DNA-Mediated Self-Organization of Polymeric Nanocompartments Leads to Interconnected Artificial Organelles

Self-organization of nanocomponents was mainly focused on solid nanoparticles, quantum dots, or liposomes to generate complex architectures with specific properties, but intrinsically limited or not developed enough, to mimic sophisticated structures with biological functions in cells. Here, we present a biomimetic strategy to self-organize synthetic nanocompartments (polymersomes) into clusters with controlled properties and topology by exploiting DNA hybridization to interconnect polymersomes. Molecular and external factors affecting the self-organization served to design clusters mimicking the connection of natural organelles: fine-tune of the distance between tethered polymersomes, different topologies, no fusion of clustered polymersomes, and no aggregation. Unexpected, extended DNA bridges that result from migration of the DNA strands inside the thick polymer membrane (about 12 nm) represent a key stability and control factor, not yet exploited for other synthetic nano-object networks. The replacement of the empty polymersomes with artificial organelles, already reported for single polymersome architecture, will provide an excellent platform for the development of artificial systems mimicking natural organelles or cells and represents a fundamental step in the engineering of molecular factories

Aktienoptionen bei Strukturveränderungen der Arbeitgebergesellschaft : der Schutz der Arbeitnehmeraktienoption bei Eingliederung, Squeeze-out, Umwandlung, Delisting, Betriebsübergang und Insolvenz

Mehr als 10.000 Unternehmen in Deutschland sind in der Rechtsform der Aktiengesellschaft organisiert, von denen wiederum mehr als 1.000 an einer deutschen Börse notiert sind. Aktienoptionsprogramme für Manager und Arbeitnehmer, als besondere Art der Entlohnung, sind etabliert und vielfach aufgelegt. Aber wie wirken sich gesellschaftsrechtliche Strukturveränderungen der begebenden Arbeitgeber-AG oder ein Betriebsübergang auf bestehende Aktienoptionsprogramme aus und welche Rechte haben die Optionsinhaber

A Discontinuous Galerkin Scheme based on a Space-Time Expansion II. Viscous Flow Equations in Multi Dimensions

In part I of these two papers we introduced for inviscid flow in one space dimension a discontinuous Galerkin scheme of arbitrary order of accuracy in space and time. In the second part we extend the scheme to the compressible Navier-Stokes equations in multi dimensions. It is based on a space-time Taylor expansion at the old time level in which all time or mixed space-time derivatives are replaced by space derivatives using the Cauchy-Kovalevskaya procedure. The surface and volume integrals in the variational formulation are approximated by Gaussian quadrature with the values of the space-time approximate solution. The numerical fluxes at grid cell interfaces are based on the approximate solution of generalized Riemann problems for both, the inviscid and viscous part. The presented scheme has to satisfy a stability restriction similar to all other explicit DG schemes which becomes more restrictive for higher orders. The loss of efficiency, especially in the case of strongly varying sizes of grid cells is circumvented by use of different time steps in different grid cells. The presented time accurate numerical simulations run with local time steps adopted to the local stability restriction in each grid cell. In numerical simulations for the two-dimensional compressible Navier-Stokes equations we show the efficiency and the optimal order of convergence being p+1, when a polynomial approximation of degree p is used

A Discontinuous Galerkin Scheme Based on a Space–Time Expansion. I. Inviscid Compressible Flow in One Space Dimension

In this paper, we propose an explicit discontinuous Galerkin scheme for conservation laws which is of arbitrary order of accuracy in space and time. The basic idea is to use a Taylor expansion in space and time to define a space–time polynomial in each space–time element. The space derivatives are given by the approximate solution at the old time level, the time derivatives and the mixed space–time derivatives are computed from these space derivatives using the so-called Cauchy–Kovalevskaya procedure. The space–time volume integral is approximated by Gauss quadrature with values at the space–time Gaussian points obtained from the Taylor expansion. The flux in the surface integral is approximated by a numerical flux with arguments given by the Taylor expansions from the left and from the right-hand side of the element interface. The locality of the presented method together with the space–time expansion gives the attractive feature that the time steps may be different in each grid cell. Hence, we drop the common global time levels and propose that every grid zone runs with its own time step which is determined by the local stability restriction. In spite of the local time steps the scheme is locally conservative, fully explicit, and arbitrary order accurate in space and time for transient calculations. Numerical results are shown for the one-dimensional Euler equations with orders of accuracy one up to six in space and time

Arbitrary high order accurate time integration schemes for linear problems

Numerical schemes for wave propagation over long distances need good wave propagation properties with low dispersion and low dissipation errors. Suitable numerical methods are methods with high order of accuracy in space and time. For space discretization on structured grids, high order finite difference schemes are efficient, and, if a complicated computational domain requires an unstructured grid, discontinuous Galerkin methods are recently employed with success. The time integration is often performed by a Runge-Kutta scheme. These schemes need for the order of accuracy O > 4 more than O stages, which reduces performance concerning CPU-time as well as storage requirements, because the numerical solution of more than one stage has to be stored. However, it is interesting to use schemes of accuracy order higher than 4, especially to capture wave propagation over long distances or if very accurate computations are needed. In this paper we consider a time integration approach for linear wave problems based on a Taylor expansion. Here we construct and analyze schemes of arbitrary high order accuracy in space and time using this time integration technique within the finite difference as well as the discontinuous Galerkin framework. We present a stability analysis as well as performance comparisons with schemes relying on other time integration methods. A modification for the DG schemes is presented that accentuates the computational performance. Numerical experiments are realized for the system of linearized Euler Equations, but the formulation allows an application of the proposed schemes to any linear hyperbolic system