Splash wave and crown breakup after disc impact on a liquid surface

In this paper we analyze the impact of a circular disc on a free surface using experiments, potential flow numerical simulations and theory. We focus our attention both on the study of the generation and possible breakup of the splash wave created after the impact and on the calculation of the force on the disc. We have experimentally found that drops are only ejected from the rim located at the top part of the splash --giving rise to what is known as the crown splash-- if the impact Weber number exceeds a threshold value \Weber_{crit}\simeq 140. We explain this threshold by defining a local Bond number $Bo_{tip}$ based on the rim deceleration and its radius of curvature, with which we show using both numerical simulations and experiments that a crown splash only occurs when $Bo_{tip}\gtrsim 1$, revealing that the rim disrupts due to a Rayleigh-Taylor instability. Neglecting the effect of air, we show that the flow in the region close to the disc edge possesses a Weber-number-dependent self-similar structure for every Weber number. From this we demonstrate that \Bond_{tip}\propto\Weber, explaining both why the transition to crown splash can be characterized in terms of the impact Weber number and why this transition occurs for $We_{crit}\simeq 140$. Next, including the effect of air, we have developed a theory which predicts the time-varying thickness of the very thin air cushion that is entrapped between the impacting solid and the liquid. Our analysis reveals that gas critically affect the velocity of propagation of the splash wave as well as the time-varying force on the disc, $F_D$. The existence of the air layer also limits the range of times in which the self-similar solution is valid and, accordingly, the maximum deceleration experienced by the liquid rim, what sets the length scale of the splash drops ejected when We>\Weber_{crit}

The Site-Diluted Ising Model in Four Dimension

In the literature, there are five distinct, fragmented sets of analytic predictions for the scaling behaviour at the phase transition in the random-site Ising model in four dimensions. Here, the scaling relations for logarithmic corrections are used to complete the scaling pictures for each set. A numerical approach is then used to confirm the leading scaling picture coming from these predictions and to discriminate between them at the level of logarithmic corrections.Comment: 15 pages, 5 ps figures. Accepted for publication in Phys. Rev.

A Study of Neo-Austrian Economics using an Artificial Stock Market

An agent-based artificial financial market (AFM) is used to study market efficiency and learning in the context of the Neo-Austrian economic paradigm. Efficiency is defined in terms of the 'excess' profits associated with different trading strategies, where excess for an active trading strategy is defined relative to a dynamic buy and hold benchmark. We define an Inefficiency matrix that takes into account the difference in excess profits of one trading strategy versus another ('signal') relative to the standard error of those profits ('noise') and use this statistical measure to gauge the degree of market efficiency. A one-parameter family of trading strategies is considered, the value of the parameter measuring the relative 'informational' advantage of one strategy versus another. Efficiency is then investigated in terms of the composition of the market defined in terms of the relative proportions of traders using a particular strategy and the parameter values associated with the strategies. We show that markets are more efficient when informational advantages are small (small signal) and when there are many coexisting signals. Learning is introduced by considering 'copycat' traders that learn the relative values of the different strategies in the market and copy the most successful one. We show how such learning leads to a more informationally efficient market but can also lead to a less efficient market as measured in terms of excess profits. It is also shown how the presence of exogeneous information shocks that change trader expectations increases efficiency and complicates the inference problem of copycats.Neoaustrian economics, Market efficiency, Artificial financial market, Learning, Adaptation

H2 in the interstitial channels of nanotube bundles

The equation of state of H2 adsorbed in the interstitial channels of a carbon nanotube bundle has been calculated using the diffusion Monte Carlo method. The possibility of a lattice dilation, induced by H2 adsorption, has been analyzed by modeling the cohesion energy of the bundle. The influence of factors like the interatomic potentials, the nanotube radius and the geometry of the channel on the bundle swelling is systematically analyzed. The most critical input is proved to be the C-H2 potential. Using the same model than in planar graphite, which is expected to be also accurate in nanotubes, the dilation is observed to be smaller than in previous estimations or even inexistent. H2 is highly unidimensional near the equilibrium density, the radial degree of freedom appearing progressively at higher densities.Comment: Accepted for publication in PR

The antiderivative understanding by students in the first university courses

ABSTARCT: In this article, we present the results of a questionnaire designed to evaluate college students’ understanding of the antiderivative. Specifically, by civil engineering students when answering the questionnaire’ tasks, in order to identify and characterize the meanings on the antiderivative that are mobilized by them. In order to analyse the answers given, we used some theoretical and methodological notions provided by the theoretical model known as the Onto-Semiotic Approach (OSA) of mathematics cognition and instruction. The results show knowledge of antiderivative by the Civil Engineering students. Furthermore, the comparison between the mathematical activity of students provides information that allows concluding that the meanings that they mobilized might be shared among their communities

Universal Amplitude Ratios in the Ising Model in Three Dimensions

We use a high-precision Monte Carlo simulation to determine the universal specific-heat amplitude ratio A+/A- in the three-dimensional Ising model via the impact angle \phi of complex temperature zeros. We also measure the correlation-length critical exponent \nu from finite-size scaling, and the specific-heat exponent \alpha through hyperscaling. Extrapolations to the thermodynamic limit yield \phi = 59.2(1.0) degrees, A+/A- = 0.56(3), \nu = 0.63048(32) and \alpha = 0.1086(10). These results are compatible with some previous estimates from a variety of sources and rule out recently conjectured exact values.Comment: 17 pages, 5 figure

Geopolímeros de tipo binario basados en una puzolana natural y escoria siderúrgica de alto horno

This study describes the synthesis at ambient temperature (25±3 °C) of binary geopolymer systems based on natural volcanic pozzolan and granulated blast furnace slag. Na2SiO3 and NaOH were used as alkaline activators. The effects of the SiO2/Al2O3, Na2O/Al2O3 ratio and the amount of slag added (from 0 to 30%) on the reaction kinetics, compressive strength and microstructure of the final product were studied. To characterise the geopolymer pastes, techniques such as X-ray diffraction (XRD), infrared spectroscopy (FTIR) and scanning electron microscopy (SEM) were used. The results indicate the possibility of obtaining a geopolymer cement with a compressive strength of up to 48.11 MPa after 28 days of curing at ambient temperature whose characteristics are comparable to those of commercial portland cement.Este trabajo describe la síntesis a temperatura ambiente (25±3 °C) de sistemas geopoliméricos de tipo binario basados en una puzolana natural de origen volcánico y escoria siderúrgica de alto horno usando activadores alcalinos basados en la combinación de Na2SiO3 y NaOH. Se estudió el efecto de la relación SiO2/Al2O3, Na2O/Al2O3 y la cantidad de escoria adicionada en niveles entre el 0 y 30% sobre la cinética de reacción, la resistencia a la compresión y la microestructura del producto final. Para la caracterización de las pastas geopoliméricas se utilizaron técnicas como difracción de rayos X (DRX), espectroscopia infrarroja (FTIR) y microscopia electrónica de barrido (MEB). Los resultados conseguidos revelan la posibilidad de obtener un cementante geopolimérico con una resistencia a la compresión de hasta 48,11 MPa a los 28 días de curado a temperatura ambiente cuyas características son comparables a las de un cemento portland comercial

Control de Posición e Inercial de Plataforma de Dos Grados de Libertad

ResumenEste artículo presenta una aplicación de control para la estabilización inercial de una plataforma de dos grados de libertad (2-GDL). El objetivo de la aplicación es, en primer lugar, controlar las posiciones angulares de la plataforma en ausencia de perturbaciones inerciales y en segundo lugar, controlar las velocidades de la plataforma medidas respecto a ejes inerciales independientemente de las perturbaciones a las que se ve sometida. Con respecto al primer objetivo, se propone una estrategia de control de conmutación con el fin de reducir los efectos del rozamiento que es la principal causa del comportamiento no deseado. Respecto al segundo objetivo, se propone un control con estructura en cascada para conseguir las especificaciones deseadas. Se presentan resultados de simulación y experimentales sobre una plataforma que ponen de manifiesto la bondad de los controladores

Self-Averaging in the Three Dimensional Site Diluted Heisenberg Model at the critical point

We study the self-averaging properties of the three dimensional site diluted Heisenberg model. The Harris criterion \cite{critharris} states that disorder is irrelevant since the specific heat critical exponent of the pure model is negative. According with some analytical approaches \cite{harris}, this implies that the susceptibility should be self-averaging at the critical temperature ($R_\chi=0$). We have checked this theoretical prediction for a large range of dilution (including strong dilution) at critically and we have found that the introduction of scaling corrections is crucial in order to obtain self-averageness in this model. Finally we have computed critical exponents and cumulants which compare very well with those of the pure model supporting the Universality predicted by the Harris criterion.Comment: 11 pages, 11 figures, 14 tables. New analysis (scaling corrections in the g2=0 scenario) and new numerical simulations. Title and conclusions chang