Tracing Beethoven Through the Ten Sonatas for Piano and Violin

Examination of Beethoven’s ten sonatas for piano and violin as a single arc, to uncover linkages between the individual sonatas and observe their stylistic evolution as a set, benefits from placing these works also in relation to the wider realm of Beethoven’s chamber music as a whole. During the years in which his sonatas for piano and violin were written, Beethoven often produced multiple works simultaneously. In fact, the first nine sonatas for piano and violin were written within a mere five-year span (1798 – 1803.) After a gap of nine years, Beethoven completed his tenth and final sonata, marking the end of his “Middle Period.” Because of this distribution, it is important to consider each of these sonatas not only as an interdependent set, but also in relation to the whole of Beethoven’s output for small ensemble. Beethoven wrote the last of his piano and violin sonatas in 1812, with a decade and a half of innovation still ahead of him. This provokes one to look beyond these sonatas to discover the final incarnation of the ideas introduced in these works. In particular, the key creative turning points within the ten sonatas for piano and violin become strikingly apparent when compared to Beethoven’s string quartets, which dramatically showcase Beethoven’s evolution in sixteen works distributed more or less evenly across his career. From the perspective of a string quartet player, studying the ten sonatas for piano and violin provides an opportunity to note similarities between the genres. This paper argues that examining the ten sonatas from a viewpoint primarily informed by Beethoven’s string quartets yields a more thorough understanding of the sonatas themselves and a broader conception of the vast network of interrelationships that produce Beethoven’s definitive voice. The body of this paper contains a full exploration of each of the ten sonatas for piano and violin, highlighting key musical, historical, and theoretical elements. Each of the sonatas is then put not only in context of the set of ten, but is contrasted with Beethoven’s sixteen string quartets, identifying unifying motives, techniques, and structural principles that recur across both bodies of work.

Thermal activation, long-range ordering, and topological frustration of artificial spin ice

Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, are ubiquitous in nature and display many rich phenomena and novel physics. Artificial spin ices (ASIs), arrays of lithographically patterned Ising-like single-domain magnetic nanostructures, are highly tunable systems that have proven to be a novel method for studying the effects of frustration and associated properties. The strength and nature of the frustrated interactions between individual magnets are readily tuned by design and the exact microstate of the system can be determined by a variety of characterization techniques. Recently, thermal activation of ASI systems has been demonstrated, introducing the spontaneous reversal of individual magnets and allowing for new explorations of novel phase transitions and phenomena using these systems. In this work, we introduce a new, robust material with favorable magnetic properties for studying thermally active ASI and use it to investigate a variety of ASI geometries. We reproduce previously reported perfect ground-state ordering in the square geometry and present studies of the kagome lattice showing the highest yet degree of ordering observed in this fully frustrated system. We consider theoretical predictions of long-range order in ASI and use both our experimental studies and kinetic Monte Carlo simulations to evaluate these predictions. Next, we introduce controlled topological defects into our square ASI samples and observe a new, extended frustration effect of the system. When we introduce a dislocation into the lattice, we still see large domains of ground-state order, but, in every sample, a domain wall containing higher energy spin arrangements originates from the dislocation, resolving a discontinuity in the ground-state order parameter. Locally, the magnets are unfrustrated, but frustration of the lattice persists due to its topology. We demonstrate the first direct imaging of spin configurations resulting from topological frustration in any system and make predictions on how dislocations could affect properties in numerous materials systems.

Essays on Information Frictions, Prices and Unemployment

I investigate the effects of information frictions in price setting decisions. I show that firms' output prices and wages are less sensitive to aggregate economic conditions when firms and workers cannot perfectly understand (or know) the aggregate state of the economy. Prices and wages respond with a lag to aggregate innovations because agents learn slowly about those changes, and this delayed adjustment in prices makes output and unemployment more sensitive to aggregate shocks. In the first chapter of this dissertation, I show that workers' noisy information about the state of the economy help us to explain why real wages are sluggish. In the context of a search and matching model, wages do not immediately respond to a positive aggregate shock because workers do not (yet) have enough information to demand higher wages. This increases firms' incentives to post more vacancies, and it makes unemployment volatile and sensitive to aggregate shocks. This mechanism is robust to two major criticisms of existing theories of sluggish wages and volatile unemployment: the flexibility of wages for new hires and the cyclicality of the opportunity cost of employment. Calibrated to U.S. data, the model explains 60% of the overall unemployment volatility. Consistent with empirical evidence, the response of unemployment to TFP shocks predicted by my model is large, hump-shaped, and peaks one year after the TFP shock, while the response of the aggregate wage is weak and delayed, peaking after two years. In the second chapter of this dissertation, I study the role of information frictions and inventories in firms' price setting decisions in the context of a monetary model. In this model, intermediate goods firms accumulate output inventories, observe aggregate variables with one period lag, and observe their nominal input prices and demand at all times. Firms face idiosyncratic shocks and cannot perfectly infer the state of nature. After a contractionary nominal shock, nominal input prices go down, and firms accumulate inventories because they perceive some positive probability that the nominal price decline is due to a good productivity shock. This prevents firms' prices from decreasing and makes current profits, households' income, and aggregate demand go down. According to my model simulations, a 1% decrease in the money growth rate causes output to decline 0.17% in the first quarter and 0.38% in the second followed by a slow recovery to the steady state. Contractionary nominal shocks also have significant effects on total investment, which remains 1% below the steady state for the first 6 quarters.