Engineering topics

Hauck, Cory

Publications and source records attributed to Hauck, Cory.

3 records

DOE OSTI2024

Modeling information flow in a computer processor with a multi-stage queuing model

In this paper, we introduce a nonlinear stochastic model to describe the propagation of information inside a computer processor. In this model, a computational task is divided into stages, and information can flow from one stage to another. The model is formulated as a spatially-extended, continuous-time Markov chain where space represents different stages. This model is equivalent to a spatially-extended version of the M/M/s queue. The main modeling feature is the throttling function which describes the processor slowdown when the amount of information falls below a certain threshold. We derive the stationary distribution for this stochastic model and develop a closure for a deterministic ODE system that approximates the evolution of the mean and variance of the stochastic model. In conclusion, we demonstrate the validity of the closure with numerical simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Towards dynamical low-rank approximation for neutrino kinetic equations. Part I: Analysis of an idealized relaxation model

Dynamical low-rank approximation (DLRA) is an emerging tool for reducing computational costs and provides memory savings when solving high-dimensional problems. Here, in this work, we propose and analyze a semi-implicit dynamical low-rank discontinuous Galerkin (DLR-DG) method for the space homogeneous kinetic equation with a relaxation operator, modeling the emission and absorption of particles by a background medium. Both DLRA and the discontinuous Galerkin (DG) scheme can be formulated as Galerkin equations. To ensure their consistency, a weighted DLRA is introduced so that the resulting DLR-DG solution is a solution to the fully discrete DG scheme in a subspace of the standard DG solution space. Similar to the standard DG method, we show that the proposed DLR-DG method is well-posed. We also identify conditions such that the DLR-DG solution converges to the equilibrium. Numerical results are presented to demonstrate the theoretical findings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Oak Ridge National Laboratory's Strategic Research and Development Insights for Digital Twins

Oak Ridge National Laboratory (ORNL) is pleased to provide our response to the NITRD RFI on Digital Twins Research and Development. Digital twins are virtual representations of physical systems, leveraging real-time data to simulate and predict behaviors. ORNL is advancing digital twin technology across various disciplines, including neutron scattering, networking, science ecosystems, supercomputing, secure facilities, mobility technologies, materials design and discovery, power systems, fusion reactors, biological sciences, and earth observation. These efforts aim to enhance scientific research, operational efficiency, and decision-making processes. ORNL facilities, such as the High Flux Isotope Reactor (HFIR), Grid-C, Spallation Neutron Source (SNS), and Oak Ridge Leadership Computing Facility (OLCF), provide the infrastructure to develop and demonstrate these digital twin technologies. In this document, we lay out key challenges, research gaps, and future opportunities based on our experience with digital twins that aim to serve as useful contributions towards a National Digital Twins R&D Strategic Plan. In the remaining document, we address nine of the thirteen topic areas specified in the RFI.

97 MATHEMATICS AND COMPUTING↗