Symmetry in stochasticity: Random walk models of large-scale structure

This paper describes the insights gained from the excursion set approach, in which various questions about the phenomenology of large-scale structure formation can be mapped to problems associated with the first crossing distribution of appropriately defined barriers by random walks. Much of this is summarized in R K Sheth, AIP Conf. Proc. 1132, 158 (2009). So only a summary is given here, and instead a few new excursion set related ideas and results which are not published elsewhere are presented. One is a generalization of the formation time distribution to the case in which formation corresponds to the time when half the mass was first assembled in pieces, each of which was at least 1/n times the final mass, and where n ≥ 2; another is an analysis of the first crossing distribution of the Ornstein–Uhlenbeck process. The first derives from the mirror-image symmetry argument for random walks which Chandrasekhar described so elegantly in 1943; the second corrects a misuse of this argument. Finally, some discussion of the correlated steps and correlated walks assumptions associated with the excursion set approach, and the relation between these and peaks theory are also included. These are problems in which Chandra’s mirror-image symmetry is broken.     

Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 1024³, 2048³, and 4096³ grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good ‘weak’ and ‘strong’ scaling for Tarang on these systems.     

Nucleophilic Substitution Reactions of Meta‐ and Para‐Substituted Benzylamines with Benzyl Bromide in Methanol Medium

The rates of reactions of para‐ and meta‐substituted benzylamines with benzyl bromide were measured using conductivity technique in methanol medium. The reaction followed a total second‐order path. The end product of the reaction is identified as dibenzylamine (X‐C₆H₄CH₂NHCH₂C₆H₅) (where X = 4‐OCH₃, 4‐CH₃, H, 4‐Cl, 4‐CF₃, 3‐CF₃, 4‐NO₂). Electron‐withdrawing groups such as chloro, trifluoromethyl, and nitro in the benzylamine moiety decrease the rate of the reaction, whereas the electron‐donating groups, such as methoxy and methyl, increase the rate compared to the unsubstituted compound. A mechanism involving formation of an S_N2‐type transition state between the amine nucleophiles and the benzyl bromide and its subsequent decomposition is proposed. Hammett's reaction constant ρ of the reaction decreases with an increase in temperature. Activation parameters were calculated and discussed.     

One Pot Reduction of Imines Generated in-situ from Aldehydes and Amines by the NaBH4-InCl3 System

A combination of sodium borohydride and a catalytic amount of indium（Ⅲ） chloride in acetonitrile reduces imines formed in-situ from aldehydes and amines to the corresponding functionalised secondary and tertiary amines in moderate to good yields. Noteworthy is that highly chemoselective reactions were achieved in the presence of other functional groups such as halogens, carbon-carbon double bonds and hydroxyl groups.     

Computation of the 3-D Unsteady Flow Past Deforming Geometries

A 3-D incompressible unsteady flow solver based on simple finite elements with adaptive remeshing and grid movement for both moving and deforming surfaces is described. We demonstrate the combination of adaptive remeshing techniques with the incompressible flow solver with the computation of flow past an eel in 2-D and a blue-fin tuna in 3-D. The flow past a swimming tuna was computed for two extreme cases of the caudal fin frequency and swimming speed. A grid refinement study was performed and a grid converged solution for the force produced by the caudal fin was obtained.     

An efficient approach for the synthesis of novel methyl sulfones in acetic acid medium and evaluation of antimicrobial activity

A series of nine methyl sulphones ( 3a –3 i ) starting from the aldehydes ( 1a–1i ) were synthesized in two consecutive steps. In the first step, preparation of allyl alcohols ( 2a–2i ) from their corresponding aldehydes by the reaction of sodium borohydride in methanol at room temperature is reported. Finally, methyl sulphones are synthesized by condensing sodium methyl sulfinates with allyl alcohols in the presence of BF ₃ .Et ₂ O in acetic acid medium at room temperature for about 2–3 h. The reaction conditions are simple, yields are high (85%–95%), and the products were obtained with good purity. All the synthesized compounds were characterized by their ¹ H, ¹³ C NMR, and mass spectral analysis. All the title compounds were screened for antimicrobial activity. Among the compounds tested, the compound 3f has inhibited both Gram positive and Gram negative bacteria effectively and compound 3i has shown potent antifungal activity. These promising components may help to develop more potent drugs in the near future for the treatment of bacterial and fungal infections.     

An efficient parallel algorithm for non-equilibrium molecular dynamics simulations of very large systems in planar Couette flow

In this paper we present an efficient parallel domain decomposition algorithm for non-equilibrium molecular dynamics (NEMD) simulations of large systems under planar Couette flow. We propose a modified deforming cell method that permits NEMD simulations with negligible penalties due to the Lees-Edwards periodic boundary conditions. The algorithm was used to study large systems of the Weeks-Chandler-Andersen fluid in order to obtain better viscosity results at the low shear rate regimes where the signal-to-noise ratio is very small.     

Free energy studies of freezing in slit pores: an order-parameter approach using Monte Carlo simulation

We report a molecular simulation study of freezing transitions for simple fluids in narrow slit pores. A major stumbling block in previous studies of freezing in pores has been the lack of any method for calculating the free energy difference between the confined solid and liquid phases. Conventional thermodynamic integration methods often fail for confined systems, due to the difficulty in choosing a suitable path of integration. We use a different approach that involves calculating the Landau free energy as a function of a suitable order parameter, using the grand canonical Monte Carlo simulation method. The grand free energy for each phase can then be obtained by one-dimensional integration of the Landau free energy over the order parameter. These calculations are carried out for two types of wall—fluid interaction, a hard wall and a strongly attractive wall modelled on carbon. The grand free energy results for both cases clearly indicate a first order fluid to solid transition. In the case of the attractive carbon wall, there are three phases. Phase A corresponds to all layers having a liquid-like structure; phase B corresponds to the contact layers (the layers adjacent to the two pore walls) being frozen and the rest of the layers being fluid-like; phase C corresponds to all the layers being frozen. Our results for the angular structure function in the individual molecular layers show strong evidence of a transition from a two-dimensional liquid phase to a hexatic phase. This is followed by a transition from the hexatic to a crystal phase.     

Synthesis of Dinaphtho-dioxaphosphepin-4-oxides, Epoxides and Bisphosphonates

A few new seven-membered phosphorus heterocyclic compounds and bis-phosphonates (5a—5g, 5f’, 5g’, 9 and 10) were prepared by the reaction of 4-bromo dioxaphosphepin (2) with various Grignard reagents followed by their oxidation with H2O2. All the compounds were thoroughly characterized by elemental analysis, IR, 1H, 13C, 31P NMR and mass spectral data. Their antimicrobial activity was evaluated and some of them possess significant activity.