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.

Feasibility study of the measurement of Higgs pair creation at a photon linear collider

We studied the feasibility of the measurement of Higgs pair creation at a photon linear collider. From the sensitivity to the anomalous self-coupling of the Higgs boson, the optimum gamma gamma collision energy was found to be around 270 GeV for a Higgs mass of 120 GeV/c(2). We found that large backgrounds such as gamma gamma -> W+W-, ZZ, and b (b) over barb (b) over bar can be suppressed if correct assignment of tracks to parent partons is achieved and Higgs pair events can be observed with a statistical significance of similar to 5 sigma by operating the photon linear collider for 5 years.

Generalized bidirectional multi-pair multi-antennawireless network coding

In this paper, we focus on increasing the throughput and diversity of network coded MIMO transmissions in bidirectional multi-pair wireless relay networks. All nodes have multi-antenna capability. Pairs of nodes want to exchange messages via a relay having multi-antenna and encoding/decoding capability. Nodes transmit their messages to the relay in the first (MAC) phase. The relay decodes all the messages and XORs them and broadcasts the XORed message in the second (BC) phase. We develop a generalized framework for bidirectional multi-pair multi-antenna wireless network coding, which models different MIMO transmission schemes including spatial multiplexing (V-BLAST), orthogonal STBC (OSTBC), and non-orthogonal STBC (NO-STBC) in a unified way. Enhanced throughputs are achieved by allowing all nodes to simultaneously transmit at their full rate. High diversity orders are achieved through the use of NO-STBCs, characterized by full rate and full transmit diversity. We evaluate and compare the performance of VBLAST, OSTBC, and NO-STBC schemes in one-dimensional 1-pair linear network (one pair of nodes and a relay) and two-dimensional 2-pair `cross' network (two pairs of nodes and a relay).

Non-rotating beams isospectral to a given rotating uniform beam

In this paper, we seek to find non-rotating beams with continuous mass and flexural stiffness distributions, that are isospectral to a given uniform rotating beam. The Barcilon-Gottlieb transformation is used to convert the fourth order governing equation of a non-rotating beam, to a canonical fourth order eigenvalue problem. If the coefficients in this canonical equation match with the coefficients of the uniform rotating beam equation, then the non-rotating beam is isospectral to the given rotating beam. The conditions on matching the coefficients leads to a pair of coupled differential equations. We solve these coupled differential equations for a particular case, and thereby obtain a class of non-rotating beams that are isospectral to a uniform rotating beam. However, to obtain isospectral beams, the transformation must leave the boundary conditions invariant. We show that the clamped end boundary condition is always invariant, and for the free end boundary condition to be invariant, we impose certain conditions on the beam characteristics. We also verify numerically that the frequencies of the non-rotating beam obtained using the finite element method (FEM) are the exact frequencies of the uniform rotating beam. Finally, the example of beams having a rectangular cross-section is presented to show the application of our analysis. Since experimental determination of rotating beam frequencies is a difficult task, experiments can be easily conducted on these rectangular non-rotating beams, to calculate the frequencies of the rotating beam. (c) 2012 Elsevier Ltd. All rights reserved.

Effect of hinged leaflets on vortex pair generation

We experimentally study the effect of having hinged leaflets at the jet exit on the formation of a two-dimensional counter-rotating vortex pair. A piston-cylinder mechanism is used to generate a starting jet from a high-aspect-ratio channel into a quiescent medium. For a rigid exit, with no leaflets at the channel exit, the measurements at a central plane show that the trailing jet in the present case is never detached from the vortex pair, and keeps feeding into the latter, unlike in the axisymmetric case. Passive flexibility is introduced in the form of rigid leaflets or flaps that are hinged at the exit of the channel, with the flaps initially parallel to the channel walls. The experimental arrangement closely approximates the limiting case of a free-to-rotate rigid flap with negligible structural stiffness, damping and flap inertia, as these limiting structural properties permit the largest flap openings. Using this arrangement, we start the flow and measure the flap kinematics and the vorticity fields for different flap lengths and piston velocity programs. The typical motion of the flaps involves a rapid opening and a subsequent more gradual return to its initial position, both of which occur when the piston is still moving. The initial opening of the flaps can be attributed to an excess pressure that develops in the channel when the flow starts, due to the acceleration that has to be imparted to the fluid slug between the flaps. In the case with flaps, two additional pairs of vortices are formed because of the motion of the flaps, leading to the ejection of a total of up to three vortex pairs from the hinged exit. The flaps' length (L-f) is found to significantly affect flap motions when plotted using the conventional time scale L/d, where L is the piston stroke and d is the channel width. However, with a newly defined time scale based on the flap length (L/L-f), we find a good collapse of all the measured flap motions irrespective of flap length and piston velocity for an impulsively started piston motion. The maximum opening angle in all these impulsive velocity program cases, irrespective of the flap length, is found to be close to 15 degrees. Even though the flap kinematics collapses well with L/L-f, there are differences in the distribution of the ejected vorticity even for the same L/L-f. Such a redistribution of vorticity can lead to important changes in the overall properties of the flow, and it gives us a better understanding of the importance of exit flexibility in such flows.

Ternary ion-pair complexation: a protocol for chiral discrimination and the assignment of absolute configuration of chiral hydroxy acids

The study demonstrates the utility of ternary ion-pair complex formed among BINOL (1,1'-Bi-2-naphthol), a carboxylic acid and an organic base, such as, dimethylpyridine (DMAP), 1,4-diazabicyclo2.2.2]octane (DABCO), as a versatile chiral solvating agent (CSA) for the enantiodiscrimination of carboxylic acids, measurement of enantiomeric excess (ee) and the assignment of absolute configuration of hydroxy acids. The proposed mechanism of ternary complex has wider application for testing the enantiopurity owing to the fact that the binary mixture using BINOL alone does not serve as a solvating agent for their discrimination. In addition, the developed protocol has an excellent utility for the assignment of the absolute configurations of hydroxy acids.

A three-component protocol for the enantiodifferentiation of amines using triphenyl borate and BINOL: is it an ion pair or an amine-coordinated complex?

The structure of the borate complex responsible for the enantiodifferentiation of amines using a previously reported three-component protocol has been established. The choice between an ion pair and an amine-coordinated complex with the N atom of the amine coordinated to the B atom is favored for the former structure based on the DFT-calculated B-11 NMR chemical shifts. In contrast to expectations, the anisotropies of the quadrupolar B-11 nucleus for the two structures were calculated to be indistinguishable with regard to their effect on the linewidth of the NMR signal. (C) 2014 Elsevier Ltd. All rights reserved.

Pair dispersion of turbulent premixed flame elements

Flame particles are mathematical points comoving with a reacting isoscalar surface in a premixed flame. In this Rapid Communication, we investigate mean square pair separation of flame particles as a function of time from their positions tracked in two sets of direct numerical simulation solutions of H-2-air turbulent premixed flames with detailed chemistry. We find that, despite flame particles and fluid particles being very different concepts, a modified Batchelor's scaling of the form = C-F ( (F)(0) Delta(F)(0))(2/3)t(2) holds for flame particle pair dispersion. The proportionality constant, however, is not universal and depends on the isosurface temperature value on which the flame particles reside. Following this, we attempt to analytically investigate the rationale behind such an observation.

Suspensions of polymer-grafted nanoparticles with added polymers-Structure and effective pair-interactions

We present the results of combined experimental and theoretical (molecular dynamics simulations and integral equation theory) studies of the structure and effective interactions of suspensions of polymer grafted nanoparticles (PGNPs) in the presence of linear polymers. Due to the absence of systematic experimental and theoretical studies of PGNPs, it is widely believed that the structure and effective interactions in such binary mixtures would be very similar to those of an analogous soft colloidal material-star polymers. In our study, polystyrene-grafted gold nanoparticles with functionality f = 70 were mixed with linear polystyrene (PS) of two different molecular weights for obtaining two PGNP: PS size ratios, xi = 0.14 and 2.76 (where, xi = M-g/M-m, M-g and M-m being the molecular weights of grafting and matrix polymers, respectively). The experimental structure factor of PGNPs could be modeled with an effective potential (Model-X), which has been found to be widely applicable for star polymers. Similarly, the structure factor of the blends with xi = 0.14 could be modeled reasonably well, while the structure of blends with xi = 2.76 could not be captured, especially for high density of added polymers. A model (Model-Y) for effective interactions between PGNPs in a melt of matrix polymers also failed to provide good agreement with the experimental data for samples with xi = 2.76 and high density of added polymers. We tentatively attribute this anomaly in modeling the structure factor of blends with xi = 2.76 to the questionable assumption of Model-X in describing the added polymers as star polymers with functionality 2, which gets manifested in both polymer-polymer and polymer-PGNP interactions especially at higher fractions of added polymers. The failure of Model-Y may be due to the neglect of possible many-body interactions among PGNPs mediated by matrix polymers when the fraction of added polymers is high. These observations point to the need for a new framework to understand not only the structural behavior of PGNPs but also possibly their dynamics and thermo-mechanical properties as well. (C) 2015 AIP Publishing LLC.

Insight into the Evaporation Dynamics of a Pair of Sessile Droplets on a Hydrophobic Substrate

In this work, we have demonstrated three unique regimes in the evaporation lifecycle of a pair of sessile droplets placed in variable proximity on a hydrophobic substrate. For small separation distance, the droplets undergo asymmetric spatiotemporal,evaporation leading to contact angle hysteresis and suppressed vaporization. The reduced evaporation has been attributed quantitatively to the existence of a constrained vapor-rich dome between the two droplets. However, a dynamic decrease in the droplet radius due to solvent removal marks a return to symmetry in terms of evaporation and contact angle. We have described the variation in evaporation flux using a universal correction factor. We have also demonstrated the existence of a critical separation distance beyond which the droplets in the, droplet pair do not affect each other. The results are crucial to a plethora of applications ranging from surface patterning to lab-on-a-chip devices.

Insight into the Evaporation Dynamics of a Pair of Sessile Droplets on a Hydrophobic Substrate

In this work, we have demonstrated three unique regimes in the evaporation lifecycle of a pair of sessile droplets placed in variable proximity on a hydrophobic substrate. For small separation distance, the droplets undergo asymmetric spatiotemporal,evaporation leading to contact angle hysteresis and suppressed vaporization. The reduced evaporation has been attributed quantitatively to the existence of a constrained vapor-rich dome between the two droplets. However, a dynamic decrease in the droplet radius due to solvent removal marks a return to symmetry in terms of evaporation and contact angle. We have described the variation in evaporation flux using a universal correction factor. We have also demonstrated the existence of a critical separation distance beyond which the droplets in the, droplet pair do not affect each other. The results are crucial to a plethora of applications ranging from surface patterning to lab-on-a-chip devices.

Effect of strain rate response and pin diameter on mechanically mixed layer formation and wear mechanisms in a Ti6Al4V-SS316L pair

Three mechanisms operate during wear of materials. These mechanisms include the Strain Rate Response (SRR - effect of strain rate on plastic deformation), Tribo-Chemical Reactions (TCR) and formation of Mechanically Mixed Layers (MML). The present work investigates the effect of these three in context of the formation of MML. For this wear experiments are done on a pin-on-disc machine using Ti64 as the pin and SS316L as the disc. It is seen that apart from the speed and load, which control the SRR and TCR, the diameter of the pin controls the formation of MML, especially at higher speeds.