6,500 research outputs found
Particle interactions mediated by dynamical networks: assessment of macroscopic descriptions
We provide a numerical study of the macroscopic model of [3] derived from an
agent-based model for a system of particles interacting through a dynamical
network of links. Assuming that the network remodelling process is very fast,
the macroscopic model takes the form of a single aggregation diffusion equation
for the density of particles. The theoretical study of the macroscopic model
gives precise criteria for the phase transitions of the steady states, and in
the 1-dimensional case, we show numerically that the stationary solutions of
the microscopic model undergo the same phase transitions and bifurcation types
as the macroscopic model. In the 2-dimensional case, we show that the numerical
simulations of the macroscopic model are in excellent agreement with the
predicted theoretical values. This study provides a partial validation of the
formal derivation of the macroscopic model from a microscopic formulation and
shows that the former is a consistent approximation of an underlying particle
dynamics, making it a powerful tool for the modelling of dynamical networks at
a large scale
Fracton pairing mechanism for "strange" superconductors: Self-assembling organic polymers and copper-oxide compounds
Self-assembling organic polymers and copper-oxide compounds are two classes
of "strange" superconductors, whose challenging behavior does not comply with
the traditional picture of Bardeen, Cooper, and Schrieffer (BCS)
superconductivity in regular crystals. In this paper, we propose a theoretical
model that accounts for the strange superconducting properties of either class
of the materials. These properties are considered as interconnected
manifestations of the same phenomenon: We argue that superconductivity occurs
in the both cases because the charge carriers (i.e., electrons or holes)
exchange {\it fracton excitations}, quantum oscillations of fractal lattices
that mimic the complex microscopic organization of the strange superconductors.
For the copper oxides, the superconducting transition temperature as
predicted by the fracton mechanism is of the order of K. We suggest
that the marginal ingredient of the high-temperature superconducting phase is
provided by fracton coupled holes that condensate in the conducting
copper-oxygen planes owing to the intrinsic field-effect-transistor
configuration of the cuprate compounds. For the gate-induced superconducting
phase in the electron-doped polymers, we simultaneously find a rather modest
transition temperature of K owing to the limitations imposed by
the electron tunneling processes on a fractal geometry. We speculate that
hole-type superconductivity observes larger onset temperatures when compared to
its electron-type counterpart. This promises an intriguing possibility of the
high-temperature superconducting states in hole-doped complex materials. A
specific prediction of the present study is universality of ac conduction for
.Comment: 12 pages (including separate abstract page), no figure
Local vs. long-range infection in unidimensional epidemics
We study the effects of local and distance interactions in the unidimensional
contact process (CP). In the model, each site of a lattice is occupied by an
individual, which can be healthy or infected. As in the standard CP, each
infected individual spreads the disease to one of its first-neighbors with rate
, and with unitary rate, it becomes healthy. However, in our model, an
infected individual can transmit the disease to an individual at a distance
apart. This step mimics a vector-mediated transmission. We observe the
host-host interactions do not alter the critical exponents significantly in
comparison to a process with only L\'evy-type interactions. Our results
confirm, numerically, early field-theoretic predictions.Comment: 8 pages, 6 figures, to appear on Frontiers in Physic
Chimera patterns in conservative systems and ultracold atoms with mediated nonlocal hopping
Chimera patterns, characterized by coexisting regions of phase coherence and
incoherence, have so far been studied in non-conservative systems with
dissipation. Here, we show that the formation of chimera patterns can also be
observed in conservative Hamiltonian systems with nonlocal hopping in which
both energy and particle number are conserved. Effective nonlocality can be
realized in a physical system with only local coupling if different time scales
exist, which can be illustrated by a minimal conservative model with an
additional mediating channel. Finally, we show that the patterns should be
observable in ultracold atomic systems. Nonlocal spatial hopping over up to
tens of lattice sites with independently tunable hopping strength and on-site
nonlinearity can be implemented in a two-component Bose-Einstein condensate
with a spin-dependent optical lattice, where the untrapped component serves as
the matter-wave mediating field. The present work highlights the connections
between chimera patterns, nonlinear dynamics, condensed matter, and ultracold
atoms.Comment: 4 figures with supplementar
Kinetic modelling of competition and depletion of shared miRNAs by competing endogenous RNAs
Non-conding RNAs play a key role in the post-transcriptional regulation of
mRNA translation and turnover in eukaryotes. miRNAs, in particular, interact
with their target RNAs through protein-mediated, sequence-specific binding,
giving rise to extended and highly heterogeneous miRNA-RNA interaction
networks. Within such networks, competition to bind miRNAs can generate an
effective positive coupling between their targets. Competing endogenous RNAs
(ceRNAs) can in turn regulate each other through miRNA-mediated crosstalk.
Albeit potentially weak, ceRNA interactions can occur both dynamically,
affecting e.g. the regulatory clock, and at stationarity, in which case ceRNA
networks as a whole can be implicated in the composition of the cell's
proteome. Many features of ceRNA interactions, including the conditions under
which they become significant, can be unraveled by mathematical and in silico
models. We review the understanding of the ceRNA effect obtained within such
frameworks, focusing on the methods employed to quantify it, its role in the
processing of gene expression noise, and how network topology can determine its
reach.Comment: review article, 29 pages, 7 figure
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