Rum Histories: Drinking in Atlantic Literature and Culture

The book examines rum in anglophone Atlantic literature between 1945 and 1973, the period of decolonization, and explains the adaptation of these images for the era of globalization. Rum’s alcoholic nature links it to stereotypes (e.g., piracy, demon rum, Caribbean tourism) that have constrained serious analysis in the field of colonial commodities. Insights from anthropology, history, and commodity theory yield new understandings of rum’s role in containing the paradox of a postcolonial world still riddled with the legacies of colonialism. The association of rum with slavery causes slippage between its specific role in economic exploitation and moral attitudes about the consequences of drinking. These attitudes mask history that enables continued sexual, environmental, and political exploitation of Caribbean people and spaces. Gendered and racialized drinking taboos transfer blame to individuals and cultures rather than international structures, as seen in examinations of works by V. S. Naipaul, Hunter S. Thompson, Jean Rhys, and Sylvia Townsend Warner. More broadly, these stereotypes and taboos threaten understanding West Indian nationalism in works by Earl Lovelace, George Lamming, and Sylvia Wynter. The conclusion articulates the popular force of rum’s image by addressing the relationship between a meme from the "Pirates of the Caribbean" films and rhetoric during the 2016 election year.

Mathematics in the Digital Age: The Case of Simulation-Based Proofs

Digital transformation has made possible the implementation of environments in which mathematics can be experienced in interplay with the computer. Examples are dynamic geometry environments or interactive computational environments, for example GeoGebra or Jupyter Notebook, respectively. We argue that a new possibility to construct and experience proofs arises alongside this development, as it enables the construction of environments capable of not only showing predefined animations, but actually allowing user interaction with mathematical objects and in this way supporting the construction of proofs. We precisely define such environments and call them “mathematical simulations.” Following a theoretical dissection of possible user interaction with these mathematical simulations, we categorize them in relation to other environments supporting the construction of mathematical proofs along the dimensions of “interactivity” and “formality.” Furthermore, we give an analysis of the functions of proofs that can be satisfied by simulation-based proofs. Finally, we provide examples of simulation-based proofs in Ariadne, a mathematical simulation for topology. The results of the analysis show that simulation-based proofs can in theory yield most functions of traditional symbolic proofs, showing promise for the consideration of simulation-based proofs as an alternative form of proof, as well as their use in this regard in education as well as in research. While a theoretical analysis can provide arguments for the possible functions of proof, they can fulfil their actual use and, in particular, their acceptance is of course subject to the sociomathematical norms of the respective communities and will be decided in the future.

COMPUTABILITY THEORY, NONSTANDARD ANALYSIS, AND THEIR CONNECTIONS

We investigate the connections between computability theory and Nonstandard Analysis. In particular, we investigate the two following topics and show that they are intimately related.(T.1) A basic property of Cantor space$2^ $ is Heine–Borel compactness: for any open covering of $2^ $, there is a finite subcovering. A natural question is: How hard is it to compute such a finite subcovering? We make this precise by analysing the complexity of so-called fan functionals that given any $G:2^ \to $, output a finite sequence $\langle f_0 , \ldots ,f_n \rangle $ in $2^ $ such that the neighbourhoods defined from $\overline {f_i } G\left( {f_i } \right)$ for $i \le n$ form a covering of $2^ $.(T.2) A basic property of Cantor space in Nonstandard Analysis is Abraham Robinson’s nonstandard compactness, i.e., that every binary sequence is “infinitely close” to a standard binary sequence. We analyse the strength of this nonstandard compactness property of Cantor space, compared to the other axioms of Nonstandard Analysis and usual mathematics.Our study of (T.1) yields exotic objects in computability theory, while (T.2) leads to surprising results in Reverse Mathematics. We stress that (T.1) and (T.2) are highly intertwined, i.e., our study is holistic in nature in that results in computability theory yield results in Nonstandard Analysis and vice versa.

Concerted proton-electron transfer reactions in the Marcus inverted region

Electron transfer reactions slow down when they become very thermodynamically favorable, a counterintuitive interplay of kinetics and thermodynamics termed the inverted region in Marcus theory. Here we report inverted region behavior for proton-coupled electron transfer (PCET). Photochemical studies of anthracene-phenol-pyridine triads give rate constants for PCET charge recombination that are slower for the more thermodynamically favorable reactions. Photoexcitation forms an anthracene excited state that undergoes PCET to create a charge-separated state. The rate constants for return charge recombination show an inverted dependence on the driving force upon changing pyridine substituents and the solvent. Calculations using vibronically nonadiabatic PCET theory yield rate constants for simultaneous tunneling of the electron and proton that account for the results.

Introduction

Highlighting the role of the epistolary in the making of Western civilization, the Introduction argues that deep within such movements and the conditions of violent duress they produce, the mundane activities of communities to reconstitute themselves—as manifest in letter correspondence—emerge discernibly as essential to social life rather than seemingly adjunct to it: facilitating a means for people to reproduce themselves at every scale of existence, from bodily integrity to subjectivity to collective and spiritual essence. Methodologically, the Introduction argues that regional approaches to spatial analysis modeled by Black geographies, alongside historical materialist approaches to literary studies modeled by Asian American, Queer, and Black cultural theory, yield unique insights into articulations of difference, power, and globality that have been under-studied while simultaneously opening new epistemological horizons for their investigation.

Plasma electron hole oscillatory velocity instability

In this paper, we report a new type of instability of electron holes (EHs) interacting with passing ions. The nonlinear interaction of EHs and ions is investigated using a new theory of hole kinematics. It is shown that the oscillation in the velocity of the EH parallel to the magnetic field direction becomes unstable when the hole velocity in the ion frame is slower than a few times the cold ion sound speed. This instability leads to the emission of ion-acoustic waves from the solitary hole and decay in its magnitude. The instability mechanism can drive significant perturbations in the ion density. The instability threshold, oscillation frequency and instability growth rate derived from the theory yield quantitative agreement with the observations from a novel high-fidelity hole-tracking particle-in-cell code.

Markov Tail Chains

The extremes of a univariate Markov chain with regularly varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper we extend this fact to Markov chains with multivariate regularly varying marginal distributions inRd. We analyze both the forward and the backward tail process and show that they mutually determine each other through a kind of adjoint relation. In a broader setting, we will show that even for non-Markovian underlying processes a Markovian forward tail chain always implies that the backward tail chain is also Markovian. We analyze the resulting class of limiting processes in detail. Applications of the theory yield the asymptotic distribution of both the past and the future of univariate and multivariate stochastic difference equations conditioned on an extreme event.

Markov Tail Chains

The extremes of a univariate Markov chain with regularly varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper we extend this fact to Markov chains with multivariate regularly varying marginal distributions in R d . We analyze both the forward and the backward tail process and show that they mutually determine each other through a kind of adjoint relation. In a broader setting, we will show that even for non-Markovian underlying processes a Markovian forward tail chain always implies that the backward tail chain is also Markovian. We analyze the resulting class of limiting processes in detail. Applications of the theory yield the asymptotic distribution of both the past and the future of univariate and multivariate stochastic difference equations conditioned on an extreme event.

Markov Tail Chains

The extremes of a univariate Markov chain with regularly varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper we extend this fact to Markov chains with multivariate regularly varying marginal distributions in R d . We analyze both the forward and the backward tail process and show that they mutually determine each other through a kind of adjoint relation. In a broader setting, we will show that even for non-Markovian underlying processes a Markovian forward tail chain always implies that the backward tail chain is also Markovian. We analyze the resulting class of limiting processes in detail. Applications of the theory yield the asymptotic distribution of both the past and the future of univariate and multivariate stochastic difference equations conditioned on an extreme event.

Intense bed-load due to a sudden dam-break

Intense bed-load, or sheet flow, occurs when a free-surface flow of water drives a thick, rapidly sheared layer of water and grains over an erodible granular bed. We examine here the transient case where flow is induced by a sudden dam-break. Aiming for greater detail than achieved previously, we investigate this case using experiment and theory. The experiments combine particle tracking velocimetry (PTV) with a novel method of concentration measurement based on recording the penetration depth of a laser light sheet. The theory incorporates more vertical detail into the shallow water equations by using piecewise linear profiles of velocity and granular concentration, constrained by constitutive relations proposed recently for intense bed-load. These relations account for Coulomb yield at the bed, immersed granular collisions at the base, and equilibration of shear rate and density stratification across the bed-load layer. Using these approaches, both experiment and theory yield time- and depth-resolved profiles of velocity and granular concentration in addition to longitudinal wave profiles. Without any parameter adjustment, the theoretical predictions are in good agreement with the experimental measurements.