Generalizing Optical Geometry

We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz and Lasota 1997, Class. Quantum Grav. 14 (1997) A23). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson, Class. Quantum Grav. 23 (2006) 1) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity.Comment: 19 pages, 1 figure. A more general analysis is presented than in the former version. See also the companion papers arXiv:0708.2493, arXiv:0708.2533 and arXiv:0708.253

Inertial forces and the foundations of optical geometry

Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in General Relativity. Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota, Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory has been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference is shearing) appears novel. For the particular case of a hypersurface-forming congruence, using a suitable rescaling of spacetime, we show that a geodesic photon is always following a line that is spatially straight with respect to the new curvature measure. This fact is intimately connected to Fermat's principle, and allows for a certain generalization of the optical geometry as will be further pursued in a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61). For the particular case when the shear-tensor vanishes, we present the inertial force equation in three-dimensional form (using the bold face vector notation), and note how similar it is to its Newtonian counterpart. From the spatial curvature measures that we introduce, we derive corresponding covariant differentiations of a vector defined along a spacetime trajectory. This allows us to connect the formalism of this paper to that of Jantzen et. al. (see e.g. Bini et. al., Int. J. Mod. Phys. D 6 (1997) 143).Comment: 42 pages, 7 figure

Non-equilibrium dynamics in an interacting nanoparticle system

Non-equilibrium dynamics in an interacting Fe-C nanoparticle sample, exhibiting a low temperature spin glass like phase, has been studied by low frequency ac-susceptibility and magnetic relaxation experiments. The non-equilibrium behavior shows characteristic spin glass features, but some qualitative differences exist. The nature of these differences is discussed.Comment: 7 pages, 11 figure

Force generation in small ensembles of Brownian motors

The motility of certain gram-negative bacteria is mediated by retraction of type IV pili surface filaments, which are essential for infectivity. The retraction is powered by a strong molecular motor protein, PilT, producing very high forces that can exceed 150 pN. The molecular details of the motor mechanism are still largely unknown, while other features have been identified, such as the ring-shaped protein structure of the PilT motor. The surprisingly high forces generated by the PilT system motivate a model investigation of the generation of large forces in molecular motors. We propose a simple model, involving a small ensemble of motor subunits interacting through the deformations on a circular backbone with finite stiffness. The model describes the motor subunits in terms of diffusing particles in an asymmetric, time-dependent binding potential (flashing ratchet potential), roughly corresponding to the ATP hydrolysis cycle. We compute force-velocity relations in a subset of the parameter space and explore how the maximum force (stall force) is determined by stiffness, binding strength, ensemble size, and degree of asymmetry. We identify two qualitatively different regimes of operation depending on the relation between ensemble size and asymmetry. In the transition between these two regimes, the stall force depends nonlinearly on the number of motor subunits. Compared to its constituents without interactions, we find higher efficiency and qualitatively different force-velocity relations. The model captures several of the qualitative features obtained in experiments on pilus retraction forces, such as roughly constant velocity at low applied forces and insensitivity in the stall force to changes in the ATP concentration.Comment: RevTex 9 pages, 4 figures. Revised version, new subsections in Sec. III, removed typo

Memory and superposition in a spin glass

Non-equilibrium dynamics in a Ag(Mn) spin glass are investigated by measurements of the temperature dependence of the remanent magnetisation. Using specific cooling protocols before recording the thermo- or isothermal remanent magnetisations on re-heating, it is found that the measured curves effectively disclose non-equilibrium spin glass characteristics such as ageing and memory phenomena as well as an extended validity of the superposition principle for the relaxation. The usefulness of this "simple" dc-method is discussed, as well as its applicability to other disordered magnetic systems.Comment: REVTeX style; 8 pages, 4 figure

On the origin of trisomy 21 Down syndrome

Background: Down syndrome, characterized by an extra chromosome 21 is the most common genetic cause for congenital malformations and learning disability. It is well known that the extra chromosome 21 most often originates from the mother, the incidence increases with maternal age, there may be aberrant maternal chromosome 21 recombination and there is a higher recurrence in young women. In spite of intensive efforts to understand the underlying reason(s) for these characteristics, the origin still remains unknown. We hypothesize that maternal trisomy 21 ovarian mosaicism might provide the major causative factor. Results: We used fluorescence in situ hybridization (FISH) with two chromosome 21-specific probes to determine the copy number of chromosome 21 in ovarian cells from eight female foetuses at gestational age 14–22 weeks. All eight phenotypically normal female foetuses were found to be mosaics, containing ovarian cells with an extra chromosome 21. Trisomy 21 occurred with about the same frequency in cells that had entered meiosis as in pre-meiotic and ovarian mesenchymal stroma cells. Conclusion: We suggest that most normal female foetuses are trisomy 21 ovarian mosaics and the maternal age effect is caused by differential selection of these cells during foetal and postnatal development until ovulation. The exceptional occurrence of high-grade ovarian mosaicism may explain why some women have a child with Down syndrome already at young age as well as the associated increased incidence at subsequent conceptions. We also propose that our findings may explain the aberrant maternal recombination patterns previously found by family linkage analysis

A comparative study of techniques used for porous membrane characterization: pore characterization

A range of commerical UF membranes have been characterized by thermoporometry, biliquid permporometry and molecular weight cut-off experiments. A comparison of results from these three independent techniques for the same types of membrane shows an indication of the strength and weakness of the methods. MWCO values determined from actual rejection values using PEG and dextran were significantly lower than the manufacturer supplied data. The data obtained using the biliquid permporometry and solute rejection tests produced contrasting results for Amicon polysulfone (PM30) and regenerated cellulose (YM30) membranes. While MWCO determination resulted in sharper cut-off curves, the biliquid permporometry offered a broader size distribution with the PM30 and vice versa with the YM30. The pore sizes obtained by thermoporometry were significantly larger than those by the biliquid permporometry. The biliquid permporometry and thermoporometry give significantly higher values than the MWCO method. The closest comparison is obtained between the EM values and the MWCO method. This suggests that the controlling pore dimension for separation is the surface skin dimension