Breakdown of disordered media by surface loads

We model an interface layer connecting two parts of a solid body by N parallel elastic springs connecting two rigid blocks. We load the system by a shear force acting on the top side. The springs have equal stiffness but are ruptured randomly when the load reaches a critical value. For the considered system, we calculate the shear modulus, G, as a function of the order parameter, \phi, describing the state of damage, and also the ``spalled'' material (burst) size distribution. In particular, we evaluate the relation between the damage parameter and the applied force and explore the behaviour in the vicinity of material breakdown. Using this simple model for material breakdown, we show that damage, caused by applied shear forces, is analogous to a first-order phase transition. The scaling behaviour of G with \phi is explored analytically and numerically, close to \phi=0 and \phi=1 and in the vicinity of \phi_c, when the shear load is close but below the threshold force that causes material breakdown. Our model calculation represents a first approximation of a system subject to wear induced loads.Comment: 15 pages, 7 figure

Single nucleotide polymorphisms for assessing genetic diversity in castor bean (Ricinus communis)

<p>Abstract</p> <p>Background</p> <p>Castor bean (<it>Ricinus communis</it>) is an agricultural crop and garden ornamental that is widely cultivated and has been introduced worldwide. Understanding population structure and the distribution of castor bean cultivars has been challenging because of limited genetic variability. We analyzed the population genetics of <it>R. communis </it>in a worldwide collection of plants from germplasm and from naturalized populations in Florida, U.S. To assess genetic diversity we conducted survey sequencing of the genomes of seven diverse cultivars and compared the data to a reference genome assembly of a widespread cultivar (Hale). We determined the population genetic structure of 676 samples using single nucleotide polymorphisms (SNPs) at 48 loci.</p> <p>Results</p> <p>Bayesian clustering indicated five main groups worldwide and a repeated pattern of mixed genotypes in most countries. High levels of population differentiation occurred between most populations but this structure was not geographically based. Most molecular variance occurred within populations (74%) followed by 22% among populations, and 4% among continents. Samples from naturalized populations in Florida indicated significant population structuring consistent with local demes. There was significant population differentiation for 56 of 78 comparisons in Florida (pairwise population ϕ_PTvalues, <it>p </it>< 0.01).</p> <p>Conclusion</p> <p>Low levels of genetic diversity and mixing of genotypes have led to minimal geographic structuring of castor bean populations worldwide. Relatively few lineages occur and these are widely distributed. Our approach of determining population genetic structure using SNPs from genome-wide comparisons constitutes a framework for high-throughput analyses of genetic diversity in plants, particularly in species with limited genetic diversity.</p

Body-assisted van der Waals interaction between two atoms

Using fourth-order perturbation theory, a general formula for the van der Waals potential of two neutral, unpolarized, ground-state atoms in the presence of an arbitrary arrangement of dispersing and absorbing magnetodielectric bodies is derived. The theory is applied to two atoms in bulk material and in front of a planar multilayer system, with special emphasis on the cases of a perfectly reflecting plate and a semi-infinite half space. It is demonstrated that the enhancement and reduction of the two-atom interaction due to the presence of a perfectly reflecting plate can be understood, at least in the nonretarded limit, by using the method of image charges. For the semi-infinite half space, both analytical and numerical results are presented.Comment: 17 pages, 9 figure

Rolling friction of a viscous sphere on a hard plane

A first-principle continuum-mechanics expression for the rolling friction coefficient is obtained for the rolling motion of a viscoelastic sphere on a hard plane. It relates the friction coefficient to the viscous and elastic constants of the sphere material. The relation obtained refers to the case when the deformation of the sphere $\xi$ is small, the velocity of the sphere $V$ is much less than the speed of sound in the material and when the characteristic time $\xi/V$ is much larger than the dissipative relaxation times of the viscoelastic material. To our knowledge this is the first ``first-principle'' expression of the rolling friction coefficient which does not contain empirical parameters.Comment: 6 pages, 2 figure

Anomalous density dependence of static friction in sand

We measured experimentally the static friction force $F_s$ on the surface of a glass rod immersed in dry sand. We observed that $F_s$ is extremely sensitive to the closeness of packing of grains. A linear increase of the grain-density yields to an exponentially increasing friction force. We also report on a novel periodicity of $F_s$ during gradual pulling out of the rod. Our observations demonstrate the central role of grain bridges and arches in the macroscopic properties of granular packings.Comment: plain tex, 6 pages, to appear in Phys.Rev.

Time-Resolved Studies of Stick-Slip Friction in Sheared Granular Layers

Sensitive and fast force measurements are performed on sheared granular layers undergoing stick-slip motion, along with simultaneous imaging. A full study has been done for spherical particles with a +-20% size distribution. Stick-slip motion due to repetitive fluidization of the layer occurs for low driving velocities. Between major slip events, slight creep occurs that is variable from one event to the next. The effects of changing the stiffness k and velocity V of the driving system are studied in detail. The stick-slip motion is almost periodic for spherical particles over a wide range of parameters, but becomes irregular when k is large and V is relatively small. At larger V, the motion becomes smoother and is affected by the inertia of the upper plate bounding the layer. Measurements of the period T and amplitude A of the relative motion are presented as a function of V. At a critical value Vc, a transition to continuous sliding motion occurs that is discontinuous for k not too large. The time dependence of the instantaneous velocity of the upper plate and the frictional force produced by the granular layer are determined within individual slipping events. The force is a multi-valued function of the instantaneous velocity, with pronounced hysteresis and a sudden drop prior to resticking. Measurements of vertical displacement reveal a small dilation of the material (about one tenth of the mean particle size in a layer 20 particles deep) associated with each slip event. Finally, optical imaging reveals that localized microscopic rearrangements precede (and follow) each slip event. The behavior of smooth particles is contrasted with that of rough particles.Comment: 20, pages, 17 figures, to appear in Phys. Rev.

Castor bean organelle genome sequencing and worldwide genetic diversity analysis

Castor bean is an important oil-producing plant in the Euphorbiaceae family. Its high-quality oil contains up to 90% of the unusual fatty acid ricinoleate, which has many industrial and medical applications. Castor bean seeds also contain ricin, a highly toxic Type 2 ribosome-inactivating protein, which has gained relevance in recent years due to biosafety concerns. In order to gain knowledge on global genetic diversity in castor bean and to ultimately help the development of breeding and forensic tools, we carried out an extensive chloroplast sequence diversity analysis. Taking advantage of the recently published genome sequence of castor bean, we assembled the chloroplast and mitochondrion genomes extracting selected reads from the available whole genome shotgun reads. Using the chloroplast reference genome we used the methylation filtration technique to readily obtain draft genome sequences of 7 geographically and genetically diverse castor bean accessions. These sequence data were used to identify single nucleotide polymorphism markers and phylogenetic analysis resulted in the identification of two major clades that were not apparent in previous population genetic studies using genetic markers derived from nuclear DNA. Two distinct sub-clades could be defined within each major clade and large-scale genotyping of castor bean populations worldwide confirmed previously observed low levels of genetic diversity and showed a broad geographic distribution of each sub-clade

Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems