Creating pseudo Kondo-resonances by field-induced diffusion of atomic hydrogen

In low temperature scanning tunneling microscopy (STM) experiments a cerium adatom on Ag(100) possesses two discrete states with significantly different apparent heights. These atomic switches also exhibit a Kondo-like feature in spectroscopy experiments. By extensive theoretical simulations we find that this behavior is due to diffusion of hydrogen from the surface onto the Ce adatom in the presence of the STM tip field. The cerium adatom possesses vibrational modes of very low energy (3-4meV) and very high efficiency (> 20%), which are due to the large changes of Ce-states in the presence of hydrogen. The atomic vibrations lead to a Kondo-like feature at very low bias voltages. We predict that the same low-frequency/high-efficiency modes can also be observed at lanthanum adatoms.Comment: five pages and four figure

Generalizing Boolean Satisfiability III: Implementation

This is the third of three papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal has been to define a representation in which this structure is apparent and can be exploited to improve computational performance. The first paper surveyed existing work that (knowingly or not) exploited problem structure to improve the performance of satisfiability engines, and the second paper showed that this structure could be understood in terms of groups of permutations acting on individual clauses in any particular Boolean theory. We conclude the series by discussing the techniques needed to implement our ideas, and by reporting on their performance on a variety of problem instances

New obstructions to symplectic embeddings

In this paper we establish new restrictions on symplectic embeddings of certain convex domains into symplectic vector spaces. These restrictions are stronger than those implied by the Ekeland-Hofer capacities. By refining an embedding technique due to Guth, we also show that they are sharp.Comment: 80 pages, 3 figures, v2: improved exposition and minor corrections, v3: Final version, expanded and improved exposition and minor corrections. The final publication is available at link.springer.co

Algebraic Torsion in Contact Manifolds

We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic fillings and exact symplectic cobordisms. A contact manifold has algebraic torsion of order zero if and only if it is algebraically overtwisted (i.e. has trivial contact homology), and any contact 3-manifold with positive Giroux torsion has algebraic torsion of order one (though the converse is not true). We also construct examples for each nonnegative k of contact 3-manifolds that have algebraic torsion of order k but not k - 1, and derive consequences for contact surgeries on such manifolds. The appendix by Michael Hutchings gives an alternative proof of our cobordism obstructions in dimension three using a refinement of the contact invariant in Embedded Contact Homology.Comment: 53 pages, 4 figures, with an appendix by Michael Hutchings; v.3 is a final update to agree with the published paper, and also corrects a minor error that appeared in the published version of the appendi

Displacement energy of unit disk cotangent bundles

We give an upper bound of a Hamiltonian displacement energy of a unit disk cotangent bundle $D^*M$ in a cotangent bundle $T^*M$, when the base manifold $M$ is an open Riemannian manifold. Our main result is that the displacement energy is not greater than $C r(M)$, where $r(M)$ is the inner radius of $M$, and $C$ is a dimensional constant. As an immediate application, we study symplectic embedding problems of unit disk cotangent bundles. Moreover, combined with results in symplectic geometry, our main result shows the existence of short periodic billiard trajectories and short geodesic loops.Comment: Title slightly changed. Close to the version published online in Math Zei

Macro-step-size selection and monitoring of the coupling error for weak coupled subsystems in the frequency-domain

A rather general approach to establish a multiphysic simulation is referred to as non-iterative co-simulation or weak coupled simulation. The involved subsystems are coupled in a weak sense and thus stepwise extrapolation of the coupling signals is required. Extrapolation is associated with an error which may influence the dynamical behavior of the coupled system. This coupling error depends significantly on the coupling step-size, i.e. the macro-step-size, and is one of the most critical parameter of a noniterative co-simulation. In practice, appropriate macro-step-sizes are determined by some numerical tests or chosen according to the experience of domain-specific engineers. But who assesses the results of a non-iterative co-simulation? Comparison between reference and co-simulation results in the time-domain is often practiced in case studies using complex subsystems to validate co-simulation performance and accuracy of the achieved results. But this approach is counter-productive and mostly not applicable in practice. In this work we consider the coupling process as single source of distortion and analyse it in the frequency-domain. As a consequence, a relation between the macro-step-size and the coupling signals is available which leads to a ’rule-of-thumb’ for a adequate macro-stepsize selection. In addition, the gained insight into the coupling process itself enables new possibilities to monitor the coupling error leading to the ability to assess the results of a weak coupled simulation. The proposed methodologies are examined using a complex mechatronic system describing a vehicle (multi-body system, MBS), which is controlled via an anti-lock braking system (ABS) during different scenarios

An exact sequence for contact- and symplectic homology

A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces a linearization of the contact homology of $M$ with corresponding linearized contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the symplectic homology $SH(W)$ of $W$ maps to $HC(M)$, which in turn maps to $HC(M)$, by a map of degree -2, which then maps to $SH(W)$. Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of $M$.Comment: Final version. Changes for v2: Proof of main theorem supplemented with detailed discussion of continuation maps. Description of degree -2 map rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for clarity (now Remark 9). Various other minor modification