17,498 research outputs found
Entropic particle transport: higher order corrections to the Fick-Jacobs diffusion equation
Transport of point-size Brownian particles under the influence of a constant
and uniform force field through a three-dimensional channel with smoothly
varying periodic cross-section is investigated. Here, we employ an asymptotic
analysis in the ratio between the difference of the widest and the most narrow
constriction divided through the period length of the channel geometry. We
demonstrate that the leading order term is equivalent to the Fick-Jacobs
approximation. By use of the higher order corrections to the probability
density we derive an expression for the spatially dependent diffusion
coefficient D(x) which substitutes the constant diffusion coefficient present
in the common Fick-Jacobs equation. In addition, we show that in the diffusion
dominated regime the average transport velocity is obtained as the product of
the zeroth-order Fick-Jacobs result and the expectation value of the spatially
dependent diffusion coefficient . The analytic findings are corroborated
with the precise numerical results of a finite element calculation of the
Smoluchowski diffusive particle dynamics occurring in a reflection symmetric
sinusoidal-shaped channel.Comment: 9 pages, 3 figure
Local stresses, dyke arrest and surface deformation in volcanic edificesand rift zones
Field studies indicate that nearly all eruptions in volcanic edifices and rift zones are supplied with magma through
fractures (dykes) that are opened by magmatic overpressure. While (inferred) dyke injections are frequent during unrest
periods, volcanic eruptions are, in comparison, infrequent, suggesting that most dykes become arrested at certain
depths in the crust, in agreement with field studies. The frequency of dyke arrest can be partly explained by the numerical
models presented here which indicate that volcanic edifices and rift zones consisting of rocks of contrasting mechanical properties, such as soft pyroclastic layers and stiff lava flows, commonly develop local stress fields that encourage dyke arrest. During unrest, surface deformation studies are routinely used to infer the geometries of arrested dykes, and some models (using homogeneous, isotropic half-spaces) infer large grabens to be induced by such dykes. Our results, however, show that the dyke-tip tensile stresses are normally much greater than the induced surface stresses, making it difficult to explain how a dyke can induce surface stresses in excess of the tensile (or shear)
strength while the same strength is not exceeded at the (arrested) dyke tip. Also, arrested dyke tips in eroded or active
rift zones are normally not associated with dyke-induced grabens or normal faults, and some dykes arrested within a few metres of the surface do not generate faults or grabens. The numerical models show that abrupt changes in Young's moduli(stiffnesses), layers with relatively high dyke-normal compressive stresses (stress barriers), and weak horizontal contacts may make the dyke-induced surface tensile stresses too small for significant fault or graben formation to occur in rift zones or volcanic edifices. Also, these small surface stresses may have no simple relation to the dyke geometry or the depth to its tip. Thus, for a layered crust with weak contacts, straightforward inversion of
surface geodetic data may lead to unreliable geometries of arrested dykes in active rift zones and volcanic edifices
Sonoluminescing air bubbles rectify argon
The dynamics of single bubble sonoluminescence (SBSL) strongly depends on the
percentage of inert gas within the bubble. We propose a theory for this
dependence, based on a combination of principles from sonochemistry and
hydrodynamic stability. The nitrogen and oxygen dissociation and subsequent
reaction to water soluble gases implies that strongly forced air bubbles
eventually consist of pure argon. Thus it is the partial argon (or any other
inert gas) pressure which is relevant for stability. The theory provides
quantitative explanations for many aspects of SBSL.Comment: 4 page
P1 finite element methods for an elliptic state-constrained distributed optimal control problem with Neumann boundary conditions
We investigate two P finite element methods for an elliptic state-constrained distributed optimal control problem with Neumann boundary conditions on general polygonal domains.
Self-assembling DNA-caged particles: nanoblocks for hierarchical self-assembly
DNA is an ideal candidate to organize matter on the nanoscale, primarily due
to the specificity and complexity of DNA based interactions. Recent advances in
this direction include the self-assembly of colloidal crystals using DNA
grafted particles. In this article we theoretically study the self-assembly of
DNA-caged particles. These nanoblocks combine DNA grafted particles with more
complicated purely DNA based constructs. Geometrically the nanoblock is a
sphere (DNA grafted particle) inscribed inside a polyhedron (DNA cage). The
faces of the DNA cage are open, and the edges are made from double stranded
DNA. The cage vertices are modified DNA junctions. We calculate the
equilibriuim yield of self-assembled, tetrahedrally caged particles, and
discuss their stability with respect to alternative structures. The
experimental feasability of the method is discussed. To conclude we indicate
the usefulness of DNA-caged particles as nanoblocks in a hierarchical
self-assembly strategy.Comment: v2: 21 pages, 8 figures; revised discussion in Sec. 2, replaced 2
figures, added new reference
Dynamics of superconducting nanowires shunted with an external resistor
We present the first study of superconducting nanowires shunted with an
external resistor, geared towards understanding and controlling coherence and
dissipation in nanowires. The dynamics is probed by measuring the evolution of
the V-I characteristics and the distributions of switching and retrapping
currents upon varying the shunt resistor and temperature. Theoretical analysis
of the experiments indicates that as the value of the shunt resistance is
decreased, the dynamics turns more coherent presumably due to stabilization of
phase-slip centers in the wire and furthermore the switching current approaches
the Bardeen's prediction for equilibrium depairing current. By a detailed
comparison between theory and experimental, we make headway into identifying
regimes in which the quasi-one-dimensional wire can effectively be described by
a zero-dimensional circuit model analogous to the RCSJ (resistively and
capacitively shunted Josephson junction) model of Stewart and McCumber. Besides
its fundamental significance, our study has implications for a range of
promising technological applications.Comment: 15 pages, 14 figure
Encapsulation of phosphorus dopants in silicon for the fabrication of a quantum computer
The incorporation of phosphorus in silicon is studied by analyzing phosphorus
delta-doped layers using a combination of scanning tunneling microscopy,
secondary ion mass spectrometry and Hall effect measurements. The samples are
prepared by phosphine saturation dosing of a Si(100) surface at room
temperature, a critical annealing step to incorporate phosphorus atoms, and
subsequent epitaxial silicon overgrowth. We observe minimal dopant segregation
(5 nm), complete electrical activation at a silicon growth temperature of 250
degrees C and a high two-dimensional electron mobility of 100 cm2/Vs at a
temperature of 4.2 K. These results, along with preliminary studies aimed at
further minimizing dopant diffusion, bode well for the fabrication of
atomically precise dopant arrays in silicon such as those found in recent
solid-state quantum computer architectures.Comment: 3 pages, 4 figure
Dispersion and collapse of wave maps
We study numerically the Cauchy problem for equivariant wave maps from 3+1
Minkowski spacetime into the 3-sphere. On the basis of numerical evidence
combined with stability analysis of self-similar solutions we formulate two
conjectures. The first conjecture states that singularities which are produced
in the evolution of sufficiently large initial data are approached in a
universal manner given by the profile of a stable self-similar solution. The
second conjecture states that the codimension-one stable manifold of a
self-similar solution with exactly one instability determines the threshold of
singularity formation for a large class of initial data. Our results can be
considered as a toy-model for some aspects of the critical behavior in
formation of black holes.Comment: 14 pages, Latex, 9 eps figures included, typos correcte
- …