2,242 research outputs found
Courant-Dorfman algebras and their cohomology
We introduce a new type of algebra, the Courant-Dorfman algebra. These are to
Courant algebroids what Lie-Rinehart algebras are to Lie algebroids, or Poisson
algebras to Poisson manifolds. We work with arbitrary rings and modules,
without any regularity, finiteness or non-degeneracy assumptions. To each
Courant-Dorfman algebra (\R,\E) we associate a differential graded algebra
\C(\E,\R) in a functorial way by means of explicit formulas. We describe two
canonical filtrations on \C(\E,\R), and derive an analogue of the Cartan
relations for derivations of \C(\E,\R); we classify central extensions of
\E in terms of H^2(\E,\R) and study the canonical cocycle
\Theta\in\C^3(\E,\R) whose class obstructs re-scalings of the
Courant-Dorfman structure. In the nondegenerate case, we also explicitly
describe the Poisson bracket on \C(\E,\R); for Courant-Dorfman algebras
associated to Courant algebroids over finite-dimensional smooth manifolds, we
prove that the Poisson dg algebra \C(\E,\R) is isomorphic to the one
constructed in \cite{Roy4-GrSymp} using graded manifolds.Comment: Corrected formulas for the brackets in Examples 2.27, 2.28 and 2.29.
The corrections do not affect the exposition in any wa
Macroscopic detection of the strong stochasticity threshold in Fermi-Pasta-Ulam chains of oscillators
The largest Lyapunov exponent of a system composed by a heavy impurity
embedded in a chain of anharmonic nearest-neighbor Fermi-Pasta-Ulam oscillators
is numerically computed for various values of the impurity mass . A
crossover between weak and strong chaos is obtained at the same value
of the energy density (energy per degree of freedom)
for all the considered values of the impurity mass . The threshold \epsi
lon_{_T} coincides with the value of the energy density at which a
change of scaling of the relaxation time of the momentum autocorrelation
function of the impurity ocurrs and that was obtained in a previous work ~[M.
Romero-Bastida and E. Braun, Phys. Rev. E {\bf65}, 036228 (2002)]. The complete
Lyapunov spectrum does not depend significantly on the impurity mass . These
results suggest that the impurity does not contribute significantly to the
dynamical instability (chaos) of the chain and can be considered as a probe for
the dynamics of the system to which the impurity is coupled. Finally, it is
shown that the Kolmogorov-Sinai entropy of the chain has a crossover from weak
to strong chaos at the same value of the energy density that the crossover
value of largest Lyapunov exponent. Implications of this result
are discussed.Comment: 6 pages, 5 figures, revtex4 styl
Simulational Study on Dimensionality-Dependence of Heat Conduction
Heat conduction phenomena are studied theoretically using computer
simulation. The systems are crystal with nonlinear interaction, and fluid of
hard-core particles. Quasi-one-dimensional system of the size of is simulated. Heat baths are put in both end:
one has higher temperature than the other. In the crystal case, the interaction
potential has fourth-order non-linear term in addition to the harmonic
term, and Nose-Hoover method is used for the heat baths. In the fluid case,
stochastic boundary condition is charged, which works as the heat baths.
Fourier-type heat conduction is reproduced both in crystal and fluid models in
three-dimensional system, but it is not observed in lower dimensional system.
Autocorrelation function of heat flux is also observed and long-time tails of
the form of , where denotes the dimensionality of the
system, are confirmed.Comment: 4 pages including 3 figure
Power-law tail distributions and nonergodicity
We establish an explicit correspondence between ergodicity breaking in a
system described by power-law tail distributions and the divergence of the
moments of these distributions.Comment: 4 pages, 1 figure, corrected typo
Information-theoretic equilibration: the appearance of irreversibility under complex quantum dynamics
The question of how irreversibility can emerge as a generic phenomena when
the underlying mechanical theory is reversible has been a long-standing
fundamental problem for both classical and quantum mechanics. We describe a
mechanism for the appearance of irreversibility that applies to coherent,
isolated systems in a pure quantum state. This equilibration mechanism requires
only an assumption of sufficiently complex internal dynamics and natural
information-theoretic constraints arising from the infeasibility of collecting
an astronomical amount of measurement data. Remarkably, we are able to prove
that irreversibility can be understood as typical without assuming decoherence
or restricting to coarse-grained observables, and hence occurs under distinct
conditions and time-scales than those implied by the usual decoherence point of
view. We illustrate the effect numerically in several model systems and prove
that the effect is typical under the standard random-matrix conjecture for
complex quantum systems.Comment: 15 pages, 7 figures. Discussion has been clarified and additional
numerical evidence for information theoretic equilibration is provided for a
variant of the Heisenberg model as well as one and two-dimensional random
local Hamiltonian
Leading Pollicott-Ruelle Resonances and Transport in Area-Preserving Maps
The leading Pollicott-Ruelle resonance is calculated analytically for a
general class of two-dimensional area-preserving maps. Its wave number
dependence determines the normal transport coefficients. In particular, a
general exact formula for the diffusion coefficient D is derived without any
high stochasticity approximation and a new effect emerges: The angular
evolution can induce fast or slow modes of diffusion even in the high
stochasticity regime. The behavior of D is examined for three particular cases:
(i) the standard map, (ii) a sawtooth map, and (iii) a Harper map as an example
of a map with nonlinear rotation number. Numerical simulations support this
formula.Comment: 5 pages, 1 figur
Understanding deterministic diffusion by correlated random walks
Low-dimensional periodic arrays of scatterers with a moving point particle
are ideal models for studying deterministic diffusion. For such systems the
diffusion coefficient is typically an irregular function under variation of a
control parameter. Here we propose a systematic scheme of how to approximate
deterministic diffusion coefficients of this kind in terms of correlated random
walks. We apply this approach to two simple examples which are a
one-dimensional map on the line and the periodic Lorentz gas. Starting from
suitable Green-Kubo formulas we evaluate hierarchies of approximations for
their parameter-dependent diffusion coefficients. These approximations converge
exactly yielding a straightforward interpretation of the structure of these
irregular diffusion coeficients in terms of dynamical correlations.Comment: 13 pages (revtex) with 5 figures (postscript
Evolution of collision numbers for a chaotic gas dynamics
We put forward a conjecture of recurrence for a gas of hard spheres that
collide elastically in a finite volume. The dynamics consists of a sequence of
instantaneous binary collisions. We study how the numbers of collisions of
different pairs of particles grow as functions of time. We observe that these
numbers can be represented as a time-integral of a function on the phase space.
Assuming the results of the ergodic theory apply, we describe the evolution of
the numbers by an effective Langevin dynamics. We use the facts that hold for
these dynamics with probability one, in order to establish properties of a
single trajectory of the system. We find that for any triplet of particles
there will be an infinite sequence of moments of time, when the numbers of
collisions of all three different pairs of the triplet will be equal. Moreover,
any value of difference of collision numbers of pairs in the triplet will
repeat indefinitely. On the other hand, for larger number of pairs there is but
a finite number of repetitions. Thus the ergodic theory produces a limitation
on the dynamics.Comment: 4 pages, published versio
Deterring Inefficient Pharmaceutical Litigation: An Economic Rationale for the FDA Regulatory Compliance Defense
This Article examines the interaction between direct regulation of pharmaceuticals under the Federal Food Drug and Cosmetic Act (FDCA) and the indirect regulation of pharmaceuticals provided by common law tort incentives. The Article concludes that tort liability is generally inappropriate in cases where manufacturers have complied with the FDCA. The Article begins with a description of the FDCA's operation, and provides an overview of the Food and Drug Administration's (FDA) role in the drug approval process and drug labeling. This overview will demonstrate the need for centralized control over drug labeling. Moreover, we will provide an explanation of the costs and benefits of the drug approval process. Next, we will focus on the regulatory effects of tort law from an economics perspective. The role of tort law in deterring inefficient accidents depends on the extent and stringency of government regulation. We will examine the sufficiency of regulatory deterrence under various regulatory schemes, including the FDCA. This economic analysis will demonstrate that tort law's applicability should be limited to those regulatory schemes that inadequately deter risks. Since the FDCA adequately deters risk, the proper role for tort law should be to provide incentives for ensuring regulatory compliance.
We then provide a critical review of the legal rules applied to pharmaceutical litigation in American courts. The uncertainty present in current pharmaceutical litigation stems largely from the failure to adopt regulatory compliance in a strict liability world.Examination of labeling litigation suggests that courts have yet to establish meaningful standards. In addition, design defect litigation, by protecting only those drugs without side-effects, leads to untoward consequences. Furthermore, the tort system has a propensity for error. Our current litigation system generates perverse incentives, which we document.
Finally, we conclude that because of the strict nature of the FDCA, the role of tort liability should be limited through federal legislation
Shear flow, viscous heating, and entropy balance from dynamical systems
A consistent description of a shear flow, the accompanied viscous heating,
and the associated entropy balance is given in the framework of a deterministic
dynamical system, where a multibaker dynamics drives two fields: the velocity
and the temperature distributions. In an appropriate macroscopic limit their
transport equations go over into the Navier-Stokes and the heat conduction
equation of viscous flows. The inclusion of an artificial heat sink can
stabilize steady states with constant temperatures. It mimics a thermostating
algorithm used in non-equilibrium molecular-dynamics simulations.Comment: LaTeX 2e (epl.cls + sty-files for Europhys Lett included); 7 pages +
1 eps-figur
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