Into the Bends of Time and Musical Forces in Jazz: Group Interaction and Double-time in “My Foolish Heart” as performed by the Bill Evans Trio with Scott LaFaro and Paul Motian.

Into the Bends of Time is a 40-minute work in seven movements for a large chamber orchestra with electronics, utilizing real-time computer-assisted processing of music performed by live musicians. The piece explores various combinations of interactive relationships between players and electronics, ranging from relatively basic processing effects to musical gestures achieved through stages of computer analysis, in which resulting sounds are crafted according to parameters of the incoming musical material. Additionally, some elements of interaction are multi-dimensional, in that they rely on the participation of two or more performers fulfilling distinct roles in the interactive process with the computer in order to generate musical material. Through processes of controlled randomness, several electronic effects induce elements of chance into their realization so that no two performances of this work are exactly alike. The piece gets its name from the notion that real-time computer-assisted processing, in which sound pressure waves are transduced into electrical energy, converted to digital data, artfully modified, converted back into electrical energy and transduced into sound waves, represents a “bending” of time.

The Bill Evans Trio featuring bassist Scott LaFaro and drummer Paul Motian is widely regarded as one of the most important and influential piano trios in the history of jazz, lauded for its unparalleled level of group interaction. Most analyses of Bill Evans’ recordings, however, focus on his playing alone and fail to take group interaction into account. This paper examines one performance in particular, of Victor Young’s “My Foolish Heart” as recorded in a live performance by the Bill Evans Trio in 1961. In Part One, I discuss Steve Larson’s theory of musical forces (expanded by Robert S. Hatten) and its applicability to jazz performance. I examine other recordings of ballads by this same trio in order to draw observations about normative ballad performance practice. I discuss meter and phrase structure and show how the relationship between the two is fixed in a formal structure of repeated choruses. I then develop a model of perpetual motion based on the musical forces inherent in this structure. In Part Two, I offer a full transcription and close analysis of “My Foolish Heart,” showing how elements of group interaction work with and against the musical forces inherent in the model of perpetual motion to achieve an unconventional, dynamic use of double-time. I explore the concept of a unified agential persona and discuss its role in imparting the song’s inherent rhetorical tension to the instrumental musical discourse.

Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.