Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations

Different thermalization scenarios for systems with large fields have been proposed in the literature based on classical-statistical lattice simulations approximating the underlying quantum dynamics. We investigate the range of validity of these simulations for condensate driven as well as fluctuation dominated initial conditions for the example of a single component scalar field theory. We show that they lead to the same phenomenon of turbulent thermalization for the whole range of (weak) couplings where the classical-statistical approach is valid. In the turbulent regime we establish the existence of a dual cascade characterized by universal scaling exponents and scaling functions. This complements previous investigations where only the direct energy cascade has been studied for the single component theory. A proposed alternative thermalization scenario for stronger couplings is shown to be beyond the range of validity of classical-statistical simulations.Comment: 11 pages, 10 figures; version published in JHEP (minor revisions

Barriers of the McKean–Vlasov energy via a mountain pass theorem in the space of probability measures

We show that the empirical process associated with a system of weakly interacting diffusion processes exhibits a form of noise-induced metastability. The result is based on an analysis of the associated McKean–Vlasov free energy, which, for suitable attractive interaction potentials, has at least two distinct global minimisers at the critical parameter value . On the torus, one of these states is the spatially homogeneous constant state, and the other is a clustered state. We show that a third critical point exists at this value. As a result, we obtain that the probability of transition of the empirical process from the constant state scales like , with Δ the energy gap at . The proof is based on a version of the mountain pass theorem for lower semicontinuous and λ-geodesically convex functionals on the space of probability measures equipped with the 2-Wasserstein metric, where M is a complete, connected, and smooth Riemannian manifold

Constraints on the Growth and Spin of the Supermassive Black Hole in M32 From High Cadence Visible Light Observations

We present 1-second cadence observations of M32 (NGC221) with the CHIMERA instrument at the Hale 200-inch telescope of the Palomar Observatory. Using field stars as a baseline for relative photometry, we are able to construct a light curve of the nucleus in the g-prime and r-prime band with 1sigma=36 milli-mag photometric stability. We derive a temporal power spectrum for the nucleus and find no evidence for a time-variable signal above the noise as would be expected if the nuclear black hole were accreting gas. Thus, we are unable to constrain the spin of the black hole although future work will use this powerful instrument to target more actively accreting black holes. Given the black hole mass of (2.5+/-0.5)*10^6 Msun inferred from stellar kinematics, the absence of a contribution from a nuclear time-variable signal places an upper limit on the accretion rate which is 4.6*10^{-8} of the Eddington rate, a factor of two more stringent than past upper limits from HST. The low mass of the black hole despite the high stellar density suggests that the gas liberated by stellar interactions was primarily at early cosmic times when the low-mass black hole had a small Eddington luminosity. This is at least partly driven by a top-heavy stellar initial mass function at early cosmic times which is an efficient producer of stellar mass black holes. The implication is that supermassive black holes likely arise from seeds formed through the coalescence of 3-100 Msun mass black holes that then accrete gas produced through stellar interaction processes.Comment: 8 pages, 3 figures, submitted to the Astrophysical Journal, comments welcom

Wind and boundary layers in Rayleigh-Benard convection. I: analysis and modeling

The aim of this paper is to contribute to the understanding and to model the processes controlling the amplitude of the wind of Rayleigh-Benard convection. We analyze results from direct simulation of an L/H = 4 aspect-ratio domain with periodic sidewalls at Ra = 1e5; 1e6; 1e7; 1e8 and at Pr = 1 by decomposing independent realizations into wind and fluctuations. It is shown that deep inside the thermal boundary layer, horizontal heat-fuxes exceed the average vertical heat-fux by a factor 3 due to the interaction between the wind and the mean temperature field. These large horizontal heat-fluxes are responsible for spatial temperature differences that drive the wind by creating pressure gradients. The wall fluxes and turbulent mixing in the bulk provide damping. Using the DNS results to parameterise the unclosed terms, a simple model capturing the essential processes governing the wind structure is derived. The model consists of two coupled differential equations for wind velocity and temperature amplitude. The equations indicate that the formation of a wind structure is inevitable due to the positive feedback resulting from the interaction between the wind and temperature field. Furthermore, the wind velocity is largely determined by the turbulence in the bulk rather than by the wall-shear stress. The model reproduces the Ra dependence of wind Reynolds number and temperature amplitude

Kinetic and Structural Analysis of the Mg2+ -binding Site of the Guanine Nucleotide-binding Protein p21 H-ras.

The coordination and binding of the Mg2+ ion in the nucleotide−binding site of p21 have been investigated using site−directed mutagenesis, kinetic methods, and phosphorous NMR. Mg2+ in the p21.nucleotide.Mg2+ complex appears to be in fast equilibrium with the solvent. The dissociation constant between Mg2+ and the p21.GDP complex was determined to be 2.8 microM. It decreases 30− or 16−fold on substituting Ser−17 or Asp−57 with alanine, respectively, whereas the T35A mutation has no effect. All three mutations influence the dissociation constants and the association and dissociation rate constants of the interaction between guanine nucleotides and p21, but to a different degree. We conclude that Thr−35 is only complexed to Mg2+ in the GTP conformation and both Asp−57 and Ser−17 appear to be critical for both GDP and GTP binding. 31P NMR spectra of the GDP and Gpp(NH)p (guanosine−5'−(beta,gamma−imido)triphosphate) complexes of mutated p21 show a remarkable perturbation of the guanine nucleotide− binding site compared to wild−type protein. The mutant proteins show reduced GTPase rates, which are not stimulated by the GTPase−activating protein GAP. p21(S17A) has been reported to function just as p21(S17N) as a dominant negative inhibitor of normal p21. We find that it inhibits oncogenic p21−induced survival of primary neuron

Analytic study of the three-urn model for separation of sand

We present an analytic study of the three-urn model for separation of sand. We solve analytically the master equation and the first-passage problem. We find that the stationary probability distribution obeys the detailed balance and is governed by the {\it free energy}. We find that the characteristic lifetime of a cluster diverges algebraically with exponent 1/3 at the limit of stability.Comment: 5pages, 4 figures include

The hippocampus and inferential reasoning: building memories to navigate future decisions

A critical aspect of inferential reasoning is the ability to form relationships between items or events that were not experienced together. This review considers different perspectives on the role of the hippocampus in successful inferential reasoning during both memory encoding and retrieval. Intuitively, inference can be thought of as a logical process by which elements of individual existing memories are retrieved and recombined to answer novel questions. Such flexible retrieval is sub-served by the hippocampus and is thought to require specialized hippocampal encoding mechanisms that discretely code events such that event elements are individually accessible from memory. In addition to retrieval-based inference, recent research has also focused on hippocampal processes that support the combination of information acquired across multiple experiences during encoding. This mechanism suggests that by recalling past events during new experiences, connections can be created between newly formed and existing memories. Such hippocampally mediated memory integration would thus underlie the formation of networks of related memories that extend beyond direct experience to anticipate future judgments about the relationships between items and events. We also discuss integrative encoding in the context of emerging evidence linking the hippocampus to the formation of schemas as well as prospective theories of hippocampal function that suggest memories are actively constructed to anticipate future decisions and actions