Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation

A new mesh adaptivity algorithm that combines a posteriori error estimation with bubble-type local mesh generation (BLMG) strategy for elliptic differential equations is proposed. The size function used in the BLMG is defined on each vertex during the adaptive process based on the obtained error estimator. In order to avoid the excessive coarsening and refining in each iterative step, two factor thresholds are introduced in the size function. The advantages of the BLMG-based adaptive finite element method, compared with other known methods, are given as follows: the refining and coarsening are obtained fluently in the same framework; the local a posteriori error estimation is easy to implement through the adjacency list of the BLMG method; at all levels of refinement, the updated triangles remain very well shaped, even if the mesh size at any particular refinement level varies by several orders of magnitude. Several numerical examples with singularities for the elliptic problems, where the explicit error estimators are used, verify the efficiency of the algorithm. The analysis for the parameters introduced in the size function shows that the algorithm has good flexibility.

Capacity determination and expansion models for rail networks

This thesis focused upon the development of improved capacity analysis and capacity planning techniques for railways. A number of innovations were made and were tested on a case study of a real national railway. These techniques can reduce the time required to perform decision making activities that planners and managers need to perform. As all railways need to be expanded to meet increasing demands, the presumption that analytical capacity models can be used to identify how best to improve an existing network at least cost, was fully investigated. Track duplication was the mechanism used to expanding a network's capacity, and two variant capacity expansion models were formulated. Another outcome of this thesis is the development and validation of bi objective models for capacity analysis. These models regulate the competition for track access and perform a trade-off analysis. An opportunity to develop more general mulch-objective approaches was identified.

Melanoma cell colony expansion parameters revealed by approximate Bayesian computation

In vitro studies and mathematical models are now being widely used to study the underlying mechanisms driving the expansion of cell colonies. This can improve our understanding of cancer formation and progression. Although much progress has been made in terms of developing and analysing mathematical models, far less progress has been made in terms of understanding how to estimate model parameters using experimental in vitro image-based data. To address this issue, a new approximate Bayesian computation (ABC) algorithm is proposed to estimate key parameters governing the expansion of melanoma cell (MM127) colonies, including cell diffusivity, D, cell proliferation rate, λ, and cell-to-cell adhesion, q, in two experimental scenarios, namely with and without a chemical treatment to suppress cell proliferation. Even when little prior biological knowledge about the parameters is assumed, all parameters are precisely inferred with a small posterior coefficient of variation, approximately 2–12%. The ABC analyses reveal that the posterior distributions of D and q depend on the experimental elapsed time, whereas the posterior distribution of λ does not. The posterior mean values of D and q are in the ranges 226–268 µm2h−1, 311–351 µm2h−1 and 0.23–0.39, 0.32–0.61 for the experimental periods of 0–24 h and 24–48 h, respectively. Furthermore, we found that the posterior distribution of q also depends on the initial cell density, whereas the posterior distributions of D and λ do not. The ABC approach also enables information from the two experiments to be combined, resulting in greater precision for all estimates of D and λ.

Birth and expansion of innovation ecosystems: A case study of copper production

Despite the growing attention innovation ecosystems have received from scholars and practitioners, rather little is known about the crucial birth and expansion phases that these ecosystems experience. Through a single case in the complex product system (CoPS) environment, this paper investigates the development of an innovation ecosystem between 1980 and 2007. The findings demonstrate that the ecosystem’s birth phase includes sub-phases, namely, invention and start-up, where the ecosystem is reconfigured to find the appropriate form and the proper actors to satisfy the first customer’s requirements. Moreover, the duration of the expansion phase is found to be remarkably long, suggesting that within the CoPS setting, expansion may also include two or more sub-phases.

Homogeneous isotropic turbulence: large momentum expansion

High temperature expansion is an effective tool for studying second order phase transitions. With this in mind, we have looked at a high momentum expansion for homogeneous isotropic turbulence. Combining our results with those of the inertial range, we give another view of extended self-similarity (ESS).

Association between aneurysm shoulder stress and abdominal aortic aneurysm expansion: A longitudinal follow-up study

Background Aneurysm expansion rate is an important indicator of the potential risk of abdominal aortic aneurysm (AAA) rupture. Stress within the AAA wall is also thought to be a trigger for its rupture. However, the association between aneurysm wall stresses and expansion of AAA is unclear. Methods and Results Forty-four patients with AAAs were included in this longitudinal follow-up study. They were assessed by serial abdominal ultrasonography and computed tomography scans if a critical size was reached or a rapid expansion occurred. Patient-specific 3-dimensional AAA geometries were reconstructed from the follow-up computed tomography images. Structural analysis was performed to calculate the wall stresses of the AAA models at both baseline and final visit. A nonlinear large-strain finite element method was used to compute the wall-stress distribution. The relationship between wall stresses and expansion rate was investigated. Slowly and rapidly expanding aneurysms had comparable baseline maximum diameters (median, 4.35 cm [interquartile range, 4.12 to 5.0 cm] versus 4.6 cm [interquartile range, 4.2 to 5.0 cm]; P=0.32). Rapidly expanding AAAs had significantly higher shoulder stresses than slowly expanding AAAs (median, 300 kPa [interquartile range, 280 to 320 kPa] versus 225 kPa [interquartile range, 211 to 249 kPa]; P=0.0001). A good correlation between shoulder stress at baseline and expansion rate was found (r=0.71; P=0.0001). Conclusion A higher shoulder stress was found to have an association with a rapidly expanding AAA. Therefore, it may be useful for estimating the expansion of AAAs and improve risk stratification of patients with AAAs.

Transmission loss analysis of rectangular expansion chamber with arbitrary location of inlet/outlet by means of Green's functions

Transmission loss of a rectangular expansion chamber, the inlet and outlet of which are situated at arbitrary locations of the chamber, i.e., the side wall or the face of the chamber, are analyzed here based on the Green's function of a rectangular cavity with homogeneous boundary conditions. The rectangular chamber Green's function is expressed in terms of a finite number of rigid rectangular cavity mode shapes. The inlet and outlet ports are modeled as uniform velocity pistons. If the size of the piston is small compared to wavelength, then the plane wave excitation is a valid assumption. The velocity potential inside the chamber is expressed by superimposing the velocity potentials of two different configurations. The first configuration is a piston source at the inlet port and a rigid termination at the outlet, and the second one is a piston at the outlet with a rigid termination at the inlet. Pressure inside the chamber is derived from velocity potentials using linear momentum equation. The average pressure acting on the pistons at the inlet and outlet locations is estimated by integrating the acoustic pressure over the piston area in the two constituent configurations. The transfer matrix is derived from the average pressure values and thence the transmission loss is calculated. The results are verified against those in the literature where use has been made of modal expansions and also numerical models (FEM fluid). The transfer matrix formulation for yielding wall rectangular chambers has been derived incorporating the structural–acoustic coupling. Parametric studies are conducted for different inlet and outlet configurations, and the various phenomena occurring in the TL curves that cannot be explained by the classical plane wave theory, are discussed.

Phosphorus nutrition and tolerance of cotton to water stress: II. Water relations, free and bound water and leaf expansion rate

In previous experiments, increased leaf-Phosphorus (P) content with increasing P supply enhanced the individual leaf expansion and water content of fresh cotton leaves in a severely drying soil. In this paper, we report on the bulk water content of leaves and its components, free and bound water, along with other measures of plant water status, in expanding cotton leaves of various ages in a drying soil with different P concentrations. The bound water in living tissue is more likely to play a major role in tolerance to abiotic stresses by maintaining the structural integrity and/or cell wall extensibility of the leaves, whilst an increased amount of free water might be able to enhance solute accumulation, leading to better osmotic adjustment and tolerance to water stress, and maintenance of the volumes of sub-cellular compartments for expansive leaf growth. There were strong correlations between leaf-P%, leaf water (total, free and bound water) and leaf expansion rate (LER) under water stress conditions in a severely drying soil. Increased soil-P enhanced the uptake of P from a drying soil, leading to increased supply of osmotically active inorganic solutes to the cells in growing leaves. This appears to have led to the accumulation of free water and more bound water, ultimately leading to increased leaf expansion rates as compared to plants in low P soil under similar water stress conditions. The greater amount of bound and free water in the high-P plants was not necessarily associated with changes in cell turgor, and appears to have maintained the cell-wall properties and extensibility under water stressed conditions in soils that are nutritionally P-deficient.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Packed bed bioreactor for the isolation and expansion of placental-derived Mesenchymal Stromal Cells

Large numbers of Mesenchymal stem/stromal cells (MSCs) are required for clinical relevant doses to treat a number of diseases. To economically manufacture these MSCs, an automated bioreactor system will be required. Herein we describe the development of a scalable closed-system, packed bed bioreactor suitable for large-scale MSCs expansion. The packed bed was formed from fused polystyrene pellets that were air plasma treated to endow them with a surface chemistry similar to traditional tissue culture plastic. The packed bed was encased within a gas permeable shell to decouple the medium nutrient supply and gas exchange. This enabled a significant reduction in medium flow rates, thus reducing shear and even facilitating single pass medium exchange. The system was optimised in a small-scale bioreactor format (160 cm2) with murine-derived green fluorescent protein-expressing MSCs, and then scaled-up to a 2800 cm2 format. We demonstrated that placental derived MSCs could be isolated directly within the bioreactor and subsequently expanded. Our results demonstrate that the closed system large-scale packed bed bioreactor is an effective and scalable tool for large-scale isolation and expansion of MSCs.

Rapid Global Expansion of the Fungal Disease Chytridiomycosis into Declining and Healthy Amphibian Populations.

The fungal disease chytridiomycosis, caused by Batrachochytrium dendrobatidis, is enigmatic because it occurs globally in both declining and apparently healthy (non-declining) amphibian populations. This distribution has fueled debate concerning whether, in sites where it has recently been found, the pathogen was introduced or is endemic. In this study, we addressed the molecular population genetics of a global collection of fungal strains from both declining and healthy amphibian populations using DNA sequence variation from 17 nuclear loci and a large fragment from the mitochondrial genome. We found a low rate of DNA polymorphism, with only two sequence alleles detected at each locus, but a high diversity of diploid genotypes. Half of the loci displayed an excess of heterozygous genotypes, consistent with a primarily clonal mode of reproduction. Despite the absence of obvious sex, genotypic diversity was high (44 unique genotypes out of 59 strains). We provide evidence that the observed genotypic variation can be generated by loss of heterozygosity through mitotic recombination. One strain isolated from a bullfrog possessed as much allelic diversity as the entire global sample, suggesting the current epidemic can be traced back to the outbreak of a single clonal lineage. These data are consistent with the current chytridiomycosis epidemic resulting from a novel pathogen undergoing a rapid and recent range expansion. The widespread occurrence of the same lineage in both healthy and declining populations suggests that the outcome of the disease is contingent on environmental factors and host resistance.