Erratum to: A Variational Approach to Givental’s Nonlinear Maslov Index

In this article we consider a variant of Rabinowitz Floer homology in order to define a homological count of discriminant points for paths of contactomorphisms. The growth rate of this count can be seen as an analogue of Givental’s nonlinear Maslov index. As an application we prove a Bott–Samelson type obstruction theorem for positive loops of contactomorphisms.     

Picosecond thermometer in the amide I band of myoglobin

The amide I and II bands in myoglobin show a heterogeneous temperature dependence, with bands at 6.17 and 6.43 microm which are more intense at low temperatures. The amide I band temperature dependence is on the long wavelength edge of the band, while the short wavelength side has almost no temperature dependence. We compare concepts of anharmonic solid-state crystal physics and chemical physics for the origins of these bands. We suggest that the long wavelength side is composed of those amino acids which hydrogen bond to the hydration shell of the protein, and that temperature dependent bands can be used to determine the time it takes vibrational energy to flow into the hydration shell. We determine that vibrational energy flow to the hydration shell from the amide I takes approximately 20 ps to occur.     

A nondisplaceable Lagrangian torus in T*S2

We show that the Lagrangian torus in the cotangent bundles of the 2‐sphere obtained by applying the geodesic flow to the unit circle in a fiber is not displaceable by computing its Lagrangian Floer homology. The computation is based on a symmetry argument. © 2007 Wiley Periodicals, Inc.     

Büschel von Raumkurven 4. Ordnung II. Art mit zwei stationären Tangenten

Ohne Zusammenfassung     

The Debye-Waller factor: From villain to hero in protein crystallography

A personal and partially anecdotal account is given of the role of the Debye–Waller factor in protein crystallography and protein dynamics.     

Hamiltonian dynamics on convex symplectic manifolds

We study the dynamics of Hamiltonian diffeomorphisms on convex symplectic manifolds. To this end we first establish an explicit isomorphism between the Floer homology and the Morse homology of such a manifold, and then use this isomorphism to construct a biinvariant metric on the group of compactly supported Hamiltonian diffeomorphisms analogous to the metrics constructed by Viterbo, Schwarz and Oh. These tools are then applied to prove and reprove results in Hamiltonian dynamics. Our applications comprise a uniform lower estimate for the slow entropy of a compactly supported Hamiltonian diffeomorphism, the existence of infinitely many non-trivial periodic points of a compactly supported Hamiltonian diffeomorphism of a subcritical Stein manifold, new cases of the Weinstein conjecture, and, most noteworthy, new existence results for closed trajectories of a charge in a magnetic field on almost all small energy levels. We shall also obtain some new Lagrangian intersection results. Partially supported by the Swiss National Foundation. Supported by the Swiss National Foundation and the von Roll Research Foundation.     

Contact geometry of the restricted three‐body problem

We show that the planar circular restricted three‐body problem is of restricted contact type for all energies below the first critical value (action of the first Lagrange point) and for energies slightly above it. This opens up the possibility of using the technology of contact topology to understand this particular dynamical system. © 2011 Wiley Periodicals, Inc.     

Mössbauer effect in proteins

In proteins, the M?ssbauer effect and neutron scattering show a broad line and a rapid increase of the conformational mean-square displacement above about 180?K. The increase, dubbed the "dynamical transition," is controversial. We introduce a new interpretation of the M?ssbauer effect in proteins and demonstrate that no dynamical transition is required. The increase in the mean-square displacement and the broad line are caused by fluctuations in the protein's hydration shell. Using the dielectric spectrum of these fluctuations, we predict the shape of the M?ssbauer spectrum from 80 to 295?K with one dimensionless coefficient.