Granular flow down a rough inclined plane: transition between thin and thick piles

The rheology of granular particles in an inclined plane geometry is studied using molecular dynamics simulations. The flow--no-flow boundary is determined for piles of varying heights over a range of inclination angles $\theta$. Three angles determine the phase diagram: $\theta_{r}$, the angle of repose, is the angle at which a flowing system comes to rest; $\theta_{m}$, the maximum angle of stability, is the inclination required to induce flow in a static system; and $\theta_{max}$ is the maximum angle for which stable, steady state flow is observed. In the stable flow region $\theta_{r}<\theta<\theta_{max}$, three flow regimes can be distinguished that depend on how close $\theta$ is to $\theta_{r}$: i) $\theta>>\theta_{r}$: Bagnold rheology, characterized by a mean particle velocity $v_{x}$ in the direction of flow that scales as $v_{x}\propto h^{3/2}$, for a pile of height $h$, ii) $\theta\gtrsim\theta_{r}$: the slow flow regime, characterized by a linear velocity profile with depth, and iii) $\theta\approx\theta_{r}$: avalanche flow characterized by a slow underlying creep motion combined with occasional free surface events and large energy fluctuations. We also probe the physics of the initiation and cessation of flow. The results are compared to several recent experimental studies on chute flows and suggest that differences between measured velocity profiles in these experiments may simply be a consequence of how far the system is from jamming.Comment: 19 pages, 14 figs, submitted to Physics of Fluid

Fractal dimensions of jammed packings with power-law particle size distributions in two and three dimensions

Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent $-\beta$. The static structure factor exhibits diverging power-law behavior for small wavenumbers, allowing us to identify a structural fractal dimension, $d_f$. In three dimensions, $d_f \approx 2.0$ for $2.5 \le \beta \le 3.8$, such that each of the structure factors can be collapsed onto a universal curve. In two dimensions, we instead find $1.0 \lesssim d_f \lesssim 1.34$ for $2.1 \le \beta \le 2.9$. Furthermore, we show that the fractal behavior persists when rattler particles are removed, indicating that the long wavelength structural properties of the packings are controlled by the large particle backbone conferring mechanical rigidity to the system. A numerical scheme for computing structure factors for triclinic unit cells is presented and employed to analyze the jammed packings.Comment: 5 figures, 1 tabl

Density of states in random lattices with translational invariance

We propose a random matrix approach to describe vibrational excitations in disordered systems. The dynamical matrix M is taken in the form M=AA^T where A is some real (not generally symmetric) random matrix. It guaranties that M is a positive definite matrix which is necessary for mechanical stability of the system. We built matrix A on a simple cubic lattice with translational invariance and interaction between nearest neighbors. We found that for certain type of disorder phonons cannot propagate through the lattice and the density of states g(w) is a constant at small w. The reason is a breakdown of affine assumptions and inapplicability of the elasticity theory. Young modulus goes to zero in the thermodynamic limit. It strongly reminds of the properties of a granular matter at the jamming transition point. Most of the vibrations are delocalized and similar to diffusons introduced by Allen, Feldman et al., Phil. Mag. B v.79, 1715 (1999).Comment: 4 pages, 5 figure

Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder

We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each configuration, there is a unique jamming threshold, $\phi_c$, at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become non-zero. The distribution of $\phi_c$ values becomes narrower as the system size increases, so that essentially all configurations jam at the same $\phi$ in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. In fact, our results provide a well-defined meaning for "random close-packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, Point J, occurring at zero temperature and applied stress and at the random close-packing density, has properties reminiscent of an ordinary critical point. As Point J is approached from higher packing fractions, power-law scaling is found for many quantities. Moreover, near Point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, Point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. All of these results suggest that Point J may control behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure

Long-ranged attraction between disordered heterogeneous surfaces

Long-ranged attractions across water between two surfaces that are randomly covered with (mobile) positive and negative charge domains have been attributed to induced correlation of the charges (positive lining up with negative) as the surfaces approach. Here we show, by directly measuring normal forces under a rapid shear field, that these attractions may not in fact be due to such correlations. It is rather the inherent interaction-asymmetry between equally- and between oppositely-charged domains that results in the long-ranged attraction even in the complete absence of any charge correlation

On the study of jamming percolation

We investigate kinetically constrained models of glassy transitions, and determine which model characteristics are crucial in allowing a rigorous proof that such models have discontinuous transitions with faster than power law diverging length and time scales. The models we investigate have constraints similar to that of the knights model, introduced by Toninelli, Biroli, and Fisher (TBF), but differing neighbor relations. We find that such knights-like models, otherwise known as models of jamming percolation, need a ``No Parallel Crossing'' rule for the TBF proof of a glassy transition to be valid. Furthermore, most knight-like models fail a ``No Perpendicular Crossing'' requirement, and thus need modification to be made rigorous. We also show how the ``No Parallel Crossing'' requirement can be used to evaluate the provable glassiness of other correlated percolation models, by looking at models with more stable directions than the knights model. Finally, we show that the TBF proof does not generalize in any straightforward fashion for three-dimensional versions of the knights-like models.Comment: 13 pages, 18 figures; Spiral model does satisfy property

The Vaginal Microbiome: Disease, Genetics and the Environment

The vagina is an interactive interface between the host and the environment. Its surface is covered by a protective epithelium colonized by bacteria and other microorganisms. The ectocervix is nonsterile, whereas the endocervix and the upper genital tract are assumed to be sterile in healthy women. Therefore, the cervix serves a pivotal role as a gatekeeper to protect the upper genital tract from microbial invasion and subsequent reproductive pathology. Microorganisms that cross this barrier can cause preterm labor, pelvic inflammatory disease, and other gynecologic and reproductive disorders. Homeostasis of the microbiome in the vagina and ectocervix plays a paramount role in reproductive health. Depending on its composition, the microbiome may protect the vagina from infectious or non-infectious diseases, or it may enhance its susceptibility to them. Because of the nature of this organ, and the fact that it is continuously colonized by bacteria from birth to death, it is virtually certain that this rich environment evolved in concert with its microbial flora. Specific interactions dictated by the genetics of both the host and microbes are likely responsible for maintaining both the environment and the microbiome. However, the genetic basis of these interactions in both the host and the bacterial colonizers is currently unknown. _Lactobacillus_ species are associated with vaginal health, but the role of these species in the maintenance of health is not yet well defined. Similarly, other species, including those representing minor components of the overall flora, undoubtedly influence the ability of potential pathogens to thrive and cause disease. Gross alterations in the vaginal microbiome are frequently observed in women with bacterial vaginosis, but the exact etiology of this disorder is still unknown. There are also implications for vaginal flora in non-infectious conditions such as pregnancy, pre-term labor and birth, and possibly fertility and other aspects of women&#x2019;s health. Conversely, the role of environmental factors in the maintenance of a healthy vaginal microbiome is largely unknown. To explore these issues, we have proposed to address the following questions:&#xd;&#xa;&#xd;&#xa;*1.&#x9;Do the genes of the host contribute to the composition of the vaginal microbiome?* We hypothesize that genes of both host and bacteria have important impacts on the vaginal microbiome. We are addressing this question by examining the vaginal microbiomes of mono- and dizygotic twin pairs selected from the over 170,000 twin pairs in the Mid-Atlantic Twin Registry (MATR). Subsequent studies, beyond the scope of the current project, may investigate which host genes impact the microbial flora and how they do so.&#xd;&#xa;*2.&#x9;What changes in the microbiome are associated with common non-infectious pathological states of the host?* We hypothesize that altered physiological (e.g., pregnancy) and pathologic (e.g., immune suppression) conditions, or environmental exposures (e.g., antibiotics) predictably alter the vaginal microbiome. Conversely, certain vaginal microbiome characteristics are thought to contribute to a woman&#x2019;s risk for outcomes such as preterm delivery. We are addressing this question by recruiting study participants from the ~40,000 annual clinical visits to women&#x2019;s clinics of the VCU Health System.&#xd;&#xa;*3.&#x9;What changes in the vaginal microbiome are associated with relevant infectious diseases and conditions?* We hypothesize that susceptibility to infectious disease (e.g. HPV, _Chlamydia_ infection, vaginitis, vaginosis, etc.) is impacted by the vaginal microbiome. In turn, these infectious conditions clearly can affect the ability of other bacteria to colonize and cause pathology. Again, we are exploring these issues by recruiting participants from visitors to women&#x2019;s clinics in the VCU Health System.&#xd;&#xa;&#xd;&#xa;Three kinds of sequence data are generated in this project: i) rDNA sequences from vaginal microbes; ii) whole metagenome shotgun sequences from vaginal samples; and iii) whole genome shotgun sequences of bacterial clones selected from vaginal samples. The study includes samples from three vaginal sites: mid-vaginal, cervical, and introital. The data sets also include buccal and perianal samples from all twin participants. Samples from these additional sites are used to test the hypothesis of a per continuum spread of bacteria in relation to vaginal health. An extended set of clinical metadata associated with these sequences are deposited with dbGAP. We have currently collected over 4,400 samples from ~100 twins and over 450 clinical participants. We have analyzed and deposited data for 480 rDNA samples, eight whole metagenome shotgun samples, and over 50 complete bacterial genomes. These data are available to accredited investigators according to NIH and Human Microbiome Project (HMP) guidelines. The bacterial clones are deposited in the Biodefense and Emerging Infections Research Resources Repository (&#x22;http://www.beiresources.org/&#x22;:http://www.beiresources.org/). &#xd;&#xa;&#xd;&#xa;In addition to the extensive sequence data obtained in this study, we are collecting metadata associated with each of the study participants. Thus, participants are asked to complete an extensive health history questionnaire at the time samples are collected. Selected clinical data associated with the visit are also obtained, and relevant information is collected from the medical records when available. This data is maintained securely in a HIPAA-compliant data system as required by VCU&#x2019;s Institutional Review Board (IRB). The preponderance of these data (i.e., that judged appropriate by NIH staff and VCU&#x2019;s IRB are deposited at dbGAP (&#x22;http://www.ncbi.nlm.nih.gov/gap&#x22;:http://www.ncbi.nlm.nih.gov/gap). Selected fields of this data have been identified by NIH staff as &#x2018;too sensitive&#x2019; and are not available in dbGAP. Individuals requiring access to these data fields are asked to contact the PI of this project or NIH Program Staff. &#xd;&#xa

Sparse random matrices and vibrational spectra of amorphous solids

A random matrix approach is used to analyze the vibrational properties of amorphous solids. We investigated a dynamical matrix M=AA^T with non-negative eigenvalues. The matrix A is an arbitrary real NxN sparse random matrix with n independent non-zero elements in each row. The average values =0 and dispersion =V^2 for all non-zero elements. The density of vibrational states g(w) of the matrix M for N,n >> 1 is given by the Wigner quarter circle law with radius independent of N. We argue that for n^2 << N this model can be used to describe the interaction of atoms in amorphous solids. The level statistics of matrix M is well described by the Wigner surmise and corresponds to repulsion of eigenfrequencies. The participation ratio for the major part of vibrational modes in three dimensional system is about 0.2 - 0.3 and independent of N. Together with term repulsion it indicates clearly to the delocalization of vibrational excitations. We show that these vibrations spread in space by means of diffusion. In this respect they are similar to diffusons introduced by Allen, Feldman, et al., Phil. Mag. B 79, 1715 (1999) in amorphous silicon. Our results are in a qualitative and sometimes in a quantitative agreement with molecular dynamic simulations of real and model glasses.Comment: 24 pages, 7 figure