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

A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations

The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$. We give details on the similarities of these dynamics in the cases $d=1$, $d=2$ and $d\geq 3$ and in the corresponding cases $\Omega=(0,1)$, $\Omega=\mathbb{T}^1$ and dim($\Omega$)$\geq 2$ respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations

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

Helicoidal surfaces rotating/translating under the mean curvature flow

We describe all possible self-similar motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding hypersurface equations. Then we present a new two-parameter family of immersed helicoidal surfaces that rotate/translate with constant velocity under the flow. We look at their limiting behaviour as the pitch of the helicoidal motion goes to 0 and compare it with the limiting behaviour of the classical helicoidal minimal surfaces. Finally, we give a classification of the immersed cylinders in the family of constant mean curvature helicoidal surfaces.Comment: 21 pages, 22 figures, final versio

Genomic insights into members of the candidate phylum Hyd24-12 common in mesophilic anaerobic digesters

Members of the candidate phylum Hyd24-12 are globally distributed, but no genomic information or knowledge about their morphology, physiology or ecology is available. In this study, members of the Hyd24-12 lineage were shown to be present and abundant in full-scale mesophilic anaerobic digesters at Danish wastewater treatment facilities. In some samples, a member of the Hyd24-12 lineage was one of the most abundant genus-level bacterial taxa, accounting for up to 8% of the bacterial biomass. Three closely related and near-complete genomes were retrieved using metagenome sequencing of full-scale anaerobic digesters. Genome annotation and metabolic reconstruction showed that they are Gram-negative bacteria likely involved in acidogenesis, producing acetate and hydrogen from fermentation of sugars, and may play a role in the cycling of sulphur in the digesters. Fluorescence in situ hybridization revealed single rod-shaped cells dispersed within the flocs. The genomic information forms a foundation for a more detailed understanding of their role in anaerobic digestion and provides the first insight into a hitherto undescribed branch in the tree of life

Biomethanation potential of biological and other wastes

Anaerobic technology has been traditionally applied for the treatment of carbon rich wastewater and organic residues. Anaerobic processes can be fully integrated in the biobased economy concept for resource recovery. After a brief introduction about applications of anaerobic processes to industrial wastewater treatment, agriculture feedstock and organic fraction of municipal solid waste, the position of anaerobic processes in biorefinery concepts is presented. Integration of anaerobic digestion with these processes can help in the maximisation of the economic value of the biomass used, while reducing the waste streams produced and mitigating greenhouse gases emissions. Besides the integration of biogas in the existing full-scale bioethanol and biodiesel production processes, the potential applications of biogas in the second generation lignocellulosic, algae and syngas-based biorefinery platforms are discussed.(undefined