Hybrid modelling of individual movement and collective behaviour

Mathematical models of dispersal in biological systems are often written in terms of partial differential equations (PDEs) which describe the time evolution of population-level variables (concentrations, densities). A more detailed modelling approach is given by individual-based (agent-based) models which describe the behaviour of each organism. In recent years, an intermediate modelling methodology – hybrid modelling – has been applied to a number of biological systems. These hybrid models couple an individual-based description of cells/animals with a PDEmodel of their environment. In this chapter, we overview hybrid models in the literature with the focus on the mathematical challenges of this modelling approach. The detailed analysis is presented using the example of chemotaxis, where cells move according to extracellular chemicals that can be altered by the cells themselves. In this case, individual-based models of cells are coupled with PDEs for extracellular chemical signals. Travelling waves in these hybrid models are investigated. In particular, we show that in contrary to the PDEs, hybrid chemotaxis models only develop a transient travelling wave

Electromagnetic structure of the deuteron

Recent measurements of the deuteron electromagnetic structure functions A, B, and $T_{20}$ extracted from high energy elastic $ed$ scattering, and the cross sections and asymmetries extracted from high energy photodisintegration $\gamma+d\to n+p$, are reviewed and compared to theory. The theoretical calculations range from nonrelativistic and relativistic models using the traditional meson and baryon degrees of freedom, to effective field theories, to models based on the underlying quark and gluon degrees of freedom of QCD, including nonperturbative quark cluster models and perturbative QCD. We review what has been learned from these experiments, and discuss why elastic $ed$ scattering and photodisintegration seem to require very different theoretical approaches, even though they are closely related experimentally.Comment: review paper; 93 pages, 35 figure

The deuteron: a mini-review

We review some recent results for elastic electron deuteron scattering (deuteron form factors) and photodisintegration of the deuteron, with emphasis on the recent high energy data from Jefferson Laboratory (JLab).Comment: 14 pages, 11 figures, Invited talk given to the Conference on Mesons & Light Nuclei, held in Prague, Czech Republic, July 2- 6, 200

FNAS computational modeling

Numerical calculations of the electronic properties of liquid II-VI semiconductors, particularly CdTe and ZnTe were performed. The measured conductivity of these liquid alloys were modeled by assuming that the dominant temperature effect is the increase in the number of dangling bonds with increasing temperature. For low to moderate values of electron correlation, the calculated conductivity as a function of dangling bond concentration closely follows the measured conductivity as a function of temperature. Both the temperature dependence of the chemical potential and the thermal smearing in region of the Fermi surface have a large effect on calculated values of conductivity

Boson stars in the centre of galaxies?

We investigate the possible gravitational redshift values for boson stars with a self-interaction, studying a wide range of possible masses. We find a limiting value of z_lim \simeq 0.687 for stable boson star configurations. We can exclude the direct observation of boson stars. X-ray spectroscopy is perhaps the most interesting possibility

Permanent and separable aerospace tubing/ fitting evaluation program, volume 1

The tube fitting evaluation program was conducted to develop a standard overall test program including methods, procedures, and equipment as well as recommended test sequences for qualifying fitting/tubing assemblies. The program consisted of testing the MS flareless (separable) fitting and utilizing the results as baseline data from which all other fittings will be evaluated. Five separable designs and five permanent designs were tested in three sizes with two types of tubing materials. The basic design requirements were 4,000 psi operating pressure within the temperature range of minus 65 F to plus 450 F while also being compatible with 21-6-9 and titanium 3Al-2.5V tubing alloys

Connexin 40 promoter-based enrichment of embryonic stem cell-derived cardiovascular progenitor cells

Background: Pluripotent embryonic stem (ES) cells that can differentiate into functional cardiomyocytes as well as vascular cells in cell culture may open the door to cardiovascular cell transplantation. However, the percentage of ES cells in embryoid bodies (EBs) which spontaneously undergo cardiovascular differentiation is low (< 10%), making strategies for their specific labeling and purification indispensable. Methods: The human connexin 40 (Cx40) promoter was isolated and cloned in the vector pEGFP. The specificity of the construct was initially assessed in Xenopus embryos injected with Cx40-EGFP plasmid DNA. Stable Cx40-EGFP ES cell clones were differentiated and fluorescent cells were enriched manually as well as via fluorescence-activated cell sorting. Characterization of these cells was performed with respect to spontaneous beating as well as via RT-PCRs and immunofluorescent stainings. Results: Cx40-EGFP reporter plasmid injection led to EGFP fluorescence specifically in the abdominal aorta of frog tadpoles. After crude manual enrichment of highly Cx40-EGFP- positive EBs, the appearance of cardiac and vascular structures was increased approximately 3-fold. Immuno fluorescent stainings showed EGFP expression exclusively in vascular-like structures simultaneously expressing von Willebrand factor and in formerly beating areas expressing alpha-actinin. Cx40-EGFP-expressing EBs revealed significantly higher numbers of beating cardiomyocytes and vascular-like structures. Semiquantitative RT-PCRs confirmed an enhanced cardiovascular differentiation as shown for the cardiac markers Nkx2.5 and MLC2v, as well as the endothelial marker vascular endothelial cadherin. Conclusions: Our work shows the feasibility of specific labeling and purification of cardiovascular progenitor cells from differentiating EBs based on the Cx40 promoter. We provide proof of principle that the deleted CD4 (Delta CD4) surface marker-based method for magnetic cell sorting developed by our group will be ideally suitable for transference to this promoter. Copyright (c) 2008 S. Karger AG, Basel

Effects of Cavitation on Rotordynamic Force Matrices

When designing a turbomachine, particularly one which is to operate at high speed, it is important to be able to predict the fluid-induced forces, both steady and unsteady, acting on the various components of the machine. This paper concentrates on the fluid-induced rotordynamic forces acting upon the impeller and therefore on the bearings. Self-excited whirl, where the rotor moves away from and whirls along a trajectory eccentric to its undeflected position, can result from these fluid-induced forces. The purpose of the present work is to study the full range of these forces so that they can be included in any rotordynamic analysis at the design stage. To study the fluid-induced rotordynamic force on an impeller vibrating around its machine axis of rotation, an experiment in forced vibration was conducted. The prescribed whirl trajectory of the rotor is a circular orbit of a fixed radius. A rotating dynamometer mounted behind the rotor measures the force on the impeller. The force measured is a combination of a steady radial force due to volute asymmetries and an unsteady force due to the eccentric motion of the rotor. These measurements have been conducted over a full range of whirl/impeller speed ratios at different flow coefficients for various turbomachines including both centrifugal impellers aand axial inducers. A destabilizing force was observed over a region of positive whirl ratio. The range of flow conditions includes an examination of the effects of cavitation on the observed rotordynamic forces

Analytic determination of dynamical and mosaic length scales in a Kac glass model

We consider a disordered spin model with multi-spin interactions undergoing a glass transition. We introduce a dynamic and a static length scales and compute them in the Kac limit (long--but--finite range interactions). They diverge at the dynamic and static phase transition with exponents (respectively) -1/4 and -1. The two length scales are approximately equal well above the mode coupling transition. Their discrepancy increases rapidly as this transition is approached. We argue that this signals a crossover from mode coupling to activated dynamics.Comment: 4 pages, 4 eps figures. New version conform to the published on