We consider scattering and transport in interacting quantum wires that are connected to leads. Such a setup can be represented by a minimal model of interacting fermions with inhomogeneities in the form of sudden changes in interaction strength and/or velocity. The inhomogeneities generally cause relevant backscattering, so it is a priori unclear if a perfectly ballistic quantum wire can exist in the low temperature limit. We are able to identify such a perfectly conducting fixed point even for large abrupt changes, which in the considered model corresponds to a velocity matching condition. The general position dependent Green's function is calculated in the presence of a sudden change, which is confirmed numerically with high accuracy. The exact form of the interference pattern in the form of density oscillations around inhomogeneities can be used to estimate the effective strength of local backscattering sources.Comment: 5 pages, 3 figures. Published version. For more information and the latest version see http://www.physik.uni-kl.de/eggert/papers/index.htm

In this article, an evacuation model describing the egress in case of danger is considered. The underlying evacuation model is based on continuous network flows, while the spread of some gaseous hazardous material relies on an advection-diffusion equation. The contribution of this work is twofold. First, we introduce a continuous model coupled to the propagation of hazardous material where special cost functions allow for incorporating the predicted spread into an optimal planning of the egress. Optimality can thereby be understood with respect to two different measures: fastest egress and safest evacuation. Since this modeling approach leads to a pde/ode-restricted optimization problem, the continuous model is transferred into a discrete network flow model under some linearity assumptions. Second, it is demonstrated that this reformulation results in an efficient algorithm always leading to the global optimum. A computational case study shows benefits and drawbacks of the models for different evacuation scenarios.

No abstract

We studied a dataset of care episodes in a regional Swedish hospital system. We followed how 2,314,477 patients moved between 8,507 units (hospital wards and outpatient clinics) over seven years. The data also included information on the date when patients tested positive with methicillin resistant Staphylococcus aureus. To simplify the complex flow of patients, we represented it as a network of units, where two units were connected if a patient moved from one unit to another, without visiting a third unit in between. From this network, we characterized the typical network position of units with a high prevalence of methicillin resistant Staphylococcus aureus, and how the patient's location in the network changed upon testing positive. On average, units with medium values of the analyzed centrality measures had the highest average prevalence. We saw a weak effect of the hospital system's response to the patient testing positive -after a positive test, the patient moved to units with a lower centrality measured as degree (i.e. number of links to other units) and in addition, the average duration of the care episodes became longer. The network of units was too random to be a strong predictor of the presence of methicillin resistant Staphylococcus aureus -would it be more regular, one could probably both identify and control outbreaks better. The migration of the positive patients with within the healthcare system, however, helps decreasing the outbreak sizes.

No abstract