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

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

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

Distances on a one-dimensional lattice from noncommutative 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 ``successor'' distances to the neighbouring odd points.Comment: LaTeX file, few minor typos corrected, 9 page

Thermodynamic and magnetic properties of metastable FexCu100−x solid solutions formed by mechanical alloying

Copyright 1993 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The article originally appeared in Journal of Applied Physics 74, 955 (1993) and may be found at http://jap.aip.org/resource/1/japiau/v74/i2/p955_s1.Metastable solid solutions of Fe and Cu, which are immiscible in equilibrium, have been formed using high-energy ball milling of elemental powder mixtures. Single-phase face-centered-cubic (fcc) solid solution was obtained for 0<x≤60, and body-entered-cubic (bcc) solid solution for 75≤x<100. The transition from fcc to bcc occurred near x=70, where a mixture of fcc and bcc phases was obtained. The enthalpy of transformation to equilibrium was measured using differential scanning calorimetry. The average atomic volume of the phases exhibits a positive deviation from Vegard’s law, in qualitative agreement with the large positive enthalpy of mixing in this system. The magnetic moments and Curie temperatures for the metastable solid solutions have been determined and compared with those reported for Fe-Cu alloys formed by vapor deposition. Calculations of the formation enthalpy (ΔH) and free energy (ΔG) have been performed based on calphad data, with corrections based on our magnetization measurements. The calculated ΔG results are used to explain the observed fcc-bcc transition under polymorphous constraints.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69705/2/JAPIAU-74-2-955-1.pd

Evidence for self-sustained MoSi2 formation during room-temperature high-energy ball milling of elemental powders

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83393/1/Ma_JMR.pd

Effect of strain rate on the formation of nanocrystallites in an Al-based amorphous alloy during nanoindentation

Copyright 2003 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The article originally appeared in Journal of Applied Physics 93, 9287 (2003) and may be found at http://jap.aip.org/resource/1/japiau/v93/i11/p9287_s1.The effect of deformation by nanoindentation on nanocrystallization in amorphous Al90Fe5Gd5Al90Fe5Gd5 was investigated by transmission electron microscopy. Massive precipitation of nanocrystallites is observed within the indents. Under the quasistatic condition used, a temperature rise due to adiabatic heating is likely negligible, confirming that plastic deformation can induce crystallization without a heating effect. The nucleation of nanocrystallites is significantly affected by the strain rate. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69990/2/JAPIAU-93-11-9287-1.pd