477 research outputs found
Cooperative Transport in a Multi-Particle, Multi-Dimensional Flashing Ratchet
Random and undirected forces are rectified in biological and synthetic systems using ratcheting mechanisms, which employ periodic asymmetric potentials and nonequilibrium conditions to produce useful transport. The density of motors or transported particles is known to strongly affect the nature and efficacy of transport in biological systems, as well as in synthetic ratchets and active swimmer systems. While experimental ratchet implementations typically employ potentials varying in two dimensions (2D), the role of the density of interacting particles in such a system has not been modeled. Prompted by experimental observations and building upon previous simulations, this paper describes the ratcheting process of interacting particles in a 2D flashing ratchet, studied using classical simulations. Increased particle density is found to allow effective ratcheting at higher driving frequencies, compared to the low-density or non-interacting case. High densities also produce a new ratcheting mode at low driving frequencies, based on independent trajectories of high kinetic-energy particles, more than doubling transport at low frequencies
On the Fermionic Quasi-particle Interpretation in Minimal Models of Conformal Field Theory
The conjecture that the states of the fermionic quasi-particles in minimal
conformal field theories are eigenstates of the integrals of motion to certain
eigenvalues is checked and shown to be correct only for the Ising model.Comment: 5 pages of Late
The Many Faces of a Character
We prove an identity between three infinite families of polynomials which are
defined in terms of `bosonic', `fermionic', and `one-dimensional configuration'
sums. In the limit where the polynomials become infinite series, they give
different-looking expressions for the characters of the two integrable
representations of the affine algebra at level one. We conjecture yet
another fermionic sum representation for the polynomials which is constructed
directly from the Bethe-Ansatz solution of the Heisenberg spin chain.Comment: 14/9 pages in harvmac, Tel-Aviv preprint TAUP 2125-9
Fusion products, Kostka polynomials, and fermionic characters of su(r+1)_k
Using a form factor approach, we define and compute the character of the
fusion product of rectangular representations of \hat{su}(r+1). This character
decomposes into a sum of characters of irreducible representations, but with
q-dependent coefficients. We identify these coefficients as (generalized)
Kostka polynomials. Using this result, we obtain a formula for the characters
of arbitrary integrable highest-weight representations of \hat{su}(r+1) in
terms of the fermionic characters of the rectangular highest weight
representations.Comment: 21 pages; minor changes, typos correcte
Minimal Models of Integrable Lattice Theory and Truncated Functional Equations
We consider the integrable XXZ model with the special open boundary
conditions. We perform Quantum Group reduction of this model in roots of unity
and use it for the definition Minimal Models of Interable lattice theory. It is
shown that after this Quantum Group reduction Sklyanin's transfer-matrices
satisfy the closed system of the truncated functional relations. We solve these
equations for the simplest case.Comment: 9 pages, LaTeX, corrected some typos, added some reference
Conflict-Free Coloring Made Stronger
In FOCS 2002, Even et al. showed that any set of discs in the plane can
be Conflict-Free colored with a total of at most colors. That is,
it can be colored with colors such that for any (covered) point
there is some disc whose color is distinct from all other colors of discs
containing . They also showed that this bound is asymptotically tight. In
this paper we prove the following stronger results:
\begin{enumerate} \item [(i)] Any set of discs in the plane can be
colored with a total of at most colors such that (a) for any
point that is covered by at least discs, there are at least
distinct discs each of which is colored by a color distinct from all other
discs containing and (b) for any point covered by at most discs,
all discs covering are colored distinctively. We call such a coloring a
{\em -Strong Conflict-Free} coloring. We extend this result to pseudo-discs
and arbitrary regions with linear union-complexity.
\item [(ii)] More generally, for families of simple closed Jordan regions
with union-complexity bounded by , we prove that there exists
a -Strong Conflict-Free coloring with at most colors.
\item [(iii)] We prove that any set of axis-parallel rectangles can be
-Strong Conflict-Free colored with at most colors.
\item [(iv)] We provide a general framework for -Strong Conflict-Free
coloring arbitrary hypergraphs. This framework relates the notion of -Strong
Conflict-Free coloring and the recently studied notion of -colorful
coloring. \end{enumerate}
All of our proofs are constructive. That is, there exist polynomial time
algorithms for computing such colorings
Critical RSOS and Minimal Models II: Building Representations of the Virasoro Algebra and Fields
We consider sl(2) minimal conformal field theories and the dual parafermion
models. Guided by results for the critical A_L Restricted Solid-on-Solid (RSOS)
models and its Virasoro modules expressed in terms of paths, we propose a
general level-by-level algorithm to build matrix representations of the
Virasoro generators and chiral vertex operators (CVOs). We implement our scheme
for the critical Ising, tricritical Ising, 3-state Potts and Yang-Lee theories
on a cylinder and confirm that it is consistent with the known two-point
functions for the CVOs and energy-momentum tensor. Our algorithm employs a
distinguished basis which we call the L_1-basis. We relate the states of this
canonical basis level-by-level to orthonormalized Virasoro states
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