Latitude and longitude vertical disparities

The literature on vertical disparity is complicated by the fact that several different definitions of the term “vertical disparity” are in common use, often without a clear statement about which is intended or a widespread appreciation of the properties of the different definitions. Here, we examine two definitions of retinal vertical disparity: elevation-latitude and elevation-longitude disparities. Near the fixation point, these definitions become equivalent, but in general, they have quite different dependences on object distance and binocular eye posture, which have not previously been spelt out. We present analytical approximations for each type of vertical disparity, valid for more general conditions than previous derivations in the literature: we do not restrict ourselves to objects near the fixation point or near the plane of regard, and we allow for non-zero torsion, cyclovergence, and vertical misalignments of the eyes. We use these expressions to derive estimates of the latitude and longitude vertical disparities expected at each point in the visual field, averaged over all natural viewing. Finally, we present analytical expressions showing how binocular eye position—gaze direction, convergence, torsion, cyclovergence, and vertical misalignment—can be derived from the vertical disparity field and its derivatives at the fovea.

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.

Compression of polymer brushes: quantitative comparison of self-consistent field theory with experiment

The self-consistent field theory (SCFT) prediction for the compression force between two semi-dilute polymer brushes is compared to the benchmark experiments of Taunton et al. [Nature, 1988, 332, 712]. The comparison is done with previously established parameters, and without any fitting parameters whatsoever. The SCFT provides a significant quantitative improvement over the classical strong-stretching theory (SST), yielding excellent quantitative agreement with the experiment. Contrary to earlier suggestions, chain fluctuations cannot be ignored for normal experimental conditions. Although the analytical expressions of SST provide invaluable aids to understanding the qualitative behavior of polymeric brushes, the numerical SCFT is necessary in order to provide quantitatively accurate predictions.

Diffraction from thermotropic copolyester molecules

Analytical expressions for the meridional scattering from highly oriented random copolyesters are presented. These procedures are utilised in developing the relationship of the features in the diffraction pattern to compositions and relative lengths of the constituent monomer units. The difference between the scattering patterns for random and block copolymers are discussed. The theory is applied to an example of a liquid crystal froming random copolyester.

Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

Cross-layer design for MIMO systems over spatially correlated and keyhole Nakagami-m fading channels

Cross-layer design is a generic designation for a set of efficient adaptive transmission schemes, across multiple layers of the protocol stack, that are aimed at enhancing the spectral efficiency and increasing the transmission reliability of wireless communication systems. In this paper, one such cross-layer design scheme that combines physical layer adaptive modulation and coding (AMC) with link layer truncated automatic repeat request (T-ARQ) is proposed for multiple-input multiple-output (MIMO) systems employing orthogonal space--time block coding (OSTBC). The performance of the proposed cross-layer design is evaluated in terms of achievable average spectral efficiency (ASE), average packet loss rate (PLR) and outage probability, for which analytical expressions are derived, considering transmission over two types of MIMO fading channels, namely, spatially correlated Nakagami-m fading channels and keyhole Nakagami-m fading channels. Furthermore, the effects of the maximum number of ARQ retransmissions, numbers of transmit and receive antennas, Nakagami fading parameter and spatial correlation parameters, are studied and discussed based on numerical results and comparisons. Copyright © 2009 John Wiley & Sons, Ltd.

The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the absence of shear, a quantity that is calculated routinely in existing drag parametrizations, the momentum flux becomes independent of the detailed shape of the orography. Unlike linear theory in the Ri → ∞ limit, the present calculations account for shear-induced amplification or reduction of the surface drag, and partial absorption of the wave momentum flux at critical levels. Profiles of the normalized momentum fluxes obtained using this model and a linear numerical model without the WKB approximation are evaluated and compared for two idealized wind profiles with directional shear, for different Richardson numbers (Ri). Agreement is found to be excellent for the first wind profile (where one of the wind components varies linearly) down to Ri = 0.5, while not so satisfactory, but still showing a large improvement relative to the Ri → ∞ limit, for the second wind profile (where the wind turns with height at a constant rate keeping a constant magnitude). These results are complementary, in the Ri > O(1) parameter range, to Broad’s generalization of the Eliassen–Palm theorem to 3D flow. They should contribute to improve drag parametrizations used in global weather and climate prediction models.

What is the shape of an air bubble on a liquid surface?

We have calculated the equilibrium shape of the axially symmetric meniscus along which a spherical bubble contacts a flat liquid surface, by analytically integrating the Young-Laplace equation in the presence of gravity, in the limit of large Bond numbers. This method has the advantage that it provides semi-analytical expressions for key geometrical properties of the bubble in terms of the Bond number. Results are in good overall agreement with experimental data and are consistent with fully numerical (Surface Evolver) calculations. In particular, we are able to describe how the bubble shape changes from hemispherical, with a shallow flat bottom, to lenticular, with a deeper, curved bottom, as the Bond number is decreased.

Contact angle of a hemispherical bubble: an analytical approach

We have calculated the equilibrium shape of the axially symmetric Plateau border along which a spherical bubble contacts a flat wall, by analytically integrating Laplace’s equation in the presence of gravity, in the limit of small Plateau border sizes. This method has the advantage that it provides closed-form expressions for the positions and orientations of the Plateau border surfaces. Results are in very good overall agreement with those obtained from a numerical solution procedure, and are consistent with experimental data. In particular we find that the effect of gravity on Plateau border shape is relatively small for typical bubble sizes, leading to a widening of the Plateau border for sessile bubbles and to a narrowing for pendant bubbles. The contact angle of the bubble is found to depend even more weakly on gravity.

An analytical method for capacity dimensioning of WCDMA with high speed wireless link

Capacity dimensioning is one of the key problems in wireless network planning. Analytical and simulation methods are usually used to pursue the accurate capacity dimensioning of wireless network. In this paper, an analytical capacity dimensioning method for WCDMA with high speed wireless link is proposed based on the analysis on relations among system performance and high speed wireless transmission technologies, such as H-ARQ, AMC and fast scheduling. It evaluates system capacity in closed-form expressions from link level and system level. Numerical results show that the proposed method can calculate link level and system level capacity for WCDMA system with HSDPA and HSUPA.

Analytical solutions of a minimal model of species migration in a bounded domain

A minimal model of species migration is presented which takes the form of a parabolic equation with boundary conditions and initial data. Solutions to the differential problem are obtained that can be used to describe the small- and large-time evolution of a species distribution within a bounded domain. These expressions are compared with the results of numerical simulations and are found to be satisfactory within appropriate temporal regimes. The solutions presented can be used to describe existing observations of nematode distributions, can be used as the basis for further work on nematode migration, and may also be interpreted more generally.

Computationally efficient expressions for the collision efficiency between electrically charged aerosol particles and cloud droplets

A multiple factor parametrization is described to permit the efficient calculation of collision efficiency (E) between electrically charged aerosol particles and neutral cloud droplets in numerical models of cloud and climate. The four-parameter representation summarizes the results obtained from a detailed microphysical model of E, which accounts for the different forces acting on the aerosol in the path of falling cloud droplets. The parametrization's range of validity is for aerosol particle radii of 0.4 to 10 mu m, aerosol particle densities of I to 2.0 g cm(-3), aerosol particle charges from neutral to 100 elementary charges and drop radii from 18.55 to 142 mu m. The parametrization yields values of E well within an order of magnitude of the detailed model's values, from a dataset of 3978 E values. Of these values 95% have modelled to parametrized ratios between 0.5 and 1.5 for aerosol particle sizes ranging between 0.4 and 2.0 mu m, and about 96% in the second size range. This parametrization speeds up the calculation of E by a factor of similar to 10(3) compared with the original microphysical model, permitting the inclusion of electric charge effects in numerical cloud and climate models.