8,907 research outputs found
Towards a unification of HRT and SCOZA
The Hierarchical Reference Theory (HRT) and the Self-Consistent
Ornstein-Zernike Approximation (SCOZA) are two liquid state theories that both
furnish a largely satisfactory description of the critical region as well as
phase separation and the equation of state in general. Furthermore, there are a
number of similarities that suggest the possibility of a unification of both
theories. As a first step towards this goal we consider the problem of
combining the lowest order gamma expansion result for the incorporation of a
Fourier component of the interaction with the requirement of consistency
between internal and free energies, leaving aside the compressibility relation.
For simplicity we restrict ourselves to a simplified lattice gas that is
expected to display the same qualitative behavior as more elaborate models. It
turns out that the analytically tractable Mean Spherical Approximation is a
solution to this problem, as are several of its generalizations. Analysis of
the characteristic equations shows the potential for a practical scheme and
yields necessary conditions any closure to the Ornstein Zernike relation must
fulfill for the consistency problem to be well posed and to have a unique
differentiable solution. These criteria are expected to remain valid for more
general discrete and continuous systems, even if consistency with the
compressibility route is also enforced where possible explicit solutions will
require numerical evaluations.Comment: Minor changes in accordance with referee comment
Infinite compressibility states in the Hierarchical Reference Theory of fluids. II. Numerical evidence
Continuing our investigation into the Hierarchical Reference Theory of fluids
for thermodynamic states of infinite isothermal compressibility kappa[T] we now
turn to the available numerical evidence to elucidate the character of the
partial differential equation: Of the three scenarios identified previously,
only the assumption of the equations turning stiff when building up the
divergence of kappa[T] allows for a satisfactory interpretation of the data. In
addition to the asymptotic regime where the arguments of part I
(cond-mat/0308467) directly apply, a similar mechanism is identified that gives
rise to transient stiffness at intermediate cutoff for low enough temperature.
Heuristic arguments point to a connection between the form of the Fourier
transform of the perturbational part of the interaction potential and the
cutoff where finite difference approximations of the differential equation
cease to be applicable, and they highlight the rather special standing of the
hard-core Yukawa potential as regards the severity of the computational
difficulties.Comment: J. Stat. Phys., in press. Minor changes to match published versio
Self-consistent Ornstein-Zernike approximation for molecules with soft cores
The Self-Consistent Ornstein-Zernike Approximation (SCOZA) is an accurate
liquid state theory. So far it has been tied to interactions composed of hard
core repulsion and long-range attraction, whereas real molecules have soft core
repulsion at short distances. In the present work, this is taken into account
through the introduction of an effective hard core with a diameter that depends
upon temperature only. It is found that the contribution to the configurational
internal energy due to the repulsive reference fluid is of prime importance and
must be included in the thermodynamic self-consistency requirement on which
SCOZA is based. An approximate but accurate evaluation of this contribution
relies on the virial theorem to gauge the amplitude of the pair distribution
function close to the molecular surface. Finally, the SCOZA equation is
transformed by which the problem is reformulated in terms of the usual SCOZA
with fixed hard core reference system and temperature-dependent interaction
(Un)anticipated Technological Change in an Endogenous Growth Model
This paper examines numerically the impact of a negative exogenous shock to marginal productivity (such as ecological government regulation that becomes effective at some point in time) in an endogenous finite-time growth model with sluggish reallocation of human capital. The policy can be anticipated or unanticipated by firms, and it can also be announced but not implemented. It turns out that these frictions have a very strong long-run effect on output, consumption and on the optimal allocation of capital and labor in particular. The qualitative properties relate to homogenous labor models with positive productivity shocks. The problem is thus to maximize a function of a continuous system, where the system is subject to frictions and stepwise changes; for such a problem the application of calculus of variations necessary conditions is problematic. A numerical optimization method, which has had much success on qualitatively similar problems in engineering, has been employed.two-sector endogenous growth model; unanticipated and anticipated technological change; frictions in reallocation of human capital; Runge-Kutta parallel shooting algorithm
Lower algebraic K-theory of certain reflection groups
For a finite volume geodesic polyhedron P in hyperbolic 3-space, with the
property that all interior angles between incident faces are integral
submultiples of Pi, there is a naturally associated Coxeter group generated by
reflections in the faces. Furthermore, this Coxeter group is a lattice inside
the isometry group of hyperbolic 3-space, with fundamental domain the original
polyhedron P. In this paper, we provide a procedure for computing the lower
algebraic K-theory of the integral group ring of such Coxeter lattices in terms
of the geometry of the polyhedron P. As an ingredient in the computation, we
explicitly calculate some of the lower K-groups of the dihedral groups and the
product of dihedral groups with the cyclic group of order two.Comment: 35 pages, 2 figure
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Energy subsidies at times of economic crisis: A comparative study and scenario analysis of Italy and Spain
From 2005-2012, Spain and Italy saw significant investment in renewable energy, most notably in onshore wind and solar, driven by generous subsidies, the expectation of rising carbon prices and falling renewables (especially solar panel) costs. As a result of the Global Financial Crisis, both countries were faced with massive fiscal deficits and were forced to curtail their renewable support schemes, although these efforts took several years to take effect after the onset of the initial crisis. Ironically, both Spain and Italy incurred the lion's share of their liability for renewables support after the onset of the crisis particularly because of the rapid drop in costs of solar PV panels, while subsidy levels remained high. In spite of changes to their support regimes, Italy is likely to meet its 2020 climate and renewable targets, whereas Spain is unlikely to meet its 2020 renewables target based on current trajectories. Following a comparative historical survey of the two large EU member states, we present a scenario analysis that contrasts alternative futures of 2030 where renewable support remain at current levels (essentially zero) or is revived and where carbon prices stay at current low levels (€5/t CO2) or rises to levels needed to accomplish the proposed 40% EU 2030 reduction target. We find that, by 2030, in large parts of Spain, solar PV will be cost-competitive even under low-carbon price and low renewable support regimes, whereas concentrated solar power (CSP) and onshore wind, will require at least either a sustained renewable support regime or a high carbon price to become cost competitive. In Italy, solar PV becomes cost competitive in the low-carbon, low-renewable support scenario except when fossil fuel prices are unusually low. By 2030, there would be large-scale penetration of onshore wind and geothermal in Italy if there is either a high-carbon price or a high renewable support regime or both. In general, if the current levels of carbon price were to exist post-2020, both Italy and Spain would find it rather difficult to increase the penetration of renewables in their electricity mix. A high subsidy world, on the other hand, would be result in the most favourable outcome, particularly for Spain, although it may incur additional costs in comparison to a high carbon price world.Spai
Morphological regions and oblique incidence dot formation in a model of surface sputtering
We study solid surface morphology created by off-normal ion-beam sputtering
with an atomistic, solid-on-solid model of sputter erosion. With respect to an
earlier version of the model, we extend this model with the inclusion of
lateral erosion. Using the 2-dimensional structure factor, we found an upper
bound , in the lateral straggle , for clear ripple formation.
Above this upper bound, for longitudinal straggle , we found
the possibility of dot formation (without sample rotation). Moreover, a
temporal crossover from a hole topography to ripple topography with the same
value of collision cascade parameters was found. Finally, a scaling analysis of
the roughness, using the consecutive gradient approach, yields the growth
exponents and 0.67 for two different topographic regimes.Comment: 8 pages, 14 figure
Capture and release of a conditional state of a cavity QED system by quantum feedback
Detection of a single photon escaping an optical cavity QED system prepares a nonclassical state of the electromagnetic field. The evolution of the state can be modified by changing the drive of the cavity. For the appropriate feedback, the conditional state can be captured (stabilized) and then released. This is observed by a conditional intensity measurement that shows suppression of vacuum Rabi oscillations for the length of the feedback pulse and their subsequent return
Fiber polytopes for the projections between cyclic polytopes
The cyclic polytope is the convex hull of any points on the
moment curve in . For , we
consider the fiber polytope (in the sense of Billera and Sturmfels) associated
to the natural projection of cyclic polytopes which
"forgets" the last coordinates. It is known that this fiber polytope has
face lattice indexed by the coherent polytopal subdivisions of which
are induced by the map . Our main result characterizes the triples
for which the fiber polytope is canonical in either of the following
two senses:
- all polytopal subdivisions induced by are coherent,
- the structure of the fiber polytope does not depend upon the choice of
points on the moment curve.
We also discuss a new instance with a positive answer to the Generalized
Baues Problem, namely that of a projection where has only
regular subdivisions and has two more vertices than its dimension.Comment: 28 pages with 1 postscript figur
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