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

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 $\mu\simeq 2$, in the lateral straggle $\mu$, for clear ripple formation. Above this upper bound, for longitudinal straggle $\sigma\gtrsim 1.7$, 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 $\beta=0.33$ 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 $C(n,d)$ is the convex hull of any $n$ points on the moment curve ${(t,t^2,...,t^d):t \in \reals}$ in $\reals^d$. For $d' >d$, we consider the fiber polytope (in the sense of Billera and Sturmfels) associated to the natural projection of cyclic polytopes $\pi: C(n,d') \to C(n,d)$ which "forgets" the last $d'-d$ coordinates. It is known that this fiber polytope has face lattice indexed by the coherent polytopal subdivisions of $C(n,d)$ which are induced by the map $\pi$. Our main result characterizes the triples $(n,d,d')$ for which the fiber polytope is canonical in either of the following two senses: - all polytopal subdivisions induced by $\pi$ 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 $\pi:P\to Q$ where $Q$ has only regular subdivisions and $P$ has two more vertices than its dimension.Comment: 28 pages with 1 postscript figur