Domain Decomposition preconditioning for high-frequency Helmholtz problems with absorption

In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations of the Helmholtz equation $-\Delta u - (k^2+ {\rm i} \varepsilon)u = f$, with absorption parameter $\varepsilon \in \mathbb{R}$. Multigrid approximations of this equation with $\varepsilon \not= 0$ are commonly used as preconditioners for the pure Helmholtz case ($\varepsilon = 0$). However a rigorous theory for such (so-called "shifted Laplace") preconditioners, either for the pure Helmholtz equation, or even the absorptive equation ($\varepsilon \not=0$), is still missing. We present a new theory for the absorptive equation that provides rates of convergence for (left- or right-) preconditioned GMRES, via estimates of the norm and field of values of the preconditioned matrix. This theory uses a $k$- and $\varepsilon$-explicit coercivity result for the underlying sesquilinear form and shows, for example, that if $|\varepsilon|\sim k^2$, then classical overlapping additive Schwarz will perform optimally for the absorptive problem, provided the subdomain and coarse mesh diameters are carefully chosen. Extensive numerical experiments are given that support the theoretical results. The theory for the absorptive case gives insight into how its domain decomposition approximations perform as preconditioners for the pure Helmholtz case $\varepsilon = 0$. At the end of the paper we propose a (scalable) multilevel preconditioner for the pure Helmholtz problem that has an empirical computation time complexity of about $\mathcal{O}(n^{4/3})$ for solving finite element systems of size $n=\mathcal{O}(k^3)$, where we have chosen the mesh diameter $h \sim k^{-3/2}$ to avoid the pollution effect. Experiments on problems with $h\sim k^{-1}$, i.e. a fixed number of grid points per wavelength, are also given

Graphene: from materials science to particle physics

Since its discovery in 2004, graphene, a two-dimensional hexagonal carbon allotrope, has generated great interest and spurred research activity from materials science to particle physics and vice versa. In particular, graphene has been found to exhibit outstanding electronic and mechanical properties, as well as an unusual low-energy spectrum of Dirac quasiparticles giving rise to a fractional quantum Hall effect when freely suspended and immersed in a magnetic field. One of the most intriguing puzzles of graphene involves the low-temperature conductivity at zero density, a central issue in the design of graphene-based nanoelectronic components. While suspended graphene experiments have shown a trend reminiscent of semiconductors, with rising resistivity at low temperatures, most theories predict a constant or even decreasing resistivity. However, lattice field theory calculations have revealed that suspended graphene is at or near the critical coupling for excitonic gap formation due to strong Coulomb interactions, which suggests a simple and straightforward explanation for the experimental data. In this contribution we review the current status of the field with emphasis on the issue of gap formation, and outline recent progress and future points of contact between condensed matter physics and Lattice QCD.Comment: 14 pages, 6 figures. Plenary talk given at the XXVIII International Symposium on Lattice Field Theory (Lattice 2010), June 14-19, 2010, Villasimius, Sardinia, Ital

On the connected component of compact composition operators on the Hardy space

We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space $H^2$ on the unit disc. This answers a question posed by Shapiro and Sundberg in 1990. We also establish an improved version of a theorem of MacCluer, giving a lower bound for the essential norm of a difference of composition operators in terms of the angular derivatives of their symbols. As a main tool we use Aleksandrov-Clark measures.Comment: 16 page

Seeing the vibrational breathing of a single molecule through time-resolved coherent anti-Stokes Raman scattering

The motion of chemical bonds within molecules can be observed in real time, in the form of vibrational wavepackets prepared and interrogated through ultrafast nonlinear spectroscopy. Such nonlinear optical measurements are commonly performed on large ensembles of molecules, and as such, are limited to the extent that ensemble coherence can be maintained. Here, we describe vibrational wavepacket motion on single molecules, recorded through time-resolved, surface-enhanced, coherent anti-Stokes Raman scattering. The required sensitivity to detect the motion of a single molecule, under ambient conditions, is achieved by equipping the molecule with a dipolar nano-antenna (a gold dumbbell). In contrast with measurements in ensembles, the vibrational coherence on a single molecule does not dephase. It develops phase fluctuations with characteristic statistics. We present the time evolution of discretely sampled statistical states, and highlight the unique information content in the characteristic, early-time probability distribution function of the signal.Comment: 17 pages, 5 figure

Glucaric acid as an indicator of use of enzyme‐inducing drugs

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/116979/1/cpt1974154417.pd

Calculating the 3D magnetic field of ITER for European TBM studies

The magnetic perturbation due to the ferromagnetic test blanket modules (TBMs) may deteriorate fast ion confinement in ITER. This effect must be quantified by numerical studies in 3D. We have implemented a combined finite element method (FEM) -- Biot-Savart law integrator method (BSLIM) to calculate the ITER 3D magnetic field and vector potential in detail. Unavoidable geometry simplifications changed the mass of the TBMs and ferritic inserts (FIs) up to 26%. This has been compensated for by modifying the nonlinear ferromagnetic material properties accordingly. Despite the simplifications, the computation geometry and the calculated fields are highly detailed. The combination of careful FEM mesh design and using BSLIM enables the use of the fields unsmoothed for particle orbit-following simulations. The magnetic field was found to agree with earlier calculations and revealed finer details. The vector potential is intended to serve as input for plasma shielding calculations.Comment: In proceedings of the 28th Symposium on Fusion Technolog

Cohesin-dockerin interaction based method to facilitate fast domain shuffling of cellobiohydrolases

Mikrobien sellulaasit kuten sellobiohydrolaasit pystyvät hajottamaan selluloosaa ja lignoselluloosaista biomassaa pienemmiksi, glukoosia sisältäviksi monomeereiksi ja oligomeereiksi. Sellulaasit ovat usein monidomeenientsyymejä, jotka koostuvat erilaisista proteiinidomeeneista (tai -moduuleista), joilla on eri toimintoja. Sellulaasien pääkomponentteina ovat usein selluloosaan sitoutuva domeeni (cellulose binding module, CBM) ja katalyyttinen domeeni. CBM:t sitoutuvat selluloosaan tuoden katalyyttiset domeenit lähelle substraattiaan ja näin nostaen entsyymien määrää substraatin pinnalla. Katalyyttiset domeenit pilkkovat substraatin ja esimerkiksi sellobiohydrolaasien kohdalla hydrolysoivat tai katkaisevat kiteisen selluloosaketjun pienemmiksi, liukoisiksi sakkarideiksi, pääasiassa sellobioosiksi. Toisin kuin aerobiset sienet, jotka käyttävät vapaita solunulkoisia entsyymejä hajottaakseen selluloosaa, anaerobiset mikrobit käyttävät usein toisenlaista strategiaa. Niiden sellulaasit ovat järjestäytyneet ja sitoutuneet solun pinnalle makromolekulaariseksi kompleksiksi nimeltään sellulosomi. Sellulosomin ydin muodostuu scaffoldin nimisestä proteiinista, joka koostuu pääasiassa useista perättäisistä cohesiini domeeneista, joihin katalyyttiset alayksiköt kiinnittyvät dockeriini domeeniensa välityksellä. Näin muodostuu proteiinikompleksi, jossa useita erilaisia katalyyttisiä domeeneja ja aktiivisuuksia järjestäytyy lähelle toisiaan. Dockeriinien ja cohesiinien tiedetään sitoutuvan toisiinsa yhdellä vahvimmista reseprotien ja ligandien välisistä voimista, joita luonnosta tunnetaan. Dockeriinin sisältäviä fuusioproteiineja on myös onnistuneesti yhdistetty niiden luonnollisen vastinparin, cohesiinin, sisältävien proteiinien kanssa in vitro tuottaen toimivia moniproteiinikomplekseja. Tässä maisterin tutkielman työssä tavoitteena oli 1) tuottaa fuusioproteiineja, joissa erilaisia CBM:iä oli yhdistetty dockeriini domeeneihin, 2) yhdistää nämä fuusioproteiinit cohesiini-katalyyttinen domeeni fuusioproteiinien kanssa luoden vakaita CBM:n ja katalyyttisen domeenin sisältäviä entsyymikomplekseja, 3) karakterisoida näitä entsyymikomplekseja niiden lämmönkestävyyden ja selluloosan hydrolyysikyvyn suhteen ja 4) lopulta luoda vakaa ja nopea domeenienvaihtometodi sellobiohydrolaaseille näiden nopeamman skriinaamisen mahdollistamiseksi. Kokeen hypoteesina oli se, että eri CBM:iä fuusioituna dockeriinien kanssa ja sellobiohydrolaasien katalyyttisiä domeeneja fuusioituna cohesiinien kanssa voitaisiin tuottaa erikseen ja yhdistää jälkikäteen tuottaen toimivia ”kaksidomeenisia” entsyymejä cohesiini-dockeriini ”linkkerillä”. Menetelmän ansiosta aikaa ja työtä voitaisiin säästää entsyymien skriinaamisessa kun kaikkia erilaisia CBM-katalyyttinen domeeni -pareja ei tarvitsisi kloonata ja tuottaa erikseen. Useiden CBM-dockeriini fuusioproteiinien (joissa CBM:t olivat joko sieni- tai bakteeriperäisiä) heterologista ekspressiota testattiin eri isäntäorganismeissa, joko Saccharomyces cerevisiae –hiivassa tai Escherichia coli –bakteerissa. Puhdistetut proteiinit yhdistettiin hiivassa tuotetun sieniperäisen glykosidihydrolaasi perhe 7:n sellobiohydrolaasi-cohesiini fuusioproteiinin kanssa. Cohesiini-dockeriini vuorovaikutuksen voimasta muodostuneen katalyyttinen domeeni-CBM -kompleksin karakterisointiin kuului lämpövakausmittauksia sekä aktiivisuusmäärityksiä käyttäen liukoista ja liukenematonta substraattia. Tuloksia verrattiin kontrollientsyymeihin, jotka koostuivat samasta CBM:stä ja katalyyttisestä domeenista, joita yhdisti yksinkertainen linkkeripeptidi. Tulokset osoittivat, että cohesiini-dockeriini vuorovaikutuksen avulla muodostettu sellobiohydrolaasikompleksi toimi selluloosan hydrolyysikokeissa yhtäläisesti peptidilinkkerillä varustetun entsyymikontrollin kanssa 50:n ja 60 ˚C:n lämpötiloissa. Kuitenkaan 70 ˚C:n lämpötilassa kompleksi ei toiminut enää yhtä hyvin kuin kontrollientsyymi, ilmeisesti cohesiini-dockeriini vuorovaikutuksen epävakaudesta johtuen. Entsyymien lämpövakausmittaukset aiemmin julkaistujen tuloksien kanssa tukivat hydrolyysituloksia ja tätä hypoteesia. Tuleva tutkimus tulisi tähdätä parantamaan cohesiini-dockeriini vuorovaikutuksen lämpövakautta ja vahvistamaan tulokset eri sellulaasifuusiokomplekseilla.Microbial cellulases, e.g. cellobiohydrolases, are able to degrade cellulose and lignocellulosic biomass to smaller glucose-containing monomers and oligomers. Cellulases are often multi-domain enzymes comprised of different protein domains (i.e. modules), which have different functions. The main two components, which often appear in cellulases, are the cellulose-binding module (CBM) and the catalytic domain. The CBMs bind to cellulose, bringing the catalytic domains close to their substrate and increasing the amount of enzymes on the substrate surface. The catalytic domain performs the cleavage of the substrate, e.g. in the case of cellobiohydrolases hydrolyses or “cuts” the crystalline cellulose chain into smaller soluble saccharides, mainly cellobiose. Unlike aerobic fungi, which utilize free extracellular enzymes to break down cellulose, anaerobic microbes often use a different kind of strategy. Their cellulases are organized and bound to the cell surface in a macromolecular protein complex, the cellulosome. The core of the cellulosome is formed of a scaffolding protein (the scaffoldin) consisting mainly of multiple consecutive cohesin domains, into which the catalytic subunits of enzymes attach via a dockerin domain. This creates a protein complex with multiple different catalytic domains and activities arranged in close proximity to each other. Dockerins and cohesins are known to bind each other with one of the strongest receptor-ligand -pair forces known to nature. Dockerin containing fusion proteins have also been successfully combined in vitro with proteins containing their natural counterparts, cohesins, to create functional multiprotein complexes. In this Master’s thesis work the goal was to 1) produce fusion proteins in which different CBMs were connected to dockerin domains, 2) combine these fusions with cohesin-catalytic domain fusion proteins to create stable CBM and catalytic domain containing enzyme complexes, 3) to characterize these enzyme complexes in respect of their thermostability and cellulose hydrolysis capacity and 4) to ultimately create a robust and fast domain shuffling method for multi-domain cellobiohydrolases (CBH) to facilitate their faster screening. The hypothesis of the experiments was that different CBMs fused with a dockerin domain and the cellobiohydrolase catalytic domain fused with a cohesin domain could be produced separately and then be combined to produce a functional two-domain enzyme with a dockerin-cohesin “linker” in between. In this way time and work could be saved because not every different CBM- catalytic domain -pair would have to be cloned and produced separately. Several CBM-dockerin fusion proteins (in which the CBM were of fungal or bacterial origin) were tested for expression in heterologous hosts, either in Saccharomyces cerevisiae or Escherichia coli. The purified proteins were combined with a fungal glycoside hydrolase family 7 (GH7) cellobiohydrolase-cohesin fusion protein produced in S. cerevisiae. The characterization of the catalytic domain-CBM -complexes formed through cohesin-dockerin interaction included thermostability measurements using circular dichroism and activity assays using soluble and insoluble cellulosic substrate. The results were compared to enzyme controls comprising of the same CBM and catalytic domain connected by a simple peptide linker. The results showed that the cohesin-dockerin –linked cellobiohydrolase complex performed in the cellulose hydrolysis studies in a similar manner as the directly linked enzyme controls at temperature of 50˚C and 60 ˚C. At temperatures of 70 ˚C the complex did not perform as well as the control enzymes, apparently due to the instability of the dockerin-cohesin interaction. The thermostability measurements of the enzymes, together with the previously published data supported the hydrolysis results and this hypothesis. The future work should be aimed at enhancing the thermostability of the cohesin-dockerin interaction as well as on verifying the results on different cellulase fusion complexes

Ecosystem metabolism of benthic and pelagic zones of a shallow productive estuary : spatio-temporal variability

Long-term deterioration of water quality is known to reduce the importance of benthic ecosystem metabolism in shallow coastal ecosystems, but drivers of spatial and short-term variability in ecosystem metabolism are poorly understood. We addressed this knowledge gap through detailed seasonal measurements of ecosystem metabolism across depth gradients from shallow (2 to 3 m) eelgrass-dominated to deeper (4 to 5 m) muddy regions of a shallow, productive estuary. Combined measurements of gross primary production (GPP), respiration (R) and, by difference, net ecosystem production (NEP) by the open-water diel oxygen technique and in situ chamber incubations showed high importance of shallow eelgrass habitats for metabolism at the system scale. Seasonal variations in GPP, R and NEP increased with light availability and temperature with highest NEP in all habitats during the warm and sunny mid-summer. The shallow eelgrass-dominated and neighboring habitats were seasonally net autotrophic (NEP = 0.54 and 0.31 mg O2 m-2 d-1, respectively), compared to net heterotrophy (NEP = -0.26 mg O2 m-2 d-1) at the deeper muddy site. Detailed studies along depth gradients further confirmed the role of eelgrass as a key driver of spatial differences in ecosystem metabolism across the estuary. Strong northerly winds (>8 m s-1) caused short-term (<24 h) periods of similar oxygen dynamics and similar apparent productivity in shallow and deeper waters, indicative of efficient lateral mixing, while calm periods (<4 m s-1) enabled formation of ‘pockets’, i.e. water masses with limited connectivity, which exacerbated the metabolic differences between shallow and deep sites.Peer reviewe

Alcohol intake, drinking patterns, and prostate cancer risk and mortality : a 30-year prospective cohort study of Finnish twins

Purpose Alcohol intake may be associated with cancer risk, but epidemiologic evidence for prostate cancer is inconsistent. We aimed to prospectively investigate the association between midlife alcohol intake and drinking patterns with future prostate cancer risk and mortality in a population-based cohort of Finnish twins. Methods Data were drawn from the Older Finnish Twin Cohort and included 11,372 twins followed from 1981 to 2012. Alcohol consumption was assessed by questionnaires administered at two time points over follow-up. Over the study period, 601 incident cases of prostate cancer and 110 deaths from prostate cancer occurred. Cox regression was used to evaluate associations between weekly alcohol intake and binge drinking patterns with prostate cancer risk and prostate cancer-specific mortality. Within-pair co-twin analyses were performed to control for potential confounding by shared genetic and early environmental factors. Results Compared to light drinkers ( Conclusion Heavy regular alcohol consumption and binge drinking patterns may be associated with increased prostate cancer risk, while abstinence may be associated with increased risk of prostate cancer-specific mortality compared to light alcohol consumption.Peer reviewe