Formal matched asymptotics for degenerate Ricci flow neckpinches

Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on $S^m$, for all $m\geq 3$. In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit

An automated and versatile ultra-low temperature SQUID magnetometer

We present the design and construction of a SQUID-based magnetometer for operation down to temperatures T = 10 mK, while retaining the compatibility with the sample holders typically used in commercial SQUID magnetometers. The system is based on a dc-SQUID coupled to a second-order gradiometer. The sample is placed inside the plastic mixing chamber of a dilution refrigerator and is thermalized directly by the 3He flow. The movement though the pickup coils is obtained by lifting the whole dilution refrigerator insert. A home-developed software provides full automation and an easy user interface.Comment: RevTex, 10 pages, 10 eps figures. High-resolution figures available upon reques

Shrinkers, expanders, and the unique continuation beyond generic blowup in the heat flow for harmonic maps between spheres

Using mixed analytical and numerical methods we investigate the development of singularities in the heat flow for corotational harmonic maps from the $d$-dimensional sphere to itself for $3\leq d\leq 6$. By gluing together shrinking and expanding asymptotically self-similar solutions we construct global weak solutions which are smooth everywhere except for a sequence of times $T_1<T_2<...<T_k<\infty$ at which there occurs the type I blow-up at one of the poles of the sphere. We show that in the generic case the continuation beyond blow-up is unique, the topological degree of the map changes by one at each blow-up time $T_i$, and eventually the solution comes to rest at the zero energy constant map.Comment: 24 pages, 8 figures, minor corrections, matches published versio

Tagging of MADS domain proteins for chromatin immunoprecipitation

<p>Abstract</p> <p>Background</p> <p>Most transcription factors fulfill their role in complexes and regulate their target genes upon binding to DNA motifs located in upstream regions or introns. To date, knowledge about transcription factor target genes and their corresponding transcription factor binding sites are still very limited. Two related methods that allow <it>in vivo </it>identification of transcription factor binding sites are chromatin immunoprecipitation (ChIP) and chromatin affinity purification (ChAP). For ChAP, the protein of interest is tagged with a peptide or protein, which can be used for affinity purification of the protein-DNA complex and hence, the identification of the target gene.</p> <p>Results</p> <p>Here, we present the results of experiments aiming at the development of a generic tagging approach for the Arabidopsis MADS domain proteins AGAMOUS, SEPALLATA3, and FRUITFULL. For this, Arabidopsis wild type plants were transformed with constructs containing a MADS-box gene fused to either a double <it>Strep</it>-tag^®II-FLAG-tag, a triple HA-tag, or an eGFP-tag, all under the control of the constitutive double 35S Cauliflower Mosaic Virus (CaMV) promoter. Strikingly, in all cases, the number of transformants with loss-of-function phenotypes was much larger than those with an overexpression phenotype. Using endogenous promoters in stead of the 35S CaMV resulted in a dramatic reduction in the frequency of loss-of-function phenotypes. Furthermore, pleiotropic defects occasionally caused by an overexpression strategy can be overcome by using the native promoter of the gene. Finally, a ChAP result is presented using GFP antibody on plants carrying a genomic fragment of a MADS-box gene fused to GFP.</p> <p>Conclusion</p> <p>This study revealed that MADS-box proteins are very sensitive to fusions with small peptide tags and GFP tags. Furthermore, for the expression of chimeric versions of MADS-box genes it is favorable to use the entire genomic region in frame to the tag of choice. Interestingly, though unexpected, it appears that the use of chimeric versions of MADS-box genes under the control of the strong 35S CaMV promoter is a very efficient method to obtain dominant-negative mutants, either caused by cosuppression or by alteration of the activity of the recombinant protein. Finally, we were able to demonstrate AGAMOUS binding to one of its targets by ChAP.</p

In planta localisation patterns of MADS domain proteins during floral development in Arabidopsis thaliana

BACKGROUND: MADS domain transcription factors play important roles in various developmental processes in flowering plants. Members of this family play a prominent role in the transition to flowering and the specification of floral organ identity. Several studies reported mRNA expression patterns of the genes encoding these MADS domain proteins, however, these studies do not provide the necessary information on the temporal and spatial localisation of the proteins. We have made GREEN FLUORESCENT PROTEIN (GFP) translational fusions with the four MADS domain proteins SEPALLATA3, AGAMOUS, FRUITFULL and APETALA1 from the model plant Arabidopsis thaliana and analysed the protein localisation patterns in living plant tissues by confocal laser scanning microscopy (CLSM). RESULTS: We unravelled the protein localisation patterns of the four MADS domain proteins at a cellular and subcellular level in inflorescence and floral meristems, during development of the early flower bud stages, and during further differentiation of the floral organs. The protein localisation patterns revealed a few deviations from known mRNA expression patterns, suggesting a non-cell autonomous action of these factors or alternative control mechanisms. In addition, we observed a change in the subcellular localisation of SEPALLATA3 from a predominantly nuclear localisation to a more cytoplasmic localisation, occurring specifically during petal and stamen development. Furthermore, we show that the down-regulation of the homeodomain transcription factor WUSCHEL in ovular tissues is preceded by the occurrence of both AGAMOUS and SEPALLATA3 proteins, supporting the hypothesis that both proteins together suppress WUSCHEL expression in the ovule. CONCLUSION: This approach provides a highly detailed in situ map of MADS domain protein presence during early and later stages of floral development. The subcellular localisation of the transcription factors in the cytoplasm, as observed at certain stages during development, points to mechanisms other than transcriptional control. Together this information is essential to understand the role of these proteins in the regulatory processes that drive floral development and leads to new hypotheses

Effect of Shear on Performance and Microbial Ecology of Continuously Stirred Anaerobic Digesters Treating Animal Manure

We Determined the Effect of Different Mixing Intensities on the Performance, Methanogenic Population Dynamics, and Juxtaposition of Syntrophic Microbes in Anaerobic Digesters Treating Cow Manure from a Dairy Farm. Computer Automated Radioactive Particle Tracking in Conjunction with Computational Fluid Dynamics Was Performed to Quantify the Shear Levels Locally. Four Continuously Stirred Anaerobic Digesters Were Operated at Different Mixing Intensities of 1,500, 500, 250, and 50 Revolutions Per Min (RPM) over a 260-Day Period at a Temperature of 34 ± 1°C. Animal Manure at a Volatile Solids (VS) Concentration of 50 G/L Was Fed into the Digesters Daily at Five Different Organic Loading Rates between 0.6 and 3.5 G vs./L Day. the Different Mixing Intensities Had No Effect on the Biogas Production Rates and Yields at Steady-State Conditions. a Methane Yield of 0.241 ± 0.007 L CH 4/g vs. Fed Was Obtained by Pooling the Data of All Four Digesters during Steady-State Periods. However, Digester Performance Was Affected Negatively by Mixing Intensity during Startup of the Digesters, with Lower Biogas Production Rates and Higher Volatile Fatty Acids Concentrations Observed for the 1,500-RPM Digester. Despite Similar Methane Production Yields and Rates, the Acetoclastic Methanogenic Populations Were Different for the High- and Low-Intensity Mixed Digesters with Methanosarcina Spp. and Methanosaeta Concilii as the Predominant Methanogens, Respectively. for All Four Digesters, Epifluorescence Microscopy Revealed Decreasing Microbial Floc Sizes Beginning at Week 4 and Continuing through Week 26 after Which No Microbial Flocs Remained. This Decrease in Size, and Subsequent Loss of Microbial Flocs Did Not, However, Produce Any Long-Term Upsets in Digester Performance. © 2007 Wiley Periodicals, Inc

Development of a Bioelectrochemical System as a Tool to Enrich H2-Producing Syntrophic Bacteria

Syntrophic microbial partnerships are found in many environments and play critical roles in wastewater treatment, global nutrient cycles, and gut systems. An important type of syntrophy for the anaerobic conversion of carboxylic acids is H2 syntrophy. In this type of microbial partnership, dissolved H2 is produced by a bacterium and rapidly consumed by an archeon (methanogen), resulting in methane gas. This is referred to as interspecies H2 transfer, and some conversions rely on this mechanism to become thermodynamically feasible. For this reason, syntrophic partners are often not possible to separate in the lab, which hampers the full understanding of their physiology. Bioelectrochemical systems (BESs) may show promise to ultimately separate and study the behavior of the syntrophic bacterium by employing an abiotic H2 oxidation reaction at the anode, actively removing dissolved H2. Here, we performed a proof-of-concept study to ascertain whether an H2-removing anode can: (1) provide a growth advantage for the syntrophic bacterium; and (2) compete with the methanogenic partner. A mathematical model was developed to design a BES to perform competition experiments. Indeed, the operated BES demonstrated the ability to provide a growth advantage to the syntrophic bacterium Syntrophus aciditrophicus compared to its methanogenic partner Methanospirillum hungatei when grown in co-culture. Further, the BES provided the never-before isolated Syntrophomonas zehnderi with a growth advantage compared to Methanobacterium formicicum. Our results demonstrate a potential to use this BES to enrich H2-sensitive syntrophic bacteria, and gives prospects for the development of an effective method for the separation of obligate syntrophs

Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq equations

We establish a connection between Optimal Transport Theory and classical Convection Theory for geophysical flows. Our starting point is the model designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal Transport problems. This model can be seen as a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized Hydrostatic-Boussinesq equations) to various models involving Optimal Transport (and the related Monge-Ampere equation. This includes the 2D semi-geostrophic equations and some fully non-linear versions of the so-called high-field limit of the Vlasov-Poisson system and of the Keller-Segel for Chemotaxis. Finally, we show how a ``stringy'' generalization of the AHT model can be related to the magnetic relaxation model studied by Arnold and Moffatt to obtain stationary solutions of the Euler equations with prescribed topology

Critical behavior of collapsing surfaces

We consider the mean curvature evolution of rotationally symmetric surfaces. Using numerical methods, we detect critical behavior at the threshold of singularity formation resembling the one of gravitational collapse. In particular, the mean curvature simulation of a one-parameter family of initial data reveals the existence of a critical initial surface that develops a degenerate neckpinch. The limiting flow of the Type II singularity is accurately modeled by the rotationally symmetric translating soliton.Comment: 23 pages, 10 figure

Dirichlet sigma models and mean curvature flow

The mean curvature flow describes the parabolic deformation of embedded branes in Riemannian geometry driven by their extrinsic mean curvature vector, which is typically associated to surface tension forces. It is the gradient flow of the area functional, and, as such, it is naturally identified with the boundary renormalization group equation of Dirichlet sigma models away from conformality, to lowest order in perturbation theory. D-branes appear as fixed points of this flow having conformally invariant boundary conditions. Simple running solutions include the paper-clip and the hair-pin (or grim-reaper) models on the plane, as well as scaling solutions associated to rational (p, q) closed curves and the decay of two intersecting lines. Stability analysis is performed in several cases while searching for transitions among different brane configurations. The combination of Ricci with the mean curvature flow is examined in detail together with several explicit examples of deforming curves on curved backgrounds. Some general aspects of the mean curvature flow in higher dimensional ambient spaces are also discussed and obtain consistent truncations to lower dimensional systems. Selected physical applications are mentioned in the text, including tachyon condensation in open string theory and the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure