Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

Mechanical properties of viral capsids

Viruses are known to tolerate wide ranges of pH and salt conditions and to withstand internal pressures as high as 100 atmospheres. In this paper we investigate the mechanical properties of viral capsids, calling explicit attention to the inhomogeneity of the shells that is inherent to their discrete and polyhedral nature. We calculate the distribution of stress in these capsids and analyze their response to isotropic internal pressure (arising, for instance, from genome confinement and/or osmotic activity). We compare our results with appropriate generalizations of classical (i.e., continuum) elasticity theory. We also examine competing mechanisms for viral shell failure, e.g., in-plane crack formation vs radial bursting. The biological consequences of the special stabilities and stress distributions of viral capsids are also discussed.

Optimized back-focal-plane interferometry directly measures forces of optically trapped particles

Back-focal-plane interferometry is used to measure displacements of optically trapped samples with very high spatial and temporal resolution. However, the technique is closely related to a method that measures the rate of change in light momentum. It has long been known that displacements of the interference pattern at the back focal plane may be used to track the optical force directly, provided that a considerable fraction of the light is effectively monitored. Nonetheless, the practical application of this idea has been limited to counter-propagating, low-aperture beams where the accurate momentum measurements are possible. Here, we experimentally show that the connection can be extended to single-beam optical traps. In particular, we show that, in a gradient trap, the calibration product κ·β (where κ is the trap stiffness and 1/β is the position sensitivity) corresponds to the factor that converts detector signals into momentum changes; this factor is uniquely determined by three construction features of the detection instrument and does not depend, therefore, on the specific conditions of the experiment. Then, we find that force measurements obtained from back-focal-plane displacements are in practice not restricted to a linear relationship with position and hence they can be extended outside that regime. Finally, and more importantly, we show that these properties are still recognizable even when the system is not fully optimized for light collection. These results should enable a more general use of back-focal-plane interferometry whenever the ultimate goal is the measurement of the forces exerted by an optical trap.

Optimized back-focal-plane interferometry directly measures forces of optically trapped particles

Back-focal-plane interferometry is used to measure displacements of optically trapped samples with very high spatial and temporal resolution. However, the technique is closely related to a method that measures the rate of change in light momentum. It has long been known that displacements of the interference pattern at the back focal plane may be used to track the optical force directly, provided that a considerable fraction of the light is effectively monitored. Nonetheless, the practical application of this idea has been limited to counter-propagating, low-aperture beams where the accurate momentum measurements are possible. Here, we experimentally show that the connection can be extended to single-beam optical traps. In particular, we show that, in a gradient trap, the calibration product κ·β (where κ is the trap stiffness and 1/β is the position sensitivity) corresponds to the factor that converts detector signals into momentum changes; this factor is uniquely determined by three construction features of the detection instrument and does not depend, therefore, on the specific conditions of the experiment. Then, we find that force measurements obtained from back-focal-plane displacements are in practice not restricted to a linear relationship with position and hence they can be extended outside that regime. Finally, and more importantly, we show that these properties are still recognizable even when the system is not fully optimized for light collection. These results should enable a more general use of back-focal-plane interferometry whenever the ultimate goal is the measurement of the forces exerted by an optical trap.

Holographic optical tweezers combined with back-focal-plane displacement detection

A major problem with holographic optical tweezers (HOTs) is their incompatibility with laser-based position detection methods, such as back-focal-plane interferometry (BFPI). The alternatives generally used with HOTs, like high-speed video tracking, do not offer the same spatial and temporal bandwidths. This has limited the use of this technique in precise quantitative experiments. In this paper, we present an optical trap design that combines digital holography and back-focal-plane displacement detection. We show that, with a particularly simple setup, it is possible to generate a set of multiple holographic traps and an additional static non-holographic trap with orthogonal polarizations and that they can be, therefore, easily separated for measuring positions and forces with the high positional and temporal resolutions of laser-based detection. We prove that measurements from both polarizations contain less than 1% crosstalk and that traps in our setup are harmonic within the typical range. We further tested the instrument in a DNA stretching experiment and we discuss an interesting property of this configuration: the small drift of the differential signal between traps.

Comparison of aortic elasticity determined by cardiovascular magnetic resonance imaging in obese versus lean adults.

The vascular properties of large vessels in the obese have not been adequately studied. We used cardiovascular magnetic resonance imaging to quantify the cross-sectional area and elastic properties of the ascending thoracic and abdominal aorta in 21 clinically healthy obese young adult men and 25 men who were age-matched lean controls. Obese subjects had greater maximal cross-sectional area of the ascending thoracic aorta (984 +/- 252 vs 786 +/- 109 mm(2), p <0.01) and of the abdominal aorta (415 +/- 71 vs 374 +/- 51 mm(2), p <0.05). When indexed for height the differences persisted, but when indexed for body surface area, a significant difference between groups was found only for the maximal abdominal aortic cross-sectional area. The obese subjects also had decreased abdominal aortic elasticity, characterized by 24% lower compliance (0.0017 +/- 0.0004 vs 0.0021 +/- 0.0005 mm(2)/kPa/mm, p <0.01), 22% higher stiffness index beta (6.0 +/- 1.5 vs 4.9 +/- 0.7, p <0.005), and 41% greater pressure-strain elastic modulus (72 +/- 25 vs 51 +/- 9, p <0.005). At the ascending thoracic aorta, only the pressure-strain elastic modulus was different between obese and lean subjects (85 +/- 42 vs 65 +/- 26 kPa, respectively; p <0.05), corresponding to a 31% difference-but arterial compliance and stiffness index were not significantly different between groups. In clinically healthy young adult obese men, obesity is associated with increased cross-sectional aortic area and decreased aortic elasticity.

Real-time MR imaging of myocardial regional function using strain-encoding (SENC) with tissue through-plane motion tracking.

PURPOSE: To implement real-time myocardial strain-encoding (SENC) imaging in combination with tracking the tissue displacement in the through-plane direction. MATERIALS AND METHODS: SENC imaging was combined with the slice-following technique by implementing three-dimensional (3D) selective excitation. Certain adjustments were implemented to reduce scan time to one heartbeat. A total of 10 volunteers and five pigs were scanned on a 3T MRI scanner. Spatial modulation of magnetization (SPAMM)-tagged images were acquired on planes orthogonal to the SENC planes for comparison. Myocardial infarction (MI) was induced in two pigs and the resulting SENC images were compared to standard delayed-enhancement (DE) images. RESULTS: The strain values computed from SENC imaging with slice-following showed significant difference from those acquired without slice-following, especially during systole (P < 0.01). The strain curves computed from the SENC images with and without slice-following were similar to those computed from the orthogonal SPAMM images, with and without, respectively, tracking the tag line displacement in the strain direction. The resulting SENC images showed good agreement with the DE images in identifying MI in infarcted pigs. CONCLUSION: Correction of through-plane motion in real-time cardiac functional imaging is feasible using slice-following. The strain measurements are more accurate than conventional SENC measurements in humans and animals, as validated with conventional MRI tagging.

Diabetic neuropathy is a more important determinant of baroreflex sensitivity than carotid elasticity in type 2 diabetes.

The object of this study was to evaluate the contribution of carotid distensibilty on baroreflex sensitivity in patients with type 2 diabetes mellitus with at least 2 additional cardiovascular risk factors. Carotid distensibility was measured bilaterally at the common carotid artery in 79 consecutive diabetic patients and 60 matched subjects without diabetes. Spontaneous baroreflex sensitivity assessment was obtained using time and frequency methods. Baroreflex sensitivity was lower in diabetic subjects as compared with nondiabetic control subjects (5.25+/-2.80 ms/mm Hg versus 7.55+/-3.79 ms/mm Hg; P<0.01, respectively). Contrary to nondiabetic subjects, diabetic subjects showed no significant correlation between carotid distensibility and baroreflex sensitivity (r2=0.08, P=0.04 and r2=0.04, P=0.13, respectively). In diabetic subjects, baroreflex sensitivity was significantly lower in subjects with peripheral neuropathy than in those with preserved vibration sensation (4.1+/-0.5 versus 6.1+/-0.4 ms/mm Hg, respectively; P=0.005). Age in nondiabetic subjects, diabetes duration, systolic blood pressure, peripheral or sensitive neuropathy, and carotid distensibility were introduced in a stepwise multivariate analysis to identify the determinants of baroreflex sensitivity. In diabetic patients, neuropathy is a more sensitive determinant of baroreflex sensitivity than the reduced carotid distensibility (stepwise analysis; F ratio=5.1, P=0.028 versus F ratio=1.9, P=0.16, respectively). In diabetic subjects with 2 additional cardiovascular risk factors, spontaneous baroreflex sensitivity is not related to carotid distensibility. Diabetic subjects represent a particular population within the spectrum of cardiovascular risk situations because of the marked neuropathy associated with their metabolic disorder. Therefore, neuropathy is a more significant determinant of baroreflex sensitivity than carotid artery elasticity in patients with type 2 diabetes.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Contemporary engagements within corridors of the past: temporal elasticity, graffiti, and the materiality of St. Rock Street, Barcelona

In a medieval Barcelonan side-street, urine, rubbish, and a bewildering array of graphic imagery splatters the narrowing walls between two major thoroughfares. A contemporary conflict between residents, unknown artists and others is played out using banners, bottles, stickers, posters, stencils, spray paint, and bodily substances. In this shadowed liminality, local and global debates are superimposed upon substructures constructed from disease, prostitution, and the Saint of the Plague. The continuing urban struggle constitutes temporal statements of dirt and purity, violence and humour, dominance and resistance, death and salvation. Like the renovated facades masking the crumbling remains of structures long neglected, the government’s literal whitewashing of the art is a temporal cover-up of a discursive symptom stretching from deeply embedded preconditions. However, from his niche in the angular bend of the alley bearing his name, the statue of St. Rock remains unblinkingly staring, raised above the contestations expressed below.

Two-dimensional probabilistic inversion of plane-wave electromagnetic data: Methodology, model constraints and joint inversion with electrical resistivity data

Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints.

LS 5039: A runaway microquasar ejected from the galactic plane

We have compiled optical and radio astrometric data of the microquasar LS 5039 and derived its proper motion. This, together with the distance and radial velocity of the system, allows us to state that this source is escaping from its own regional standard of rest, with a total systemic velocity of about 150 km/s and a component perpendicular to the galactic plane larger than 100 km/s. This is probably the result of an acceleration obtained during the supernova event that created the compact object in this binary system. We have computed the trajectory of LS 5039 in the past, and searched for OB associations and supernova remnants in its path. In particular, we have studied the possible association between LS 5039 and the supernova remnant G016.8-01.1, which, despite our efforts, remains dubious. We have also discovered and studied an HI cavity in the ISM, which could have been created by the stellar wind of LS 5039 or by the progenitor of the compact object in the system. Finally, in the symmetric supernova explosion scenario, we estimate that at least 17 solar masses were lost in order to produce the high eccentricity observed. Such a mass loss could also explain the observed runaway velocity of the microquasar.

Synthesis of highly focused fields with circular polarization at any transverse plane

We develop a method for generating focused vector beams with circular polarization at any transverse plane. Based on the Richards-Wolf vector model, we derive analytical expressions to describe the propagation of these set of beams near the focal area. Since the polarization and the amplitude of the input beam are not uniform, an interferometric system capable of generating spatially-variant polarized beams has to be used. In particular, this wavefront is manipulated by means of spatial light modulators displaying computer generated holograms and subsequently focused using a high numerical aperture objective lens. Experimental results using a NA=0.85 system are provided: irradiance and Stokes images of the focused field at different planes near the focal plane are presented and compared with those obtained by numerical simulation.

Variable-stiffness composite panels: Defect tolerance under in-plane tensile loading

Automated Fiber Placement is being extensively used in the production of major composite components for the aircraft industry. This technology enables the production of tow-steered panels, which have been proven to greatly improve the structural efficiency of composites by means of in-plane stiffness variation and load redistribution. However, traditional straight-fiber architectures are still preferred. One of the reasons behind this is related to the uncertainties, as a result of process-induced defects, in the mechanical performance of the laminates. This experimental work investigates the effect of the fiber angle discontinuities between different tow courses in a ply on the un-notched and open-hole tensile strength of the laminate. The influence of several manufacturing parameters are studied in detail. The results reveal that 'ply staggering' and '0% gap coverage' is an effective combination in reducing the influence of defects in these laminates