University of Paderborn

About: University of Paderborn is a education organization based out in Paderborn, Nordrhein-Westfalen, Germany. It is known for research contribution in the topics: Computer science & Context (language use). The organization has 6684 authors who have published 16929 publications receiving 323154 citations.

How Far Can Chemotactic Cross-diffusion Enforce Exceeding Carrying Capacities?

Abstract: We consider nonnegative solutions of the Neumann initial-boundary value problem for the chemotaxis-growth system $$\begin{aligned} \left\{ \begin{array}{l} u_t=\varepsilon u_{xx} -(uv_x)_x +ru -\mu u^2, \qquad x\in \Omega , \ t>0, \\ 0=v_{xx}-v+u, \qquad x\in \Omega , \ t>0, \end{array} \right. \quad (\star ) \end{aligned}$$ in \(\Omega :=(0,L)\subset \mathbb {R}\) with \(L>0, \varepsilon >0, r\ge 0\) and \(\mu >0\), along with the corresponding limit problem formally obtained upon taking \(\varepsilon \searrow 0\). For the latter hyperbolic–elliptic problem, we establish results on local existence and uniqueness within an appropriate generalized solution concept. In this context we shall moreover derive an extensibility criterion involving the norm of \(u(\cdot ,t)\) in \(L^\infty (\Omega )\). This will enable us to conclude that in this case \(\varepsilon =0\), if \(\mu \ge 1\), then all solutions emanating from sufficiently regular initial data are global in time, whereas if \(\mu <1\), then some solutions blow-up in finite time. The latter will reveal that the original parabolic–elliptic problem (\(\star \)), though known to possess no such exploding solutions, exhibits the following property of dynamical structure generation: given any \(\mu \in (0,1)\), one can find smooth bounded initial data with the property that for each prescribed number \(M>0\) the solution of (\(\star \)) will attain values above \(M\) at some time, provided that \(\varepsilon \) is sufficiently small. In particular, this means that the associated carrying capacity given by \(\frac{r}{\mu }\) can be exceeded during evolution to an arbitrary extent. We finally present some numerical simulations that illustrate this type of solution behavior and that, moreover, inter alia, indicate that achieving large population densities is a transient dynamical phenomenon occurring on intermediate time scales only.

Pentagon adjacency as a determinant of fullerene stability

Abstract: Optimisation of geometries of all 40 fullerene isomers of C40, using methods from molecular mechanics and tight-binding to full abinitio SCF and DFT approaches, confirms minimisation of pentagon adjacency as a major factor in relative stability. The consensus predictions of 11 out of 12 methods are that the isomer of lowest total energy is the D2 cage with the smallest possible adjacency count, and that energies rise linearly with the number of adjacencies. Quantum mechanical methods predict a slope of 80–100 kJ mol-1 per adjacency. Molecular mechanics methods are outliers, with the Tersoff potential giving a different minimum and its Brenner modification a poor correlation and much smaller penalty.