Jamming II: Edwards' statistical mechanics of random packings of hard spheres

The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. This problem finds applications spanning from the mathematician's pencil, the processing of granular materials, the jamming and glass transitions, all the way to fruit packing in every grocery. There are presently numerous experiments showing that the loosest way to pack spheres gives a density of ~55% (RLP) while filling all the loose voids results in a maximum density of ~63-64% (RCP). While those values seem robustly true, to this date there is no physical explanation or theoretical prediction for them. Here we show that random packings of monodisperse hard spheres in 3d can pack between the densities 4/(4 + 2 \sqrt 3) or 53.6% and 6/(6 + 2 \sqrt 3) or 63.4%, defining RLP and RCP, respectively. The reason for these limits arises from a statistical picture of jammed states in which the RCP can be interpreted as the ground state of the ensemble of jammed matter with zero compactivity, while the RLP arises in the infinite compactivity limit. We combine an extended statistical mechanics approach 'a la Edwards' (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. Ultimately, our results lead to a phase diagram that provides a unifying view of the disordered hard sphere packing problem.Comment: 55 pages, 19 figures, C. Song, P. Wang, H. A. Makse, A phase diagram for jammed matter, Nature 453, 629-632 (2008

PUCM Practice Development Programme (PDP): February 2005

The purpose of this report is to identify a Practice Development Programme (PDP) for the presentation of relevant innovative practices and tools arising out of the first two Phases of PUCM (Planning Under Co-operative Mandates). During Phase 3 of the research (2004-2006) the PDP will be extended as new findings come to hand

UK energy strategies under uncertainty: synthesis report

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Collaborative Communication And Storage In Energy-Synchronized Sensor Networks

In a battery-less sensor network, all the operation of sensor nodes are strictly constrained by and synchronized with the fluctuations of harvested energy, causing nodes to be disruptive from network and hence unstable network connectivity. Such wireless sensor network is named as energy-synchronized sensor networks. The unpredictable network disruptions and challenging communication environments make the traditional communication protocols inefficient and require a new paradigm-shift in design. In this thesis, I propose a set of algorithms on collaborative data communication and storage for energy-synchronized sensor networks. The solutions are based on erasure codes and probabilistic network codings. The proposed set of algorithms significantly improve the data communication throughput and persistency, and they are inherently amenable to probabilistic nature of transmission in wireless networks. The technical contributions explore collaborative communication with both no coding and network coding methods. First, I propose a collaborative data delivery protocol to exploit the optimal performance of multiple energy-synchronized paths without network coding, i.e. a new max-flow min-variance algorithm. In consort with this data delivery protocol, a localized TDMA MAC protocol is designed to synchronize nodes\u27 duty-cycles and mitigate media access contentions. However, the energy supply can change dynamically over time, making determined duty cycles synchronization difficult in practice. A probabilistic approach is investigated. Therefore, I present Opportunistic Network Erasure Coding protocol (ONEC), to collaboratively collect data. ONEC derives the probability distribution of coding degree in each node and enable opportunistic in-network recoding, and guarantee the recovery of original sensor data can be achieved with high probability upon receiving any sufficient amount of encoded packets. Next, OnCode, an opportunistic in-network data coding and delivery protocol is proposed to further improve data communication under the constraints of energy synchronization. It is resilient to packet loss and network disruptions, and does not require explicit end-to-end feedback message. Moreover, I present a network Erasure Coding with randomized Power Control (ECPC) mechanism for collaborative data storage in disruptive sensor networks. ECPC only requires each node to perform a single broadcast at each of its several randomly selected power levels. Thus it incurs very low communication overhead. Finally, I propose an integrated algorithm and middleware (Ravine Stream) to improve data delivery throughput as well as data persistency in energy-synchronized sensor network

Perfect Matchings, Tilings and Hamilton Cycles in Hypergraphs

This thesis contains problems in finding spanning subgraphs in graphs, such as, perfect matchings, tilings and Hamilton cycles. First, we consider the tiling problems in graphs, which are natural generalizations of the matching problems. We give new proofs of the multipartite Hajnal-Szemeredi Theorem for the tripartite and quadripartite cases. Second, we consider Hamilton cycles in hypergraphs. In particular, we determine the minimum codegree thresholds for Hamilton l-cycles in large k-uniform hypergraphs for l less than k/2. We also determine the minimum vertex degree threshold for loose Hamilton cycle in large 3-uniform hypergraphs. These results generalize the well-known theorem of Dirac for graphs. Third, we determine the minimum codegree threshold for near perfect matchings in large k-uniform hypergraphs, thereby confirming a conjecture of Rodl, Rucinski and Szemeredi. We also show that the decision problem on whether a k-uniform hypergraph with certain minimum codegree condition contains a perfect matching can be solved in polynomial time, which solves a problem of Karpinski, Rucinski and Szymanska completely. At last, we determine the minimum vertex degree threshold for perfect tilings of C_4^3 in large 3-uniform hypergraphs, where C_4^3 is the unique 3-uniform hypergraph on four vertices with two edges

Soil Chemical Properties Under Conservation Agriculture and Cereal-Based Cropping System in Eastern Tarai of Nepal

Field experiments were conducted for four years (2014-2017) at five locations namely Salbani, Bhokraha, Simariya, Bhaluwa and Kaptanganj of Sunsari district to assess the changes in soil chemical properties under conservation agriculture (CA)-based practices in two cropping systems namely rice-kidney bean-maize at Salbani and rice-wheat at rest of the locations. In rice-wheat cropping system, there were four treatments: (1) conventional tillage (CT) for rice transplantation and subsequent wheat sowing, (2) conventional tillage rice transplantation followed by zero tillage (ZT) wheat, (3) unpuddled rice transplantation followed by zero tillage wheat, (4) zero tillage in both rice and wheat. Similarly, in rice-kidney bean-maize cropping system, there were four treatments; (1) conventional tillage for rice transplantation and sowing of both kidney bean and maize, (2) conventional tillage rice transplantation followed by zero tillage in both kidney bean and maize, (3) unpuddled rice transplantation followed by zero tillage in both kidney bean and maize, (4) zero tillage in all three crops. Soil samples were taken at initial and every year after rice harvest.The soil samples were analyzed for total nitrogen, available phosphorus, available potassium, pH and soil organic matter.Total nitrogen (N) showed a slightly decreasing trend in the first three years and showed a slight increase at the end of experiment under ZT in all locations. The total N under ZT changed from 0.12 to 0.13%, 0.05 to 0.06%, 0.10 to 0.12%, 0.11 to 0.08% and 0.09 to 0.13% in Salbani, Bhokraha, Simariya, Bhaluwa and Kaptanganj, respectively.  All locations showed the positive values of available potassium; Salbani  revealing considerable change of 64.3 to 78.5 mg/kg in CT while 68.4 to 73.3 mg/kg in ZT condition. The treatment where rice was transplanted in unpuddled condition and zero tilled to wheat, had a mean value of available phosphorus and potassium as 87.3 and 81.9 mg/kg respectively. Soil pH ranged from 4.8 to 7.1 in CT while it was 5.2 to 6.8 in ZT across the locations. The change in soil organic matter in CT of all locations except Salbani was narrower as compared to ZT

An Energy-Efficient Distributed Algorithm for k-Coverage Problem in Wireless Sensor Networks

Wireless sensor networks (WSNs) have recently achieved a great deal of attention due to its numerous attractive applications in many different fields. Sensors and WSNs possesses a number of special characteristics that make them very promising in many applications, but also put on them lots of constraints that make issues in sensor network particularly difficult. These issues may include topology control, routing, coverage, security, and data management. In this thesis, we focus our attention on the coverage problem. Firstly, we define the Sensor Energy-efficient Scheduling for k-coverage (SESK) problem. We then solve it by proposing a novel, completely localized and distributed scheduling approach, naming Distributed Energy-efficient Scheduling for k-coverage (DESK) such that the energy consumption among all the sensors is balanced, and the network lifetime is maximized while still satisfying the k-coverage requirement. Finally, in related work section we conduct an extensive survey of the existing work in literature that focuses on with the coverage problem

A microwave dielectric biosensor based on suspended distributed MEMS transmission lines

Design and characterization of a miniature microwave dielectric biosensor based on distributed microelectromechanical systems (MEMS) transmission lines (DMTL) is reported in this paper. The biosensor has been realized by bonding the DMTL device with an acrylic fluidic channel. In order to demonstrate the sensing mechanism, the sensor is used to detect the small variation of the concentration of aqueous glucose solutions by measuring the electromagnetic resonant frequency shift of the device. It is observed from the results that the second notch of the reflection coefficient (S-11) varies from 7.66 to 7.93 GHz and the third notch of the reflection coefficient varies from 15.81 to 15.24 GHz when the concentration of the glucose solution ranges from 0 to 347 mg/ml, which indicates that higher order notches have higher sensitivities if looking at the absolute change in frequency