Rheology of fractal networks

We model the cytoskeleton as a fractal network by identifying each segment with a simple Kelvin-Voigt element, with a well defined equilibrium length. The final structure retains the elastic characteristics of a solid or a gel, which may support stress, without relaxing. By considering a very simple regular self-similar structure of segments in series and in parallel, in 1, 2 or 3 dimensions, we are able to express the viscoelasticity of the network as an effective generalised Kelvin-Voigt model with a power law spectrum of retardation times, $\cal L\sim\tau^{\alpha}$. We relate the parameter $\alpha$ with the fractal dimension of the gel. In some regimes ($0<\alpha<1$), we recover the weak power law behaviours of the elastic and viscous moduli with the angular frequencies, $G'\sim G''\sim w^\alpha$, that occur in a variety of soft materials, including living cells. In other regimes, we find different power laws for $G'$ and $G''$.Comment: 5 pages, 3 figure

Electromagnetism and multiple-valued loop-dependent wave functionals

We quantize the Maxwell theory in the presence of a electric charge in a "dual" Loop Representation, i.e. a geometric representation of magnetic Faraday's lines. It is found that the theory can be seen as a theory without sources, except by the fact that the wave functional becomes multivalued. This can be seen as the dual counterpart of what occurs in Maxwell theory with a magnetic pole, when it is quantized in the ordinary Loop Representation. The multivaluedness can be seen as a result of the multiply-connectedness of the configuration space of the quantum theory.Comment: 5 page

Loop representation of charged particles interacting with Maxwell and Chern-Simons fields

The loop representation formulation of non-relativistic particles coupled with abelian gauge fields is studied. Both Maxwell and Chern-Simons interactions are separately considered. It is found that the loop-space formulations of these models share significant similarities, although in the Chern-Simons case there exists an unitary transformation that allows to remove the degrees of freedom associated with the paths. The existence of this transformation, which allows to make contact with the anyonic interpretation of the model, is subjected to the fact that the charge of the particles be quantized. On the other hand, in the Maxwell case, we find that charge quantization is necessary in order to the geometric representation be consistent.Comment: 6 pages, improved versio

Spatially resolved physical and chemical properties of the planetary nebula NGC 3242

Optical integral-field spectroscopy was used to investigate the planetary nebula NGC 3242. We analysed the main morphological components of this source, including its knots, but not the halo. In addition to revealing the properties ofthe physical and chemical nature of this nebula, we also provided reliable spatially resolved constraints that can be used for future photoionisation modelling of the nebula. The latter is ultimately necessary to obtain a fully self-consistent 3D picture of the physical and chemical properties of the object. The observations were obtained with the VIMOS instrument attached to VLT-UT3. Maps and values for specific morphological zones for the detected emission-lines were obtained and analysed with routines developed by the authors to derive physical and chemical conditions of the ionised gas in a 2D fashion. We obtained spatially resolved maps and mean values of the electron densities, temperatures, and chemical abundances, for specific morphological structures in NGC 3242. These results show the pixel-to-pixel variations of the the small- and large-scale structures of the source. These diagnostic maps provide information free from the biases introduced by traditional single long-slit observations. In general, our results are consistent with a uniform abundance distribution for the object, whether we look at abundance maps or integrated fluxes from specified morphological structures. The results indicate that special care should be taken with the calibration of the data and that only data with extremely good signal-to-noise ratio and spectral coverage should be used to ensure the detection of possible spatial variations.Comment: 11 pages, 8 figures accepted for publication in Astronomy & Astrophysic

Living bacteria rheology: population growth, aggregation patterns and cooperative behaviour under different shear flows

The activity of growing living bacteria was investigated using real-time and in situ rheology -- in stationary and oscillatory shear. Two different strains of the human pathogen Staphylococcus aureus -- strain COL and its isogenic cell wall autolysis mutant -- were considered in this work. For low bacteria density, strain COL forms small clusters, while the mutant, presenting deficient cell separation, forms irregular larger aggregates. In the early stages of growth, when subjected to a stationary shear, the viscosity of both strains increases with the population of cells. As the bacteria reach the exponential phase of growth, the viscosity of the two strains follow different and rich behaviours, with no counterpart in the optical density or in the population's colony forming units measurements. While the viscosity of strain COL keeps increasing during the exponential phase and returns close to its initial value for the late phase of growth, where the population stabilizes, the viscosity of the mutant strain decreases steeply, still in the exponential phase, remains constant for some time and increases again, reaching a constant plateau at a maximum value for the late phase of growth. These complex viscoelastic behaviours, which were observed to be shear stress dependent, are a consequence of two coupled effects: the cell density continuous increase and its changing interacting properties. The viscous and elastic moduli of strain COL, obtained with oscillatory shear, exhibit power-law behaviours whose exponent are dependent on the bacteria growth stage. The viscous and elastic moduli of the mutant have complex behaviours, emerging from the different relaxation times that are associated with the large molecules of the medium and the self-organized structures of bacteria. These behaviours reflect nevertheless the bacteria growth stage.Comment: 9 pages, 10 figure

Interacting Particles and Strings in Path and Surface Representations

Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a Kalb-Ramond field in four dimensions, the topological interaction of two particles due to a BF term in 2+1 dimensions, and the string-particle interaction mediated by a BF term in 3+1 dimensions. In the first case one finds that a consistent "surface-representation" can be built provided that the coupling constant is quantized. The geometrical setting that arises corresponds to a generalized version of the Faraday's lines picture: quantum states are labeled by the shape of the string, from which emanate "Faraday`s surfaces". In the other models, the topological interaction can also be described by geometrical means. It is shown that the open-path (or open-surface) dependence carried by the wave functional in these models can be eliminated through an unitary transformation, except by a remaining dependence on the boundary of the path (or surface). These feature is closely related to the presence of anomalous statistics in the 2+1 model, and to a generalized "anyonic behavior" of the string in the other case.Comment: RevTeX 4, 28 page

The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy

A technique for measuring velocity gradients in laminar flows by homodyne light scattering is presented. A theory which describes the light-scattering spectrum is derived that includes the effects of different types of linear flow fields, particle diffusion and the intensity profile in the scattering volume. The conditions which must be satisfied in order that the theory describe the experimental situation are outlined and complementary experiments are performed which both verify the theory and apply the technique. Verification is provided using the flow in a Couette device, and the flow due to single rotating cylinder in a large bath of fluid. The technique is then applied to measure the spatial variation of the shear rate in a four-roll mill