17,460 research outputs found
Self Trapping of a Single Bacterium in its Own Chemoattractant
Bacteria (e.g. E. Coli) are very sensitive to certain chemoattractants (e.g.
asparate) which they themselves produce. This leads to chemical instabilities
in a uniform population. We discuss here the different case of a single
bacterium, following the general scheme of Brenner, Levitov and Budrene. We
show that in one and two dimensions (in a capillary or in a thin film) the
bacterium can become self-trapped in its cloud of attractant. This should occur
if a certain coupling constant is larger than unity. We then estimate the
reduced diffusion D_eff of the bacterium in the strong coupling limit, and find
D_eff ~ 1/g.Comment: 4 pages, absolutely no figure
Experimental and numerical study of error fields in the CNT stellarator
Sources of error fields were indirectly inferred in a stellarator by
reconciling computed and numerical flux surfaces. Sources considered so far
include the displacements and tilts (but not the deformations, yet) of the four
circular coils featured in the simple CNT stellarator. The flux surfaces were
measured by means of an electron beam and phosphor rod, and were computed by
means of a Biot-Savart field-line tracing code. If the ideal coil locations and
orientations are used in the computation, agreement with measurements is poor.
Discrepancies are ascribed to errors in the positioning and orientation of the
in-vessel interlocked coils. To that end, an iterative numerical method was
developed. A Newton-Raphson algorithm searches for the coils' displacements and
tilts that minimize the discrepancy between the measured and computed flux
surfaces. This method was verified by misplacing and tilting the coils in a
numerical model of CNT, calculating the flux surfaces that they generated, and
testing the algorithm's ability to deduce the coils' displacements and tilts.
Subsequently, the numerical method was applied to the experimental data,
arriving at a set of coil displacements whose resulting field errors exhibited
significantly improved quantitative and qualitative agreement with experimental
results.Comment: Special Issue on the 20th International Stellarator-Heliotron
Worksho
Shear-dependent apparent slip on hydrophobic surfaces: The Mattress Model
Recent experiments (Zhu & Granick (2001) Phys. Rev. Lett. 87 096105) have
measured a large shear dependent fluid slip at partially wetting fluid-solid
surfaces. We present a simple model for such slip, motivated by the recent
observations of nanobubbles on hydrophobic surfaces. The model considers the
dynamic response of bubbles to change in hydrodynamic pressure due to the
oscillation of a solid surface. Both the compression and diffusion of gas in
the bubbles decrease the force on the oscillating surface by a ``leaking
mattress'' effect, thereby creating an apparent shear-dependent slip. With
bubbles similar to those observed by atomic force microscopy to date, the model
is found to lead to force decreases consistent with the experimental
measurements of Zhu & Granick
Applications of BGP-reflection functors: isomorphisms of cluster algebras
Given a symmetrizable generalized Cartan matrix , for any index , one
can define an automorphism associated with of the field of rational functions of independent indeterminates It is an isomorphism between two cluster algebras associated to the
matrix (see section 4 for precise meaning). When is of finite type,
these isomorphisms behave nicely, they are compatible with the BGP-reflection
functors of cluster categories defined in [Z1, Z2] if we identify the
indecomposable objects in the categories with cluster variables of the
corresponding cluster algebras, and they are also compatible with the
"truncated simple reflections" defined in [FZ2, FZ3]. Using the construction of
preprojective or preinjective modules of hereditary algebras by Dlab-Ringel
[DR] and the Coxeter automorphisms (i.e., a product of these isomorphisms), we
construct infinitely many cluster variables for cluster algebras of infinite
type and all cluster variables for finite types.Comment: revised versio
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
Noise compliant macromodel synthesis for RF and Mixed-Signal applications
This paper proposes a compact synthesis approach for reduced-order behavioral macromodels of linear circuit blocks for RF and Mixed-Signal design. The proposed approach revitalizes the classical synthesis of lumped linear and timeinvariant multiport networks by reactance extraction, which is here exploited to obtain reduced-order equivalent SPICE netlists that can be used in any type of system-level simulations, including transient and noise analysis. The effectiveness of proposed approach is demonstrated on a real design applicatio
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
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
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