Elastic collapse in disordered isostatic networks

Isostatic networks are minimally rigid and therefore have, generically, nonzero elastic moduli. Regular isostatic networks have finite moduli in the limit of large sizes. However, numerical simulations show that all elastic moduli of geometrically disordered isostatic networks go to zero with system size. This holds true for positional as well as for topological disorder. In most cases, elastic moduli decrease as inverse power-laws of system size. On directed isostatic networks, however, of which the square and cubic lattices are particular cases, the decrease of the moduli is exponential with size. For these, the observed elastic weakening can be quantitatively described in terms of the multiplicative growth of stresses with system size, giving rise to bulk and shear moduli of order exp{-bL}. The case of sphere packings, which only accept compressive contact forces, is considered separately. It is argued that these have a finite bulk modulus because of specific correlations in contact disorder, introduced by the constraint of compressivity. We discuss why their shear modulus, nevertheless, is again zero for large sizes. A quantitative model is proposed that describes the numerically measured shear modulus, both as a function of the loading angle and system size. In all cases, if a density p>0 of overconstraints is present, as when a packing is deformed by compression, or when a glass is outside its isostatic composition window, all asymptotic moduli become finite. For square networks with periodic boundary conditions, these are of order sqrt{p}. For directed networks, elastic moduli are of order exp{-c/p}, indicating the existence of an "isostatic length scale" of order 1/p.Comment: 6 pages, 6 figues, to appear in Europhysics Letter

A fast algorithm for backbones

A matching algorithm for the identification of backbones in percolation problems is introduced. Using this procedure, percolation backbones are studied in two- to five-dimensional systems containing 1.7x10^7 sites, two orders of magnitude larger than was previously possible using burning algorithms.Comment: 8 pages, 6 .eps figures. Uses epsfig and ijmpc.sty (included). To appear in Int. J. Mod. Phys.

Statistical Laws and Mechanics of Voronoi Random Lattices

We investigate random lattices where the connectivities are determined by the Voronoi construction, while the location of the points are the dynamic degrees of freedom. The Voronoi random lattices with an associated energy are immersed in a heat bath and investigated using a Monte Carlo simulation algorithm. In thermodynamic equilibrium we measure coordination number distributions and test the Aboav-Weaire and Lewis laws.Comment: 14 pages (figures not included), LaTeX, HLRZ-26/9

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

Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe Lattices

We show that negative of the number of floppy modes behaves as a free energy for both connectivity and rigidity percolation, and we illustrate this result using Bethe lattices. The rigidity transition on Bethe lattices is found to be first order at a bond concentration close to that predicted by Maxwell constraint counting. We calculate the probability of a bond being on the infinite cluster and also on the overconstrained part of the infinite cluster, and show how a specific heat can be defined as the second derivative of the free energy. We demonstrate that the Bethe lattice solution is equivalent to that of the random bond model, where points are joined randomly (with equal probability at all length scales) to have a given coordination, and then subsequently bonds are randomly removed.Comment: RevTeX 11 pages + epsfig embedded figures. Submitted to Phys. Rev.

First-order transition in small-world networks

The small-world transition is a first-order transition at zero density $p$ of shortcuts, whereby the normalized shortest-path distance undergoes a discontinuity in the thermodynamic limit. On finite systems the apparent transition is shifted by $\Delta p \sim L^{-d}$. Equivalently a ``persistence size'' $L^* \sim p^{-1/d}$ can be defined in connection with finite-size effects. Assuming $L^* \sim p^{-\tau}$, simple rescaling arguments imply that $\tau=1/d$. We confirm this result by extensive numerical simulation in one to four dimensions, and argue that $\tau=1/d$ implies that this transition is first-order.Comment: 4 pages, 3 figures, To appear in Europhysics Letter

Yard-Sale exchange on networks: Wealth sharing and wealth appropriation

Yard-Sale (YS) is a stochastic multiplicative wealth-exchange model with two phases: a stable one where wealth is shared, and an unstable one where wealth condenses onto one agent. YS is here studied numerically on 1d rings, 2d square lattices, and random graphs with variable average coordination, comparing its properties with those in mean field (MF). Equilibrium properties in the stable phase are almost unaffected by the introduction of a network. Measurement of decorrelation times in the stable phase allow us to determine the critical interface with very good precision, and it turns out to be the same, for all networks analyzed, as the one that can be analytically derived in MF. In the unstable phase, on the other hand, dynamical as well as asymptotic properties are strongly network-dependent. Wealth no longer condenses on a single agent, as in MF, but onto an extensive set of agents, the properties of which depend on the network. Connections with previous studies of coalescence of immobile reactants are discussed, and their analytic predictions are successfully compared with our numerical results.Comment: 10 pages, 7 figures. Submitted to JSTA

A qualitative examination of barriers against effective medical education and practices related to breastfeeding promotion and support in Lebanon.

Background: Insufficient breastfeeding promotion and support by physicians contribute to suboptimal breastfeeding rates globally. Understanding setting-specific barriers against breastfeeding promotion and support from the perspective of medical students and addressing those that can be modified through undergraduate medical education may help improve learning outcomes, medical practice, and ultimately health outcomes associated with breastfeeding.Objectives: We selected the underserved and under-supported public medical school in Lebanon to explore psychosocial, institutional, and societal barriers hindering effective preventative medicine practices using breastfeeding promotion and support as an exemplar case.Methods: One-on-one semi-structured interviews, each lasting around 60 min, were conducted with medical interns (in Med III and Med IV) at their training hospitals. Interviews were voice-recorded, transcribed verbatim, coded, and analyzed thematically based on Theory of Planned Behavior.Results: Interns (n= 49; 96% response rate) completed the study. Five major themes emerged addressing barriers at various levels. At the health care system level at large, interns identified the predominant focus on pathophysiology and treatment rather than on disease prevention and health promotion as a barrier. At the level of trainees and their education experiences, interns reported limited and optional clerkship training in obstetrics/gynecology and in neonatology which contributes to their insufficient knowledge and low self-efficacy. Competing financial interests from infant formula companies and social pressures to promote infant formula were identified as two main barriers at the level of physicians and clinical practice.Conclusions: Our work using breastfeeding as an exemplary case highlights how undergraduate medical education and its learning outcomes and how medical practices and patient behavior are highly intertwined with psychosocial, institutional, and social drivers and constraints. Re-evaluating the success of undergraduate medical curricula in light of overcoming these constraints and not only based on meeting national accreditation and certification guidelines might prove helpful in improving medical education and ultimately clinical practice

Spreading and shortest paths in systems with sparse long-range connections

Spreading according to simple rules (e.g. of fire or diseases), and shortest-path distances are studied on d-dimensional systems with a small density p per site of long-range connections (``Small-World'' lattices). The volume V(t) covered by the spreading quantity on an infinite system is exactly calculated in all dimensions. We find that V(t) grows initially as t^d/d for t>t^*$, generalizing a previous result in one dimension. Using the properties of V(t), the average shortest-path distance \ell(r) can be calculated as a function of Euclidean distance r. It is found that \ell(r) = r for r<r_c=(2p \Gamma_d (d-1)!)^{-1/d} log(2p \Gamma_d L^d), and \ell(r) = r_c for r>r_c. The characteristic length r_c, which governs the behavior of shortest-path lengths, diverges with system size for all p>0. Therefore the mean separation s \sim p^{-1/d} between shortcut-ends is not a relevant internal length-scale for shortest-path lengths. We notice however that the globally averaged shortest-path length, divided by L, is a function of L/s only.Comment: 4 pages, 1 eps fig. Uses psfi

Sliding Blocks Revisited: A simulational Study

A computational study of sliding blocks on inclined surfaces is presented. Assuming that the friction coefficient $\mu$ is a function of position, the probability $P(\lambda)$ for the block to slide down over a length $\lambda$ is numerically calculated. Our results are consistent with recent experimental data suggesting a power-law distribution of events over a wide range of displacements when the chute angle is close to the critical one, and suggest that the variation of $\mu$ along the surface is responsible for this.Comment: 6 pages, 4 figures. submitted to Int. J. Mod. Phys. (Proc. Brazilian Wokshop on Simulational Physics