Constraint methods for determining pathways and free energy of activated processes

Activated processes from chemical reactions up to conformational transitions of large biomolecules are hampered by barriers which are overcome only by the input of some free energy of activation. Hence, the characteristic and rate-determining barrier regions are not sufficiently sampled by usual simulation techniques. Constraints on a reaction coordinate r have turned out to be a suitable means to explore difficult pathways without changing potential function, energy or temperature. For a dense sequence of values of r, the corresponding sequence of simulations provides a pathway for the process. As only one coordinate among thousands is fixed during each simulation, the pathway essentially reflects the system's internal dynamics. From mean forces the free energy profile can be calculated to obtain reaction rates and insight in the reaction mechanism. In the last decade, theoretical tools and computing capacity have been developed to a degree where simulations give impressive qualitative insight in the processes at quantitative agreement with experiments. Here, we give an introduction to reaction pathways and coordinates, and develop the theory of free energy as the potential of mean force. We clarify the connection between mean force and constraint force which is the central quantity evaluated, and discuss the mass metric tensor correction. Well-behaved coordinates without tensor correction are considered. We discuss the theoretical background and practical implementation on the example of the reaction coordinate of targeted molecular dynamics simulation. Finally, we compare applications of constraint methods and other techniques developed for the same purpose, and discuss the limits of the approach

Detecting a stochastic gravitational wave background with the Laser Interferometer Space Antenna

The random superposition of many weak sources will produce a stochastic background of gravitational waves that may dominate the response of the LISA (Laser Interferometer Space Antenna) gravitational wave observatory. Unless something can be done to distinguish between a stochastic background and detector noise, the two will combine to form an effective noise floor for the detector. Two methods have been proposed to solve this problem. The first is to cross-correlate the output of two independent interferometers. The second is an ingenious scheme for monitoring the instrument noise by operating LISA as a Sagnac interferometer. Here we derive the optimal orbital alignment for cross-correlating a pair of LISA detectors, and provide the first analytic derivation of the Sagnac sensitivity curve.Comment: 9 pages, 11 figures. Significant changes to the noise estimate

Search for a diffuse flux of astrophysical muon neutrinos with the IceCube 40-string detector

The IceCube Neutrino Observatory is a 1 km(3) detector currently taking data at the South Pole. One of the main strategies used to look for astrophysical neutrinos with IceCube is the search for a diffuse flux of high-energy neutrinos from unresolved sources. A hard energy spectrum of neutrinos from isotropically distributed astrophysical sources could manifest itself as a detectable signal that may be differentiated from the atmospheric neutrino background by spectral measurement. This analysis uses data from the IceCube detector collected in its half completed configuration which operated between April 2008 and May 2009 to search for a diffuse flux of astrophysical muon neutrinos. A total of 12 877 upward-going candidate neutrino events have been selected for this analysis. No evidence for a diffuse flux of astrophysical muon neutrinos was found in the data set leading to a 90% C. L. upper limit on the normalization of an E-2 astrophysical nu(mu) flux of 8.9 x 10(-9) GeV cm(-2) s(-1) sr(-1). The analysis is sensitive in the energy range between 35 TeV and 7 PeV. The 12 877 candidate neutrino events are consistent with atmospheric muon neutrinos measured from 332 GeV to 84 TeV and no evidence for a prompt component to the atmospheric neutrino spectrum is found

Measurement of acoustic attenuation in South Pole ice

Using the South Pole Acoustic Test Setup (SPATS) and a retrievable transmitter deployed in holes drilled for the IceCube experiment, we have measured the attenuation of acoustic signals by South Pole ice at depths between 190 m and 500 m. Three data sets, using different acoustic sources, have been analyzed and give consistent results. The method with the smallest systematic uncertainties yields an amplitude attenuation coefficient α = 3.20 ± 0.57 km−1 between 10 and 30 kHz, considerably larger than previous theoretical estimates. Expressed as an attenuation length, the analyses give a consistent result for λ ≡ 1/α of ∼300 m with 20% uncertainty. No significant depth or frequency dependence has been found