Related papers: Topologically-based fractional diffusion and emerg…
We provide a bird's eye view on developments in analyzing the long time, large crowd behavior of Cucker-Smale alignment dynamics. We consider a class of (fully-)discrete models, paying particular attention to general alignment protocols in…
Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
The spontaneous emergence of collective motion patterns is usually associated with the presence of a velocity alignment mechanism that mediates the interactions among the moving individuals. Despite of this widespread view, it has been…
We introduce a rigorous approach to the study of the symmetry breaking and pattern formation phenomenon for isotropic functionals with local/nonlocal interactions in competition. We consider a general class of nonlocal variational problems…
We study the emergent dynamics of the relativistic kinetic Cucker-Smale (RKCS) model without assuming compactness in spatial and velocity support. In this setting, the lower bound of the kernel function in the nonlocal velocity alignment…
We consider systems that are well modelled as a networks that evolve in time, which we call {\it Moving Neighborhood Networks}. These models are relevant in studying cooperative behavior of swarms and other phenomena where emergent…
The correlated motion of flocks is an instance of global order emerging from local interactions. An essential difference with analogous ferromagnetic systems is that flocks are active: animals move relative to each other, dynamically…
It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors, the dimensions of the spaces can be…
We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent…
Non-reciprocal interactions are a defining feature of many complex systems, biological, ecological, and technological, often pushing them far from equilibrium and enabling rich dynamical responses. These asymmetries can arise at multiple…
Fermi gases in two dimensions display a surprising collective behavior originating from the head-on carrier collisions. The head-on processes dominate angular relaxation at not-too-high temperatures $T\ll T_F$ owing to the interplay of…
On the basis of the "molecular-orbital" representation which describes generic flat-band models, we propose a systematic way to construct a class of flat-band models with finite-range hoppings that have topological natures. In these models,…
With the aim of understanding the emergence of collective motion from local interactions of organisms in a "noisy" environment, we study biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
Non-reciprocal interactions, where the influence of agent $i$ on $j$ differs from that of $j$ on $i$, are fundamental in active and living matter. Yet, most models implement such asymmetry phenomenologically. Here we show that…
We consider a family of interaction energies given by kernels having a ''well-barrier'' shape, and investigate how these kernels drive the formation of multiple flocks within a larger population. We use the dichotomy case of the…
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…
A major achievement in the study of complex networks is the observation that diverse systems, from sub-cellular biology to social networks, exhibit universal topological characteristics. Yet this universality does not naturally translate to…
Recent investigations have provided important insights into the complex structure and dynamics of collectively moving flocks of living organisms. Two intriguing observations are, scale-free correlations in the velocity fluctuations, in the…