A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

Twisted conjugacy classes in nilpotent groups

A group is said to have the R(infinity) property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R(infinity) property when G is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer n >= 5, there is a compact nilmanifold of dimension n on which every homeomorphism is isotopic to a fixed point free homeomorphism. As a by-product, we give a purely group theoretic proof that the free group on two generators has the R(infinity) property. The R(infinity) property for virtually abelian and for C-nilpotent groups are also discussed.

Banach spaces without minimal subspaces

We prove three new dichotomies for Banach spaces a la W.T. Gowers` dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers` program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size K I into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. (c) 2009 Elsevier Inc. All fights reserved.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Equivariant Nielsen root theory for G-maps

Let X be a compact Hausdorff space, Y be a connected topological manifold, f : X -> Y be a map between closed manifolds and a is an element of Y. The vanishing of the Nielsen root number N(f; a) implies that f is homotopic to a root free map h, i.e., h similar to f and h(-1) (a) = empty set. In this paper, we prove an equivariant analog of this result for G-maps between G-spaces where G is a finite group. (C) 2010 Elsevier B.V. All rights reserved.

The 3-colored Ramsey number of even cycles

Denote by R(L, L, L) the minimum integer N such that any 3-coloring of the edges of the complete graph on N vertices contains a monochromatic copy of a graph L. Bondy and Erdos conjectured that when L is the cycle C(n) on n vertices, R(C(n), C(n), C(n)) = 4n - 3 for every odd n > 3. Luczak proved that if n is odd, then R(C(n), C(n), C(n)) = 4n + o(n), as n -> infinity, and Kohayakawa, Simonovits and Skokan confirmed the Bondy-Erdos conjecture for all sufficiently large values of n. Figaj and Luczak determined an asymptotic result for the `complementary` case where the cycles are even: they showed that for even n, we have R(C(n), C(n), C(n)) = 2n + o(n), as n -> infinity. In this paper, we prove that there exists n I such that for every even n >= n(1), R(C(n), C(n), C(n)) = 2n. (C) 2009 Elsevier Inc. All rights reserved.

Effects of Micelles and Vesicles on the Oximolysis of p-Nitrophenyl Diphenyl Phosphate: A Model System for Surfactant-Based Skin-defensive Formulations against Organophosphates

The rates of oximolysis of p-nitrophenyl diphenyl phosphate (PNPDPP) by Acetophenoxime; 10-phenyl-10-hydi-oxyiminodecanoic acid; 4-(9-carboxynonanyl)-1-(9-carboxy-1-hydroyiminononanyl) benzene; 1-dodecyl-2-[(hydroxyimino)methyl]-pyridinium chloride (IV) and N-methylpyridinium-2-aldoxime chloride were determined in micelles of N-hexadecyl-N,N,N-trimethylammonium chloride (CTAC), N-hexadecyl-N,N-dimethylammonium propanesulfonate and dioctadecyldimethylammonium chloride (DODAC) vesicles. The effects of CTAC micelles and DODAC vesicles on the rates of oxymolysis of O,O-Diethyl O-(4-nitrophenyl) phosphate (paraoxon) by oxime IV were also determined. Analysis of micellar and vesicular effects on oximolysis of PNPDPP, using pseudophase or pseudophase with explicit consideration of ion exchange models, required the determination of the aggregate`s effects on the pK(a), of oximes and on the rates of PNPDPP hydrolysis. All aggregates increased the rate of oximolysis of PNPDPP and the results were analyzed quantitatively. In particular, DODAC vesicles catalyzed the reaction and increased the rate of oximolysis of PNPDPP by IV several million fold at pH`s compatible with pharmaceutical formulations. The rate increase produced by DODAC vesicles on the rate of oximolysis paraoxon by IV demonstrates the pharmaceutical potential of this system, since the substrate is used as an agricultural defensive agent and the surfactant is extensively employed in cosmetic formulations. (C) 2008 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 98:1040-1052, 2009

GRASSIUS: A Platform for Comparative Regulatory Genomics across the Grasses

Transcription factors (TFs) are major players in gene regulatory networks and interactions between TFs and their target genes furnish spatiotemporal patterns of gene expression. Establishing the architecture of regulatory networks requires gathering information on TFs, their targets in the genome, and the corresponding binding sites. We have developed GRASSIUS (Grass Regulatory Information Services) as a knowledge-based Web resource that integrates information on TFs and gene promoters across the grasses. In its initial implementation, GRASSIUS consists of two separate, yet linked, databases. GrassTFDB holds information on TFs from maize (Zea mays), sorghum (Sorghum bicolor), sugarcane (Saccharum spp.), and rice (Oryza sativa). TFs are classified into families and phylogenetic relationships begin to uncover orthologous relationships among the participating species. This database also provides a centralized clearinghouse for TF synonyms in the grasses. GrassTFDB is linked to the grass TFome collection, which provides clones in recombination-based vectors corresponding to full-length open reading frames for a growing number of grass TFs. GrassPROMDB contains promoter and cis-regulatory element information for those grass species and genes for which enough data are available. The integration of GrassTFDB and GrassPROMDB will be accomplished through GrassRegNet as a first step in representing the architecture of grass regulatory networks. GRASSIUS can be accessed from www.grassius.org.

Vision in click beetles (Coleoptera: Elateridae): pigments and spectral correspondence between visual sensitivity and species bioluminescence emission

Among lampyrids, intraspecific sexual communication is facilitated by spectral correspondence between visual sensitivity and bioluminescence emission from the single lantern in the tail. Could a similar strategy be utilized by the elaterids (click beetles), which have one ventral abdominal and two dorsal prothoracic lanterns? Spectral sensitivity [S(lambda)] and bioluminescence were investigated in four Brazilian click beetle species Fulgeochlizus bruchii, Pyrearinus termitilluminans, Pyrophorus punctatissimus and P. divergens, representing three genera. In addition, in situ microspectrophotometric absorption spectra were obtained for visual and screening pigments in P. punctatissimus and P. divergens species. In all species, the electroretinographic S(lambda) functions showed broad peaks in the green with a shoulder in the near-ultraviolet, suggesting the presence of short- and long-wavelength receptors in the compound eyes. The long-wavelength receptor in Pyrophorus species is mediated by a P540 rhodopsin in conjunction with a species-specific screening pigment. A correspondence was found between green to yellow bioluminescence emissions and its broad S(lambda) maximum in each of the four species. It is hypothesized that in elaterids, bioluminescence of the abdominal lantern is an optical signal for intraspecifc sexual communication, while the signals from the prothoracic lanterns serve to warn predators and may also provide illumination in flight.

Room Temperature Ionic Liquid-Lithium Salt Mixtures: Optical Kerr Effect Dynamical Measurements

The addition of lithium salts to ionic liquids causes an increase in viscosity and a decrease in ionic mobility that hinders their possible application as an alternative solvent in lithium ion batteries. Optically heterodyne-detected optical Kerr effect spectroscopy was used to study the change in dynamics, principally orientational relaxation, caused by the addition of lithium bis(trifluoromethylsulfonyl)imide to the ionic liquid 1-buty1-3-methylimidazolium bis(trifluoromethylsulfonyl)imide. Over the time scales studied (1 ps-16 ns) for the pure ionic liquid, two temperature-independent power laws were observed: the intermediate power law (1 ps to similar to 1 ns), followed by the von Schweidler power law. The von Schweidler power law is followed by the final complete exponential relaxation, which is highly sensitive to temperature. The lithium salt concentration, however, was found to affect both power laws, and a discontinuity could be found in the trend observed for the intermediate power law when the concentration (mole fraction) of lithium salt is close to chi(LiTf(2)N) = 0.2. A mode coupling theory (MCT) schematic model was also used to fit the data for both the pure ionic liquid and the different salt concentration mixtures. It was found that dynamics in both types of liquids are described very well by MCT.

Single-wall carbon nanotubes modified with organic dyes: Synthesis, characterization and potential cytotoxic effects

This work deals with the covalent functionalization of single-wall carbon nanotubes (SWNTs) with phenosafranine (PS) and Nile Blue (NB) dyes. These dyes can act as photosensitizers in energy and electron transfer reactions, with a potential to be applied in photodynamic therapy. Several changes in the characteristic Raman vibrational features of the dyes suggest that a covalent modification of the nanotubes with the organic dyes occurs. Specifically, the vibrational modes assigned to the NH(2) moieties of the dyes are seen to disappear in the SWNT-dye nanocomposites, corroborating the bond formation between amine groups in the dyes and carboxyl groups in the oxidized nanotubes. The X-ray absorption (XANES) data also show, that the intense band at 398.6 eV attributed to 1s -> 2p pi* transition of the nitrogen of the aromatic PS ring, is shifted due to the bonding with the carbonic structure of the SWNTs. The cytotoxicity data of dyes-modified SWNT composites in the presence and absence of light shows that the SWNT-NB (4 mu g/mL) composite presents a good photodynamic effect, namely a low toxicity in the dark, higher toxicity in the presence of light and also a reduced dye photobleaching by auto-oxidation. (C) 2010 Elsevier B.V. All rights reserved.

(+)- and (-)-Mutisianthol: First Total Synthesis, Absolute Configuration, and Antitumor Activity

The first synthesis of the natural product (+)-mutisianthol was accomplished in 11 steps and in 21% overall yield from 2-methylanisole. The synthesis of its enantiomer was also performed in a similar overall yield. The absolute configuration of the sesquiterpene (+)-mutisianthol was assigned as (1S,3R). Key steps in the route are the asymmetric hydrogenation of a nonfunctionalized olefin using chiral iridium catalysts and the ring contraction of 1,2-dihydronaphthalenes using thallium(III) or iodine(III). The target molecules show moderate activity against the human tumor cell lines SF-295, HCT-8, and MDA-MB-435.

Charge-transfer behavior of polyaniline single wall carbon nanotubes nanocomposites monitored by resonance Raman spectroscopy

Highly dispersed nanocomposites of polyaniline(PANI) and oxidized single wall carbon nanotubes(SWNTs) have been prepared using dodecylbenzenesulfonic acid as dispersant. The materials were characterized via resonance Raman and electronic absorption spectroscopies. The behavior of the composites as a function of the applied potential was also investigated using in situ Raman electrochemical measurements. The results obtained at E(laser) = 1.17 eV suggest that a charge-transfer process occur between PANI and semiconducting nanotubes for samples where the metallic tubes are previously oxidized. The spectroelectrochemical data show that the presence of SWNTs prevents the oxidation of PANI rings. Copyright (C) 2010 John Wiley & Sons, Ltd.

Entropy Drives an Attached Water Molecule from the C- to N-Terminus on Protonated Proline

Results from infrared photodissociation (IRPD) spectroscopy and kinetics of singly hydrated, protonated proline indicate that the water molecule hydrogen bonds preferentially to the formally neutral carboxylic acid at low temperatures and at higher temperatures to the protonated N-terminus, which bears the formal charge. Hydration isomer populations obtained from IRPD kinetic data as a function of temperature are used to generate a van`t Hoff plot that reveals that C-terminal binding is enthalpically favored by 4.2-6.4 kJ/mol, whereas N-terminal binding is entropically favored by 31-43 J/(mol K), consistent with a higher calculated barrier for water molecule rotation at the C-terminus.