Efficient bacterial chromosome segregation typically requires the coordinated action of a three-component machinery, fueled by adenosine triphosphate, called the partition complex. We present a phenomenological model accounting for the dynamic activity of this system that is also relevant for the physics of catalytic particles in active environments. The model is obtained by coupling simple linear reaction-diffusion equations with a proteophoresis, or “volumetric” chemophoresis, force field that arises from protein-protein interactions and provides a physically viable mechanism for complex translocation. This minimal description captures most known experimental observations: dynamic oscillations of complex components, complex separation, and subsequent symmetrical positioning. The predictions of our model are in phenomenological agreement with and provide substantial insight into recent experiments. From a nonlinear physics view point, this system explores the active separation of matter at micrometric scales with a dynamical instability between static positioning and traveling wave regimes triggered by the dynamical spontaneous breaking of rotational symmetry.

In previous papers, [M1, M2], [M3], we proved the existence as well as regularity of a finite range decomposition for the resolvent $G_{\alpha} (x-y,m^2) = ((-\Delta)^{\alpha\over 2} + m^{2})^{-1} (x-y) $, for $0<\alpha <2$ and all real $m$, in the lattice ${\bf Z}^{d}$ for dimension $d\ge 2$. In this paper, which is a continuation of the previous one, we extend those results by proving the existence as well as regularity of a finite range decomposition for the same resolvent but now on the lattice torus ${\bf Z}^{d}/L^{N+1}{\bf Z}^{d} $ for $d\ge 2$ provided $m\neq 0$ and $0<\alpha <2$. We also prove differentiability and uniform continuity properties with respect to the resolvent parameter $m^{2}$. Here $L$ is any odd positive integer and $N\ge 2$ is any positive integer.

Erratum to: On a Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian

We investigate the opto-electronic properties of hexagonal boron nitride grown by high temperature plasma-assisted molecular beam epitaxy. We combine atomic force microscopy, spectroscopic ellipsometry, and photoluminescence spectroscopy in the deep ultraviolet to compare the quality of hexagonal boron nitride grown either on sapphire or highly oriented pyrolytic graphite. For both substrates, the emission spectra peak at 235 nm, indicating the high optical quality of hexagonal boron nitride grown by molecular beam epitaxy. The epilayers on highly oriented pyrolytic graphite demonstrate superior performance in the deep ultraviolet (down to 210 nm) compared to those on sapphire. These results reveal the potential of molecular beam epitaxy for the growth of hexagonal boron nitride on graphene, and more generally, for fabricating van der Waals heterostructures and devices by means of a scalable technology.

We comparatively study the onset of photo-induced non-radiative intrinsic Auger recombination processes for red, yellow and green light emitting InGaNsingle bondGaN hetero-structures grown along the polar orientation. We find a dramatic reduction of the photo excitation densities triggering the domination of Auger effect with increasing emission wavelength; that is to say in concert with the enhancement of the internal electric field in the structure. In long wavelength emitters, the internal electric field is stronger, and hence reducing the impact of the internal electric field is more critical.

In this work, the ellipsometric measurements of small molecular size polypeptides deposited onto silicon are analyzed. Results of ellipsometric evaluation procedures based on transparent layer, absorbing layer and discontinuous layer approaches are compared. Although these models result in similar fitting quality and can predict the amount of the deposited material, the gained optical properties can be rather differ- ent due to the different assumptions of the models. To choose the physically correct results, independent measurements as atomic force microscopy or transmission measurement of peptide solutions are nec- essary. It is shown that the measured ellipsometric depolarization can provide also useful information about the sample properties.

A promising route towards nanodevice applications relies on the association of graphene and transition metal dichalcogenides with hexagonal boron nitride (h-BN). Due to its insulating nature, h-BN has emerged as a natural substrate and gate dielectric for graphene-based electronic devices. However, some fundamental properties of bulk h-BN remain obscure. For example, the band structure and the position of the Fermi level have not been experimentally resolved. Here, we report a direct observation of parabolic dispersions of h-BN crystals using high-resolution angle-resolved photoemission spectroscopy (ARPES). We find that h-BN exfoliation on epitaxial graphene enables overcoming the technical difficulties of using ARPES with insulating materials. We show trigonal warping of the intensity maps at constant energy. The valence-band maxima are located around the K points, 2.5 eV below the Fermi level, thus confirming the residual p-type character of typical h-BN.