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.

Variation of diffusivity with the cation radii in molten salts of superionic conductors containing iodine anion: A molecular dynamics study

A molecular dynamics study of the dependence of diffusivity of the cation on ionic radii in molten AgI is reported. We have employed modified Parinello-Rahman-Vashistha interionic pair potential proposed by Shimojo and Kobayashi.(1) Our results suggest that the diffusivity of the cation exhibits an increase followed by a decrease as the ionic radius is increased. Several structural and dynamical properties are reported.

Mass of highly magnetized white dwarfs exceeding the Chandrasekhar limit: An analytical view

In recent years a number of white dwarfs have been observed with very high surface magnetic fields. We can expect that the magnetic field in the core of these stars would be much higher (similar to 10(14) G). In this paper, we analytically study the effect of high magnetic field on relativistic cold electron, and hence its effect on the stability and the mass-radius relation of a magnetic white dwarf. In strong magnetic fields, the equation of state of the Fermi gas is modified and Landau quantization comes into play. For relatively very high magnetic fields (with respect to the average energy density of matter) the number of Landau levels is restricted to one or two. We analyze the equation of states for magnetized electron degenerate gas analytically and attempt to understand the conditions in which transitions from the zeroth Landau level to first Landau level occurs. We also find the effect of the strong magnetic field on the star collapsing to a white dwarf, and the mass-radius relation of the resulting star. We obtain an interesting theoretical result that it is possible to have white dwarfs with mass more than the mass set by Chandrasekhar limit.

Spacelike pion form factor from analytic continuation and the onset of perturbative QCD

The factorization theorem for exclusive processes in perturbative QCD predicts the behavior of the pion electromagnetic form factor F(t) at asymptotic spacelike momenta t(= -Q(2)) < 0. We address the question of the onset energy using a suitable mathematical framework of analytic continuation, which uses as input the phase of the form factor below the first inelastic threshold, known with great precision through the Fermi-Watson theorem from pi pi elastic scattering, and the modulus measured from threshold up to 3 GeV by the BABAR Collaboration. The method leads to almost model-independent upper and lower bounds on the spacelike form factor. Further inclusion of the value of the charge radius and the experimental value at -2.45 GeV2 measured at JLab considerably increases the strength of the bounds in the region Q(2) less than or similar to 10 GeV2, excluding the onset of the asymptotic perturbative QCD regime for Q(2) < 7 GeV2. We also compare the bounds with available experimental data and with several theoretical models proposed for the low and intermediate spacelike region.

A study on seismicity and seismic hazard for Karnataka State

This paper presents a detailed study on the seismic pattern of the state of Karnataka and also quantifies the seismic hazard for the entire state. In the present work, historical and instrumental seismicity data for Karnataka (within 300 km from Karnataka political boundary) were compiled and hazard analysis was done based on this data. Geographically, Karnataka forms a part of peninsular India which is tectonically identified as an intraplate region of Indian plate. Due to the convergent movement of the Indian plate with the Eurasian plate, movements are occurring along major intraplate faults resulting in seismic activity of the region and hence the hazard assessment of this region is very important. Apart from referring to seismotectonic atlas for identifying faults and fractures, major lineaments in the study area were also mapped using satellite data. The earthquake events reported by various national and international agencies were collected until 2009. Declustering of earthquake events was done to remove foreshocks and aftershocks. Seismic hazard analysis was done for the state of Karnataka using both deterministic and probabilistic approaches incorporating logic tree methodology. The peak ground acceleration (PGA) at rock level was evaluated for the entire state considering a grid size of 0.05A degrees x 0.05A degrees. The attenuation relations proposed for stable continental shield region were used in evaluating the seismic hazard with appropriate weightage factors. Response spectra at rock level for important Tier II cities and Bangalore were evaluated. The contour maps showing the spatial variation of PGA values at bedrock are presented in this work.

Insights to urban dynamics through landscape spatial pattern analysis

Urbanisation is a dynamic complex phenomenon involving large scale changes in the land uses at local levels. Analyses of changes in land uses in urban environments provide a historical perspective of land use and give an opportunity to assess the spatial patterns, correlation, trends, rate and impacts of the change, which would help in better regional planning and good governance of the region. Main objective of this research is to quantify the urban dynamics using temporal remote sensing data with the help of well-established landscape metrics. Bangalore being one of the rapidly urbanising landscapes in India has been chosen for this investigation. Complex process of urban sprawl was modelled using spatio temporal analysis. Land use analyses show 584% growth in built-up area during the last four decades with the decline of vegetation by 66% and water bodies by 74%. Analyses of the temporal data reveals an increase in urban built up area of 342.83% (during 1973-1992), 129.56% (during 1992-1999), 106.7% (1999-2002), 114.51% (2002-2006) and 126.19% from 2006 to 2010. The Study area was divided into four zones and each zone is further divided into 17 concentric circles of 1 km incrementing radius to understand the patterns and extent of the urbanisation at local levels. The urban density gradient illustrates radial pattern of urbanisation for the period 1973-2010. Bangalore grew radially from 1973 to 2010 indicating that the urbanisation is intensifying from the central core and has reached the periphery of the Greater Bangalore. Shannon's entropy, alpha and beta population densities were computed to understand the level of urbanisation at local levels. Shannon's entropy values of recent time confirms dispersed haphazard urban growth in the city, particularly in the outskirts of the city. This also illustrates the extent of influence of drivers of urbanisation in various directions. Landscape metrics provided in depth knowledge about the sprawl. Principal component analysis helped in prioritizing the metrics for detailed analyses. The results clearly indicates that whole landscape is aggregating to a large patch in 2010 as compared to earlier years which was dominated by several small patches. The large scale conversion of small patches to large single patch can be seen from 2006 to 2010. In the year 2010 patches are maximally aggregated indicating that the city is becoming more compact and more urbanised in recent years. Bangalore was the most sought after destination for its climatic condition and the availability of various facilities (land availability, economy, political factors) compared to other cities. The growth into a single urban patch can be attributed to rapid urbanisation coupled with the industrialisation. Monitoring of growth through landscape metrics helps to maintain and manage the natural resources. (C) 2012 Elsevier B.V. All rights reserved.

Confinement and viscoelastic effects on chain closure dynamics

Chemical reactions inside cells are typically subject to the effects both of the cell's confining surfaces and of the viscoelastic behavior of its contents. In this paper, we show how the outcome of one particular reaction of relevance to cellular biochemistry - the diffusion-limited cyclization of long chain polymers - is influenced by such confinement and crowding effects. More specifically, starting from the Rouse model of polymer dynamics, and invoking the Wilemski-Fixman approximation, we determine the scaling relationship between the mean closure time t(c) of a flexible chain (no excluded volume or hydrodynamic interactions) and the length N of its contour under the following separate conditions: (a) confinement of the chain to a sphere of radius d and (b) modulation of its dynamics by colored Gaussian noise. Among other results, we find that in case (a) when d is much smaller than the size of the chain, t(c) similar to Nd-2, and that in case (b), t(c) similar to N-2/(2 (2H)), H being a number between 1/2 and 1 that characterizes the decay of the noise correlations. H is not known a priori, but values of about 0.7 have been used in the successful characterization of protein conformational dynamics. At this value of H (selected for purposes of illustration), t(c) similar to N-3.4, the high scaling exponent reflecting the slow relaxation of the chain in a viscoelastic medium. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4729041]

Dendrimer building toolkit: Model building and characterization of various dendrimer architectures

We have developed a graphical user interface based dendrimer builder toolkit (DBT) which can be used to generate the dendrimer configuration of desired generation for various dendrimer architectures. The validation of structures generated by this tool was carried out by studying the structural properties of two well known classes of dendrimers: ethylenediamine cored poly(amidoamine) (PAMAM) dendrimer, diaminobutyl cored poly(propylene imine) (PPI) dendrimer. Using full atomistic molecular dynamics (MD) simulation we have calculated the radius of gyration, shape tensor and monomer density distribution for PAMAM and PPI dendrimer at neutral and high pH. A good agreement between the available simulation and experimental (small angle X-ray and neutron scattering; SAXS, SANS) results and calculated radius of gyration was observed. With this validation we have used DBT to build another new class of nitrogen cored poly(propyl ether imine) dendrimer and study it's structural features using all atomistic MD simulation. DBT is a versatile tool and can be easily used to generate other dendrimer structures with different chemistry and topology. The use of general amber force field to describe the intra-molecular interactions allows us to integrate this tool easily with the widely used molecular dynamics software AMBER. This makes our tool a very useful utility which can help to facilitate the study of dendrimer interaction with nucleic acids, protein and lipid bilayer for various biological applications. © 2012 Wiley Periodicals, Inc.

Vapor-liquid-solid growth of Si nanowires: A kinetic analysis

A steady state kinetic model has been developed for the vapor-liquid-solid growth of Si whiskers or nanowires from liquid catalyst droplets. The steady state is defined as one in which the net injection rate of Si into the droplet is equal to the ejection rate due to wire growth. Expressions that represent specific mechanisms of injection and ejection of Si atoms from the liquid catalyst droplet have been used and their relative importance has been discussed. The analysis shows that evaporation and reverse reaction rates need to be invoked, apart from just surface cracking of the precursor, in order to make the growth rate radius dependent. When these pathways can be neglected, the growth rate become radius independent and can be used to determine the activation energies for the rate limiting step of heterogeneous precursor decomposition. The ejection rates depend on the mechanism of wire growth at the liquid-solid interface or the liquid-solid-vapor triple phase boundary. It is shown that when wire growth is by nucleation and motion of ledges, a radius dependence of growth rate does not just come from the Gibbs-Thompson effect on supersaturation in the liquid, but also from the dependence of the actual area or length available for nucleation. Growth rates have been calculated using the framework of equations developed and compared with experimental results. The agreement in trends is found to be excellent. The same framework of equations has also been used to account for the diverse pressure and temperature dependence of growth rates reported in the literature. © 2012 American Institute of Physics.

Rainbow connection number and connected dominating sets

The rainbow connection number of a connected graph is the minimum number of colors needed to color its edges, so that every pair of its vertices is connected by at least one path in which no two edges are colored the same. In this article we show that for every connected graph on n vertices with minimum degree delta, the rainbow connection number is upper bounded by 3n/(delta + 1) + 3. This solves an open problem from Schiermeyer (Combinatorial Algorithms, Springer, Berlin/Hiedelberg, 2009, pp. 432437), improving the previously best known bound of 20n/delta (J Graph Theory 63 (2010), 185191). This bound is tight up to additive factors by a construction mentioned in Caro et al. (Electr J Combin 15(R57) (2008), 1). As an intermediate step we obtain an upper bound of 3n/(delta + 1) - 2 on the size of a connected two-step dominating set in a connected graph of order n and minimum degree d. This bound is tight up to an additive constant of 2. This result may be of independent interest. We also show that for every connected graph G with minimum degree at least 2, the rainbow connection number, rc(G), is upper bounded by Gc(G) + 2, where Gc(G) is the connected domination number of G. Bounds of the form diameter(G)?rc(G)?diameter(G) + c, 1?c?4, for many special graph classes follow as easy corollaries from this result. This includes interval graphs, asteroidal triple-free graphs, circular arc graphs, threshold graphs, and chain graphs all with minimum degree delta at least 2 and connected. We also show that every bridge-less chordal graph G has rc(G)?3.radius(G). In most of these cases, we also demonstrate the tightness of the bounds.

Synchrotron Small-Angle X-ray Scattering Studies of Hemoglobin Nonaggregation Confined inside Polymer Capsules

The effect of confinement on the structure of hemoglobin (Hb) within polymer capsules was investigated here. Hemoglobin transformed from an aggregated state in solution to a nonaggregated state when confined inside the polymer capsules. This was directly confirmed using synchrotron small-angle X-ray scattering (SAXS) studies. The radius of gyration (R-g) and polydispersity (p) of the proteins in the confined state were smaller compared to those in solution. In fact, the R-g value is very similar to theoretical values obtained using protein structures generated from the Protein Databank. In the temperature range (25-85 degrees C, Tm 59 degrees C), the R-g values for the confined Hb remained constant. This observation is in contrary to the increasing R-g values obtained for the bare Hb in solution. This suggested higher thermal stability of Hb when confined inside the polymer capsule than when in solution. Changes in protein configuration were also reflected in the protein function. Confinement resulted in a beneficial enhancement of the electroactivity of Hb. While Hb in solution showed dominance of the cathodic process (Fe3+ -> Fe2+), efficient reversible Fe3+/Fe2+ redox response is observed in the case of the confined Hb. This has important protein functional implications. Confinement allows the electroactive heme to take up positions favorable for various biochemical activities such as sensing of analytes of various sizes from small to macromolecules and controlled delivery of drugs.

Dendrimer building toolkit: Model building and characterization of various dendrimer architectures

We have developed a graphical user interface based dendrimer builder toolkit (DBT) which can be used to generate the dendrimer configuration of desired generation for various dendrimer architectures. The validation of structures generated by this tool was carried out by studying the structural properties of two well known classes of dendrimers: ethylenediamine cored poly(amidoamine) (PAMAM) dendrimer, diaminobutyl cored poly(propylene imine) (PPI) dendrimer. Using full atomistic molecular dynamics (MD) simulation we have calculated the radius of gyration, shape tensor and monomer density distribution for PAMAM and PPI dendrimer at neutral and high pH. A good agreement between the available simulation and experimental (small angle X-ray and neutron scattering; SAXS, SANS) results and calculated radius of gyration was observed. With this validation we have used DBT to build another new class of nitrogen cored poly(propyl ether imine) dendrimer and study it's structural features using all atomistic MD simulation. DBT is a versatile tool and can be easily used to generate other dendrimer structures with different chemistry and topology. The use of general amber force field to describe the intra-molecular interactions allows us to integrate this tool easily with the widely used molecular dynamics software AMBER. This makes our tool a very useful utility which can help to facilitate the study of dendrimer interaction with nucleic acids, protein and lipid bilayer for various biological applications. (c) 2012 Wiley Periodicals, Inc.

Nonextremality, chemical potential, and the infrared limit of large N thermal QCD

Nonextremal solution with warped resolved-deformed conifold background is important to study the infrared limit of large N thermal QCD. Earlier works in this direction have not taken into account all the backreactions on the geometry, namely from the branes, fluxes, and black-hole carefully. In the present work we make some progress in this direction by solving explicitly the supergravity equations of motions in the presence of the backreaction from the black hole. The backreactions from the branes and the fluxes on the other hand and to the order that we study, are comparatively suppressed. Our analysis reveal, among other things, how the resolution parameter would depend on the horizon radius and how the renormalization group flows of the coupling constants should be understood in these scenarios, including their effects on the background three-form fluxes. We also study the effect of switching on a chemical potential in the background and, in a particularly simplified scenario, compute the actual value of the chemical potential for our case.

Model independent bounds on the modulus of the pion form factor on the unitarity cut below the omega pi threshold

We calculate upper and lower bounds on the modulus of the pion electromagnetic form factor on the unitarity cut below the omega pi inelastic threshold, using as input the phase in the elastic region known via the Fermi-Watson theorem from the pi pi P-wave phase shift, and a suitably weighted integral of the modulus squared above the inelastic threshold. The normalization at t = 0, the pion charge radius and experimental values at spacelike momenta are used as additional input information. The bounds are model independent, in the sense that they do not rely on specific parametrizations and do not require assumptions on the phase of the form factor above the inelastic threshold. The results provide nontrivial consistency checks on the recent experimental data on the modulus available below the omega pi threshold from e(+)e(-) annihilation and tau-decay experiments. In particular, at low energies the calculated bounds offer a more precise description of the modulus than the experimental data.

Deterministic seismic hazard macrozonation of India

Earthquakes are known to have occurred in Indian subcontinent from ancient times. This paper presents the results of seismic hazard analysis of India (6 degrees-38 degrees N and 68 degrees-98 degrees E) based on the deterministic approach using latest seismicity data (up to 2010). The hazard analysis was done using two different source models (linear sources and point sources) and 12 well recognized attenuation relations considering varied tectonic provinces in the region. The earthquake data obtained from different sources were homogenized and declustered and a total of 27,146 earthquakes of moment magnitude 4 and above were listed in the study area. The sesismotectonic map of the study area was prepared by considering the faults, lineaments and the shear zones which are associated with earthquakes of magnitude 4 and above. A new program was developed in MATLAB for smoothing of the point sources. For assessing the seismic hazard, the study area was divided into small grids of size 0.1 degrees x 0.1 degrees (approximately 10 x 10 km), and the hazard parameters were calculated at the center of each of these grid cells by considering all the seismic sources within a radius of 300 to 400 km. Rock level peak horizontal acceleration (PHA) and spectral accelerations for periods 0.1 and 1 s have been calculated for all the grid points with a deterministic approach using a code written in MATLAB. Epistemic uncertainty in hazard definition has been tackled within a logic-tree framework considering two types of sources and three attenuation models for each grid point. The hazard evaluation without logic tree approach also has been done for comparison of the results. The contour maps showing the spatial variation of hazard values are presented in the paper.