Permeability and conductivity of platelet-reinforced membranes and composites

We present large scale simulations of the diffusion constant $D$ of a random composite consisting of aligned platelets with aspect ratio $a/b>>1$ in a matrix (with diffusion constant $D_0$) and find that $D/D_0 = 1/(1+ c_1 x + c_2 x^2)$, where $x= a v_f/b$ and $v_f$ is the platelet volume fraction. We demonstrate that for large aspect ratio platelets the pair term ($x^2$) dominates suggesting large property enhancements for these materials. However a small amount of face-to-face ordering of the platelets markedly degrades the efficiency of platelet reinforcement.Comment: RevTeX, 5 pages, 4 figures, submitted to PR

Combinatorial models of rigidity and renormalization

We first introduce the percolation problems associated with the graph theoretical concepts of $(k,l)$-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization transformation for $(k,l)$-percolation problems, and investigate its domain of validity. In particular, we show that it allows an exact solution of $(k,l)$-percolation problems on hierarchical graphs, for $k\leq l<2k$. We introduce and solve by renormalization such a model, which has the interesting feature of showing both ordinary percolation and rigidity percolation phase transitions, depending on the values of the parameters.Comment: 22 pages, 6 figure

Large well-relaxed models of vitreous silica, coordination numbers and entropy

A Monte Carlo method is presented for the simulation of vitreous silica. Well-relaxed networks of vitreous silica are generated containing up to 300,000 atoms. The resulting networks, quenched under the BKS potential, display smaller bond-angle variations and lower defect concentrations, as compared to networks generated with molecular dynamics. The total correlation functions T(r) of our networks are in excellent agreement with neutron scattering data, provided that thermal effects and the maximum inverse wavelength used in the experiment are included in the comparison. A procedure commonly used in experiments to obtain coordination numbers from scattering data is to fit peaks in rT(r) with a gaussian. We show that this procedure can easily produce incorrect results. Finally, we estimate the configurational entropy of vitreous silica.Comment: 7 pages, 4 figures (two column version to save paper

Rings and rigidity transitions in network glasses

Three elastic phases of covalent networks, (I) floppy, (II) isostatically rigid and (III) stressed-rigid have now been identified in glasses at specific degrees of cross-linking (or chemical composition) both in theory and experiments. Here we use size-increasing cluster combinatorics and constraint counting algorithms to study analytically possible consequences of self-organization. In the presence of small rings that can be locally I, II or III, we obtain two transitions instead of the previously reported single percolative transition at the mean coordination number $\bar r=2.4$, one from a floppy to an isostatic rigid phase, and a second one from an isostatic to a stressed rigid phase. The width of the intermediate phase $~ \bar r$ and the order of the phase transitions depend on the nature of medium range order (relative ring fractions). We compare the results to the Group IV chalcogenides, such as Ge-Se and Si-Se, for which evidence of an intermediate phase has been obtained, and for which estimates of ring fractions can be made from structures of high T crystalline phases.Comment: 29 pages, revtex, 7 eps figure

Rigidity percolation in a field

Rigidity Percolation with g degrees of freedom per site is analyzed on randomly diluted Erdos-Renyi graphs with average connectivity gamma, in the presence of a field h. In the (gamma,h) plane, the rigid and flexible phases are separated by a line of first-order transitions whose location is determined exactly. This line ends at a critical point with classical critical exponents. Analytic expressions are given for the densities n_f of uncanceled degrees of freedom and gamma_r of redundant bonds. Upon crossing the coexistence line, n_f and gamma_r are continuous, although their first derivatives are discontinuous. We extend, for the case of nonzero field, a recently proposed hypothesis, namely that the density of uncanceled degrees of freedom is a ``free energy'' for Rigidity Percolation. Analytic expressions are obtained for the energy, entropy, and specific heat. Some analogies with a liquid-vapor transition are discussed. Particularizing to zero field, we find that the existence of a (g+1)-core is a necessary condition for rigidity percolation with g degrees of freedom. At the transition point gamma_c, Maxwell counting of degrees of freedom is exact on the rigid cluster and on the (g+1)-rigid-core, i.e. the average coordination of these subgraphs is exactly 2g, although gamma_r, the average coordination of the whole system, is smaller than 2g. gamma_c is found to converge to 2g for large g, i.e. in this limit Maxwell counting is exact globally as well. This paper is dedicated to Dietrich Stauffer, on the occasion of his 60th birthday.Comment: RevTeX4, psfig, 16 pages. Equation numbering corrected. Minor typos correcte

Transfer-matrix scaling from disorder-averaged correlation lengths for diluted Ising systems

A transfer matrix scaling technique is developed for randomly diluted systems, and applied to the site-diluted Ising model on a square lattice in two dimensions. For each allowed disorder configuration between two adjacent columns, the contribution of the respective transfer matrix to the decay of correlations is considered only as far as the ratio of its two largest eigenvalues, allowing an economical calculation of a configuration-averaged correlation length. Standard phenomenological-renormalisation procedures are then used to analyse aspects of the phase boundary which are difficult to assess accurately by alternative methods. For magnetic site concentration $p$ close to $p_c$, the extent of exponential behaviour of the $T_c \times p$ curve is clearly seen for over two decades of variation of $p - p_c$. Close to the pure-system limit, the exactly-known reduced slope is reproduced to a very good approximation, though with non-monotonic convergence. The averaged correlation lengths are inserted into the exponent-amplitude relationship predicted by conformal invariance to hold at criticality. The resulting exponent $\eta$ remains near the pure value (1/4) for all intermediate concentrations until it crosses over to the percolation value at the threshold.Comment: RevTeX 3, 11 pages +5 figures, uuencoded, to appear in Phys. Rev. B (1994), PUC/RJ preprin

Patterned nanostructure in AgCo/Pt/MgO(001) thin film

The formation of patterned nanostructure in AgCo/Pt/MgO(001) thin film is simulated by a technique of combining molecular dynamics and phase-field theory. The dislocation (strain) network existing in Pt/MgO is used as a template whose pattern is transferred to AgCo phase in spinodal decomposition, resulting in regular arrays of Co islands that are attracted by the dislocations. The influence of various factors, such as component concentration and film thickness, is studied. It is found that the spinodal decomposition of AgCo in this system is mainly characterized by a competition between a surface-directed layer structure and the strain-induced patterned structure, where the patterned Ag-Co structure only dominates in a small range near the interface (less than 10 atomic layers). However, if the interlayer diffusion can be minimized by controlling film growth conditions, it is shown that the patterned structure can be formed throughout the entire film.Comment: 8 pages, 12 figure

Influence of gestational age at initiation of antihypertensive therapy: secondary analysis of CHIPS trial data (control of hypertension in pregnancy study)

For hypertensive women in CHIPS (Control of Hypertension in Pregnancy Study), we assessed whether the maternal benefits of tight control could be achieved, while minimizing any potentially negative effect on fetal growth, by delaying initiation of antihypertensive therapy until later in pregnancy. For the 981 women with nonsevere, chronic or gestational hypertension randomized to less-tight (target diastolic blood pressure, 100 mm Hg), or tight (target, 85 mm Hg) control, we used mixed-effects logistic regression to examine whether the effect of less-tight (versus tight) control on major outcomes was dependent on gestational age at randomization, adjusting for baseline factors as in the primary analysis and including an interaction term between gestational age at randomization and treatment allocation. Gestational age was considered categorically (quartiles) and continuously (linear or quadratic form), and the optimal functional form selected to provide the best fit to the data based on the Akaike information criterion. Randomization before (but not after) 24 weeks to less-tight (versus tight) control was associated with fewer babies with birth weight 48 hours (Pinteraction=0.354). For the mother, less-tight (versus tight) control was associated with more severe hypertension at all gestational ages but particularly so before 28 weeks (Pinteraction=0.076). In women with nonsevere, chronic, or gestational hypertension, there seems to be no gestational age at which less-tight (versus tight) control is the preferred management strategy to optimize maternal or perinatal outcomes

Combination of searches for Higgs boson pairs in pp collisions at \sqrts = 13 TeV with the ATLAS detector

This letter presents a combination of searches for Higgs boson pair production using up to 36.1 fb(-1) of proton-proton collision data at a centre-of-mass energy root s = 13 TeV recorded with the ATLAS detector at the LHC. The combination is performed using six analyses searching for Higgs boson pairs decaying into the b (b) over barb (b) over bar, b (b) over barW(+)W(-), b (b) over bar tau(+)tau(-), W+W-W+W-, b (b) over bar gamma gamma and W+W-gamma gamma final states. Results are presented for non-resonant and resonant Higgs boson pair production modes. No statistically significant excess in data above the Standard Model predictions is found. The combined observed (expected) limit at 95% confidence level on the non-resonant Higgs boson pair production cross-section is 6.9 (10) times the predicted Standard Model cross-section. Limits are also set on the ratio (kappa(lambda)) of the Higgs boson self-coupling to its Standard Model value. This ratio is constrained at 95% confidence level in observation (expectation) to -5.0 &lt; kappa(lambda) &lt; 12.0 (-5.8 &lt; kappa(lambda) &lt; 12.0). In addition, limits are set on the production of narrow scalar resonances and spin-2 Kaluza-Klein Randall-Sundrum gravitons. Exclusion regions are also provided in the parameter space of the habemus Minimal Supersymmetric Standard Model and the Electroweak Singlet Model. For complete list of authors see http://dx.doi.org/10.1016/j.physletb.2019.135103</p