In this paper, we solve Einsteins' field equations for a circularly symmetric anisotropic fluid, with kinematic self-similarity of the first kind, in (2 + 1)-dimensional spacetimes. Considering the case where the radial pressure vanishes, we show that there exists a solution that represents the gravitational collapse of an anisotropic fluid, and the collapse will finally form a black hole, even if the fluid is constituted by phantom energy.

A new experimental facility constructed at UCLA for the simulation of high heat flux effects on plasma-facing materials is described. The High Energy Flux Test Facility (HEFTY) is equipped with a Praxair model SG-100 plasma gun, which is nominally rated at 80 kW of continuous operation, of which approximately 30 kW reaches the target due to thermal losses. The gun is used to impart high intermittent heat flux to metal samples mounted within a cylindrical chamber. The system is capable of delivering an instantaneous heat flux in the range of 30-300 MW/m 2 , depending on sample proximity to the gun. The duration of the plasma heat flux is in the range of 1-1000 s, making it ideal for studies of mild plasma transients of relatively long duration. Tungsten and tungsten-copper alloy metal samples are tested in these transient heat flux conditions, and the surface is characterized for damage evaluation using optical, SEM, XRD, and micro-fabrication techniques. Results from a Finite Element (FE) thermo-elastoplasticity model indicate that during the heat-up phase of a plasma transient pulse, the majority of the sample surface is under compressive stresses leading to plastic deformation of the surface. Upon sample cooling, the recovered elastic strain of cooler parts of the sample exceeds that from parts that deformed plastically, resulting is a tensile surface self-stress (residual surface stress). The intensity of the residual tensile surface stress is experimentally correlated with the onset of complex surface fracture morphology on the tungsten surface, and extending below the surface region. Micro-compression mechanical tests of W micro-pillars show that the material has significant plasticity, failing by a "barreling"mode before plasma exposure, and by normal dislocation slip and localized shear after plasma exposure. Ongoing modeling of the complex thermo-fracture process, coupled with elasto-plasticity is based on a phase field approach for distributed fracture, and a discrete cracking approach, with cracks represented by Volterra dislocations.

The discrete crack mechanics (DCM) method is a dislocation-based crack modeling technique where cracks are constructed using Volterra dislocation loops.The method allows for the natural introduction of displacement discontinuities, avoiding numerically expensive techniques. Mesh dependence in existing computational modeling of crack growth is eliminated by utilizing a superposition procedure. The elastic field of cracks in finite bodies is separated into two parts: the infinite-medium solution of discrete dislocations and an finite element method solution of a correction problem that satisfies external boundary conditions. In the DCM, a crack is represented by a dislocation array with a fixed outer loop determining the crack tip position encompassing additional concentric loops free to expand or contract. Solving for the equilibrium positions of the inner loops gives the crack shape and stress field. The equation of motion governing the crack tip is developed for quasi-static growth problems. Convergence and accuracy of the DCM method are verified with two-and three-dimensional problems with well-known solutions. Crack growth is simulated under load and displacement (rotation) control. In the latter case, a semicircular surface crack in a bent prismatic beam is shown to change shape as it propagates inward, stopping as the imposed rotation is accommodated. KEYWORDS dislocations, finite element methods, fracture, solids 38

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Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent approximations to various derivative functions, including those used in modeling important physical processes on uniform grids. However, our research reveals that difference approximations on uniform grids cannot be applied blindly on nonuniform grids, nor can difference formulas to form consistent approximations to second derivatives. At best, they may lose accuracy; at worst they are inconsistent. Detailed consistency and error analysis, together with simulated examples, will be given.