Related papers: Algebraic approach to directed stochastic avalanch…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We investigate two-dimensional turbulence within the Instanton formalism which determines the most probable field in a stochastic classical field theory starting from the Martin-Siggia-Rose path integral. We perform an approximate analysis…
An asymmetric stochastic process describing the avalanche dynamics on a ring is proposed. A general kinetic equation which incorporates the exclusion and avalanche processes is considered. The Bethe ansatz method is used to calculate the…
This thesis presents several aspects of the physics of disordered elastic systems and of the analytical methods used for their study. On one hand we will be interested in universal properties of avalanche processes in the statics and…
We introduce a natural Boltzmann measure over polyominoes induced by boundary avalanches in the Abelian Sandpile Model. Through the study of a suitable associated process, we give an argument suggesting that the probability distribution of…
This work extends the study of mean field equations arising in two-dimensional (2D) turbulence by introducing generalized weighted Sobolev operators. Employing variational methods, particularly the mountain pass theorem and a refined…
In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the…
We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular, we utilize string diagrams, tools similar to tensor…
Since their introduction, anchoring methods in extragradient-type saddlepoint problems have inspired a flurry of research due to their ability to provide order-optimal rates of accelerated convergence in very general problem settings. Such…
We consider a stochastic variant of the Abelian Sandpile Model (ASM) on a finite graph, introduced by Chan, Marckert and Selig. Even though it is a more general model, some nice properties still hold. We show that on a certain probability…
A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and the existence of two alternative…
We study probability distributions of waves of topplings in the Bak-Tang-Wiesenfeld model on hypercubic lattices for dimensions D>=2. Waves represent relaxation processes which do not contain multiple toppling events. We investigate bulk…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
Mean-field coupled lattice maps are used to approximate the physics of driven threshold systems with long range interactions. However, they are incapable of modeling specific features of the dynamic instability responsible for generating…
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.
Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular…
We study the energy minimization problem for an elastic interface in a random potential plus a quadratic well. As the position of the well is varied, the ground state undergoes jumps, called shocks or static avalanches. We introduce an…
We study several probability distributions relevant to the avalanche dynamics of elastic interfaces driven on a random substrate: The distribution of size, duration, lateral extension or area, as well as velocities. Results from the…
For the stochastic six-vertex model on the quadrant $\mathbb{Z}_{\geq0}\times\mathbb{Z}_{\geq0}$ with step initial conditions and a single second-class particle at the origin, we show almost sure convergence of the speed of the second-class…
We consider the Abelian sandpile model on triangular and hexagonal lattices. We compute several height probabilities on the full plane and on half-planes, and discuss some properties of the universality of the model.