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We provide a new definition of a local walk dimension $\beta$ that depends only on the metric and not on the existence of a particular regular Dirichlet form or heat kernel asymptotics. Moreover, we study the local Hausdorff dimension…
Following Assiotis (2020), we study general $\beta$-Hua-Pickrell diffusions of $N$ particles on $\mathbb R$ as solutions of the stochastic differential equations (SDEs) $$dX_{j,t}=\sqrt{2(1+X_{j,t}^2)}\,dB_{j,t}+\beta\left[b-a…
We develop a systematic extension of mode-coupling theory (MCT) that incorporates critical dynamical fluctuations. Starting from a microscopic diagrammatic theory, we identify dominant classes of divergent diagrams near the mode-coupling…
We consider a single-interface model for the description of Barkhausen noise in soft ferromagnetic materials. Previously, the model had been used only in the adiabatic regime of infinitely slow field ramping. We introduce finite driving…
A theory of flow stress (FS), reviewing and developing our research,e.g. arxiv:1803.08247;1908.09338, is proposed,including yield strength (YS) of PC materials for quasi-static plastic loading for grain of average size d in range…
The classical Heisenberg model is one of the most fundamental models in statistical and condensed matter physics. Extensive theoretical and numerical studies suggest that, in two dimensions, this model does not exhibit a finite-temperature…
Large-scale magnetic fields are relevant for a number of dynamical processes in accretion disks, including driving turbulence, reconnection events, and launching outflows. Numerical simulations have indicated that the initial strengths and…
One of the primitive aims of the two-dimensional BTW model had been to explain the $1/f^{\alpha}$ noise which is widely seen in the natural systems. In this paper we study some time signals, namely the activity inside an avalanche ($x(t)$),…
Nonresonant current instability was identified by Bell (2004) as an important mechanism for magnetic field amplification in supernova remnants. In this paper we focus on studying the nonlinear stage of this instability using the…
A shear flow of liquid metal (Galinstan) is driven in an annular channel by counter-rotating traveling magnetic fields imposed at the endcaps. When the traveling velocities are large, the flow is turbulent and its azimuthal component…
We study the error scaling properties of large-eddy simulation (LES) in the outer region of wall-bounded turbulence at moderately high Reynolds numbers. In order to avoid the additional complexity of wall-modeling, we perform LES of…
We present a phenomenological theory for phase turbulence (PT) in Rayleigh-B\'{e}nard convection, based on the generalized Swift-Hohenberg model. We apply a Hartree-Fock approximation to PT and conjecture a scaling form for the structure…
Turbulence is a dominant feature operating in gaseous flows across nearly all scales in astrophysical environments. Accordingly, accurately estimating the statistical properties of such flows is necessary for developing a comprehensive…
We explore one-point and two-point statistics of the Navier-Stokes-alpha-beta regularization model at moderate Reynolds number in homogeneous isotropic turbulence. The results are compared to the limit cases of the Navier-Stokes-alpha model…
Super-Heisenberg scaling, which scales as $N^{-\beta}$ with $\beta>1$ in terms of the number of particles $N$ or $T^{-\beta}$ in terms of the evolution time $T$, is better than Heisenberg scaling in quantum metrology. It has been proven…
We study the directed polymer model in dimension ${1+1}$ when the environment is heavy-tailed, with a decay exponent $\alpha\in(0,2)$. We give all possible scaling limits of the model in the weak-coupling regime, i.e., when the inverse…
A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension $d\in\mathbb{N}$. It is a regularised and inertial version of the…
We present high-resolution direct numerical simulation studies of turbulent Rayleigh-Benard convection in a closed cylindrical cell with an aspect ratio of one. The focus of our analysis is on the finest scales of convective turbulence, in…
In turbulent thermal convection in cylindrical samples of aspect ratio \Gamma = D/L (D is the diameter and L the height) the Nusselt number Nu is enhanced when the sample is rotated about its vertical axis, because of the formation of Ekman…
We report evidence of irregular unsteady flow of two-dimensional polymer solutions in the absence of inertia in cross-slot geometry using numerical simulations of Oldroyd-B model. By exploring the transition to time-dependent flow versus…