Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series. The relevant condition, the analyticity at infinity of certain meromorphic functions within particular sectors, is significantly more concrete and easier to test than the previous criterion, based on the existence of admissible functions.

Dispersion of a point-source release of a passive scalar through an urban-like array for different wind directions

The dispersion of a point-source release of a passive scalar in a regular array of cubical, urban-like, obstacles is investigated by means of direct numerical simulations. The simulations are conducted under conditions of neutral stability and fully rough turbulent flow, at a roughness Reynolds number of Reτ = 500. The Navier–Stokes and scalar equations are integrated assuming a constant rate release from a point source close to the ground within the array. We focus on short-range dispersion, when most of the material is still within the building canopy. Mean and fluctuating concentrations are computed for three different pressure gradient directions (0◦ , 30◦ , 45◦). The results agree well with available experimental data measured in a water channel for a flow angle of 0◦ . Profiles of mean concentration and the three-dimensional structure of the dispersion pattern are compared for the different forcing angles. A number of processes affecting the plume structure are identified and discussed, including: (i) advection or channelling of scalar down ‘streets’, (ii) lateral dispersion by turbulent fluctuations and topological dispersion induced by dividing streamlines around buildings, (iii) skewing of the plume due to flow turning with height, (iv) detrainment by turbulent dispersion or mean recirculation, (v) entrainment and release of scalar in building wakes, giving rise to ‘secondary sources’, (vi) plume meandering due to unsteady turbulent fluctuations. Finally, results on relative concentration fluctuations are presented and compared with the literature for point source dispersion over flat terrain and urban arrays. Keywords Direct numerical simulation · Dispersion modelling · Urban array

From symmetry breaking to Poisson Point Process in 2D Voronoi Tessellations: the generic nature of hexagons

We bridge the properties of the regular triangular, square, and hexagonal honeycomb Voronoi tessellations of the plane to the Poisson-Voronoi case, thus analyzing in a common framework symmetry breaking processes and the approach to uniform random distributions of tessellation-generating points. We resort to ensemble simulations of tessellations generated by points whose regular positions are perturbed through a Gaussian noise, whose variance is given by the parameter α2 times the square of the inverse of the average density of points. We analyze the number of sides, the area, and the perimeter of the Voronoi cells. For all valuesα >0, hexagons constitute the most common class of cells, and 2-parameter gamma distributions provide an efficient description of the statistical properties of the analyzed geometrical characteristics. The introduction of noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α = 0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise withα <0.12. For all tessellations and for small values of α, we observe a linear dependence on α of the ensemble mean of the standard deviation of the area and perimeter of the cells. Already for a moderate amount of Gaussian noise (α >0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α >2, results converge to those of Poisson-Voronoi tessellations. The geometrical properties of n-sided cells change with α until the Poisson- Voronoi limit is reached for α > 2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established. This law allows for an easy link to the Lewis law for areas and agrees with exact asymptotic results. Finally, for α >1, the ensemble mean of the cells area and perimeter restricted to the hexagonal cells agree remarkably well with the full ensemble mean; this reinforces the idea that hexagons, beyond their ubiquitous numerical prominence, can be interpreted as typical polygons in 2D Voronoi tessellations.

Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

Numerical Methods for Stiff Two-Point Boundary Value Problems

We consider the two-point boundary value problem for stiff systems of ordinary differential equations. For systems that can be transformed to essentially diagonally dominant form with appropriate smoothness conditions, a priori estimates are obtained. Problems with turning points can be treated with this theory, and we discuss this in detail. We give robust difference approximations and present error estimates for these schemes. In particular we give a detailed description of how to transform a general system to essentially diagonally dominant form and then stretch the independent variable so that the system will satisfy the correct smoothness conditions. Numerical examples are presented for both linear and nonlinear problems.

Latching control of a point absorber

In this paper the authors investigate the use of optimal control techniques for improving the efficiency of the power conversion system in a point absorber wave power device. A simple mathematical model of the system is developed and an optimal control strategy for power generation is determined. They describe an algorithm for solving the problem numerically, provided the incident wave force is given. The results show that the performance of the device is significantly improved with the handwidth of the response being widened by the control strategy.

The importance of attractive three-point interaction in enantioselective surface chemistry: stereospecific adsorption of serine on the intrinsically chiral Cu{531} surface

Both enantiomers of serine adsorb on the intrinsically chiral Cu{531} surface in two different adsorption geometries, depending on the coverage. At saturation, substrate bonds are formed through the two oxygen atoms of the carboxylate group and the amino group (μ3 coordination), whereas at lower coverage, an additional bond is formed through the deprotonated β−OH group (μ4 coordination). The latter adsorption geometry involves substrate bonds through three side groups of the chiral center, respectively, which leads to significantly larger enantiomeric differences in adsorption geometries and energies compared to the μ3 coordination, which involves only two side groups. This relatively simple model system demonstrates, in direct comparison, that attractive interactions of three side groups with the substrate are much more effective in inducing strong enantiomeric differences in heterogeneous chiral catalyst systems than hydrogen bonds or repulsive interactions.

Comparison of different boundary layer surface schemes using single point micrometeorological field data

 In the last decade, a vast number of land surface schemes has been designed for use in global climate models, atmospheric weather prediction, mesoscale numerical models, ecological models, and models of global changes. Since land surface schemes are designed for different purposes they have various levels of complexity in the treatment of bare soil processes, vegetation, and soil water movement. This paper is a contribution to a little group of papers dealing with intercomparison of differently designed and oriented land surface schemes. For that purpose we have chosen three schemes for classification: i) global climate models, BATS (Dickinson et al., 1986; Dickinson et al., 1992); ii) mesoscale and ecological models, LEAF (Lee, 1992) and iii) mesoscale models, LAPS (Mihailović, 1996; Mihailović and Kallos, 1997; Mihailović et al., 1999) according to the Shao et al. (1995) classification. These schemes were compared using surface fluxes and leaf temperature outputs obtained by time integrations of data sets derived from the micrometeorological measurements above a maize field at an experimental site in De Sinderhoeve (The Netherlands) for 18 August, 8 September, and 4 October 1988. Finally, comparison of the schemes was supported applying a simple statistical analysis on the surface flux outputs.

10,000 years in the life of the river Wandle: excavations at the former Vinamul site, Butter Hill, Wallington

Archaeological excavations alongside the river Wandle in Wallington produced evidence of the environmental history and human exploitation of the area. The recovery of a large assemblage of struck flint provided information on the nature of the prehistoric activities represented, while a detailed environmental archaeological programme permitted an examination of both the local sediment successions and thus an opportunity to reconstruct the environmental history of the site. The site revealed a complex sedimentary sequence deposited in riverine conditions, commencing during the early Holocene (from c 10,000 years before present) and continuing through the late Holocene (c last 3000 years). Large flint nodules were washed by the river onto the site where they were procured and worked by Mesolithic and Bronze Age communities. Potentially usable nodules had been tested, and suitable pieces completely reduced, while the majority of useful flakes and blades had been removed for use elsewhere. Small numbers of retouched pieces, such as scrapers and piercers, indicate that domestic activities took place nearby. By the Saxon period the site had begun to stabilise, although it remained marshy and probably peripheral to habitation. Two pits from this period were excavated, one of which contained an antler pick. A small quantity of cereal grain also suggests that cultivated land lay in the vicinity of the site. During the 19th century a mill race was dug across the site, redirecting water from the river Wandle, which resulted in episodic flooding.

Source splitting via the point source method

We introduce a new algorithm for source identification and field splitting based on the point source method (Potthast 1998 A point-source method for inverse acoustic and electromagnetic obstacle scattering problems IMA J. Appl. Math. 61 119–40, Potthast R 1996 A fast new method to solve inverse scattering problems Inverse Problems 12 731–42). The task is to separate the sound fields uj, j = 1, ..., n of sound sources supported in different bounded domains G1, ..., Gn in from measurements of the field on some microphone array—mathematically speaking from the knowledge of the sum of the fields u = u1 + + un on some open subset Λ of a plane. The main idea of the scheme is to calculate filter functions , to construct uℓ for ℓ = 1, ..., n from u|Λ in the form We will provide the complete mathematical theory for the field splitting via the point source method. In particular, we describe uniqueness, solvability of the problem and convergence and stability of the algorithm. In the second part we describe the practical realization of the splitting for real data measurements carried out at the Institute for Sound and Vibration Research at Southampton, UK. A practical demonstration of the original recording and the splitting results for real data is available online.

Law of large numbers for super-brownian motions with a single point source

We investigate the super-Brownian motion with a single point source in dimensions 2 and 3 as constructed by Fleischmann and Mueller in 2004. Using analytic facts we derive the long time behavior of the mean in dimension 2 and 3 thereby complementing previous work of Fleischmann, Mueller and Vogt. Using spectral theory and martingale arguments we prove a version of the strong law of large numbers for the two dimensional superprocess with a single point source and finite variance.

Tobit estiamtion with unknown point of censoring with an application to milk market participation in the Ethiopian highlands

Data augmentation is a powerful technique for estimating models with latent or missing data, but applications in agricultural economics have thus far been few. This paper showcases the technique in an application to data on milk market participation in the Ethiopian highlands. There, a key impediment to economic development is an apparently low rate of market participation. Consequently, economic interest centers on the “locations” of nonparticipants in relation to the market and their “reservation values” across covariates. These quantities are of policy interest because they provide measures of the additional inputs necessary in order for nonparticipants to enter the market. One quantity of primary interest is the minimum amount of surplus milk (the “minimum efficient scale of operations”) that the household must acquire before market participation becomes feasible. We estimate this quantity through routine application of data augmentation and Gibbs sampling applied to a random-censored Tobit regression. Incorporating random censoring affects markedly the marketable-surplus requirements of the household, but only slightly the covariates requirements estimates and, generally, leads to more plausible policy estimates than the estimates obtained from the zero-censored formulation