Related papers: Strongly self-interacting processes on the circle
The charging of insulating samples degrades the quality and complicates the interpretation of images in scanning electron microscopy and is important in other applications, such as particle detectors. In this paper we analyze this…
We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive…
In this paper we consider two processes driven by diffusions and jumps. The jump components are Levy processes and they can both have finite activity and infinite activity. Given discrete observations we estimate the covariation between the…
The way particles interact with turbulent structures, particularly in regions of high vorticity and strain rate, has been investigated in simulations of homogeneous turbulence and in simple flows which have a periodic or persistent…
We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state…
Continuous-time long-term event prediction plays an important role in many application scenarios. Most existing works rely on autoregressive frameworks to predict event sequences, which suffer from error accumulation, thus compromising…
A hyperscaling relation for the critical exponents of absorbing phase transitions is tested in the bosonic pair contact process with diffusion. To this end spreading is considered, i.e. the time evolution out of an initial seed. It is shown…
We study the problem of diffusing particles which coalesce upon contact. With the aid of a non-perturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply…
We formulate the theory for a self-propelled domain in an excitable reaction-diffusion system in two dimensions where the domain deforms from a circular shape when the propagation velocity is increased. In the singular limit where the width…
Synchronization is one of the emerging collective phenomena in interacting particle systems. Its ubiquitous presence in nature, science, and technology has fascinated the scientific community over the decades. Moreover, a great deal of…
In this paper we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the…
Improving the understanding of diffusive processes in networks with complex topologies is one of the main challenges of today's complexity science. Each network possesses an intrinsic diffusive potential that depends on its structural…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
We study the diffusion equation with an appropriate change of variables. This equation is in general a partial differential equation (PDE). With the self-similar and related Ansat\"atze we transform the PDE of diffusion to an ordinary…
Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth…
Reaction dynamics involving subdiffusive species is an interesting topic with only few known results, especially when the motion of different species is characterized by different anomalous diffusion exponents. Here we study the reaction…
We investigate a class of reaction processes in which particles move ballistically and react upon colliding. We show that correlations between velocities of colliding particles play a crucial role in the long time behavior. In the…
We briefly review some aspects of the anomalous diffusion, and its relevance in reactive systems. In particular we consider {\it strong anomalous} diffusion characterized by the moment behaviour $\langle x(t)^q \rangle \sim t^{q \nu(q)}$,…
Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex…
To offer a view into the rapidly developing theory of fractional diffusion processes we describe in some detail three topics of present interest: (i) the well-scaled passage to the limit from continuous time random walk under power law…