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Asymptotic Relaxation of Moment Equations for a Multi-species, Homogeneous BGK Model
Multi-species BGK models describe the dynamics of rarefied gases with constituent particles of different elements or compounds with potentially nontrivial velocity distributions. Here, in this paper, moment equations for the bulk velocities, energies, and temperatures of a spatially homogeneous multi-species BGK model are examined. A key challenge in analyzing these equations is the fact that the collision frequencies are allowed to depend on the species temperatures, which allows for more realistic simulations of dilute gas flow. Therefore, a positive lower bound is established for the species temperatures. With this lower bound, a global existence and uniqueness of solutions to the coupled velocity-energy ODE system is established. The lower bound also enables a proof of exponential decay to a unique steady-state solution. Numerical results are presented to demonstrate how the bulk velocities and temperatures relax for large times.
A solvable quantum field theory with asymptotic freedom in (3+1) dimensions
Recently, Ai, Bender and Sarkar gave a prescription on how to obtain [Formula: see text]-symmetric field theory results from an analytic continuation of Hermitian field theories. We perform this analytic continuation for the massless (critical) [Formula: see text] model with quartic interaction in (3+1) dimensions. In the large-[Formula: see text] limit, this theory is exactly solvable, and has negative [Formula: see text]-function in the ultraviolet, and a stable bound state in the infrared. The coupling diverges at a scale [Formula: see text], but can be continued into the far infrared. At finite temperature, the theory exhibits two phases separated by a second-order phase transition near [Formula: see text].
Asymptotic structure of higher dimensional Yang-Mills theory
Using the covariant phase space formalism, we construct the phase space for non-Abelian gauge theories in (d+2)-dimensional Minkowski spacetime for any d ≥ 2, including the edge modes that symplectically pair to the low energy degrees of freedom of the gauge field. Despite the fact that the symplectic form in odd and even-dimensional spacetimes appear ostensibly different, we demonstrate that both cases can be treated in a unified manner by utilizing the shadow transform. Upon quantization, we recover the algebra of the vacuum sector of the Hilbert space and derive a Ward identity that implies the leading soft gluon theorem in (d+2)-dimensional spacetime.
Nucleon and pion PDFs: large-x asymptotics meets functional mimicry
We review strategies to unveil the primordial large- x x structure of the nucleons as well as the pion from hard-scattering experiments. Ideas are presented for learning about the x\to 1 x → 1 limit of nonperturbative QCD dynamics at energy scales of order 1 GeV from collider experiments at much higher scales. The behavior of parton distributions at x\to 1 x → 1 predicted by the quark counting rules and other low-energy theoretical approaches is contrasted with phenomenological PDFs. Polynomial mimicry of PDF parametrizations is one of many factors that influence the apparent power of the (1-x) ( 1 − x ) falloff. We discuss implications of the mimicry for the large- x x falloff of the pion PDFs.
Analysis into Asymptotic Convergence to Full Nonlinear Solutions and Exploration of the Implication of Numerical Operator Mutation of Differential Systems
A robust, sufficiently accurate and practical hydrodynamic simulation toolset is required as a key component of the modeling and simulation of air-gap electrostatic discharge events. This work was performed to complement these ongoing efforts. In particular, hydrodynamic simulations must be vetted to ensure they are robust and sufficiently accurate over relevant characteristic scales. Verification models were generated in order to cultivate the technical knowledge and expertise needed to properly create, implement and execute numerical simulations. Furthermore, this effort was utilized extensively to educate students on the mathematical and numerical principles underlying hydrodynamic simulations. This education opportunity, provided in a holistic and rigorous manner, has greatly benefited developing scientists and engineers with the necessary understandings and toolsets required to excel at accomplishing the task at hand, and, more generally, it has enabled them to generate key programmatic deliverables. This report articulates several subtilties; specifically, how perturbations, nonlinear behavior, and dissipative mechanisms influence numerical stability, how to properly structure mathematical and numerical solutions, and how to properly generate error estimation/assignment. A more rigorous discussion of the consequences of such topics can be found in the body of this report in Chapters 2 and 3 with qualitative findings discussed in Chapter 4.
ASCeND: ASymptotically Compatible Strong Form Foundations for Nonlocal Discretization.
Abstract not provided.
Shock Induced Particle Curtain Dispersion: Asymptotic Drag Law Scaling Formulations and Relationship to Streamwise Pressure Difference Models.
Abstract not provided.
Asymptotic scaling laws for the stagnation conditions of Z-pinches
A theoretical exposition of the in-flight dynamics of metal cylindrical annuli driven by magnetic fields, and their affect on the generation of x-rays and neutrons.
Self-similar mesh convergence, asymptotic convergence, and energy transport analysis
Explore the source record for details and available documents.
Shock Induced Particle Curtain Dispersion: Asymptotic Drag Law Scaling Formulations and Relationship to Streamwise Pressure Difference Models.
Abstract not provided.