Lateral instability in normal viscous fingers

We study a low-amplitude, long-wavelength lateral instability of the Saffman-Taylor finger by means of a phase-field model. We observe such an instability in two situations in which small dynamic perturbations are overimposed to a constant pressure drop. We first study the case in which the perturbation consists of a single oscillatory mode and then a case in which the perturbation consists of temporal noise. In both cases the instability undergoes a process of selection.

External fluctuations in a pattern-forming instability

The effect of external fluctuations on the formation of spatial patterns is analyzed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the bifurcation point controlled by the intensity of the multiplicative noise. This shift takes place in the ordering direction (i.e., produces patterns), but its magnitude decreases with that of the noise correlation length. Analytical arguments are presented to explain these facts.

Statistical dynamics of dislocation systems: The influence of dislocation-dislocation correlations.

During plastic deformation of crystalline materials, the collective dynamics of interacting dislocations gives rise to various patterning phenomena. A crucial and still open question is whether the long range dislocation-dislocation interactions which do not have an intrinsic range can lead to spatial patterns which may exhibit well-defined characteristic scales. It is demonstrated for a general model of two-dimensional dislocation systems that spontaneously emerging dislocation pair correlations introduce a length scale which is proportional to the mean dislocation spacing. General properties of the pair correlation functions are derived, and explicit calculations are performed for a simple special case, viz pair correlations in single-glide dislocation dynamics. It is shown that in this case the dislocation system exhibits a patterning instability leading to the formation of walls normal to the glide plane. The results are discussed in terms of their general implications for dislocation patterning.

Pair production by and electric field in (1+1)-dimensional de Sitter space

We use the method of Bogolubov transformations to compute the rate of pair production by an electric field in (1+1)-dimensional de Sitter space. The results are in agreement with those obtained previously using the instanton methods. This is true even when the size of the instanton is comparable to the size of the de Sitter horizon.

In defense of the "tunneling" wave function of the universe

The tunneling approach to the wave function of the Universe has been recently criticized by Bousso and Hawking who claim that it predicts a catastrophic instability of de Sitter space with respect to pair production of black holes. We show that this claim is unfounded. First, we argue that different horizon size regions in de Sitter space cannot be treated as independently created, as they contend. And second, the WKB tunneling wave function is not simply the inverse of the Hartle-Hawking one, except in very special cases. Applied to the related problem of pair production of massive particles, we argue that the tunneling wave function leads to a small constant production rate, and not to a catastrophe as the argument of Bousso and Hawking would suggest.

Pair Creation of Black Holes Joined by Cosmic Strings

We argue that production of charged black hole pairs joined by a cosmic string in the presence of a magnetic field can be analyzed using the Ernst metric. The effect of the cosmic string is to pull the black holes towards each other, opposing to the background field. An estimation of the production rate using the Euclidean action shows that the process is suppressed as compared to the formation of black holes without strings.

The assignment game: core bounds for mixed-pair coalitions

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the coreof the game. These games will be called buyer¿seller exact games and satisfy the condition that each mixed¿pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyerseller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer¿seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed¿pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a ¿45o¿lattice¿ by means of the core of an assignment game can now be answered

Dynamics of sweeping through an instability: Passage-time statistics for colored noise

A calculation of passage-time statistics is reported for the laser switch-on problem, under the influence of colored noise, when the net gain is continuously swept from below to above threshold. Cases of fast and slow sweeping are considered. In the weak-noise limit, asymptotic results are given for small and large correlation times of the noise. The mean first passage time increases with the correlation time of the noise. This effect is more important for fast sweeping than for slow sweeping.

Growth and melting of the nematic phase: sample thickness dependence of the Mullins-Sekerka instability

In this article we report our systematic studies of the dependence on the sample thickness of the onset parameters of the instability of the nematic-isotropic interface during directional growth and melting, in homeotropic or planar anchoring.

Evidence for different expression profiles for c-Met, EGFR, PTEN and the mTOR pathway in low and high grade endometrial carcinomas in a cohort of consecutive women. Occurrence of PIK3CA and K-Ras mutations and microsatellite instability.

Molecular and genetic investigations in endometrial carcinogenesis may have prognostic and therapeutic implications. We studied the expression of EGFR, c-Met, PTEN and the mTOR signalling pathway (phospho-AKT/phospho-mTOR/phospho-RPS6) in 69 consecutive tumours and 16 tissue microarrays. We also analysed PIK3CA, K-Ras mutations and microsatellite instability (MSI). We distinguished two groups: group 1 (grade 1 and 2 endometrioid cancers) and group 2 (grade 3 endometrioid and type II clear and serous cell cancers). We hypothesised that these histological groups might have different features. We found that a) survival was higher in group 1 with less aggressive tumours (P⟨0.03); b) EGFR (P=0.01), PTEN and the AKT/mTOR/RPS6 signalling pathway were increased in group 1 versus group 2 (P=0.05 for phospho-mTOR); c) conversely, c-Met was higher (P⟨0.03) in group 2 than in group 1; d) In group 1, EGFR was correlated with c-Met, phospho-mTOR, phospho-RPS6 and the global activity of the phospho-AKT/phospho-mTOR/phospho-RPS6 pathway. In group 2, EGFR was correlated only with the phospho-AKT/phospho-mTOR/phospho-RPS6 pathway, whereas c-Met was correlated with PTEN; e) survival was higher for tumours with more than 50% PTEN-positive cells; f) K-RAS and PIK3CA mutations occurred in 10-12% of the available tumours and MSI in 40.4%, with a loss of MLH1 and PMS2 expression. Our results for endometrial cancers provide the first evidence for a difference in status between groups 1 and 2. The patients may benefit from different targeted treatments, anti-EGFR agents and rapamycin derivatives (anti-mTOR) for group 1 and an anti c-MET/ligand complex for group 2.