Phenomenological Models of Socio-Economic Network Dynamics

We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is defined by the particular process taking place on the network. The interplay between the two processes produces phase transitions and hysteresis, as seen using numerical simulations for three specific processes. We obtain analytic results using mean field approximations, and for a particular case we derive an exact solution for the network. In common with real-world social networks, we find coexistence of high and low connectivity phases and history dependence.Comment: 11 pages, 8 figure

On the soliton width in the incommensurate phase of spin-Peierls systems

We study using bosonization techniques the effects of frustration due to competing interactions and of the interchain elastic couplings on the soliton width and soliton structure in spin-Peierls systems. We compare the predictions of this study with numerical results obtained by exact diagonalization of finite chains. We conclude that frustration produces in general a reduction of the soliton width while the interchain elastic coupling increases it. We discuss these results in connection with recent measurements of the soliton width in the incommensurate phase of CuGeO_3.Comment: 4 pages, latex, 2 figures embedded in the tex

The optical conductivity of the quasi one-dimensional conductors: the role of forward scattering by impurities

We calculate the average conductivity sigma (omega) of interacting electrons in one dimension in the presence of a long-range random potential (forward scattering disorder). Taking the curvature of the energy dispersion into account, we show that weak disorder leads to a transport scattering rate that vanishes as omega^2 for small frequency omega. This implies that the real part of the conductivity remains finite for omega -> 0, while the imaginary part diverges. These effects are lost within the usual bosonization approach, which relies on the linearization of the energy dispersion. We discuss our result in the light of a recent experiment.Comment: 5 RevTex pages; more careful comparison with experiments and discussion of interchain hopping added; some references added; to appear in Phys. Rev.

Elementary excitations, exchange interaction and spin-Peierls transition in CuGeO3_3

The microscopic description of the spin-Peierls transition in pure and doped CuGeO_3 is developed taking into account realistic details of crystal structure. It it shown that the presence of side-groups (here Ge) strongly influences superexchange along Cu-O-Cu path, making it antiferromagnetic. Nearest-neighbour and next-nearest neighbour exchange constants $J_{nn}$ and $J_{nnn}$ are calculated. Si doping effectively segments the CuO_2-chains leading to $J_{nn}(Si)\simeq0$ or even slightly ferromagnetic. Strong sensitivity of the exchange constants to Cu-O-Cu and (Cu-O-Cu)-Ge angles may be responsible for the spin-Peierls transition itself (``bond-bending mechanism'' of the transition). The nature of excitations in the isolated and coupled spin-Peierls chains is studied and it is shown that topological excitations (solitons) play crucial role. Such solitons appear in particular in doped systems (Cu_{1-x}Zn_xGeO_3, CuGe_{1-x}Si_xO_3) which can explain the $T_{SP}(x)$ phase diagram.Comment: 7 pages, revtex, 7 Postscript figure

Rapid Suppression of the Spin Gap in Zn-doped CuGeO_3 and SrCu_2O_3

The influence of non-magnetic impurities on the spectrum and dynamical spin structure factor of a model for CuGeO$_3$ is studied. A simple extension to Zn-doped ${\rm Sr Cu_2 O_3}$ is also discussed. Using Exact Diagonalization techniques and intuitive arguments we show that Zn-doping introduces states in the Spin-Peierls gap of CuGeO$_3$. This effect can beunderstood easily in the large dimerization limit where doping by Zn creates ``loose'' S=1/2 spins, which interact with each other through very weak effective antiferromagnetic couplings. When the dimerization is small, a similar effect is observed but now with the free S=1/2 spins being the resulting S=1/2 ground state of severed chains with an odd number of sites. Experimental consequences of these results are discussed. It is interesting to observe that the spin correlations along the chains are enhanced by Zn-doping according to the numerical data presented here. As recent numerical calculations have shown, similar arguments apply to ladders with non-magnetic impurities simply replacing the tendency to dimerization in CuGeO$_3$ by the tendency to form spin-singlets along the rungs in SrCu$_2$O$_3$.Comment: 7 pages, 8 postscript figures, revtex, addition of figure 8 and a section with experimental predictions, submmited to Phys. Rev. B in May 199

Hemodynamics in the thoracic aorta using OpenFOAM: 4D PCMRI versus CFD

The aim of this work is the study of fluid dynamics models using the CFD software OpenFOAM, an open source software allowing meshing, manipulation, simulation and post-processing of many problems involving fluid mechanics. The work consists of a study with OpenFOAM of a real engineering problem, namely to analyze hemodynamics in the thoracic aorta in collaboration with CIMNE (Centre Internacional de Metodes Numerics a l'Enginyeria) and LABSON-UPC (Laboratorio de Sistemas Oleohidricos y Neumcos). Speci cally, the study aims to compute the shear stress that blood causes to aorta walls

From spinons to magnons in explicit and spontaneously dimerized antiferromagnetic chains

We reconsider the excitation spectra of a dimerized and frustrated antiferromagnetic Heisenberg chain. This model is taken as the simpler example of compiting spontaneous and explicit dimerization relevant for Spin-Peierls compounds. The bosonized theory is a two frequency Sine-Gordon field theory. We analize the excitation spectrum by semiclassical methods. The elementary triplet excitation corresponds to an extended magnon whose radius diverge for vanishing dimerization. The internal oscilations of the magnon give rise to a series of excited state until another magnon is emited and a two magnon continuum is reached. We discuss, for weak dimerization, in which way the magnon forms as a result of a spinon-spinon interaction potential.Comment: 5 pages, latex, 3 figures embedded in the tex

Hippocampal Dendritic Spines Modifications Induced by Perinatal Asphyxia

Perinatal asphyxia (PA) affects the synaptic function and morphological organization. In previous works, we have shown neuronal and synaptic changes in rat neostriatum subjected to hypoxia leading to long-term ubi-protein accumulation. Since F-actin is highly concentrated in dendritic spines, modifications in its organization could be related with alterations induced by hypoxia in the central nervous system (CNS). In the present study, we investigate the effects of PA on the actin cytoskeleton of hippocampal postsynaptic densities (PSD) in 4-month-old rats. PSD showed an increment in their thickness and in the level of ubiquitination. Correlative fluorescence-electron microscopy photooxidation showed a decrease in the number of F-actin-stained spines in hippocampal excitatory synapses subjected to PA. Although Western Blot analysis also showed a slight decrease in β-actin in PSD in PA animals, the difference was not significant. Taken together, this data suggests that long-term actin cytoskeleton might have role in PSD alterations which would be a spread phenomenon induced by PA

On the stability problem in the O(N) nonlinear sigma model

The stability problem for the O(N) nonlinear sigma model in the 2+\epsilon dimensions is considered. We present the results of the 1/N^{2} order calculations of the critical exponents (in the 2<d<4 dimensions) of the composite operators relevant for this problem. The arguments in the favor of the scenario with the conventional fixed point are given.Comment: 9 pages, revtex, 1 Postscript figur