Field dependence of the temperature at the peak of the ZFC magnetization

The effect of an applied magnetic field on the temperature at the maximum of the ZFC magnetization, $M_{ZFC}$, is studied using the recently obtained analytic results of Coffey et al. (Phys. Rev. Lett. {\bf 80}(1998) 5655) for the prefactor of the N\'{e}el relaxation time which allow one to precisely calculate the prefactor in the N\'{e}el-Brown model and thus the blocking temperature as a function of the coefficients of the Taylor series expansion of the magnetocrystalline anisotropy. The present calculations indicate that even a precise determination of the prefactor in the N\'{e}el-Brown theory, which always predicts a monotonic decrease of the relaxation time with increasing field, is insufficient to explain the effect of an applied magnetic field on the temperature at the maximum of the ZFC magnetization. On the other hand, we find that the non linear field-dependence of the magnetization along with the magnetocrystalline anisotropy appears to be of crucial importance to the existence of this maximum.Comment: 14 LaTex209 pages, 6 EPS figures. To appear in J. Phys.: Condensed Matte

Physical properties of the jet from DG Tauri on sub-arcsecond scales with HST/STIS

We derive the physical properties at the base of the jet from DG Tau both along and across the flow and as a function of velocity. We analysed seven optical spectra of the DG Tau jet, taken with the Hubble Space Telescope Imaging Spectrograph. The spectra were obtained by placing a long-slit parallel to the jet axis and stepping it across the jet width. The resulting position-velocity diagrams in optical forbidden emission lines allowed access to plasma conditions via calculation of emission line ratios. We find at the base of the jet high electron density, $n_e \sim$ 10$^5$, and very low ionisation, $x_e \sim 0.02-0.05$, which combine to give a total density up to $n_H \sim$ 3 10$^6$. This analysis confirms previous reports of variations in plasma parameters along the jet, (i.e. decrease in density by several orders of magnitude, increase of $x_e$ from 0.05 to a plateau at 0.7 downstream at 2$''$ from the star). Furthermore, a spatial coincidence is revealed between sharp gradients in the total density and supersonic velocity jumps. This strongly suggests that the emission is caused by shock excitation. The position-velocity diagrams indicate the presence of both fast accelerating gas and slower, less collimated material. We derive the mass outflow rate, $\dot{M}_j$, in the blue-shifted lobe in different velocity channels, that contribute to a total of $\dot{M}_j \sim$ 8 $\pm$ 4 10$^{-9}$ M$_\odot$ yr$^{-1}$. We estimate that a symmetric bipolar jet would transport at the low and intermediate velocities probed by rotation measurements, an angular momentum flux of $\dot{L}_j \sim$ 2.9 $\pm$ 1.5 10$^{-6}$ M$_\odot$ yr$^{-1}$ AU km s$^{-1}$. The derived properties of the DG Tau jet are demonstrated to be consistent with magneto-centrifugal theory. However, non-stationary modelling is required in order to explain all of the features revealed at high resolution.Comment: 16 pages, 18 figure

Thermally activated escape rates of uniaxial spin systems with transverse field

Classical escape rates of uniaxial spin systems are characterized by a prefactor differing from and much smaller than that of the particle problem, since the maximum of the spin energy is attained everywhere on the line of constant latitude: theta=const, 0 =< phi =< 2*pi. If a transverse field is applied, a saddle point of the energy is formed, and high, moderate, and low damping regimes (similar to those for particles) appear. Here we present the first analytical and numerical study of crossovers between the uniaxial and other regimes for spin systems. It is shown that there is one HD-Uniaxial crossover, whereas at low damping the uniaxial and LD regimes are separated by two crossovers.Comment: 4 PR pages, 3 figures, final published versio

On hypergeometric series reductions from integral representations, the Kampe de Feriet function, and elsewhere

Single variable hypergeometric functions pFq arise in connection with the power series solution of the Schrodinger equation or in the summation of perturbation expansions in quantum mechanics. For these applications, it is of interest to obtain analytic expressions, and we present the reduction of a number of cases of pFp and p+1F_p, mainly for p=2 and p=3. These and related series have additional applications in quantum and statistical physics and chemistry.Comment: 17 pages, no figure

Integral Relaxation Time of Single-Domain Ferromagnetic Particles

The integral relaxation time \tau_{int} of thermoactivating noninteracting single-domain ferromagnetic particles is calculated analytically in the geometry with a magnetic field H applied parallel to the easy axis. It is shown that the drastic deviation of \tau_{int}^{-1} from the lowest eigenvalue of the Fokker-Planck equation \Lambda_1 at low temperatures, starting from some critical value of H, is the consequence of the depletion of the upper potential well. In these conditions the integral relaxation time consists of two competing contributions corresponding to the overbarrier and intrawell relaxation processes.Comment: 8 pages, 3 figure

Monte Carlo simulation with time step quantification in terms of Langevin dynamics

For the description of thermally activated dynamics in systems of classical magnetic moments numerical methods are desirable. We consider a simple model for isolated magnetic particles in a uniform field with an oblique angle to the easy axis of the particles. For this model, a comparison of the Monte Carlo method with Langevin dynamics yields new insight in the interpretation of the Monte Carlo process, leading to the implementation of a new algorithm where the Monte Carlo step is time-quantified. The numeric results for the characteristic time of the magnetisation reversal are in excellent agreement with asymptotic solutions which itself are in agreement with the exact numerical results obtained from the Fokker-Planck equation for the Neel-Brown model.Comment: 5 pages, Revtex, 4 Figures include

Development and testing of laser Doppler system components for wake vortex monitoring. Volume 1: Scanner development, laboratory and field testing and system modeling

A servo-controlled range/elevation scanner for the laser Doppler velocimeter (LDV) was developed and tested in the field to assess its performance in detecting and monitoring aircraft trailing vortices in an airport environment. The elevation scanner provides a capability to manually point the LDV telescope at operator chosen angles from 3.2 deg. to 89.6 deg within 0.2 deg, or to automatically scan the units between operator chosen limits at operator chosen rates of 0.1 Hz to 0.5 Hz. The range scanner provides a capability to manually adjust the focal point of the system from a range of 32 meters to a range of 896 meters under operator control, or to scan between operator chosen limits and at rates from 0.1 Hz to 6.9 Hz. The scanner controls are designed to allow simulataneous range and elevation scanning so as to provide finger scan patterns, arc scan patterns, and vertical line scan patterns. The development and testing of the unit is discussed, along with a fluid dynamic model of the wake vortex developed in a laser Doppler vortex sensor simulation program

Organic molecules in the protoplanetary disk of DG Tau revealed by ALMA

Planets form in protoplanetary disks and inherit their chemical compositions. It is thus crucial to map the distribution and investigate the formation of simple organics, such as formaldehyde and methanol, in protoplanetary disks. We analyze ALMA observations of the nearby disk-jet system around the T Tauri star DG Tau in the o-H$_2$CO $3_{1,2}-2_{1,1}$ and CH$_3$OH $3_{-2,2}-4_{-1,4}$ E, $5_{0,5}-4_{0,4}$ A transitions at an unprecedented resolution of $\sim0.15"$, i.e., $\sim18$ au at a distance of 121 pc. The H$_2$CO emission originates from a rotating ring extending from $\sim40$ au with a peak at $\sim62$ au, i.e., at the edge of the 1.3mm dust continuum. CH$_3$OH emission is not detected down to an r.m.s. of 3 mJy/beam in the 0.162 km/s channel. Assuming an ortho-to-para ratio of 1.8-2.8 the ring- and disk-height-averaged H$_2$CO column density is $\sim0.3-4\times10^{14}$ cm$^{-2}$, while that of CH$_3$OH is $<0.04-0.7\times10^{14}$ cm$^{-2}$. In the inner $40$ au no o-H$_2$CO emission is detected with an upper limit on its beam-averaged column density of $\sim0.5-6\times10^{13}$ cm$^{-2}$. The H$_2$CO ring in the disk of DG Tau is located beyond the CO iceline (R$_{\rm CO}\sim30$ au). This suggests that the H$_2$CO abundance is enhanced in the outer disk due to formation on grain surfaces by the hydrogenation of CO ice. The emission peak at the edge of the mm dust continuum may be due to enhanced desorption of H$_2$CO in the gas phase caused by increased UV penetration and/or temperature inversion. The CH$_3$OH/H$_2$CO abundance ratio is $<1$, in agreement with disk chemistry models. The inner edge of the H$_2$CO ring coincides with the radius where the polarization of the dust continuum changes orientation, hinting at a tight link between the H$_2$CO chemistry and the dust properties in the outer disk and at the possible presence of substructures in the dust distribution.Comment: 8 pages, 6 figures, accepted for publication on A&A Letter