20,556 research outputs found
Sunward-propagating Alfv\'enic fluctuations observed in the heliosphere
The mixture/interaction of anti-sunward-propagating Alfv\'enic fluctuations
(AFs) and sunward-propagating Alfv\'enic fluctuations (SAFs) is believed to
result in the decrease of the Alfv\'enicity of solar wind fluctuations with
increasing heliocentric distance. However, SAFs are rarely observed at 1 au and
solar wind AFs are found to be generally outward. Using the measurements from
Voyager 2 and Wind, we perform a statistical survey of SAFs in the heliosphere
inside 6 au. We first report two SAF events observed by Voyager 2. One is in
the anti-sunward magnetic sector with a strong positive correlation between the
fluctuations of magnetic field and solar wind velocity. The other one is in the
sunward magnetic sector with a strong negative magnetic field-velocity
correlation. Statistically, the percentage of SAFs increases gradually with
heliocentric distance, from about 2.7% at 1.0 au to about 8.7% at 5.5 au. These
results provide new clues for understanding the generation mechanism of SAFs
Formation of Structure in Snowfields: Penitentes, Suncups, and Dirt Cones
Penitentes and suncups are structures formed as snow melts, typically high in
the mountains. When the snow is dirty, dirt cones and other structures can form
instead. Building on previous field observations and experiments, this work
presents a theory of ablation morphologies, and the role of surface dirt in
determining the structures formed. The glaciological literature indicates that
sunlight, heating from air, and dirt all play a role in the formation of
structure on an ablating snow surface. The present work formulates a
mathematical model for the formation of ablation morphologies as a function of
measurable parameters. The dependence of ablation morphologies on weather
conditions and initial dirt thickness are studied, focusing on the initial
growth of perturbations away from a flat surface. We derive a single-parameter
expression for the melting rate as a function of dirt thickness, which agrees
well with a set of measurements by Driedger. An interesting result is the
prediction of a dirt-induced travelling instability for a range of parameters.Comment: 28 pages, 13 figure
Perturbation theorems for Hele-Shaw flows and their applications
In this work, we give a perturbation theorem for strong polynomial solutions
to the zero surface tension Hele-Shaw equation driven by injection or suction,
so called the Polubarinova-Galin equation. This theorem enables us to explore
properties of solutions with initial functions close to but are not polynomial.
Applications of this theorem are given in the suction or injection case. In the
former case, we show that if the initial domain is close to a disk, most of
fluid will be sucked before the strong solution blows up. In the later case, we
obtain precise large-time rescaling behaviors for large data to Hele-Shaw flows
in terms of invariant Richardson complex moments. This rescaling behavior
result generalizes a recent result regarding large-time rescaling behavior for
small data in terms of moments. As a byproduct of a theorem in this paper, a
short proof of existence and uniqueness of strong solutions to the
Polubarinova-Galin equation is given.Comment: 25 page
Evolution of an elliptical bubble in an accelerating extensional flow
Mathematical models that describe the dynamical behavior of a thin gas bubble embedded in a glass fiber during a fiber drawing process have been discussed and analyzed.
The starting point for the mathematical modeling was the equations presented in [1] for a glass fiber with a hole undergoing extensional flow. These equations were reconsidered here with the additional reduction that the hole, i.e. the gas bubble, was thin as compared to the radius of the fiber and of finite extent. The primary model considered was one in which the mass of the gas inside the bubble was fixed. This fixed-mass model involved equations for the axial velocity and fiber radius, and equations for the radius of the bubble and the gas pressure inside the bubble. The model equations assumed that the temperature of the furnace of the drawing tower was known.
The governing equations of the bubble are hyperbolic and predict that the bubble cannot extend beyond the limiting characteristics specified by the ends of the initial bubble shape. An analysis of pinch-off was performed, and it was found that pinch-off can occur, depending on the parameters of the model, due to surface tension when the bubble radius is small.
In order to determine the evolution of a bubble, a numerical method of solution was presented. The method was used to study the evolution of two different initial bubble shapes, one convex and the other non-convex. Both initial bubble shapes had fore-aft symmetry, and it was found that the bubbles stretched and elongated severely during the drawing process. For the convex shape, fore-aft symmetry was lost in the middle of the drawing process, but the symmetry was re-gained by the end of the drawing tower. A small amount of pinch-off was observed at each end for this case, so that the final bubble length was slightly shorter than its theoretical maximum length. For the non-convex initial shape, pinch-off occurred in the middle of the bubble resulting in two bubbles by the end of the fiber draw.
The two bubbles had different final pressures and did not have fore-aft symmetry.
An extension of the fixed-mass model was considered in which the gas in the bubble was allowed to diffuse into the surrounding glass. The governing equations for this leaky-mass model were developed and manipulated into a form suitable for a numerical treatment
Duality, thermodynamics, and the linear programming problem in constraint-based models of metabolism
It is shown that the dual to the linear programming problem that arises in
constraint-based models of metabolism can be given a thermodynamic
interpretation in which the shadow prices are chemical potential analogues, and
the objective is to minimise free energy consumption given a free energy drain
corresponding to growth. The interpretation is distinct from conventional
non-equilibrium thermodynamics, although it does satisfy a minimum entropy
production principle. It can be used to motivate extensions of constraint-based
modelling, for example to microbial ecosystems.Comment: 4 pages, 2 figures, 1 table, RevTeX 4, final accepted versio
Calibrating and monitoring the western gray whale mitigation zone and estimating acoustic transmission during a 3D seismic survey, Sakhalin Island, Russia
A 3D marine seismic survey of the Odoptu license area off northeastern Sakhalin Island, Russia, was conducted by DalMorNefteGeofizika (DMNG) on behalf of Exxon Neftegas Limited and the Sakhalin-1 consortium during mid-August through early September 2001. The key environmental issue identified in an environmental impact assessment was protection of the critically endangered western gray whale (Eschrichtius robustus), which spends the summer–fall open water period feeding off northeast Sakhalin Island in close proximity to the seismic survey area. Seismic mitigation and monitoring guidelines and recommendations were developed and implemented to reduce impacts on the feeding activity of western gray whales. Results of the acoustic monitoring program indicated that the noise monitoring and mitigation program was successful in reducing exposure of feeding western gray whales to seismic noise
Exactly Solvable Pairing Model Using an Extension of Richardson-Gaudin Approach
We introduce a new class of exactly solvable boson pairing models using the
technique of Richardson and Gaudin. Analytical expressions for all energy
eigenvalues and first few energy eigenstates are given. In addition, another
solution to Gaudin's equation is also mentioned. A relation with the
Calogero-Sutherland model is suggested.Comment: 9 pages of Latex. In the proceedings of Blueprints for the Nucleus:
From First Principles to Collective Motion: A Festschrift in Honor of
Professor Bruce Barrett, Istanbul, Turkey, 17-23 May 200
Thermodynamic properties of a small superconducting grain
The reduced BCS Hamiltonian for a metallic grain with a finite number of
electrons is considered. The crossover between the ultrasmall regime, in which
the level spacing, , is larger than the bulk superconducting gap, ,
and the small regime, where , is investigated analytically
and numerically. The condensation energy, spin magnetization and tunneling peak
spectrum are calculated analytically in the ultrasmall regime, using an
approximation controlled by as small parameter, where is the
number of interacting electron pairs. The condensation energy in this regime is
perturbative in the coupling constant , and is proportional to . We find that also in a large regime with
, in which pairing correlations are already rather well developed,
the perturbative part of the condensation energy is larger than the singular,
BCS, part. The condition for the condensation energy to be well approximated by
the BCS result is found to be roughly . We show how
the condensation energy can, in principle, be extracted from a measurement of
the spin magnetization curve, and find a re-entrant susceptibility at zero
temperature as a function of magnetic field, which can serve as a sensitive
probe for the existence of superconducting correlations in ultrasmall grains.
Numerical results are presented which suggest that in the large limit the
1/N correction to the BCS result for the condensation energy is larger than
.Comment: 17 pages, 7 figures, Submitted to Phys. Rev.
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