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We consider the critical behaviour of the continuous-time weakly self-avoiding walk with contact self-attraction on $\mathbb{Z}^4$, for sufficiently small attraction. We prove that the susceptibility and correlation length of order $p$ (for…
Magnetic topological insulators provide a platform for emergent phenomena arising from the interplay between magnetism and band topology. Here we report the single crystal growth, crystal structure, magnetic and transport properties, as…
We investigate neighbor-avoiding walks on the simple cubic lattice in the presence of an adsorbing surface. This class of lattice paths has been less studied using Monte Carlo simulations. Our investigation follows on from our previous…
We show that the compact self avoiding walk configurations, kinetically generated by the recently introduced Interacting Growth Walk (IGW) model, can be considered as members of a canonical ensemble if they are assigned random values of…
We study the automorphism groups of countable homogeneous directed graphs (and some additional homogeneous structures) from the point of view of topological dynamics. We determine precisely which of these automorphism groups are amenable…
The sluggish and heterogeneous dynamics of glass forming liquids is frequently associated to the transient coexistence of two phases of particles, respectively with an high and low mobility. In the absence of a dynamical order parameter…
Random walks on networks are widely used to model stochastic processes such as search strategies, transportation problems or disease propagation. A prominent example of such process is the guiding of naive T cells by the lymph node conduits…
Transitions in structural heterogeneity of colloidal depletion gels formed through short-range attractive interactions are correlated with their dynamical arrest. The system is a density and refractive index matched suspension of 0.20…
We consider a directed walk model of a homopolymer (in two dimensions) which is self-interacting and can undergo a collapse transition, subject to an applied tensile force. We review and interpret all the results already in the literature…
In this paper we study topological and dynamical features of isolated invariant continua of continuous flows defined on surfaces. We show that near an isolated invariant continuum the flow is topologically equivalent to a C1 flow. We deduce…
A lattice model of the directed self-avoiding walk is used to estimate the possibility on the formation of an infinitely long linear semi-flexible copolymer chain. The copolymer chain is assumed to composed of four different types of the…
Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz small-world networks, rewired from a two-dimensional square lattice. The maximum length L of this kind of walks is limited in regular lattices by an attrition effect,…
The density of ions trapped in a harmonic potential in one dimension is not uniform. Consequently the eigenmodes are not phonons. We calculate the long wavelength modes in the continuum limit, and evaluate the density of states in the short…
We study $C^r$ ($5 \le r \le \infty$) diffeomorphisms on closed manifolds of dimension at least three with a heteroclinic cycle between two hyperbolic periodic points. At each point, the unstable direction is one dimensional, and the stable…
We investigate ice polyamorphism in the context of the two-dimensional Mercedes-Benz model of water. We find a first-order phase transition between a crystalline phase and a high-density amorphous phase. Furthermore we find a reversible…
We study self-avoiding walks on restricted square lattices, more precisely on the lattice strips $\mathbb{Z} \times \{-1,0,1\}$ and $\mathbb{Z}\times \{-1,0,1,2\}$. We obtain the value of the connective constant for the $\mathbb{Z} \times…
Discrete dynamical models of walking droplets ("walkers") have allowed swift numerical experiments revealing heretofore unobserved quantum statistics and related behaviors in a classical hydrodynamic system. We present evidence that one…
Let $\mathcal H$ be a finite connected undirected graph and $\mathcal H_{walk}$ be the graph of bi-infinite walks on $\mathcal H$; two such walks $\{x_i\}_{i\in \mathbb Z}$ and $\{y_i\}_{i \in \mathbb Z}$ are said to be adjacent if $x_i$ is…
In many complex systems, for the activity f(i) of the constituents or nodes i, a power-law relationship was discovered between the standard deviation sigma(i) and the average strength of the activity: sigma(i) ~ <f(i)>^alpha; universal…
Collective phenomena emerge from the interaction of natural or artificial units with a complex organization. The interplay between structural patterns and dynamics might induce functional clusters that, in general, are different from…