Class and rank of differential modules

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a substitute for the length of a free complex--and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over noetherian commutative rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.Comment: 27 pages. Minor changes; mainly stylistic. To appear in Inventiones Mathematica

Analysis of the doubly heavy baryons in the nuclear matter with the QCD sum rules

In this article, we study the doubly heavy baryon states $\Xi_{cc}$, $\Omega_{cc}$, $\Xi_{bb}$ and $\Omega_{bb}$ in the nuclear matter using the QCD sum rules, and derive three coupled QCD sum rules for the masses, vector self-energies and pole residues. The predictions for the mass-shifts in the nuclear matter $\Delta M_{\Xi_{cc}}=-1.11\,\rm{GeV}$, $\Delta M_{\Omega_{cc}}=-0.33\,\rm{GeV}$, $\Delta M_{\Xi_{bb}}=-3.37\,\rm{GeV}$ and $\Delta M_{\Omega_{bb}}=-1.05\,\rm{GeV}$ can be confronted with the experimental data in the future.Comment: 10 pages, 4 figure

Markovian MC simulation of QCD evolution at NLO level with minimum k_T

We present two Monte Carlo algorithms of the Markovian type which solve the modified QCD evolution equations at the NLO level. The modifications with respect to the standard DGLAP evolution concern the argument of the strong coupling constant alpha_S. We analyze the z - dependent argument and then the k_T - dependent one. The evolution time variable is identified with the rapidity. The two algorithms are tested to the 0.05% precision level. We find that the NLO corrections in the evolution of parton momentum distributions with k_T - dependent coupling constant are of the order of 10 to 20%, and in a small x region even up to 30%, with respect to the LO contributions.Comment: 32 pages, 9 pdf figure

Light Gluinos and the Parton Structure of the Nucleon

We study the effects of light gluinos with mass below about 1 GeV on the nucleon parton densities and the running of alpha_(S). It is shown that from the available high-statistics DIS data no lower bound on the gluino mass can be derived. Also in the new kinematical region accessible at HERA the influence of such light gluinos on structure f unctions is found to be very small and difficult to detect. For use in more direct searches involving final state signatures we present a radiative estimate of the gluino distribution in the nucleon.Comment: 23 pages, LateX, 8 figures, MPI-PhT/94-22, LMU-3/9

Propagation of Long-Wavelength Nonlinear Slow Sausage Waves in Stratified Magnetic Flux Tubes

The propagation of nonlinear, long-wavelength, slow sausage waves in an expanding magnetic flux tube, embedded in a non-magnetic stratified environment, is discussed. The governing equation for surface waves, which is akin to the Leibovich–Roberts equation, is derived using the method of multiple scales. The solitary wave solution of the equation is obtained numerically. The results obtained are illustrative of a solitary wave whose properties are highly dependent on the degree of stratification

Probing Sub-Micron Forces by Interferometry of Bose-Einstein Condensed Atoms

We propose a technique, using interferometry of Bose-Einstein condensed alkali atoms, for the detection of sub-micron-range forces. It may extend present searches at 1 micron by 6 to 9 orders of magnitude, deep into the theoretically interesting regime of 1000 times gravity. We give several examples of both four-dimensional particles (moduli), as well as higher-dimensional particles -- vectors and scalars in a large bulk-- that could mediate forces accessible by this technique.Comment: 32 pages, 5 figures, RevTeX4, expanded discussion of interactions, references added, to appear in PR

Current status of turbulent dynamo theory: From large-scale to small-scale dynamos

Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed.Comment: 36 pages, 11 figures, Spa. Sci. Rev., submitted to the special issue "Magnetism in the Universe" (ed. A. Balogh

Observation of the Ankle and Evidence for a High-Energy Break in the Cosmic Ray Spectrum

We have measured the cosmic ray spectrum at energies above $10^{17}$ eV using the two air fluorescence detectors of the High Resolution Fly's Eye experiment operating in monocular mode. We describe the detector, PMT and atmospheric calibrations, and the analysis techniques for the two detectors. We fit the spectrum to models describing galactic and extragalactic sources. Our measured spectrum gives an observation of a feature known as the ``ankle'' near $3\times 10^{18}$ eV, and strong evidence for a suppression near $6\times 10^{19}$ eV.Comment: 14 pages, 9 figures. To appear in Physics Letters B. Accepted versio

Electromotive Force and Large-Scale Magnetic Dynamo in a Turbulent Flow with a Mean Shear

An effect of sheared large-scale motions on a mean electromotive force in a nonrotating turbulent flow of a conducting fluid is studied. It is demonstrated that in a homogeneous divergence-free turbulent flow the alpha-effect does not exist, however a mean magnetic field can be generated even in a nonrotating turbulence with an imposed mean velocity shear due to a new ''shear-current" effect. A contribution to the electromotive force related with the symmetric parts of the gradient tensor of the mean magnetic field (the kappa-effect) is found in a nonrotating turbulent flows with a mean shear. The kappa-effect and turbulent magnetic diffusion reduce the growth rate of the mean magnetic field. It is shown that a mean magnetic field can be generated when the exponent of the energy spectrum of the background turbulence (without the mean velocity shear) is less than 2. The ''shear-current" effect was studied using two different methods: the Orszag third-order closure procedure and the stochastic calculus. Astrophysical applications of the obtained results are discussed.Comment: 12 pages, REVTEX4, submitted to Phys. Rev.

X-Ray and Radio Observations of Bright GeV Sources

We present X-ray and radio studies of sources which are brightabove 1 GeV (F_{>1GeV} > 4e-8 ph/cm^2/s. Only 11 out of ~30 of these gamma-ray sources have been identified with lower energy counterparts: 5 blazars and 6 pulsars. Three of these pulsars are surrounded by radio pulsar wind nebulae (PWN), two of which are also seen as bright, extended X-ray synchrotron nebulae. The ASCA X-ray telescope has observed 28 of the bright GeV sources, revealing an excess of F_{2-10keV} > 10e-12 ergs/cm^2/s sources within the {\it EGRET} error contours of the unidentified sources. Although several supernova remnants are positionally coincident with these sources, we find no X-ray evidence of high energy particle production in SNR shell shocks consistent with the GeV positions. We also present initial results from follow on radio imaging studies of several fields containing unidentified sources. We have discovered new X-ray/radio nebulae in three of these fields which are strong candidates for PWN. These sources, along with a similar nebula in CTA 1 and the PWN around PSR B1853+01 in W44, are all positionally coincident with variable EGRET sources. This suggests a class of variable gamma-ray sources associated with synchrotron emitting regions powered by the winds of young pulsars.Comment: 18 pages, 26 figures, To appear in the proceedings of the workshop: "The Nature of the Unidentified Galactic Gamma-Ray Sources" held at INAOE, Mexico, October 2000, (A.Carraminana, O. Reiner and D. Thompson,