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.

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

Convergence of density expansions of correlation functions and the Ornstein-Zernike equation

We prove absolute convergence of the multi-body correlation functions as a power series in the density uniformly in their arguments. This is done by working in the context of the cluster expansion in the canonical ensemble and by expressing the correlation functions as the derivative of the logarithm of an appropriately extended partition function. In the thermodynamic limit, due to combinatorial cancellations, we show that the coeffi- cients of the above series are expressed by sums over some class of two-connected graphs. Furthermore, we prove the convergence of the density expansion of the “direct correlation function” which is based on a completely different approach and it is valid only for some inte- gral norm. Precisely, this integral norm is suitable to derive the Ornstein-Zernike equation. As a further outcome, we obtain a rigorous quantification of the error in the Percus-Yevick approximation

The Blume-Emery-Griffiths model at the FAD and AD interfaces

We analyse the Blume-Emery-Griffiths (BEG) model on the lattice \Zd at the ferromagnetic-antiquadrupolar-disordered (FAD) and antiquadrupolar-disordered (AD) interfaces of parameters. In our analysis of the FAD interface we introduce a Gibbs sampler of the ground states at zero temperature, and we exploit it in two different ways: first, we perform via perfect sampling an empirical evaluation of the spontaneous magnetization at zero temperature, finding a non-zero value in $d=3$ and a vanishing value in $d=2$. Second, using a careful coupling with the Bernoulli site percolation model in $d=2$, we prove rigorously that imposing $+$ boundary conditions, the magnetization in the center of a square box tends to zero in the thermodynamical limit and the two-point correlations decay exponentially. Also, using again a coupling argument, we show that the infinite volume Gibbs measure of the zero-temperature BEG exists and it is unique. In our analysis of the AD interface we restrict ourselves to $d=2$ and, by comparing the BEG model with a Bernoulli site percolation in a matching graph of $\mathbb{Z}^2$, we get a condition for the vanishing of the infinite volume limit magnetization improving, for low temperatures, earlier results obtained via expansion techniques

The Blume–Emery–Griffiths Model on the FAD Point and on the AD Line

We analyse the Blume-Emery-Griffiths (BEG) model on the lattice Z(d) on the ferromagnetic-antiquadrupolar-disordered (FAD) point and on the antiquadrupolar-disordered (AD) line. In our analysis on the FAD point, we introduce a Gibbs sampler of the ground states at zero temperature, and we exploit it in two different ways: first, we perform via perfect sampling an empirical evaluation of the spontaneous magnetization at zero temperature, finding a non(z)ero value in d = 3 and a vanishing value in d = 2. Second, using a careful coupling with the Bernoulli site percolation model in d = 2, we prove rigorously that under imposing + boundary conditions, the magnetization in the center of a square box tends to zero in the thermodynamical limit and the two-point correlations decay exponentially. Also, using again a coupling argument, we show that there exists a unique zero-temperature infinite-volume Gibbs measure for the BEG. In our analysis of the AD line we restrict ourselves to d = 2 and, by comparing the BEG model with a Bernoulli site percolation in a matching graph of Z(2), we get a condition for the vanishing of the infinite-volume limit magnetization improving, for low temperatures, earlier results obtained via expansion techniques

Anisotropic Ising model in d+s dimensions

In this note, we consider the asymmetric nearest neighbor ferromagnetic Ising model on the $(d+s)$-dimensional unit cubic lattice $\Z^{d+s}$, at inverse temperature $\beta=1$ and with coupling constants $J_s>0$ and $J_d>0$ for edges of $\Z^s$ and $\Z^d$, respectively. We obtain a lower bound for the critical curve in the phase diagram of $(J_s,J_d)$. In particular, as $J_d$ approaches its critical value from below, our result is directly related to the so-called dimensional crossover phenomenon

Effects of Na-DNA mouthwash solutions on oral soft tissues. A bioreactor-based reconstituted human oral epithelium model

Purpose: To investigate whether the addition of sodium-DNA (Na-DNA) to chlorhexidine (CHX)-containing mouthwash influenced morphology and viability of a reconstituted human oral epithelium (ROE), and protects ROE against oxidative stress. Methods: Multi-layered 0.5 cm2 ROE specimens were positioned inside a continuous flow bioreactor and grown air-lifted for 24 hours. They were treated with phosphate-buffered saline (PBS) (n= 16) or 1 vol% H2O2 for 1 minute (n= 16). Then, they were treated for 5 (n= 8) or 30 minutes (n= 8) with the experimental mouthwash solutions containing: 0.2 wt% CHX, 0.2 wt% CHX + 0.2 wt% Na-DNA, 0.2 wt% Na-DNA, PBS. After 60 minutes washout specimens were subjected to tetrazolium-based viability assay (MTT) confocal laser-scanning microscopy (CLSM), and histological evaluation using optical microscopy and transmission electron microscopy (TEM). Results: ROE treated with Na-DNA for 30 minutes revealed significantly higher viability than PBS, and CHX + Na-DNA showed higher viability after 30-minute treatment than after 5 minutes, suggesting a significant protective activity of Na-DNA. Moreover, the protective effect of Na-DNA on cell viability was higher after the induction of oxidative stress. After treatment with CHX, CLSM revealed cell stress, leading to cell death in the outer layer. On the contrary, specimens treated with Na-DNA showed a much lower number of dead cells compared to PBS, both in the absence or presence of oxidative stress. Histological examination showed that the protective action of Na-DNA formulations reached more in-depth into the epithelium exposed to oxidative stress, due to intercellular spaces opening in the outer epithelium layers, giving way to Na-DNA to the inner parts of the epithelium. It can be concluded that Na-DNA had a topical protective activity when applied for 30 minutes unless the epithelium barrier is damaged, allowing it to act more in-depth. Clinical significance: Na-DNA showed a clear and protective action against cellular degeneration due to oxidative stress and, partly, to the exposure to CHX. Its addition to chlorhexidine mouthwash or gels could be clinically helpful in contrasting the detrimental activity of CHX on oral tissues, and in the preservation of cell viability, control of inflammation and wound healing