2,270 research outputs found
Singularity results for functional equations driven by linear fractional transformations
We consider functional equations driven by linear fractional transformations,
which are special cases of de Rham's functional equations. We consider
Hausdorff dimension of the measure whose distribution function is the solution.
We give a necessary and sufficient condition for singularity. We also show that
they have a relationship with stationary measures.Comment: 14 pages, Title changed, to appear in Journal of Theoretical
Probabilit
Long-Ranged Orientational Order in Dipolar Fluids
Recently Groh and Dietrich claimed the thermodynamic state of a dipolar fluid
depends on the shape of the fluid's container. For example, a homogeneous fluid
in a short fat container would phase separate when transferred to a tall skinny
container of identical volume and temperature. Their calculation thus lacks a
thermodynamic limit. We show that removal of demagnetizing fields restores the
true, shape independent, thermodynamic limit. As a consequence, spontaneously
magnetized liquids display inhomogeneous magnetization textures.Comment: 3 pages, LaTex, no figures. Submitted as comment to PRL, May 199
Charge-Fluctuation-Induced Non-analytic Bending Rigidity
In this Letter, we consider a neutral system of mobile positive and negative
charges confined on the surface of curved films. This may be an appropriate
model for: i) a highly charged membrane whose counterions are confined to a
sheath near its surface; ii) a membrane composed of an equimolar mixture of
anionic and cationic surfactants in aqueous solution. We find that the charge
fluctuations contribute a non-analytic term to the bending rigidity that varies
logarithmically with the radius of curvature. This may lead to spontaneous
vesicle formation, which is indeed observed in similar systems.Comment: Revtex, 9 pages, no figures, submitted to PR
Polyelectrolyte Bundles
Using extensive Molecular Dynamics simulations we study the behavior of
polyelectrolytes with hydrophobic side chains, which are known to form
cylindrical micelles in aqueous solution. We investigate the stability of such
bundles with respect to hydrophobicity, the strength of the electrostatic
interaction, and the bundle size. We show that for the parameter range relevant
for sulfonated poly-para-phenylenes (PPP) one finds a stable finite bundle
size. In a more generic model we also show the influence of the length of the
precursor oligomer on the stability of the bundles. We also point out that our
model has close similarities to DNA solutions with added condensing agents,
hinting to the possibility that the size of DNA aggregates is under certain
circumstances thermodynamically limited.Comment: 10 pages, 8 figure
Organized condensation of worm-like chains
We present results relevant to the equilibrium organization of DNA strands of
arbitrary length interacting with a spherical organizing center, suggestive of
DNA-histone complexation in nucleosomes. We obtain a rich phase diagram in
which a wrapping state is transformed into a complex multi-leafed, rosette
structure as the adhesion energy is reduced. The statistical mechanics of the
"melting" of a rosette can be mapped into an exactly soluble one-dimensional
many-body problem.Comment: 15 pages, 2 figures in a pdf fil
Hill's Equation with Random Forcing Parameters: Determination of Growth Rates through Random Matrices
This paper derives expressions for the growth rates for the random 2 x 2
matrices that result from solutions to the random Hill's equation. The
parameters that appear in Hill's equation include the forcing strength and
oscillation frequency. The development of the solutions to this periodic
differential equation can be described by a discrete map, where the matrix
elements are given by the principal solutions for each cycle. Variations in the
forcing strength and oscillation frequency lead to matrix elements that vary
from cycle to cycle. This paper presents an analysis of the growth rates
including cases where all of the cycles are highly unstable, where some cycles
are near the stability border, and where the map would be stable in the absence
of fluctuations. For all of these regimes, we provide expressions for the
growth rates of the matrices that describe the solutions.Comment: 22 pages, 3 figure
Identification of Immunoreactive Material in Mammoth Fossils
The fossil record represents a history of life on this planet. Attempts to obtain molecular information from this record by analysis of nucleic acids found within fossils of extreme age have been unsuccessful or called into question. However, previous studies have demonstrated the long-term persistence of peptides within fossils and have used antibodies to extant proteins to demonstrate antigenic material. In this study we address two questions: Do immunogenic/antigenic materials persist in fossils? and; Can fossil material be used to raise antibodies that will cross-react with extant proteins? We have used material extracted from a well-preserved 100,000-300,000-year-old mammoth skull to produce antisera. The specificity of the antisera was tested by ELISA, western blotting, and immunohistochemistry. It was demonstrated that antisera reacted specifically with the fossils and no the surrounding sediments. Reactivity of antisera with modern proteins and tissues was also demonstrated, as was the ability to detect evolutionary relationships via antibody-antigen interactions. Mass spectrometry demonstrated the response of amino acids and specific peptides within the fossil. Peptides were purified by anion-exchange chromatography and sequenced by tandem mass spectrometry. The collagen-derived peptides may have been the source of at least some of the immunologic reactivity, but the antisera identified molecules that were not observed by mass spectrometry, indicating that immunologic methods may have greater sensitivity. Although the presence of peptides and amino acids was demonstrated, the exact nature of the antigenic material was not fully clarified. This report demonstrated that antibodies may be used to obtain information from the fossil record
Exact Lyapunov Exponent for Infinite Products of Random Matrices
In this work, we give a rigorous explicit formula for the Lyapunov exponent
for some binary infinite products of random real matrices. All
these products are constructed using only two types of matrices, and ,
which are chosen according to a stochastic process. The matrix is singular,
namely its determinant is zero. This formula is derived by using a particular
decomposition for the matrix , which allows us to write the Lyapunov
exponent as a sum of convergent series. Finally, we show with an example that
the Lyapunov exponent is a discontinuous function of the given parameter.Comment: 1 pages, CPT-93/P.2974,late
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