From individual behaviour to an evaluation of the collective evolution of crowds along footbridges

This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real world problems is tested by considering the pedestrian traffic along footbridges, of interest for Structural and Transportation Engineering. The genuinely macroscopic quantitative description of the crowd flow directly matches the engineering need of bulk results. However, three issues beyond the sole modelling are of primary importance: the pedestrian inflow conditions, the numerical approximation of the equations for non trivial footbridge geometries, and the calibration of the free parameters of the model on the basis of in situ measurements currently available. These issues are discussed and a solution strategy is proposed.Comment: 23 pages, 10 figures in J. Engrg. Math., 201

PRECONDITIONERS AND TENSOR PRODUCT SOLVERS FOR OPTIMAL CONTROL PROBLEMS FROM CHEMOTAXIS

In this paper, we consider the fast numerical solution of an optimal control formulation of the Keller--Segel model for bacterial chemotaxis. Upon discretization, this problem requires the solution of huge-scale saddle point systems to guarantee accurate solutions. We consider the derivation of effective preconditioners for these matrix systems, which may be embedded within suitable iterative methods to accelerate their convergence. We also construct low-rank tensor-train techniques which enable us to present efficient and feasible algorithms for problems that are finely discretized in the space and time variables. Numerical results demonstrate that the number of preconditioned GMRES iterations depends mildly on the model parameters. Moreover, the low-rank solver makes the computing time and memory costs sublinear in the original problem size.Comment: 23 page

Continuum and discrete approach in modeling biofilm development and structure: a review

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions

Differential Models, Numerical Simulations and Applications

This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems

Color transformation modeling for printed images using interpolation based on barycentric coordinates

This document is a report on the research of a potentially superior method of color image transformation for producing rapid and accurate printed color output from a digitized color image. The primary objective is to reduce the complexities, inaccuracies, objectionable artifacts, and processing time common to current methods of color modeling. A new method of vector-corrected mathematical modeling combined with improved color space interpolation is studied. This achievement allows for rapid automatic closed-loop color-match calibration between image capture and output devices. Currently, digital image creation or manipulation systems rely on image proof printing which is slow and often of poor color fidelity or proprietary. The ideal system would provide optimum color reproduction fidelity and rapid proof printing at a low cost. Existing systems often rely on mathematical models for image con version for printing. These models are usually a bottleneck in the proofing process and are not accurate enough for many applica tions. Increasing their accuracy rapidly increases processing time to the point of impracticality well before graphic arts quality levels are achieved. A common solution to this problem in larger systems is a massive and tediously generated color look-up table based on actual measured print samples. This method is costly and does not readily accommodate printing process changes such as paper grade or ink color. Attempts to reduce the size of these look-up tables and the large quantity of required sample measurements have been disappointing. In this thesis, new methods will be reported which should allow practical small-system color proof printing with excellent color fidelity and rapid processing. By eliminating common problems associated with color space interpolation, these new methods make closed-loop control practical with a relatively small quantity of sample measurements which can be automatically printed, scanned, and incorporated into conversion processes

Modelling the Eddy Pattern in the harbour of Zeebrugge

Hydrodynamic