Using an analytical model to design liquid crystal microlenses

We have developed new analytical expressions for designing liquid crystal (LC) microlenses. These equations are based on a novel equivalent electric circuit and can be used to create an optimum design for the LC lenses in which the lens diameter ranges from a few micrometers to several millimeters. Thus far, only experimental studies have been conducted on the LC lenses. The analytical expressions developed in this letter depend on various manufacturing parameters and can be used to design lenses with specific focal lengths and a parabolic phase profile. The required driving scheme (modal or hole-patterned) can be predicted. The LC microlenses were manufactured and electrooptically characterized: the measurements were compared using an analytical approach.

A three-dimensional dynamical model of Amundsenisen icefield, Svalbard.

Amundsenisen is an ice field, 80 km2 in area, located in Southern Spitsbergen, Svalbard. Radio-echo sounding measurements at 20 MHz show high intensity returns from a nearly flat basal reflector at four zones, all of them with ice thickness larger than 500m. These reflections suggest possible subglacial lakes. To determine whether basal liquid water is compatible with current pressure and temperature conditions, we aim at applying a thermo mechanical model with a free boundary at the bed defined as solution of a Stefan problem for the interface ice-subglaciallake. The complexity of the problem suggests the use of a bi-dimensional model, but this requires that well-defined flowlines across the zones with suspected subglacial lakes are available. We define these flow lines from the solution of a three-dimensional dynamical model, and this is the main goal of the present contribution. We apply a three-dimensional full-Stokes model of glacier dynamics to Amundsenisen icefield. We are mostly interested in the plateau zone of the icefield, so we introduce artificial vertical boundaries at the heads of the main outlet glaciers draining Amundsenisen. At these boundaries we set velocity boundary conditions. Velocities near the centres of the heads of the outlets are known from experimental measurements. The velocities at depth are calculated according to a SIA velocity-depth profile, and those at the rest of the transverse section are computed following Nye’s (1952) model. We select as southeastern boundary of the model domain an ice divide, where we set boundary conditions of zero horizontal velocities and zero vertical shear stresses. The upper boundary is a traction-free boundary. For the basal boundary conditions, on the zones of suspected subglacial lakes we set free-slip boundary conditions, while for the rest of the basal boundary we use a friction law linking the sliding velocity to the basal shear stress,in such a way that, contrary to the shallow ice approximation, the basal shear stress is not equal to the basal driving stress but rather part of the solution.

Experimental analysis of the breakage of a liquid bridge under microgravity conditions

The experimental results obtained in experiment “STACO” made on board the Spacelab D-2 are re-visited, with image-analysis tools not then available. The configuration consisted of a liquid bridge between two solid supporting discs. An expected breakage occurred during the experiment. The recorded images are analysed and the measured behaviour compared with the results of a three dimensional model of the liquid dynamics, obtaining a much better fit than with linear models

Control rod drop surveillance using two friction coefficients

In the case of large burnup, a control rod (CR) guide tube in the pressurized water reactor of a commercial nuclear power plant might bend. As a consequence, a CR drop experiment may indicate an event of a CR partially inserted and whether the CR should be deemed inoperable. Early prevention of such an event can be achieved by measuring two friction coefficients: the hydraulic coefficient and the sliding coefficient. The hydraulic coefficient hardly changes, so that the curvature of the guide tube can only be detected thanks to a variation of the sliding coefficient. A simple model for the CR drop is established and validated with CR drop experiments. If tmx denotes the instant of CR maximum velocity, a linear relationship between (tmx)_2 and the sliding coefficient is found.

The interurban DRAG-Spain model: the main factors of influence on road accidents in Spain

This paper presents the results of applying DRAG methodology to the identification of the main factors of influence on the number of injury and fatal accidents occurring on Spain’s interurban network. Nineteen independent variables have been included in the model grouped together under ten categories: exposure, infrastructure, weather, drivers, economic variables, vehicle stock, surveillance, speed and legislative measures. Highly interesting conclusions can be reached from the results on the basis of the different effects of a single variable on each of the accident types according to severity. The greatest influence revealed by the results is exposure, which together with inexperienced drivers, speed and an ageing vehicle stock, have a negative effect, while the increased surveillance on roads, the improvement in the technological features of vehicles and the proportion of high capacity networks have a positive effect, since the results obtained show a significant drop in accidents.

A new hard-particle model for anisotropic fluids

We report a new hard-particle model system consisting of hard cylinders, we have determined the geometrical conditions that let us know whether or not two given cylinders overlap. In addition we have carried out Monte Carlo simulations sampling the canonical ensemble on this system, the numerical results indicate that this system exhibits mesomorphic behaviour.

Optically Induced Modulation of a Laser Beam in Nematic Liquid Crystals Structures

In this paper we report the experimental results obtained when an He-Ne laser beam crosses an MBBA homeotropic sandwich structure and is modulated by the influence of another laser beam, in our case an Ar+ laser, crossing through the same region. We extend some results previously reported by us1 2 concerning the influence of the ratio of the diameters of the laser beams on the modulation characteristics. A theoretical model, based on the one reported in Ref6 , shows good agreement with the experimental results. If the Ar+ laser is intensity chopped, the resulting He-Ne diffracted image is also intensity modulated. The highest frequency observed has been 500 p. p. s.

Increasing the accuracy of positive displacement meters for the measurement of volume in liquid hydrocarbon logistics

Accuracy in the liquid hydrocarbons custody transfer is mandatory because it has a great economic impact. By far the most accurate meter is the positive displacement (PD) meter. Increasing such an accuracy may adversely affect the cost of the custody transfer, unless simple models are developed in order to lower the cost, which is the purpose of this work. PD meter consists of a fixed volume rotating chamber. For each turn a pulse is counted, hence, the measured volume is the number of pulses times the volume of the chamber. It does not coincide with the real volume, so corrections have to be made. All the corrections are grouped by a meter factor. Among corrections highlights the slippage flow. By solving the Navier-Stokes equations one can find an analytical expression for this flow. It is neither easy nor cheap to apply straightforward the slippage correction; therefore we have made a simple model where slippage is regarded as a single parameter with dimension of time. The model has been tested for several PD meters. In our careful experiments, the meter factor grows with temperature at a constant pace of 8?10?5?ºC?1. Be warned

The influence of axial microgravity on the breakage of axisymmetric slender liquid bridges

The dynamics of inviscid, axisymmetric liquid bridges permits a simplified treatment if the bridge is long enough. Under such condition the evolution of the liquid zone is satisfactorily explained through a non-linear one-dimensional model. In the case of breaking, the one-dimensional model fails when the neck radius of the liquid column is close to zero; however, the model allows the calculation of the time variation of the liquid-bridge interface as well as of the fluid velocity field and, because the last part of the evolution is not needed, the overall results such as the breaking time and the volume of each of the two drops resulting after breakage can be calculated. In this paper numerical results concerning the behavior of clinical liquid bridges subjected to a small axial gravitational field are presented.

Numerical and experimental study of the dynamics of axisymmetric slender liquid bridges

A one-dimensional inviscid slice model has been used to study numerically the influence of axial microgravity on the breaking of liquid bridges having a volume close to that of gravitationless minimum volume stability limit. Equilibrium shapes and stability limits have been obtained as well as the dependence of the volume of the two drops formed after breaking on both the length and the volume of the liquid bridge. The breaking process has also been studied experimentally. Good agreement has been found between theory and experiment for neutrally buoyant systems

One-dimensional linear analysis of the liquid injection or removal in a liquid bridge

The filling-withdrawal process of a long liquid bridge is analyzed using a one-dimensional linearized model for the dynamics of the liquid column. To carry out this study, a well-known standard operational method (Laplace transform) has been used, and time variation of both liquid velocity field and interface shape are obtained.

Axisymmetric long liquid bridges in a time-dependent microgravity field

This paper deals with the dynamics of liquid bridges when subjected to an oscillatory microgravity field. The analysis has been performed by using a one-dimensional slice model, already used in liquid bridge problems, which allows to calculate not only the resonance frequencies of a wide range of such fluid configurations but also the dependence of the dynamic response of the liquid bridge on the frequency on the imposed perturbations. Theoretical results are compared with experimental ones obtained aboard Spacelab-Dl, the agreement between theoretical and experimental results being satisfactory

Disjoining pressure and the film-height-dependent surface tension of thin liquid films: New insight from capillary wave fluctuations

In this paper we review simulation and experimental studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial Hamiltonian Model. We discuss recent simulation results that reveal a film-height-dependent surface tension not accounted for in the classical Interfacial Hamiltonian Model. We show how this observation may be explained bottom-up from sound principles of statistical thermodynamics and discuss some of its implications

A simple mathematical model that describes the growth of the area and the number of total and viable cells in yeast colonies

We propose a model, based on the Gompertz equation, to describe the growth of yeasts colonies on agar medium. This model presents several advantages: (i) one equation describes the colony growth, which previously needed two separate ones (linear increase of radius and of the squared radius); (ii) a similar equation can be applied to total and viable cells, colony area or colony radius, because the number of total cells in mature colonies is proportional to their area; and (iii) its parameters estimate the cell yield, the cell concentration that triggers growth limitation and the effect of this limitation on the specific growth rate. To elaborate the model, area, total and viable cells of 600 colonies of Saccharomyces cerevisiae, Debaryomyces fabryi, Zygosaccharomyces rouxii and Rhodotorula glutinis have been measured. With low inocula, viable cells showed an initial short exponential phase when colonies were not visible. This phase was shortened with higher inocula. In visible or mature colonies, cell growth displayed Gompertz-type kinetics. It was concluded that the cells growth in colonies is similar to liquid cultures only during the first hours, the rest of the time they grow, with near-zero specific growth rates, at least for 3 weeks.

Stability limits of minimum volume and breaking axisymmetric liquid bridges between unequal disks

This paper deals with the stability limits of minimum volume and the breaking of axisymmetric liquid columns held by capillary forces between two concentric,circular solid disk of different radii. The problem has been analyzed both theoreti-cally and experimentally. A theoretical analysis concerning the breaking of liquid bridges has been performed by using a one-dimensional slice model already used in liquid bridge problems. Experiments have been carried out by using milli-metric liquid bridges, and minimum volume stability limits as well as the volumes of the drops resulting after breaking have been measured for a large number of liquid bridge configurations. Experimental results being in agreement with theoretical prediction.