4,872 research outputs found
Simple Viscous Flows: from Boundary Layers to the Renormalization Group
The seemingly simple problem of determining the drag on a body moving through
a very viscous fluid has, for over 150 years, been a source of theoretical
confusion, mathematical paradoxes, and experimental artifacts, primarily
arising from the complex boundary layer structure of the flow near the body and
at infinity. We review the extensive experimental and theoretical literature on
this problem, with special emphasis on the logical relationship between
different approaches. The survey begins with the developments of matched
asymptotic expansions, and concludes with a discussion of perturbative
renormalization group techniques, adapted from quantum field theory to
differential equations. The renormalization group calculations lead to a new
prediction for the drag coefficient, one which can both reproduce and surpass
the results of matched asymptotics
Critical Casimir amplitudes for -component models with O(n)-symmetry breaking quadratic boundary terms
Euclidean -component theories whose Hamiltonians are O(n)
symmetric except for quadratic symmetry breaking boundary terms are studied in
films of thickness . The boundary terms imply the Robin boundary conditions
at the boundary
planes at and . Particular attention is paid
to the cases in which of the variables
take the special value corresponding to critical
enhancement while the remaining ones are subcritically enhanced. Under these
conditions, the semi-infinite system bounded by has a
multicritical point, called -special, at which an symmetric
critical surface phase coexists with the O(n) symmetric bulk phase, provided
is sufficiently large. The -dependent part of the reduced free energy
per area behaves as as at the bulk critical
point. The Casimir amplitudes are determined for small
in the general case where components are
critically enhanced at both boundary planes, components are
enhanced at one plane but satisfy asymptotic Dirichlet boundary conditions at
the respective other, and the remaining components satisfy asymptotic
Dirichlet boundary conditions at both . Whenever ,
these expansions involve integer and fractional powers with
(mod logarithms). Results to for general values of
, , and are used to estimate the
of 3D Heisenberg systems with surface spin anisotropies when , , and .Comment: Latex source file with 5 eps files; version with minor amendments and
corrected typo
Critical Casimir effect in films for generic non-symmetry-breaking boundary conditions
Systems described by an O(n) symmetrical Hamiltonian are considered
in a -dimensional film geometry at their bulk critical points. A detailed
renormalization-group (RG) study of the critical Casimir forces induced between
the film's boundary planes by thermal fluctuations is presented for the case
where the O(n) symmetry remains unbroken by the surfaces. The boundary planes
are assumed to cause short-ranged disturbances of the interactions that can be
modelled by standard surface contributions corresponding
to subcritical or critical enhancement of the surface interactions. This
translates into mesoscopic boundary conditions of the generic
symmetry-preserving Robin type .
RG-improved perturbation theory and Abel-Plana techniques are used to compute
the -dependent part of the reduced excess free energy per
film area to two-loop order. When , it takes the scaling
form as
, where are scaling fields associated with the
surface-enhancement variables , while is a standard
surface crossover exponent. The scaling function
and its analogue for the Casimir force
are determined via expansion in and extrapolated to
dimensions. In the special case , the expansion
becomes fractional. Consistency with the known fractional expansions of D(0,0)
and to order is achieved by appropriate
reorganisation of RG-improved perturbation theory. For appropriate choices of
and , the Casimir forces can have either sign. Furthermore,
crossovers from attraction to repulsion and vice versa may occur as
increases.Comment: Latex source file, 40 pages, 9 figure
Quantum Criticality via Magnetic Branes
Holographic methods are used to investigate the low temperature limit,
including quantum critical behavior, of strongly coupled 4-dimensional gauge
theories in the presence of an external magnetic field, and finite charge
density. In addition to the metric, the dual gravity theory contains a Maxwell
field with Chern-Simons coupling. In the absence of charge, the magnetic field
induces an RG flow to an infrared AdS geometry, which is
dual to a 2-dimensional CFT representing strongly interacting fermions in the
lowest Landau level. Two asymptotic Virasoro algebras and one chiral Kac-Moody
algebra arise as {\sl emergent symmetries} in the IR. Including a nonzero
charge density reveals a quantum critical point when the magnetic field reaches
a critical value whose scale is set by the charge density. The critical theory
is probed by the study of long-distance correlation functions of the boundary
stress tensor and current. All quantities of major physical interest in this
system, such as critical exponents and scaling functions, can be computed
analytically. We also study an asymptotically AdS system whose magnetic
field induced quantum critical point is governed by a IR Lifshitz geometry,
holographically dual to a D=2+1 field theory. The behavior of these holographic
theories shares important similarities with that of real world quantum critical
systems obtained by tuning a magnetic field, and may be relevant to materials
such as Strontium Ruthenates.Comment: To appear in Lect. Notes Phys. "Strongly interacting matter in
magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A.
Schmitt, H.-U. Ye
On the running coupling constant in QCD
We try to review the main current ideas and points of view on the running
coupling constant in QCD. We begin by recalling briefly the classic analysis
based on the Renormalization Group with some emphasis on the exact solutions of
the RG equation for a given number of loops, in comparison with the usual
approximate expressions. We give particular attention to the problem of
eliminating the unphysical Landau singularities, and of defining a coupling
that remains significant at the infrared scales. We consider various proposals
of couplings directly related to the quark-antiquark potential or to other
physical quantities (effective charges) and discuss optimization in the choice
of the scale parameter and of the RS. Our main focus is, however, on dispersive
methods, their application, their relation with non-perturbative effects. We
try also to summarize the main results obtained by Lattice simulations in
various MOM schemes. We conclude briefly recalling the traditional comparison
with the experimental data.Comment: 75 pages, 8 figures. Corrected typos, added references, replaced 1
figure. Accepted for publication in Progress in Particle and Nuclear Physic
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