A PDE-constrained optimization formulation for discrete fracture network flows

We investigate a new numerical approach for the computation of the 3D flow in a discrete fracture network that does not require a conforming discretization of partial differential equations on complex 3D systems of planar fractures. The discretization within each fracture is performed independently of the discretization of the other fractures and of their intersections. Independent meshing process within each fracture is a very important issue for practical large scale simulations making easier mesh generation. Some numerical simulations are given to show the viability of the method. The resulting approach can be naturally parallelized for dealing with systems with a huge number of fractures

The XFEM with an Explicit-Implicit Crack Description for Hydraulic Fracture Problems

The Extended Finite Element Method (XFEM) approach is applied to the coupled problem of fluid flow, solid deformation, and fracture propagation. The XFEM model description of hydraulic fracture propagation is part of a joint project in which the developed numerical model will be verified against large-scale laboratory experiments. XFEM forms an important basis towards future combination with heat and mass transport simulators and extension to more complex fracture systems. The crack is described implicitly using three level-sets to evaluate enrichment functions. Additionally, an explicit crack representation is used to update the crack during propagation. The level-set functions are computed exactly from the explicit representation. This explicit/implicit representation is applied to a fluid-filled crack in an impermeable, elastic solid and compared to the early-time solution of a plane-strain hydraulic fracture problem with a fluid lag

Synchronization of Excitatory Neurons with Strongly Heterogeneous Phase Responses

In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system by dealing explicitly with the heterogeneous phase response curves. We develop a novel method to solve the self-consistent equations for order parameters by using formal complex-valued phase variables, and apply our theory to networks of in vitro cortical neurons. We find a novel state transition that is not observed in previous oscillator network models.Comment: 4 pages, 3 figure

Chemical composition of the decaying glasma

The the initial stage of a relativistic heavy ion collision can be described by a classical color field configuration known as the Glasma. The production of quark pairs from this background field is then computed nonperturbatively by numerically solving the Dirac equation in the classical background. The result seems to point towards an early chemical equilibration of the plasma.Comment: 8 pages, 5 figures, invited talk at Stangeness in Quark Matter 2006 (SQM06), UCLA, March 200

Hadron production in heavy ion collisions: Fragmentation and recombination from a dense parton phase

We discuss hadron production in heavy ion collisions at RHIC. We argue that hadrons at transverse momenta P_T < 5 GeV are formed by recombination of partons from the dense parton phase created in central collisions at RHIC. We provide a theoretical description of the recombination process for P_T > 2 GeV. Below P_T = 2 GeV our results smoothly match a purely statistical description. At high transverse momentum hadron production is well described in the language of perturbative QCD by the fragmentation of partons. We give numerical results for a variety of hadron spectra, ratios and nuclear suppression factors. We also discuss the anisotropic flow v_2 and give results based on a flow in the parton phase. Our results are consistent with the existence of a parton phase at RHIC hadronizing at a temperature of 175 MeV and a radial flow velocity of 0.55c.Comment: 25 pages LaTeX, 18 figures; v2: some references updated; v3: some typos fixe