlinear…
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are critical, in the sense that they are expected to mediate…
We present experimental results on hydrothermal traveling-waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels,…
Employing a two-species Cahn-Hilliard model with nonreciprocal interactions we show that the interplay of nonreciprocity and conservation laws results in the robust coexistence of uniform stationary and oscillatory phases as well as of…
The present work is devoted to the modelling which is based on the modified Cahn-Hilliard equation, the interplay of equilibrium and non-equilibrium phase transitions. The non-equilibrium phase transitions are modelled by the Schl\"ogl…
Although effective non-reciprocal interactions have been investigated in a variety of fields, their consequences have not been explored in hydrodynamical turbulence. We initiate such an exploration by introducing non-reciprocal binary-fluid…
A wave front and a wave back that spontaneously connect two hyperbolic equilibria, known as a heteroclinic wave loop, give rise to periodic waves with arbitrarily large spatial periods through the heteroclinic bifurcation. The nonlinear…
Patterns and waves are basic and important phenomena that govern the dynamics of physical and biological systems. A common theme in investigating such systems is to identify the intrinsic factors responsible for such self-organization. The…
We investigate diffusion-driven instabilities in a FitzHugh-Nagumo reaction-diffusion system with superdiffusive transport, modeled by fractional Laplacian operators with different diffusion orders for the activator and the inhibitor. A…
Non-reciprocal interactions are among the simplest mechanisms that drive a physical system out of thermal equilibrium, leading to novel phenomena such as oscillatory pattern formation. In this paper, we introduce a ternary phase separation…
The dynamics of phase-separated interfaces shape the behavior of both passive and active condensates. While surface tension in equilibrium systems minimizes interface length, non-equilibrium fluxes can destabilize flat or constantly curved…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
The topic of this paper are nonlinear traveling waves occuring in a system of damped waves equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this…
Investigating the robustness of non-reciprocity in the presence of competing interactions is central to understanding non-reciprocal quantum matter. In this work, we use reservoir engineering to induce non-reciprocal hopping and pairing in…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…