Coordinate families for the Schwarzschild geometry based on radial timelike geodesics

We explore the connections between various coordinate systems associated with observers moving inwardly along radial geodesics in the Schwarzschild geometry. Painlev\'e-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from infinity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at infinity with non-zero initial inward velocity; Gautreau-Hoffmann (GH) time coordinates are adapted to observers dropped from rest from a finite distance from the black hole horizon. We construct from these an LMP family and a proper-time family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lema\^itre coordinates as well.Comment: 13 pages and 10 figures. New title and abstract; expanded discussion on Gautreau-Hoffmann coordinates, and coordinate classifications; figures added; references added. Submitted for publicatio

Spectral minimal partitions for a family of tori

We study partitions of the rectangular two-dimensional flat torus of length 1 and width b into k domains, with b a parameter in (0, 1] and k an integer. We look for partitions which minimize the energy, definedas the largest first eigenvalue of the Dirichlet Laplacian on the domains of the partition. We are inparticular interested in the way these minimal partitions change when b is varied. We present herean improvement, when k is odd, of the results on transition values of b established by B. Helffer andT. Hoffmann-Ostenhof (2014) and state a conjecture on those transition values. We establishan improved upper bound of the minimal energy by explicitly constructing hexagonal tilings of thetorus. These tilings are close to the partitions obtained from a systematic numerical study based on an optimization algorithm adapted from B. Bourdin, D. Bucur, and {\'E}. Oudet (2009). These numerical results also support our conjecture concerning the transition values and give betterestimates near those transition values

Studien zur Altägyptischen Kultur Nr. 23 (1996) - Abstracts

Abstracts der Artikel zu SAK 23 (1996). Die Autoren sind: H. Altenmüller, B. Bohleke, M. Chermette/ J.-C. Goyon, K. Daoud, H. Engelmann/ J. Hallof, S. Grallert, F. Hoffmann, K. Jansen-Winkeln, C. Karlshausen, R. Krauss, D. Kurth, P. Pamminger, J. Quack, S. Rzepka, L.K. Sabbahy, A. Spalinger und S. Voß

Near threshold Lambda and Sigma production in pp collisions

A model calculation for the reactions $pp\to p\Lambda K^+$ and $pp\to N\Sigma K$ near their thresholds is presented. It is argued that the experimentally observed strong suppression of $\Sigma^0$ production compared to $\Lambda$ production at the same excess energy could be due to a destructive interference between the $\pi$ and $K$ exchange contributions in the reaction $pp\to p\Sigma^0 K^+$. Predictions for $pp\to p\Sigma^+ K^0$ and $pp\to n\Sigma^+ K^+$ are given.Comment: 3 pages, 1 figure, uses espcrc1.sty, contribution presented at the 16th International Conference on Few-Body Problems in Physics, Taipei, Taiwan, 6-10 March 200

Numerical analysis of nodal sets for eigenvalues of Aharonov-Bohm Hamiltonians on the square and application to minimal partitions

International audienceUsing the double covering approach introduced by B. Helffer, M. and T. Hoffmann-Ostenhof and M. Owen and further developed for questions of isospectrality by the authors in collaboration with T. Hoffmann-Ostenhof, we analyze the variation of the eigenvalues of the one pole Aharonov-Bohm Hamiltonian on the square and the nodal picture of the associated eigenfunctions as a function of the pole. This leads us to discover new candidates for minimal $k$-partitions of the square with a specific topological type. This illustrates also recent results of B. Noris and S. Terracini. This finally supports or disproves conjectures for the minimal $3$ and $5$-partitions on the square

Minimum and maximum against k lies

A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element totally ordered set. The set is accessed via an oracle for pairwise comparisons. More recently, the problem has been studied in the context of the Renyi-Ulam liar games, where the oracle may give up to k false answers. For large k, an upper bound due to Aigner shows that (k+O(\sqrt{k}))n comparisons suffice. We improve on this by providing an algorithm with at most (k+1+C)n+O(k^3) comparisons for some constant C. The known lower bounds are of the form (k+1+c_k)n-D, for some constant D, where c_0=0.5, c_1=23/32=0.71875, and c_k=\Omega(2^{-5k/4}) as k goes to infinity.Comment: 11 pages, 3 figure