3-D kinematical conservation laws (KCL): Evolution of a surface in R-3 - in particular propagation of a nonlinear wavefront

3-D KCL are equations of evolution of a propagating surface (or a wavefront) Omega(t), in 3-space dimensions and were first derived by Giles, Prasad and Ravindran in 1995 assuming the motion of the surface to be isotropic. Here we discuss various properties of these 3-D KCL.These are the most general equations in conservation form, governing the evolution of Omega(t) with singularities which we call kinks and which are curves across which the normal n to Omega(t) and amplitude won Omega(t) are discontinuous. From KCL we derive a system of six differential equations and show that the KCL system is equivalent to the ray equations of 2, The six independent equations and an energy transport equation (for small amplitude waves in a polytropic gas) involving an amplitude w (which is related to the normal velocity m of Omega(t)) form a completely determined system of seven equations. We have determined eigenvalues of the system by a very novel method and find that the system has two distinct nonzero eigenvalues and five zero eigenvalues and the dimension of the eigenspace associated with the multiple eigenvalue 0 is only 4. For an appropriately defined m, the two nonzero eigenvalues are real when m > 1 and pure imaginary when m < 1. Finally we give some examples of evolution of weakly nonlinear wavefronts.

Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT)

System of kinematical conservation laws (KCL) govern evolution of a curve in a plane or a surface in space, even if the curve or the surface has singularities on it. In our recent publication K. R. Arun, P. Prasad, 3-D kinematical conservation laws (KCL): evolution of a surface in R-3-in particular propagation of a nonlinear wavefront, Wave Motion 46 (2009) 293-311] we have developed a mathematical theory to study the successive positions and geometry of a 3-D weakly nonlinear wavefront by adding an energy transport equation to KCL. The 7 x 7 system of equations of this KCL based 3-D weakly nonlinear ray theory (WNLRT) is quite complex and explicit expressions for its two nonzero eigenvalues could not be obtained before. In this short note, we use two different methods: (i) the equivalence of KCL and ray equations and (ii) the transformation of surface coordinates, to derive the same exact expressions for these eigenvalues. The explicit expressions for nonzero eigenvalues are important also for checking stability of any numerical scheme to solve 3-D WNLRT. (C) 2010 Elsevier Inc. All rights reserved.

Stereochemical properties and x-ray structure of a water-soluble diastereomeric (arene)ruthenium(II) Schiff-base complex: [Ru(.eta.-MeC6H4Pri-p)(H2O)(L*)](ClO4), containing a weakly bound aqua ligand [HL* = (S)-(.alpha.-methylbenzyl)salicylaldimine]

An air-stable and water-soluble diastereomeric half-sandwich ruthenium(I1) complex, [Ru(s-MeCsH4Pr'-p)(H*O)-(L*)] (C104) (l), has been isolated and structurally characterized [HL* = (27)-(a methylbenzyl)salicylaldimine,2-HOC6H4CH-NCHMePhI. Complex 1, Czd-I3oNO&lRu, crystallizes in the noncentric triclinic space group P1 with a = 9.885(1) A, b = 10.185(1) A, c = 14.187(2) A, a = 110.32(1)', 6 = 102.17(1)', y = 102.41(1)O, V=1243( 1) A3, and 2 = 2. The X-ray structure shows the presence of two diastereomers in a 1:l ratio having RR,,,SCand SR,,,&c onfigurations. The Ru-OHz bond distances are considerably long, and the values for RR, - a~n d SRu-1isomers are 2.1 19(5) and 2.203(5) A, respectively. The aqua complex (1) exists as a single diastereomer in solution,and it forms stable adducts with P-, N-, and halide-donor ligands. The stereochemical changes associated with adduct-forming reactions follow an inversion order: PPhs >> P(OMe)3 > pyridine bases >> halides (I, Br, Cl) >H20.

Rashbons: properties and their significance

In the presence of a synthetic non-Abelian gauge field that produces a Rashba-like spin-orbit interaction, a collection of weakly interacting fermions undergoes a crossover from a Bardeen-Cooper-Schrieffer (BCS) ground state to a Bose-Einstein condensate (BEC) ground state when the strength of the gauge field is increased (Vyasanakere et al 2011 Phys. Rev. B 84 014512). The BEC that is obtained at large gauge coupling strengths is a condensate of tightly bound bosonic fermion pairs. The properties of these bosons are solely determined by the Rashba gauge field-hence called rashbons. In this paper, we conduct a systematic study of the properties of rashbons and their dispersion. This study reveals a new qualitative aspect of the problem of interacting fermions in non-Abelian gauge fields, i.e. that the rashbon state ceases to exist when the center-of-mass momentum of the fermions exceeds a critical value that is of the order of the gauge coupling strength. The study allows us to estimate the transition temperature of the rashbon BEC and suggests a route to enhance the exponentially small transition temperature of the system with a fixed weak attraction to the order of the Fermi temperature by tuning the strength of the non-Abelian gauge field. The nature of the rashbon dispersion, and in particular the absence of the rashbon states at large momenta, suggests a regime in parameter space where the normal state of the system will be a dynamical mixture of uncondensed rashbons and unpaired helical fermions. Such a state should show many novel features including pseudogap physics.

Observation of trap-assisted space charge limited conductivity in short channel MoS2 transistor

We present temperature dependent I-V measurements of short channel MoS2 field effect devices at high source-drain bias. We find that, although the I-V characteristics are ohmic at low bias, the conduction becomes space charge limited at high V-DS, and existence of an exponential distribution of trap states was observed. The temperature independent critical drain-source voltage (V-c) was also determined. The density of trap states was quantitatively calculated from V-c. The possible origin of exponential trap distribution in these devices is also discussed. (C) 2013 AIP Publishing LLC.

Fiber Bragg Grating Sensor Instrumentation for Parking Space Occupancy Management

This work aims at providing an effective parking management system by reducing the drivers' searching time for vacant car-parking space, in turn improving the traffic flow in the car park areas. This is achieved by the use of Fiber Bragg Grating Sensor (FBG) sensor instrumentation in vehicle parking management system. Present work involves embedding an array of FBG sensors underground in the parking space, then determining the strain changes on the FBG sensor due to load applied by the vehicle parked in the parking space, occupancy of the parking space is determined. To validate the FBG sensor parking management system, three most common cases have been considered. This closed loop FBG parking management system can give real-time feed-back to space-guidance display board helping the driver in maneuvering the vehicle to the appropriate parking space. The proposed technique offers optimized usage of parking space for the various segments of cars and also facilitates in a conjoined automated billing system, as compared to conventional method of parking systems.

Role of orography in modulating space-time scales of convection over South Asia

Propagation of convective systems in the meridional direction during boreal summer is responsible for active and break phases of monsoon over south Asia. This region is unique in the world in its characteristics of monsoon variability and is in close proximity of mountains like the Himalayas. Here, using an atmospheric general circulation model, we try to understand the role of orography in determining spatial and temporal scales of these convective systems. Absence of orography (noGlOrog) decreased the simulated seasonal mean precipitation over India by 23 % due to delay in onset by about a month vis-a-vis the full-mountain case. In noGlOrog, poleward propagations were absent during the delayed period prior to onset. Post-onset, both simulations had similar patterns of poleward propagations. The spatial and temporal scales of propagating clouds bands were determined using wavelet analysis. These scales were found to be different in full-mountain and no-mountain experiments in June-July. However, after the onset of monsoon in noGlOrog, these scales become similar to that with orography. Simulations with two different sets of convection schemes confirmed this result. Further analysis shows that the absence (presence) of meridional propagations during early (late) phase of summer monsoon in noGlOrog was associated with weaker (stronger) vertical shear of zonal wind over south Asia. Our study shows that orography plays a major role in determining the time of onset over the Indian region. However, after onset, basic characteristics of propagating convective systems and therefore the monthly precipitation over India, are less sensitive to the presence of orography and are modulated by moist convective processes.

Divvying up an incubator: How parasitic and mutualistic fig wasps use space within their nursery microcosm

Differential occupancy of space can lead to species coexistence. The fig-fig wasp pollination system hosts species-specific pollinating and parasitic wasps that develop within galls in a nursery comprising a closed inflorescence, the syconium. This microcosm affords excellent opportunities for investigating spatial partitioning since it harbours a closed community in which all wasp species are dependent on securing safe sites inside the syconium for their developing offspring while differing in life history, egg deposition strategies and oviposition times relative to nursery development. We determined ontogenetic changes in oviposition sites available to the seven-member fig wasp community of Ficus racemosa comprising pollinators, gallers and parasitoids. We used species distribution models (SDMs) for the first time at a microcosm scale to predict patterns of spatial occurrence of nursery occupants. SDMs gave high true-positive and low false-positive site occupancy rates for most occupants indicating species specificity in oviposition sites. The nursery microcosm itself changed with syconium development and sequential egg-laying by different wasp species. The number of sites occupied by offspring of the different wasp species was negatively related to the risk of syconium abortion by the plant host following oviposition. Since unpollinated syconia are usually aborted, parasitic wasps ovipositing into nurseries at the same time as the pollinator targeted many sites, suggesting response to lower risk of syconium abortion owing to reduced risk of pollination failure compared to those species ovipositing before pollination. Wasp life history and oviposition time relative to nursery development contributed to the co-existence of nursery occupants.

Multivariate PLS Modeling of Apicomplexan FabD-Ligand Interaction Space for Mapping Target-Specific Chemical Space and Pharmacophore Fingerprints

Biomolecular recognition underlying drug-target interactions is determined by both binding affinity and specificity. Whilst, quantification of binding efficacy is possible, determining specificity remains a challenge, as it requires affinity data for multiple targets with the same ligand dataset. Thus, understanding the interaction space by mapping the target space to model its complementary chemical space through computational techniques are desirable. In this study, active site architecture of FabD drug target in two apicomplexan parasites viz. Plasmodium falciparum (PfFabD) and Toxoplasma gondii (TgFabD) is explored, followed by consensus docking calculations and identification of fifteen best hit compounds, most of which are found to be derivatives of natural products. Subsequently, machine learning techniques were applied on molecular descriptors of six FabD homologs and sixty ligands to induce distinct multivariate partial-least square models. The biological space of FabD mapped by the various chemical entities explain their interaction space in general. It also highlights the selective variations in FabD of apicomplexan parasites with that of the host. Furthermore, chemometric models revealed the principal chemical scaffolds in PfFabD and TgFabD as pyrrolidines and imidazoles, respectively, which render target specificity and improve binding affinity in combination with other functional descriptors conducive for the design and optimization of the leads.

Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. (C) 2015 Acoustical Society of America.

Some remarks on the symplectic pairing on the moduli space of representations of the fundamental group of surfaces

This work grew out of an attempt to understand a conjectural remark made by Professor Kyoji Saito to the author about a possible link between the Fox-calculus description of the symplectic structure on the moduli space of representations of the fundamental group of surfaces into a Lie group and pairs of mutually dual sets of generators of the fundamental group. In fact in his paper [3] , Prof. Kyoji Saito gives an explicit description of the system of dual generators of the fundamental group.

Leveraging coherent distributed space-time codes for noncoherent communication in relay networks via training

For point to point multiple input multiple output systems, Dayal-Brehler-Varanasi have proved that training codes achieve the same diversity order as that of the underlying coherent space time block code (STBC) if a simple minimum mean squared error estimate of the channel formed using the training part is employed for coherent detection of the underlying STBC. In this letter, a similar strategy involving a combination of training, channel estimation and detection in conjunction with existing coherent distributed STBCs is proposed for noncoherent communication in Amplify-and-Forward (AF) relay networks. Simulation results show that the proposed simple strategy outperforms distributed differential space-time coding for AF relay networks. Finally, the proposed strategy is extended to asynchronous relay networks using orthogonal frequency division multiplexing.

Hydrogen bonding in peptide helices - Analysis of two independent helices in the crystal structure of a peptide Boc-Val-Ala-Leu-Aib-Val-Ala-Phe-OMe

The crystal structure determination of the heptapeptide Boc-Val-Ala-Leu-Aib-Val-Ala-Phe-OMe reveals two peptide helices in the asymmetric unit, Crystal parameters are: space group P2(1), a = 10.356(2) Angstrom, b = 19.488(5) Angstrom, c = 23.756(6) Angstrom, beta = 102.25(2)degrees), V = 4685.4 Angstrom(3), Z = 4 and R = 5.7% for 7615 reflections [I>3 sigma(I)]. Both molecules adopt largely alpha-helical conformations with variations at the C-terminus, Helix type Is determined by analysing both 4-->1 and 5-->1 hydrogen-bond interactions and comparison with the results of analysis of protein structures. The presence of two 4-->1 hydrogen-bond interactions, besides four 5-->1 interact ions in both the conformations provides an opportunity to characterize bifurcated hydrogen bonds at high resolution, Comparison of the two helical conformations with related peptide structures suggests that distortions at the C-terminus are more facile than at the N-terminus.

Constraining the low-energy pion electromagnetic form factor with space-like and phase of time-like data

The Taylor coefficients c and d of the EM form factor of the pion are constrained using analyticity, knowledge of the phase of the form factor in the time-like region, 4m(pi)(2) <= t <= t(in) and its value at one space-like point, using as input the (g - 2) of the muon. This is achieved using the technique of Lagrange multipliers, which gives a transparent expression for the corresponding bounds. We present a detailed study of the sensitivity of the bounds to the choice of time-like phase and errors present in the space-like data, taken from recent experiments. We find that our results constrain c stringently. We compare our results with those in the literature and find agreement with the chiral perturbation-theory results for c. We obtain d similar to O(10) GeV-6 when c is set to the chiral perturbation-theory values.

Axial binding of 2-methylimidazole to the tetraarylcarboxylatodiruthenium (II, III) core: X-ray crystal structure of [Ru-2(O2CC6H4-p-OMe)(4)(2-mimH)(2)](ClO4). 1.75CH(2)Cl(2).H2O

Diruthenium (II. III) complexes of the type [Ru-2(O2CAr)(4) (2-mimH)(2)](ClO4) (Ar = C6H4-p-X : X=OMe,1, X=Me, 2, 2-mimH=2-methylimidazole) have been isolated from the reaction of Ru2Cl(O2CAr)(4) with 2-mimH in CH2Cl2 followed by the addition of NaClO4. The crystal structure of 1.1.75CH(2)Cl(2).H2O has been determined. The crystal belongs to the monoclinic space group p2(1)/c with the following unit cell dimensions for the C40H40N4O16ClRu2.1.75CH(2)Cl(2).H2O (M = 1237.0) : a = 12.347(3)Angstrom, b = 17.615(5)Angstrom, c = 26.148(2)Angstrom,beta = 92.88(1)degrees. v = 5679(2)Angstrom(3). Z=4, D-c = 1.45 g cm(-3). lambda(Mo-K-alpha) = 0.7107 Angstrom, mu(Mo-K-alpha) = 8.1 cm(-1), T = 293 K, R = 0.0815 (wR(2) = 0.2118) for 5834 reflections with 1 > 2 sigma(I). The complex has a tetracarboxylatodiruthenium (II, III) core and two axially bound 2-methylimidazole ligands. The Ru-Ru bond length is 2.290(1)Angstrom. The Ru-Ru bond order is 2.5 and the complex is three-electron paramagnetic. The complex shows an irreversible Ru-2(II,III)-->Ru-2(Il,II) reduction near -0.2 V vs SCE in CH2Cl2-0. 1 MTBAP. The complexes exemplify the first adduct of the tetracarboxylatodiruthenium (II,III) core having N-donor ligands