Jamming Criticality Revealed by Removing Localized Buckling Excitations

Recent theoretical advances offer an exact, first-principle theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small inter-particle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the inter-particle gaps is known to be constant in all spatial dimensions $d$ -- including the physically relevant $d=2$ and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.Comment: 12 pages, 4 figure

High mortality associated with an outbreak of hepatitis E among displaced persons in Darfur, Sudan

BACKGROUND: Hepatitis E virus (HEV) causes acute onset of jaundice and a high case-fatality ratio in pregnant women. We provide a clinical description of hospitalized case patients and assess the specific impact on pregnant women during a large epidemic of HEV infection in a displaced population in Mornay camp (78,800 inhabitants), western Darfur, Sudan. METHODS: We reviewed hospital records. A sample of 20 clinical cases underwent laboratory confirmation. These patients were tested for immunoglobulin G (IgG) and immunoglobulin M (IgM) antibody to HEV (serum) and for amplification of the HEV genome (serum and stool). We performed a cross-sectional survey in the community to determine the attack rate and case-fatality ratio in pregnant women. RESULTS: Over 6 months, 253 HEV cases were recorded at the hospital, of which 61 (24.1%) were in pregnant women. A total of 72 cases (39.1% of those for whom clinical records were available) had a diagnosis of hepatic encephalopathy. Of the 45 who died (case-fatality ratio, 17.8%), 19 were pregnant women (specific case-fatality ratio, 31.1%). Acute hepatitis E was confirmed in 95% (19/20) of cases sampled; 18 case-patients were positive for IgG (optical density ratio > or =3), for IgM (optical density ratio >2 ), or for both, whereas 1 was negative for IgG and IgM but positive for HEV RNA in serum. The survey identified 220 jaundiced women among the 1133 pregnant women recorded over 3 months (attack rate, 19.4%). A total of 18 deaths were recorded among these jaundiced pregnant women (specific case-fatality ratio, 8.2%). CONCLUSIONS: This large epidemic of HEV infection illustrates the dramatic impact of this disease on pregnant women. Timely interventions and a vaccine are urgently needed to prevent mortality in this special group

A Sublinear Variance Bound for Solutions of a Random Hamilton Jacobi Equation

We estimate the variance of the value function for a random optimal control problem. The value function is the solution $w^\epsilon$ of a Hamilton-Jacobi equation with random Hamiltonian $H(p,x,\omega) = K(p) - V(x/\epsilon,\omega)$ in dimension $d \geq 2$. It is known that homogenization occurs as $\epsilon \to 0$, but little is known about the statistical fluctuations of $w^\epsilon$. Our main result shows that the variance of the solution $w^\epsilon$ is bounded by $O(\epsilon/|\log \epsilon|)$. The proof relies on a modified Poincar\'e inequality of Talagrand

From interacting particle systems to random matrices

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. Some of the fluctuation laws were first discovered in random matrix models. Moreover, the limit process for curved limit shape turned out to show up in a dynamical version of hermitian random matrices, but this analogy does not extend to the case of symmetric matrices. Therefore the connections between growth models and random matrices is only partial.Comment: 18 pages, 8 figures; Contribution to StatPhys24 special issue; minor corrections in scaling of section 2.

Structure of marginally jammed polydisperse packings of frictionless spheres

We model the packing structure of a marginally jammed bulk ensemble of polydisperse spheres. To this end we expand on the granocentric model [Clusel et al., Nature (London) 460, 611 (2009)], explicitly taking into account rattlers. This leads to a relationship between the characteristic parameters of the packing, such as the mean number of neighbors and the fraction of rattlers, and the radial distribution function g(r). We find excellent agreement between the model predictions for g(r) and packing simulations, as well as experiments on jammed emulsion droplets. The observed quantitative agreement opens the path towards a full structural characterization of jammed particle systems for imaging and scattering experiments

A class of Poisson-Nijenhuis structures on a tangent bundle

Equipping the tangent bundle TQ of a manifold with a symplectic form coming from a regular Lagrangian L, we explore how to obtain a Poisson-Nijenhuis structure from a given type (1,1) tensor field J on Q. It is argued that the complete lift of J is not the natural candidate for a Nijenhuis tensor on TQ, but plays a crucial role in the construction of a different tensor R, which appears to be the pullback under the Legendre transform of the lift of J to co-tangent manifold of Q. We show how this tangent bundle view brings new insights and is capable also of producing all important results which are known from previous studies on the cotangent bundle, in the case that Q is equipped with a Riemannian metric. The present approach further paves the way for future generalizations.Comment: 22 page

Free-energy distribution of the directed polymer at high temperature

We study the directed polymer of length $t$ in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods. The universal regime of high temperature $T$ is described, upon scaling 'time' $t \sim T^5/\kappa$ and space $x = T^3/\kappa$ (with $\kappa=T$ for the discrete model) by a continuum model with $\delta$-function disorder correlation. Using the Bethe Ansatz solution for the attractive boson problem, we obtain all positive integer moments of the partition function. The lowest cumulants of the free energy are predicted at small time and found in agreement with numerics. We then obtain the exact expression at any time for the generating function of the free energy distribution, in terms of a Fredholm determinant. At large time we find that it crosses over to the Tracy Widom distribution (TW) which describes the fixed $T$ infinite $t$ limit. The exact free energy distribution is obtained for any time and compared with very recent results on growth and exclusion models.Comment: 6 pages, 3 figures large time limit corrected and convergence to Tracy Widom established, 1 figure changed