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.

Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

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.

Automatic road extraction using high resolution satellite images based on Level Set and Mean Shift methods

Analysis of high resolution satellite images has been an important research topic for urban analysis. One of the important features of urban areas in urban analysis is the automatic road network extraction. Two approaches for road extraction based on Level Set and Mean Shift methods are proposed. From an original image it is difficult and computationally expensive to extract roads due to presences of other road-like features with straight edges. The image is preprocessed to improve the tolerance by reducing the noise (the buildings, parking lots, vegetation regions and other open spaces) and roads are first extracted as elongated regions, nonlinear noise segments are removed using a median filter (based on the fact that road networks constitute large number of small linear structures). Then road extraction is performed using Level Set and Mean Shift method. Finally the accuracy for the road extracted images is evaluated based on quality measures. The 1m resolution IKONOS data has been used for the experiment.

Structure, molecular dynamics, and stress in a linear polymer

We present a study correlating uniaxial stress in a polymer with its underlying structure when it is strained. The uniaxial stress is significantly influenced by the mean-square bond length and mean bond angle. In contrast, the size and shape of the polymer, typically represented by the end-to-end length, mass ratio, and radius of gyration, contribute negligibly. Among externally set control variables, density and polymer chain length play a critical role in influencing the anisotropic uniaxial stress. Short chain polymers more or less behave like rigid molecules. Temperature and rate of loading, in the range considered, have a very mild effect on the uniaxial stress.

Molecular Dynamics Perspective on the Protein Thermal Stability: A Case Study Using SAICAR Synthetase

The enzyme SAICAR synthetase ligates aspartate with CAIR (5'-phosphoribosyl-4-carboxy-5-aminoimidazole) forming SAICAR (5-amino-4-imidazole-N-succinocarboxamide ribonucleotide) in the presence of ATP. In continuation with our previous study on the thermostability of this enzyme in hyper-/thermophiles based on the structural aspects, here, we present the dynamic aspects that differentiate the mesophilic (E. coli, E. chaffeensis), thermophilic (G. kaustophilus), and hyperthermophilic (M. jannaschii, P. horikoshii) SAICAR synthetases by carrying out a total of 11 simulations. The five functional dimers from the above organisms were simulated using molecular dynamics for a period of 50 ns each at 300 K, 363 K, and an additional simulation at 333 K for the thermophilic protein. The basic features like root-mean-square deviations, root-mean-square fluctuations, surface accessibility, and radius of gyration revealed the instability of mesophiles at 363 K. Mean square displacements establish the reduced flexibility of hyper-/thermophiles at all temperatures. At the simulations time scale considered here, the long-distance networks are considerably affected in mesophilic structures at 363 K. In mesophiles, a comparatively higher number of short-lived (having less percent existence time) C alpha, hydrogen bonds, hydrophobic interactions are formed, and long-lived (with higher percentage existence time) contacts are lost. The number of time-averaged salt-bridges is at least 2-fold higher in hyperthermophiles at 363 K. The change in surface accessibility of salt-bridges at 363 K from 300 K is nearly doubled in mesophilic protein compared to proteins from other temperature classes.

Transition in vortex breakdown modes in a coaxial isothermal unconfined swirling jet

This paper reports first observations of transition in recirculation pattern from an open-bubble type axisymmetric vortex breakdown to partially open bubble mode through an intermediate, critical regime of conical sheet formation in an unconfined, co-axial isothermal swirling flow. This time-mean transition is studied for two distinct flow modes which are characterized based on the modified Rossby number (Ro(m)), i.e., Ro(m) <= 1 and Ro(m) > 1. Flow modes with Ro(m) <= 1 are observed to first undergo cone-type breakdown and then to partially open bubble state as the geometric swirl number (S-G) is increased by similar to 20% and similar to 40%, respectively, from the baseline open-bubble state. However, the flow modes with Ro(m) > 1 fail to undergo such sequential transition. This distinct behavior is explained based on the physical significance associated with Ro(m) and the swirl momentum factor (xi). In essence, xi represents the ratio of angular momentum distributed across the flow structure to that distributed from central axis to the edge of the vortex core. It is observed that xi increases by similar to 100% in the critical swirl number band where conical breakdown occurs as compared to its magnitude in the S-G regime where open bubble state is seen. This results from the fact that flow modes with Ro(m) <= 1 are dominated by radial pressure gradient due to swirl/rotational effect when compared to radial pressure deficit arising from entrainment (due to the presence of co-stream). Consequently, the imparted swirl tends to penetrate easily towards the central axis causing it to spread laterally and finally undergo conical sheet breakdown. However, the flow modes with Ro(m) > 1 are dominated by pressure deficit due to entrainment effect. This blocks the radial inward penetration of imparted angular momentum thus preventing the lateral spread of these flow modes. As such these structures fail to undergo cone mode of vortex breakdown which is substantiated by a mere 30%-40% rise in xi in the critical swirl number range. (C) 2014 AIP Publishing LLC.

Fluctuating micro-heterogeneity in water-tert-butyl alcohol mixtures and lambda-type divergence of the mean cluster size with phase transition-like multiple anomalies

Water-tert-butyl alcohol (TBA) binary mixture exhibits a large number of thermodynamic and dynamic anomalies. These anomalies are observed at surprisingly low TBA mole fraction, with x(TBA) approximate to 0.03-0.07. We demonstrate here that the origin of the anomalies lies in the local structural changes that occur due to self-aggregation of TBA molecules. We observe a percolation transition of the TBA molecules at x(TBA) approximate to 0.05. We note that ``islands'' of TBA clusters form even below this mole fraction, while a large spanning cluster emerges above that mole fraction. At this percolation threshold, we observe a lambda-type divergence in the fluctuation of the size of the largest TBA cluster, reminiscent of a critical point. Alongside, the structure of water is also perturbed, albeit weakly, by the aggregation of TBA molecules. There is a monotonic decrease in the tetrahedral order parameter of water, while the dipole moment correlation shows a weak nonlinearity. Interestingly, water molecules themselves exhibit a reverse percolation transition at higher TBA concentration, x(TBA) approximate to 0.45, where large spanning water clusters now break-up into small clusters. This is accompanied by significant divergence of the fluctuations in the size of largest water cluster. This second transition gives rise to another set of anomalies around. Both the percolation transitions can be regarded as manifestations of Janus effect at small molecular level. (C) 2014 AIP Publishing LLC.

Improved quasiparticle wave functions and mean field for G(0)W(0) calculations: Initialization with the COHSEX operator

The GW approximation to the electron self-energy has become a standard method for ab initio calculation of excited-state properties of condensed-matter systems. In many calculations, the G W self-energy operator, E, is taken to be diagonal in the density functional theory (DFT) Kohn-Sham basis within the G0 W0 scheme. However, there are known situations in which this diagonal Go Wo approximation starting from DFT is inadequate. We present two schemes to resolve such problems. The first, which we called sc-COHSEX-PG W, involves construction of an improved mean field using the static limit of GW, known as COHSEX (Coulomb hole and screened exchange), which is significantly simpler to treat than GW W. In this scheme, frequency-dependent self energy E(N), is constructed and taken to be diagonal in the COHSEX orbitals after the system is solved self-consistently within this formalism. The second method is called off diagonal-COHSEX G W (od-COHSEX-PG W). In this method, one does not self-consistently change the mean-field starting point but diagonalizes the COHSEX Hamiltonian within the Kohn-Sham basis to obtain quasiparticle wave functions and uses the resulting orbitals to construct the G W E in the diagonal form. We apply both methods to a molecular system, silane, and to two bulk systems, Si and Ge under pressure. For silane, both methods give good quasiparticle wave functions and energies. Both methods give good band gaps for bulk silicon and maintain good agreement with experiment. Further, the sc-COHSEX-PGW method solves the qualitatively incorrect DFT mean-field starting point (having a band overlap) in bulk Ge under pressure.

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.

Dynamics of intermittent force fluctuations in vesicular nanotubulation

Irregular force fluctuations are seen in most nanotubulation experiments. The dynamics behind their presence has, however, been neither commented upon nor modeled. A simple estimate of the mean energy dissipated in force drops turns out to be several times the thermal energy. This coupled with the rate dependent nature of the deformation reported in several experiments point to a dynamical origin of the serrations. We simplify the whole process of tether formation through a three-stage model of successive deformations of sphere to ellipsoid, neck-formation, and tubule birth and extension. Based on this, we envisage a rate-softening frictional force at the neck that must be overcome before a nanotube can be pulled out. Our minimal model includes elastic and visco-elastic deformation of the vesicle, and has built-in dependence on pull velocity, vesicle radius, and other material parameters, enabling us to capture various kinds of serrated force-extension curves for different parameter choices. Serrations are predicted in the nanotubulation region. Other features of force-extension plots reported in the literature such as a plateauing serrated region beyond a force drop, serrated flow region with a small positive slope, an increase in the elastic threshold with pull velocity, force-extension curves for vesicles with larger radius lying lower than those for smaller radius, are all also predicted by the model. A toy model is introduced to demonstrate that the role of the friction law is limited to inducing stick-slip oscillations in the force, and all other qualitative and quantitative features emerging from the model can only be attributed to other physical mechanisms included in the deformation dynamics of the vesicle. (C) 2014 AIP Publishing LLC.

Improved tuning of the extended concentric tube resonator for wide-band transmission loss

Transmission loss (TL) of a simple expansion chamber (SEC) consists of periodic domes with sharp troughs. This limits practical application of the SEC in the variable-speed automobile exhaust systems. Three-fourths of the troughs of the SEC can be lifted by appropriate tuning of the extended inlet/outlet lengths. However, such mufflers suffer from high back pressure and generation of aerodynamic noise due to free shear layers at the area discontinuities. Therefore, a perforate bridge is made between the extended inlet and outlet. It is shown that the TL curve of a concentric tube resonator (CTR) can also be lifted in a similar way by proper tuning of the extended unperforated lengths. Differential lengths have to be used to correct the inlet/outlet lengths in order to account for the perforate inertance. The resonance peak frequencies calculated by means of the 1-D analysis are compared with those of the 3-D FEM, and appropriate differential lengths are calculated. It is shown how different geometric characteristics of the muffler and mean flow affect the differential lengths. A general correlation is obtained for the differential lengths by considering seven relevant geometric and environmental parameters in a comprehensive parametric study. The resulting expressions would help in design of extended-tube CTR for wide-band TL. (C) 2014 Institute of Noise Control Engineering.

Reply to ``Comment on `Strongly magnetized cold degenerate electron gas: Mass-radius relation of the magnetized white dwarf'''

We show that the upper bound for the central magnetic field of a super-Chandrasekhar white dwarf calculated by Nityananda and Konar Phys. Rev. D 89, 103017 (2014)] and in the concerned comment, by the same authors, against our work U. Das and B. Mukhopadhyay, Phys. Rev. D 86, 042001 (2012)] is erroneous. This in turn strengthens the argument in favor of the stability of the recently proposed magnetized super-Chandrasekhar white dwarfs. We also point out several other numerical errors in their work. Overall we conclude that the arguments put forth by Nityananda and Konar are misleading.