Min-oscillations in Escherichia coli induced by interactions of membrane-bound proteins

During division it is of primary importance for a cell to correctly determine the site of cleavage. The bacterium Escherichia coli divides in the center, producing two daughter cells of equal size. Selection of the center as the correct division site is in part achieved by the Min-proteins. They oscillate between the two cell poles and thereby prevent division at these locations. Here, a phenomenological description for these oscillations is presented, where lateral interactions between proteins on the cell membrane play a key role. Solutions to the dynamic equations are compared to experimental findings. In particular, the temporal period of the oscillations is measured as a function of the cell length and found to be compatible with the theoretical prediction.Comment: 17 pages, 5 figures. Submitted to Physical Biolog

Persistent quantum interfering electron trajectories

The emission of above-ionization-threshold harmonics results from the recombination of two electron wavepackets moving along a "short" and a "long" trajectory in the atomic continuum. Attosecond pulse train generation has so far been attributed to the short trajectory, attempted to be isolated through targeted trajectory-selective phase matching conditions. Here, we provide experimental evidence for the contribution of both trajectories to the harmonic emission, even under phase matching conditions unfavorable for the long trajectory. This is finger printed in the interference modulation of the harmonic yield as a function of the driving laser intensity. The effect is also observable in the sidebands yield resulting from the frequency mixing of the harmonics and the driving laser field, an effect with consequences in cross-correlation pulse metrology approaches.Comment: 13 pages, 3 figure

Environmental and Health Disparities in Appalachian Ohio: Perceptions and Realities

Background. Appalachia is a region of the United States that faces significant environmental and health disparities. Understanding these disparities and the social determinants that contribute to them will help public health practitioners make better decisions. The purpose of this research is two-fold. First, through secondary data analysis, we document environmental and health disparities as well as demographic and economic conditions that may contribute to these disparities between Appalachian and non-Appalachian Ohio. Second, we examine perceptions of environmental health practitioners about the differences in environmental conditions between Appalachian and non-Appalachian Ohio. Methods. We gathered secondary data about economics, health, and the environment from the Ohio Department of Health, Healthy Ohio Community Profiles, the U.S. Environmental Protection Agency, and the U.S. Census. In addition, we conducted an online survey of 76 environmental health professionals across Ohio. Results. The secondary data indicates that there are significant differences between Appalachian and non-Appalachian Ohio in terms of socioeconomic, health, and environmental indicators. In addition, environmental health professionals perceive worse environmental conditions in the Appalachian region and indicate that there are environmental and health disparities found in this part of the state that do not exist elsewhere. Conclusions. The results contribute to understanding environmental and health conditions that contribute to health disparities in the Appalachian region as well as suggest approaches for public health practitioners to reduce these disparities

On the Hamiltonian structure and three-dimensional instabilities of rotating liquid bridges

We consider a rotating inviscid liquid drop trapped between two parallel plates. The liquid–air interface is a free surface and the boundaries of the wetted regions in the plates are also free. We assume that the two contact angles at the plates are equal. We present drop shapes that generalize the catenoids, nodoids and unduloids in the presence of rotation. We describe profile curves of these drops and investigate their stability to three-dimensional perturbations. The instabilities are associated with degeneracies of eigenvalues of the corresponding Hamiltonian linear stability problem. We observe that these instabilities are present even in the case when the analogue of the Rayleigh criterion for two-dimensional stability is satisfie

On uniformly rotating fluid drops trapped between two parallel plates

This contribution is about the dynamics of a liquid bridge between two fixed parallel plates. We consider a mathematical model and present some results from the doctoral thesis [10] of the first author. He showed that there is a Poisson bracket and a corresponding Hamiltonian, so that the model equations are in Hamiltonian form. The result generalizes previous results of Lewis et al. on the dynamics of free boundary problems for "free" liquid drops to the case of a drop between two parallel plates, including, especially the effect of capillarity and the angle of contact between the plates and the free fluid surface. Also, we prove the existence of special solutions which represent uniformly rotating fluid ridges, and we present specific stability conditions for these solutions. These results extend work of Concus and Finn [2] and Vogel [18],[19] on static capillarity problems (see also Finn [5]). Using the Hamiltonian structure of the model equations and symmetries of the solutions, the stability conditions can be derived in a systematic way. The ideas that are described will be useful for other situations involving capillarity and free boundary problems as well

The limits of Hamiltonian structures in three-dimensional elasticity, shells, and rods

This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material andderive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to the well-known Euler elastica if one adds an additional single constraint that the director lines up with the Frenet frame