Gauge Variant Symmetries for the Schr\"odinger Equation

The last multiplier of Jacobi provides a route for the determination of families of Lagrangians for a given system. We show that the members of a family are equivalent in that they differ by a total time derivative. We derive the Schr\"odinger equation for a one-degree-of-freedom system with a constant multiplier. In the sequel we consider the particular example of the simple harmonic oscillator. In the case of the general equation for the simple harmonic oscillator which contains an arbitrary function we show that all Schr\"odinger equations possess the same number of Lie point symmetries with the same algebra. From the symmetries we construct the solutions of the Schr\"odinger equation and find that they differ only by a phase determined by the gauge.Comment: 12 page

A polyphonic acoustic vortex and its complementary chords

Using an annular phased array of eight loudspeakers, we generate sound beams that simultaneously contain phase singularities at a number of different frequencies. These frequencies correspond to different musical notes and the singularities can be set to overlap along the beam axis, creating a polyphonic acoustic vortex. Perturbing the drive amplitudes of the speakers means that the singularities no longer overlap, each note being nulled at a slightly different lateral position, where the volume of the other notes is now nonzero. The remaining notes form a tri-note chord. We contrast this acoustic phenomenon to the optical case where the perturbation of a white light vortex leads to a spectral spatial distribution

Quantum process tomography via completely positive and trace-preserving projection

We present an algorithm for projecting superoperators onto the set of completely positive, trace-preserving maps. When combined with gradient descent of a cost function, the procedure results in an algorithm for quantum process tomography: finding the quantum process that best fits a set of sufficient observations. We compare the performance of our algorithm to the diluted iterative algorithm as well as second-order solvers interfaced with the popular CVX package for MATLAB, and find it to be significantly faster and more accurate while guaranteeing a physical estimate.Comment: 13pp, 8 fig

Analytic Behaviour of Competition among Three Species

We analyse the classical model of competition between three species studied by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity and symmetry analyses.Comment: 14 pages, to appear in Journal of Nonlinear Mathematical Physic

Circadian, endocrine, and metabolic effects of prolonged bedrest: Two 56-day bedrest studies

Two bedrest studies of 56 days each have been conducted to evaluate the effects of prolonged bedrest on circadian synchrony and endocrine and metabolic function. Measurements included the pituitary-adrenal, thyroid, parathyroid, insulin-glucose-growth hormones, catecholamine excretion, body temperature, and heart rate. The results indicated that a rigorous regimen of exercise did not prevent the endocrine and metabolic effects of prolonged bedrest. Changes in circadian, endocrine, and metabolic functions in bedrest appear to be due to changes in hydrostatic pressure and lack of postural cues rather than to inactivity, confinement, or the bleeding schedule. Prolonged bedrest, particularly beyond 24 days, resulted in rhythm desynchronization in spite of well regulated light/dark cycles, temperature, humidity, activity, and meal times and meal composition and in increased lability of all endocrine parameter measured. It also resulted in an apparent insensitivity of the glucose response to insulin, of cortisol secretion to ACTH, and of growth hormone secretion to hypoglycemia

Ermakov's Superintegrable Toy and Nonlocal Symmetries

We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2,R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Ceramic identity contributes to mechanical properties and osteoblast behavior on macroporous composite scaffolds.

Implants formed of metals, bioceramics, or polymers may provide an alternative to autografts for treating large bone defects. However, limitations to each material motivate the examination of composites to capitalize on the beneficial aspects of individual components and to address the need for conferring bioactive behavior to the polymer matrix. We hypothesized that the inclusion of different bioceramics in a ceramic-polymer composite would alter the physical properties of the implant and the cellular osteogenic response. To test this, composite scaffolds formed from poly(lactide-co-glycolide) (PLG) and either hydroxyapatite (HA), β-tricalcium phosphate (TCP), or bioactive glass (Bioglass 45S®, BG) were fabricated, and the physical properties of each scaffold were examined. We quantified cell proliferation by DNA content, osteogenic response of human osteoblasts (NHOsts) to composite scaffolds by alkaline phosphatase (ALP) activity, and changes in gene expression by qPCR. Compared to BG-PLG scaffolds, HA-PLG and TCP-PLG composite scaffolds possessed greater compressive moduli. NHOsts on BG-PLG substrates exhibited higher ALP activity than those on control, HA-, or TCP-PLG scaffolds after 21 days, and cells on composites exhibited a 3-fold increase in ALP activity between 7 and 21 days versus a minimal increase on control scaffolds. Compared to cells on PLG controls, RUNX2 expression in NHOsts on composite scaffolds was lower at both 7 and 21 days, while expression of genes encoding for bone matrix proteins (COL1A1 and SPARC) was higher on BG-PLG scaffolds at both time points. These data demonstrate the importance of selecting a ceramic when fabricating composites applied for bone healing

Endocrine and fluid metabolism in males and females of different ages after bedrest, acceleration and lower body negative pressure

Space shuttle flight simulations were conducted to determine the effects of weightlessness, lower body negative pressure (LBNP), and acceleration of fluid and electrolyte excretion and the hormones that control it. Measurements were made on male and female subjects of different ages before and after bedrest. After admission to a controlled environment, groups of 6 to 14 subjects in the age ranges 25 to 35, 35 to 45, 45 to 55 to 65 years were exposed to +3 G sub z for 15 minutes (G1) and to LBNP (LBNP1) on different days. On 3 days during this prebedrest period, no tests were conducted. Six days of bedrest followed, and the G sub z (G2) and LBNP (LBNP2) tests were run again. Hormones, electrolytes, and other parameters were measured in 24-hour urine pools throughout the experiment. During bedrest, cortisol and aldosterone excretion increased. Urine volume decreased, and specific gravity and osmolality increased. Urinary electrolytes were statistically unchanged from levels during the non-stress control period. During G2, cortisol increased significantly over its control and bedrest levels. Urine volume, sodium, and chloride were significantly lower; specific gravity and osmolality were higher during the control period or bedrest. The retention of fluids and electrolytes after +G sub z may at least partially explain decreased urine volume and increased osmolality observed during bedrest in this study. There were some who indicated that space flight would not affect the fluid and electrolyte metabolism of females or older males any more severely than it has affected that of male astronauts