Twisting commutative algebraic groups

If $V$ is a commutative algebraic group over a field $k$, $O$ is a commutative ring that acts on $V$, and $I$ is a finitely generated free $O$-module with a right action of the absolute Galois group of $k$, then there is a commutative algebraic group $I \otimes_O V$ over $k$, which is a twist of a power of $V$. These group varieties have applications to cryptography (in the cases of abelian varieties and algebraic tori over finite fields) and to the arithmetic of abelian varieties over number fields. For purposes of such applications we devote this article to making explicit this tensor product construction and its basic properties.Comment: To appear in Journal of Algebra. Minor changes from original versio

Anharmonic Torsional Stiffness of DNA Revealed under Small External Torques

DNA supercoiling plays an important role in a variety of cellular processes. The torsional stress related with supercoiling may be also involved in gene regulation through the local structure and dynamics of the double helix. To check this possibility steady torsional stress was applied to DNA in the course of all-atom molecular dynamics simulations. It is found that small static untwisting significantly reduces the torsional persistence length ($l_t$) of GC-alternating DNA. For the AT-alternating sequence a smaller effect of the opposite sign is observed. As a result, the measured $l_t$ values are similar under zero stress, but diverge with untwisting. The effect is traced to sequence-specific asymmetry of local torsional fluctuations, and it should be small in long random DNA due to compensation. In contrast, the stiffness of special short sequences can vary significantly, which gives a simple possibility of gene regulation via probabilities of strong fluctuations. These results have important implications for the role of local DNA twisting in complexes with transcription factors.Comment: 8 pages, 5 figures, to appear in Phys. Rev. Let

NGC 4654: polarized radio continuum emission as a diagnostic tool for a galaxy--cluster interaction

A recent comparison between deep VLA HI observations and dynamical models of the Virgo cluster spiral galaxy NGC 4654 has shown that only a model involving a combination of a tidal interaction and ram pressure can reproduce the data. Deep radio polarization studies, together with detailed MHD modeling, can independently verify those conclusions, that are based on HI observations and dynamical models. We performed deep polarized radio-continuum observations of the Virgo cluster spiral galaxy NGC 4654 with the Effelsberg 100m telescope at 8.35 GHz and the VLA at 4.85 GHz. Detailed 3D MHD simulations were made to determine the large-scale magnetic field and the emission distribution of the polarized radio continuum in the model, during the galaxy evolution within the cluster environment. This direct comparison between the observed and simulated polarized radio continuum emission corroborates the earlier results, that the galaxy had a recent rapid close encounter with NGC 4639 and is undergoing weak ram pressure by the intracluster medium. This combination of deep radio polarization studies and detailed MHD modeling thus gives us unique insight into the interactions of a galaxy with its cluster environment. It represents a diagnostic tool that is complementary to deep HI observations.Comment: Corrected galaxy name in captions of figures (1 & 2

Large-scale radio continuum properties of 19 Virgo cluster galaxies The influence of tidal interactions, ram pressure stripping, and accreting gas envelopes

Deep scaled array VLA 20 and 6cm observations including polarization of 19 Virgo spirals are presented. This sample contains 6 galaxies with a global minimum of 20cm polarized emission at the receding side of the galactic disk and quadrupolar type large-scale magnetic fields. In the new sample no additional case of a ram-pressure stripped spiral galaxy with an asymmetric ridge of polarized radio continuum emission was found. In the absence of a close companion, a truncated HI disk, together with a ridge of polarized radio continuum emission at the outer edge of the HI disk, is a signpost of ram pressure stripping. 6 out of the 19 observed galaxies display asymmetric 6cm polarized emission distributions. Three galaxies belong to tidally interacting pairs, two galaxies host huge accreting HI envelopes, and one galaxy had a recent minor merger. Tidal interactions and accreting gas envelopes can lead to compression and shear motions which enhance the polarized radio continuum emission. In addition, galaxies with low average star formation rate per unit area have a low average degree of polarization. Shear or compression motions can enhance the degree of polarization. The average degree of polarization of tidally interacting galaxies is generally lower than expected for a given rotation velocity and star formation activity. This low average degree of polarization is at least partly due to the absence of polarized emission from the thin disk. Ram pressure stripping can decrease whereas tidal interactions most frequently decreases the average degree of polarization of Virgo spiral galaxies. We found that moderate active ram pressure stripping has no influence on the spectral index, but enhances the global radio continuum emission with respect to the FIR emission, while an accreting gas envelope can but not necessarily enhances the radio continuum emission with respect to the FIR emission.Comment: 37 pages, 26 figures, accepted for publication in A&

A dynamical model for the heavily ram pressure stripped Virgo spiral galaxy NGC 4522

A dynamical model including ram pressure stripping is applied to the strongly HI deficient Virgo spiral galaxy NGC 4522. A carefully chosen model snapshot is compared with existing VLA HI observations. The model successfully reproduces the large-scale gas distribution and the velocity field. However it fails to reproduce the large observed HI linewidths in the extraplanar component, for which we give possible explanations. In a second step, we solve the induction equation on the velocity fields of the dynamical model and calculate the large scale magnetic field. Assuming a Gaussian distribution of relativistic electrons we obtain the distribution of polarized radio continuum emission which is also compared with our VLA observations at 6 cm. The observed maximum of the polarized radio continuum emission is successfully reproduced. Our model suggests that the ram pressure maximum occurred only ~50 Myr ago. Since NGC 4522 is located far away from the cluster center (~1 Mpc) where the intracluster medium density is too low to cause the observed stripping if the intracluster medium is static and smooth, two scenarios are envisaged: (i) the galaxy moves very rapidly within the intracluster medium and is not even bound to the cluster; in this case the galaxy has just passed the region of highest intracluster medium density; (ii) the intracluster medium is not static but moving due to the infall of the M49 group of galaxies. In this case the galaxy has just passed the region of highest intracluster medium velocity. This study shows the strength of combining high resolution HI and polarized radio continuum emission with detailed numerical modeling of the evolution of the gas and the large-scale magnetic field.Comment: 15 pages, 11 figures, accepted for publication in A&

Magnetic field evolution in galaxies interacting with the intracluster medium. 3D numerical simulations

A fully three-dimensional (3D) magnetohydrodynamical (MHD) model is applied to simulate the evolution of the large-scale magnetic field in cluster galaxies interacting with the intra-cluster medium (ICM). As the model input we use a time dependent gas velocity field resulting from 3D N-body sticky-particle simulations of a galaxy. The modeled clouds are affected by the ram pressure due to their rapid motion through the ICM in the central part of a cluster. Numerical simulations have shown that after the initial compression phase due to ram pressure a process of gas re-accretion onto the galactic disk takes place. We find that the gas re-accretion leads to an increase of the total magnetic energy without any dynamo action. The simulated magnetic fields are used to construct the model maps of high-frequency (Faraday rotation-free) polarized radio emission. We show that the evolution of the polarized intensity shows features that are characteristic for different evolutionary stages of an ICM-ISM interaction. The comparison of polarized radio continuum emission maps with our model permits to determine whether the galaxy is in the compression or in the re-accretion phase. It also provides an important constraint upon the dynamical modeling of an ICM-ISM interactions.Comment: 12 pages with 11 figures. Accepted for publication in A&

Characteristic Energy of the Coulomb Interactions and the Pileup of States

Tunneling data on $\mathrm{La_{1.28}Sr_{1.72}Mn_2O_7}$ crystals confirm Coulomb interaction effects through the $\sqrt{\mathrm{E}}$ dependence of the density of states. Importantly, the data and analysis at high energy, E, show a pileup of states: most of the states removed from near the Fermi level are found between ~40 and 130 meV, from which we infer the possibility of universal behavior. The agreement of our tunneling data with recent photoemission results further confirms our analysis.Comment: 4 pages, 4 figures, submitted to PR

Formation of gaseous arms in barred galaxies with dynamically important magnetic field : 3D MHD simulations

We present results of three-dimensional nonlinear MHD simulations of a large-scale magnetic field and its evolution inside a barred galaxy with the back reaction of the magnetic field on the gas. The model does not consider the dynamo process. To compare our modeling results with observations, we construct maps of the high-frequency (Faraday-rotation-free) polarized radio emission on the basis of simulated magnetic fields. The model accounts for the effects of projection and the limited resolution of real observations. We performed 3D MHD numerical simulations of barred galaxies and polarization maps. The main result is that the modeled magnetic field configurations resemble maps of the polarized intensity observed in barred galaxies. They exhibit polarization vectors along the bar and arms forming coherent structures similar to the observed ones. In the paper, we also explain the previously unsolved issue of discrepancy between the velocity and magnetic field configurations in this type of galaxies. The dynamical influence of the bar causes gas to form spiral waves that travel outwards. Each gaseous spiral arm is accompanied by a magnetic counterpart, which separates and survives in the inter-arm region. Because of a strong compression, shear of non-axisymmetric bar flows and differential rotation, the total energy of modeled magnetic field grows constantly, while the azimuthal flux grows slightly until 0.05\Gyr and then saturates.Comment: 4 pages, 4 figure