Fatigue crack growth model RANDOM2 user manual. Appendix 1: Development of advanced methodologies for probabilistic constitutive relationships of material strength models

FORTRAN program RANDOM2 is presented in the form of a user's manual. RANDOM2 is based on fracture mechanics using a probabilistic fatigue crack growth model. It predicts the random lifetime of an engine component to reach a given crack size. Details of the theoretical background, input data instructions, and a sample problem illustrating the use of the program are included

Fatigue crack growth model RANDOM2 user manual, appendix 1

The FORTRAN program RANDOM2 is documented. RANDOM2 is based on fracture mechanics using a probabilistic fatigue crack growth model. It predicts the random lifetime of an engine component to reach a given crack size. Included in this user manual are details regarding the theoretical background of RANDOM2, input data, instructions and a sample problem illustrating the use of RANDOM2. Appendix A gives information on the physical quantities, their symbols, FORTRAN names, and both SI and U.S. Customary units. Appendix B includes photocopies of the actual computer printout corresponding to the sample problem. Appendices C and D detail the IMSL, Ver. 10(1), subroutines and functions called by RANDOM2 and a SAS/GRAPH(2) program that can be used to plot both the probability density function (p.d.f.) and the cumulative distribution function (c.d.f.)

Electro-Mechanical Resonant Magnetic Field Sensor

We describe a new type of magnetic field sensor which is termed an Electro-Mechanical Resonant Sensor (EMRS). The key part of this sensor is a small conductive elastic element with low damping rate and therefore a high Q fundamental mode of frequency $f_1$. An AC current is driven through the elastic element which, in the presence of a magnetic field, causes an AC force on the element. When the frequency of the AC current matches the resonant frequency of the element, maximum vibration of the element occurs and this can be measured precisely by optical means. We have built and tested a model sensor of this type using for the elastic element a length of copper wire of diameter 0.030 mm formed into a loop shape. The wire motion was measured using a light emitting diode photo-transistor assembly. This sensor demonstrated a sensitivity better than 0.001G for an applied magnetic field of $\sim 1$G and a good selectivity for the magnetic field direction. The sensitivity can be easily improved by a factor of $\sim 10 - 100$ by more sensitive measurement of the elastic element motion and by having the element in vacuum to reduce the drag force.Comment: 8 pages, 9 figure

Some Issues In The Loop Variable Approach to Open Strings and an Extension to Closed Strings

Some issues in the loop variable renormalization group approach to gauge invariant equations for the free fields of the open string are discussed. It had been shown in an earlier paper that this leads to a simple form of the gauge transformation law. We discuss in some detail some of the curious features encountered there. The theory looks a little like a massless theory in one higher dimension that can be dimensionally reduced to give a massive theory. We discuss the origin of some constraints that are needed for gauge invariance and also for reducing the set of fields to that of standard string theory. The mechanism of gauge invariance and the connection with the Virasoro algebra is a little different from the usual story and is discussed. It is also shown that these results can be extended in a straightforward manner to closed strings.Comment: 24 page

Holomorphic Factorization and Renormalization Group in Closed String Theory

The prescription of Kawai, Lewellen and Tye for writing the closed string tree amplitudes as sums of products of open string tree amplitudes, is applied to the world sheet renormalization group equation. The main point is that regularization of the Minkowski (rather than Euclidean) world sheet theory allows factorization into left-moving and right-moving sectors to be maintained. Explicit calculations are done for the tachyon and the (gauge-fixed) graviton.Comment: 19 pages, Latex File, 9 figure

Loop Variables with Chan-Paton Factors

The Loop Variable method that has been developed for the U(1) bosonic open string is generalized to include non-Abelian gauge invariance by incorporating "Chan-Paton" gauge group indices. The scale transformation symmetry $k(s) \to k(s) \lambda (s)$ that was responsible for gauge invariance in the U(1) case continues to be a symmetry. In addition there is a "rotation" symmetry. Both symmetries crucially involve the massive modes. However it is plausible that only a linear combination, which is the usual Yang-Mills transformation on massless fields, has a smooth (world sheet) continuum limit. We also illustrate how an infinite number of terms in the equation of motion in the cutoff theory add up to give a term that has a smooth continuum limit, and thus contributes to the low energy Yang-Mills equation of motion.Comment: One paragraph has been modified and the connection with the Renormalization Group is explaine

Magneto-centrifugally driven winds: comparison of MHD simulations with theory

Stationary magnetohydrodynamic (MHD) outflows from a rotating, conducting Keplerian accretion disk threaded by B-field are investigated numerically by time-dependent, axisymmetric (2.5D) simulations using a Godunov-type code. A large class of stationary magneto-centrifugally driven winds are found where matter is accelerated from a thermal speed at the disk to much larger velocity, greater than the fast magnetosonic speed and larger than the escape speed. The flows are approximately spherical outflows with only small collimation within the simulation region. Numerical results are shown to coincide with the theoretical predictions of ideal, axisymmetric MHD to high accuracy. Investigation of the influence of outer boundary conditions, particularly that on the toroidal component of magnetic field shows that the commonly used ``free'' boundary condition leads to artificial magnetic forces which can act to give spurious collimation. New boundary conditions are proposed which do not generate artificial forces. Artificial results may also arise for cases where the Mach cones on the outer boundaries are partially directed into the simulation region.Comment: 19 pages, 18 figures, emulapj.sty is use

Vortex migration in protoplanetary disks

We consider the radial migration of vortices in two-dimensional isothermal gaseous disks. We find that a vortex core, orbiting at the local gas velocity, induces velocity perturbations that propagate away from the vortex as density waves. The resulting spiral wave pattern is reminiscent of an embedded planet. There are two main causes for asymmetries in these wakes: geometrical effects tend to favor the outer wave, while a radial vortensity gradient leads to an asymmetric vortex core, which favors the wave at the side that has the lowest density. In the case of asymmetric waves, which we always find except for a disk of constant pressure, there is a net exchange of angular momentum between the vortex and the surrounding disk, which leads to orbital migration of the vortex. Numerical hydrodynamical simulations show that this migration can be very rapid, on a time scale of a few thousand orbits, for vortices with a size comparable to the scale height of the disk. We discuss the possible effects of vortex migration on planet formation scenarios.Comment: 13 pages, 13 figures, accepted for publication in Ap

BZ-MC-BP Model for Jet Production from Black Hole Accretion Disc

Three energy mechanisms invoking large-scale magnetic fields are incorporated in a model to interpret jet production in black hole (BH) systems, i.e., the Blandford-Znajek (BZ), the magnetic coupling (MC) and Blandford-Payne (BP) processes. These energy mechanisms can coexist in BH accretion disc based on the magnetic field configurations constrained by the screw instability, provided that the BH spin and the power-law index indicating the variation of the magnetic field at an accretion disc are greater than some critical values. In this model the jets are driven by the BZ process in the Poynting flux regime and by the BP process in the hydromagnetic regime, being consistent with the spine/sheath jet structure observed in BH sources of stellar and supermassive size.Comment: 9 pages, 6 figures, accepted by MNRA