266 research outputs found
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
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
Evolution of elastic thin films with curvature regularization via minimizing movements
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
Phase Slips and the Eckhaus Instability
We consider the Ginzburg-Landau equation, , with complex amplitude . We first analyze the phenomenon of
phase slips as a consequence of the {\it local} shape of . 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
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
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
A variational formulation of anisotropic geometric evolution equations in higher dimensions
Accepted versio
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