Optimal finite-time processes in stochastic thermodynamics

For a small system like a colloidal particle or a single biomolecule embedded in a heat bath, the optimal protocol of an external control parameter minimizes the mean work required to drive the system from one given equilibrium state to another in a finite time. In general, this optimal protocol obeys an integro-differential equation. Explicite solutions both for a moving laser trap and a time-dependent strength of such a trap show finite jumps of the optimal protocol to be typical both at the beginning and the end of the process.Comment: 4 pages, 1 figure, accepted for publication in Phys. Rev. Let

Laser power stabilization for second-generation gravitational wave detectors

We present results on the power stabilization of a Nd:YAG laser in the frequency band from 1 Hz to 100 kHz. High-power, low-noise photodetectors are used in a dc-coupled control loop to achieve relative power fluctuations down to 5×10−9 Hz−1/2 at 10 Hz and 3.5×10−9 Hz−1/2 up to several kHz, which is very close to the shot-noise limit for 80 mA of detected photocurrent on each detector. We investigated and eliminated several noise sources such as ground loops and beam pointing. The achieved stability level is close to the requirements for the Advanced LIGO gravitational wave detector

Non-linear properties of supercooled liquids in the system Na2O---SiO2

The physical properties, viscosity, density, heat capacity and thermal expansivity, of relaxed supercooled liquids in the temperature range just above the glass transition have been determined for ten compositions along the compositional binary Na2O---SiO2, in the range of 2–45 mole% Na2O, by a combination of scanning calorimetry, dilatometry and micropenetration viscometry. The viscosity, density, heat capacity and thermal expansivity in the glassy state have also been determined. The heat capacities illustrate a linear composition dependence for the glassy state and a smooth but strongly non-linear composition dependence for the supercooled liquid state. The thermal expansivities were determined by dilatometry up to the glass transition and, by a normalized comparison of relaxation behavior in the glass transition interval, to temperatures 50°C above the glass transition. The expansivity is a linear function of the molar composition in the glass but a strongly non-linear function of molar composition in the supercooled liquid. The viscosity data just above the glass transition temperature, combined with data from high temperature using the concentric cylinder method, illustrate that the composition dependence of viscosity is strongly non-linear and exhibits an inflection as a function of composition. The glass transition temperature, taken as the peak temperature of the calorimetric measurements, is not in general an isokom in this system. The data for these property determinations in the Na2O---SiO2 system provide much improved constraints on the partial molar properties of SiO2 liquid and partial molar properties of the SiO2 component in silicate melts. The complex behavior of the transport properties, i.e. the glass transition temperature and the viscosity, point to complexities in viscous flow beyond that of simple binary mixing of the Na2O and SiO2 components

Nonparametric regression penalizing deviations from additivity

Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions imposed can lead to serious bias. Here, a new estimator is proposed which allows penalizing the nonadditive part of a regression function. This offers a smooth choice between the full and the additive model. As a byproduct, this penalty leads to a regularization in sparse regions. If the additive model does not hold, a small penalty introduces an additional bias compared to the full model which is compensated by the reduced bias due to using smaller bandwidths. For increasing penalties, this estimator converges to the additive smooth backfitting estimator of Mammen, Linton and Nielsen [Ann. Statist. 27 (1999) 1443-1490]. The structure of the estimator is investigated and two algorithms are provided. A proposal for selection of tuning parameters is made and the respective properties are studied. Finally, a finite sample evaluation is performed for simulated and ozone data.Comment: Published at http://dx.doi.org/10.1214/009053604000001246 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Can the Tajmar effect be explained using a modification of inertia?

The Tajmar effect is an unexplained acceleration observed by accelerometers and laser gyroscopes close to rotating supercooled rings. The observed ratio between the gyroscope and ring accelerations was 3+/-1.2x10^-8. Here, a new model for inertia which has been tested quite successfully on the Pioneer and flyby anomalies is applied to this problem. The model assumes that the inertia of the gyroscope is caused by Unruh radiation that appears as the ring and the fixed stars accelerate relative to it, and that this radiation is subject to a Hubble-scale Casimir effect. The model predicts that the sudden acceleration of the nearby ring causes a slight increase in the inertial mass of the gyroscope, and, to conserve momentum in the reference frame of the spinning Earth, the gyroscope rotates clockwise with an acceleration ratio of 1.8+/-0.25x10^-8 in agreement with the observed ratio. However, this model does not explain the parity violation seen in some of the gyroscope data. To test these ideas the Tajmar experiment (setup B) could be exactly reproduced in the southern hemisphere, since the model predicts that the anomalous acceleration should then be anticlockwise.Comment: 9 pages, 1 figure. Accepted by EPL on the 4th December, 200

X-ray absorption study of Ti-bearing silicate glasses

Ti K-edge XANES spectra have been collected on a series of Ti-bearing silicate glasses with metasilicate and tetrasilicate compositions. The intensity of the preedge feature in these spectra has been found to change with glass composition and varies from 29 to 58% (normalized intensity) suggesting a variation in structural environent around the absorbing atom. The pre-edge peak intensity increases for the alkali titanium tetrasilicate glasses from 35% to 58% in the order Li < Na < K < Rb, Cs whereas for the metasilicate compositions there is a maximum for the K-bearing glass. The pre-edge peak intensity remains constant for the alkaline earth titanium metasilicate glasses, Ca and Sr (34%) but increases slightly for Ba (41%). As the intensity of this feature is inversely correlated with coordination number, a comparison of the pre-edge intensity data for the investigated glasses with those of materials of known coordination number leads us to establish a regression equation and to infer that the average coordination number of Ti in these glasses ranges from 4.8 to 5.8. Large alkali cations appear to stabilize a relatively low average coordination number for Ti in silicate melts. The Ti structural environment results appear also to vary as a function of SiO2 content within the K2O-TiO2-SiO2 system. A number of physical properties of the melts from which these glasses were quenched and of other Ti-bearing silicate melts, have been determined in recent years. Clear evidence of a variable coordination number of Ti, consistent with the interpretation of the present XANES data is available from density measurements. These and other property determinations are compared with the present spectroscopic observations in an attempt to relate structure and properties in these melts which contain a major component with variable coordination number

Measurement of Gravitomagnetic and Acceleration Fields Around Rotating Superconductors

It is well known that a rotating superconductor produces a magnetic field proportional to its angular velocity. The authors conjectured earlier, that in addition to this so-called London moment, also a large gravitomagnetic field should appear to explain an apparent mass increase of Niobium Cooper-pairs. A similar field is predicted from Einstein's general relativity theory and the presently observed amount of dark energy in the universe. An experimental facility was designed and built to measure small acceleration fields as well as gravitomagnetic fields in the vicinity of a fast rotating and accelerating superconductor in order to detect this so-called gravitomagnetic London moment. This paper summarizes the efforts and results that have been obtained so far. Measurements with Niobium superconductors indeed show first signs which appear to be within a factor of 2 of our theoretical prediction. Possible error sources as well as the experimental difficulties are reviewed and discussed. If the gravitomagnetic London moment indeed exists, acceleration fields could be produced in a laboratory environment.Comment: To appear in the proceedings of the STAIF-2007 conference published by AI

Dynamical Evolution of Galaxies in Clusters

Tidal forces acting on galaxies in clusters lead to a strong dynamical evolution. In order to quantify the amount of evolution, I run self-consistent N-body simulations of disk galaxies for a variety of models in the hierarchically forming clusters. The tidal field along the galactic orbits is extracted from the simulations of cluster formation in the Omega_0=1; Omega_0=0.4; and Omega_0=0.4, Omega_Lambda=0.6 cosmological scenarios. For large spiral galaxies with the rotation speed of 250 km/s, tidal interactions truncate massive dark matter halos at 30 +- 6 kpc, and thicken stellar disks by a factor 2 to 3, increasing Toomre's parameter to Q > 2 and halting star formation. Low density galaxies, such as the dwarf spheroidals with the circular velocity of 20 km/s and the extended low surface brightness galaxies with the scale length of 10-15 kpc, are completely disrupted by tidal shocks. Their debris contribute to the diffuse intracluster light. The tidal effects are significant not only in the core but throughout the cluster and can be parametrized by the critical tidal density. The tidally-induced evolution results in the transformation of the infalling spirals into S0 galaxies and in the depletion of the LSB population. In the low Omega_0 cosmological models, clusters form earlier and produce stronger evolution of galaxies.Comment: accepted to Ap