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

Complete Embedded Self-Translating Surfaces under Mean Curvature Flow

We describe a construction of complete embedded self-translating surfaces under mean curvature flow by desingularizing the intersection of a finite family of grim reapers in general position.Comment: 42 pages, 8 figures. v2: typos correcte

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

On well-posedness, stability, and bifurcation for the axisymmetric surface diffusion flow

In this article, we study the axisymmetric surface diffusion flow (ASD), a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2 + \alpha)-little-H\"older regular surfaces of revolution embedded in R^3 and satisfying periodic boundary conditions. We also give conditions for global existence of solutions and prove that solutions are real analytic in time and space. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetric surfaces with constant mean curvature, we characterize the equilibria of ASD. Then, focusing on the family of cylinders, we establish results regarding stability, instability and bifurcation behavior, with the radius acting as a bifurcation parameter for the problem.Comment: 37 pages, 6 figures, To Appear in SIAM J. Math. Ana

Improved Design of Anaerobic Digesters for Household Biogas Production in Indonesia: One Cow, One Digester, and One Hour of Cooking per Day

A government-sponsored initiative in Indonesia to design and implement low-cost anaerobic digestion systems resulted in 21 full-scale systems with the aim to satisfy the cooking fuel demands of rural households owning at least one cow. The full-scale design consisted of a 0.3 m diameter PVC pipe, which was operated as a conventional plug-flow system. The system generated enough methane to power a cooking stove for ∼1 h. However, eventual clogging from solids accumulation inside the bioreactor proved to be a major drawback. Here, we improved the digester configuration to remedy clogging while maintaining system performance. Controlled experiments were performed using four 9-L laboratory-scale digesters operated at a temperature of 27±1°C, a volatile solids loading rate of 2.0 g VS·L−1·day−1, and a 21-day hydraulic retention time. Two of the digesters were replicates of the original design (control digesters), while the other two digesters included internal mixing or effluent recycle (experimental digesters). The performance of each digester was compared based on methane yields, VS removal efficiencies, and steady-state solids concentrations during an operating period of 311 days. Statistical analyses revealed that internal mixing and effluent recycling resulted in reduced solids accumulation compared to the controls without diminishing methane yields or solids removal efficiencies

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

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

The rin, nor and Cnr spontaneous mutations inhibit tomato fruit ripening in additive and epistatic manners

Tomato fruit ripening is regulated by transcription factors (TFs), their downstream effector genes, and the ethylene biosynthesis and signalling pathway. Spontaneous non-ripening mutants ripening inhibitor (rin), non-ripening (nor) and Colorless non-ripening (Cnr) correspond with mutations in or near the TF-encoding genes MADS-RIN, NAC-NOR and SPL-CNR, respectively. Here, we produced heterozygous single and double mutants of rin, nor and Cnr and evaluated their functions and genetic interactions in the same genetic background. We showed how these mutations interact at the level of phenotype, individual effector gene expression, and sensory and quality aspects, in a dose-dependent manner. Rin and nor have broadly similar quantitative effects on all aspects, demonstrating their additivity in fruit ripening regulation. We also found that the Cnr allele is epistatic to rin and nor and that its pleiotropic effects on fruit size and volatile production, in contrast to the well-known dominant effect on ripening, are incompletely dominant, or recessive.</p

Phase Slips and the Eckhaus Instability

We consider the Ginzburg-Landau equation, $\partial_t u= \partial_x^2 u + u - u|u|^2$, with complex amplitude $u(x,t)$. We first analyze the phenomenon of phase slips as a consequence of the {\it local} shape of $u$. We next prove a {\it global} theorem about evolution from an Eckhaus unstable state, all the way to the limiting stable finite state, for periodic perturbations of Eckhaus unstable periodic initial data. Equipped with these results, we proceed to prove the corresponding phenomena for the fourth order Swift-Hohenberg equation, of which the Ginzburg-Landau equation is the amplitude approximation. This sheds light on how one should deal with local and global aspects of phase slips for this and many other similar systems.Comment: 22 pages, Postscript, A