Flame propagation in random media

We introduce a phase-field model to describe the dynamics of a self-sustaining propagating combustion front within a medium of randomly distributed reactants. Numerical simulations of this model show that a flame front exists for reactant concentration $c > c^* > 0$, while its vanishing at $c^*$ is consistent with mean-field percolation theory. For $c > c^*$, we find that the interface associated with the diffuse combustion zone exhibits kinetic roughening characteristic of the Kardar-Parisi-Zhang equation.Comment: 4, LR541

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

A hysteresis model with dipole interaction: one more devil-staircase

Magnetic properties of 2D systems of magnetic nanoobjects (2D regular lattices of the magnetic nanoparticles or magnetic nanostripes) are considered. The analytical calculation of the hysteresis curve of the system with interaction between nanoobjects is provided. It is shown that during the magnetization reversal system passes through a number of metastable states. The kinetic problem of the magnetization reversal was solved for three models. The following results have been obtained. 1) For 1D system (T=0) with the long-range interaction with the energy proportional to $r^{-p}$, the staircase-like shape of the magnetization curve has self-similar character. The nature of the steps is determined by interplay of the interparticle interaction and coercivity of the single nanoparticle. 2) The influence of the thermal fluctuations on the kinetic process was examined in the framework of the nearest-neighbor interaction model. The thermal fluctuations lead to the additional splitting of the steps on the magnetization curve. 3) The magnetization curve for system with interaction and coercivity dispersion was calculated in mean field approximation. The simple method to experimentally distinguish the influence of interaction and coercivity dispersion on the magnetization curve is suggested.Comment: 22 pages, 8 figure

Fuzzy Riemann Surfaces

We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras

Universal criterion for the breakup of invariant tori in dissipative systems

The transition from quasiperiodicity to chaos is studied in a two-dimensional dissipative map with the inverse golden mean rotation number. On the basis of a decimation scheme, it is argued that the (minimal) slope of the critical iterated circle map is proportional to the effective Jacobian determinant. Approaching the zero-Jacobian-determinant limit, the factor of proportion becomes a universal constant. Numerical investigation on the dissipative standard map suggests that this universal number could become observable in experiments. The decimation technique introduced in this paper is readily applicable also to the discrete quasiperiodic Schrodinger equation.Comment: 13 page

Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields

We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space.Comment: 22 pages, 2 figures, JHEP3 style. v2: This paper is a thoroughly revised version. We thank P.A. Horvathy, L. Martina and P.C. Stichel for illuminating comments that led us to reconsider some of our previously reported results; see note added at the end of the paper. v3: Acknowledgements adde

Delusions in frontotemporal lobar degeneration

We assessed the significance and nature of delusions in frontotemporal lobar degeneration (FTLD), an important cause of young-onset dementia with prominent neuropsychiatric features that remain incompletely characterised. The case notes of all patients meeting diagnostic criteria for FTLD attending a tertiary level cognitive disorders clinic over a three year period were retrospectively reviewed and eight patients with a history of delusions were identified. All patients underwent detailed clinical and neuropsychological evaluation and brain MRI. The diagnosis was confirmed pathologically in two cases. The estimated prevalence of delusions was 14 %. Delusions were an early, prominent and persistent feature. They were phenomenologically diverse; however paranoid and somatic delusions were prominent. Behavioural variant FTLD was the most frequently associated clinical subtype and cerebral atrophy was bilateral or predominantly right-sided in most cases. We conclude that delusions may be a clinical issue in FTLD, and this should be explored further in future work

Anomalous Fluctuations of Directed Polymers in Random Media

A systematic analysis of large scale fluctuations in the low temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ``ground states''. The probability distribution of their sizes is found to have a power law tail. The rare regions in the tail dominate much of the physics. The analysis presented here takes advantage of the mapping to the noisy-Burgers' equation. It complements a phenomenological description of glassy phases based on a scaling picture of droplet excitations and a recent variational approach with ``broken replica symmetry''. It is argued that the power law distribution of large thermally active excitations is a consequence of the continuous statistical ``tilt'' symmetry of the directed polymer, the breaking of which gives rise to the large active excitations in a manner analogous to the appearance of Goldstone modes in pure systems with a broken continuous symmetry.Comment: 59 pages including 8 figures ( REVTEX 3.0 )E-mail: [email protected]

CFIm-mediated alternative polyadenylation remodels cellular signaling and miRNA biogenesis

The mammalian cleavage factor I (CFIm) has been implicated in alternative polyadenylation (APA) in a broad range of contexts, from cancers to learning deficits and parasite infections. To determine how the CFIm expression levels are translated into these diverse phenotypes, we carried out a multi-omics analysis of cell lines in which the CFIm25 (NUDT21) or CFIm68 (CPSF6) subunits were either repressed by siRNA-mediated knockdown or over-expressed from stably integrated constructs. We established that >800 genes undergo coherent APA in response to changes in CFIm levels, and they cluster in distinct functional classes related to protein metabolism. The activity of the ERK pathway traces the CFIm concentration, and explains some of the fluctuations in cell growth and metabolism that are observed upon CFIm perturbations. Furthermore, multiple transcripts encoding proteins from the miRNA pathway are targets of CFIm-dependent APA. This leads to an increased biogenesis and repressive activity of miRNAs at the same time as some 3' UTRs become shorter and presumably less sensitive to miRNA-mediated repression. Our study provides a first systematic assessment of a core set of APA targets that respond coherently to changes in CFIm protein subunit levels (CFIm25/CFIm68). We describe the elicited signaling pathways downstream of CFIm, which improve our understanding of the key role of CFIm in integrating RNA processing with other cellular activities

Evolution of avalanche conducting states in electrorheological liquids

Charge transport in electrorheological fluids is studied experimentally under strongly nonequlibrium conditions. By injecting an electrical current into a suspension of conducting nanoparticles we are able to initiate a process of self-organization which leads, in certain cases, to formation of a stable pattern which consists of continuous conducting chains of particles. The evolution of the dissipative state in such system is a complex process. It starts as an avalanche process characterized by nucleation, growth, and thermal destruction of such dissipative elements as continuous conducting chains of particles as well as electroconvective vortices. A power-law distribution of avalanche sizes and durations, observed at this stage of the evolution, indicates that the system is in a self-organized critical state. A sharp transition into an avalanche-free state with a stable pattern of conducting chains is observed when the power dissipated in the fluid reaches its maximum. We propose a simple evolution model which obeys the maximum power condition and also shows a power-law distribution of the avalanche sizes.Comment: 15 pages, 6 figure