Vacuum structure and string tension in Yang-Mills dimeron ensembles

We numerically simulate ensembles of SU(2) Yang-Mills dimeron solutions with a statistical weight determined by the classical action and perform a comprehensive analysis of their properties. In particular, we examine the extent to which these ensembles capture topological and confinement properties of the Yang-Mills vacuum. This further allows us to test the classic picture of meron-induced quark confinement as triggered by dimeron dissociation. At small bare couplings, spacial, topological-charge and color correlations among the dimerons generate a short-range order which screens topological charges. With increasing coupling this order weakens rapidly, however, in part because the dimerons gradually dissociate into their meron constituents. Monitoring confinement properties by evaluating Wilson-loop expectation values, we find the growing disorder due to these progressively liberated merons to generate a finite and (with the coupling) increasing string tension. The short-distance behavior of the static quark-antiquark potential, on the other hand, is dominated by small, "instanton-like" dimerons. String tension, action density and topological susceptibility of the dimeron ensembles in the physical coupling region turn out to be of the order of standard values. Hence the above results demonstrate without reliance on weak-coupling or low-density approximations that the dissociating dimeron component in the Yang-Mills vacuum can indeed produce a meron-populated confining phase. The density of coexisting, hardly dissociated and thus instanton-like dimerons seems to remain large enough, on the other hand, to reproduce much of the additional phenomenology successfully accounted for by non-confining instanton vacuum models. Hence dimeron ensembles should provide an efficient basis for a rather complete description of the Yang-Mills vacuum.Comment: 36 pages, 17 figure

Mathematical techniques for free boundary problems with multiple boundaries

In this thesis, we study six different free boundary problems arising in the field of fluid mechanics, and the mathematical methods used to solve them. The free boundary problems are all characterised by having more than one boundary and the solution of these problems requires special mathematical treatment. The challenge in each of these problems is to determine the shape of the multiple fluid interfaces making up the particular system under consideration. In each of the free boundary problems we employ aspects of complex function theory, conformal mapping between multiply connected domains, and specialist techniques devised in recent years by Crowdy and collaborators. At the heart of these techniques lies a special transcendental function known as the Schottky-Klein prime function. This thesis makes use of this function in a variety of novel contexts. We first examine a single row of so-called hollow vortices in free space. This problem has been solved before but we present a new methodology which is convenient in being extendible to the case of a double row, or von Karman vortex street, of hollow vortices. We find a concise formula for the conformal mapping describing the shapes of the free boundaries of two hollow vortices in a typical period window in the vortex street and thereby solve the free boundary problem. We next focus on the problem of a pair of hollow vortices in an infinite channel. This free boundary problem exhibits similar mathematical features to the vortex street problem but now involves the new ingredient of solid impenetrable walls. Again we solve the free boundary problem by finding a concise formula for the conformal mapping governing the hollow vortex shapes. We then extend this analysis to a single row of hollow vortices occupying the channel. The problem of a pair of hollow vortices of equal and opposite circulation positioned behind a circular cylinder, superposed with a uniform flow, is then considered. This system is a desingularisation of the so-called Foppl point vortex equilibrium. For this free boundary problem, we employ a hybrid analytical-numerical scheme and we are able to offer a Fourier-Laurent series expansion for the conformal mapping determining the shape of the hollow vortex boundaries. Finally, we investigate an asymmetric assembly of steadily translating bubbles in a Hele- Shaw channel. This free boundary problem can be formulated as a special Riemann-Hilbert problem solvable in terms of the Schottky-Klein prime function. Our method of solution can be used to determine the shapes of any finite number of bubbles in a given assembly

MHD stability and disruptions in the SPARC tokamak

SPARC is being designed to operate with a normalized beta of beta(N) = 1.0, a normalized density of n(G) = 0.37 and a safety factor of q(95) approximate to 3.4, providing a comfortable margin to their respective disruption limits. Further, a low beta poloidal beta(p) = 0.19 at the safety factor q = 2 surface reduces the drive for neoclassical tearing modes, which together with a frozen-in classically stable current profile might allow access to a robustly tearing-free operating space. Although the inherent stability is expected to reduce the frequency of disruptions, the disruption loading is comparable to and in some cases higher than that of ITER. The machine is being designed to withstand the predicted unmitigated axisymmetric halo current forces up to 50 MN and similarly large loads from eddy currents forced to flow poloidally in the vacuum vessel. Runaway electron (RE) simulations using GO+CODE show high flattop-to-RE current conversions in the absence of seed losses, although NIMROD modelling predicts losses of similar to 80 %; self-consistent modelling is ongoing. A passive RE mitigation coil designed to drive stochastic RE losses is being considered and COMSOL modelling predicts peak normalized fields at the plasma of order 10(-2) that rises linearly with a change in the plasma current. Massive material injection is planned to reduce the disruption loading. A data-driven approach to predict an oncoming disruption and trigger mitigation is discussed

How to integrate geochemistry at affordable costs into reactive transport for large-scale systems: Abstract Book

This international workshop entitled “How to integrate geochemistry at affordable costs into reac-tive transport for large-scale systems” was organized by the Institute of Resource Ecology of the Helmholtz-Zentrum Dresden Rossendorf in Feb-ruary 2020. A mechanistic understanding and building on that an appropriate modelling of geochemical processes is essential for reliably predicting contaminant transport in groundwater systems, but also in many other cases where migration of hazardous substances is expected and consequently has to be assessed and limited. In case of already present contaminations, such modelling may help to quantify the threads and to support the development and application of suitable remediation measures. Typical application areas are nuclear waste disposal, environmental remediation, mining and milling, carbon capture & storage, or geothermal energy production. Experts from these fields were brought together to discuss large-scale reactive transport modelling (RTM) because the scales covered by such pre-dictions may reach up to one million year and dozens of kilometers. Full-fledged incorporation of geochemical processes, e.g. sorption, precipitation, or redox reactions (to name just a few important basic processes) will thus create inacceptable long computing times. As an effective way to integrate geochemistry at affordable costs into RTM different geochemical concepts (e.g. multidimensional look-up tables, surrogate functions, machine learning, utilization of uncertainty and sensitivity analysis etc.) exist and were extensively discussed throughout the workshop. During the 3-day program of the workshop keynote and regular lectures from experts in the field, a poster session, and a radio lab tour had been offered. In total, 40 scientists from 28 re-search institutes and 8 countries participated

Exact Solutions in Classical Field Theory: Solitons, Black Holes and Boson Stars

Special Issue in honour of Prof. Yves Brihaye, on the occasion of his 65th birthday. The issue is mainly dedicated to the study of compact objects and solutions to Einstein-Yang-Mills equations and extensions thereof, topics to which Prof. Y. Brihaye contributed very significantly

Probing Particle Physics with Gravitational Waves

The direct detection of gravitational waves offers an exciting new window onto our Universe. At the same time, multiple observational evidence and theoretical considerations motivate the presence of physics beyond the Standard Model. In this thesis, we explore new ways of probing particle physics in the era of gravitational-wave astronomy. We focus on the signatures of ultralight bosons on the gravitational waves emitted by binary systems, demonstrating how binary black holes are novel detectors of this class of dark matter. We also discuss probes of other types of new physics through their finite-size imprints on gravitational waveforms, and examine the extent to which current template-bank searches could be used to detect these signals. In the first two chapters of this thesis, we review several aspects of gravitational-wave physics and particle physics at the weak coupling frontier; we hope the reader would find these reviews helpful in delving further into the literature and in their research.Comment: PhD Thesis, University of Amsterdam, 2020; 298 page

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Instabilities in solids and structures are ubiquitous across all length and time scales, and engineering design principles have commonly aimed at preventing instability. However, over the past two decades, engineering mechanics has undergone a paradigm shift, away from avoiding instability and toward taking advantage thereof. At the core of all instabilities—both at the microstructural scale in materials and at the macroscopic, structural level—lies a nonconvex potential energy landscape which is responsible, e.g., for phase transitions and domain switching, localization, pattern formation, or structural buckling and snapping. Deliberately driving a system close to, into, and beyond the unstable regime has been exploited to create new materials systems with superior, interesting, or extreme physical properties. Here, we review the state-of-the-art in utilizing mechanical instabilities in solids and structures at the microstructural level in order to control macroscopic (meta)material performance. After a brief theoretical review, we discuss examples of utilizing material instabilities (from phase transitions and ferroelectric switching to extreme composites) as well as examples of exploiting structural instabilities in acoustic and mechanical metamaterials