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This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic…
We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of…
We study graph-directed conjugate functional equations on the unit interval indexed by the complete digraph with self-loops on two vertices. We focus on the singularity and regularity of the solutions for compatible systems of weak…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
Formation control is concerned with the design of control laws that stabilize agents at given distances from each other, with the constraint that an agent's dynamics can depend only on a subset of other agents. When the information flow…
Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities,…
This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and…
The discovery of colour-kinematic duality has led to significant progress in the computation of scattering amplitudes in quantum field theories. At tree level, the origin of the duality can be traced back to the monodromies of open-string…
We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by…
Numerical simulations of the approach to the singularity in vacuum spacetimes are presented here. The spacetimes examined have no symmetries and can be regarded as representing the general behavior of singularities. It is found that the…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
Autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as extinction of…
Optical singularities, which are positions within an electromagnetic field where certain field parameters become undefined, hold significant potential for applications in areas such as super-resolution microscopy, sensing, and…
A numerical method based on Matrix Product Formalism is proposed to study the phase transitions and shock formation in the Asymmetric Simple Exclusion Process with open boundaries and parallel dynamics. By working in a canonical ensemble,…
The effects of fluctuating boundaries on a superposition state of a quantum particle in a box is studied. We consider a model in one space dimension in which the initial state is a coherent superposition of two energy eigenstates. The…
Calculation of hadronization, decay or scattering processes at non-zero temperatures and densities within the Nambu-Jona-Lasinio-like models requires some techniques for computation of Feynmann diagrams. Decomposition of Feynman diagrams at…
We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets…
The generic behavior of purely dissipative open quantum many-body systems with local dissipation processes can be investigated using random matrix theory, revealing a hierarchy of decay timescales of observables organized by their…
Dephasing of one-particle states in closed quantum dots is analyzed within the framework of random matrix theory and Master equation. Combination of this analysis with recent experiments on the magnetoconductance allows for the first time…