arXiv subjects

D. Fuchs

Publications and source records attributed to D. Fuchs.

59 records · Page 4Linked to original sources

arXiv2015

On Lagrangian tangent sweeps and Lagrangian outer billiards

Given a Lagrangian submanifold in linear symplectic space, its tangent sweep is the union of its (affine) tangent spaces, and its tangent cluster is the result of parallel translating these spaces so that the foot point of each tangent space becomes the origin. This defines a multivalued map from the tangent sweep to the tangent cluster, and we show that this map is a local symplectomorphism (a well known fact, in dimension two). We define and study the outer billiard correspondence associated with a Lagrangian submanifold. Two points are in this correspondence if they belong to the same tangent space and are symmetric with respect to its foot pointe. We show that this outer billiard correspondence is symplectic and establish the existence of its periodic orbits. This generalizes the well studied outer billiard map in dimension two.

math.SG↗

arXiv2011

Cooperation between Top-Down and Bottom-Up Theorem Provers

Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages. Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are goal-oriented but often have weak calculi when their proof lengths are considered. In order to integrate both approaches, we try to achieve cooperation between a top-down and a bottom-up prover in two different ways: The first technique aims at supporting a bottom-up with a top-down prover. A top-down prover generates subgoal clauses, they are then processed by a bottom-up prover. The second technique deals with the use of bottom-up generated lemmas in a top-down prover. We apply our concept to the areas of model elimination and superposition. We discuss the ability of our techniques to shorten proofs as well as to reorder the search space in an appropriate manner. Furthermore, in order to identify subgoal clauses and lemmas which are actually relevant for the proof task, we develop methods for a relevancy-based filtering. Experiments with the provers SETHEO and SPASS performed in the problem library TPTP reveal the high potential of our cooperation approaches.

cs.AI↗

arXiv2009

Soft x-ray magnetic circular dichroism of LaCoO$_{3}$, La$_{0.7}$Ce$_{0.3}$CoO$_{3}$, and La$_{0.7}$Sr$_{0.3}$CoO$_{3}$ films: Evidence for Co valency-dependent magnetism and magnetic anisotropy

Epitaxial thin films of undoped LaCoO$_{3}$\@, of electron-doped La$_{0.7}$Ce$_{0.3}$CoO$_{3}$\@, and of hole-doped La$_{0.7}$Sr$_{0.3}$CoO$_{3}$\@ exhibit ferromagnetic order with a transition temperature $T_{\rm{C}}$ $\approx$ 85 K, 22 K, and 240 K, respectively. The spin-state structure for these compounds was studied by soft x-ray magnetic circular dichroism at the Co $L_{2,3}$ and O $K$ edges. It turns out that a higher spin state of the Co$^{3+}$ ions is responsible for the magnetism in LaCoO$_{3}$\@ while for La$_{0.7}$Ce$_{0.3}$CoO$_{3}$ the Co$^{3+}$ ions are in a low-spin state and the ferromagnetism is predominantly determined by Co$^{2+}$\@. For La$_{0.7}$Sr$_{0.3}$CoO$_{3}$\@, on the other hand, the magnetism originates from higher spin states of Co$^{3+}$ and Co$^{4+}$\@. Moreover, a strong magnetic anisotropy is observed for all systems.

cond-mat.str-el↗

arXiv2008

Suppression of the ferromagnetic state in LaCoO3 films by rhombohedral distortion

Epitaxially strained LaCoO3 (LCO) thin films were grown with different film thickness, t, on (001) oriented (LaAlO3)0.3(SrAl0.5Ta0.5O3)0.7 (LSAT) substrates. After initial pseudomorphic growth the films start to relieve their strain partly by the formation of periodic nano-twins with twin planes predominantly along the <100> direction. Nano-twinning occurs already at the initial stage of growth, albeit in a more moderate way. Pseudomorphic grains, on the other hand, still grow up to a thickness of at least several tenths of nanometers. The twinning is attributed to the symmetry lowering of the epitaxially strained pseudo-tetragonal structure towards the relaxed rhombohedral structure of bulk LCO. However, the unit-cell volume of the pseudo-tetragonal structure is found to be nearly constant over a very large range of t. Only films with t > 130 nm show a significant relaxation of the lattice parameters towards values comparable to those of bulk LCO.

cond-mat.str-el↗

arXiv2008

Suppression of spin-state transition in epitaxially strained LaCoO_{3}

Epitaxial thin films of LaCoO_{3} (E-LCO) exhibit ferromagnetic order with a transition temperature T_c = 85 K, while polycrystalline thin LaCoO_{3} films (P-LCO) remain paramagnetic. The temperature-dependent spin-state structure for both E-LCO and P-LCO was studied by x-ray absorption spectroscopy at the Co L_{2,3} and O K edges. Considerable spectral redistributions over temperature are observed for P-LCO. The spectra for E-LCO, on the other hand, do not show any significant changes for temperatures between 30 K and 450 K at both edges, indicating that the spin state remains constant and that the epitaxial strain inhibits any population of the low-spin (S = 0) state with decreasing temperature. This observation identifies an important prerequisite for ferromagnetism in E-LCO thin films.

cond-mat.str-el↗