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In recent work, we developed a screening theory for describing the effect of plastic events in amorphous solids on its emergent mechanics. The suggested theory uncovered an anomalous mechanical response of amorphous solids where plastic…
Motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations, we investigate its implications in a paradigmatic model for the evolution of a single species density $u(x,t)$. The…
The effects of the finite size of the network on the evolutionary dynamics of a Boolean network are analyzed. In the model considered, Boolean networks evolve via a competition between nodes that punishes those in the majority. It is found…
When the structure deformation is dominated by the low-energy deformation mode, the structure hardens with the increase in the size (number of units) at small sizes. This anomalous behavior will eventually disappear with the decay length of…
We investigate the equilibrium and off-equilibrium behaviors of systems at thermal first-order transitions (FOTs) when the boundary conditions favor one of the two phases. As a theoretical laboratory we consider the two-dimensional Potts…
Moir\'e patterns are omnipresent. They are important for any overlapping periodic phenomenon, from vibrational and electromagnetic, to condensed matter. Here we show, both theoretically and via experimental simulations by ultracold atoms,…
Diffusion occurs in numerous physical systems throughout nature, drawing its generality from the universality of the central limit theorem. Around a century ago it was realized that an extension to this type of dynamics can be obtained in…
We point out how geometric features affect the scaling properties of non-equilibrium dynamic processes, by a model for surface growth where particles can deposit and evaporate only in dimer form, but dissociate on the surface. Pinning…
We introduce a new model of evolution on a fitness landscape possessing a tunable degree of neutrality. The model allows us to study the general properties of molecular species undergoing neutral evolution. We find that a number of…
A model of the passive vector field advected by the uncorrelated in time Gaussian velocity with power-like covariance is studied by means of the renormalization group and the operator product expansion. The structure functions of the…
In this research notes, we investigate some remain problems in the uniqueness of meromorphic function. Using some deep results of Yamanoii, we obtain some results in this notes.
In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation…
One possibility to explain the current accelerated expansion of the universe may be related with the presence of cosmologically evolving scalar whose mass depends on the local matter density (chameleon cosmology). We point out that matter…
We report on the calculation of the inclusive semileptonic decay of the $D_s$ meson on the lattice. We simulate the $D_s \rightarrow X_s\ell\nu_\ell$ process with M\"obius domain-wall charm and strange quarks, whose masses were…
Observations are inconsistent with a homogeneous and isotropic universe with ordinary matter and gravity. The universe is far from exact homogeneity and isotropy at late times, and the effect of the non-linear structures has to be…
Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…
We study the evolution of diffuse elastodynamic spectral energy density under the influence of weak nonlinearity. It is shown that the rate of change of this quantity is given by a convolution of the linear energy at two frequencies.…
We investigate the dynamical properties of an interacting many-body system with a non-trivial energy potential landscape that may induce a singular continuous single-particle energy spectrum. Focusing on the Aubry-Andr\'e model, whose…
In this letter we discuss a phase transition-like anomalous behavior of Faraday rotation angles in a simple parity-time ($\mathcal{P}\mathcal{T}$) symmetric model with two complex $\delta$-potential placed at both boundaries of a regular…
We report on recent progress in the study of evolution processes involving degenerate parabolic equations what may exhibit free boundaries. The equations we have selected follow to recent trends in diffusion theory: considering anomalous…