29,880 research outputs found
Perfect Lattice Actions with and without Chiral Symmetry
We use perturbation theory to construct perfect lattice actions for fermions
and gauge fields by blocking directly from the continuum. When one uses a
renormalization group transformation that preserves chiral symmetry the
resulting lattice action for massless fermions is chirally symmetric but
nonlocal. When the renormalization group transformation breaks chiral symmetry,
the lattice action becomes local but chiral symmetry is explicitly broken. In
particular, starting with a chiral gauge theory in the continuum one either
obtains a lattice theory which is gauge invariant but nonlocal, or a local
theory with explicitly broken gauge invariance. In both cases the spectrum of
the lattice theory is identical with the one of the continuum and the anomaly
is correctly reproduced. We also apply our techniques to vector-like theories.
In particular we propose a new renormalization group transformation for QCD and
we optimize its parameters for locality of the perfect action.Comment: LaTex, 8 pages, Contribution to Lattice 95; Some minor typing errors
are correcte
Non-Gaussian numerical errors versus mass hierarchy
We probe the numerical errors made in renormalization group calculations by
varying slightly the rescaling factor of the fields and rescaling back in order
to get the same (if there were no round-off errors) zero momentum 2-point
function (magnetic susceptibility). The actual calculations were performed with
Dyson's hierarchical model and a simplified version of it. We compare the
distributions of numerical values obtained from a large sample of rescaling
factors with the (Gaussian by design) distribution of a random number generator
and find significant departures from the Gaussian behavior. In addition, the
average value differ (robustly) from the exact answer by a quantity which is of
the same order as the standard deviation. We provide a simple model in which
the errors made at shorter distance have a larger weight than those made at
larger distance. This model explains in part the non-Gaussian features and why
the central-limit theorem does not apply.Comment: 26 pages, 7 figures, uses Revte
Lattice Fluid Dynamics from Perfect Discretizations of Continuum Flows
We use renormalization group methods to derive equations of motion for large
scale variables in fluid dynamics. The large scale variables are averages of
the underlying continuum variables over cubic volumes, and naturally live on a
lattice. The resulting lattice dynamics represents a perfect discretization of
continuum physics, i.e. grid artifacts are completely eliminated. Perfect
equations of motion are derived for static, slow flows of incompressible,
viscous fluids. For Hagen-Poiseuille flow in a channel with square cross
section the equations reduce to a perfect discretization of the Poisson
equation for the velocity field with Dirichlet boundary conditions. The perfect
large scale Poisson equation is used in a numerical simulation, and is shown to
represent the continuum flow exactly. For non-square cross sections we use a
numerical iterative procedure to derive flow equations that are approximately
perfect.Comment: 25 pages, tex., using epsfig, minor changes, refernces adde
Inference of the genetic network regulating lateral root initiation in Arabidopsis thaliana
Regulation of gene expression is crucial for organism growth, and it is one of the challenges in Systems Biology to reconstruct the underlying regulatory biological networks from transcriptomic data. The formation of lateral roots in Arabidopsis thaliana is stimulated by a cascade of regulators of which only the interactions of its initial elements have been identified. Using simulated gene expression data with known network topology, we compare the performance of inference algorithms, based on different approaches, for which ready-to-use software is available. We show that their performance improves with the network size and the inclusion of mutants. We then analyse two sets of genes, whose activity is likely to be relevant to lateral root initiation in Arabidopsis, by integrating sequence analysis with the intersection of the results of the best performing methods on time series and mutants to infer their regulatory network. The methods applied capture known interactions between genes that are candidate regulators at early stages of development. The network inferred from genes significantly expressed during lateral root formation exhibits distinct scale-free, small world and hierarchical properties and the nodes with a high out-degree may warrant further investigation
Loop Groups and Discrete KdV Equations
A study is presented of fully discretized lattice equations associated with
the KdV hierarchy. Loop group methods give a systematic way of constructing
discretizations of the equations in the hierarchy. The lattice KdV system of
Nijhoff et al. arises from the lowest order discretization of the trivial,
lowest order equation in the hierarchy, b_t=b_x. Two new discretizations are
also given, the lowest order discretization of the first nontrivial equation in
the hierarchy, and a "second order" discretization of b_t=b_x. The former,
which is given the name "full lattice KdV" has the (potential) KdV equation as
a standard continuum limit. For each discretization a Backlund transformation
is given and soliton content analyzed. The full lattice KdV system has, like
KdV itself, solitons of all speeds, whereas both other discretizations studied
have a limited range of speeds, being discretizations of an equation with
solutions only of a fixed speed.Comment: LaTeX, 23 pages, 1 figur
QCD as a Quantum Link Model
QCD is constructed as a lattice gauge theory in which the elements of the
link matrices are represented by non-commuting operators acting in a Hilbert
space. The resulting quantum link model for QCD is formulated with a fifth
Euclidean dimension, whose extent resembles the inverse gauge coupling of the
resulting four-dimensional theory after dimensional reduction. The inclusion of
quarks is natural in Shamir's variant of Kaplan's fermion method, which does
not require fine-tuning to approach the chiral limit. A rishon representation
in terms of fermionic constituents of the gluons is derived and the quantum
link Hamiltonian for QCD with a U(N) gauge symmetry is expressed in terms of
glueball, meson and constituent quark operators. The new formulation of QCD is
promising both from an analytic and from a computational point of view.Comment: 27 pages, including three figures. ordinary LaTeX; Submitted to Nucl.
Phys.
Tracing the sites of obscured star formation in the Antennae galaxies with Herschel-PACS
FIR imaging of interacting galaxies allows locating even hidden sites of star
formation and measuring of the relative strength of nuclear and extra-nuclear
star formation. We want to resolve the star-forming sites in the nearby system
of the Antennae. Thanks to the unprecedented sharpness and depth of the PACS
camera onboard ESA's Herschel Space Observatory, it is possible for the first
time to achieve a complete assessment of individual star-forming knots in the
FIR with scan maps at 70, 100, and 160 um. We used clump extraction photometry
and SED diagnostics to derive the properties related to star-forming activity.
The PACS 70, 100, and 160 um maps trace the knotty structure of the most recent
star formation along an arc between the two nuclei in the overlap area. The
resolution of the starburst knots and additional multi-wavelength data allow
their individual star formation history and state to be analysed. In
particular, the brightest knot in the mid-infrared (K1), east of the southern
nucleus, exhibits the highest activity by far in terms of dust heating and star
formation rate, efficiency, and density. With only 2 kpc in diameter, this area
has a 10-1000 um luminosity, which is as high as that of our Milky Way. It
shows the highest deficiency in radio emission in the radio-to-FIR luminosity
ratio and a lack of X-ray emission, classifying it as a very young complex. The
brightest 100 and 160 um emission region (K2), which is close to the collision
front and consists of 3 knots, also shows a high star formation density and
efficiency and lack of X-ray emission in its most obscured part, but an excess
in the radio-to-FIR luminosity ratio. This suggests a young stage, too, but
different conditions in its interstellar medium. Our results provide important
checkpoints for numerical simulations of interacting galaxies when modelling
the star formation and stellar feedback.Comment: 4 pages, 4 figures, 2 tables (A&A Herschel special issue
Universality in Turbulence: an Exactly Soluble Model
The present note contains the text of lectures discussing the problem of
universality in fully developed turbulence. After a brief description of
Kolmogorov's 1941 scaling theory of turbulence and a comparison between the
statistical approach to turbulence and field theory, we discuss a simple model
of turbulent advection which is exactly soluble but whose exact solution is
still difficult to analyze. The model exhibits a restricted universality. Its
correlation functions contain terms with universal but anomalous scaling but
with non-universal amplitudes typically diverging with the growing size of the
system. Strict universality applies only after such terms have been removed
leaving renormalized correlators with normal scaling. We expect that the
necessity of such an infrared renormalization is a characteristic feature of
universality in turbulence.Comment: 31 pages, late
Evolution with hole doping of the electronic excitation spectrum in the cuprate superconductors
The recent scanning tunnelling results of Alldredge et al on Bi-2212 and of
Hanaguri et al on Na-CCOC are examined from the perspective of the BCS/BEC
boson-fermion resonant crossover model for the mixed-valent HTSC cuprates. The
model specifies the two energy scales controlling the development of HTSC
behaviour and the dichotomy often now alluded to between nodal and antinodal
phenomena in the HTSC cuprates. Indication is extracted from the data as to how
the choice of the particular HTSC system sees these two basic energy scales
(cursive-U, the local pair binding energy and, Delta-sc, the nodal BCS-like gap
parameter) evolve with doping and change in degree of metallization of the
structurally and electronically perturbed mixed-valent environment.Comment: 19 pages, 5 figure
Two flavor chiral phase transition from nonperturbative flow equations
We employ nonperturbative flow equations to compute the equation of state for
two flavor QCD within an effective quark meson model. This yields the
temperature and quark mass dependence of quantities like the chiral condensate
or the pion mass. A precision estimate of the universal critical equation of
state for the three-dimensional O(4) Heisenberg model is presented. We
explicitly connect the O(4) universal behavior near the critical temperature
and zero quark mass with the physics at zero temperature and a realistic pion
mass. For realistic quark masses the pion correlation length near T_c turns out
to be smaller than its zero temperature value.Comment: 49 pages including 15 figures, LaTeX, uses epsf.sty and rotate.st
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