25,594 research outputs found
Power-counting theorem for non-local matrix models and renormalisation
Solving the exact renormalisation group equation a la Wilson-Polchinski
perturbatively, we derive a power-counting theorem for general matrix models
with arbitrarily non-local propagators. The power-counting degree is determined
by two scaling dimensions of the cut-off propagator and various topological
data of ribbon graphs. As a necessary condition for the renormalisability of a
model, the two scaling dimensions have to be large enough relative to the
dimension of the underlying space. In order to have a renormalisable model one
needs additional locality properties--typically arising from orthogonal
polynomials--which relate the relevant and marginal interaction coefficients to
a finite number of base couplings. The main application of our power-counting
theorem is the renormalisation of field theories on noncommutative R^D in
matrix formulation.Comment: 35 pages, 70 figures, LaTeX with svjour macros. v2: proof simplified
because a discussion originally designed for \phi^4 on noncommutative R^2 was
actually not necessary, see hep-th/0307017. v3: consistency conditions
removed because models of interest relate automatically the relevant/marginal
interactions to a finite number of base couplings, see hep-th/0401128. v4:
integration procedure improved so that the initial cut-off can be directly
removed; to appear in Commun. Math. Phy
Field Theory on Noncommutative Spacetimes: Quasiplanar Wick Products
We give a definition of admissible counterterms appropriate for massive
quantum field theories on the noncommutative Minkowski space, based on a
suitable notion of locality. We then define products of fields of arbitrary
order, the so-called quasiplanar Wick products, by subtracting only such
admissible counterterms. We derive the analogue of Wick's theorem and comment
on the consequences of using quasiplanar Wick products in the perturbative
expansion.Comment: 22 pages, 2 figures, v2: minor changes, v3: minor changes, reference
adde
Molecular motors robustly drive active gels to a critically connected state
Living systems often exhibit internal driving: active, molecular processes
drive nonequilibrium phenomena such as metabolism or migration. Active gels
constitute a fascinating class of internally driven matter, where molecular
motors exert localized stresses inside polymer networks. There is evidence that
network crosslinking is required to allow motors to induce macroscopic
contraction. Yet a quantitative understanding of how network connectivity
enables contraction is lacking. Here we show experimentally that myosin motors
contract crosslinked actin polymer networks to clusters with a scale-free size
distribution. This critical behavior occurs over an unexpectedly broad range of
crosslink concentrations. To understand this robustness, we develop a
quantitative model of contractile networks that takes into account network
restructuring: motors reduce connectivity by forcing crosslinks to unbind.
Paradoxically, to coordinate global contractions, motor activity should be low.
Otherwise, motors drive initially well-connected networks to a critical state
where ruptures form across the entire network.Comment: Main text: 21 pages, 5 figures. Supplementary Information: 13 pages,
8 figure
Surface networks
© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physico-chemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2-dimensional surfaces by storing only the most important (also called fundamental, critical or surface-specific) points and lines in the surfaces. Surface networks are intelligent and “natural ” data structures because they store a surface as a framework of “surface ” elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has fou
Low Energy Properties of the Kondo chain in the RKKY regime
We study the Kondo chain in the regime of high spin concentration where the
low energy physics is dominated by the Ruderman-Kittel-Kasuya-Yosida (RKKY)
interaction. As has been recently shown (A. M. Tsvelik and O. M. Yevtushenko,
Phys. Rev. Lett 115, 216402 (2015)), this model has two phases with drastically
different transport properties depending on the anisotropy of the exchange
interaction. In particular, the helical symmetry of the fermions is
spontaneously broken when the anisotropy is of the easy plane type (EP). This
leads to a parametrical suppression of the localization effects. In the present
paper we substantially extend the previous theory, in particular, by analyzing
a competition of forward- and backward- scattering, including into the theory
short range electron interactions and calculating spin correlation functions.
We discuss applicability of our theory and possible experiments which could
support the theoretical findings.Comment: 24 pages, 8 figures, 5 appendice
Lattice QCD calculation of hadronic light-by-light scattering
We perform a lattice QCD calculation of the hadronic light-by-light
scattering amplitude in a broad kinematical range. At forward kinematics, the
results are compared to a phenomenological analysis based on dispersive sum
rules for light-by-light scattering. The size of the pion pole contribution is
investigated for momenta of typical hadronic size. The presented numerical
methods can be used to compute the hadronic light-by-light contribution to the
anomalous magnetic moment of the muon. Our calculations are carried out in
two-flavor QCD with the pion mass in the range of 270 to 450MeV, and contain so
far only the diagrams with fully connected quark lines.Comment: 5 pages, 5 figure
Tensegrity and Motor-Driven Effective Interactions in a Model Cytoskeleton
Actomyosin networks are major structural components of the cell. They provide
mechanical integrity and allow dynamic remodeling of eukaryotic cells,
self-organizing into the diverse patterns essential for development. We provide
a theoretical framework to investigate the intricate interplay between local
force generation, network connectivity and collective action of molecular
motors. This framework is capable of accommodating both regular and
heterogeneous pattern formation, arrested coarsening and macroscopic
contraction in a unified manner. We model the actomyosin system as a motorized
cat's cradle consisting of a crosslinked network of nonlinear elastic filaments
subjected to spatially anti-correlated motor kicks acting on motorized (fibril)
crosslinks. The phase diagram suggests there can be arrested phase separation
which provides a natural explanation for the aggregation and coalescence of
actomyosin condensates. Simulation studies confirm the theoretical picture that
a nonequilibrium many-body system driven by correlated motor kicks can behave
as if it were at an effective equilibrium, but with modified interactions that
account for the correlation of the motor driven motions of the actively bonded
nodes. Regular aster patterns are observed both in Brownian dynamics
simulations at effective equilibrium and in the complete stochastic
simulations. The results show that large-scale contraction requires correlated
kicking.Comment: 38 pages, 13 figure
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