Gravitational dynamics for all tensorial spacetimes carrying predictive, interpretable and quantizable matter

Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations that are predictive, interpretable and quantizable. These three conditions on matter translate into three corresponding algebraic conditions on the underlying tensorial geometry, namely to be hyperbolic, time-orientable and energy-distinguishing. Lorentzian metrics, on which general relativity and the standard model of particle physics are built, present just the simplest tensorial spacetime geometry satisfying these conditions. The problem of finding gravitational dynamics---for the general tensorial spacetime geometries satisfying the above minimum requirements---is reformulated in this paper as a system of linear partial differential equations, in the sense that their solutions yield the actions governing the corresponding spacetime geometry. Thus the search for modified gravitational dynamics is reduced to a clear mathematical task.Comment: 47 pages, no figures, minor update

Purple dwarfs : New L subdwarfs from UKIDSS and SDSS

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The first L subdwarf was a discovered only ten years ago. Less than ten L subdwarfs been published in the literature to date. Metal-poor ultracool atmospheres has not been well understood. Halo mass function cross substellar limit has not been measured. We used UKIDSS and SDSS to search for L subdwarfs. We have confirmed some new L subdwarfs and are following up more candidates with ground based large telescopes. We discussed spectral features of L subdwarfs and halo brown dwarfs

Relative Reactivity of the Metal-Amido versus Metal-Imido Bond in Linked Cp-Amido and Half-Sandwich Complexes of Vanadium

Treatment of (η5-C5H4C2H4NR)V(N-t-Bu)Me (R = Me, i-Pr) and CpV(N-p-Tol)(N-i-Pr2)Me (Cp = η5-C5H5) with B(C6F5)3 or [Ph3C][B(C6F5)4] results in formation of the corresponding cations, [(η5-C5H4C2H4NR)V(N-t-Bu)]+ and [CpV(N-p-Tol)(N-i-Pr2)]+. The latter could also be generated as its N,N-dimethylaniline adduct by treatment of the methyl complex with [PhNMe2H][BAr4] (Ar = Ph, C6F5). Instead, the analogous reaction with the linked Cp-amido precursor results in protonation of the imido-nitrogen atom. Sequential cyclometalation of the amide substituents gave cationic imine complexes [(η5-C5H4C2H4NCR'2)V(NH-t-Bu)]+ (R' = H, Me) and methane. Reaction of cationic [(η5-C5H4C2H4NR)V(N-t-Bu)]+ with olefins affords the corresponding olefin adducts, whereas treatment with 1 or 2 equiv of 2-butyne results in insertion of the alkyne into the vanadium-nitrogen single bond, affording the mono- and bis-insertion products [(η5-C5H4C2H4N(i-Pr)C2Me2)V(N-t-Bu)]+ and [(η5-C5H4C2H4N(i-Pr)C4Me4)V(N-t-Bu)]+. The same reaction with the half-sandwich compound [CpV(N-p-Tol)(N-i-Pr2)]+ results in a paramagnetic compound that, upon alcoholysis, affords sec-butylidene-p-tolylamine, suggesting an initial [2+2] cycloaddition reaction. The difference in reactivity between the V-N bond versus the V=N bond was further studied using computational methods. Results were compared to the isoelectronic titanium system CpTi(NH)(NH2). These studies indicate that the kinetic product in each system is derived from a [2+2] cycloaddition reaction. For titanium, this was found as the thermodynamic product as well, whereas the insertion reaction was found to be thermodynamically more favorable in the case of vanadium.

Electrical and network properties of flexible silver-nanowire composite electrodes under mechanical strain

Flexible and conductive silver-nanowire photopolymer composites are fabricated and studied under mechanical strain. The initial resistances of the unstretched flexible composites are between 0.27 Ω mm−1 and 1.2 Ω mm−1 for silver-nanowire concentrations between 120 μg cm−2 and 40 μg cm−2. Stretching of the samples leads to an increased resistance by a factor of between 72 for 120 μg cm−2 and 343 for 40 μg cm−2 at elongations of 23%. In order to correlate network morphology and electrical properties, micrographs are recorded during stretching. The Fiber Image Network Evaluation (FINE) algorithm determines morphological silver-nanowire network properties under stretching. For unstretched and stretched samples, an isotropic nanowire network is found with only small changes in fiber orientation. Monte-Carlo simulations on 2D percolation networks of 1D conductive wires and the corresponding network resistance due to tunneling of electrons at nanowire junctions confirm that the elastic polymer matrix under strain exhibits forces in agreement with Hooke's law. By variation of a critical force distribution the resistance curves are accurately reproduced. This results in a model that is dominated by quantum-mechanical tunneling at nanowire junctions explaining the electrical behavior and the sensitivity of nanowire-composites with different filler concentrations under mechanical strain

Interacting Binaries with Eccentric Orbits. Secular Orbital Evolution Due To Conservative Mass Transfer

We investigate the secular evolution of the orbital semi-major axis and eccentricity due to mass transfer in eccentric binaries, assuming conservation of total system mass and orbital angular momentum. Assuming a delta function mass transfer rate centered at periastron, we find rates of secular change of the orbital semi-major axis and eccentricity which are linearly proportional to the magnitude of the mass transfer rate at periastron. The rates can be positive as well as negative, so that the semi-major axis and eccentricity can increase as well as decrease in time. Adopting a delta-function mass-transfer rate of 10^{-9} M_\sun {\rm yr}^{-1} at periastron yields orbital evolution timescales ranging from a few Myr to a Hubble time or more, depending on the binary mass ratio and orbital eccentricity. Comparison with orbital evolution timescales due to dissipative tides furthermore shows that tides cannot, in all cases, circularize the orbit rapidly enough to justify the often adopted assumption of instantaneous circularization at the onset of mass transfer. The formalism presented can be incorporated in binary evolution and population synthesis codes to create a self-consistent treatment of mass transfer in eccentric binaries.Comment: 16 pages, 8 figures, Accepted by The Astrophysical Journa

Longitudinal 7T MRI reveals volumetric changes in subregions of human medial temporal lobe to sex hormone fluctuations

The hippocampus and surrounding medial temporal lobe (MTL) are critical for memory processes, with local atrophy linked to memory deficits. Animal work shows that MTL subregions densely express sex hormone receptors and exhibit rapid structural changes synchronized with hormone fluctuations. Such transient effects in humans have thus far not been shown. By combining a dense-sampling protocol, ultra-high field neuroimaging and individually-derived segmentation analysis, we demonstrate how estradiol and progesterone fluctuations affect MTL subregion volumes across the human menstrual cycle. Twenty-seven healthy women (19-34 years) underwent 7T MRI at six timepoints to acquire T1-weighted and T2-weighted images. Linear mixed-effects modeling showed positive associations between estradiol and parahippocampal cortex volume, progesterone and subiculum and perirhinal Area 35 volumes, and an estradiol*progesterone interaction with CA1 volume. We confirmed volumetric changes were not driven by hormone-related water (cerebral spinal fluid) or blood-flow (pulsed arterial spin labeling) changes. These findings suggest that sex hormones alter structural brain plasticity in subregions that are differentially sensitive to hormones. Mapping how endogenous endocrine factors shape adult brain structure has critical implications for women’s health during the reproductive years as well as later in life, such as increased dementia risk following perimenopause, a period of pronounced sex hormone fluctuations

Switchable synchronisation of pirouetting motions in a redox-active [3]rotaxane

In this study, the crown/ammonium [3]rotaxane R2 is reported which allows a switchable synchronisation of wheel pirouetting motions. The rotaxane is composed of a dumbbell-shaped axle molecule with two mechanically interlocked macrocycles which are decorated with a redox-active tetrathiafulvalene (TTF) unit. Electrochemical, spectroscopic, and electron paramagnetic resonance experiments reveal that rotaxane R2 can be reversibly switched between four stable oxidation states (R2, R2˙+, R22(˙+), and R24+). The oxidations enable non-covalent, cofacial interactions between the TTF units in each state—including a stabilised mixed-valence (TTF2)˙+ and a radical-cation (TTF˙+)2 dimer interaction—which dictate a syn (R2, R2˙+, and R22(˙+)) or anti (R24+) ground state co-conformation of the wheels in the rotaxane. Furthermore, the strength of these wheel–wheel interactions varies with the oxidation state, and thus electrochemical switching allows a controllable synchronisation of the wheels’ pirouetting motions. DFT calculations explore the potential energy surface of the counter-rotation of the two interacting wheels in all oxidation states. The controlled coupling of pirouetting motions in rotaxanes can lead to novel molecular gearing systems which transmit rotational motion by switchable non-covalent interactions

Hierarchical model for the scale-dependent velocity of seismic waves

Elastic waves of short wavelength propagating through the upper layer of the Earth appear to move faster at large separations of source and receiver than at short separations. This scale dependent velocity is a manifestation of Fermat's principle of least time in a medium with random velocity fluctuations. Existing perturbation theories predict a linear increase of the velocity shift with increasing separation, and cannot describe the saturation of the velocity shift at large separations that is seen in computer simulations. Here we show that this long-standing problem in seismology can be solved using a model developed originally in the context of polymer physics. We find that the saturation velocity scales with the four-third power of the root-mean-square amplitude of the velocity fluctuations, in good agreement with the computer simulations.Comment: 7 pages including 3 figure

Universal corrections to scaling for block entanglement in spin-1/2 XX chains

We consider the R\'enyi entropies $S_n(\ell)$ in the one dimensional spin-1/2 Heisenberg XX chain in a magnetic field. The case n=1 corresponds to the von Neumann ``entanglement'' entropy. Using a combination of methods based on the generalized Fisher-Hartwig conjecture and a recurrence relation connected to the Painlev\'e VI differential equation we obtain the asymptotic behaviour, accurate to order ${\cal O}(\ell^{-3})$, of the R\'enyi entropies $S_n(\ell)$ for large block lengths $\ell$. For n=1,2,3,10 this constitutes the 3,6,10,48 leading terms respectively. The o(1) contributions are found to exhibit a rich structure of oscillatory behaviour, which we analyze in some detail both for finite $n$ and in the limit $n\to\infty$.Comment: 25 pages, 5 figure