A new 3D maser code applied to flaring events

This paper sets forth the theoretical background and basic numerical expressions for the incorporation of elastic‐plastic constitutive equations for ductile rock into a finite element computer code. The derivation of an expression for the total strain rate is performed both for a total stress formulation and for a formulation that employs the concept of effective stress for inelastic behaviour. Specific expressions for the incremental strain rate are presented for the case of a porous material having a quadratic initial yield surface and observing the associated flow rule with a special hardening law for subsequent plastic deformation. A final section of the paper summarizes the expressions required to insert the quadratic yield surface model into a finite element code.

To alleviate the nonuniqueness problem of the solution of the integral equation derived by Hovenier for the exit function, a generating function for reflection and transmission functions for homogeneous, plane-parallel media, we have derived an integrodifferential equation, so that the function can be obtained in the form of the initial value problem. The numerical stability of our equation was then tested against the problem of multiple scattering in layers of a wide range of optical thickness, characterized by the Henyey-Greenstein phase function of varying degrees of anisotropy. The main features of the present technique are (1) an application of the fast invariant embedding method of Sato et al. and (2) an effective interpolation scheme to estimate numerically the limiting values of the singular terms involved in the equation. The results were compared with those of the doubling method. It was found that the maximum relative errors of the reflection function, ranging from 0.005% to 0.03%, generated from the exit function was 1 to 2 orders of magnitude smaller than those of the transmission function. Nevertheless, even the transmission functions rarely show errors larger than 2%, unless the optical thickness is substantially less than 0.1. Our results indicate that the equation presented in this work has a high degree of numerical stability and that it can be potentially useful for multiple scattering computations.

The heating and vaporization of dust grains in the protosolar environment is modeled in order to assess the survivability of interstellar solids during the formation of the solar system. A multidimensional, discrete ordinate radiative transfer code is used to compute thermal transport in the collapsing protosolar cloud. The results are combined with estimates of heating at the shock where infalling material arrives at the surface of the solar nebula/accretion disk, and in the interior of the disk, to determine the distances at which various solid phases are vaporized. The thermal coupling between the envelope and the accretion disk (backheating) is treated self-consistently, so its effect on the disk's radial temperature profile is included. This treatment also permits evaluation of the effect of backheating on the observational inference of disk properties. Calculations are performed for various values of cloud collapse rate, rotation rate, and disk accretion rate. The latter factor is the main determinant of the total luminosity, and we consider both low-luminosity cases, in which disk accretion is inefficient, and high-luminosity cases, in which disk accretion keeps pace with cloud collapse. We also examine situations in which a polar, optically thin cavity is swept clear by a protosolar wind. We conclude that refractory grains, such as silicates, can generally survive the envelope and accretion shock, and enter the nebula at or within 1 AU. Inside the nebula, their vaporization distances are controlled by the disk accretion rate and optical depth. In contrast, the vaporization distances of volatiles such as water ice are sensitive to envelope conditions, which control the thermal state of the outer, optically thin regions of the disk. The ice vaporization distance lies between about 2 and 30 AU, depending on the total source luminosity and characteristics of the collapsing cloud. Moderately volatile organics (methanol, formaldehyde, and polymerized formaldehyde) may survive as solids in the terrestrial planet region; they generally are not vaporized outside of several AU, which supports the idea that comets inherit this material from the parent molecular cloud.

This report summarizes the results of a three-year research project sponsored by the U.S. Department of Energy (DOE) Nuclear Energy University Program (NEUP) to develop and implement advanced acceleration schemes for the DOE NEAMS neutronics code PROTEUSSN. The project team included the University of Massachusetts Lowell, The Ohio State University, University of Michigan, and Argonne National Laboratory. The PROTEUS code is a high-fidelity capable deterministic neutron transport code based on unstructured finite element meshes, which solves the steady-state and transient neutron transport problem using the 2nd-order discrete ordinate method (SN2ND), the method of characteristics (MOC), and the advanced nodal transport method (NODAL). The DSA scheme has been implemented in PROTEUS to speed up SN transport calculations. The existing DSA scheme employs a consistent finite element formulation on the same fine mesh structure as the SN solution While the use of consistent discretizations makes the DSA method effective, it does not necessarily make it efficient because the numerical solution of a discretized elliptic diffusion problem itself can be costly, particularly when the problem size becomes large. We developed a new discontinuous Galerkin (DG) discretization of the diffusion equation, called DG-DSA, which can effectively and efficiently accelerate the SN transport iterations. As compared with the previous work, the novelty of our method is that the diffusion equation is solved on a coarse-mesh grid using the DG methods, and the DG diffusion discretization incorporates local hp adaptation, i.e., local adaptation of mesh size and/or polynomial degree, based on local total cross section (or optical thickness). Therefore, the resulting number of degrees of freedom (DOF) of the DG discretization is much less than the conventional consistent DSA discretizations, and thus DG-DSA can achieve significant improvement in computational efficiency. We implemented this scheme in PROTEUS-SN. In addition, we developed a new stabilization scheme named linear prolongation CMFD (lpCMFD). A novel feature of this scheme is that the conventional flat flux ratio–based scaling approach is replaced with a linear interpolation of the scalar flux differences at the coarse-mesh cell edges between the neutron transport and CMFD calculations. Fourier convergence analysis and numerical results show that lpCMFD is unconditionally stable and more effective than other CMFD based on acceleration schemes such as pCMFD, odCMFD. We also developed a new nonlinear diffusion acceleration scheme for solving neutron transport equations. This scheme, called LR-NDA, employs a local refinement approach on the framework of CMFD by solving a local boundary value problem of the scalar flux on the coarse-mesh structure to replace the piecewise constant scalar flux obtained by CMFD. The refined flux is then used to update the scalar flux in the neutron transport source iteration. It has been demonstrated that that LR-NDA is much more effective and stable than CMFD for a wide range of optical thicknesses. LR-NDA is a local adaptive method, which means LR-NDA does not necessarily require local refinement for all the coarse-mesh cells on the problem domain, i.e., it can be used only for relatively optically thick regions where the standard CMFD scheme would encounter the convergence problem.

Deformation of some specimens produced by a stereolithography system was studied experimentally and numerically. Three steps in the rapid prototyping process (part building, part removal, and postcure) imposed significant effects on dimensional accuracy. Dimensions of the specimens were measured after each step. Distortion during part building was much smaller than that caused by the part removal step. The internal residual stress developed during the building process was partially released by the removal of the part from the platform. Considerable distortion was also observed after postcure. A finite-element computer code was developed to predict the deformation after each step. Shrinkage of each layer cured by the laser beam was simulated by considering thermal shrinkage of a solid layer. In order to simulate shrinkage during the postcure process, it was assumed that the postcure occurred from the exterior surface to the interior surface. Heat sink was also assumed on the boundary of the part for the thermal stress analysis. Numerical results were consistent with experimental results for the simple geometry employed in this study.

Computational method for soil/structure interaction problems

We present new numerical simulations in the thin-disk approximation which characterize the burst mode of protostellar accretion. The burst mode begins upon the formation of a centrifugally balanced disk around a newly formed protostar. It is comprised of prolonged quiescent periods of low accretion rate (typically $\la 10^{-7} \Msun$ yr$^{-1}$) which are punctuated by intense bursts of accretion (typically $\ga 10^{-4} \Msun$ yr$^{-1}$, with duration $\la 100$ yr) during which most of the protostellar mass is accumulated. The accretion bursts are associated with the formation of dense protostellar/protoplanetary embryos, which are later driven onto the protostar by the gravitational torques that develop in the disk. Gravitational instability in the disk, driven by continuing infall from the envelope, is shown to be an effective means of transporting angular momentum outward, and mass inward to the protostar. We show that the disk mass always remains significantly less than the central protostar mass throughout this process. The burst phenomenon is robust enough to occur for a variety of initial values of rotation rate, frozen-in (supercritical) magnetic field, and density-temperature relations. Even in cases where the bursts are nearly entirely suppressed, a moderate increase in cloud size or rotation rate can lead to vigorous burst activity. We conclude that most (if not all) protostars undergo a burst mode of evolution during their early accretion history, as inferred empirically from observations of FU Orionis variables.

With the object of determining the atmospheric turbidity (aerosol optical depth) from upward emerging spectral radiances, an evaluation was made of that wavelength at which the variability of the radiance owing to the variability of the turbidity predominates the variability caused by the perturbing optical parameters. This has been done by numerical modeling of the variability of the radiances owing to the variability of all optically acting atmospheric constituents (no clouds) and the underlying rough ocean for maritime aerosols and Saharan dust. It is found that the optimum wavelengths are 0.75 and 0.87 μm. In addition, it has been found that low sun and low observation elevation angles are preferable.

We have mapped 27 massive star-forming regions associated with water masers using three dense gas tracers: HC3N 10-9, HNC 1-0 and C2H 1-0. The FWHM sizes of HNC clumps and C2H clumps are about 1.5 and 1.6 times higher than those of HC3N, respectively, which can be explained by the fact that HC3N traces more dense gas than HNC and C2H. We found evidence for increase in optical depth of C2H with `radius' from center to outer regions in some targets, supporting the chemical model of C2H. The C2H optical depth is found to decline as molecular clouds evolve to later stage, suggesting that C2H might be used as "chemical clock" for molecular clouds. Large-scale kinematic structure of clouds was investigated with three molecular lines. All these sources show significant velocity gradients. The magnitudes of gradient are found to increase towards the inner region, indicating differential rotation of clouds. Both the ratio of rotational to gravitational energy and specific angular momentum seem to decrease toward the inner region, implying obvious angular momentum transfer, which might be caused by magnetic braking. The average magnetic field strength and number density of molecular clouds is derived using the uniformly magnetic sphere model. The derived magnetic field strengths range from 3 to 88 \mu G, with a median value of 13 \mu G. The mass-to-flux ratio of molecular cloud is calculated to be much higher than critical value with derived parameters, which agrees well with numerical simulations.

Effect of Radiation on Mixed Convection Inside a Lid-Driven Square Cavity With Various Optical Thicknesses and Richardson Numbers

In this paper, we propose a new prolongation method to replace the conventional flat flux ratio–based scaling approach of coarse-mesh finite difference (CMFD) for updating the flux. The new prolongation method employs a linear interpolation of the scalar flux differences at the coarse-mesh cell edges between the neutron transport and CMFD calculations. This linear prolongation scheme, called lpCMFD, can greatly improve the stability of CMFD, particularly for problems with large optical thickness. A detailed convergence study of lpCMFD based on Fourier analysis and numerical testing shows that lpCMFD is unconditionally stable and effective for a wide range of optical thicknesses.

Making the conversion from the geometrical spatial scale to the optical depth spatial scale is useful in obtaining numerical solutions for the radiative transfer equation. This is because it allows for the use of exponential integrators, while enforcing numerical stability. Such a conversion involves the integration of the total opacity of the medium along the considered ray path. This is usually approximated by applying a piecewise quadrature in each spatial cell of the discretized medium. However, a rigorous analysis of this numerical step is lacking. This work is aimed at clearly assessing the performance of different optical depth conversion schemes with respect to the solution of the radiative transfer problem for polarized radiation, out of the local thermodynamic equilibrium. We analyzed different optical depth conversion schemes and their combinations with common formal solvers, both in terms of the rate of convergence as a function of the number of spatial points and the accuracy of the emergent Stokes profiles. The analysis was performed in a 1D semi-empirical model of the solar atmosphere, both in the absence and in the presence of a magnetic field. We solved the transfer problem of polarized radiation in different settings: the continuum, the photospheric Sr i AA modeled under the assumption of complete frequency redistribution, and the chromospheric Ca i AA taking the partial frequency redistribution effects into account during the modeling. High-order conversion schemes generally outperform low-order methods when a sufficiently high number of spatial grid points is considered. In the synthesis of the emergent Stokes profiles, the convergence rate, as a function of the number of spatial points, is impacted by both the conversion scheme and formal solver. The use of low-order conversion schemes significantly reduces the accuracy of high-order formal solvers. In practical applications, the use of low-order optical depth conversion schemes introduces large numerical errors in the formal solution. To fully exploit high-order formal solvers and obtain accurate synthetic emergent Stokes profiles, it is necessary to use high-order optical depth conversion schemes.

With broad spectral coverage and high spatial and temporal resolutions, satellite sensors can provide the data needed for the analysis of spatial and temporal variations of climate parameters in data-sparse regions such as the Arctic and Antarctic. The newly available Advanced Very High Resolution Radiometer (AVHRR) Polar Pathfinder (APP) dataset was used to retrieve cloud fraction, cloud optical depth, cloud particle phase and size, cloud-top pressure and temperature, surface skin temperature, surface broadband albedo, radiative fluxes, and cloud forcing over the Arctic Ocean and surrounding landmasses for the 18-yr period from 1982 to 1999. In the Arctic, Greenland is the coldest region with the highest surface albedo, while northeastern Russia has the highest surface temperature in summer. Arctic annual mean cloud coverage is about 70%, with the largest cloudiness occurring in September and the lowest cloudiness occurring in April. On annual average, Arctic cloud visible optical depth is about 5–6. Arctic precipitable water is near 0.2 cm in winter and 1.5 cm in summer. The largest downwelling shortwave radiative flux at the surface occurs in June; the largest upwelling shortwave radiative flux occurs in May. The largest downwelling and upwelling longwave radiative fluxes as well as the net all-wave radiative flux occur in July, with the largest loss of longwave radiation from the surface in April.

The study of the Earth radiation budget is important for understanding the long-term impact of industrialization on the environment. Clouds exert the single most important influence on the Earth radiation budget. The ideal situation for predicting the effect of clouds is to have one of two extremes: either a cloud-free sky or a completely overcast sky. Each of these cases can easily be treated with a simple one-dimensional model. However, the more usual partly-cloudy sky condition introduces the possibility of an unlimited variety of cloud geometries, size and spatial distributions, and properties. In most of these cases the interaction among neighboring clouds presents a set of problems which cannot be accurately simulated with plane-parallel or even two-dimensional models. Only in recent years have researchers begun to understand the relationships between cloud three-dimensional effects and the anisotropy of Earth-reflected radiance. In the real world, the influence of clouds on radiation depends not only on liquid water content, or optical depth, but also on cloud microphysical properties such as particle shape, size distribution, and on cloud morphology and spatial distribution (Parol, et al., 1994). As shown by Stevens and Greenwald (1991), cloud morphology is likely to have a larger impact on the Earth radiation budget than cloud microphysics. Thus, it is very important to quantify and parameterize the influence of cloud inhomogeneities on the radiation field. The anisotropy of any radiation field can be studied by normalizing the emitted or reflected radiance by the equivalent Lambertian directional distribution of energy leaving the field. The work in this paper deals entirely with the shortwave portion of the spectrum; longwave emitted energy is not treated.

Numerical evaluation of the effective elastic moduli of rocks