Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Rat splanchnic net oxygen consumption. Energetic implications

1. The blood flow, PO2, pH and PCO2 have been estimated in portal and suprahepatic veins as well as in hepatic artery of fed and overnight starved rats given an oral glucose load. From these data the net intestinal, hepatic and splanchnic balances for oxygen and bicarbonate were calculated. The oxygen consumption of the intact animal has also been measured under comparable conditions. 2. The direct utilization of oxygen balances as energy equivalents when establishing the contribution of energy metabolism of liver and intestine to the overall energy expenses of the rat, has been found to be incorrect, since it incorporates the intrinsic error of interorgan proton transfer through bicarbonate. Liver and intestine produced high net bicarbonate balances in all situations tested, implying the elimination (by means of oxidative pathways, i.e. consuming additional oxygen) of high amounts of H+ generated with bicarbonate. The equivalence in energy output of the oxygen balances was then corrected for bicarbonate production to 11-54% lower values. 3. Intestine and liver consume a high proportion of available oxygen, about one-half in basal (fed or starved) conditions and about one-third after gavage, the intestine consumption being about 15% in all situations tested and the liver decreasing its oxygen consumption with gavage.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

Diffusion in spatially and temporarily inhomogeneous media

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B, whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B, we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion "constant" goes like t-1/3 to a constant asymptotic value D¿. The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence.

Front propagation in spatially modulated media

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.

Wave competition in excitable modulated media.

The propagation of an initially planar front is studied within the framework of the photosensitive Belousov-Zhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steady-state velocity are experimentally validated.

Noise-enhanced excitability in bistable activator-inhibitor media

We show that external fluctuations induce excitable behavior in a bistable spatially extended system with activator-inhibitor dynamics of the FitzHugh-Nagumo type. This can be understood as a mechanism for sustained signal propagation in bistable media. The phase diagram of the stochastic system is analytically obtained and numerically verified. For small-noise intensities, front propagation becomes unstable, and excitable pulses arise as the only possible spatiotemporal behavior of the system. For large-noise intensities, on the other hand, the system enters an effective regime of oscillatory behavior, where it exhibits spontaneous nucleation of pulses and synchronized firing.

Percolation thresholds in chemical disordered excitable media

The behavior of chemical waves advancing through a disordered excitable medium is investigated in terms of percolation theory and autowave properties in the framework of the light-sensitive Belousov-Zhabotinsky reaction. By controlling the number of sites with a given illumination, different percolation thresholds for propagation are observed, which depend on the relative wave transmittances of the two-state medium considered.

Expanding scroll rings and negative tension turbulence in a model of excitable media

Scroll waves in excitable media, described by the Barkley model, are studied. In the parameter region of weak excitability, negative tension of wave filaments is found. It leads to expansion of scroll rings and instability of wave filaments. A circular filament tends to stretch, bend, loop, and produce an expanding tangle that fills up the volume. The filament does not undergo fragmentation before it touches the boundaries. Statistical properties of such Winfree turbulence of scroll waves are numerically investigated.

Periodic forcing of scroll rings and control of Winfree turbulence in excitable media

By simulations of the Barkley model, action of uniform periodic nonresonant forcing on scroll rings and wave turbulence in three-dimensional excitable media is investigated. Sufficiently strong rapid forcing converts expanding scroll rings into the collapsing ones and suppresses the Winfree turbulence caused by the negative tension of wave filaments. Slow strong forcing has an opposite effect, leading to expansion of scroll rings and induction of the turbulence. These effects are explained in the framework of the phenomenological kinematic theory of scroll waves.

Front dynamics in turbulent media

A study of a stable front propagating in a turbulent medium is presented. The front is generated through a reaction-diffusion equation, and the turbulent medium is statistically modeled using a Langevin equation. Numerical simulations indicate the presence of two different dynamical regimes. These regimes appear when the turbulent flow either wrinkles a still rather sharp propagating interfase or broadens it. Specific dependences of the propagating velocities on stirring intensities appropriate to each case are found and fitted when possible according to theoretically predicted laws. Different turbulent spectra are considered.

Regular wave propagation out of noise in chemical active media

A pacemaker, regularly emitting chemical waves, is created out of noise when an excitable photosensitive Belousov-Zhabotinsky medium, strictly unable to autonomously initiate autowaves, is forced with a spatiotemporal patterned random illumination. These experimental observations are also reproduced numerically by using a set of reaction-diffusion equations for an activator-inhibitor model, and further analytically interpreted in terms of genuine coupling effects arising from parametric fluctuations. Within the same framework we also address situations of noise-sustained propagation in subexcitable media.

Embodied pollution in Spanish household consumption: a disaggregate analysis

[spa] En este artículo aplicamos un modelo input-output ampliado medioambientalmente para analizar un aspecto específico de la hipótesis de la curva de Kuznets ambiental. El propósito del estudio es analizar si las estructuras de consumo de los hogares con una mejor ‘posición económica’ pueden tener un efecto positivo para reducir las presiones medioambientales. Para ello combinamos información de diferentes bases de datos para analizar el impacto de la contaminación atmosférica del consumo de diferentes hogares españoles en el año 2000. Consideramos nueve gases, i.e. los seis gases de efecto invernadero (CO2, CH4, N2O, SF6, HFCs, y PFCs) y otros tres gases (SO2, NOx, y NH3). Clasificamos los hogares en quintiles de gasto per capita y quintiles de gasto equivalente. Los resultados obtenidos muestran que hay una relación positiva y elevada entre el nivel de gasto y las emisiones directas e indirectas generadas por el consumo de los hogares; sin embargo, las intensidades de emisión tienden a disminuir con el nivel de gasto para los diferentes gases, con la excepción de SF6, HFCs, y PFCs.

Consumption of macrophytes by invertebrates in Tancada lagoon (NE Spain)

Gammarus aequicauda and Sphaeroma hookeri are the most abundant macroinvertebrates on Ruppia cirrhosa (1275 and 1290 individuals.m-2) and Potamogeton pectinatus (140 and 680 individuals. m-2) in Tancada lagoon, a Mediterranean coastal lagoon in the Ebro Delta (NE Spain). Consumption and assimilation efficiencies were calculated from bell jar experiments. Gammarus grazing effects are higher than Sphaeroma on both Ruppia cirrhosa and Potamogeton pectinatus. Green Ruppia leaves lost 0.3 mg per mg Gammarus per day, while Potamogeton leaves lost 0.2 mg per mg Gammarus per day. Decomposing Ruppia leaves lost 0.35-0.54 mg per mg Gammarus per day. Losses of weight by both Ruppia and Potamogeton due to Sphaeroma feeding were less than half those by Gammarus. Assimilation efficiencies are higher for Gammarus (44-78% feeding on Ruppia 2% feeding on Potamogeton) than for Sphaeroma (26-48%) feeding on Ruppia). These assimilation efficiencies were higher than those reported by other authors working at higher latitudes perhaps because of the higher temperature under which the experiments were carried out.