The high energy limit of the trajectory representation of quantum mechanics

The trajectory representation in the high energy limit (Bohr correspondence principle) manifests a residual indeterminacy. This indeterminacy is compared to the indeterminacy found in the classical limit (Planck's constant to 0) [Int. J. Mod. Phys. A 15, 1363 (2000)] for particles in the classically allowed region, the classically forbiden region, and near the WKB turning point. The differences between Bohr's and Planck's principles for the trajectory representation are compared with the differences between these correspondence principles for the wave representation. The trajectory representation in the high energy limit is shown to go to neither classical nor statistical mechanics. The residual indeterminacy is contrasted to Heisenberg uncertainty. The relationship between indeterminacy and 't Hooft's information loss and equivalence classes is investigated.Comment: 12 pages of LaTeX. No figures. Incorporated into the "Proceedings of the Seventh International Wigner Symposium" (ed. M. E. Noz), 24-29 August 2001, U. of Maryland. Proceedings available at http://www.physics.umd.edu/robo

An Evaluation of the Effect of Discharging a High Quality Effluent into a Small Ozark Mountain Stream

Recently the newly constructed Fayetteville wastewater treatment plant went on line and directed a portion of its discharge to a point in the Mud Creek drainage basin that had previously not received any effluent. Prior to the discharge, a background study had been performed to establish the water quality in the basin. The background data, when compared to the data collected by this study, allowed any alteration of the stream water quality to be evaluated. Also the modeling procedure used to set the effluent limits for the treatment plant was analyzed. All stream data were compared to the limits set forth for surface water quality by the Department of Pollution Control and Ecology. The new discharge had some effect on the receiving stream, however, the stream still meets Arkansas water quality standards for all parameters

The Equivalence Postulate of Quantum Mechanics

The Equivalence Principle (EP), stating that all physical systems are connected by a coordinate transformation to the free one with vanishing energy, univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories depend on the Planck length through hidden variables which arise as initial conditions. The formulation has manifest p-q duality, a consequence of the involutive nature of the Legendre transform and of its recently observed relation with second-order linear differential equations. This reflects in an intrinsic psi^D-psi duality between linearly independent solutions of the Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even for bound states. No use of any axiomatic interpretation of the wave-function is made. Tunnelling is a direct consequence of the quantum potential which differs from the usual one and plays the role of particle's self-energy. The QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of the extended real line. This is an important feature as the L^2 condition, which in the usual formulation is a consequence of the axiomatic interpretation of the wave-function, directly follows as a basic theorem which only uses the geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP. As a result, the EP itself implies a dynamical equation that does not require any further assumption and reproduces both tunnelling and energy quantization. Several features of the formulation show how the Copenhagen interpretation hides the underlying nature of QM. Finally, the non-stationary higher dimensional quantum HJ equation and the relativistic extension are derived.Comment: 1+3+140 pages, LaTeX. Invariance of the wave-function under the action of SL(2,R) subgroups acting on the reduced action explicitly reveals that the wave-function describes only equivalence classes of Planck length deterministic physics. New derivation of the Schwarzian derivative from the cocycle condition. "Legendre brackets" introduced to further make "Legendre duality" manifest. Introduction now contains examples and provides a short pedagogical review. Clarifications, conclusions, ackn. and references adde

Interference, reduced action, and trajectories

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function's trajectory. The quantum effective mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality.Comment: 12 pages text, 5 figures. Typos corrected. Author's final submission. A companion paper to "Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment", quant-ph/0605121. Keywords: interference, nonlocality, trajectory representation, entanglement, dwell time, determinis

Effects of Reinforcer Quality on Behavioral Momentum: Coordinated Applied and Basic Research

The high-probability (high-p) instructional sequence has been an effective treatment for noncompliance. However, treatment failures have also been reported. We hypothesized that the efficacy of the high-p treatment may be improved by using higher quality reinforcers for compliance to high-p instructions. The resistance of compliance to change was tested by varying reinforcer quality in two applied studies and a basic laboratory experiment. Experiment 1 tested the hypothesis that an increase in reinforcer quality for high-p compliance will increase the effectiveness of the high-p treatment when it fails to increase compliance. Experiment 2 assessed the effects of reinforcer quality on resistance of compliance to change by presenting successive low-p requests following the high-p treatment. A basic laboratory study (Experiment 3) was conducted to further isolate the relation between reinforcer quality and behavioral momentum. Two different liquid reinforcers (sucrose and citric acid solutions) were presented in a two-component multiple variable-interval variable-interval schedule followed by a single extinction test session. Results of all three experiments showed a generally consistent relationship between reinforcer quality and behavioral momentum

STAT 5 activators can replace the requirement of FBS in the adipogenesis of 3T3-L1 cells

The 3T3-L1 cells differentiate into fat cells that have many properties of native adipocytes including: substantial lipid accumulation, insulin sensitivity, and the ability to secrete endocrine hormones. A substantial expense in using these cells is fetal bovine serum (FBS), a critical component of efficient adipogenesis. Our recent studies on STAT 5 proteins have revealed that these transcription factors are phosphorylated and translocate to the nucleus immediately after the initiation of differentiation. Studies by several other laboratories also suggest that STAT 5 proteins can have pro-adipogenic properties. Growth hormone (GH) and prolactin (PRL) are both potent activators of STAT 5A and STAT 5B proteins. Since, FBS has high concentrations of GH; we examined the ability of GH to replace FBS as a component of the differentiation cocktail for 3T3-L1 cells. Our studies revealed that FBS was not required for the adipogenesis of 3T3-L1 cells if GH or PRL was added to the differentiation cocktail. Adipogenesis was judged by Oil Red O staining and expression of adipocyte marker genes. Hence, we have developed a substantially less expensive method for differentiating 3T3-L1 cells without FBS, thiazolidinediones, or expensive cytokines. © 2004 Elsevier Inc. All rights reserved

Chondrule sizes within the CM carbonaceous chondrites and measurement methodologies

The sizes of chondrules are a valuable tool for understanding relationships between meteorite groups and the affinity of ungrouped chondrites, documenting temporal/spatial variability in the solar nebula, and exploring the effects of parent body processing. Many of the recently reported sizes of chondrules within the CM carbonaceous chondrites differ significantly from the established literature average and are more closely comparable to those of chondrules within CO chondrites. Here, we report an updated analysis of chondrule dimensions within the CM group based on data from 1937 chondrules, obtained across a suite of CM lithologies ranging from petrologic subtypes CM2.2 to CM2.7. Our revised average CM chondrule size is 194 μm. Among the samples examined, a relationship was observed between petrologic subtype and chondrule size such that chondrule long‐axis lengths are greater in the more highly aqueously altered lithologies. These findings suggest a greater similarity between the CM and CO chondrites than previously thought and support arguments for a genetic link between the two groups (i.e., the CM‐CO clan). Using the 2‐D and 3‐D data gathered, we also apply numerous stereological corrections to examine their usefulness in correcting 2‐D chondrule measurements within the CM chondrites. Alongside this analysis, we present the details of a standardized methodology for 2‐D chondrule size measurement to facilitate more reliable inter‐study comparisons