A novel variable resolution global spectral method on the sphere

A variable resolution global spectral method is created on the sphere using High resolution Tropical Belt Transformation (HTBT). HTBT belongs to a class of map called reparametrisation maps. HTBT parametrisation of the sphere generates a clustering of points in the entire tropical belt; the density of the grid point distribution decreases smoothly in the domain outside the tropics. This variable resolution method creates finer resolution in the tropics and coarser resolution at the poles. The use of FFT procedure and Gaussian quadrature for the spectral computations retains the numerical efficiency available with the standard global spectral method. Accuracy of the method for meteorological computations are demonstrated by solving Helmholtz equation and non-divergent barotropic vorticity equation on the sphere. (C) 2011 Elsevier Inc. All rights reserved.

Real-time monitoring of critical nodes with minimal number of Phasor Measurement Units

This paper presents a method for placement of Phasor Measurement Units, ensuring the monitoring of vulnerable buses which are obtained based on transient stability analysis of the overall system. Real-time monitoring of phase angles across different nodes, which indicates the proximity to instability, the very purpose will be well defined if the PMUs are placed at buses which are more vulnerable. The issue is to identify the key buses where the PMUs should be placed when the transient stability prediction is taken into account considering various disturbances. Integer Linear Programming technique with equality and inequality constraints is used to find out the optimal placement set with key buses identified from transient stability analysis. Results on IEEE-14 bus system are presented to illustrate the proposed approach.

Electrical Treeing and the Associated PD Characteristics in LDPE Nanocomposites

Treeing in low density polyethylene (LDPE) filled with alumina nanocomposite as well as unfilled LDPE samples stressed with 50 Hz ac voltage has been studied. The tree inception voltage was monitored for various samples with different nano-filler loadings and it is seen that there is an increase in tree inception voltage with filler loading in LDPE. Treeing pattern and tree growth duration for unfilled and nano-filled LDPE samples have also been studied. Different tree growth patterns as well as a slower tree growth with increase in filler loading in LDPE nanocomposites were observed. The observed slow propagation of tree growth with filler loading is attributed to the changes in the polymer crystalline morphology induced by the presence of nano-particles and the greater ability of the nanoparticles to resist discharge growth. SEM studies carried out to determine the morphology of unfilled and nano-filled LDPE showed an increase in lamellae packing in LDPE nanocomposites and this increased lamellar density leads to a reduction in the tree propagation rate. Partial discharge activities were also monitored during the electrical tree growth in both the unfilled and the nano-filled LDPE samples and were found to be significantly different. PD magnitude and the number of PD pulses per cycle were found to be lower with electrical tree growth duration in LDPE nanocomposites as compared to unfilled LDPE. The same trend was seen with increased filler loading also.

Synthesis and an Evaluation of Molecular Conformation and Crystal Packing in Two Substituted 4-Phenylquinolines

The title compounds, namely Methyl 2-methyl-4 -phenylquinoline-3-carboxylate (I), C18H15NO2, and (2E)-3-(3,4-dimethoxyphenyl)-1-(2-methyl-4 -phenylquinolin-3-yl)prop-2-en-1-one (II), C27H23NO3, comprising of the phenyl ring, exhibit differences in conformational behaviour with respect to the plane of the quinoline fragment. (I) contains the methyl ester moiety whereas (II) contains the chalcone fragment, consisting of a double bond and phenyl group containing dimethoxy groups as substituents. The dihedral angles between the phenyl group and the quinoline ring is 82.77 (7)A degrees in (I), and 79.02 (8)A degrees in (II) respectively. It is the weak C-H center dot center dot center dot O=C H-bond and C-H center dot center dot center dot pi interactions which dictate packing of molecules in (I). In (II), it is C-H center dot center dot center dot N and C-H center dot center dot center dot pi, involving the dimethoxy ring, which controls packing of molecules in the crystal lattice. In addition, pi center dot center dot center dot pi aromatic stacking interactions involving the quinoline fragment is present in all the molecules. The title compounds, namely methyl-2-methyl-4 -phenylquinoline-3-carboxylate (I), C18H15NO2, and (2E)-3-(3,4-dimethoxyphenyl)-1-(2-methyl-4 -phenylquinolin-3-yl)prop-2-en-1-one (II), C27H23NO3, comprising of the phenyl ring, exhibit differences in conformational behaviour with respect to the plane of the quinoline fragment. (I) contains the methyl ester moiety whereas (III) contains the chalcone fragment, consisting of a double bond and phenyl group containing dimethoxy groups as substituents. The dihedral angles between the phenyl group and the quinoline ring is 82.77 (7)A degrees in (I), and 79.02 (8)A degrees in (II) respectively. It is the weak C-H center dot center dot center dot O=C H-bond and C-H center dot center dot center dot pi interactions which dictate packing of molecules in (I). In (II), it is C-H center dot center dot center dot N and C-H center dot center dot center dot pi, involving the dimethoxy ring, which controls packing of molecules in the crystal lattice. In addition, pi center dot center dot center dot pi aromatic stacking interactions involving the quinoline fragment is present in all the molecules.

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]

AIWIN - A fast and jigless inspection technique for machined parts

Precision inspection of manufactured components having multiple complex surfaces and variable tolerance definition is an involved, complex and time-consuming function. In routine practice, a jig is used to present the part in a known reference frame to carry out the inspection process. Jigs involve both time and cost in their development, manufacture and use. This paper describes 'as is where is inspection' (AIWIN), a new automated inspection technique that accelerates the inspection process by carrying out a fast registration procedure and establishing a quick correspondence between the part to inspect and its CAD geometry. The main challenge in doing away with a jig is that the inspection reference frame could be far removed from the CAD frame. Traditional techniques based on iterative closest point (ICP) or Newton methods require either a large number of iterations for convergence or fail in such a situation. A two-step coarse registration process is proposed to provide a good initial guess for a modified ICP algorithm developed earlier (Ravishankar et al., Int J Adv Manuf Technol 46(1-4):227-236, 2010). The first step uses a calibrated sphere for local hard registration and fixing the translation error. This transformation locates the centre for the sphere in the CAD frame. In the second step, the inverse transformation (involving pure rotation about multiple axes) required to align the inspection points measured on the manufactured part with the CAD point dataset of the model is determined and enforced. This completes the coarse registration enabling fast convergence of the modified ICP algorithm. The new technique has been implemented on complex freeform machined components and the inspection results clearly show that the process is precise and reliable with rapid convergence. © 2011 Springer-Verlag London Limited.

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.

Small-Angle Neutron-Scattering Studies of Mixed Micellar Structures Made of Dimeric Surfactants Having Imidazolium and Ammonium Headgroups

Planar imidazolium cation based gemini surfactants 16-Im-n-Im-16], 2Br(-) (where n = 2, 3, 4, 5, 6, 8, 10, and 12), exhibit different morphologies and internal packing arrangements by adopting different supramolecular assemblies in aqueous media depending on their number of spacer methylene units (CH2)(n). Detailed measurements of the small-angle neutron-scattering (SANS) cross sections from different imidazolium-based surfactant micelles in aqueous media (D2O) are reported. The SANS data, containing the information of aggregation behavior of such surfactants in the molecular level, have been analyzed on the basis of the Hayter and Penfold model for the macro ion solution to compute the interparticle structure factor S(Q) taking into account the screened Coulomb interactions between the dimeric surfactant micelles. The characteristic changes in the SANS spectra of the dimeric surfactant with n = 4 due to variation of temperature have also been investigated. These data are then compared with the SANS characterization data of the corresponding gemini micelles containing tetrahedral ammonium ion based polar headgroups. The critical micellar concentration of each surfactant micelle (cmc) has been determined using pyrene as an extrinsic fluorescence probe. The variation of cmc as a function of spacer chain length has been explained in terms of conformational variation and progressive looping of the spacer into the micellar interior upon increasing the n values. Small-angle neutron-scattering (SANS) cross sections from different mixed micelles composed of surfactants with ammonium headgroups, 16-A(0), 16-Am-n-Am-16], 2Br(-) (where n = 4), 16-I-0, and 16-Im-n-Im-16], 2Br(-) (where n = 4), in aqueous media (D2O) have also been analyzed. The aggregate composition matches with that predicted from the ideal mixing model.

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.

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).

Dual Role of Acetate as a Nucleophile and as an Internal Base in Cycloplatination Reaction of sym-N,N `,N `'-Triarylguanidines

Reaction of cis-Cl2Pt(S(O)Me-2)(2)] with 1 equiv of sym-N,N',N `'-triarylguanidines, ArN=C(NHAr)(2) (sym = symmetrical; Ar = 2-MeC6H4 (LH22-tolyl), 2-(MeO)C6H4 (LH22-anisyl), 4-MeC6H4 (LH24-tolyl), 2,5-Me2C6H3 (LH22,5-xylyl), and 2,6-Me2C6H3 (LH22,6-xylyl)) in toluene under reflux condition for 3 h afforded cis- or trans-Cl2Pt(S(O)Me-2)(ArN=C(NHAr)(2))] (Ar = 2-MeC6H4 (1), 2-(MeO)C6H4 (2), 4-MeC6H4 (3), 2,5-h Me2C6H3 (4), and 2,6-Me2C6H3 (5), respectively) in 83-96% yield. Reaction of cis-Cl2Pt(S(O)Me-2)(2)] with 1 equiv of LH22-tolyl and LH24-tolyl in the presence of 1 equiv of NaOAc in methanol under reflux condition for 3 h afforded acetate-substituted products, cis-(AcO)ClPt(S(O)Me-2)(ArN=C(NHAr)(2))] (Ar = 2-MeC6H4 (6) and 4-MeC6H4 (7)) in 83% and 84% yields, respectively. Reaction of cis-Cl2Pt(S(O)Me-2)(2)] with 1 equiv of LH22-anisyl and LH22-tolyl in the presence of 1 equiv of NaOAc in methanol under reflux condition for 3 and 12 h afforded six-membered C,N] platinacycles, Pt{kappa(2)(C,N)-C6H3R-3(NHC(NHAr)(=NAr))-2}Cl(S(O)Me-2)] (Ar = 2-RC6H4; R = OMe (8) and Me (9)), in 92% and 79% yields, respectively. The new complexes have been characterized by analytical and spectroscopic techniques, and further the molecular structures of 1, 2, 4, 5, 6, and 8 have been determined by single-crystal X-ray diffraction. The platinum atom in 1, 4, and 5 exhibited the trans configuration, while that in 2, 6, and 8 exhibited the cis configuration. Complex 6 is shown to be the precursor for 9, and the former is suggested to transform to the latter possibly via an intramolecular C-H activation followed by elimination of AcOH. The solution behavior of new complexes has been studied by multinuclear NMR (H-1, Pt-195, and C-13) spectroscopy. The new complexes exist exclusively as a single isomer (trans (1 and 5) and cis (6 and 7)), a mixture of cis and trans isomers with the former isomer being predominant in the case of 2 and the latter isomer being predominant in the case of 3. Complex 5 in the trans form revealed the presence of one isomer at 0.007 mM concentration and two isomers in about 1.00:0.12 ratio at 0.154 mM concentration as revealed by H-1 NMR spectroscopy, and this has been ascribed to the restricted Pt-S bond rotation at higher concentration. Platinacycle 8 exists as one isomer, while 9 exists as a mixture of seven isomers in solution. The influence of steric factor, pi-acceptor property of the guanidine, subtle solid-state packing forces upon the configuration of the platinum atom, and the number of isomers in solution have been outlined. Factors that accelerate or slow down the cycloplatination reaction, the role of NaOAc, and a plausible mechanism of this reaction have been discussed.

Packing in molten globules and native states

Close packing of hydrophobic residues in the protein interior is an important determinant of protein stability. Cavities introduced by large to small substitutions are known to destabilize proteins. Conversely, native states of proteins and protein fragments can be stabilized by filling in existing cavities. Molten globules (MGs) were initially used to describe a state of protein which has well-defined secondary structure but little or no tertiary packing. Subsequent studies have shown that MGs do have some degree of native-like topology and specific packing. Wet molten globules (WMGs) with hydrated cores and considerably decreased packing relative to the native state have been studied extensively. Recently there has been renewed interest in identification and characterization of dry molten globules (DMGs). These are slightly expanded forms of the native state which show increased conformational flexibility, native-like main-chain hydrogen bonding and dry interiors. The generality of occurrence of DMGs during protein unfolding and the extent and nature of packing in DMGs remain to be elucidated. Packing interactions in native proteins and MGs can be probed through mutations. Next generation sequencing technologies make it possible to determine relative populations of mutants in a large pool. When this is coupled to phenotypic screens or cell-surface display, it becomes possible to rapidly examine large panels of single-site or multi-site mutants. From such studies, residue specific contributions to protein stability and function can be estimated in a highly parallelized fashion. This complements conventional biophysical methods for characterization of packing in native states and molten globules.

Evaluation of kissing bond in composite adhesive lap joints using digital image correlation: Preliminary studies

The assembly of aerospace and automotive structures in recent years is increasingly carried out using adhesives. Adhesive joints have advantages of uniform stress distribution and less stress concentration in the bonded region. Nevertheless, they may suffer due to the presence of defects in bond line and at the interface or due to improper curing process. While defects like voids, cracks and delaminations present in the adhesive bond line may be detected using different NDE methods, interfacial defects in the form of kissing bond may go undetected. Attempts using advanced ultrasonic methods like nonlinear ultrasound and guided wave inspection to detect kissing bond have met with limited success stressing the need for alternate methods. This paper concerns the preliminary studies carried out on detectability of dry contact kissing bonds in adhesive joints using the Digital Image Correlation (DIC) technique. In this attempt, adhesive joint samples containing varied area of kissing bond were prepared using the glass fiber reinforced composite (GFRP) as substrates and epoxy resin as the adhesive layer joining them. The samples were also subjected to conventional and high power ultrasonic inspection. Further, these samples were loaded till failure to determine the bond strength during which digital images were recorded and analyzed using the DIC method. This noncontact method could indicate the existence of kissing bonds at less than 50% failure load. Finite element studies carried out showed a similar trend. Results obtained from these preliminary studies are encouraging and further tests need to be done on a larger set of samples to study experimental uncertainties and scatter associated with the method. (C) 2013 Elsevier Ltd. All rights reserved.

Coulomb-hole summations and energies for GW calculations with limited number of empty orbitals: a modified static remainder approach

Ab initio GW calculations are a standard method for computing the spectroscopic properties of many materials. The most computationally expensive part in conventional implementations of the method is the generation and summation over the large number of empty orbitals required to converge the electron self-energy. We propose a scheme to reduce the summation over empty states by the use of a modified static remainder approximation, which is simple to implement and yields accurate self-energies for both bulk and molecular systems requiring a small fraction of the typical number of empty orbitals.

Analysis of designed beta-hairpin peptides: molecular conformation and packing in crystals

The crystal structures of several designed peptide hairpins have been determined in order to establish features of molecular conformations and modes of aggregation in the crystals. Hairpin formation has been induced using a centrally positioned (D)Pro-Xxx segment (Xxx = (L)Pro, Aib, Ac(6)c, Ala; Aib = alpha-aminoisobutyric acid; Ac(6)c = 1-aminocyclohexane-1-carboxylic acid). Structures of the peptides Boc-Leu-Phe-Val-(D)Pro-(L)Pro-Leu-Phe-Val-OMe (1), Boc-Leu-Tyr-Val-(D)Pro-(L)Pro-Leu-Phe-Val-OMe (2, polymorphic forms labeled as 2a and 2b), Boc-Leu-Val-Val-(D)Pro-(L)Pro-Leu-Val-Val-OMe (3), Boc-Leu-Phe-Val-(D)Pro-Aib-Leu-Phe-Val-OMe (4, polymorphic forms labeled as 4a and 4b), Boc-Leu-Phe-Val-(D)Pro-Ac(6)c-Leu-Phe-Val-OMe (5) and Boc-Leu-Phe-Val-(D)Pro-Ala-Leu-Phe-Val-OMe (6) are described. All the octapeptides adopt type II' beta-turn nucleated hairpins, stabilized by three or four cross-strand intramolecular hydrogen bonds. The angle of twist between the two antiparallel strands lies in the range of -9.8 degrees to -26.7 degrees. A detailed analysis of packing motifs in peptide hairpin crystals is presented, revealing three broad modes of association: parallel packing, antiparallel packing and orthogonal packing. An attempt to correlate aggregation modes in solution with observed packing motifs in crystals has been made by indexing of crystal faces in the case of three of the peptide hairpins. The observed modes of hairpin aggregation may be of relevance in modeling multiple modes of association, which may provide insights into the structure of insoluble polypeptide aggregates.