Doping dependence of the lattice dynamics in Ba(Fe1−x_{1-x}Cox_x)2_2As2_2 studied by Raman spectroscopy

We report Raman scattering spectra of iron-pnictide superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ single crystals with varying cobalt $x$ content. Upon cooling through the tetragonal-to-orthorhombic transition, we observe a large splitting of the E$_g$ in-plane phonon modes involving Fe and As displacements. The splitting of the in-plane phonons at the transition is strongly reduced upon doping and disappears for $x=0.06$ qualitatively following the trend displayed by the Fe magnetic moment. The origin of the splitting is discussed in terms of magnetic frustration inherent to iron-pnictide systems and we argue that such enhanced splitting may be linked to strong spin-phonon coupling.Comment: 6 pages, 6 figure

Inelastic x-ray scattering investigations of lattice dynamics in SmFeAsO1−x_{1-x}Fy_y superconductors

We report measurements of the phonon density of states as measured with inelastic x-ray scattering in SmFeAsO$_{1-x}$F$_y$ powders. An unexpected strong renormalization of phonon branches around 23 meV is observed as fluorine is substituted for oxygen. Phonon dispersion measurements on SmFeAsO$_{1-x}$F$_y$ single crystals allow us to identify the 21 meV A$_{1g}$ in-phase (Sm,As) and the 26 meV B$_{1g}$ (Fe,O) modes to be responsible for this renormalization, and may reveal unusual electron-phonon coupling through the spin channel in iron-based superconductors.Comment: 4 pages, 3 figures, submitted for SNS2010 conference proceeding

A Measure-Theoretic Model for Collective Cell Migration and Aggregation

The aim of this paper is to present a measure-theoretic approach able to derive an Eulerian model of the dynamics of a cell population with a nite number of cells out of a microscopic Lagrangian description of the underlying cellular particle system. By looking at the spatial distribution of cells in terms of a time-evolving probability measure, rather than at individual cell paths, an ensemble representation of the cell colony is obtained, which can then result either in discrete, continuous, or hybrid approaches according to the spatial structure of such a probability measure. Remarkably, such an approach does not call for any assumption on the number of cells taken into account, thus providing consistency of the same modeling framework across all levels of representation. In addition, it is suitable to cope with the often ambiguous translation of microscopic arguments (i.e., cell dimensions and interaction radii) into macroscopic descriptions. The proposed approach, also extended to the case of multiple coexisting cell populations, is then tested with sample simulations that provide a useful sensitivity analysis of the model parameters

Two-scale Moving Boundary Dynamics of Cancer Invasion:Heterotypic Cell Populations Evolution in Heterogeneous ECM

This book contains a collection of original research articles and review articles that describe novel mathematical modeling techniques and the application of those techniques to models of cell motility in a variety of contexts. The aim is to highlight some of the recent mathematical work geared at understanding the coordination of intracellular processes involved in the movement of cells. This collection will benefit researchers interested in cell motility as well graduate students taking a topics course in this area.

Cell-scale degradation of peritumoural extracellular matrix fibre network and its role within tissue-scale cancer invasion

Local cancer invasion of tissue is a complex, multiscale process which plays an essential role in tumour progression. Occurring over many different temporal and spatial scales, the first stage of invasion is the secretion of matrix degrading enzymes (MDEs) by the cancer cells that consequently degrade the surrounding extracellular matrix (ECM). This process is vital for creating space in which the cancer cells can progress and it is driven by the activities of specific matrix metalloproteinases (MMPs). In this paper, we consider the key role of two MMPs by developing further the novel two-part multiscale model introduced in [33] to better relate at micro-scale the two micro-scale activities that were considered there, namely, the micro-dynamics concerning the continuous rearrangement of the naturally oriented ECM fibres within the bulk of the tumour and MDEs proteolytic micro-dynamics that take place in an appropriate cell-scale neighbourhood of the tumour boundary. Focussing primarily on the activities of the membrane-tethered MT1-MMP and the soluble MMP-2 with the fibrous ECM phase, in this work we investigate the MT1-MMP/MMP-2 cascade and its overall effect on tumour progression. To that end, we will propose a new multiscale modelling framework by considering the degradation of the ECM fibres not only to take place at macro-scale in the bulk of the tumour but also explicitly in the micro-scale neighbourhood of the tumour interface as a consequence of the interactions with molecular fluxes of MDEs that exercise their spatial dynamics at the invasive edge of the tumour

Crossover from Collective to Incoherent Spin Excitations in Superconducting Cuprates Probed by Detuned Resonant Inelastic X-Ray Scattering

Spin excitations in the overdoped high temperature superconductors Tl2Ba2CuO6+δ and (Bi,Pb)2(Sr,La)2CuO6+δ were investigated by resonant inelastic x-ray scattering (RIXS) as functions of doping and detuning of the incoming photon energy above the Cu-L3 absorption peak. The RIXS spectra at optimal doping are dominated by a paramagnon feature with peak energy independent of photon energy, similar to prior results on underdoped cuprates. Beyond optimal doping, the RIXS data indicate a sharp crossover to a regime with a strong contribution from incoherent particle-hole excitations whose maximum shows a fluorescencelike shift upon detuning. The spectra of both compound families are closely similar, and their salient features are reproduced by exact-diagonalization calculations of the single-band Hubbard model on a finite cluster. The results are discussed in the light of recent transport experiments indicating a quantum phase transition near optimal doping

A review of mathematical models for the formation of vascular networks

Two major mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former term describes the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter term describes the sprouting of new vessels from an existing capillary or post-capillary venule. Similar mechanisms are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis. A number of mathematical approaches have been used to analyse these phenomena. In this article, we review the different types of models, with special emphasis on their ability to reproduce different biological systems and to predict measurable quantities which describe the overall processes. Finally, we highlight the advantages specific to each of the different modelling approaches. The research that led to the present paper was partially supported by a grant of the group GNFM of INdA