409 research outputs found
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 , for all . 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
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
Some results on blow up for semilinear parabolic problems
The authors describe the asymptotic behavior of blow-up for the semilinear heat equation ut=uxx+f(u) in R×(0,T), with initial data u0(x)>0 in R, where f(u)=up, p>1, or f(u)=eu. A complete description of the types of blow-up patterns and of the corresponding blow-up final-time profiles is given. In the rescaled variables, both are governed by the structure of the Hermite polynomials H2m(y). The H2-behavior is shown to be stable and generic. The existence of H4-behavior is proved. A nontrivial blow-up pattern with a blow-up set of nonzero measure is constructed. Similar results for the absorption equation ut=uxx−up, 0<p<1, are discussed
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
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
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 on and those
of the parabolic equations on a bounded
domain . We give details on the similarities of these dynamics in the
cases , and and in the corresponding cases ,
and dim() 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
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
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
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