The analyticity region of the hard sphere gas. Improved bounds

We find an improved estimate of the radius of analyticity of the pressure of the hard-sphere gas in $d$ dimensions. The estimates are determined by the volume of multidimensional regions that can be numerically computed. For $d=2$, for instance, our estimate is about 40% larger than the classical one.Comment: 4 pages, to appear in Journal of Statistical Physic

Effects of boundary conditions on irreversible dynamics

We present a simple one-dimensional Ising-type spin system on which we define a completely asymmetric Markovian single spin-flip dynamics. We study the system at a very low, yet non-zero, temperature and we show that for empty boundary conditions the Gibbs measure is stationary for such dynamics, while introducing in a single site a $+$ condition the stationary measure changes drastically, with macroscopical effects. We achieve this result defining an absolutely convergent series expansion of the stationary measure around the zero temperature system. Interesting combinatorial identities are involved in the proofs

Cluster expansion for abstract polymer models. New bounds from an old approach

We revisit the classical approach to cluster expansions, based on tree graphs, and establish a new convergence condition that improves those by Kotecky-Preiss and Dobrushin, as we show in some examples. The two ingredients of our approach are: (i) a careful consideration of the Penrose identity for truncated functions, and (ii) the use of iterated transformations to bound tree-graph expansions.Comment: 16 pages. This new version, written en reponse to the suggestions of the referees, includes more detailed introductory sections, a proof of the generalized Penrose identity and some additional results that follow from our treatmen

Abstract polymer models with general pair interactions

A convergence criterion of cluster expansion is presented in the case of an abstract polymer system with general pair interactions (i.e. not necessarily hard core or repulsive). As a concrete example, the low temperature disordered phase of the BEG model with infinite range interactions, decaying polynomially as $1/r^{d+\lambda}$ with $\lambda>0$, is studied.Comment: 19 pages. Corrected statement for the stability condition (2.3) and modified section 3.1 of the proof of theorem 1 consistently with (2.3). Added a reference and modified a sentence at the end of sec. 2.

Analyticity of the SRB measure of a lattice of coupled Anosov diffeomorphisms of the torus

We consider the "thermodynamic limit"of a d-dimensional lattice of hyperbolic dynamical systems on the 2-torus, interacting via weak and nearest neighbor coupling. We prove that the SRB measure is analytic in the strength of the coupling. The proof is based on symbolic dynamics techniques that allow us to map the SRB measure into a Gibbs measure for a spin system on a (d+1)-dimensional lattice. This Gibbs measure can be studied by an extension (decimation) of the usual "cluster expansion" techniques.Comment: 28 pages, 2 figure

Decay Properties of the Connectivity for Mixed Long Range Percolation Models on Zd\Z^d

In this short note we consider mixed short-long range independent bond percolation models on $\Z^{k+d}$. Let $p_{uv}$ be the probability that the edge $(u,v)$ will be open. Allowing a $x,y$-dependent length scale and using a multi-scale analysis due to Aizenman and Newman, we show that the long distance behavior of the connectivity $\tau_{xy}$ is governed by the probability $p_{xy}$. The result holds up to the critical point.Comment: 6 page

On the convergence of cluster expansions for polymer gases

We compare the different convergence criteria available for cluster expansions of polymer gases subjected to hard-core exclusions, with emphasis on polymers defined as finite subsets of a countable set (e.g. contour expansions and more generally high- and low-temperature expansions). In order of increasing strength, these criteria are: (i) Dobrushin criterion, obtained by a simple inductive argument; (ii) Gruber-Kunz criterion obtained through the use of Kirkwood-Salzburg equations, and (iii) a criterion obtained by two of us via a direct combinatorial handling of the terms of the expansion. We show that for subset polymers our sharper criterion can be proven both by a suitable adaptation of Dobrushin inductive argument and by an alternative --in fact, more elementary-- handling of the Kirkwood-Salzburg equations. In addition we show that for general abstract polymers this alternative treatment leads to the same convergence region as the inductive Dobrushin argument and, furthermore, to a systematic way to improve bounds on correlations

Photochemical pump and NMR probe : Chemically created NMR coherence on a microsecond time scale

We report pump-probe experiments employing laser-synchronized reactions of para-hydrogen (para-H2) with transition metal dihydride complexes in conjunction with nuclear magnetic resonance (NMR) detection. The pump-probe experiment consists of a single nanosecond laser pump pulse followed, after a precisely defined delay, by a single radio frequency (rf) probe pulse. Laser irradiation eliminates H2 from either Ru(PPh3) 3(CO)(H)2 1 or cis-Ru(dppe)2(H)2 2 in C6D6 solution. Reaction with para-H2 then regenerates 1 and 2 in a well-defined nuclear spin state. The rf probe pulse produces a high-resolution, single-scan 1H NMR spectrum that can be recorded after a pump-probe delay of just 10 μs. The evolution of the spectra can be followed as the pump-probe delay is increased by micro- or millisecond increments. Due to the sensitivity of this para-H2 experiment, the resulting NMR spectra can have hydride signal-to-noise ratios exceeding 750:1. The spectra of 1 oscillate in amplitude with frequency 1101 ± 3 Hz, the chemical shift difference between the chemically inequivalent hydrides. The corresponding hydride signals of 2 oscillate with frequency 83 ± 5 Hz, which matches the difference between couplings of the hydrides to the equatorial 31P nuclei. We use the product operator formalism to show that this oscillatory behavior arises from a magnetic coherence in the plane orthogonal to the magnetic field that is generated by use of the laser pulse without rf initialization. In addition, we demonstrate how chemical shift imaging can differentiate the region of laser irradiation thereby distinguishing between thermal and photochemical reactivity within the NMR tube

Heat transfer in drop-laden low-Prandtl-number channel turbulence

In this work, we numerically investigate heat transfer in low-Prandtl-number drop-laden wall-bounded turbulence. These flows are characteristic of nuclear and fusion technologies, where liquid metals - known for their high thermal conductivity - are laden with drops or bubbles of another liquid or pressurised gas. To this end, we consider forced convection turbulence between two differentially heated parallel plates. The carrier phase (i.e. liquid metal) is characterised by a low Prandtl number, while for the dispersed phase, we explore a range of Prandtl numbers from (matched case) to (super-unitary Prandtl number in the dispersed phase). Simulations are conducted at constant friction Reynolds number, and for each dispersed phase Prandtl number, two volume fractions are examined: and. The simulation framework relies on direct numerical simulation of the Navier-Stokes equations, coupled with a phase-field method and the energy equation. Results show that an increase of the dispersed phase Prandtl number reduces heat transfer, leading to a lower Nusselt number for both volume fractions. To explain this behaviour, we analyse how the drops modify the temperature field, and demonstrate that the heat transfer reduction stems from a decreased diffusive heat flux within the dispersed phase. Finally, we propose a phenomenological model to predict the Nusselt number as a function of both the dispersed phase volume fraction and Prandtl number