Hamiltonian structure for a neutrally buoyant rigid body interacting with N vortex rings of arbitrary shape: the case of arbitrary smooth body shape

We present a (noncanonical) Hamiltonian model for the interaction of a neutrally buoyant, arbitrarily shaped smooth rigid body with N thin closed vortex filaments of arbitrary shape in an infinite ideal fluid in Euclidean three-space. The rings are modeled without cores and, as geometrical objects, viewed as N smooth closed curves in space. The velocity field associated with each ring in the absence of the body is given by the Biot–Savart law with the infinite self-induced velocity assumed to be regularized in some appropriate way. In the presence of the moving rigid body, the velocity field of each ring is modified by the addition of potential fields associated with the image vorticity and with the irrotational flow induced by the motion of the body. The equations of motion for this dynamically coupled body-rings model are obtained using conservation of linear and angular momenta. These equations are shown to possess a Hamiltonian structure when written on an appropriately defined Poisson product manifold equipped with a Poisson bracket which is the sum of the Lie–Poisson bracket from rigid body mechanics and the canonical bracket on the phase space of the vortex filaments. The Hamiltonian function is the total kinetic energy of the system with the self-induced kinetic energy regularized. The Hamiltonian structure is independent of the shape of the body, (and hence) the explicit form of the image field, and the method of regularization, provided the self-induced velocity and kinetic energy are regularized in way that satisfies certain reasonable consistency conditions.      

Oblique Incidence Reflection Microscopy (OIRM) Study on Hydrocarbon Films

Studies on thin dotriacontane hydrocarbon in the form of thin films were made by employing Oblique Incidence Reflection Microscopy (OIRM). Information related to substructure and striations were discussed.     

Doxorubicin‐Anchored Curcumin Nanoparticles for Multimode Cancer Treatment against Human Liver Carcinoma Cells

Curcumin (Curcuma longa L), a yellow‐colored Indian spice, receives immense attention for the prevention and treatment of various cancers. Despite the superlative therapeutic efficacy, its poor solubility and instability in the aqueous medium hinder the effectiveness of cancer treatment. The novel preparation of curcumin nanoparticles by mechanical grinding of curcumin crystals without any toxic organic solvents is described here for the first time. The surface of curcumin nanoparticles is modified with the negatively charged polyelectrolyte poly(sodium 4‐strynesulfonate) through hydrogen bonding, which is the key to increasing the solubility and stability in the aqueous medium. The negative surface charge is exploited to conjugate doxorubicin drug molecule on the surface of curcumin nanoparticles as evidenced by fluorescence quenching experiments. Doxorubicin‐conjugated curcumin nanoparticles have a higher solubility with an enhanced cytotoxic effect toward the human hepatocellular carcinoma cell line by a reactive‐oxygen‐species‐mediated p53‐dependent apoptotic pathway. The combination of chemotherapy and photodynamic therapy significantly enhances antitumor activity of doxorubicin‐conjugated curcumin nanoparticles, and is expected to be a promising anticancer agent with special reference to human liver carcinoma cells.     

Comparing Hydrogen Deuterium Exchange and Fast Photochemical Oxidation of Proteins: a Structural Characterisation of Wild-Type and ΔN6 β<Subscript>2</Subscript>-Microglobulin

Hydrogen deuterium exchange (HDX) coupled to mass spectrometry (MS) is a well-established technique employed in the field of structural MS to probe the solvent accessibility, dynamics and hydrogen bonding of backbone amides in proteins. By contrast, fast photochemical oxidation of proteins (FPOP) uses hydroxyl radicals, liberated from the photolysis of hydrogen peroxide, to covalently label solvent accessible amino acid side chains on the microsecond-millisecond timescale. Here, we use these two techniques to study the structural and dynamical differences between the protein β₂-microglobulin (β₂m) and its amyloidogenic truncation variant, ΔN6. We show that HDX and FPOP highlight structural/dynamical differences in regions of the proteins, localised to the region surrounding the N-terminal truncation. Further, we demonstrate that, with carefully optimised LC-MS conditions, FPOP data can probe solvent accessibility at the sub-amino acid level, and that these data can be interpreted meaningfully to gain more detailed understanding of the local environment and orientation of the side chains in protein structures.

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Synthesis,characterisation and antibacterial studies of carbon nanoparticle and carbon nanoparticle encapsulated in functionally modified β-cyclodextrin with {5-[4-(dimethylamino) benzylidene]-4-oxo-2-thioxo-1, 3-thiazolidin-3-yl} acetic acid

This paper describes the synthesis of carbon nanoparticle (CNP) from natural sources such as kitchen soot, synthesis of a chromophoric system {5-[4-(dimethylamino) benzylidene]-4-oxo-2-thioxo1, 3-thiazolidin-3-yl} acetic acid and its incorporation into β-cyclodextrin (β-CD) through the esterification of the hydroxyl group with the free carboxyl function of the chromophoric system by DCC coupling. Encapsulation of CNP into functionally modified β-CD system was achieved. Characterisation of the products was undertaken by UV–visible, FT-IR, NMR, fluorescence spectroscopic methods, SEM, TEM and X-ray diffraction methods. Their antibacterial activities were addressed. The antibacterial activity of CNP and functionally modified β-CD-CNP products were tested against various pathogenic bacterial strains such as Streptcoccus haemoliticus (+ve), Staphylococcus aureus (+ve), Klebsiella pneumonia (?ve) and E. coli (MTCC1687) (?ve) by disc diffusion method. The results showed that the CNPs and functionally modified products have good antibacterial activity against selected pathogenic bacterial strains.     

The organization of aromatic side groups in an amyloid fibril probed by solid-state 2H and 19F NMR spectroscopy

Some 25 diseases are associated with proteins and peptides that assemble into amyloid fibrils composed of beta-strands connected by hydrogen bonds oriented parallel to the fiber long axis. There is mounting evidence that amyloid formation involves specific interactions between amino acid side groups, which bring together beta-sheets to form layers with buried and exposed faces. This work demonstrates how a combination of solid-state 2H and 19F NMR experiments can provide constraints on fibril architecture by probing the environment and spatial organisation of aromatic side groups. It is shown that phenylalanine rings within fibrils formed by a decapeptide fragment of the islet amyloid polypeptide, amylin, are highly motionally restrained and are situated within 6.5 A of one another. Taken together with existing structural constraints for this peptide, these results are consistent with a fibril architecture that comprises layers of two or more beta-sheets, with the aromatic residues facing into the inter-sheet space and possibly engaged in pi-pi interactions. The methods presented will be of general utility in exploring the architecture of fibrils of larger, full-length peptides and proteins, including amylin itself.     

A facile synthesis of dihydrobenzofuranols by photocyclization of (2‐alkoxy‐5‐methyl‐phenyl)(aryl) methanone and ethyl 2‐aroyl‐4‐methylphenyloxyacetates

Irradiation of 2‐alkoxy substituted benzophenones 2a–f and ethyl 2‐aroyl‐4‐methylphenyloxyacetates 2g–i in benzene and in acetonitrile underwent photocyclization to substituted dihydrobenzofuranols 3a–i with 3a–c in very less yield being racemate and 3d–i in good yield being mixture of cis‐trans isomers showing high stereoselectivity in benzene and decreased stereoselectivity in acetonitrile. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:212–217, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20111     

Policy analytics need more than a spreadsheet: a case study in funding formulae

This article presents two case studies, concerning the allocation of £Billions by a mechanism communicated via spreadsheet models. It argues that technical analytic skills as well as policy development skills are a vital component of governance. In the UK, Central Government uses funding formulae to distribute money to local service providers. One commonly stated goal of such formulae is equity of service provision. However, given the complexity of public services, together with variations in need, delivery style and the exercise of stakeholder judgement as to which needs should be met and how, such formulae frequently obscure the process by which equity has been taken into account. One policy ‘solution’ to managing such tensions is to seek ‘transparency’. With respect to funding formulae, this commonly involves publishing the underlying data and formulae in spreadsheets. This paper extends the argument that such ‘transparency’ requires an audience that understands the policy assumptions (and related conceptualisations), data sources, methodological approaches and interpretation of results. It demonstrates how the search for policy ‘transparency’ is also met by the technical quality assurance goals that the operational research community would recognise as best practice in the development both of software generally and spreadsheet models specifically. Illustrative examples of complex formulae acting to subvert equity are drawn from the English Fire and Rescue Service and Police Service allocation formulae. In the former, an increase in the amount of deprivation, as measured by one of six indicators, has the perverse effect of decreasing the financial allocation. In the latter, metropolitan areas such as London are found to gain most from the inclusion of variables measuring sparsity. The conclusion from these scenarios is that the steps needed to for technical quality assurance and policy transparency are mutually reinforcing goals, with policy analysts urged to make greater use of technical analytic skills in software development.     

Dissipative N-point-vortex Models in the Plane

A method is presented for constructing point vortex models in the plane that dissipate the Hamiltonian function at any prescribed rate and yet conserve the level sets of the invariants of the Hamiltonian model arising from the SE (2) symmetries. The method is purely geometric in that it uses the level sets of the Hamiltonian and the invariants to construct the dissipative field and is based on elementary classical geometry in ℝ³. Extension to higher-dimensional spaces, such as the point vortex phase space, is done using exterior algebra. The method is in fact general enough to apply to any smooth finite-dimensional system with conserved quantities, and, for certain special cases, the dissipative vector field constructed can be associated with an appropriately defined double Nambu–Poisson bracket. The most interesting feature of this method is that it allows for an infinite sequence of such dissipative vector fields to be constructed by repeated application of a symmetric linear operator (matrix) at each point of the intersection of the level sets.