2,770 research outputs found
Geometry of Multiplicative Preprojective Algebra
Crawley-Boevey and Shaw recently introduced a certain multiplicative analogue
of the deformed preprojective algebra, which they called the multiplicative
preprojective algebra. In this paper we study the moduli space of (semi)stable
representations of such an algebra (the multiplicative quiver variety), which
in fact has many similarities to the quiver variety. We show that there exists
a complex analytic isomorphism between the nilpotent subvariety of the quiver
variety and that of the multiplicative quiver variety (which can be extended to
a symplectomorphism between these tubular neighborhoods). We also show that
when the quiver is star-shaped, the multiplicative quiver variety parametrizes
Simpson's (poly)stable filtered local systems on a punctured Riemann sphere
with prescribed filtration type, weight and associated graded local system
around each puncture.Comment: 51pages; corrected typos and references; changed font; v4 is the same
as v3 except margi
Effect of the spin-orbit interaction and the electron phonon coupling on the electronic state in a silicon vacancy
The electronic state around a single vacancy in silicon crystal is
investigated by using the Green's function approach. The triply degenerate
charge states are found to be widely extended and account for extremely large
elastic softening at low temperature as observed in recent ultrasonic
experiments. When we include the LS coupling on each Si
atom, the 6-fold spin-orbital degeneracy for the state with the valence
+1 and spin 1/2 splits into doublet groundstates and
quartet excited states with a reduced excited energy of . We also consider the effect of couplings between electrons and
Jahn-Teller phonons in the dangling bonds within the second order perturbation
and find that the groundstate becomes quartet which is responsible
for the magnetic-field suppression of the softening in B-doped silicon.Comment: 4 pages, 2 figure
Overdamped Stress Relaxation in Buckled Rods
We present a comprehensive theoretical analysis of the stress relaxation in a
multiply but weakly buckled incompressible rod in a viscous solvent. In the
bulk two interesting regimes of generic self--similar intermediate asymptotics
are distinguished, which give rise to two classes of approximate and exact
power--law solutions, respectively. For the case of open boundary conditions
the corresponding non--trivial boundary--layer scenarios are derived by a
multiple--scale perturbation (``adiabatic'') method. Our results compare well
with -- and provide the theoretical explanation for -- previous results from
numerical simulations, and they suggest new directions for further fruitful
numerical and experimental investigations.Comment: 20 pages, 12 figure
Diffusion-limited loop formation of semiflexible polymers: Kramers theory and the intertwined time scales of chain relaxation and closing
We show that Kramers rate theory gives a straightforward, accurate estimate
of the closing time of a semiflexible polymer that is valid in cases
of physical interest. The calculation also reveals how the time scales of chain
relaxation and closing are intertwined, illuminating an apparent conflict
between two ways of calculating in the flexible limit.Comment: Europhys. Lett., 2003 (in press). 8 pages, 3 figures. See also,
physics/0101087 for physicist's approach to and the importance of
semiflexible polymer looping, in DNA replicatio
Renormalized one-loop theory of correlations in polymer blends
The renormalized one-loop theory is a coarse-grained theory of corrections to
the self-consistent field theory (SCFT) of polymer liquids, and to the random
phase approximation (RPA) theory of composition fluctuations. We present
predictions of corrections to the RPA for the structure function and to
the random walk model of single-chain statics in binary homopolymer blends. We
consider an apparent interaction parameter that is defined by
applying the RPA to the small limit of . The predicted deviation of
from its long chain limit is proportional to , where
is chain length. This deviation is positive (i.e., destabilizing) for weakly
non-ideal mixtures, with \chi_{a} N \alt 1, but negative (stabilizing) near
the critical point. The positive correction to for low values of
is a result of the fact that monomers in mixtures of shorter
chains are slightly less strongly shielded from intermolecular contacts. The
depression in near the critical point is a result of long-wavelength
composition fluctuations. The one-loop theory predicts a shift in the critical
temperature of , which is much greater than the predicted
width of the Ginzburg region. Chain dimensions deviate
slightly from those of a random walk even in a one-component melt, and contract
slightly with increasing . Predictions for and single-chain
properties are compared to published lattice Monte Carlo simulations.Comment: submitted to J. Chem. Phy
A general theory of DNA-mediated and other valence-limited interactions
We present a general theory for predicting the interaction potentials between
DNA-coated colloids, and more broadly, any particles that interact via
valence-limited ligand-receptor binding. Our theory correctly incorporates the
configurational and combinatorial entropic factors that play a key role in
valence-limited interactions. By rigorously enforcing self-consistency, it
achieves near-quantitative accuracy with respect to detailed Monte Carlo
calculations. With suitable approximations and in particular geometries, our
theory reduces to previous successful treatments, which are now united in a
common and extensible framework. We expect our tools to be useful to other
researchers investigating ligand-mediated interactions. A complete and
well-documented Python implementation is freely available at
http://github.com/patvarilly/DNACC .Comment: 18 pages, 10 figure
Electronic State of Na_xCoO_2 Based on the Two Dimensional Triangular Lattice d-p Model
The electronic state in a CoO_2 plane of the layered cobalt oxides
Na_{x}CoO_2 is investigated by using the 11 band d-p model on a two-dimensional
triangular lattice, where the tight-binding parameters are determined so as to
fit the LDA band structure. Effects of the Coulomb interaction at a Co site:
the intra- and inter-orbital direct terms U and U', the exchange coupling J and
the pair-transfer J', are treated within the Hartree-Fock approximation. We
also consider the effect of the Na order at x=0.5, where Na ions form one
dimensional chains, by taking into account of an effective one-dimensional
potential Delta epsilon_{d} on the CoO_2 plane. It is found that the Na order
enhances the Fermi surface nesting resulting in the antiferromagnetism (AFM)
which is suppressed due to the frustration effect in the case without the Na
order. When U and Delta epsilon_{d} are varied, we observe three types of the
AFM: (1) the metallic AFM with large density of states N_F at the Fermi level
for small values of U and Delta epsilon_{d}, (2) the semimetallic AFM with tiny
N_F for large U with small Delta epsilon_{d} and (3) the insulating AFM with a
finite energy gap for large values of U and Delta epsilon_{d}.Comment: 6 pages, 4 figure
Orientational order and glassy states in networks of semiflexible polymers
Motivated by the structure of networks of cross-linked cytoskeletal
biopolymers, we study the orientationally ordered phases in two-dimensional
networks of randomly cross-linked semiflexible polymers. We consider permanent
cross-links which prescribe a finite angle and treat them as quenched disorder
in a semi-microscopic replica field theory. Starting from a fluid of
un-cross-linked polymers and small polymer clusters (sol) and increasing the
cross-link density, a continuous gelation transition occurs. In the resulting
gel, the semiflexible chains either display long range orientational order or
are frozen in random directions depending on the value of the crossing angle,
the crosslink concentration and the stiffness of the polymers. A crossing angle
leads to long range -fold orientational order, e.g.,
"hexatic" or "tetratic" for or , respectively.
The transition is discontinuous and the critical cross-link density depends on
the bending stiffness of the polymers and the cross-link geometry: the higher
the stiffness and the lower , the lower the critical number of cross-links.
In between the sol and the long range ordered state, we always observe a gel
which is a statistically isotropic amorphous solid (SIAS) with random
positional and random orientational localization of the participating polymers.Comment: 20 pages, added references, minor changes, final version as published
in PR
Static Scaling Behavior of High-Molecular-Weight Polymers in Dilute Solution: A Reexamination
Previous theories of dilute polymer solutions have failed to distinguish
clearly between two very different ways of taking the long-chain limit: (I) at fixed temperature , and (II) ,
with fixed. I argue that the modern
two-parameter theory (continuum Edwards model) applies to case II --- not case
I --- and in fact gives exactly the crossover scaling functions for
modulo two nonuniversal scale factors. A Wilson-type renormalization group
clarifies the connection between crossover scaling functions and continuum
field theories. [Also contains a general discussion of the connection between
the Wilson and field-theoretic renormalization groups. Comments solicited.]Comment: 10 pages including 1 figure, 181159 bytes Postscript
(NYU-TH-93/05/01
Multiscale Modeling of Binary Polymer Mixtures: Scale Bridging in the Athermal and Thermal Regime
Obtaining a rigorous and reliable method for linking computer simulations of
polymer blends and composites at different length scales of interest is a
highly desirable goal in soft matter physics. In this paper a multiscale
modeling procedure is presented for the efficient calculation of the static
structural properties of binary homopolymer blends. The procedure combines
computer simulations of polymer chains on two different length scales, using a
united atom representation for the finer structure and a highly coarse-grained
approach on the meso-scale, where chains are represented as soft colloidal
particles interacting through an effective potential. A method for combining
the structural information by inverse mapping is discussed, allowing for the
efficient calculation of partial correlation functions, which are compared with
results from full united atom simulations. The structure of several polymer
mixtures is obtained in an efficient manner for several mixtures in the
homogeneous region of the phase diagram. The method is then extended to
incorporate thermal fluctuations through an effective chi parameter. Since the
approach is analytical, it is fully transferable to numerous systems.Comment: in press, 13 pages, 7 figures, 6 table
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