A multi-stage model for drop breakage in stirred vessels

Existing models for dmax predict that, in the limit of μd → ∞, dmax increases with 3/4 power of μd. Further, at low values of interfacial tension, dmax becomes independent of σ even at moderate values of μd. However, experiments contradict both the predictions show that dmax dependence on μd is much weaker, and that, even at very low values of σ,dmax does not become independent of it. A model is proposed to explain these results. The model assumes that a drop circulates in a stirred vessel along with the bulk fluid and repeatedly passes through a deformation zone followed by a relaxation zone. In the deformation zone, the turbulent inertial stress tends to deform the drop, while the viscous stress generated in the drop and the interfacial stress resist deformation. The relaxation zone is characterized by absence of turbulent stress and hence the drop tends to relax back to undeformed state. It is shown that a circulating drop, starting with some initial deformation, either reaches a steady state or breaks in one or several cycles. dmax is defined as the maximum size of a drop which, starting with an undeformed initial state for the first cycle, passes through deformation zone infinite number of times without breaking. The model predictions reduce to that of Lagisetty. (1986) for moderate values of μd and σ. The model successfully predicts the reduced dependence of dmax on μd at high values of μd as well as the dependence of dmax on σ at low values of σ. The data available in literature on dmax could be predicted to a greater accuracy by the model in comparison with existing models and correlations.

A nanosecond molecular dynamics study of antiparallel d(G)(7) quadruplex structures: Effect of the coordinated cations

Nanosecond scale molecular dynamics simulations have been performed on antiparallel Greek key type d(G(7)) quadruplex structures with different coordinated ions, namely Na+ and K+ ion, water and Na+ counter ions, using the AMBER force field and Particle Mesh Ewald technique for electrostatic interactions. Antiparallel structures are stable during the simulation, with root mean square deviation values of similar to1.5 Angstrom from the initial structures. Hydrogen bonding patterns within the G-tetrads depend on the nature of the coordinated ion, with the G-tetrad undergoing local structural variation to accommodate different cations. However, alternating syn-anti arrangement of bases along a chain as well as in a quartet is maintained through out the MD simulation. Coordinated Na+ ions, within the quadruplex cavity are quite mobile within the central channel and can even enter or exit from the quadruplex core, whereas coordinated K+ ions are quite immobile. MD studies at 400 K indicate that K+ ion cannot come out from the quadruplex core without breaking the terminal G-tetrads. Smaller grooves in antiparallel structures are better binding sites for hydrated counter ions, while a string of hydrogen bonded water molecules are observed within both the small and large grooves. The hydration free energy for the K+ ion coordinated structure is more favourable than that for the Na+ ion coordinated antiparallel quadruplex structure.

A multi-stage model for drop breakage in stirred vessels

Existing models for dmax predict that, in the limit of μd → ∞, dmax increases with 3/4 power of μd. Further, at low values of interfacial tension, dmax becomes independent of σ even at moderate values of μd. However, experiments contradict both the predictions show that dmax dependence on μd is much weaker, and that, even at very low values of σ,dmax does not become independent of it. A model is proposed to explain these results. The model assumes that a drop circulates in a stirred vessel along with the bulk fluid and repeatedly passes through a deformation zone followed by a relaxation zone. In the deformation zone, the turbulent inertial stress tends to deform the drop, while the viscous stress generated in the drop and the interfacial stress resist deformation. The relaxation zone is characterized by absence of turbulent stress and hence the drop tends to relax back to undeformed state. It is shown that a circulating drop, starting with some initial deformation, either reaches a steady state or breaks in one or several cycles. dmax is defined as the maximum size of a drop which, starting with an undeformed initial state for the first cycle, passes through deformation zone infinite number of times without breaking. The model predictions reduce to that of Lagisetty. (1986) for moderate values of μd and σ. The model successfully predicts the reduced dependence of dmax on μd at high values of μd as well as the dependence of dmax on σ at low values of σ. The data available in literature on dmax could be predicted to a greater accuracy by the model in comparison with existing models and correlations.

A new approach to the kinetics of size reduction in ball milling

The rate of breakage of feed in ball milling is usually represented in the form of a first-order rate equation. The equation was developed by treating a simple batch test mill as a well mixed reactor. Several case of deviation from the rule have been reported in the literature. This is attributed to the fact that accumulated fines interfere with the feed material and breaking events are masked by these fines. In the present paper, a new rate equation is proposed which takes into account the retarding effect of fines during milling. For this purpose the analogy of diffusion of ions through permeable membranes is adopted, with suitable modifications. The validity of the model is cross checked with the data obtained in batch grinding of ?850/+600 ?m size quartz. The proposed equation enables calculation of the rate of breakage of the feed at any instant of time.

Is tetramethyleneethane a ground state triplet?

We have examined a number of possible ways by which tetramethyleneethane (TME) can be a ground state triplet, as claimed by experimental studies, in violation of Ovchinnikov’s theorem for alternant hydrocarbons of equal bond lengths. Model exact π calculations of the low-lying states of TME, 3,4-dimethylenefuran and 3,4-dimethylenepyrrole were carried out using a diagrammatic valence bond approach. The calculations failed to yield a triplet ground state even after (a) tuning of electron correlation, (b) breaking alternancy symmetry, and (c) allowing for geometric distortions. In contrast to earlier studies of fine structure constants in other conjugated systems, the computedD andE values of all the low-lying triplet states of TME for various geometries are at least an order of magnitude different from the experimentally reported values. Incorporation of σ-π mixing by means of UHF MNDO calculations is found to favour a singlet ground state even further. A reinterpretation of the experimental results of TME is therefore suggested to resolve the conflict.

Kaon B parameter with Wilson fermions

We calculate the kaon B parameter in quenched lattice QCD at beta=6.0 using Wilson fermions at kappa=0.154 and 0.155. We use two kinds of nonlocal (''smeared'') sources for quark propagators to calculate the matrix elements between states of definite momentum. The use of smeared sources yields results with much smaller errors than obtained in previous calculations with Wilson fermions. By combining results for p=(0,0,0) and p=(0,0,1), we show that one can carry out the noperturbative subtraction necessary to remove the dominant lattice artifacts induced by the chiral-symmetry-breaking term in the Wilson action. Our final results are in good agreement with those obtained using staggered fermions. We also present results for B parameters of the DELTAI = 3/2 part of the electromagnetic penguin operators, and preliminary results for B(K) in the presence of two flavors of dynamical quarks.

A monolithic strategy for fluid-structure interaction problems

In this work, we present a new monolithic strategy for solving fluid-structure interaction problems involving incompressible fluids, within the context of the finite element method. This strategy, similar to the continuum dynamics, conserves certain properties, and thus provides a rational basis for the design of the time-stepping strategy; detailed proofs of the conservation of these properties are provided. The proposed algorithm works with displacement and velocity variables for the structure and fluid, respectively, and introduces no new variables to enforce velocity or traction continuity. Any existing structural dynamics algorithm can be used without change in the proposed method. Use of the exact tangent stiffness matrix ensures that the algorithm converges quadratically within each time step. An analytical solution is presented for one of the benchmark problems used in the literature, namely, the piston problem. A number of benchmark problems including problems involving free surfaces such as sloshing and the breaking dam problem are used to demonstrate the good performance of the proposed method. Copyright (C) 2010 John Wiley & Sons, Ltd.

Quantum Properties in Transport Through Nanoscopic Rings:Charge-Spin Separation and Interference Effects

Many of the most intriguing quantum effects are observed or could be measured in transport experiments through nanoscopic systems such as quantum dots, wires and rings formed by large molecules or arrays of quantum dots. In particular, the separation of charge and spin degrees of freedom and interference effects have important consequences in the conductivity through these systems. Charge-spin separation was predicted theoretically in one-dimensional strongly inter-acting systems (Luttinger liquids) and, although observed indirectly in several materials formed by chains of correlated electrons, it still lacks direct observation. We present results on transport properties through Aharonov-Bohmrings (pierced by a magnetic flux) with one or more channels represented by paradigmatic strongly-correlated models. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic flux which are a signature of spin and charge separation. Interference effects could also be controlled in certain molecules and interesting properties could be observed. We analyze transport properties of conjugated molecules, benzene in particular, and find that the conductance depends on the lead configuration. In molecules with translational symmetry, the conductance can be controlled by breaking or restoring this symmetry, e.g. by the application of a local external potential. These results open the possibility of observing these peculiar physical properties in anisotropic ladder systems and in real nanoscopic and molecular devices.

Synthesis, Reactivity, Structural Aspects, and Solution Dynamics of Cyclopalladated Compounds of N,N `,N `'-Tris(2-anisyl)guanidine

N,N',N `'-Tris(2-anisyl)guanidine, (ArNH)(2)C=NAr (Ar = 2-(MeO)C6H4), was cyclopallaclated with Pd(OC(O)R)(2) (R = Me, CF3) in toluene at 70 degrees C to afford palladacycles Pd{kappa(2)(C,N)-C6H3-(OMe)-3(NHC(NHAr)(=NAr))-2}(mu-OC(O)R)](2)(R = Me (1a) and CF3 (1b)) in 87% and 95% yield, respectively. Palladacycle 1a was subjected to a metathetical reaction with LiBr in aqueous ethanol at 78 degrees C to afford palladacycle Pd{kappa(2)(C,N)-C6H3(OMe)-3(NHC(NHAr)(=NAr))-2}(mu-Br)](2) (2) in 90% yield. Palladacycle 2 was subjected to a bridge-splitting reaction with Lewis bases in CH2Cl2 to afford the monomeric palladacycles Pd{kappa(2)(C,N)-C6H3(OMe)-3(NHC(NHAr)(=NAr))-2}Br(L)] (L = 2,6-Me2C5H3N (3a), 2,4-Me2C5H3N (3b), 3,5-Me2C5H3N (3c), XyNC (Xy = 2,6-Me2C6H3; 4a), (BuNC)-Bu-t (4b), and PPh3 (5)) in 87-95% yield. Palladacycle 2 upon reaction with 2 equiv of XyNC in CH2Cl2 afforded an unanticipated palladacycle, Pd{kappa(2)(C,N)-C(=NXy)(C6H3(OMe)-4)-2(N=C-(NH Ar)(2))-3} Br(CNXy)] (6) in 93% yield, and the driving force for the formation of 6 was ascribed to a ring contraction followed by amine-imine tautomerization. Palladacycles 1 a,b revealed a dimeric transoid in-in conformation with ``open book'' framework in the solid state. In solution, 1 a exhibited a fluxional behavior ascribed to the six-membered ``(C,N)Pd'' ring inversion and partly dissociates to the pincer type and kappa(2)-O,O'-OAc monomeric palladacycles by an anchimerically assisted acetate cleavage process as studied by variable-temperature H-1 NMR data. Palladacycles 3a,b revealed a unique trans configuration around the palladium with lutidine being placed trans to the Pd-C bond, whereas cis stereochemistry was observed between the Pd-C bond and the Lewis base in 4a (as determined by X-ray diffraction data) and 5 (as determined by P-31 and C-13 NMR data). The aforementioned stereochemical difference was explained by invoking relative hardness/softness of the donor atoms around the palladium center. In solution, palladacycles 3a-c exist as a mixture of two interconverting boat conformers via a planar intermediate without any bond breaking due to the six-membered ``(C,N)Pd'' ring inversion, whereas palladacycles 4a,b and 5 exist as a single isomer, as deduced from detailed H-1 NMR studies.

Extended gravitational action and novel consequences

It is found that the inclusion of higher derivative terms in the gravitational action along with concepts of phase transition and spontaneous symmetry breaking leads to some novel consequence. The Ricci scalar plays the dual role, like a physical field as well as a geometrical field. One gets Klein-Gordon equation for the emerging field and the corresponding quanta of geometry are called Riccions. For the early universe the model removes singularity along with inflation. In higher dimensional gravity the Riccions can break into spin half particle and antiparticle along with breaking of left-right symmetry. Most tantalizing consequences is the emergence of the physical universe from the geometry in the extreme past. Riccions can Bose condense and may account for the dark matter.

Assortative mating and the adaptive landscape

The ability of a population to shift from one adaptive peak to another was examined for a two-locus model with different degrees of assortative mating, selection, and linkage. As expected, if the proportion of the population that mates assortatively increases, so does its ability to shift to a new peak. Assortative mating affects this process by allowing the mean fitness of a population to increase monotonically as it passes through intermediate gene frequencies on the way to a new, higher, homozygotic peak. Similarly, if the height of the new peak increases or selection against intermediates becomes less severe, the population becomes more likely to shift to a new peak. Close linkage also helps the shift to a new adaptive peak and acts similarly to assortative mating, but it is not necessary for such a shift as was previously thought. When a population shifts to a new peak, the number of generations required is significantly less than that needed to return to the original peak when that happens. The short period of time required may be an explanation for rapid changes in the geological record. Under extremely high degrees of assortative mating, the shift takes longer, presumably because of the difficulty of breaking up less favored allelic combinations.

Inherent structures of phase-separating binary mixtures: Nucleation, spinodal decomposition, and pattern formation

An energy landscape view of phase separation and nonideality in binary mixtures is developed by exploring their potential energy landscape (PEL) as functions of temperature and composition. We employ molecular dynamics simulations to study a model that promotes structure breaking in the solute-solvent parent binary liquid, at low temperatures. The PEL of the system captures the potential energy distribution of the inherent structures (IS) of the system and is obtained by removing the kinetic energy (including that of intermolecular vibrations). The broader distribution of the inherent structure energy for structure breaking liquid than that of the structure making liquid demonstrates the larger role of entropy in stabilizing the parent liquid of the structure breaking type of binary mixtures. At high temperature, although the parent structure of the structure breaking binary mixture is homogenous, the corresponding inherent structure is found to be always phase separated, with a density pattern that exhibits marked correlation with the energy of its inherent structure. Over a broad range of intermediate inherent structure energy, bicontinuous phase separation prevails with interpenetrating stripes as signatures of spinodal decomposition. At low inherent structure energy, the structure is largely phase separated with one interface where as at high inherent structure energy we find nucleation type growth. Interestingly, at low temperature, the average inherent structure energy (< EIS >) exhibits a drop with temperature which signals the onset of crystallization in one of the phases while the other remains in the liquid state. The nonideal composition dependence of viscosity is anticorrelated with average inherent structure energy.

A profile of adenosine triphosphate

An attempt is made to draw a profile of adenosine triphosphate (ATP) and to project its many actions. The amazing versatility of its participation in a number of synthetic reactions lies in the oligophosphate structure. Many proteins that use ATP have conserved binding 'P-loop' but this gives no clue what makes it so special. The energy transducing reactions leading to synthesis of the terminal phosphodiester had at least three strategies. Of these, direct dehydration and transfer of inorganic phosphate using respiratory energy operate through mechano-coupling in a multisubunit protein. This tripartite, knob-stalk-base structure provides a novel mechanism of rotational catalysis and the tiniest molecular motor, All the reactions occur in concert with no sign of energized chemical intermediate. With the new knowledge on the crystal structure of F-1-ATPase, proton translocation needs a relook. An alternative perspective is emerging on energy being received and stored in polypeptide structure by breaking hydrogen bonds. Membrane serves the purpose of mobilizing the constituent proteins and also as a potential energy carrier of proteins with little loss of energy.

Biological water: Femtosecond dynamics of macromolecular hydration

The unique features of a macromolecule and water as a solvent make the issue of solvation unconventional, with questions about the static versus dynamic nature of hydration and the, physics of orientational and translational diffusion at the boundary. For proteins, the hydration shell that covers the surface is critical to the stability of its structure and function. Dynamically speaking, the residence time of water at the surface is a signature of its mobility and binding. With femtosecond time resolution it is possible to unravel the shortest residence times which are key for the description of the hydration layer, static or dynamic. In this article we review these issues guided by experimental studies, from this laboratory, of polar hydration dynamics at the surfaces of two proteins (Subtilisin Carlsberg (SC) and Monellin). The natural probe tryptophan amino acid was used for the interrogation of the dynamics, and for direct comparison we also studied the behavior in bulk water - a complete hydration in 1 ps. We develop a theoretical description of solvation and relate the theory to the experimental observations. In this - theoretical approach, we consider the dynamical equilibrium in the hydration shell, defining the rate processes for breaking and making the transient hydrogen bonds, and the effective friction in the layer which is defined by the translational and orientational motions of water molecules. The relationship between the residence time of water molecules and the observed slow component in solvation dynamics is a direct one. For the two proteins studied, we observed a "bimodal decay" for the hydration correlation function, with two primary relaxation times: ultrafast, typically 1 ps or less, and longer, typically 15-40 ps, and both are related to the residence time at the protein surface, depending on the binding energies. We end by making extensions to studies of the denatured state of the protein, random coils, and the biomimetic micelles, and conclude with our thoughts on the relevance of the dynamics of native structures to their functions.

Topological phases, Majorana modes and quench dynamics in a spin ladder system

We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z(2) symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the presence or absence of a vortex in each plaquette of the ladder. We show that vortex patterns can yield a rich parameter space for tuning into topologically non-trivial phases. We introduce and employ a new topological invariant for explicitly determining the presence of zero energy Majorana modes at the boundaries of such phases. Finally, we discuss dynamic quenching between topologically non-trivial phases in the Kitaev ladder and, in particular, the post-quench dynamics governed by tuning through a quantum critical point.