The Behavior of Granular Materials under Cyclic Shear

The design and development of a parallel plate shear cell for the study of large scale shear flows in granular materials is presented. The parallel plate geometry allows for shear studies without the effects of curvature found in the more common Couette experiments. A system of independently movable slats creates a well with side walls that deform in response to the motions of grains within the pack. This allows for true parallel plate shear with minimal interference from the containing geometry. The motions of the side walls also allow for a direct measurement of the velocity profile across the granular pack. Results are presented for applying this system to the study of transients in granular shear and for shear-induced crystallization. Initial shear profiles are found to vary from packing to packing, ranging from a linear profile across the entire system to an exponential decay with a width of approximately 6 bead diameters. As the system is sheared, the velocity profile becomes much sharper, resembling an exponential decay with a width of roughly 3 bead diameters. Further shearing produces velocity profiles which can no longer be fit to an exponential decay, but are better represented as a Gaussian decay or error function profile. Cyclic shear is found to produce large scale ordering of the granular pack, which has a profound impact on the shear profile. There exist periods of time in which there is slipping between layers as well as periods of time in which the layered particles lock together resulting in very little relative motion.Comment: 10 pages including 12 figure

Unusual thermoelectric behavior of packed crystalline granular metals

Loosely packed granular materials are intensively studied nowadays. Electrical and thermal transport properties should reflect the granular structure as well as intrinsic properties. We have compacted crystalline $CaAl$ based metallic grains and studied the electrical resistivity and the thermoelectric power as a function of temperature ($T$) from 15 to 300K. Both properties show three regimes as a function of temperature. It should be pointed out : (i) The electrical resistivity continuously decreases between 15 and 235 K (ii) with various dependences, e.g. $\simeq$ $T^{-3/4}$ at low $T$, while (iii) the thermoelectric power (TEP) is positive, (iv) shows a bump near 60K, and (v) presents a rather unusual square root of temperature dependence at low temperature. It is argued that these three regimes indicate a competition between geometric and thermal processes, - for which a theory seems to be missing in the case of TEP. The microchemical analysis results are also reported indicating a complex microstructure inherent to the phase diagram peritectic intricacies of this binary alloy.Comment: to be published in J. Appl. Phys.22 pages, 8 figure

Assortative mixing in close-packed spatial networks

Background In recent years, there is aroused interest in expressing complex systems as networks of interacting nodes. Using descriptors from graph theory, it has been possible to classify many diverse systems derived from social and physical sciences alike. In particular, folded proteins as examples of self-assembled complex molecules have also been investigated intensely using these tools. However, we need to develop additional measures to classify different systems, in order to dissect the underlying hierarchy. Methodology and Principal Findings In this study, a general analytical relation for the dependence of nearest neighbor degree correlations on degree is derived. Dependence of local clustering on degree is shown to be the sole determining factor of assortative versus disassortative mixing in networks. The characteristics of networks constructed from spatial atomic/molecular systems exemplified by self-organized residue networks built from folded protein structures and block copolymers, atomic clusters and well-compressed polymeric melts are studied. Distributions of statistical properties of the networks are presented. For these densely-packed systems, assortative mixing in the network construction is found to apply, and conditions are derived for a simple linear dependence. Conclusions Our analyses (i) reveal patterns that are common to close-packed clusters of atoms/molecules, (ii) identify the type of surface effects prominent in different close-packed systems, and (iii) associate fingerprints that may be used to classify networks with varying types of correlations

Fragility and hysteretic creep in frictional granular jamming

The granular jamming transition is experimentally investigated in a two-dimensional system of frictional, bi-dispersed disks subject to quasi-static, uniaxial compression at zero granular temperature. Currently accepted results show the jamming transition occurs at a critical packing fraction $\phi_c$. In contrast, we observe the first compression cycle exhibits {\it fragility} - metastable configuration with simultaneous jammed and un-jammed clusters - over a small interval in packing fraction ($\phi_1 < \phi < \phi_2$). The fragile state separates the two conditions that define $\phi_c$ with an exponential rise in pressure starting at $\phi_1$ and an exponential fall in disk displacements ending at $\phi_2$. The results are explained through a percolation mechanism of stressed contacts where cluster growth exhibits strong spatial correlation with disk displacements. Measurements with several disk materials of varying elastic moduli $E$ and friction coefficients $\mu$, show friction directly controls the start of the fragile state, but indirectly controls the exponential slope. Additionally, we experimentally confirm recent predictions relating the dependence of $\phi_c$ on $\mu$. Under repetitive loading (compression), the system exhibits hysteresis in pressure, and the onset $\phi_c$ increases slowly with repetition number. This friction induced hysteretic creep is interpreted as the granular pack's evolution from a metastable to an eventual structurally stable configuration. It is shown to depend upon the quasi-static step size $\Delta \phi$ which provides the only perturbative mechanism in the experimental protocol, and the friction coefficient $\mu$ which acts to stabilize the pack.Comment: 12 pages, 10 figure

Power-law distributions for the areas of the basins of attraction on a potential energy landscape

Energy landscape approaches have become increasingly popular for analysing a wide variety of chemical physics phenomena. Basic to many of these applications has been the inherent structure mapping, which divides up the potential energy landscape into basins of attraction surrounding the minima. Here, we probe the nature of this division by introducing a method to compute the basin area distribution and applying it to some archetypal supercooled liquids. We find that this probability distribution is a power law over a large number of decades with the lower-energy minima having larger basins of attraction. Interestingly, the exponent for this power law is approximately the same as that for a high-dimensional Apollonian packing, providing further support for the suggestion that there is a strong analogy between the way the energy landscape is divided into basins, and the way that space is packed in self-similar, space-filling hypersphere packings, such as the Apollonian packing. These results suggest that the basins of attraction provide a fractal-like tiling of the energy landscape, and that a scale-free pattern of connections between the minima is a general property of energy landscapes.Comment: 4 pages, 3 figure

Chaotic Mixing in Three Dimensional Porous Media

Under steady flow conditions, the topological complexity inherent to all random 3D porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a three-dimensional (3D) fluid mechanical analogue of the baker's map which rapidly accelerates scalar mixing in the presence of molecular diffusion. Hence pore-scale fluid mixing is governed by the interplay between chaotic advection, molecular diffusion and the broad (power-law) distribution of fluid particle travel times which arise from the non-slip condition at pore walls. To understand and quantify mixing in 3D porous media, we consider these processes in a model 3D open porous network and develop a novel stretching continuous time random walk (CTRW) which provides analytic estimates of pore-scale mixing which compare well with direct numerical simulations. We find that chaotic advection inherent to 3D porous media imparts scalar mixing which scales exponentially with longitudinal advection, whereas the topological constraints associated with 2D porous media limits mixing to scale algebraically. These results decipher the role of wide transit time distributions and complex topologies on porous media mixing dynamics, and provide the building blocks for macroscopic models of dilution and mixing which resolve these mechanisms.Comment: 36 page

A Latent Parameter Node-Centric Model for Spatial Networks

Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological interactions between users, but spatial interactions as well. The defining property of spatial networks is that edge distances are associated with a cost, which may subtly influence the topology of the network. However, the cost function over distance is rarely known, thus developing a model of connections in spatial networks is a difficult task. In this paper, we introduce a novel model for capturing the interaction between spatial effects and network structure. Our approach represents a unique combination of ideas from latent variable statistical models and spatial network modeling. In contrast to previous work, we view the ability to form long/short-distance connections to be dependent on the individual nodes involved. For example, a node's specific surroundings (e.g. network structure and node density) may make it more likely to form a long distance link than other nodes with the same degree. To capture this information, we attach a latent variable to each node which represents a node's spatial reach. These variables are inferred from the network structure using a Markov Chain Monte Carlo algorithm. We experimentally evaluate our proposed model on 4 different types of real-world spatial networks (e.g. transportation, biological, infrastructure, and social). We apply our model to the task of link prediction and achieve up to a 35% improvement over previous approaches in terms of the area under the ROC curve. Additionally, we show that our model is particularly helpful for predicting links between nodes with low degrees. In these cases, we see much larger improvements over previous models

Statistical Analysis of Bus Networks in India

Through the past decade the field of network science has established itself as a common ground for the cross-fertilization of exciting inter-disciplinary studies which has motivated researchers to model almost every physical system as an interacting network consisting of nodes and links. Although public transport networks such as airline and railway networks have been extensively studied, the status of bus networks still remains in obscurity. In developing countries like India, where bus networks play an important role in day-to-day commutation, it is of significant interest to analyze its topological structure and answer some of the basic questions on its evolution, growth, robustness and resiliency. In this paper, we model the bus networks of major Indian cities as graphs in \textit{L}-space, and evaluate their various statistical properties using concepts from network science. Our analysis reveals a wide spectrum of network topology with the common underlying feature of small-world property. We observe that the networks although, robust and resilient to random attacks are particularly degree-sensitive. Unlike real-world networks, like Internet, WWW and airline, which are virtual, bus networks are physically constrained. The presence of various geographical and economic constraints allow these networks to evolve over time. Our findings therefore, throw light on the evolution of such geographically and socio-economically constrained networks which will help us in designing more efficient networks in the future.Comment: Submitted to PLOS ON