3,574 research outputs found
The attractive nonlinear delta-function potential
We solve the continuous one-dimensional Schr\"{o}dinger equation for the case
of an inverted {\em nonlinear} delta-function potential located at the origin,
obtaining the bound state in closed form as a function of the nonlinear
exponent. The bound state probability profile decays exponentially away from
the origin, with a profile width that increases monotonically with the
nonlinear exponent, becoming an almost completely extended state when this
approaches two. At an exponent value of two, the bound state suffers a
discontinuous change to a delta-like profile. Further increase of the exponent
increases again the width of the probability profile, although the bound state
is proven to be stable only for exponents below two. The transmission of plane
waves across the nonlinear delta potential increases monotonically with the
nonlinearity exponent and is insensitive to the sign of its opacity.Comment: submitted to Am. J. of Phys., sixteen pages, three figure
A two-state kinetic model for the unfolding of single molecules by mechanical force
We investigate the work dissipated during the irreversible unfolding of
single molecules by mechanical force, using the simplest model necessary to
represent experimental data. The model consists of two levels (folded and
unfolded states) separated by an intermediate barrier. We compute the
probability distribution for the dissipated work and give analytical
expressions for the average and variance of the distribution. To first order,
the amount of dissipated work is directly proportional to the rate of
application of force (the loading rate), and to the relaxation time of the
molecule. The model yields estimates for parameters that characterize the
unfolding kinetics under force in agreement with those obtained in recent
experimental results (Liphardt, J., et al. (2002) {\em Science}, {\bf 296}
1832-1835). We obtain a general equation for the minimum number of repeated
experiments needed to obtain an equilibrium free energy, to within , from
non-equilibrium experiments using the Jarzynski formula. The number of
irreversible experiments grows exponentially with the ratio of the average
dissipated work, \bar{\Wdis}, to .}Comment: PDF file, 5 page
Tests hidrodinàmics amb el codi multidimensional FLASH
El FLASH és un codi estable i flexible, desenvolupat a la Universitat de Chicago, que permet estudiar diferents fenòmens hidrodinàmics. L'objectiu futur és desenvolupar models multidimensionals centrats en el camp de les noves per a caracteritzar algunes fases complexes del fenomen, però degut a la complexitat del codi (més de 500000 línies de programació en C++ i Fortran90), la realització d'una simulació estel.lar necessita tenir un coneixement bàsic del FLASH. Per tant, l'objectiu d'aquest treball és la realització d'alguns tests numèrics per aprendre'n el funcionament. Però a la vegada, l'objectiu és doble, ja que per utilitzar una eina de treball com el FLASH, necessitem testejar el propi codi i comprovar que és capaç de resoldre correctament diferents problemes hidrodinàmics que ja s'han simulat prèviament. Així, s'han treballat els diferents tests i hem observat que el codi FLASH és eficaç per simular-los correctament i, per tant, podem esperar que serà un bon codi per a les futures simulacions estel.lars. D'altra banda, aquest primer contacte amb el codi ens ha permès familiaritzar-nos amb l'estructura, adquirir destresa en el seu ús i començar a entendre'l, tot deixant per a més endavant l'estudi detallat dels diferents models numèrics implementats en el codi i eines auxiliars de representació gràfica
Interplay between the Beale-Kato-Majda theorem and the analyticity-strip method to investigate numerically the incompressible Euler singularity problem
Numerical simulations of the incompressible Euler equations are performed
using the Taylor-Green vortex initial conditions and resolutions up to
. The results are analyzed in terms of the classical analyticity strip
method and Beale, Kato and Majda (BKM) theorem. A well-resolved acceleration of
the time-decay of the width of the analyticity strip is observed at
the highest resolution for while preliminary 3D visualizations
show the collision of vortex sheets. The BKM criterium on the power-law growth
of supremum of the vorticity, applied on the same time-interval, is not
inconsistent with the occurrence of a singularity around .
These new findings lead us to investigate how fast the analyticity strip
width needs to decrease to zero in order to sustain a finite-time singularity
consistent with the BKM theorem. A new simple bound of the supremum norm of
vorticity in terms of the energy spectrum is introduced and used to combine the
BKM theorem with the analyticity-strip method. It is shown that a finite-time
blowup can exist only if vanishes sufficiently fast at the
singularity time. In particular, if a power law is assumed for then
its exponent must be greater than some critical value, thus providing a new
test that is applied to our Taylor-Green numerical simulation.
Our main conclusion is that the numerical results are not inconsistent with a
singularity but that higher-resolution studies are needed to extend the
time-interval on which a well-resolved power-law behavior of takes
place, and check whether the new regime is genuine and not simply a crossover
to a faster exponential decay
A family of Nikishin systems with periodic recurrence coefficients
Suppose we have a Nikishin system of measures with the th generating
measure of the Nikishin system supported on an interval \Delta_k\subset\er
with for all . It is well known that
the corresponding staircase sequence of multiple orthogonal polynomials
satisfies a -term recurrence relation whose recurrence coefficients,
under appropriate assumptions on the generating measures, have periodic limits
of period . (The limit values depend only on the positions of the intervals
.) Taking these periodic limit values as the coefficients of a new
-term recurrence relation, we construct a canonical sequence of monic
polynomials , the so-called \emph{Chebyshev-Nikishin
polynomials}. We show that the polynomials themselves form a sequence
of multiple orthogonal polynomials with respect to some Nikishin system of
measures, with the th generating measure being absolutely continuous on
. In this way we generalize a result of the third author and Rocha
\cite{LopRoc} for the case . The proof uses the connection with block
Toeplitz matrices, and with a certain Riemann surface of genus zero. We also
obtain strong asymptotics and an exact Widom-type formula for the second kind
functions of the Nikishin system for .Comment: 30 pages, minor change
Identification of new transitional disk candidates in Lupus with Herschel
New data from the Herschel Space Observatory are broadening our understanding
of the physics and evolution of the outer regions of protoplanetary disks in
star forming regions. In particular they prove to be useful to identify
transitional disk candidates. The goals of this work are to complement the
detections of disks and the identification of transitional disk candidates in
the Lupus clouds with data from the Herschel Gould Belt Survey. We extracted
photometry at 70, 100, 160, 250, 350 and 500 m of all spectroscopically
confirmed Class II members previously identified in the Lupus regions and
analyzed their updated spectral energy distributions. We have detected 34 young
disks in Lupus in at least one Herschel band, from an initial sample of 123
known members in the observed fields. Using the criteria defined in Ribas et
al. (2013) we have identified five transitional disk candidates in the region.
Three of them are new to the literature. Their PACS-70 m fluxes are
systematically higher than those of normal T Tauri stars in the same
associations, as already found in T Cha and in the transitional disks in the
Chamaeleon molecular cloud. Herschel efficiently complements mid-infrared
surveys for identifying transitional disk candidates and confirms that these
objects seem to have substantially different outer disks than the T Tauri stars
in the same molecular clouds.Comment: Accepted for publication in A&A. 16 pages, 9 figures, 7 table
Relationship between Exotic Plant Species Richness, Native Vegetation and Climate in Forest Ecosystems of Chile
In this chapter, we evaluated how native species cover, native species richness, and foliage periodicity of forests are related to exotic species richness in different forest ecosystems distributed through the Mediterranean-type and temperate climate regions of Chile. We compiled published and unpublished data on Chilean vegetation (mainly phytosociological studies) located between 30º and 41º S in which plant species composition and abundance (percentage of cover) per plot was evaluated and published. When all forests were analysed together, we found that exotic species richness was not significantly related to native species richness; it was negatively related to native species cover in both Mediterranean and temperate climatic regions and was greater in deciduous than evergreen forests, although only in the temperate region. In an analysis considering separately every forest type, we observed that only in 50% of these communities, exotic species richness was negatively related to native species cover. Furthermore, in 25% of forest types, exotic species richness was negatively related to native species richness, and in only one forest type, this relationship was positive. Our results suggest that native species produce some resistance against invasion of exotic plants, but this effect may depend on climate and forest type
Two-phase stretching of molecular chains
While stretching of most polymer chains leads to rather featureless
force-extension diagrams, some, notably DNA, exhibit non-trivial behavior with
a distinct plateau region. Here we propose a unified theory that connects
force-extension characteristics of the polymer chain with the convexity
properties of the extension energy profile of its individual monomer subunits.
Namely, if the effective monomer deformation energy as a function of its
extension has a non-convex (concave up) region, the stretched polymer chain
separates into two phases: the weakly and strongly stretched monomers.
Simplified planar and 3D polymer models are used to illustrate the basic
principles of the proposed model. Specifically, we show rigorously that when
the secondary structure of a polymer is mostly due to weak non-covalent
interactions, the stretching is two-phase, and the force-stretching diagram has
the characteristic plateau. We then use realistic coarse-grained models to
confirm the main findings and make direct connection to the microscopic
structure of the monomers. We demostrate in detail how the two-phase scenario
is realized in the \alpha-helix, and in DNA double helix. The predicted plateau
parameters are consistent with single molecules experiments. Detailed analysis
of DNA stretching demonstrates that breaking of Watson-Crick bonds is not
necessary for the existence of the plateau, although some of the bonds do break
as the double-helix extends at room temperature. The main strengths of the
proposed theory are its generality and direct microscopic connection.Comment: 16 pges, 22 figure
Condensation transition in DNA-polyaminoamide dendrimer fibers studied using optical tweezers
When mixed together, DNA and polyaminoamide (PAMAM) dendrimers form fibers
that condense into a compact structure. We use optical tweezers to pull
condensed fibers and investigate the decondensation transition by measuring
force-extension curves (FECs). A characteristic plateau force (around 10 pN)
and hysteresis between the pulling and relaxation cycles are observed for
different dendrimer sizes, indicating the existence of a first-order transition
between two phases (condensed and extended) of the fiber. The fact that we can
reproduce the same FECs in the absence of additional dendrimers in the buffer
medium indicates that dendrimers remain irreversibly bound to the DNA backbone.
Upon salt variation FECs change noticeably confirming that electrostatic forces
drive the condensation transition. Finally, we propose a simple model for the
decondensing transition that qualitatively reproduces the FECs and which is
confirmed by AFM images.Comment: Latex version, 4 pages+3 color figure
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