Evolving Random Geometric Graph Models for Mobile Wireless Networks

We consider evolving exponential RGGs in one dimension and characterize the time dependent behavior of some of their topological properties. We consider two evolution models and study one of them detail while providing a summary of the results for the other. In the first model, the inter-nodal gaps evolve according to an exponential AR(1) process that makes the stationary distribution of the node locations exponential. For this model we obtain the one-step conditional connectivity probabilities and extend it to the k-step case. Finite and asymptotic analysis are given. We then obtain the k-step connectivity probability conditioned on the network being disconnected. We also derive the pmf of the first passage time for a connected network to become disconnected. We then describe a random birth-death model where at each instant, the node locations evolve according to an AR(1) process. In addition, a random node is allowed to die while giving birth to a node at another location. We derive properties similar to those above.

Length of near-wall plumes in turbulent convection

We present planforms of line plumes formed on horizontal surfaces in turbulent convection, along with the length of line plumes measured from these planforms, in a six decade range of Rayleigh numbers (10(5) < Ra < 10(11)) and at three Prandtl numbers (Pr = 0.7, 5.2, 602). Using geometric constraints on the relations for the mean plume spacings, we obtain expressions for the total length of near-wall plumes on horizontal surfaces in turbulent convection. The plume length per unit area (L(p)/A), made dimensionless by the near-wall length scale in turbulent convection (Z(w)), remains constant for a given fluid. The Nusselt number is shown to be directly proportional to L(p)H/A for a given fluid layer of height H. The increase in Pr has a weak influence in decreasing L(p)/A. These expressions match the measurements, thereby showing that the assumption of laminar natural convection boundary layers in turbulent convection is consistent with the observed total length of line plumes. We then show that similar relationships are obtained based on the assumption that the line plumes are the outcome of the instability of laminar natural convection boundary layers on the horizontal surfaces.

Pillar height dependent formation of unprecedented Pd-8 molecular swing and Pd-6 molecular boat via multicomponent self-assembly

Three-component self-assembly of a cis-blocked 90 degrees Pd(II) acceptor with a mixture of a tetraimidazole and a linear dipyridyl donor self-discriminated into unusual Pd-8 molecular swing (1) and Pd-6 molecular boat (2), which are characterized by single-crystal X-ray diffraction analysis; their ability to bind C-60 in solution is established by fluorescence titration.

Geometric Decision Tree

In this paper, we present a new algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess the goodness of hyperplanes at each node while learning a decision tree in top-down fashion. These impurity measures do not properly capture the geometric structures in the data. Motivated by this, our algorithm uses a strategy for assessing the hyperplanes in such a way that the geometric structure in the data is taken into account. At each node of the decision tree, we find the clustering hyperplanes for both the classes and use their angle bisectors as the split rule at that node. We show through empirical studies that this idea leads to small decision trees and better performance. We also present some analysis to show that the angle bisectors of clustering hyperplanes that we use as the split rules at each node are solutions of an interesting optimization problem and hence argue that this is a principled method of learning a decision tree.

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.

Analysis of the temperature-dependent current-voltage characteristics and the barrier-height inhomogeneities of Au/GaN Schottky diodes

In this report, the currentvoltage (IV) characteristics of Au/GaN Schottky diodes have been carried out in the temperature range of 300510?K. The estimated values of the Schottky-barrier height (SBH) and the ideality factor of the diodes based on the thermionic emission (TE) mechanism were found to be temperature dependent. The barrier height was found to increase and the ideality factor to decrease with increasing temperature. The conventional Richardson plot of ln(Is/T2) versus 1/kT gives the SBH of 0.51?eV and Richardson constant value of 3.23?X?10-5?A?cm-2?K-2 which is much lower than the known value of 26.4?A?cm-2?K-2 for GaN. Such discrepancies of the SBH and Richardson constant value were attributed to the existence of barrier-height inhomogeneities at the Au/GaN interface. The modified Richardson plot of ln(Is/T2)q2 sigma 2/2k2T2 versus q/kT, by assuming a Gaussian distribution of barrier heights at the Au/GaN interface, provided the SBH of 1.47?eV and Richardson constant value of 38.8?A?cm-2?K-2. The temperature dependence of the barrier height is interpreted on the basis of existence of the Gaussian distribution of the barrier heights due to the barrier-height inhomogeneities at the Au/GaN interface.

Theory and Algorithms for Hop-Count-Based Localization with Random Geometric Graph Models of Dense Sensor Networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes in a region of Euclidean space. Following deployment, the nodes self-organize into a mesh topology with a key aspect being self-localization. Having obtained a mesh topology in a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this work, we analyze this approximation through two complementary analyses. We assume that the mesh topology is a random geometric graph on the nodes; and that some nodes are designated as anchors with known locations. First, we obtain high probability bounds on the Euclidean distances of all nodes that are h hops away from a fixed anchor node. In the second analysis, we provide a heuristic argument that leads to a direct approximation for the density function of the Euclidean distance between two nodes that are separated by a hop distance h. This approximation is shown, through simulation, to very closely match the true density function. Localization algorithms that draw upon the preceding analyses are then proposed and shown to perform better than some of the well-known algorithms present in the literature. Belief-propagation-based message-passing is then used to further enhance the performance of the proposed localization algorithms. To our knowledge, this is the first usage of message-passing for hop-count-based self-localization.

On the height of fall of dropping mass in SASW measurements for asphaltic road pavements

A number of spectral analysis of surface waves (SASW) tests were performed on asphaltic road pavements by dropping a metallic 6.5 kg sphere, from a height (H) ranging from 1 to 3 m. Various combinations of source to first receiver distance (S) and receiver spacing (X) were employed. By increasing the height of the fall of the dropping mass, the maximum wavelength (lambda(max)), up to which the shear wave velocity profile can be predicted with the usage of the SASW measurements, was found to increase continuously. The height of fall of the dropping mass also seems to affect the admissible range of the wavelength for given combinations of X and S. Irrespective of different chosen combinations of S, X and H, a unique combined dispersion curve was generated in all the cases for a given pavement site as long as the threshold minimum value of the coherence function is greater than 0.90.

Nonuniform random geometric graphs with location-dependent radii

We propose a distribution-free approach to the study of random geometric graphs. The distribution of vertices follows a Poisson point process with intensity function n f(center dot), where n is an element of N, and f is a probability density function on R-d. A vertex located at x connects via directed edges to other vertices that are within a cut-off distance r(n)(x). We prove strong law results for (i) the critical cut-off function so that almost surely, the graph does not contain any node with out-degree zero for sufficiently large n and (ii) the maximum and minimum vertex degrees. We also provide a characterization of the cut-off function for which the number of nodes with out-degree zero converges in distribution to a Poisson random variable. We illustrate this result for a class of densities with compact support that have at most polynomial rates of decay to zero. Finally, we state a sufficient condition for an enhanced version of the above graph to be almost surely connected eventually.

Relation between the work function and Young's modulus of RhSi and estimate of Schottky-barrier height at RhSi/Si interface: An ab-initio study

Density-functional calculations are performed to explore the relationship between the work function and Young's modulus of RhSi, and to estimate the p-Schottky-barrier height (SBH) at the Si/RhSi(010) interface. It is shown that the Young's modulus and the workfunction of RhSi satisfy the generic sextic relation, proposed recently for elemental metals. The calculated p-SBH at the Si/RhSi interface is found to differ only by 0.04 eV in opposite limits, viz., no-pinning and strong pinning. We find that the p-SBH is reduced as much as by 0.28 eV due to vacancies at the interface. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4761994]

Further results on geometric properties of a family of relative entropies

This paper extends some geometric properties of a one-parameter family of relative entropies. These arise as redundancies when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the Kullback-Leibler divergence. They satisfy the Pythagorean property and behave like squared distances. This property, which was known for finite alphabet spaces, is now extended for general measure spaces. Existence of projections onto convex and certain closed sets is also established. Our results may have applications in the Rényi entropy maximization rule of statistical physics.

Effects of initial height on the steady-state persistence probability of linear growth models

The effects of the initial height on the temporal persistence probability of steady-state height fluctuations in up-down symmetric linear models of surface growth are investigated. We study the (1 + 1)-dimensional Family model and the (1 + 1)-and (2 + 1)-dimensional larger curvature (LC) model. Both the Family and LC models have up-down symmetry, so the positive and negative persistence probabilities in the steady state, averaged over all values of the initial height h(0), are equal to each other. However, these two probabilities are not equal if one considers a fixed nonzero value of h(0). Plots of the positive persistence probability for negative initial height versus time exhibit power-law behavior if the magnitude of the initial height is larger than the interface width at saturation. By symmetry, the negative persistence probability for positive initial height also exhibits the same behavior. The persistence exponent that describes this power-law decay decreases as the magnitude of the initial height is increased. The dependence of the persistence probability on the initial height, the system size, and the discrete sampling time is found to exhibit scaling behavior.

On the possible variation of the lightning striking distance as assumed in the IEC lightning protection standard as a function of structure height

The effect of structure height on the lightning striking distance is estimated using a lightning strike model that takes into account the effect of connecting leaders. According to the results, the lightning striking distance may differ significantly from the values assumed in the IEC standard for structure heights beyond 30m. However, for structure heights smaller than about 30m, the results show that the values assumed by IEC do not differ significantly from the predictions based on a lightning attachment model taking into account the effect of connecting leaders. However, since IEC assumes a smaller striking distance than the ones predicted by the adopted model one can conclude that the safety is not compromised in adhering to the IEC standard. Results obtained from the model are also compared with Collection Volume Method (CVM) and other commonly used lightning attachment models available in the literature. The results show that in the case of CVM the calculated attractive distances are much larger than the ones obtained using the physically based lightning attachment models. This indicates the possibility of compromising the lightning protection procedures when using CVM. (C) 2014 Elsevier B.V. All rights reserved.

New Insights into Electronic and Geometric Effects in the Enhanced Photoelectrooxidation of Ethanol Using ZnO Nanorod/Ultrathin Au Nanowire Hybrids

Oxidation of small organic molecules in a fuel cell is a viable method for energy production. However, the key issue is the development of suitable catalysts that exhibit high efficiencies and remain stable during operation. Here, we demonstrate that amine-modified ZnO nanorods on which ultrathin Au nanowires are grown act as an excellent catalyst for the oxidation of ethanol. We show that the modification of the ZnO nanorods with oleylamine not only modifies the electronic structure favorably but also serves to anchor the Au nanowires on the nanorods. The adsorption of OH- species on the Au nanowires that is essential for ethanol oxidation is facilitated at much lower potentials as compared to bare Au nanowires leading to high activity. While ZnO shows negligible electrocatalytic activity under normal conditions, there is significant enhancement in the activity under light irradiation. We demonstrate a synergistic enhancement in the photoelectrocatalytic activity of the ZnO/Au nanowire hybrid and provide mechanistic explanation for this enhancement based on both electronic as well as geometric effects. The principles developed are applicable for tuning the properties of other metal/semiconductor hybrids with potentially interesting applications beyond the fuel cell application demonstrated here.

Double Gaussian distribution of barrier height observed in densely packed GaN nanorods over Si (111) heterostructures

GaN nanorods were grown by plasma assisted molecular beam epitaxy on intrinsic Si (111) substrates which were characterized by powder X-ray diffraction, field emission scanning electron microscopy, and photoluminescence. The current-voltage characteristics of the GaN nanorods on Si (111) heterojunction were obtained from 138 to 493K which showed the inverted rectification behavior. The I-V characteristics were analyzed in terms of thermionic emission model. The temperature variation of the apparent barrier height and ideality factor along with the non-linearity of the activation energy plot indicated the presence of lateral inhomogeneities in the barrier height. The observed two temperature regimes in Richardson's plot could be well explained by assuming two separate Gaussian distribution of the barrier heights. (C) 2014 AIP Publishing LLC.