1,072 research outputs found
Combinatorics of bicubic maps with hard particles
We present a purely combinatorial solution of the problem of enumerating
planar bicubic maps with hard particles. This is done by use of a bijection
with a particular class of blossom trees with particles, obtained by an
appropriate cutting of the maps. Although these trees have no simple local
characterization, we prove that their enumeration may be performed upon
introducing a larger class of "admissible" trees with possibly doubly-occupied
edges and summing them with appropriate signed weights. The proof relies on an
extension of the cutting procedure allowing for the presence on the maps of
special non-sectile edges. The admissible trees are characterized by simple
local rules, allowing eventually for an exact enumeration of planar bicubic
maps with hard particles. We also discuss generalizations for maps with
particles subject to more general exclusion rules and show how to re-derive the
enumeration of quartic maps with Ising spins in the present framework of
admissible trees. We finally comment on a possible interpretation in terms of
branching processes.Comment: 41 pages, 19 figures, tex, lanlmac, hyperbasics, epsf. Introduction
and discussion/conclusion extended, minor corrections, references adde
Folds in 2D String Theories
We study maps from a 2D world-sheet to a 2D target space which include folds.
The geometry of folds is discussed and a metric on the space of folded maps is
written down. We show that the latter is not invariant under area preserving
diffeomorphisms of the target space. The contribution to the partition function
of maps associated with a given fold configuration is computed. We derive a
description of folds in terms of Feynman diagrams. A scheme to sum up the
contributions of folds to the partition function in a special case is suggested
and is shown to be related to the Baxter-Wu lattice model. An interpretation of
folds as trajectories of particles in the adjoint representation of
gauge group in the large limit which interact in an unusual way with the
gauge fields is discussed.Comment: 56 pages, latex, followed by epsf, 13 uuencoded epsf figure
Roughening Induced Deconstruction in (100) Facets of CsCl Type Crystals
The staggered 6-vertex model describes the competition between surface
roughening and reconstruction in (100) facets of CsCl type crystals. Its phase
diagram does not have the expected generic structure, due to the presence of a
fully-packed loop-gas line. We prove that the reconstruction and roughening
transitions cannot cross nor merge with this loop-gas line if these degrees of
freedom interact weakly. However, our numerical finite size scaling analysis
shows that the two critical lines merge along the loop-gas line, with strong
coupling scaling properties. The central charge is much larger than 1.5 and
roughening takes place at a surface roughness much larger than the conventional
universal value. It seems that additional fluctuations become critical
simultaneously.Comment: 31 pages, 9 figure
Granular discharge and clogging for tilted hoppers
We measure the flux of spherical glass beads through a hole as a systematic
function of both tilt angle and hole diameter, for two different size beads.
The discharge increases with hole diameter in accord with the Beverloo relation
for both horizontal and vertical holes, but in the latter case with a larger
small-hole cutoff. For large holes the flux decreases linearly in cosine of the
tilt angle, vanishing smoothly somewhat below the angle of repose. For small
holes it vanishes abruptly at a smaller angle. The conditions for zero flux are
discussed in the context of a {\it clogging phase diagram} of flow state vs
tilt angle and ratio of hole to grain size
Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
We study quartic matrix models with partition function Z[E,J]=\int dM
\exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of
Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0
is a scalar coupling constant and the matrix J is used to generate correlation
functions. For E not a multiple of the identity matrix, we prove a universal
algebraic recursion formula which gives all higher correlation functions in
terms of the 2-point function and the distinct eigenvalues of E. The 2-point
function itself satisfies a closed non-linear equation which must be solved
case by case for given E. These results imply that if the 2-point function of a
quartic matrix model is renormalisable by mass and wavefunction
renormalisation, then the entire model is renormalisable and has vanishing
\beta-function.
As main application we prove that Euclidean \phi^4-quantum field theory on
four-dimensional Moyal space with harmonic propagation, taken at its
self-duality point and in the infinite volume limit, is exactly solvable and
non-trivial. This model is a quartic matrix model, where E has for N->\infty
the same spectrum as the Laplace operator in 4 dimensions. Using the theory of
singular integral equations of Carleman type we compute (for N->\infty and
after renormalisation of E,\lambda) the free energy density
(1/volume)\log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear
integral equation. Existence of a solution is proved via the Schauder fixed
point theorem.
The derivation of the non-linear integral equation relies on an assumption
which we verified numerically for coupling constants 0<\lambda\leq (1/\pi).Comment: LaTeX, 64 pages, xypic figures. v4: We prove that recursion formulae
and vanishing of \beta-function hold for general quartic matrix models. v3:
We add the existence proof for a solution of the non-linear integral
equation. A rescaling of matrix indices was necessary. v2: We provide
Schwinger-Dyson equations for all correlation functions and prove an
algebraic recursion formula for their solutio
Symmetries of Large N Matrix Models for Closed Strings
We obtain the symmetry algebra of multi-matrix models in the planar large N
limit. We use this algebra to associate these matrix models with quantum spin
chains. In particular, certain multi-matrix models are exactly solved by using
known results of solvable spin chain systems.Comment: 12 pages, 1 eps figure, RevTex, some minor typos in the publised
version are correcte
Next generation multiplexing for digital PCR using a novel melt-based hairpin probe design
Digital PCR (dPCR) is a powerful tool for research and diagnostic applications that require absolute quantification of target molecules or detection of rare events, but the number of nucleic acid targets that can be distinguished within an assay has limited its usefulness. For most dPCR systems, one target is detected per optical channel and the total number of targets is limited by the number of optical channels on the platform. Higher-order multiplexing has the potential to dramatically increase the usefulness of dPCR, especially in scenarios with limited sample. Other potential benefits of multiplexing include lower cost, additional information generated by more probes, and higher throughput. To address this unmet need, we developed a novel melt-based hairpin probe design to provide a robust option for multiplexing digital PCR. A prototype multiplex digital PCR (mdPCR) assay using three melt-based hairpin probes per optical channel in a 16-well microfluidic digital PCR platform accurately distinguished and quantified 12 nucleic acid targets per well. For samples with 10,000 human genome equivalents, the probe-specific ranges for limit of blank were 0.00%–0.13%, and those for analytical limit of detection were 0.00%–0.20%. Inter-laboratory reproducibility was excellent (r2 = 0.997). Importantly, this novel melt-based hairpin probe design has potential to achieve multiplexing beyond the 12 targets/well of this prototype assay. This easy-to-use mdPCR technology with excellent performance characteristics has the potential to revolutionize the use of digital PCR in research and diagnostic settings
Stringing Spins and Spinning Strings
We apply recently developed integrable spin chain and dilatation operator
techniques in order to compute the planar one-loop anomalous dimensions for
certain operators containing a large number of scalar fields in N =4 Super
Yang-Mills. The first set of operators, belonging to the SO(6) representations
[J,L-2J,J], interpolate smoothly between the BMN case of two impurities (J=2)
and the extreme case where the number of impurities equals half the total
number of fields (J=L/2). The result for this particular [J,0,J] operator is
smaller than the anomalous dimension derived by Frolov and Tseytlin
[hep-th/0304255] for a semiclassical string configuration which is the dual of
a gauge invariant operator in the same representation. We then identify a
second set of operators which also belong to [J,L-2J,J] representations, but
which do not have a BMN limit. In this case the anomalous dimension of the
[J,0,J] operator does match the Frolov-Tseytlin prediction. We also show that
the fluctuation spectra for this [J,0,J] operator is consistent with the string
prediction.Comment: 27 pages, 4 figures, LaTex; v2 reference added, typos fixe
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