Invariant Kinematics on a One-Dimensional Lattice in Noncommutative Geometry

In a one-dimensional lattice, the induced metric (from a noncommutative geometry calculation) breaks translation invariance. This leads to some inconsistencies among different spectator frames, in the observation of the hoppings of a test particle between lattice sites. To resolve the inconsistencies between the different spectator frames, we replace the test particle's bare mass by an effective locally dependent mass. This effective mass also depends on the lattice constant - i.e. it is a scale dependent variable (a "running" mass). We also develop an alternative approach based on a compensating potential. The induced potential between a spectator frame and the test particle is attractive on the average. We then show that the entire formalism holds for a quantum particle represented by a wave function, just as it applies to the mechanics of a classical point particle.Comment: 17 pages, latex, epsf, amssymbols, 2 figures. Final version to be published in IJMP

Dream work: the art and science of Fin de Siècle fantasy imagery

In this dissertation, I argue that the fantasy imagery of tum-of-the-century British illustrators Arthur Rackham, Aubrey Beardsley, and Sidney Sime, and French filmmakers Georges Méliès and Emile Cohl functions as visual rhetorical "texts" that explicate contemporaneous ideas about the self. At the fin de siecle, models of the self were shaped, in part, by scientific thought that interrogated themes of materiality and immateriality, visibility and invisibility, univalence and multivalence, permanence and impermanence. Dream Work grapples with these oppositions, the questions they brought up, and the provisional answers they elicited. I argue that both the science and the design considered in this study dealt with these oppositions, and the models of the self they elaborated, through a shared visual rhetoric of literal representation or hazy abstraction. I reveal this shared visual rhetoric through analysis of the form of the design considered in this study and its relationship to visual aspects of contemporaneous scientific discourse. I first show how Rackham's imagery, which echoes the visual vocabulary of physiognomical diagrams, deals with material aspects of self and mind. But Rackham's work likewise positions the mind as part of a grand continuum with the natural world. I describe the ways that Beardsley's imagery fluctuates between expression of material and ethereal elaborations of the self manifested in contemporaneous dream theory. And I show how Sime's imagery - which mirrors late nineteenth-century notions of the realms of other dimensions - probes abstract qualities of the self in strangely material forms. Finally, I discuss the ways that the mystifying abstraction that characterizes tum-of-the-century ideas about time, space, and motion marks the mutable selves expressed in Méliès and Cohl's work. In this dissertation, I likewise challenge the hegemony of the written word and of verbal analytical methods for interpreting visual entities. My goal, however, is not to dispense with the verbal analysis of visual artifacts. Rather, my intention is to foreground visual rhetorical analysis as a powerful method for understanding the visuality of both visual and verbal entities

The Associated Metric for a Particle in a Quantum Energy Level

We show that the probabilistic distribution over the space in the spectator world, can be associated via noncommutative geometry (with some modifications) to a metric in which the particle lives. According to this geometrical view, the metric in the particle world is ``contracted'' or ``stretched'' in an inverse proportion to the probability distribution.Comment: 14 pages, latex, epsf, 3 figures. Some clarifications were adde

Monte-Carlo simulations of spinodal ordering and decomposition in compositionally modulated alloys

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83399/1/Atzmon_JMR.pd

The pitfalls of empirical fitting of glass relaxation data with stretched exponents

A stretched exponent is commonly used to fit experimental relaxation data for glasses, which typically exhibit a range of time constants. While it has been supported by theory for various processes, mostly near and above the glass transition temperature, Tg, it is also commonly used in phenomenological fits below Tg without a mechanistic model. The properties of the stretched exponent, and sample data for the enthalpy release and dynamic-mechanical response of metallic glasses, are used to show that in the absence of a mechanistic model, stretched-exponent fits easily lead to artifacts and flawed conclusions.National Science FoundationPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163330/1/Atzmon JAP 2018.pdf-1Description of Atzmon JAP 2018.pdf : ArticleSEL

Distances on a one-dimensional lattice from noncomutative geometry

In the following paper we continue the work of Bimonte-Lizzi-Sparano on distances on a one dimensional lattice. We succeed in proving analytically the exact formulae for such distances. We find that the distance to an even point on the lattice is the geometrical average of the "predecessor" and "succesor" distances to the neighbouring odd points