Applied/ACMS/absS23

ACMS Abstracts: Spring 2023

Paul Milewski (Bath)

Title: Embedded solitary internal waves

Abstract: The ocean and atmosphere are density stratified fluids. Stratified fluids with narrow regions of rapid density variation with respect to depth (pycnoclines) are often modelled as layered flows. In this talk we shall examine horizontally propagating internal waves within a three-layer fluid, with a focus on mode-2 waves which have oscillatory vertical structure. Mode-2 nonlinear waves (typically) occur within the linear spectrum of mode-1 waves (i.e. they travel at lower speeds than mode-1 waves), and are hence generically associated with an unphysical resonant mode-1 oscillatory tail. We will present evidence that these tail oscillations can be found to have zero amplitude, thus resulting in families of localised solutions (so called embedded solitary waves) in the Euler equations. This is the first example we know of embedded solitary waves in the Euler equations.

Nimish Pujara (UW)

Title: Flow and friction on a beach due to breaking waves

Abstract: As water waves approach a beach, they undergo dramatic transformations that have significant consequences for beach morphology. The most important transformations for the flow dynamics are that waves usually break before they reach the shoreline and that their height collapses when they do reach the shoreline. In this talk, we consider these processes and the subsequent flow that is driven up the beach. We present measurements of this flow in large-scale experiments with a focus on understanding the flow evolution in space and time, its friction with the beach surface, and its potential to transport large amounts of sediment. We demonstrate the link between wave-driven flow on a beach and canonical solutions to the shallow water equations, which allows us to describe the flow using reduced-parameter models. Using measurements of the wall shear stress, we also show that the importance of friction is confined to a narrow region within the flow at the interface between the wet and dry portions of the beach, and we present a simplified model that considers the dynamics of this region. Finally, we discuss a few extensions of this work that have applications to understanding sediment transport and the risk of coastal flooding.

Dimitris Giannakis (Dartmouth)

Title: Quantum information for simulation of classical dynamics

Abstract: We present a framework for simulating classical dynamical systems by finite-dimensional quantum system amenable to implementation on a quantum computer. Using ideas from kernel-based machine learning, the framework employs a quantum feature map for representing classical states by density operators on a reproducing kernel Hilbert space (RKHS). Simultaneously, a mapping is employed to represent classical observables by quantum observables on the RKHS such that quantum mechanical expectation values are consistent with pointwise function evaluation. With this approach, quantum states and observables evolve under the Koopman operator of the dynamical system in a consistent manner with classical evolution. Moreover, the state of the quantum system can be projected onto a finite-rank density operator on a tensor product Hilbert space, enabling efficient implementation in a quantum circuit. We illustrate our approach with quantum circuit simulations of low-dimensional dynamical systems, as well as actual experiments on the IBM Quantum System One.

Steve Wright (UW)

Title: Optimization in theory and practice

Abstract: Complexity analysis in optimization seeks upper bounds on the amount of work required to find approximate solutions of problems in a given class with a given algorithm, and also lower bounds, usually in the form of a worst-case example from a given problem class. The relationship between theoretical complexity bounds and practical performance of algorithms on “typical” problems varies widely across problem and algorithm classes. Over the years, research emphasis has switched between the theoretical and practical aspects of algorithm design and analysis. This talk surveys complexity analysis and its relationship to practice in optimization, with an emphasis on linear programming and convex and nonconvex nonlinear optimization, providing historical (and cultural) perspectives on research in these areas.

Ehud Yariv (Technion)

Title: Flows about superhydrophobic surfaces

Abstract: Superhydrophobic surfaces, formed by air entrapment within the cavities of hydrophobic solid substrates, offer a promising potential for hydrodynamic drag reduction. In several of the prototypical surface geometries the flows are two-dimensional, governed by Laplace’s equation in the longitudinal problem and the biharmonic equation in the transverse problem. Moreover, low-drag configurations are typically associated with singular limits. Thus, the analysis of liquid slippage past superhydrophobic surfaces naturally invites the use of both singular-perturbation methods and conformal-mapping techniques. I will discuss the combined application of these methodologies to several emerging problems in the field.