Related papers: Random initial data and average shock time in the …
We consider the Random-Cluster model on $(\mathbb{Z}/n\mathbb{Z})^d$ with parameters $p \in (0,1)$ and $q\ge 1$. This is a generalization of the standard bond percolation (with open probability $p$) which is biased by a factor $q$ raised to…
A property common to several different astrophysical sources of high-energy gamma-rays is the presence of bulk motion at relativistic speed. The intrinsic spectra of the nonthermal radiating particles also show interesting similarities,…
The integrable nonlinear Schr\"odinger equation (NLSE) is a fundamental model of nonlinear science which also has important consequences in engineering. The powerful framework of the periodic inverse scattering transform (IST) provides a…
We study a distribution of thermal states given by random Hamiltonians with a local structure. We show that the ensemble of thermal states monotonically approaches the unitarily invariant ensemble with decreasing temperature if all…
The prompt GRB emission is thought to arise from electrons accelerated in internal shocks propagating within a highly relativistic outflow. The launch of Fermi offers the prospect of observations with unprecedented sensitivity in…
The pioneering computer simulations of the energy relaxation mechanisms performed by Fermi, Pasta and Ulam can be considered as the first attempt of understanding energy relaxation and thus heat conduction in lattices of nonlinear…
We show that even small dissipation can strongly affect the Fermi-Pasta-Ulam-Tsingou recurrence phenomenon. Taking the fully nonlinear stage of modulational instability as an experimentally accessible example, we show that the linear…
We study the long-term average evolution of the random ensemble along integrable Hamiltonian systems with time $T$-periodic transitions. More precisely, for any observable $G$, it is demonstrated that the ensemble under $G$ in long time…
We consider the Hammersley interacting particle system starting from a shock initial profile with densities $\lambda,\rho\in\mathbb{R}$ ($\lambda > \rho$). The microscopic shock is taken as the position of a second-class particle initially…
The dynamics of quantum entanglement plays a central role in explaining the emergence of thermal equilibrium in isolated many-body systems. However, entanglement is notoriously hard to measure. Recent works have introduced a notion of…
This work extends the thermodynamic analysis of random bond percolation to explosive and hybrid percolation models. We show that this thermodynamic analysis is well applicable to both explosive and hybrid percolation models by using the…
The prompt emission of gamma-ray bursts remains mysterious since the mechanism is difficult to understand even though there are much more observations with the development of detection technology. But most of the gamma-ray bursts spectra…
We use the mapping between Burgers' equation and the problem of a directed polymer in a random medium in order to study the fully developped turbulence in the $N$ dimensional forced Burgers' equation. The stirring force corresponds to a…
Using two extremely different models of glass formers in two and three dimensions we demonstrate how to encode the subtle changes in the geometric rearrangement of particles during the scenario of the glass transition. We construct a…
We analyze the relationship between the lowest energy configurations of an infinite harmonic chain of particles in a periodic potential and the evolution of characteristics in a periodically-forced inviscid Burgers equation. The shock…
A lagrangian approach to Burgers turbulence is carried out along the lines of the field theoretical Martin-Siggia-Rose formalism of stochastic hydrodynamics. We derive, from an analysis based on the hypothesis of unbroken galilean…
A mechanism is proposed for initial stage of instability development that can induce the fragmentation of nuclear matter, arising as a result of collisions of non-relativistic heavy nuclei. Collision of heavy nuclei is simulated as a…
Let $X_1,X_2,\ldots $ be independent random variables observed sequentially and such that $X_1,\ldots,X_{\theta-1}$ have a common probability density $p_0$, while $X_\theta,X_{\theta+1},\ldots $ are all distributed according to $p_1\neq…
The spherical spin model with infinite-range ferromagnetic interactions is investigated analytically in the framework of non-extensive thermostatics generalizing the Boltzmann-Gibbs statistical mechanics. We show that for repulsive…
In this letter, a multi-wave quasi-resonance framework is established to analyze energy diffusion in classical lattices, uncovering that it is fundamentally determined by the characteristics of eigenmodes. Namely, based on the presence and…