Multisymplectic formulation of fluid dynamics using the inverse map

We construct multisymplectic formulations of fluid dynamics using the inverse of the Lagrangian path map. This inverse map, the ‘back-to-labels’ map, gives the initial Lagrangian label of the fluid particle that currently occupies each Eulerian position. Explicitly enforcing the condition that the fluid particles carry their labels with the flow in Hamilton's principle leads to our multisymplectic formulation. We use the multisymplectic one-form to obtain conservation laws for energy, momentum and an infinite set of conservation laws arising from the particle relabelling symmetry and leading to Kelvin's circulation theorem. We discuss how multisymplectic numerical integrators naturally arise in this approach.</p

Discrete momentum maps for lattice EPDiff

We focus on the spatial discretization produced by the Variational Particle-Mesh (VPM) method for a prototype fluid equation the known as the EPDiff equation}, which is short for Euler-Poincar\'e equation associated with the diffeomorphism group (of $\mathbb{R}^d$, or of a $d$-dimensional manifold $\Omega$). The EPDiff equation admits measure valued solutions, whose dynamics are determined by the momentum maps for the left and right actions of the diffeomorphisms on embedded subspaces of $\mathbb{R}^d$. The discrete VPM analogs of those dynamics are studied here. Our main results are: (i) a variational formulation for the VPM method, expressed in terms of a constrained variational principle principle for the Lagrangian particles, whose velocities are restricted to a distribution D_{\VPM} which is a finite-dimensional subspace of the Lie algebra of vector fields on $\Omega$; (ii) a corresponding constrained variational principle on the fixed Eulerian grid which gives a discrete version of the Euler-Poincar\'e equation; and (iii) discrete versions of the momentum maps for the left and right actions of diffeomorphisms on the space of solutions

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow

A jetlet hierarchy for ideal fluid dynamics

European Research Council Advanced Grant 267382 FCCA

Variational water-wave model with accurate dispersion and vertical vorticity

A new water-wave model has been derived which is based on variational techniques and combines a depth-averaged vertical (component of) vorticity with depth-dependent potential flow. The model facilitates the further restriction of the vertical profile of the velocity potential to n-th order polynomials or a finite-element profile with a small number of elements (say), leading to a framework for efficient modeling of the interaction of steepening and breaking waves near the shore with a large-scale horizontal flow. The equations are derived from a constrained variational formulation which leads to conservation laws for energy, mass, momentum and vertical vorticity. It is shown that the potential-flow water-wave equations and the shallow-water equations are recovered in the relevant limits. Approximate shock relations are provided, which can be used in numerical schemes to model breaking waves

Weak dual pairs and Jetlet methods for ideal incompressible fluid models in n≥2 dimensions

We review the role of dual pairs in mechanics and use them to derive particle-like solutions to regularized incompressible fluid systems. In our case we have a dual pair resulting from the action of diffeomorphisms on point particles (essentially by moving the points). We then augment our dual pair by considering the action of diffeomorphisms on Taylor series, also known as jets. The augmented weak dual pairs induce a hierarchy of particle-like solutions and conservation laws with particles carrying a copy of a jet group. We call these augmented particles jetlets. The jet groups serve as finite-dimensional models of the diffeomorphism group itself, and so the jetlet particles serve as a finite-dimensional model of the self-similarity exhibited by ideal incompressible fluids. The conservation law associated to jetlet solutions is shown to be a shadow of Kelvin’s circulation theorem. Finally, we study the dynamics of infinite time particle mergers. We prove that two merging particles at the zeroth level in the hierarchy yield dynamics which asymptotically approach that of a single particle in the first level in the hierarchy. This merging behavior is then verified numerically as well as the exchange of angular momentum which must occur during a near collision of two particles. The resulting particle-like solutions suggest a new class of meshless methods which work in dimensions [Math Processing Error] n≥2 and which exhibit a shadow of Kelvin’s circulation theorem. More broadly, this provides one of the first finite-dimensional models of self-similarity in ideal fluids

An optimized TOPS+ comparison method for enhanced TOPS models

This article has been made available through the Brunel Open Access Publishing Fund.Background Although methods based on highly abstract descriptions of protein structures, such as VAST and TOPS, can perform very fast protein structure comparison, the results can lack a high degree of biological significance. Previously we have discussed the basic mechanisms of our novel method for structure comparison based on our TOPS+ model (Topological descriptions of Protein Structures Enhanced with Ligand Information). In this paper we show how these results can be significantly improved using parameter optimization, and we call the resulting optimised TOPS+ method as advanced TOPS+ comparison method i.e. advTOPS+. Results We have developed a TOPS+ string model as an improvement to the TOPS [1-3] graph model by considering loops as secondary structure elements (SSEs) in addition to helices and strands, representing ligands as first class objects, and describing interactions between SSEs, and SSEs and ligands, by incoming and outgoing arcs, annotating SSEs with the interaction direction and type. Benchmarking results of an all-against-all pairwise comparison using a large dataset of 2,620 non-redundant structures from the PDB40 dataset [4] demonstrate the biological significance, in terms of SCOP classification at the superfamily level, of our TOPS+ comparison method. Conclusions Our advanced TOPS+ comparison shows better performance on the PDB40 dataset [4] compared to our basic TOPS+ method, giving 90 percent accuracy for SCOP alpha+beta; a 6 percent increase in accuracy compared to the TOPS and basic TOPS+ methods. It also outperforms the TOPS, basic TOPS+ and SSAP comparison methods on the Chew-Kedem dataset [5], achieving 98 percent accuracy. Software Availability: The TOPS+ comparison server is available at http://balabio.dcs.gla.ac.uk/mallika/WebTOPS/.This article is available through the Brunel Open Access Publishing Fun

Presence of extracellular DNA in the Candida albicans biofilm matrix and its contribution to biofilms

DNA has been described as a structural component of the extracellular matrix (ECM) in bacterial biofilms. In Candida albicans, there is a scarce knowledge concerning the contribution of extracellular DNA (eDNA) to biofilm matrix and overall structure. This work examined the presence and quantified the amount of eDNA in C. albicans biofilm ECM and the effect of DNase treatment and the addition of exogenous DNA on C. albicans biofilm development as indicators of a role for eDNA in biofilm development. We were able to detect the accumulation of eDNA in biofilm ECM extracted from C. albicans biofilms formed under conditions of flow, although the quantity of eDNA detected differed according to growth conditions, in particular with regards to the medium used to grow the biofilms. Experiments with C. albicans biofilms formed statically using a microtiter plate model indicated that the addition of exogenous DNA (>160 ng/ml) increases biofilm biomass and, conversely, DNase treatment (>0.03 mg/ml) decreases biofilm biomass at later time points of biofilm development. We present evidence for the role of eDNA in C. albicans biofilm structure and formation, consistent with eDNA being a key element of the ECM in mature C. albicans biofilms and playing a predominant role in biofilm structural integrity and maintenance.National Institute of Dental & Craniofacial ResearchFundação para a Ciência e Tecnologia (FCT) - SFRH/BD/28222/2006National Institute of Allergy and Infectious Disease

Ribosomal oxygenases are structurally conserved from prokaryotes to humans

2-Oxoglutarate (2OG)-dependent oxygenases have important roles in the regulation of gene expression via demethylation of N-methylated chromatin components1,2 and in the hydroxylation of transcription factors3 and splicing factor proteins4. Recently, 2OG-dependent oxygenases that catalyse hydroxylation of transfer RNA5,6,7 and ribosomal proteins8 have been shown to be important in translation relating to cellular growth, TH17-cell differentiation and translational accuracy9,10,11,12. The finding that ribosomal oxygenases (ROXs) occur in organisms ranging from prokaryotes to humans8 raises questions as to their structural and evolutionary relationships. In Escherichia coli, YcfD catalyses arginine hydroxylation in the ribosomal protein L16; in humans, MYC-induced nuclear antigen (MINA53; also known as MINA) and nucleolar protein 66 (NO66) catalyse histidine hydroxylation in the ribosomal proteins RPL27A and RPL8, respectively. The functional assignments of ROXs open therapeutic possibilities via either ROX inhibition or targeting of differentially modified ribosomes. Despite differences in the residue and protein selectivities of prokaryotic and eukaryotic ROXs, comparison of the crystal structures of E. coli YcfD and Rhodothermus marinus YcfD with those of human MINA53 and NO66 reveals highly conserved folds and novel dimerization modes defining a new structural subfamily of 2OG-dependent oxygenases. ROX structures with and without their substrates support their functional assignments as hydroxylases but not demethylases, and reveal how the subfamily has evolved to catalyse the hydroxylation of different residue side chains of ribosomal proteins. Comparison of ROX crystal structures with those of other JmjC-domain-containing hydroxylases, including the hypoxia-inducible factor asparaginyl hydroxylase FIH and histone Nε-methyl lysine demethylases, identifies branch points in 2OG-dependent oxygenase evolution and distinguishes between JmjC-containing hydroxylases and demethylases catalysing modifications of translational and transcriptional machinery. The structures reveal that new protein hydroxylation activities can evolve by changing the coordination position from which the iron-bound substrate-oxidizing species reacts. This coordination flexibility has probably contributed to the evolution of the wide range of reactions catalysed by oxygenases

Compounds from Silicones Alter Enzyme Activity in Curing Barnacle Glue and Model Enzymes

Background: Attachment strength of fouling organisms on silicone coatings is low. We hypothesized that low attachment strength on silicones is, in part, due to the interaction of surface available components with natural glues. Components could alter curing of glues through bulk changes or specifically through altered enzyme activity. Methodology/Principal Findings: GC-MS analysis of silicone coatings showed surface-available siloxanes when the coatings were gently rubbed with a cotton swab for 15 seconds or given a 30 second rinse with methanol. Mixtures of compounds were found on 2 commercial and 8 model silicone coatings. The hypothesis that silicone components alter glue curing enzymes was tested with curing barnacle glue and with commercial enzymes. In our model, barnacle glue curing involves trypsin-like serine protease(s), which activate enzymes and structural proteins, and a transglutaminase which cross-links glue proteins. Transglutaminase activity was significantly altered upon exposure of curing glue from individual barnacles to silicone eluates. Activity of purified trypsin and, to a greater extent, transglutaminase was significantly altered by relevant concentrations of silicone polymer constituents. Conclusions/Significance: Surface-associated silicone compounds can disrupt glue curing and alter enzyme properties