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Results of experimental investigation are presented of evolutionary dynamics of several stochastic pattern formation and growth models designed by modifications of the famous mathematical Game of Life. The modifications are two-fold: Game…
In asymptotic free field theories we show that part of the OPE of the trace of the stress-energy tensor and an arbitrary composite field is determined by the anomalous dimension of the composite field. We take examples from the…
A detailed comparative qualitative analysis and numerical simulation of evolution of the cosmological models based on the doublet of classical and phantom scalar fields with self-action. The 2-dimensional and 3-dimensional projections of…
The structure of stellar atmospheres can be modified if they include embedded diverging magnetic fields. This is due to the presence of speed filters. Here we examine some of the relevant effects through the numerical simulation of the…
We examine the focusing of kinetic energy and the amplification of various quantities during the snapping motion of the free end of a flexible structure. This brief but violent event appears to be a regularized finite-time singularity, with…
The role that translational-rotational degrees of freedom play in nucleation theories is reconsidered by the introduction of a new formalism that properly accounts for the effects of motion of clusters in nucleation rate. The analysis of…
We investigate the impact of diffeomorphisms where more than one nonequivalent spinor structure is built upon a given base manifold endowed with nontrivial topology. We call attention to the fact that a relatively straightforward…
Evolution occurs in populations of reproducing individuals. Reproduction depends on the payoff a strategy receives. The payoff depends on the environment that may change over time, on intrinsic uncertainties, and on other sources of…
We theoretically evaluate the impact of drift-free noise on the dynamics of $\mathcal{PT}$-symmetric non-Hermitian systems with an exceptional point, which have recently been proposed for sensors. Such systems are currently considered as…
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.
Continuum elasticity is a powerful tool applicable in a broad range of physical systems and phenomena. Yet, understanding how and on what scales material disorder may lead to the breakdown of continuum elasticity is not fully understood. We…
An ergodic self-joining of an infinite rank-one transformation is a part of the weak limit of off-diagonal measures. A class of uncountaible cardinality of nonisomorphic transformations with polynomial weak closure is presented. Such…
Anomalous features of models with nonlinear symmetry realization are addressed. It is shown that such models can have anomalous amplitudes breaking of its original symmetry realization. An illustrative example of a simple models with a…
We investigate how the spectral and topological properties of electron systems evolve on a lattice that interpolates between the honeycomb and its 1/6-depleted structures through the introduction of selective random defects. We find that in…
A theoretical and experimental analysis is made of the effects of self-adaptation in a simple evolving system. Specifically, we consider the effects of coding the mutation and crossover probabilities of a genetic algorithm evolving in…
The influence of uniaxial small-scale anisotropy on the stability of the scaling regimes and on the anomalous scaling of the structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation…
We review a recent progress on fluid dynamics applied to strongly interacting nuclear matter. The efforts are made to highlight consequences of scale invariance breaking on the hydrodynamic description of a nuclear medium. Both…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
Conformal symmetry underlies many massless quantum field theories, but little is known about the consequences of this powerful symmetry for on-shell scattering amplitudes. Working in a dimensionally-regularised $\phi^3$ model at the…
Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of…