59 research outputs found
Depinning with dynamic stress overshoots: A hybrid of critical and pseudohysteretic behavior
A model of an elastic manifold driven through a random medium by an applied
force F is studied focussing on the effects of inertia and elastic waves, in
particular {\it stress overshoots} in which motion of one segment of the
manifold causes a temporary stress on its neighboring segments in addition to
the static stress. Such stress overshoots decrease the critical force for
depinning and make the depinning transition hysteretic. We find that the steady
state velocity of the moving phase is nevertheless history independent and the
critical behavior as the force is decreased is in the same universality class
as in the absence of stress overshoots: the dissipative limit which has been
studied analytically. To reach this conclusion, finite-size scaling analyses of
a variety of quantities have been supplemented by heuristic arguments.
If the force is increased slowly from zero, the spectrum of avalanche sizes
that occurs appears to be quite different from the dissipative limit. After
stopping from the moving phase, the restarting involves both fractal and
bubble-like nucleation. Hysteresis loops can be understood in terms of a
depletion layer caused by the stress overshoots, but surprisingly, in the limit
of very large samples the hysteresis loops vanish. We argue that, although
there can be striking differences over a wide range of length scales, the
universality class governing this pseudohysteresis is again that of the
dissipative limit. Consequences of this picture for the statistics and dynamics
of earthquakes on geological faults are briefly discussed.Comment: 43 pages, 57 figures (yes, that's a five followed by a seven), revte
Central extensions of current groups in two dimensions
In this paper we generalize some of these results for loop algebras and
groups as well as for the Virasoro algebra to the two-dimensional case. We
define and study a class of infinite dimensional complex Lie groups which are
central extensions of the group of smooth maps from a two dimensional
orientable surface without boundary to a simple complex Lie group G. These
extensions naturally correspond to complex curves. The kernel of such an
extension is the Jacobian of the curve. The study of the coadjoint action shows
that its orbits are labelled by moduli of holomorphic principal G-bundles over
the curve and can be described in the language of partial differential
equations. In genus one it is also possible to describe the orbits as conjugacy
classes of the twisted loop group, which leads to consideration of difference
equations for holomorphic functions. This gives rise to a hope that the
described groups should possess a counterpart of the rich representation theory
that has been developed for loop groups. We also define a two-dimensional
analogue of the Virasoro algebra associated with a complex curve. In genus one,
a study of a complex analogue of Hill's operator yields a description of
invariants of the coadjoint action of this Lie algebra. The answer turns out to
be the same as in dimension one: the invariants coincide with those for the
extended algebra of currents in sl(2).Comment: 17 page
Roughness at the depinning threshold for a long-range elastic string
In this paper, we compute the roughness exponent zeta of a long-range elastic
string, at the depinning threshold, in a random medium with high precision,
using a numerical method which exploits the analytic structure of the problem
(`no-passing' theorem), but avoids direct simulation of the evolution
equations. This roughness exponent has recently been studied by simulations,
functional renormalization group calculations, and by experiments (fracture of
solids, liquid meniscus in 4He). Our result zeta = 0.390 +/- 0.002 is
significantly larger than what was stated in previous simulations, which were
consistent with a one-loop renormalization group calculation. The data are
furthermore incompatible with the experimental results for crack propagation in
solids and for a 4He contact line on a rough substrate. This implies that the
experiments cannot be described by pure harmonic long-range elasticity in the
quasi-static limit.Comment: 4 pages, 3 figure
Magnetism of small V clusters embedded in a Cu fcc matrix: an ab initio study
We present extensive first principles density functional theory (DFT)
calculations dedicated to analyze the magnetic and electronic properties of
small V clusters (n=1,2,3,4,5,6) embedded in a Cu fcc matrix. We consider
different cluster structures such as: i) a single V impurity, ii) several
V dimers having different interatomic distance and varying local atomic
environment, iii) V and iv) V clusters for which we assume compact
as well as 2- and 1-dimensional atomic configurations and finally, in the case
of the v) V and vi) V structures we consider a square pyramid and a
square bipyramid together with linear arrays, respectively. In all cases, the V
atoms are embedded as substitutional impurities in the Cu network. In general,
and as in the free standing case, we have found that the V clusters tend to
form compact atomic arrays within the cooper matrix. Our calculated non
spin-polarized density of states at the V sites shows a complex peaked
structure around the Fermi level that strongly changes as a function of both
the interatomic distance and local atomic environment, a result that
anticipates a non trivial magnetic behavior. In fact, our DFT calculations
reveal, in each one of our clusters systems, the existence of different
magnetic solutions (ferromagnetic, ferrimagnetic, and antiferromagnetic) with
very small energy differences among them, a result that could lead to the
existence of complex finite-temperature magnetic properties. Finally, we
compare our results with recent experimental measurements.Comment: 7 pages and 4 figure
2-loop Functional Renormalization Group Theory of the Depinning Transition
We construct the field theory which describes the universal properties of the
quasi-static isotropic depinning transition for interfaces and elastic periodic
systems at zero temperature, taking properly into account the non-analytic form
of the dynamical action. This cures the inability of the 1-loop flow-equations
to distinguish between statics and quasi-static depinning, and thus to account
for the irreversibility of the latter. We prove two-loop renormalizability,
obtain the 2-loop beta-function and show the generation of "irreversible"
anomalous terms, originating from the non-analytic nature of the theory, which
cause the statics and driven dynamics to differ at 2-loop order. We obtain the
roughness exponent zeta and dynamical exponent z to order epsilon^2. This
allows to test several previous conjectures made on the basis of the 1-loop
result. First it demonstrates that random-field disorder does indeed attract
all disorder of shorter range. It also shows that the conjecture zeta=epsilon/3
is incorrect, and allows to compute the violations, as zeta=epsilon/3 (1 +
0.14331 epsilon), epsilon=4-d. This solves a longstanding discrepancy with
simulations. For long-range elasticity it yields zeta=epsilon/3 (1 + 0.39735
epsilon), epsilon=2-d (vs. the standard prediction zeta=1/3 for d=1), in
reasonable agreement with the most recent simulations. The high value of zeta
approximately 0.5 found in experiments both on the contact line depinning of
liquid Helium and on slow crack fronts is discussed.Comment: 32 pages, 17 figures, revtex
Higgs Bundles, Gauge Theories and Quantum Groups
The appearance of the Bethe Ansatz equation for the Nonlinear Schr\"{o}dinger
equation in the equivariant integration over the moduli space of Higgs bundles
is revisited. We argue that the wave functions of the corresponding
two-dimensional topological U(N) gauge theory reproduce quantum wave functions
of the Nonlinear Schr\"{o}dinger equation in the -particle sector. This
implies the full equivalence between the above gauge theory and the
-particle sub-sector of the quantum theory of Nonlinear Schr\"{o}dinger
equation. This also implies the explicit correspondence between the gauge
theory and the representation theory of degenerate double affine Hecke algebra.
We propose similar construction based on the gauged WZW model leading to
the representation theory of the double affine Hecke algebra. The relation with
the Nahm transform and the geometric Langlands correspondence is briefly
discussed.Comment: 48 pages, typos corrected, one reference adde
On Global Aspects Of Gauged Wess-Zumino-Witten Model
This is a thesis for Rigaku-Hakushi( Ph. D.). It clarifies the
geometric meaning and field theoretical consequences of the spectral flows
acting on the space of states of the ` coset model'. As suggested by Moore
and Seiberg, the spectral flow is realized as the response of states to certain
change of background gauge field together with the gauge transformation on a
circle. Applied to the boundary circle of a disc with field insertion, such a
realization leads to a certain relation among correlators of the gauged WZW
model for various principal -bundles. In the course of derivation, we find
an expression of a (dressed) gauge invariant field as an integral over the flag
manifold of and an expression of a correlator as an integral over a certain
moduli space of holomorphic -bundles with quasi-flag structure at the insertion point. We also find
that the gauge transformation on the circle corresponding to the spectral flow
determines a bijection of the set of isomorphism classes of holomorphic -bundles with quasi-flag structure of one topological type to that of
another. As an application, it is pointed out that problems arising from the
field identification fixed points may be resolved by taking into account of all
principal -bundles.Comment: (Thesis) 125 pages, UT-Komaba/94-3 (Latex errors are corrected
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