Counting polygon dissections in the projective plane

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Lateral instability in normal viscous fingers

We study a low-amplitude, long-wavelength lateral instability of the Saffman-Taylor finger by means of a phase-field model. We observe such an instability in two situations in which small dynamic perturbations are overimposed to a constant pressure drop. We first study the case in which the perturbation consists of a single oscillatory mode and then a case in which the perturbation consists of temporal noise. In both cases the instability undergoes a process of selection.

Experiments of periodic forcing of Saffman-Taylor fingers

We report on an experimental study of long normal Saffman-Taylor fingers subject to periodic forcing. The sides of the finger develop a low amplitude, long wavelength instability. We discuss the finger response in stationary and nonstationary situations, as well as the dynamics towards the stationary states. The response frequency of the instability increases with forcing frequency at low forcing frequencies, while, remarkably, it becomes independent of forcing frequency at large forcing frequencies. This implies a process of wavelength selection. These observations are in good agreement with previous numerical results reported in [Ledesma-Aguilar et al., Phys. Rev. E 71, 016312 (2005)]. We also study the average value of the finger width, and its fluctuations, as a function of forcing frequency. The average finger width is always smaller than the width of the steady-state finger. Fluctuations have a nonmonotonic behavior with a maximum at a particular frequency.

Phase-field approach to spatial perturbations in normal Saffman-Taylor fingers

We make a numerical study of the effect that spatial perturbations have in normal Saffman-Taylor fingers driven at constant pressure gradients. We use a phase field model that allows for spatial variations in the Hele-Shaw cell. We find that, regardless of the specific way in which spatial perturbations are introduced, a lateral instability develops on the sides of the propagating Saffman-Taylor finger. Moreover, the instability exists regardless of the intensity of spatial perturbations in the cell as long as the perturbations are felt by the finger tip. If, as the finger propagates, the spatial perturbations felt by the tip change, the instability is nonperiodic. If, as the finger propagates, the spatial perturbations felt by the tip are persistent, the instability developed is periodic. In the later case, the instability is symmetrical or asymmetrical depending on the intensity of the perturbation.

Fluctuations in Saffman-Taylor fingers with quenched disorder

We make an experimental characterization of the effect that static disorder has on the shape of a normal Saffman-Taylor finger. We find that static noise induces a small amplitude and long wavelength instability on the sides of the finger. Fluctuations on the finger sides have a dominant wavelength, indicating that the system acts as a selective amplifier of static noise. The dominant wavelength does not seem to be very sensitive to the intensity of static noise present in the system. On the other hand, at a given flow rate, rms fluctuations of the finger width, decrease with decreasing intensity of static noise. This might explain why the sides of the fingers are flat for typical Saffman-Taylor experiments. Comparison with previous numerical studies of the effect that temporal noise has on the Saffman-Taylor finger, leads to conclude that the effect of temporal noise and static noise are similar. The behavior of fluctuations of the finger width found in our experiments, is qualitatively similar to one recently reported, in the sense that, the magnitude of the width fluctuations decays as a power law of the capillary number, at low flow rates, and increases with capillary number for larger flow rates.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Simultaneous determination of gross alpha, gross beta and Ra-226 in natural water by liquid scintillation counting.

The determination of gross alpha, gross beta and 226Ra activity in natural waters is useful in a wide range of environmental studies. Furthermore, gross alpha and gross beta parameters are included in international legislation on the quality of drinking water [Council Directive 98/83/EC].1 In this work, a low-background liquid scintillation counter (Wallac, Quantulus 1220) was used to simultaneously determine gross alpha, gross beta and 226Ra activity in natural water samples. Sample preparation involved evaporation to remove 222Rn and its short-lived decay daughters. The evaporation process concentrated the sample ten-fold. Afterwards, a sample aliquot of 8 mL was mixed with 12 mL of Ultima Gold AB scintillation cocktail in low-diffusion vials. In this study, a theoretical mathematical model based on secular equilibrium conditions between 226Ra and its short-lived decay daughters is presented. The proposed model makes it possible to determine 226Ra activity from two measurements. These measurements also allow determining gross alpha and gross beta simultaneously. To validate the proposed model, spiked samples with different activity levels for each parameter were analysed. Additionally, to evaluate the model's applicability in natural water, eight natural water samples from different parts of Spain were analysed. The eight natural water samples were also characterised by alpha spectrometry for the naturally occurring isotopes of uranium (234U, 235U and 238U), radium (224Ra and 226Ra), 210Po and 232Th. The results for gross alpha and 226Ra activity were compared with alpha spectrometry characterization, and an acceptable concordance was obtained.

Sherali-Adams Relaxations and Indistinguishability in Counting Logics

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional isomorphism. We show that the levels of the Sherali--Adams (SA) hierarchy of linear programming relaxations applied to fractional isomorphism interleave in power with the levels of a well-known color-refinement heuristic for graph isomorphism called the Weisfeiler--Lehman algorithm, or, equivalently, with the levels of indistinguishability in a logic with counting quantifiers and a bounded number of variables. This tight connection has quite striking consequences. For example, it follows immediately from a deep result of Grohe in the context of logics with counting quantifiers that a fixed number of levels of SA suffice to determine isomorphism of planar and minor-free graphs. We also offer applications in both finite model theory and polyhedral combinatorics. First, we show that certain properties of graphs, such as that of having a flow circulation of a prescribed value, are definable in the infinitary logic with counting with a bounded number of variables. Second, we exploit a lower bound construction due to Cai, Fürer, and Immerman in the context of counting logics to give simple explicit instances that show that the SA relaxations of the vertex-cover and cut polytopes do not reach their integer hulls for up to $\Omega(n)$ levels, where $n$ is the number of vertices in the graph.

Simultaneous determination of gross alpha, gross beta and Ra-226 in natural water by liquid scintillation counting.

The determination of gross alpha, gross beta and 226Ra activity in natural waters is useful in a wide range of environmental studies. Furthermore, gross alpha and gross beta parameters are included in international legislation on the quality of drinking water [Council Directive 98/83/EC].1 In this work, a low-background liquid scintillation counter (Wallac, Quantulus 1220) was used to simultaneously determine gross alpha, gross beta and 226Ra activity in natural water samples. Sample preparation involved evaporation to remove 222Rn and its short-lived decay daughters. The evaporation process concentrated the sample ten-fold. Afterwards, a sample aliquot of 8 mL was mixed with 12 mL of Ultima Gold AB scintillation cocktail in low-diffusion vials. In this study, a theoretical mathematical model based on secular equilibrium conditions between 226Ra and its short-lived decay daughters is presented. The proposed model makes it possible to determine 226Ra activity from two measurements. These measurements also allow determining gross alpha and gross beta simultaneously. To validate the proposed model, spiked samples with different activity levels for each parameter were analysed. Additionally, to evaluate the model's applicability in natural water, eight natural water samples from different parts of Spain were analysed. The eight natural water samples were also characterised by alpha spectrometry for the naturally occurring isotopes of uranium (234U, 235U and 238U), radium (224Ra and 226Ra), 210Po and 232Th. The results for gross alpha and 226Ra activity were compared with alpha spectrometry characterization, and an acceptable concordance was obtained.

Optical Encryption using Photon-Counting Polarimetric Imaging

We present a polarimetric-based optical encoder for image encryption and verification. A system for generating random polarized vector keys based on a Mach-Zehnder configuration combined with translucent liquid crystal displays in each path of the interferometer is developed. Polarization information of the encrypted signal is retrieved by taking advantage of the information provided by the Stokes parameters. Moreover, photon-counting model is used in the encryption process which provides data sparseness and nonlinear transformation to enhance security. An authorized user with access to the polarization keys and the optical design variables can retrieve and validate the photon-counting plain-text. Optical experimental results demonstrate the feasibility of the encryption method.

Quantum-to-classical crossover in full counting statistics

The reduction of quantum scattering leads to the suppression of shot noise. In this Letter, we analyze the crossover from the quantum transport regime with universal shot noise to the classical regime where noise vanishes. By making use of the stochastic path integral approach, we find the statistics of transport and the transmission properties of a chaotic cavity as a function of a system parameter controlling the crossover. We identify three different scenarios of the crossover.

Bounding right-arm rotation distances

Rotation distance quantifies the difference in shape between two rooted binary trees of the same size by counting the minimum number of elementary changes needed to transform one tree to the other. We describe several types of rotation distance, and provide upper bounds on distances between trees with a fixed number of nodes with respect to each type. These bounds are obtained by relating each restricted rotation distance to the word length of elements of Thompson's group F with respect to different generating sets, including both finite and infinite generating sets.

Random graphs on surfaces

Counting labelled planar graphs, and typical properties of random labelled planar graphs, have received much attention recently. We start the process here of extending these investigations to graphs embeddable on any fixed surface S. In particular we show that the labelled graphs embeddable on S have the same growth constant as for planar graphs, and the same holds for unlabelled graphs. Also, if we pick a graph uniformly at random from the graphs embeddable on S which have vertex set {1, . . . , n}, then with probability tending to 1 as n → ∞, this random graph either is connected or consists of one giant component together with a few nodes in small planar components.

Visió per computador en una plataforma basada en un DSP

En aquest projecte s'usa el servidor de vídeo d'Axis Communications 242s IV, basat en el DSP TMS320DM642 de Texas Instruments, com a plataforma per a la implementació d'un algorisme d'extracció de fons i pel desenvolupament d'una solució completa de comptatge de persones per a càmera zenital. En el primer cas, s'ha optimitzat i comparat el rendiment de l'algorisme amb el d'una versió per a PC per a avaluar el DSP com a processador per a lamigració d'una aplicació completa de vídeovigilància. En el segon cas s'han integrat tots els components del servidor en el desenvolupament del comptador per avaluar la plataforma com a base per a solucions completes.