Equilibria of biological aggregations with nonlocal repulsive-attractive interactions

We consider the aggregation equation $\rho_{t}-\nabla\cdot(\rho\nabla K\ast\rho) =0$ in $\mathbb{R}^{n}$, where the interaction potential $K$ incorporates short-range Newtonian repulsion and long-range power-law attraction. We study the global well-posedness of solutions and investigate analytically and numerically the equilibrium solutions. We show that there exist unique equilibria supported on a ball of $\mathbb{R}^n$. By using the method of moving planes we prove that such equilibria are radially symmetric and monotone in the radial coordinate. We perform asymptotic studies for the limiting cases when the exponent of the power-law attraction approaches infinity and a Newtonian singularity, respectively. Numerical simulations suggest that equilibria studied here are global attractors for the dynamics of the aggregation model

Reverse undercompressive shock structures in driven thin film flow

We show experimental evidence of a new structure involving an undercompressive and reverse undercompressive shock for draining films driven by a surface tension gradient against gravity. The reverse undercompressive shock is unstable to transverse perturbations while the leading undercompressive shock is stable. Depending on the pinch-off film thickness, as controlled by the meniscus, either a trailing rarefaction wave or a compressive shock separates from the reverse undercompressive shock

"Marginal pinching" in soap films

We discuss the behaviour of a thin soap film facing a frame element: the pressure in the Plateau border around the frame is lower than the film pressure, and the film thins out over a certain distance lambda(t), due to the formation of a well-localized pinched region of thickness h(t) and extension w(t). We construct a hydrodynamic theory for this thinning process, assuming a constant surface tension: Marangoni effects are probably important only at late stages, where instabilitites set in. We find lambda(t) ~ t^{1/4}, and for the pinch dimensions h(t) ~ t^{-1/2}$ and w(t) ~ t^{-1/4}. These results may play a useful role for the discussion of later instabilitites leading to a global film thinning and drainage, as first discussed by K. Mysels under the name ``marginal regeneration''.Comment: 7 pages, 2 figure

Decay rates for a class of diffusive-dominated interaction equations

We analyse qualitative properties of the solutions to a mean-field equation for particles interacting through a pairwise potential while diffusing by Brownian motion. Interaction and diffusion compete with each other depending on the character of the potential. We provide sufficient conditions on the relation between the interaction potential and the initial data for diffusion to be the dominant term. We give decay rates of Sobolev norms showing that asymptotically for large times the behavior is then given by the heat equation. Moreover, we show an optimal rate of convergence in the $L^1$-norm towards the fundamental solution of the heat equation.Comment: 22 page

Scaling dependence on the fluid viscosity ratio in the selective withdrawal transition

In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above a two-fluid interface. At sufficiently low withdrawal rates, Q, the interface forms a steady state hump and only the upper fluid is withdrawn. When Q is increased (or S decreased), the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming a thin steady-state spout. Near this transition the hump curvature becomes very large and displays power-law scaling behavior. This scaling allows for steady-state hump profiles at different flow rates and tube heights to be scaled onto a single similarity profile. I show that the scaling behavior is independent of the viscosity ratio.Comment: 33 Pages, 61 figures, 1 tabl

μ\mu-ee conversion in nuclei and Z′^\prime physics

Together with the existence of new neutral gauge bosons, models based on extended gauge groups (rank $> 4$) often predict also new charged fermions. A mixing of the known fermions with new states with {\it exotic} weak-isospin assignments (left-handed singlets and right-handed doublets) will induce tree level flavour changing neutral interactions mediated by $Z$ exchange, while if the mixing is only with new states with {\it ordinary} weak-isospin assignments, the flavour changing neutral currents are mainly due to the exchange of the lightest new neutral gauge boson $Z^\prime$. We show that the present experimental limits on $\mu-e$ conversion in nuclei give a nuclear-model-independent bound on the $Z$-$e$-$\mu$ vertex which is twice as strong as that obtained from $\mu\to e e e$. In the case of E$_6$ models these limits provide quite stringent constraints on the $Z^\prime$ mass and on the $Z-Z^\prime$ mixing angle. We point out that the proposed experiments to search for $\mu-e$ conversion in nuclei have good chances to find evidence of lepton flavour violation, either in the case that new exotic fermions are present at the electroweak scale, or if a new neutral gauge boson $Z^\prime$ of E$_6$ origin lighter than a few TeV exists.Comment: Plain Tex, 24 pages, + 2 PostScript figure appended after \bye (and available upon request), UM-TH 93--08, FTUV 93-1

Responsible Research and Innovation in Science Education: the IRRESISTIBLE Project

The EU funded IRRESISTIBLE-project (Project Coordinator: Jan Apotheker, University of Groningen, Netherlands) develop activities designed to foster the involvement of high school and elementary students and the public in Responsible Research and Innovation (RRI). In the project, awareness about RRI is raised in two ways: increasing content knowledge about research by bringing topics of cutting edge research into the program; fostering a discussion among the students on RRI issues about the topics that are introduced. Responsible Research and Innovation focuses on six key issues: Engagement, Gender equality, Science education, Ethics, including societal relevance and acceptability of research and innovation outcomes , Open access, Governance. The project combines formal and informal teaching to familiarize schoolchildren with science. Sixteen partners in ten countries are involved and coordinated by Science LinX. Each participants will establish a community of learners (CoL). The communities include school teachers together with university experts in the field of science communication and science centre staff. Each CoL will develop materials that the teachers will use at their own schools and students will develop an exhibit for a science centre in their own country. Once they have completed their teaching module, the teachers will each train five colleagues, in using the developed modules from the first year. Ultimately, this project will train almost ten thousand pupils to consider the social impact of scientific research

Adaptive Vaccination Strategies to Mitigate Pandemic Influenza: Mexico as a Case Study

Background We explore vaccination strategies against pandemic influenza in Mexico using an age-structured transmission model calibrated against local epidemiological data from the Spring 2009 A(H1N1) pandemic. Methods and Findings In the context of limited vaccine supplies, we evaluate age-targeted allocation strategies that either prioritize youngest children and persons over 65 years of age, as for seasonal influenza, or adaptively prioritize age groups based on the age patterns of hospitalization and death monitored in real-time during the early stages of the pandemic. Overall the adaptive vaccination strategy outperformed the seasonal influenza vaccination allocation strategy for a wide range of disease and vaccine coverage parameters. Conclusions This modeling approach could inform policies for Mexico and other countries with similar demographic features and vaccine resources issues, with regard to the mitigation of the S-OIV pandemic. We also discuss logistical issues associated with the implementation of adaptive vaccination strategies in the context of past and future influenza pandemics