Related papers: Percolation threshold and critical point of a nucl…
A multifractal model is used to analyze neutron evolution within a reactor. For chain reactions, various characteristics of multifractal neutron behavior have been determined. These include the dimension of the multifractal carrier,…
The trajectories of neutrons in the reactor, the points of their fission of uranium nuclei, the points of neutron absorption, fission chains and chain reactions are considered from the standpoint of fractal geometry and percolation theory.…
Reactor physics aims at studying the neutron population in a reactor core under the influence of feedback mechanisms, such as the Doppler temperature effect. Numerical schemes to calculate macroscopic properties emerging from such coupled…
We study continuum percolation in nuclear collisions for the realistic case in which the nuclear matter distribution is not uniform over the collision volume, and show that the percolation threshold is increased compared to the standard,…
Neutron behavior in a nuclear reactor is described using a directed percolation model. The preferred direction is created by generations of neutrons oriented in time. Using the example of the time it takes for a dangerous neutron flux or…
Stochastic fluctuations of the neutron population within a nuclear reactor are typically prevented by operating the core at a sufficient power, since a deterministic behavior of the neutron population is required by automatic safety systems…
Based on the theory of hierarchical structures, a correspondence has been established between the dynamics for the number of neutrons obtained from the theory of branching processes, the number of neutrons of the n-th generation, the number…
Applying boundary functionals of random risk processes to various physical problems makes it possible to determine many important characteristics of these problems. For example, a special case of boundary functionals is the time to first…
An essential prerequisite for quark-gluon plasma production in nuclear collisions is cross-talk between the partons from different nucleons in the colliding nuclei. The initial density of partons is determined by the parton distribution…
We study percolation on the hierarchical lattice of order $N$ where the probability of connection between two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)},\; \delta >-1$. Since the distance is an ultrametric, there…
Signatures of critical behaviour in nuclear fragmentation are often based on arguments from percolation theory. We demonstrate with general thermodynamic considerations and studies of the Ising model that the reliance on percolation as a…
Nuclear reactor cores achieve sustained fission chain reactions through the so-called 'critical state' -a subtle equilibrium between their material properties and their geometries. Observed at macroscopic scales during operations, the…
For more than half a century, nucleons are considered to move continuously in the nuclei. Recent electron-scattering experiments indicate about 20$\sim$25\% nucleons in heavier nuclei are involved in the neutron-proton short-range…
Quantum percolation describes the problem of a quantum particle moving through a disordered system. While certain similarities to classical percolation exist, the quantum case has additional complexity due to the possibility of Anderson…
A recent description of diffusion-limited nucleation based on fluctuating hydrodynamics that extends classical nucleation theory predicts a very non-classical two-step scenario whereby nucleation is most likely to occur in…
The neutron population in a nuclear reactor is subject to fluctuations in time and in space due to the competition of diffusion by scattering, births by fission events, and deaths by absorptions. As such, fission chains provide a prototype…
In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009)]. This Brief Report presents a modest, though more insightful extension of…
The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase…
Tree models for rigidity percolation are introduced and solved. A probability vector describes the propagation of rigidity outward from a rigid border. All components of this ``vector order parameter'' are singular at the same rigidity…
Keeping in view applications to numerical simulations of the evolution of a nuclear reactor core around criticality, we use a general mathematical framework for describing the evolutions of multiplicative processes (processes involving…