105 research outputs found
Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals
We derive the Ornstein-Zernike equation for molecular crystals of axially
symmetric particles and apply the Percus-Yevick approximation to this system.
The one-particle orientational distribution function has a nontrivial
dependence on the orientation and is needed as an input. Despite some
differences, the Ornstein-Zernike equation for molecular crystals has a similar
structure as for liquids. We solve both equations for hard ellipsoids on a sc
lattice. Compared to molecular liquids, the tensorial orientational correlators
exhibit less structure. However, depending on the lengths a and b of the
rotation axis and the perpendicular axes of the ellipsoids, different behavior
is found. For oblate and prolate ellipsoids with b >= 0.35 (units of the
lattice constant), damped oscillations in distinct directions of direct space
occur for some correlators. They manifest themselves in some correlators in
reciprocal space as a maximum at the Brillouin zone edge, accompanied by maxima
at the zone center for other correlators. The oscillations indicate alternating
orientational fluctuations, while the maxima at the zone center originate from
nematic-like orientational fluctuations. For a <= 2.5 and b <= 0.35, the
oscillations are weaker. For a >= 3.0 and b <= 0.35, no oscillations occur any
longer. For many of the correlators in reciprocal space, an increase of a at
fixed b leads to a divergence at the zone center q = 0, consistent with
nematic-like long range fluctuations, and for some oblate and prolate systems
with b ~< 1.0 a simultaneous tendency to divergence of few other correlators at
the zone edge is observed. Comparison with correlators from MC simulations
shows satisfactory agreement. We also obtain a phase boundary for
order-disorder transitions.Comment: 20 pages, 13 figures, submitted to Phys. Rev.
The emerging energy web
There is a general need of elaborating energy-effective solutions for managing our increasingly dense interconnected world. The problem should be tackled in multiple dimensions -technology, society, economics, law, regulations, and politics- at different temporal and spatial scales. Holistic approaches will enable technological solutions to be supported by socio-economic motivations, adequate incentive regulation to foster investment in green infrastructures coherently integrated with adequate energy provisioning schemes. In this article, an attempt is made to describe such multidisciplinary challenges with a coherent set of solutions to be identified to significantly impact the way our interconnected energy world is designed and operated. Graphical abstrac
Quantum Multibaker Maps: Extreme Quantum Regime
We introduce a family of models for quantum mechanical, one-dimensional
random walks, called quantum multibaker maps (QMB). These are Weyl
quantizations of the classical multibaker models previously considered by
Gaspard, Tasaki and others. Depending on the properties of the phases
parametrizing the quantization, we consider only two classes of the QMB maps:
uniform and random. Uniform QMB maps are characterized by phases which are the
same in every unit cell of the multibaker chain. Random QMB maps have phases
that vary randomly from unit cell to unit cell. The eigenstates in the former
case are extended while in the latter they are localized. In the uniform case
and for large , analytic solutions can be obtained for the time
dependent quantum states for periodic chains and for open chains with absorbing
boundary conditions. Steady state solutions and the properties of the
relaxation to a steady state for a uniform QMB chain in contact with
``particle'' reservoirs can also be described analytically. The analytical
results are consistent with, and confirmed by, results obtained from numerical
methods. We report here results for the deep quantum regime (large ) of
the uniform QMB, as well as some results for the random QMB. We leave the
moderate and small results as well as further consideration of the
other versions of the QMB for further publications.Comment: 17 pages, referee's and editor's comments addresse
Entropy Production, Fractals, and Relaxation to Equilibrium
The theory of entropy production in nonequilibrium, Hamiltonian systems,
previously described for steady states using partitions of phase space, is here
extended to time dependent systems relaxing to equilibrium. We illustrate the
main ideas by using a simple multibaker model, with some nonequilibrium initial
state, and we study its progress toward equilibrium. The central results are
(i) the entropy production is governed by an underlying, exponentially decaying
fractal structure in phase space, (ii) the rate of entropy production is
largely independent of the scale of resolution used in the partitions, and
(iii) the rate of entropy production is in agreement with the predictions of
nonequilibrium thermodynamics
Classical Scattering for a driven inverted Gaussian potential in terms of the chaotic invariant set
We study the classical electron scattering from a driven inverted Gaussian
potential, an open system, in terms of its chaotic invariant set. This chaotic
invariant set is described by a ternary horseshoe construction on an
appropriate Poincare surface of section. We find the development parameters
that describe the hyperbolic component of the chaotic invariant set. In
addition, we show that the hierarchical structure of the fractal set of
singularities of the scattering functions is the same as the structure of the
chaotic invariant set. Finally, we construct a symbolic encoding of the
hierarchical structure of the set of singularities of the scattering functions
and use concepts from the thermodynamical formalism to obtain one of the
measures of chaos of the fractal set of singularities, the topological entropy.Comment: accepted in Phy. Rev.
A time series of hydroxylamine (NH2OH) in the southwestern Baltic Sea
Hydroxylamine (NH(2)OH) is an intermediate of the marine nitrogen cycle and in marine environments dissolved NH(2)OH is short-lived. In order to investigate the distribution of NH(2)OH under varying oxygen conditions, its seasonal variability was investigated on a monthly basis from July 2005 to May 2006 at the time series station Boknis Eck located in the Eckernforde Bay (southwestern Baltic Sea). NH(2)OH concentrations were generally low and close to the detection limit. However, a pronounced increase was observed after the seasonal thermohaline stratification period with low oxygen/anoxic conditions in the deep layers was terminated in November 2005. The increase of NH(2)OH was associated with the re-oxygenation of the water column. We conclude that NH(2)OH was produced in-situ during nitrification. We suggest that the detection of significant amounts of NH(2)OH can be used as an indicator for a "fresh" nitrifying system
Refining value-at-risk estimates using a Bayesian Markov-switching GJR-GARCH copula-EVT model
In this paper, we propose a model for forecasting Value-at-Risk (VaR) using a Bayesian Markov-switching GJR-GARCH(1,1) model with skewed Student’s-t innovation, copula functions and extreme value theory. A Bayesian Markov-switching GJR-GARCH(1,1) model that identifies non-constant volatility over time and allows the GARCH parameters to vary over time following a Markov process, is combined with copula functions and EVT to formulate the Bayesian Markov-switching GJR-GARCH(1,1) copula-EVT VaR model, which is then used to forecast the level of risk on financial asset returns. We further propose a new method for threshold selection in EVT analysis, which we term the hybrid method. Empirical and back-testing results show that the proposed VaR models capture VaR reasonably well in periods of calm and in periods of crisis
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