KPP reaction-diffusion equations with a non-linear loss inside a cylinder

We consider in this paper a reaction-diffusion system in presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of the corresponding system with a Lewis number not equal to 1 is still quite open. Here, we will prove some results about the existence of travelling fronts and generalized travelling fronts solutions of such a system with the presence of a non-linear spacedependent loss term inside the domain. In particular, we will point out the existence of a minimal speed, above which any real value is an admissible speed. We will also give some spreading results for initial conditions decaying exponentially at infinity

Enhancing single-molecule photostability by optical feedback from quantum-jump detection

We report an optical technique that yields an enhancement of single-molecule photostability, by greatly suppressing photobleaching pathways which involve photoexcitation from the triplet state. This is accomplished by dynamically switching off the excitation laser when a quantum-jump of the molecule to the triplet state is optically detected. This procedure leads to a lengthened single-molecule observation time and an increased total number of detected photons. The resulting improvement in photostability unambiguously confirms the importance of photoexcitation from the triplet state in photobleaching dynamics, and may allow the investigation of new phenomena at the single-molecule level

Spatial and spatio-temporal patterns in a cell-haptotaxis model

We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation

An analysis of one- and two-dimensional patterns in a mechanical model for morphogenesis

In early embryonic development, fibroblast cells move through an extracellular matrix (ECM) exerting large traction forces which deform the ECM. We model these mechanical interactions mathematically and show that the various effects involved can combine to produce pattern in cell density. A linear analysis exhibits a wide selection of dispersion relations, suggesting a richness in pattern forming capability of the model. A nonlinear bifurcation analysis is presented for a simple version of the governing field equations. The one-dimensional analysis requires a non-standard element. The two-dimensional analysis shows the possibility of roll and hexagon pattern formation. A realistic biological application to the formation of feather germ primordia is briefly discussed

A mechanical model for biological pattern formation: A nonlinear bifurcation analysis

We present a mechanical model for cell aggregation in embryonic development. The model is based on the large traction forces exerted by fibroblast cells which deform the extracellular matrix (ECM) on which they move. It is shown that the subsequent changes in the cell environment can combine to produce pattern. A linear analysis is carried out for this model. This reveals a wide spectrum of different types of dispersion relations. A non-linear bifurcation analysis is presented for a simple version of the field equations: a non-standard element is required. Biological applications are briefly discussed

Rapidity-dependent chemical potentials in a statistical approach

We present a single-freeze-out model with thermal and geometric parameters dependent on the position within the fireball and use it to describe the rapidity and transverse-momentum spectra of pions, kaons, protons, and antiprotons measured at RHIC at 200 GeV} by BRAHMS. THERMINATOR is used to perform the necessary simulation, which includes all resonance decays. The result of the fit to the data is the expected growth of the baryon and strange chemical potentials with the spatial rapidity\alpha_\parallel. The value of the baryon chemical potential at \alpha_\parallel ~ 3 is about 200 MeV, i.e. lies in the range of the highest SPS energies. The chosen geometry of the fireball has a decreasing transverse size as the magnitude of \alpha_\parallel is increased, which also corresponds to decreasing transverse flow. The strange chemical potential obtained from the fit to the K+/K- ratio is such that the local strangeness density in the fireball is compatible with zero. The resulting rapidity spectra of net protons are described qualitatively within the statistical approach. As a result of our study, the knowledge of the ``topography'' of the fireball is acquired, allowing for other analyses and predictions.Comment: 6 pages, tals at SQM 200

A Chandra X-ray Study of the Globular Cluster M80

We report our analysis of a Chandra X-ray observation of the rich globular cluster M80, in which we detect some 19 sources to a limiting 0.5-2.5 keV X-ray luminosity of 7*10^30 ergs/s within the half-mass radius. X-ray spectra indicate that two of these sources are quiescent low-mass X-ray binaries (qLMXBs) containing neutron stars. We identify five sources as probable cataclysmic variables (CVs), one of which seems to be heavily absorbed, implying high inclination. The brightest CV may be the X-ray counterpart of Nova 1860 T Sco. The concentration of the X-ray sources within the cluster core implies an average mass of 1.2+/-0.2 Msun, consistent with the binary nature of these systems and very similar to the radial distribution of the blue stragglers in this cluster. The X-ray and blue straggler source populations in M80 are compared to those in the similar globular cluster 47 Tuc.Comment: Submitted to ApJ. 15 pages, 6 figure

Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation

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