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Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Theoretical Investigation of Microstructure Evolution and Deformation of Zirconium Under Cascade Damage Conditions

This work is based on our reaction-diffusion model of radiation growth of Zr-based materials proposed recently in "On the Origin of Radiation Growth of HCP Crystals". In "On the Origin of Radiation Growth of HCP Crystals", the equations for the strain rates in unloaded pure crystal under cascade damage conditions of, e.g., neutron or heavy-ion irradiation were derived as functions of dislocation densities, which include contributions from dislocation loops, and spatial distribution of their Burgers vectors. The model takes into account the intra-cascade clustering of self-interstitial atoms and their one-dimensional diffusion; explains the growth stages, including the break-away growth of pre-annealed samples; and accounts for some striking observations, such as of negative strain in prismatic direction, and co-existence of vacancy- and interstitial-type prismatic loops. In this report, the change of dislocation densities due to accumulation of sessile dislocation loops is taken into account explicitly to investigate the dose dependence of radiation growth. The dose dependence of climb rates of dislocations is calculated, which is important for the climb-induced glide model of radiation creep. The results of fitting the model to available experimental data and some numerical calculations of the strain behavior of Zr for different initial dislocation structures are presented and discussed. The computer code RIMD-ZR.V1 (Radiation Induced Microstructure and Deformation of Zr) developed is described and attached to this report.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Pulsed laser generation of ultrasound in a metal plate between the melting and ablation thresholds

The generation of ultrasound in a metal plate exposed to nanosecond pulsed laser heating, sufficient to cause melting but not ablation, is treated. Consideration is given to the spatial and temporal profiles of the laser pulse, penetration of the laser beam into the sample, the evolution of the melt pool, and thermal conduction in the melt and surrounding solid. The excitation of the ultrasound takes place over a few nanoseconds, and occurs predominantly within the thermal diffusion length of a micron or so beneath the surface. Because of this, the output of the thermal simulations can be represented as axially symmetric transient radial and normal surface force distributions. The epicentral displacement response at the opposite surface to these forces is obtained by two methods, the one based on the elastodynamic Green’s functions for plate geometry determined by the Cagniard generalized ray method, and the other using a finite element numerical method. The two approaches are in very close agreement. Numerical simulations are reported of the epicentral displacement response of a 3.12mm thick tungsten plate irradiated with a 4 ns pulsed laser beam with Gaussian spatial profile, at intensities below and above the melt threshold. Comparison is made between results obtained using available temperature dependent thermophysical data, and room temperature materials constants except near the melting point.

36 MATERIALS SCIENCE↗

Effect of fuel rate and annealing process of LiFePO{sub 4} cathode material for Li-ion batteries synthesized by flame spray pyrolysis method

In this study the effect of fuel rate and annealing on particle formation of LiFePO{sub 4} as battery cathode using flame spray pyrolysis method was investigated numerically and experimentally. Numerical study was done using ANSYS FLUENT program. In experimentally, LiFePO{sub 4} was synthesized from inorganic aqueous solution followed by annealing. LPG was used as fuel and air was used as oxidizer and carrier gas. Annealing process attempted in inert atmosphere at 700°C for 240 min. Numerical result showed that the increase of fuel rate caused the increase of flame temperature. Microscopic observation using Scanning Electron Microscopy (SEM) revealed that all particles have sphere and polydisperse. Increasing fuel rate caused decreasing particle size and increasing particles crystallinity. This phenomenon attributed to the flame temperature. However, all produced particles still have more amorphous phase. Therefore, annealing needed to increase particles crystallinity. Fourier Transform Infrared (FTIR) analysis showed that all particles have PO4 function group. Increasing fuel rate led to the increase of infrared spectrum absorption corresponding to the increase of particles crystallinity. This result indicated that phosphate group vibrated easily in crystalline phase. From Electrochemical Impedance Spectroscopy (EIS) analysis, annealing can cause the increase of Li{sup +} diffusivity. The diffusivity coefficient of without and with annealing particles were 6.84399×10{sup −10} and 8.59888×10{sup −10} cm{sup 2} s{sup −1}, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Hybrid Finite-Volume, Discontinuous Galerkin Discretization for the Radiative Transport Equation

In this report we propose a hybrid spatial discretization for the radiative transport equation that combines a second-order discontinuous Galerkin (DG) method and a second-order finite-volume (FV) method. The strategy relies on a simple operator splitting that has been used previously to combine different angular discretizations. Unlike standard FV methods with upwind fluxes, the hybrid approach is able to accurately simulate problems in scattering dominated regimes. However, it requires less memory and yields a faster computational time than a uniform DG discretization. In addition, the underlying splitting allows naturally for hybridization in both space and angle. Numerical results are given to demonstrate the efficiency of the hybrid approach in the context of discrete ordinate angular discretizations and Cartesian spatial grids.

97 MATHEMATICS AND COMPUTING↗

Advanced Finite-Volume Numerics and Source Term Assumptions for Kernel and G-Equation Modelling of Propane/Air Flames

Here G-Equation models represent propagating flame fronts with an implicit two-dimensional surface representation (level-set). Level-set methods are fast, as transport source terms for the implicit surface can be solved with finite-volume operators on the finite-volume domain, without having to build the actual surface. However, they include approximations whose practical effects are not properly understood. In this study, we improved the numerics of the FRESCO CFD code’s G-Equation solver and developed a new method to simulate kernel growth using signed distance functions and the analytical sphere-mesh overlap. We analyzed their role for simulating propane/air flames, using three well-established constant-volume configurations: a one-dimensional, freely propagating laminar flame; a disc-shaped, constant-volume swirl combustor; and torch-jet flame development through an orifice from a two-chamber device. We tested the explicit (sub-cycled) vs. implicit formulation for the standard transport operators (advection, diffusion, compressibility). In addition to the accurate flame swept-volume method for chemistry and species source term, we developed a more accurate estimator for the burnt/unburnt split cell composition. Then, we developed a signed-distance-function (SDF) based method which provides a more stable reinitialization of the level-set field at every time-step. We found that simplifying assumptions common to several G-Equation implementations, for straightforward terms such as compressibility and advection, lead to large errors in predicting the propagation of even laminar flames, with deviations up to ~300% in simulated vs. formulated flame speed. Conversely, the enhanced numerics enabled through the SDF field reinitialization and improved chemistry source term improve simulation stability and smooth flame propagation even with significantly larger solver time-steps.

42 ENGINEERING↗

Improvements to a class of hybrid methods for radiation transport: Nyström reconstruction and defect correction methods

In this study, two modifications are introduced for improving the accuracy, versatility, and robustness of a class of hybrid methods for radiation transport. In general, such methods are constructed by splitting the radiative flux into collided and uncollided components to which low- and high-resolution angular approximations are applied, respectively. In this work we focus on discrete ordinates discretizations of high and low order. The first modification we introduce changes the way in which the collided component is mapped into the uncollided component at the end of each time step in a simulation. The new mapping is a Nyström-type reconstruction that is applicable to arbitrary discrete ordinates quadratures, is guaranteed to preserve positivity of the solution provided that all ordinate weights are positive, is significantly more accurate than previous methods, and can be readily extended to other discretizations such as moment methods, finite element methods, and diffusion approximations. The second modification leverages integral deferred correction (IDC) to iteratively correct for the splitting error introduced by the inconsistency in angular discretization between the collided and uncollided components, in addition to improving the accuracy of the low-order temporal error that is treated by traditional IDC methods. Numerical tests in one- and two-dimensional geometries are used to demonstrate the increased accuracy and efficiency of the proposed modifications. It is found that the two techniques combined yield methods with solution accuracy and memory requirements comparable to that of monolithic discrete ordinates methods while reducing runtime by as much as a factor of between two and ten, depending on the problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Local nonlinear rf forces in inhomogeneous magnetized plasmas

The local nonlinear forces induced by radio frequency (rf) waves are derived in inhomogeneous magnetized plasmas, where the inhomogeneity exists in the rf fields, in the static magnetic field as well as in the equilibrium density and temperature. The local parallel force is completely resonant, but a novel component dependent on those inhomogeneities is obtained as the result of the inhomogeneous transport of parallel resonant-absorbed momentum by the nonlinear perpendicular drift flux. In the local poloidal force, the component induced by the inhomogeneity of rf power absorption is also confirmed and it can be recognized as the residual effect from the incomplete cancellation between the rate of the diamagnetic poloidal momentum gain and the Lorentz force due to the radial diffusion-like flux. The compact expression for radial force is also obtained for the first time, whose nonresonant component is expressed as the sum of the ponderomotive force on particles and the gradients of the nonresonant perpendicular pressure and of the nonresonant momentum flux due to the finite temperature effect. Numerical calculations in a 1-D slab model show that the resonant component dependent on the inhomogeneities may be significant when the ion absorption dominates the resonant wave-particle interaction. A quantitative estimation shows that the novel component in the parallel force is important to understand the experiments of the ion-cyclotron-frequency mode-conversion flow drive.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effects of q-profile structure on turbulence spreading: A fluctuation intensity transport analysis

This paper studies effects of q-profile structure on turbulence spreading. It reports results of numerical experiments using global gyrokinetic simulations. We examine propagation of turbulence, triggered by an identical linear instability in a source region, into an adjacent, linearly stable region with variable q-profile. The numerical experiments are designed so as to separate the physics of turbulence spreading from that of linear stability. The strength of turbulence spreading is measured by the penetration depth of turbulence. Dynamics of spreading are elucidated by fluctuation intensity balance analysis, using a model intensity evolution equation which retains nonlinear diffusion and damping, and linear growth. It is found that turbulence spreading is strongly affected by magnetic shear s, but is hardly altered by the safety factor q itself. There is an optimal range of modest magnetic shear which maximizes turbulence spreading. For high to modest shear values, the spreading is enhanced by the increase of the mode correlation length with decreasing magnetic shear. However, the efficiency of spreading drops for sufficiently low magnetic shear even though the mode correlation length is comparable to that for the case of optimal magnetic shear. The reduction of spreading is attributed to the increase in time required for the requisite nonlinear mode-mode interactions. The effect of increased interaction time dominates that of increased mode correlation length. Our findings of the reduction of spreading and the increase in interaction time at weak magnetic shear are consistent with the well-known benefit of weak or reversed magnetic shear for core confinement enhancement. Weak shear is shown to promote locality, as well as stability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

BIPOLAR MAGNETIC STRUCTURES DRIVEN BY STRATIFIED TURBULENCE WITH A CORONAL ENVELOPE

We report the spontaneous formation of bipolar magnetic structures in direct numerical simulations of stratified forced turbulence with an outer coronal envelope. The turbulence is forced with transverse random waves only in the lower (turbulent) part of the domain. Our initial magnetic field is either uniform in the entire domain or confined to the turbulent layer. After about 1-2 turbulent diffusion times, a bipolar magnetic region of vertical field develops with two coherent circular structures that live during one turbulent diffusion time, and then decay during 0.5 turbulent diffusion times. The resulting magnetic field strengths inside the bipolar region are comparable to the equipartition value with respect to the turbulent kinetic energy. The bipolar magnetic region forms a loop-like structure in the upper coronal layer. We associate the magnetic structure formation with the negative effective magnetic pressure instability in the two-layer model.

79 ASTRONOMY AND ASTROPHYSICS↗

Solution of the Feynman Equation for Time Evolving Fission Chains

The partial differential equation proposed by Feynman describing the time evolution of a fission chain in metal is solved by a method also proposed by Feynman. The partial differential equation is reduced to a transcendental algebraic equation. The solution involves roots of a 7th order polynomial. Both the roots and the transcendental equation are then solved numerically. Two populations are computed from the probability generating function, the internal number of neutrons in time, and the accumulated number of leaked neutrons in time. This same equation also describes a limit of a thermal reactor, where induced fission is totally driven by neutrons that have thermalized and are diffusing in a moderator.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Tandem particle-slurry batch reactors for solar water splitting (Final Scientific/Technical Report)

Economically, particle slurry reactors are projected to be one of the most promising technologies for solar photoelectrochemical hydrogen production, according to a 2009 techno-economic analysis commissioned by the US DOE and performed by Directed Technologies, Inc. The Fuel Cell Technologies Office’s Multi-Year Research, Development and Demonstration (MYRD&D) goals and targets are to reduce the cost of H 2 produced from renewable sources at the plant gate (i.e. not including delivery, dispensing, or storage) to < $2.00/gge, equivalent to ~$2.00/kg H 2 . Research results from our techno-economic modeling research suggest that this target could be met using particle slurry reactors assuming STH efficiencies in the range of 5 – 10%, materials lifetimes of < 1 year, and nanoparticles that cost up to 20 times more than projected costs of TiO 2 -coated Fe 2 O 3 nanoparticles. Although most large worldwide research efforts directed at solar photoelectrochemical hydrogen production focus on wafer-based designs, the projected lower cost for a particle slurry reactor at these disparate projected STH efficiencies clearly suggests that particle slurry reactors could be a scalable and deployable technology, assuming several challenges are overcome. These major technological challenges include the demonstration of a vertically-stacked-vessel architecture that is capable of operating sustainably while mostly relying on diffusion and natural convection to mix the redox shuttles between the vessels, and the demonstration that photocatalyst particles can operate at an overall 1% STH efficiency or larger when incorporated into this two-vessel design. Our research adds to the understanding of photocatalytic reactors for solar water splitting through numerical modeling results and experimental results. Numerical models were developed to simulate relevant device physics including particle and reactor dimensions which affect optical, transport, and rheological properties, electrocatalytic and photovoltaic properties of particles at various temperatures, and properties of redox shuttles and separators. Moreover, theoretical maximum solar-to-hydrogen efficiencies for ensembles of particles like in photocatalyst reactors were modeled and simulated and shown to equal or exceed those of photoelectrochemical designs under most scenarios. These results help determine constraints on the reactor that will enable more optimal designs for future prototypes. In parallel, experiments were performed to identify the most effective redox shuttles and to empirically validate the numerical models and simulations. Toward the latter, state-of-the-art light-absorbing particles and electrocatalysts were synthesized and characterized physically and photoelectrochemically for water electrolysis and redox chemistry with redox shuttles in the form factor of mesoporous electrodes and free-floating particles. The most promising materials candidates were used in a suspension reactor to evaluate performance toward photocatalytic H 2 production and results from the two measurements were compared. Predominantly, state-of-the-art cocatalyst-modified Rh-doped SrTiO 3 and BiVO 4 particles were further characterized to assess for their ability to perform visible-light-driven H 2 and O 2 evolution, respectively, and results were similar to those reported for the state-of-the-art in the peer-reviewed literature. Outcomes from this work inform the public of the effectiveness and promise of solar photocatalytic water splitting for clean and renewable hydrogen production. This work may also help increase research interest and funding for photocatalysis projects, which will accelerate development of a technology that will benefit the public by generating fuel while emitting few greenhouse gases and pollutants.

08 HYDROGEN↗

Remarks on the thesis of Aitor Bengoechea Fernández: Generalization of Doppler effect processing using S(α,β) thermal diffusion laws

The thesis titled “Generalization of Doppler effect processing using S(α,β) thermal diffusion laws” addresses a critical gap in the modeling of neutron scattering phenomena in nuclear materials, particularly where crystal lattice effects intersect with low-energy resonances. Conducted within the Doctoral School ED 352 at Aix-Marseille Université and hosted at CEA Cadarache, the research presents a theoretical and numerical framework for extending the applicability of Thermal Scattering Laws (TSLs) using higher-order correlation functions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A parallel in energy Krylov solution algorithm for the variational nodal method

To reduce the computational expense caused by the large number of energy groups in thermal and fast reactor calculations, we researched using parallelization in energy (i.e. group) of the multi-group response matrix equations derived from the Variational Nodal Method. This study focuses on solving steady-state eigenvalue problems in diffusion theory that are typically needed for depletion and reactivity coefficient calculations. To examine serial and parallel performance, GMRES, a Krylov algorithm, is applied to the multi-group system of equations at each fission source iteration. We also study the impact of using Wielandt acceleration on the eigenvalue/eigenvector problem. Numerical results based on a 72 group thermal and a 216 group fast reactor core problems are obtained for both serial and parallel calculations. The results show reduced CPU times when using GMRES and Wielandt acceleration in both serial and parallel calculations. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Tracking Radioactive Isotopes in HVAC and Application for Hot Cell Analyses - 20155

In recent years, the surge in the number of isotope production facilities under design has increased the need to analyze isotope migration in facility Heating, Ventilation, and Air Conditioning (HVAC) during normal operations and accident scenarios. These facilities are used to produce isotopes for medical, security, and industrial applications and as such are subject to license and regulatory requirements 10CFR20, 10CFR30, 10CFR50, and 10CFR70. GOTHIC, a general-purpose thermal-hydraulics software package, includes the ability to model isotopic tracers, radioactive decay and isotope migration as well as HEPA and charcoal filters for isotope retention. A GOTHIC model was developed by Zachry Nuclear Engineering (ZNE) to examine the effect of negative room pressure, HEPA filtration, and HVAC fluctuations on radiation areas, hot cells and gloveboxes. Radioactive tracers were used to simulate the concentration of spills within contaminated areas, track the migration of isotopes of interest, and determine the isotopic retention and buildup on facility HEPA filters. A variety of isotopes with concern to dose (e.g., Kr-85, Sr-90, I-131, etc.), including their decay and progeny, are included in the analysis. Negative pressures are maintained in the regions of interest by a representative central HVAC system equipped with a volumetric fan that exhausts to the environment after a series of isolation valves and HEPA filters. GOTHIC is an industry trusted tool for providing engineering solutions for a variety of applications, including fission product tracking, aerosol and particulate transport and ventilation assessments. The software provides an integrated analysis environment that includes a graphical user interface (GUI) for constructing analysis models, a numerical solver that includes parallel processing capabilities and a post-processor for evaluating simulation results. It solves the conservation equations for mass, momentum and energy for multicomponent, multi-phase flow in lumped parameter and multi-dimensional geometries (1, 2, or full 3D), including the effects of turbulence, diffusion and buoyancy. It has been developed and maintained under a Quality Assurance program in compliance with the requirements of 10CFR50 Appendix B and applicable portions of ASME NQA-1 since 1995. GOTHIC has been used for assessing both forced and natural convection conditions for a wide range of applications, including: - Tracking concentration of hazardous gases and chemicals for habitability and safety assessments - Determining ventilation and filtration requirements and optimizing location and arrangement of these systems - Room heat-up, including diverse and Flexible coping strategies for Extended Loss of AC Power (FLEX/ELAP) - Equipment Qualification (EQ) A distinctive feature of GOTHIC is the ability to track many different fields/substances in a simulation, including user defined tracer elements, in the liquid, vapor and droplet fields as well as surfaces and filters. This capability allows GOTHIC to model fission product transport and release or the removal of particulates or harmful toxins from exhaust gases using a spray scrubber or other types of filtration systems. GOTHIC also includes models for engineered equipment, such as fans, filters, charcoal filters, dryers/demisters, dampers, etc. The aerosols and other filtered material are removed or accumulated in these components. The range of aerosol and radiological applications that GOTHIC has been used for includes: - Source Term: Primary Coolant (Equilibrium) Activity; Non-Water Coolant Source/Leakage. - Conditions for Iodine Re-evolution: Sump/Suppression Pool Conditions and pH; - RWST Conditions and pH. - Isotope Removal Mechanisms: Containment Sprayed and Unsprayed Region Mixing; Charcoal Filter Heating due to Iodine decay. - Radionuclide Transport and Decay: Post-LOCA Release in containment; Transport between connected Compartments and vent systems; Groundwater transport of radionuclides. - Non-Newtonian Fluid modeling for sludge, waste tanks, etc. ADAMS ML071581053 (titled 'Best Practice Guidelines for the use of CFD in Nuclear Reactor Safety Applications') poses guidelines for applying single phase CFD codes in nuclear reactor safety problems and GOTHIC is listed as a 'tool for 3D flows' and 'dispersal and deposition of radionuclides.' The Nuclear Quality Assurance (NQA) pedigree of GOTHIC is an important aspect for applications in the nuclear industry. The fundamental tracer models (convective transport, molecular and turbulent diffusion, removal mechanisms, etc.) have been verified using analytical solutions and validated against applicable separate effects tests. Also, GOTHIC has been benchmarked to many integrated effects tests, including Phebus FP (Fission Product). GOTHIC gives good agreement for the buildup and decay of fission products in Phebus Test 3. The model developed by ZNE demonstrates GOTHIC's applicability and acceptability for use in analyzing the migration and retention of radioactive isotopes and their progeny in normal operation and accident scenario analyses for isotope production facilities, hot cells, and gloveboxes. The tracer activities calculated by GOTHIC can then be used in downstream radiation transport and shielding codes like RADTRAD-NAI{sup C}, MCNP{sup R}, and MicroShield{sup R} to determine on-site and of-site doses. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Effects of irradiation on the interface between U-Mo and zirconium diffusion barrier

Irradiated fuel plates were characterized by microscopy that focused on the interface between U–Mo and Zr. Before irradiation, there were three major sub-layers identified in the U–Mo/Zr interface, namely, UZr 2 , Mo 2 Zr, and U with low Mo. The typical total thickness of this U–Mo/Zr interaction is 2–3 microns. The UZr 2 sub-layer formed during fuel fabrication remains stable after irradiation, without large bubbles/porosity accumulation. However, this sub-layer becomes increasingly discontinuous as burnup increases. The low-Mo sub-layer exhibits numerous sub-micron bubbles/porosity at low burnup. Larger, interconnected porosity in this sub-layer was observed in a medium-burnup fuel specimen. However, at higher burnup, regions with the extra-large bubbles/porosity (i.e., larger than 5 ?m) were observed at least 5 microns away from the original location of this sub-layer. The mechanism for the formation of the extra-large bubbles/porosity is still unclear at this time. In general, the U–Mo/Zr interface in monolithic U–Mo fuels is relatively stable after irradiation. As a result, no large detrimental defects, such as large interfacial bubbles or cracks/delamination, were observed in the fuel plates characterized.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

THREE-DIMENSIONAL HYDRODYNAMIC CORE-COLLAPSE SUPERNOVA SIMULATIONS FOR AN 11.2 M{sub Sun} STAR WITH SPECTRAL NEUTRINO TRANSPORT

We present numerical results on three-dimensional (3D) hydrodynamic core-collapse simulations of an 11.2 M{sub Sun} star. By comparing one-dimensional (1D) and two-dimensional (2D) results with those of 3D, we study how the increasing spacial multi-dimensionality affects the postbounce supernova dynamics. The calculations were performed with an energy-dependent treatment of the neutrino transport that is solved by the isotropic diffusion source approximation scheme. In agreement with previous study, our 1D model does not produce explosions for the 11.2 M{sub Sun} star, while the neutrino-driven revival of the stalled bounce shock is obtained in both the 2D and 3D models. The standing accretion-shock instability (SASI) is observed in the 3D models, in which the dominant mode of the SASI is bipolar (l = 2) with its saturation amplitudes being slightly smaller than 2D. By performing a tracer-particle analysis, we show that the maximum residency time of material in the gain region becomes longer in 3D than in 2D due to non-axisymmetric flow motions, which is one of advantageous aspects of 3D models to obtain neutrino-driven explosions. Our results show that convective matter motions below the gain radius become much more violent in 3D than in 2D, making the neutrino luminosity larger for 3D. Nevertheless, the emitted neutrino energies are made smaller due to the enhanced cooling. Our results indicate whether these advantages for driving 3D explosions could or could not overwhelm the disadvantages is sensitive to the employed numerical resolutions. An encouraging finding is that the shock expansion tends to become more energetic for models with finer resolutions. To draw a robust conclusion, 3D simulations with much higher numerical resolutions and with more advanced treatment of neutrino transport and of gravity are needed, which could be practicable by utilizing forthcoming Petaflops-class supercomputers.

79 ASTRONOMY AND ASTROPHYSICS↗

THE FORNAX DWARF GALAXY AS A REMNANT OF RECENT DWARF-DWARF MERGING IN THE LOCAL GROUP

We present results from the first numerical analysis to support the hypothesis, first proposed in Coleman et al., that the Fornax dwarf galaxy was formed from the minor merging of two dwarfs about 2 Gyr ago. Using orbits for the Fornax dwarf that are consistent with the latest proper motion measurements, our dynamical evolution models show that the observed asymmetric shell-like substructures can be formed from the remnant of a smaller dwarf during minor merging. These models also predict the formation of diffuse stellar streams. We discuss how these stellar substructures depend on model parameters of dwarf-dwarf merging, and how the intermediate-age subpopulations found in the vicinity of these substructures may be formed from gas accretion in past merger events. We also suggest that one of Fornax's globular clusters originates from a merged dwarf companion, and demonstrate where as yet undetected tidal streams or H I gas formed from the dwarf merging may be found in the outer halo of the Galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗