Universal Formulae for Percolation Thresholds

A power law is postulated for both site and bond percolation thresholds. The formula writes $p_c=p_0[(d-1)(q-1)]^{-a}d^{\ b}$, where $d$ is the space dimension and $q$ the coordination number. All thresholds up to $d\rightarrow \infty$ are found to belong to only three universality classes. For first two classes $b=0$ for site dilution while $b=a$ for bond dilution. The last one associated to high dimensions is characterized by $b=2a-1$ for both sites and bonds. Classes are defined by a set of value for $\{p_0; \ a\}$. Deviations from available numerical estimates at $d \leq 7$ are within $\pm 0.008$ and $\pm 0.0004$ for high dimensional hypercubic expansions at $d \geq 8$. The formula is found to be also valid for Ising critical temperatures.Comment: 11 pages, latex, 3 figures not include

The Role of Genes in Defining a Molecular Biology of PTSD

Because environmental exposure to trauma is the sine qua non for the development of Post Traumatic Stress Disorder (PTSD), the recent focus on genetic studies has been noteworthy. The main catalyst for such studies is the observation from epidemiological studies that not all trauma survivors develop this disorder. Furthermore, neuroendocrine findings suggest pre-existing hormonal alterations that confer risk for PTSD. This paper presents the rationale for examining genetic factors in PTSD and trauma exposure, but suggests that studies of genotype may only present a limited picture of the molecular biology of this disorder. We describe the type of information that can be obtained from candidate gene and genomic studies that incorporate environmental factors in the design (i.e., gene – environment interaction and gene-environment correlation studies) and studies that capitalize on the idea that environment modifies gene expression, via epigenetic or other molecular mechanisms. The examination of epigenetic mechanisms in tandem with gene expression will help refine models that explain how PTSD risk, pathophysiology, and recovery is mediated by the environment. Since inherited genetic variation may also influence the extent of epigenetic or gene expression changes resulting from the environment, such studies should optimally be followed up by studies of genotype

Role of chemokines and cytokines in a reactivation model of arthritis in rats induced by injection with streptococcal cell walls

Intraarticular injection of streptococcal cell wall (SCW) antigen followed by intravenous challenge results in a T cellâ mediated monoarticular arthritis in female Lewis rats. Initial studies showed that this reactivation response to intravenous SCW antigen is dependent on the presence of interleukinâ 1 (ILâ 1) and tumor necrosis factor α (TNFâ α) and that the early phase of swelling is neutrophilâ dependent. Neutrophil depletion or passive immunization with antibodies to Pâ selectin or macrophage inflammatory proteinâ 2 reduced the intensity of ankle edema and the influx of neutrophils. After the first few days, however, the arthritic response is mediated primarily by mononuclear cells. Joint tissues showed upâ regulation of mRNA for monocyte chemotactic proteinâ 1 (MCPâ 1), which could be inhibited in part by antiâ ILâ 4; treatment of rats with antibodies to ILâ 4 or MCPâ 1 significantly suppressed development of ankle edema and histopathological evidence of inflammation. Antibodies to interferonâ γ or ILâ 10 had no effect. Treatment with antiâ MCPâ 1 also suppressed influx of 111Inâ labeled T cells into the ankle joint. These data suggest that the late, mononuclearâ dependent phase of SCWâ induced arthritis in female Lewis rats requires cytokines that upâ regulate MCPâ 1, which in turn may facilitate recruitment and extravasation of mononuclear cells into the joint. J. Leukoc. Biol. 63: 359â 363; 1998.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142294/1/jlb0359.pd

Microscopic formulation of the Zimm-Bragg model for the helix-coil transition

A microscopic spin model is proposed for the phenomenological Zimm-Bragg model for the helix-coil transition in biopolymers. This model is shown to provide the same thermophysical properties of the original Zimm-Bragg model and it allows a very convenient framework to compute statistical quantities. Physical origins of this spin model are made transparent by an exact mapping into a one-dimensional Ising model with an external field. However, the dependence on temperature of the reduced external field turns out to differ from the standard one-dimensional Ising model and hence it gives rise to different thermophysical properties, despite the exact mapping connecting them. We discuss how this point has been frequently overlooked in the recent literature.Comment: 11 pages, 2 figure

Elasticity near the vulcanization transition

Signatures of the vulcanization transition--amorphous solidification induced by the random crosslinking of macromolecules--include the random localization of a fraction of the particles and the emergence of a nonzero static shear modulus. A semi-microscopic statistical-mechanical theory is presented of the latter signature that accounts for both thermal fluctuations and quenched disorder. It is found (i) that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess cross-link density and, quite surprisingly, (ii) that near the transition the external stresses do not spoil the spherical symmetry of the localization clouds of the particles.Comment: REVTEX, 5 pages. Minor change

Percolation and jamming in random sequential adsorption of linear segments on square lattice

We present the results of study of random sequential adsorption of linear segments (needles) on sites of a square lattice. We show that the percolation threshold is a nonmonotonic function of the length of the adsorbed needle, showing a minimum for a certain length of the needles, while the jamming threshold decreases to a constant with a power law. The ratio of the two thresholds is also nonmonotonic and it remains constant only in a restricted range of the needles length. We determine the values of the correlation length exponent for percolation, jamming and their ratio

A two-parameter random walk with approximate exponential probability distribution

We study a non-Markovian random walk in dimension 1. It depends on two parameters eps_r and eps_l, the probabilities to go straight on when walking to the right, respectively to the left. The position x of the walk after n steps and the number of reversals of direction k are used to estimate eps_r and eps_l. We calculate the joint probability distribution p_n(x,k) in closed form and show that, approximately, it belongs to the exponential family.Comment: 12 pages, updated reference to companion paper cond-mat/060126

The competition of hydrogen-like and isotropic interactions on polymer collapse

We investigate a lattice model of polymers where the nearest-neighbour monomer-monomer interaction strengths differ according to whether the local configurations have so-called ``hydrogen-like'' formations or not. If the interaction strengths are all the same then the classical $\theta$-point collapse transition occurs on lowering the temperature, and the polymer enters the isotropic liquid-drop phase known as the collapsed globule. On the other hand, strongly favouring the hydrogen-like interactions give rise to an anisotropic folded (solid-like) phase on lowering the temperature. We use Monte Carlo simulations up to a length of 256 to map out the phase diagram in the plane of parameters and determine the order of the associated phase transitions. We discuss the connections to semi-flexible polymers and other polymer models. Importantly, we demonstrate that for a range of energy parameters two phase transitions occur on lowering the temperature, the second being a transition from the globule state to the crystal state. We argue from our data that this globule-to-crystal transition is continuous in two dimensions in accord with field-theory arguments concerning Hamiltonian walks, but is first order in three dimensions

Fluctuating Filaments I: Statistical Mechanics of Helices

We examine the effects of thermal fluctuations on thin elastic filaments with non-circular cross-section and arbitrary spontaneous curvature and torsion. Analytical expressions for orientational correlation functions and for the persistence length of helices are derived, and it is found that this length varies non-monotonically with the strength of thermal fluctuations. In the weak fluctuation regime, the local helical structure is preserved and the statistical properties are dominated by long wavelength bending and torsion modes. As the amplitude of fluctuations is increased, the helix ``melts'' and all memory of intrinsic helical structure is lost. Spontaneous twist of the cross--section leads to resonant dependence of the persistence length on the twist rate.Comment: 5 figure

Effects of Impurities in Random Sequential Adsorption on a One-Dimensional Substrate

We have solved the kinetics of random sequential adsorption of linear $k$-mers on a one-dimensional disordered substrate for the random sequential adsorption initial condition and for the random initial condition. The jamming limits $\theta(\infty, k', k)$ at fixed length of linear $k$-mers have a minimum point at a particular density of the linear $k'$-mers impurity for both cases. The coverage of the surface and the jamming limits are compared to the results for Monte Carlo simulation. The Monte Carlo results for the jamming limits are in good agreement with the analytical results. The continuum limits are derived from the analytical results on lattice substrates.Comment: 9 pages, latex, 1 figure not included, accepted in Phys. Rev.