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Motivated by the ubiquity of turbulent flows in realistic conditions, effects of turbulent advection on two models of classical non-linear systems are investigated. In particular, we analyze model A (according to the Hohenberg-Halperin…
A one-dimensional white-in-time passive scalar model is introduced. Strong and persistent structures are shown to be present. A perturbative expansion for the scaling exponents is performed around a Gaussian limit of the model. The…
We have investigated the advection of a passive scalar quantity by incompressible helical turbulent flow in the frame of extended Kraichnan model. Turbulent fluctuations of velocity field are assumed to have the Gaussian statistics with…
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion…
Spontaneous stochasticity refers to the emergence of intrinsic randomness in deterministic systems under singular limits, a phenomenon conjectured to be fundamental in turbulence. Armstrong and Vicol \citep{AV23,AV24} recently constructed a…
We show that the statistics of a turbulent passive scalar at scales larger than the pumping may exhibit multiscaling due to a weaker mechanism than the presence of statistical conservation laws. We develop a general formalism to give…
Understanding the dynamic nature of biological systems is fundamental to deciphering cellular behavior, developmental processes, and disease progression. Single-cell RNA sequencing (scRNA-seq) has provided static snapshots of gene…
We consider the advection of a passive scalar by a divergence free random Gaussian field, white in time and H\"older regular in space (rough Kraichnan's model), a well established synthetic model of passive scalar turbulence. By studying…
We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems…
Two dimensional passive scalar turbulence is studied by means of a k-space diffusion model based on a third order differential approximation. This simple description of local nonlinear interactions in Fourier space is shown to present a…
Anomalous scaling problem in the stochastic Navier-Stokes equation is treated in the framework of the field theoretical approach, successfully applied earlier to the Kraichnan rapid advection model. Two cases of the space dimensions d=2 and…
The Lagrangian view of passive scalar turbulence has recently produced interesting results and interpretations. Innovations in theory, experiments, simulations and data analysis of Lagrangian turbulence are reviewed here in brief. Part of…
We present a framework for the scale-invariance characterization of stochastic processes in reconstructed finite-dimensional phase spaces. This framework analyses the structural and dynamical properties of the phase space and is based on a…
The field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…
Shell models of turbulence have a finite-time blowup in the inviscid limit, i.e., the enstrophy diverges while the single-shell velocities stay finite. The signature of this blowup is represented by self-similar instantonic structures…
We present results of direct numerical simulations of passive scalar advection and diffusion in turbulent rotating flows. Scaling laws and the development of anisotropy are studied in spectral space, and in real space using an axisymmetric…
The stochastic dynamics of a scalar field in de Sitter spacetime can be regarded as a non-perturbative diffusion process, to which exact distribution and correlation functions are constructed by utilising the correspondence between…
Infrared asymptotic behaviour of a scalar field, passively advected by a random shear flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in…
A model of the passive vector quantity advected by a Gaussian time-decorrelated self-similar velocity field is studied; the effects of pressure and large-scale anisotropy are discussed. The inertial-range behavior of the pair correlation…