Related papers: Statistical Complexity in Traveling Densities
This paper is devoted to the use of the entropy and duality methods for the existence theory of reaction-cross diffusion systems consisting of two equations, in any dimension of space. Those systems appear in population dynamics when the…
We study the notion of positive and negative complexity of pairs of objects in cluster categories. The first main result shows that the maximal complexity occurring is either one, two or infinite, depending on the representation type of the…
Systems are studied in which transport is possible due to large extension with open boundaries in certain directions but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction…
Given a set of entities each holding a Boolean state, the Density Classification Task (DCT) asks them to converge to the most represented state. Given a directed graph of entities where each node synchronously updates to the local majority…
In this paper I present a new method of studying the densities of the Collatz trajectories generated by a set $S \subset \mathbb{N}$. This method is used to furnish an alternative proof that $d(\{y \in \mathbb{N} : \exists k \text{ where }…
Pair fluctuation theory has been used to study the crossover from the weak coupling BCS theory to the strong coupling Bose Einstein Condensation. The effect of fluctuations has been studied over the whole crossover regime. It has been shown…
We analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finite-size particles which cannot overlap and repel each other when they are too…
Dissipative features of dark matter affect its clustering properties and could lead to observable consequences for the evolution of large--scale structure. We analyse the evolution of cold dark matter density perturbations allowing for the…
We study collective dynamics of interacting deformable self-propelled particles whose migration velocity increases when the local density of particles is increased. Numerical simulations in two dimensions reveal that traveling bands similar…
By summarizing and extending the Lagrangian densities of the general relativity and the Kibble's gauge theory of gravitation,a further generalized Lagrangian density for a gravitational system is obtained and analyzed in greater detail,…
We analyse the motion of a system of particles subjected a random force fluctuating in both space and time, and experiencing viscous damping. When the damping exceeds a certain threshold, the system undergoes a phase transition: the…
The structure of Gaussian random fields over high levels is a well researched and well understood area, particularly if the field is smooth. However, the question as to whether or not two or more points which lie in an excursion set belong…
Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is…
Equations of motion of spinning density for extended objects, and corresponding deviation equations are derived. The problem of motion for a variable mass to a spinning extended object is obtained. Spinning fluids may be considered as a…
We develop a framework to determine the complete statistical behavior of a fundamental quantity in the theory of random walks, namely, the probability that $n_1$, $n_2$, $n_3$, . . . distinct sites are visited at times $t_1$, $t_2$, $t_3$,…
We present an efficient approach, based on a number-conditioned master equation, for large-deviation analysis in mesoscopic transports. Beyond the conventional full-counting-statistics study, the large-deviation approach encodes complete…
We find the three-dimensional gravity dual of a process in which two clouds of (1+1)-dimensional conformal matter moving in opposite directions collide. This gives the most general conformally invariant holographic flow in the 1+1…
We use X-ray tomography to investigate the translational and rotational dynamical heterogeneities of a three dimensional hard ellipsoids granular packing driven by oscillatory shear. We find that particles which translate quickly form…
The rate of adoption of new information depends on reinforcement from multiple sources in a way that often cannot be described by simple contagion processes. In such cases, contagion is said to be complex. Complex contagion happens in the…
We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval $[0,T]$ via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class…