We study the Cahn-Hilliard equation in a bounded domain without any symmetry assumptions. We assume that the mean curvature of the boundary has a nongenerate critical point. Then we show that there exists a spike-like stationary solution whose global maximum lies on the boundary. Our method is based on Lyapunov-Schmidt reduction and the Brouwer fixed-point theorem. Résumé. Nous étudions l’équat...

Research Update: Behind the high efficiency of hybrid perovskite solar cells Azhar Fakharuddin,1,2,a Francesca De Rossi,3,a Trystan M. Watson,3 Lukas Schmidt-Mende,1 and Rajan Jose4,a 1Department of Physics, University of Konstanz, D-78457 Konstanz, Germany 2School of Chemical and Materials Engineering, National University of Sciences and Technology, H-12, Islamabad, Pakistan 3College of Engine...

Incomparability of pure bipartite entangled states under deterministic LOCC is a very strange phenomena. We find two possible ways of getting our desired pure entangled state which is incomparable with the given input state, by collective LOCC with certainty. The first one is by providing some pure entanglement through the lower dimensional maximally-entangled states or using further less amoun...

* Parts of this contribution were presented as a lecture during the annual meeting of the Water Chemistry Division in the German Chemical Society (Fachgruppe Wasserchemie in der GDCh), Lindau, May 1997. ** Dr. Thomas Heberer, Dipl.-Lebensmittelchem. Kathrin Schmidt-Bäumler, Prof. Dr. Hans-Jürgen Stan, Institute of Food Chemistry, Technical University of Berlin, GustavMeyer-Allee 25, D-13355 Ber...

Let NSymm be the Hopf algebra of non-commutative symmetric functions (in an infinity of indeterminates): NSymm=Z 1 2 , ,... Z Z   . It is shown that an associative algebra A with a Hasse-Schmidt derivation 1 2 ( , , ,...) d id d d  on it is exactly the same as an NSymm module algebra. The primitives of NSymm act as ordinary derivations. There are many formulas for the generators Zi in terms ...

Josef Pochodzalla, Lech Mankiewicz, Murray Moinester, Gunther Piller , Andrzej Sandacz, Marc Vanderhaeghen Max-Planck-Institut für Kernphysik, 69029 Heidelberg, Germany Physics Department, Technical University Munich, D-85747 Garching, Germany School of Physics and Astronomy, R. and B. Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Ramat Aviv, Israel Soltan Institute for Nuclear ...

Two popular model reduction methods, the proper orthogonal decomposition (POD), and balanced truncation, are applied together with Galerkin projection to the twodimensional Burgers’ equation. This scalar equation is chosen because it has a nonlinearity that is similar to the NavierStokes equation, but it can be accurately simulated using far fewer states. However, the number of states required ...