Renormalized Equilibria of a Schloegl Model Lattice Gas

A lattice gas model for Schloegl's second chemical reaction is described and analyzed. Because the lattice gas does not obey a semi-detailed-balance condition, the equilibria are non-Gibbsian. In spite of this, a self-consistent set of equations for the exact homogeneous equilibria are described, using a generalized cluster-expansion scheme. These equations are solved in the two-particle BBGKY approximation, and the results are compared to numerical experiment. It is found that this approximation describes the equilibria far more accurately than the Boltzmann approximation. It is also found, however, that spurious solutions to the equilibrium equations appear which can only be removed by including effects due to three-particle correlations.Comment: 21 pages, REVTe

Scaling, Propagation, and Kinetic Roughening of Flame Fronts in Random Media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density, below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with mean field theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time dependent width and equal time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.Comment: Standard LaTeX, no figures, 29 pages; (to appear in J. Stat. Phys. vol.81, 1995). Complete file available at http://www.physics.helsinki.fi/tft/tft.html or anonymous ftp at ftp://rock.helsinki.fi/pub/preprints/tft

The branch processes of vortex filaments and Hopf Invariant Constraint on Scroll Wave

In this paper, by making use of Duan's topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of a complex function $Z(\vec{x},t)$. It is also shown that the Hopf invariant of knotted scroll wave filaments is preserved in the branch processes (splitting, merging, or encountering) during the evolution of these knotted scroll wave filaments. Furthermore, it also revealed that the "exclusion principle" in some chemical media is just the special case of the Hopf invariant constraint, and during the branch processes the "exclusion principle" is also protected by topology.Comment: 9 pages, 5 figure

Transition to Stochastic Synchronization in Spatially Extended Systems

Spatially extended dynamical systems, namely coupled map lattices, driven by additive spatio-temporal noise are shown to exhibit stochastic synchronization. In analogy with low-dymensional systems, synchronization can be achieved only if the maximum Lyapunov exponent becomes negative for sufficiently large noise amplitude. Moreover, noise can suppress also the non-linear mechanism of information propagation, that may be present in the spatially extended system. A first example of phase transition is observed when both the linear and the non-linear mechanisms of information production disappear at the same critical value of the noise amplitude. The corresponding critical properties can be hardly identified numerically, but some general argument suggests that they could be ascribed to the Kardar-Parisi-Zhang universality class. Conversely, when the non-linear mechanism prevails on the linear one, another type of phase transition to stochastic synchronization occurs. This one is shown to belong to the universality class of directed percolation.Comment: 21 pages, Latex - 14 EPS Figs - To appear on Physical Review

Streaming instability of slime mold amoebae: An analytical model

During the aggregation of amoebae of the cellular slime mould Dictyostelium, the interaction of chemical waves of the signaling molecule cAMP with cAMP-directed cell movement causes the breakup of a uniform cell layer into branching patterns of cell streams. Recent numerical and experimental investigations emphasize the pivotal role of the cell-density dependence of the chemical wave speed for the occurrence of the streaming instability. A simple, analytically tractable, model of Dictyostelium aggregation is developed to test this idea. The interaction of cAMP waves with cAMP-directed cell movement is studied in the form of coupled dynamics of wave front geometries and cell density. Comparing the resulting explicit instability criterion and dispersion relation for cell streaming with the previous findings of model simulations and numerical stability analyses, a unifying interpretation of the streaming instability as a cAMP wave-driven chemotactic instability is proposed

Atrioventricular thrombus in a 14-year-old patient: a case report

Right atrioventricular thrombus was diagnosed by echocardiography in a 14-year-old boy. Thrombus was reached through the right ventricle to the pulmonary artery and it was caused to tricuspit valve insufficiency. Surgical thrombectomy was performed and, he was treated with oral anticoagulation in postoperative period

Stochastic Growth Equations and Reparametrization Invariance

It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach provides a particularly transparent way to obtain continuum growth equations for interfaces. It is straightforward to derive equations which describe the coarse grained evolution of discrete lattice models and analyze their small gradient expansion. In this way, the authors identify the basic mechanisms which lead to the most commonly used growth equations. The advantages of this formulation of growth processes is that it allows one to go beyond the frequently used no-overhang approximation. The reparametrization invariant form also displays explicitly the conservation laws for the specific process and all the symmetries with respect to space-time transformations which are usually lost in the small gradient expansion. Finally, it is observed, that the knowledge of the full equation of motion, beyond the lowest order gradient expansion, might be relevant in problems where the usual perturbative renormalization methods fail.Comment: 42 pages, Revtex, no figures. To appear in Rev. of Mod. Phy

A modified Ehrenfest formalism for efficient large-scale ab initio molecular dynamics

We present in detail the recently derived ab-initio molecular dynamics (AIMD) formalism [Phys. Rev. Lett. 101 096403 (2008)], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major drawback of traditional AIMD methods is the necessity to enforce the orthogonalization of the wave-functions, which can become the bottleneck for very large systems. Alternatively, one can handle the electron-ion dynamics within the Ehrenfest scheme where no explicit orthogonalization is necessary, however the time step is too small for practical applications. Here we preserve the desirable properties of Ehrenfest in a new scheme that allows for a considerable increase of the time step while keeping the system close to the Born-Oppenheimer surface. We show that the automatically enforced orthogonalization is of fundamental importance for large systems because not only it improves the scaling of the approach with the system size but it also allows for an additional very efficient parallelization level. In this work we provide the formal details of the new method, describe its implementation and present some applications to some test systems. Comparisons with the widely used Car-Parrinello molecular dynamics method are made, showing that the new approach is advantageous above a certain number of atoms in the system. The method is not tied to a particular wave-function representation, making it suitable for inclusion in any AIMD software package.Comment: 28 pages, 5 figures, published in a special issue of J. Chem. Theory Comp. in honour of John Perde

Cancer survival in England and Wales at the end of the 20th century

Survival has risen steadily since the 1970s for most cancers in adults in England and Wales, but persistent inequalities exist between those living in affluent and deprived areas. These differences are not seen for children. For many of the common adult cancers, these inequalities in survival (the 'deprivation gap') became more marked in the 1990s. This volume presents extended analyses of survival for adults diagnosed during the 14 years 1986-1999 and followed up to 2001, including trends in overall survival in England and Wales and trends in the deprivation gap in survival. The analyses include individual tumour data for 2.2 million cancer patients. This article outlines the structure of the supplement - an article for each of the 20 most common cancers in adults, followed by an expert commentary from one of the leading UK clinicians specialising in malignancies of that organ or system. The available data, quality control and methods of analysis are described here, rather than repeated in each of the 20 articles. We open the discussion between clinicians and epidemiologists on how to interpret the observed trends and inequalities in cancer survival, and we highlight some of the most important contrasts in these very different points of view. Survival improved substantially for adult cancer patients in England and Wales up to the end of the 20th century. Although socioeconomic inequalities in survival are remarkably persistent, the overall patterns suggest that these inequalities are largely avoidable

Socioeconomic inequalities in cancer survival in England after the NHS cancer plan

BACKGROUND: Socioeconomic inequalities in survival were observed for many cancers in England during 1981-1999. The NHS Cancer Plan (2000) aimed to improve survival and reduce these inequalities. This study examines trends in the deprivation gap in cancer survival after implementation of the Plan. MATERIALS AND METHOD: We examined relative survival among adults diagnosed with 1 of 21 common cancers in England during 1996-2006, followed up to 31 December 2007. Three periods were defined: 1996-2000 (before the Cancer Plan), 2001-2003 (initialisation) and 2004-2006 (implementation). We estimated the difference in survival between the most deprived and most affluent groups (deprivation gap) at 1 and 3 years after diagnosis, and the change in the deprivation gap both within and between these periods. RESULTS: Survival improved for most cancers, but inequalities in survival were still wide for many cancers in 2006. Only the deprivation gap in 1-year survival narrowed slightly over time. A majority of the socioeconomic disparities in survival occurred soon after a cancer diagnosis, regardless of the cancer prognosis. CONCLUSION: The recently observed reduction in the deprivation gap was minor and limited to 1-year survival, suggesting that, so far, the Cancer Plan has little effect on those inequalities. Our findings highlight that earlier diagnosis and rapid access to optimal treatment should be ensured for all socioeconomic groups