7,620 research outputs found
Two-Sided Derivatives for Regular Expressions and for Hairpin Expressions
The aim of this paper is to design the polynomial construction of a finite
recognizer for hairpin completions of regular languages. This is achieved by
considering completions as new expression operators and by applying derivation
techniques to the associated extended expressions called hairpin expressions.
More precisely, we extend partial derivation of regular expressions to
two-sided partial derivation of hairpin expressions and we show how to deduce a
recognizer for a hairpin expression from its two-sided derived term automaton,
providing an alternative proof of the fact that hairpin completions of regular
languages are linear context-free.Comment: 28 page
Heavy Quark Thermalization in Classical Lattice Gauge Theory: Lessons for Strongly-Coupled QCD
Thermalization of a heavy quark near rest is controlled by the correlator of
two electric fields along a temporal Wilson line. We address this correlator
within real-time, classical lattice Yang-Mills theory, and elaborate on the
analogies that exist with the dynamics of hot QCD. In the weak-coupling limit,
it can be shown analytically that the dynamics on the two sides are closely
related to each other. For intermediate couplings, we carry out
non-perturbative simulations within the classical theory, showing that the
leading term in the weak-coupling expansion significantly underestimates the
heavy quark thermalization rate. Our analytic and numerical results also yield
a general understanding concerning the overall shape of the spectral function
corresponding to the electric field correlator, which may be helpful in
subsequent efforts to reconstruct it from Euclidean lattice Monte Carlo
simulations.Comment: 22 pages. v2: a reference and clarifications added; published versio
Density Matrix Renormalization Group Applied to the Ground State of the XY-Spin-Peierls System
We use the density matrix renormalization group (DMRG) to map out the ground
state of a XY-spin chain coupled to dispersionless phonons of frequency . We confirm the existence of a critical spin-phonon coupling for the onset of the spin gap bearing the signature of
a Kosterlitz-Thouless transition. We also observe a classical-quantum crossover
when the spin-Peierls gap is of order . In the classical
regime, , the mean-field parameters are strongly renormalized
by non-adiabatic corrections. This is the first application of the DMRG to
phonons.Comment: 10 pages, 5 figures. To be published in PR
Contrasting carbonate depositional systems for Pliocene cool-water limestones cropping out in central Hawke's Bay, New Zealand
Pliocene limestone formations in central Hawke's Bay (eastern North Island, New Zealand) accumulated on and near the margins of a narrow forearc basin seaway within the convergent Australia/Pacific plate boundary zone. The active tectonic setting and varied paleogeographic features of the limestone units investigated, in association with probable glacioeustatic sea-level fluctuations, resulted in complex stratigraphic architectures and contrasting types of carbonate accumulation on either side of the seaway. Here, we recognise recurring patterns of sedimentary facies, and sequences and systems tracts bounded by key physical surfaces within the limestone sheets. The facies types range from Bioclastic (B) to Siliciclastic (S) end-members via Mixed (M) carbonate-siliciclastic deposits. Skeletal components are typical cool-water associations dominated by epifaunal calcitic bivalves, bryozoans, and especially barnacles. Siliciclastic contents vary from one formation to another, and highlight siliciclastic-rich limestone units in the western ranges versus siliciclastic-poor limestone units in the eastern coastal hills. Heterogeneities in facies types, stratal patterns, and also in diagenetic pathways between eastern and western limestone units are considered to originate in the coeval occurrence in different parts of the forearc basin of two main morphodynamic carbonate systems over time
Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors
The two-body dynamics in general relativity has been solved perturbatively
using the post-Newtonian (PN) approximation. The evolution of the orbital phase
and the emitted gravitational radiation are now known to a rather high order up
to O(v^8), v being the characteristic velocity of the binary. The orbital
evolution, however, cannot be specified uniquely due to the inherent freedom in
the choice of parameter used in the PN expansion as well as the method pursued
in solving the relevant differential equations. The goal of this paper is to
determine the (dis)agreement between different PN waveform families in the
context of initial and advanced gravitational-wave detectors. The waveforms
employed in our analysis are those that are currently used by Initial
LIGO/Virgo, that is the time-domain PN models TaylorT1, TaylorT2, TaylorT3,
TaylorT4 and TaylorEt, the effective one-body (EOB) model, and the
Fourier-domain representation TaylorF2. We examine the overlaps of these models
with one another and with the prototype effective one-body model (calibrated to
numerical relativity simulations, as currently used by initial LIGO) for a
number of different binaries at 2PN, 3PN and 3.5PN orders to quantify their
differences and to help us decide whether there exist preferred families that
are the most appropriate as search templates. We conclude that as long as the
total mass remains less than a certain upper limit M_crit, all template
families at 3.5PN order (except TaylorT3 and TaylorEt) are equally good for the
purpose of detection. The value of M_crit is found to be ~ 12M_Sun for Initial,
Enhanced and Advanced LIGO. From a purely computational point of view we
recommend that 3.5PN TaylorF2 be used below Mcrit and EOB calibrated to
numerical relativity simulations be used for total binary mass M > Mcrit.Comment: 27 pages, 8 figures, 4 tables, submitted to PR
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Evidence for the Universal Scaling Behaviour of a Freely Relaxing DNA Molecule
Relaxation measurements on a fluorescently labelled free DNA molecule after stretching by a Poiseuille flow in a capillary vessel reveal universal scaling features: at intermediate times the scaling exponent of the decay law for the molecule length as a function of time is found to be 0.51 +/- 0.05. This law is in agreement with the prediction of the Brochard-Wyart "stem and flower" model for the relaxation of a stretched polymer chain.Molecular and Cellular BiologyPhysic
Gravitational waves about curved backgrounds: a consistency analysis in de Sitter spacetime
Gravitational waves are considered as metric perturbations about a curved
background metric, rather than the flat Minkowski metric since several
situations of physical interest can be discussed by this generalization. In
this case, when the de Donder gauge is imposed, its preservation under
infinitesimal spacetime diffeomorphisms is guaranteed if and only if the
associated covector is ruled by a second-order hyperbolic operator which is the
classical counterpart of the ghost operator in quantum gravity. In such a wave
equation, the Ricci term has opposite sign with respect to the wave equation
for Maxwell theory in the Lorenz gauge. We are, nevertheless, able to relate
the solutions of the two problems, and the algorithm is applied to the case
when the curved background geometry is the de Sitter spacetime. Such vector
wave equations are studied in two different ways: i) an integral
representation, ii) through a solution by factorization of the hyperbolic
equation. The latter method is extended to the wave equation of metric
perturbations in the de Sitter spacetime. This approach is a step towards a
general discussion of gravitational waves in the de Sitter spacetime and might
assume relevance in cosmology in order to study the stochastic background
emerging from inflation.Comment: 17 pages. Misprints amended in Eqs. 50, 54, 55, 75, 7
Influence of the anion potential on the charge ordering in quasi-one dimensional charge transfer salts
We examine the various instabilities of quarter-filled strongly correlated
electronic chains in the presence of a coupling to the underlying lattice. To
mimic the physics of the (TMTTF)X Bechgaard-Fabre salts we also include
electrostatic effects of intercalated anions. We show that small displacements
of the anion can stabilize new mixed Charged Density Wave-Bond Order Wave
phases in which central symmetry centers are suppressed. This finding is
discussed in the context of recent experiments. We suggest that the recently
observed charge ordering is due to a cooperative effect between the Coulomb
interaction and the coupling of the electronic stacks to the anions. On the
other hand, the Spin-Peierls instability at lower temperature requires a
Peierls-like lattice coupling.Comment: Latex, 4 pages, 4 postscript figure
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