Cosmic censorship in two-dimensional gravity

A weak version of the cosmic censorship hypothesis is implemented as a set of boundary conditions on exact semiclassical solutions of two-dimensional dilaton gravity. These boundary conditions reflect low-energy matter from the strong coupling region and they also serve to stabilize the vacuum of the theory against decay into negative energy states. Information about low-energy incoming matter can be recovered in the final state but at high energy black holes are formed and inevitably lead to information loss at the semiclassical level.

Soluble models in two-dimensional dilaton gravity

A one-parameter class of simple models of two-dimensional dilaton gravity, which can be exactly solved including back-reaction effects, is investigated at both classical and quantum levels. This family contains the RST model as a special case, and it continuously interpolates between models having a flat (Rindler) geometry and a constant curvature metric with a nontrivial dilaton field. The processes of formation of black hole singularities from collapsing matter and Hawking evaporation are considered in detail. Various physical aspects of these geometries are discussed, including the cosmological interpretation.

Spatial competition between two candidates of different quality: the effects of candidate ideology and private information

This paper examines competition in a spatial model of two-candidate elections, where one candidate enjoys a quality advantage over the other candidate. The candidates care about winning and also have policy preferences. There is two-dimensional private information. Candidate ideal points as well as their tradeoffs between policy preferences and winning are private information. The distribution of this two-dimensional type is common knowledge. The location of the median voter's ideal point is uncertain, with a distribution that is commonly known by both candidates. Pure strategy equilibria always exist in this model. We characterize the effects of increased uncertainty about the median voter, the effect of candidate policy preferences, and the effects of changes in the distribution of private information. We prove that the distribution of candidate policies approaches the mixed equilibrium of Aragones and Palfrey (2002a), when both candidates' weights on policy preferences go to zero.

Period-Luminosity-Colour distribution and classification of Galactic oxygen-rich LPVs I. Luminosity calibrations

The absolute K magnitudes and kinematic parameters of about 350 oxygen-rich Long-Period Variable stars are calibrated, by means of an up-to-date maximum-likelihood method, using HIPPARCOS parallaxes and proper motions together with radial velocities and, as additional data, periods and V-K colour indices. Four groups, differing by their kinematics and mean magnitudes, are found. For each of them, we also obtain the distributions of magnitude, period and de-reddened colour of the base population, as well as de-biased period-luminosity-colour relations and their two-dimensional projections. The SRa semiregulars do not seem to constitute a separate class of LPVs. The SRb appear to belong to two populations of different ages. In a PL diagram, they constitute two evolutionary sequences towards the Mira stage. The Miras of the disk appear to pulsate on a lower-order mode. The slopes of their de-biased PL and PC relations are found to be very different from the ones of the Oxygen Miras of the LMC. This suggests that a significant number of so-called Miras of the LMC are misclassified. This also suggests that the Miras of the LMC do not constitute a homogeneous group, but include a significant proportion of metal-deficient stars, suggesting a relatively smooth star formation history. As a consequence, one may not trivially transpose the LMC period-luminosity relation from one galaxy to the other.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

SIMSAFADIM-CLASTIC: A new approach to mathematical 3D forward simulation modelling for terrigenous and carbonate marine sedimentation

Most sedimentary modelling programs developed in recent years focus on either terrigenous or carbonate marine sedimentation. Nevertheless, only a few programs have attempted to consider mixed terrigenous-carbonate sedimentation, and most of these are two-dimensional, which is a major restriction since geological processes take place in 3D. This paper presents the basic concepts of a new 3D mathematical forward simulation model for clastic sediments, which was developed from SIMSAFADIM, a previous 3D carbonate sedimentation model. The new extended model, SIMSAFADIM-CLASTIC, simulates processes of autochthonous marine carbonate production and accumulation, together with clastic transport and sedimentation in three dimensions of both carbonate and terrigenous sediments. Other models and modelling strategies may also provide realistic and efficient tools for prediction of stratigraphic architecture and facies distribution of sedimentary deposits. However, SIMSAFADIM-CLASTIC becomes an innovative model that attempts to simulate different sediment types using a process-based approach, therefore being a useful tool for 3D prediction of stratigraphic architecture and facies distribution in sedimentary basins. This model is applied to the neogene Vallès-Penedès half-graben (western Mediterranean, NE Spain) to show the capacity of the program when applied to a realistic geologic situation involving interactions between terrigenous clastics and carbonate sediments.

Numerical signs fos a transition in the 2d Random Field Ising Model at T=0

Intensive numerical studies of exact ground states of the two-dimensional ferromagnetic random field Ising model at T=0, with a Gaussian distribution of fields, are presented. Standard finite size scaling analysis of the data suggests the existence of a transition at ¿c=0.64±0.08. Results are compared with existing theories and with the study of metastable avalanches in the same model.

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.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

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.