Percolation and connectivity in AB random geometric graphs

Given two independent Poisson point processes Phi((1)), Phi((2)) in R-d, the AB Poisson Boolean model is the graph with the points of Phi((1)) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centered at these points contains at least one point of Phi((2)). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolation for all d >= 2 and derive bounds fora critical intensity. We also provide a characterization for this critical intensity when d = 2. To study the connectivity problem, we consider independent Poisson point processes of intensities n and tau n in the unit cube. The AB random geometric graph is defined as above but with balls of radius r. We derive a weak law result for the largest nearest-neighbor distance and almost-sure asymptotic bounds for the connectivity threshold.

Texture and Microstructural Evolution in Pearlitic Steel During Triaxial Compression

This article presents the deformation behavior of high-strength pearlitic steel deformed by triaxial compression to achieve ultra-fine ferrite grain size with fragmented cementite. The consequent evolution of microstructure and texture has been studied using scanning electron microscopy, electron back-scatter diffraction, and X-ray diffraction. The synergistic effect of diffusion and deformation leads to the uniform dissolution of cementite at higher temperature. At lower temperature, significant grain refinement of ferrite phase occurs by deformation and exhibits a characteristic deformation texture. In contrast, the high-temperature deformed sample shows a weaker texture with cube component for the ferrite phase, indicating the occurrence of recrystallization. The different mechanisms responsible for the refinement of ferrite as well as the fragmentation of cementite and their interaction with each other have been analyzed. Viscoplastic self-consistent simulation was employed to understand deformation texture in the ferrite phase during triaxial compression.

Further evidence for room temperature, indentation-induced nanocrystallization in a bulk metallic glass

Room temperature nanoindentation experiments, employing two different pyramidal (Berkovich and cube-corner) indenters, were performed on a Zr-based bulk metallic glass (BMG) to critically examine the possibility of indentation-induced nanocrystallization in BMGs. Cross-sectional transmission electron microscopy images obtained from high angle annular dark field ( HAADF) and high resolution (HR) modes clearly indicate to the occurrence of nanocrystallization. Pronounced nanocrystallite formation in the case of sharper cube-corner indenter suggests that the structural transformation is favored by the high strains introduced during nanoindentation. (c) 2012 Elsevier B.V. All rights reserved.

Carrier concentration dependence of donor activation energy in n-type GaN epilayers grown on Si (111) by plasma-assisted MBE

The n-type GaN layers were grown by plasma-assisted MBE and either intentionally doped with Si or unintentionally doped. The optical characteristics of a donor level in Si-doped, GaN were studied in terms of photoluminescence (PL) spectroscopy as a function of electron concentration. Temperature dependent PL measurements allowed us to estimate the activation energy of a Si-related donor from temperature-induced decay of PL intensity. PL peak positions, full width at half maximum of PL and activation energies are found to be proportional to the cube root of carrier density. The involvement of donor levels is supported by the temperature-dependent electron concentration measurements. (C) 2012 Elsevier Ltd. All rights reserved.

A study on the formation of crystalline phases during solidification and crystallisation in the bulk metallic glass of Zr53Cu21Al10Ni8Ti8 composition

The present paper considers the formation of crystalline phases during solidification and crystallisation of the Zr53Cu21Al10Ni8Ti8 alloy. Solidification was carried out by a copper mould casting technique, which yielded a partially crystalline microstructure comprising a `big cube phase' in a dendritic morphology and a bct Zr2Ni phase. Detailed high-resolution microscopy was carried out to determine possible mechanisms for the formation of the crystalline phases. Based on microstructural examinations, it was established that the dendrites grew by the attachment of atomistic ledges. The bct Zr2Ni phase, formed during solidification and crystallisation, showed various types of faults depending on the crystallite size, and its crystallography was examined in detail. It has been shown that the presence of these faults could be explained by anti-site occupancy in the bct lattice of the Zr2Ni phase.

Development of microstructure and texture in Copper during warm accumulative roll bonding

The evolution of microstructure and texture gradient in warm Accumulative Roll Bonded Cu-Cu multilayer has been studied. Grain size distribution is multimodal and exhibits variation from middle to surface layer. Evolution of texture is largely influenced by shear, in addition to rolling deformation. This leads to the formation of a texture comprising of high fraction of Brass and rolling direction-rotated cube components. Partial recrystallization was observed. Deformed and recrystallized grains were separated using a partition scheme based on grain orientation spread and textures were analyzed for both the partition. Retention of deformation texture components in recrystallized grains suggests the mechanism of recrystallization as continuous recrystallization. Shear deformation plays an important role in grain refinement through continuous recrystallization. (C) 2012 Elsevier Inc. All rights reserved.

Cubicity and Bandwidth

A unit cube in (or a k-cube in short) is defined as the Cartesian product R (1) x R (2) x ... x R (k) where R (i) (for 1 a parts per thousand currency sign i a parts per thousand currency sign k) is a closed interval of the form a (i) , a (i) + 1] on the real line. A k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that two vertices in G are adjacent if and only if their corresponding k-cubes have a non-empty intersection. The cubicity of G is the minimum k such that G has a k-cube representation. From a geometric embedding point of view, a k-cube representation of G = (V, E) yields an embedding such that for any two vertices u and v, ||f(u) - f(v)||(a) a parts per thousand currency sign 1 if and only if . We first present a randomized algorithm that constructs the cube representation of any graph on n vertices with maximum degree Delta in O(Delta ln n) dimensions. This algorithm is then derandomized to obtain a polynomial time deterministic algorithm that also produces the cube representation of the input graph in the same number of dimensions. The bandwidth ordering of the graph is studied next and it is shown that our algorithm can be improved to produce a cube representation of the input graph G in O(Delta ln b) dimensions, where b is the bandwidth of G, given a bandwidth ordering of G. Note that b a parts per thousand currency sign n and b is much smaller than n for many well-known graph classes. Another upper bound of b + 1 on the cubicity of any graph with bandwidth b is also shown. Together, these results imply that for any graph G with maximum degree Delta and bandwidth b, the cubicity is O(min{b, Delta ln b}). The upper bound of b + 1 is used to derive upper bounds for the cubicity of circular-arc graphs, cocomparability graphs and AT-free graphs in terms of the maximum degree Delta.

Optimal Linear Codes with a Local-Error-Correction Property

Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such ``local'' parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.

Cubicity, degeneracy, and crossing number

A $k$-box $B=(R_1,...,R_k)$, where each $R_i$ is a closed interval on the real line, is defined to be the Cartesian product $R_1\times R_2\times ...\times R_k$. If each $R_i$ is a unit length interval, we call $B$ a $k$-cube. Boxicity of a graph $G$, denoted as $\boxi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-boxes. Similarly, the cubicity of $G$, denoted as $\cubi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-cubes. It was shown in [L. Sunil Chandran, Mathew C. Francis, and Naveen Sivadasan: Representing graphs as the intersection of axis-parallel cubes. MCDES-2008, IISc Centenary Conference, available at CoRR, abs/cs/ 0607092, 2006.] that, for a graph $G$ with maximum degree $\Delta$, $\cubi(G)\leq \lceil 4(\Delta +1)\log n\rceil$. In this paper, we show that, for a $k$-degenerate graph $G$, $\cubi(G) \leq (k+2) \lceil 2e \log n \rceil$. Since $k$ is at most $\Delta$ and can be much lower, this clearly is a stronger result. This bound is tight. We also give an efficient deterministic algorithm that runs in $O(n^2k)$ time to output a $8k(\lceil 2.42 \log n\rceil + 1)$ dimensional cube representation for $G$. An important consequence of the above result is that if the crossing number of a graph $G$ is $t$, then $\boxi(G)$ is $O(t^{1/4}{\lceil\log t\rceil}^{3/4})$ . This bound is tight up to a factor of $O((\log t)^{1/4})$. We also show that, if $G$ has $n$ vertices, then $\cubi(G)$ is $O(\log n + t^{1/4}\log t)$. Using our bound for the cubicity of $k$-degenerate graphs we show that cubicity of almost all graphs in $\mathcal{G}(n,m)$ model is $O(d_{av}\log n)$, where $d_{av}$ denotes the average degree of the graph under consideration. model is O(davlogn).

IceCube: efficient targeted mining in data cubes

We address the problem of mining targeted association rules over multidimensional market-basket data. Here, each transaction has, in addition to the set of purchased items, ancillary dimension attributes associated with it. Based on these dimensions, transactions can be visualized as distributed over cells of an n-dimensional cube. In this framework, a targeted association rule is of the form {X -> Y} R, where R is a convex region in the cube and X. Y is a traditional association rule within region R. We first describe the TOARM algorithm, based on classical techniques, for identifying targeted association rules. Then, we discuss the concepts of bottom-up aggregation and cubing, leading to the CellUnion technique. This approach is further extended, using notions of cube-count interleaving and credit-based pruning, to derive the IceCube algorithm. Our experiments demonstrate that IceCube consistently provides the best execution time performance, especially for large and complex data cubes.

Effects of different modes of hot cross-rolling in 7010 aluminum alloy: part I. evolution of microstructure and texture

The current study describes the evolution of microstructure and texture in an Al-Zn-Mg-Cu-Zr-based 7010 aluminum alloy during different modes of hot cross-rolling. Processing of materials involves three different types of cross-rolling. The development of texture in the one-step cross-rolled specimen can be described by a typical beta-fiber having the maximum intensity near Copper (Cu) component. However, for the multi-step cross-rolled specimens, the as-rolled texture is mainly characterized by a strong rotated-Brass (Bs) component and a very weak rotated-cube component. Subsequent heat treatment leads to sharpening of the major texture component (i.e., rotated-Bs). Furthermore, the main texture components in all the specimens appear to be significantly rotated in a complex manner away from their ideal positions because of non-symmetric deformations in the two rolling directions. Detailed microstructural study indicates that dynamic recovery is the dominant restoration mechanism operating during the hot rolling. During subsequent heat treatment, static recovery dominates, while a combination of particle-stimulated nucleation (PSN) and strain-induced grain boundary migration (SIBM) causes partial recrystallization of the grain structure. The aforementioned restoration mechanisms play an important role in the development of texture components. The textural development in the current study could be attributed to the combined effects of (a) cross-rolling and inter-pass annealing that reduce the intensity of Cu component after each successive pass, (b) recrystallization resistance of Bs-oriented grains, (c) stability of Bs texture under cross-rolling, and (d) Zener pinning by Al3Zr dispersoids.

Rotating beams isospectral to axially loaded nonrotating uniform beams

In this paper, the stiffness and mass per unit length distributions of a rotating beam, which is isospectral to a given uniform axially loaded nonrotating beam, are determined analytically. The Barcilon-Gottlieb transformation is extended so that it transforms the governing equation of a rotating beam into the governing equation of a uniform, axially loaded nonrotating beam. Analysis is limited to a certain class of Euler-Bernoulli cantilever beams, where the product between the stiffness and the cube of mass per unit length is a constant. The derived mass and stiffness distributions of the rotating beam are used in a finite element analysis to confirm the frequency equivalence of the given and derived beams. Examples of physically realizable beams that have a rectangular cross section are shown as a practical application of the analysis.

Evolution of microstructure and texture during deformation and recrystallization of heavily rolled Cu-Cu multilayer

A Cu-Cu multilayer processed by accumulative roll bonding was deformed to large strains and further annealed. The texture of the deformed Cu-Cu multilayer differs from the conventional fcc rolling textures in terms of higher fractions of Bs and RD-rotated cube components, compared with the volume fraction of Cu component. The elongated grain shape significantly affects the deformation characteristics. Characteristic microstructural features of both continuous dynamic recrystallization and discontinuous dynamic recrystallization were observed in the microtexture measurements. X-ray texture measurements of annealing of heavily deformed multilayer demonstrate constrained recrystallization and resulted in a bimodal grain size distribution in the annealed material at higher strains. The presence of cube- and BR-oriented grains in the deformed material confirms the oriented nucleation as the major influence on texture change during recrystallization. Persistence of cube component throughout the deformation is attributed to dynamic recrystallization. Evolution of RD-rotated cube is attributed to the deformation of cube components that evolve from dynamic recrystallization. The relaxation of strain components leads to Bs at larger strains. Further, the Bs component is found to recover rather than recrystallize during deformation. The presence of predominantly Cu and Bs orientations surrounding the interface layer suggests constrained annealing behavior.

Wireless network-coded three-way relaying using Latin Cubes

The design of modulation schemes for the physical layer network-coded three-way wireless relaying scenario is considered. The protocol employs two phases: Multiple Access (MA) phase and Broadcast (BC) phase with each phase utilizing one channel use. For the two-way relaying scenario, it was observed by Koike-Akino et al. [4], that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA phase and all these network coding maps should satisfy a requirement called exclusive law. This paper does the equivalent for the three-way relaying scenario. We show that when the three users transmit points from the same 4-PSK constellation, every such network coding map that satisfies the exclusive law can be represented by a Latin Cube of Second Order. The network code map used by the relay for the BC phase is explicitly obtained and is aimed at reducing the effect of interference at the MA stage.

Velocity Fluctuations in Helical Propulsion: How Small Can a Propeller Be

Helical propulsion is at the heart of locomotion strategies utilized by various natural and artificial swimmers. We used experimental observations and a numerical model to study the various fluctuation mechanisms that determine the performance of an externally driven helical propeller as the size of the helix is reduced. From causality analysis, an overwhelming effect of orientational noise at low length scales is observed, which strongly affects the average velocity and direction of motion of a propeller. For length scales smaller than a few micrometers in aqueous media, the operational frequency for the propulsion system would have to increase as the inverse cube of the size, which can be the limiting factor for a helical propeller to achieve locomotion in the desired direction.