Asymptotic properties of turbulent magnetohydrodynamics

Arjun Berera; David Hochberg

Home/Archive/arXiv

arXiv · cond-mat/0103447

Asymptotic properties of turbulent magnetohydrodynamics

Arjun Berera·David Hochberg

View original source ↗Read source document ↗Export metadata ↓

Abstract

The dynamic renormalization group (RG) is used to study the large-distance and long-time limits of viscous and resistive incompressible magnetohydrodynamics subject to random forces and currents. The scale-dependent viscosity and magnetic resistivity are derived and used for carrying out RG-improved perturbation theory. This is applied to derive both the asymptotic scaling and the overall proportionality coefficients for both the velocity and magnetic field correlation functions as well as the kinetic and magnetic energy density spectral functions. The Kolmogorov, Iroshnikov-Kraichnan, as well as other energy spectra, formally can be obtained by suitable choice of injected noise, although the method limits the validity of these energy spectra only to the asymptotic regime . Injection of a random magnetic helicity is considered, its RG-improved spectral density derived, and its contribution to the velocity and magnetic field correlation functions determined. The RG scaling solutions are used to determine information at asymptotic scales about energy and helicity cascade directions and mixing between magnetic and kinetic energy. Some of the results found here also are shown to be valid for the Navier-Stokes hydrodynamic equation. The results have applicability to geomagnetism as well as cosmic magnetic fields at astrophysical and cosmological scales.

Explore related subjects

cond-mat.stat-mech astro-ph hep-th

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Arjun Berera, David Hochberg. 2002-02-12. Asymptotic properties of turbulent magnetohydrodynamics. https://arxiv.org/abs/cond-mat/0103447

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Universal sampling of spin systems across quenched disorder

Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.

cond-mat.stat-mech↗

arXiv2026

Information-Theoretic Characterization of Macroscopic Chaos Emerging from the Chemical Master Equation

Open chemical reaction networks exhibit stochastic concentration dynamics at finite system sizes, whereas their macroscopic limit is governed by deterministic rate equations that can display chaos. In this Letter, we show theoretically that a rate of information loss constructed from two-time mutual information recovers the Kolmogorov-Sinai entropy in the deterministic limit. We verify this result through numerical simulations of a Markov jump process for a three-species system involving seven reactions.

cond-mat.stat-mech↗

arXiv2026

Orientational order on non-orientable domains

We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.

cond-mat.stat-mech↗