Hartmut Schwandt

Trajectory extraction and density analysis of intersecting pedestrian flows from video recordings

Empirical data of human crowd behaviors are indispensable for the further understanding of pedestrian dynamics. In this paper, we describe a technique for the semi-automatic extraction of pedestrian trajectories from video recordings of human crowds. This method works on data obtained from an arbitrary observation angle and does not require additional information like the heights of the pedestrians etc. It is thus suitable for the analysis of data that have not been specifically prepared for this purpose, such as surveillance videos. We employ this method to analyze video recordings from a series of experiments that we conducted last year to reproduce pedestrian flows under controlled conditions. From these data we also estimate the continuous density of these pedestrian flows via a nearest-neighbor kernel density method which we argue is particularly suited for particle densities in general and human crowds consisting of multiple populations in particular.

A Unified Representation and Theory of Algebraic Additive Schwarz and Multisplitting Methods

We develop a unified representation of two well-known approaches for the solution of linear systems of equations by partitioning the original system into overlapping subsystems. The representation generalizes the algebraic form of both the additive Schwarz and multisplitting methods. In the new formulation we obtain convergence results similar to those known for multisplittings, considering one- and two-stage variants. We report on some numerical experiments on a CRAY T3D which suggest a slight preference for algebraic additive Schwarz methods over multisplitting methods. These experiments also demonstrate the efficiency of our approach in a parallel computing environment.

Rapid manufacturing techniques for the tissue engineering of human heart valves

Three-dimensional (3D) printing technologies have reached a level of quality that justifies considering rapid manufacturing for medical applications. Herein, we introduce a new approach using 3D printing to simplify and improve the fabrication of human heart valve scaffolds by tissue engineering (TE). Custom-made human heart valve scaffolds are to be fabricated on a selective laser-sintering 3D printer for subsequent seeding with vascular cells from human umbilical cords. The scaffolds will be produced from resorbable polymers that must feature a number of specific properties: the structure, i.e. particle granularity and shape, and thermic properties must be feasible for the printing process. They must be suitable for the cell-seeding process and at the same time should be resorbable. They must be applicable for implementation in the human body and flexible enough to support the full functionality of the valve. The research focuses mainly on the search for a suitable scaffold material that allows the implementation of both the printing process to produce the scaffolds and the cell-seeding process, while meeting all of the above requirements. Computer tomographic data from patients were transformed into a 3D data model suitable for the 3D printer. Our current activities involve various aspects of the printing process, material research and the implementation of the cell-seeding process. Different resorbable polymeric materials have been examined and used to fabricate heart valve scaffolds by rapid manufacturing. Human vascular cells attached to the scaffold surface should migrate additionally into the inner structure of the polymeric samples. The ultimate intention of our approach is to establish a heart valve fabrication process based on 3D rapid manufacturing and TE. Based on the computer tomographic data of a patient, a custom-made scaffold for a valve will be produced on a 3D printer and populated preferably by autologous cells. The long-term goal is to support the growth of a new valve by a 3D structure resorbed by the human body in the course of the growth process. Our current activities can be characterized as basic research in which the fundamental steps of the technical process and its feasibility are investigated.

Interval arithmetic methods for systems of nonlinear equations arising from discretizations of quasilinear elliptic and parabolic partial differential equations

A stability analysis is presented for staggered schemes for the governing equations of compressible flow. The method is based on Fourier analysis. The approximate nature of pressure-correction solution methods is taken into account.

Newton-like interval methods for large nonlinear systems of equations on vector computers

Abstract We describe algorithms for Newton-like interval methods on vector computers. These methods converge under relatively weak conditions to the solution of systems arising from discretizations of nonlinear elliptic PDE. The methods combine the ideas of Newton-like methods and fast solvers by using interval arithmetic tools.

An adaptive finite-volume method for a model of two-phase pedestrian flow

A flow composed of two populations of pedestrians moving in different directions is modeled by a two-dimensional system of convection-diffusion equations. An efficient simulation of the two-dimensional model is obtained by a finite-volume scheme combined with a fully adaptive multiresolution strategy. Numerical tests show the flow behavior in various settings of initial and boundary conditions, where different species move in countercurrent or perpendicular directions. The equations are characterized as hyperbolic-elliptic degenerate, with an elliptic region in the phase space, which in one space dimension is known to produce oscillation waves. When the initial data are chosen inside the elliptic region, a spatial segregation of the populations leads to pattern formation. The entries of the diffusion-matrix determine the stability of the model and the shape of the patterns.

Asynchronous parallel methods for enclosing solutions of nonlinear equations

We consider interval arithmetic based parallel methods for enclosing solutions of nonlinear systems of equations, where processors are allowed to proceed asynchronously. We present a general study on the convergence of asynchronous iterations in interval spaces and apply them to a variety of methods for the nonlinear equations case. The convergence results turn out to be very similar to those known for synchronous methods. Several practical examples on shared memory architectures are included. The asynchronous methods sometimes perform substantially better than their synchronous counterparts.

A study of step calculations in traffic cellular automaton models

We give some formal description for the cellular automaton (CA) models applied in the traffic simulation of vehicular and pedestrian dynamics in both one- and two-dimensional cases. In the two-dimensional case, we present a new solution for the step choice problem vmax > 1 on the local operational level, with the aim of projecting the intended step exactly onto the underlying geometry. This method can be used in combination with the more advanced modeling techniques on higher levels for better simulation results.

An interval arithmetic method for the solution of nonlinear systems of equations on a vector computer

Abstract We describe a vectorized algorithm for an interval arithmetic Newton-like method for a class of systems of nonlinear equations arising from discretizations of nonlinear elliptic PDE. This method converges to a solution under relatively weak conditions. It is founded on a combination of a Newton-like interval method and interval arithmetic ‘fast’ direct solver. In the present paper we focus our attention on aspects of the vectorization, in particular that of a simulation of an interval arithmetic and that of the direct solver.

On Measuring Pedestrian Density and Flow Fields in Dense as well as Sparse Crowds

In the framework of macroscopic human crowd models, pedestrian dynamics are described via local density and flow fields. In theory at least, these density and flow fields are often required to have a certain degree of regularity such as being smooth. In this paper, we describe a new method for the calculation of spatio-temporally smooth, locally defined density and flow fields from pedestrian trajectories. This method is based on kernel density estimation with variable bandwidth and—for a large range of scale—yields spatially averaged values close to the density or flow defined in the standard way.