Twist Deformation of Rotationally Invariant Quantum Mechanics

Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally-invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential) and the Coulomb potential.Comment: 20 page

Decomposition of symmetric tensor fields in the presence of a flat contact projective structure

Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we consider symmetric tensor fields with coefficients in tensor densities, the vertical cotangent lift of contact form $\alpha$ is a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symmetric density valued tensor fields. This generalized Hamiltonian operator on the symbol space is invariant with respect to the action of the projective contact algebra $sp(2n+2)$. The preceding invariant operators lead to a decomposition of the symbol space (expect for some critical density weights), which generalizes a splitting proposed by V. Ovsienko

Improvement of the mass separation power of a cyclotron by using the vertical selection method

International audienceIt is well known that cyclotrons are very good mass separators, specially when the number of turns in the machine is large. This property is particularly interesting if the cyclotron unavoidably accelerates multiple species of radioactive beams simultaneously, which is the case for the cyclotron CIME at GANIL. We propose to improve the natural mass separation power by using a vertical resonance effect: it consists of putting two small electrodes between the poles, which provide a vertical electric field operating at two frequencies close to twice the RF frequency and which are tuned with respect to the vertical betatron oscillation. A prototype has been designed and built at GANIL, and tested successfully in the cyclotron CIME this September

Comparative Assessment of the Cytotoxicity of Various Substrates in Organ Culture and Cell Culture: A Scanning Electron Microscopy Study

A comparative study of the behavior of chick embryo endothelial cells grown on various substrates was performed in order to establish the reliability and the limitation of both cell and organ culture methods. Following substrates were analyzed to compare these two different culture techniques: bovine serum albumin, pigskin gelatin and albumin + gelatin cross-linked by glutaraldehyde or carbodiimide, fibrin glue and negative control (Thermanox*). Parameters of cell growth and adhesion were calculated and compared with electron microscopic observations of cell morphology and of the extracellular matrix. Both culture methods provided complementary results and led to a similar classification of the biomaterials. However, the cell culture method exhibited a higher sensitivity to the surface properties of biomaterials which limited further experimentation. This was well illustrated by glutaraldehyde cross-linked protein membranes which did not support the growth of dispersed cells but enabled the formation of a cellular tissue in organ culture, thus allowing a cytocompatibility assessment. Endothelial cell morphology and extracellular matrix elaborated on biomaterials were compared to chicken blood vessels. Both methods showed that cells grown on fibrin glue and on gelatin or albumin + gelatin cross-linked by carbodiimide had a microscopic morphology similar to that of vessel wall. Organ and dispersed cell cultures provide complementary information relative to the cell behavior towards vascular prosthesis materials

Non-commuting coordinates, exotic particles, & anomalous anyons in the Hall effect

Our previous ``exotic'' particle, together with the more recent anomalous anyon model (which has arbitrary gyromagnetic factor $g$) are reviewed. The non-relativistic limit of the anyon generalizes the exotic particle which has $g=0$ to any $g$.When put into planar electric and magnetic fields, the Hall effect becomes mandatory for all $g\neq2$, when the field takes some critical value.Comment: A new reference added. Talk given by P. Horvathy at the International Workshop "Nonlinear Physics: Theory and Experiment. III. July'04, Gallipoli (Lecce, Italy). To be published in Theor. Math. Phys. Latex 9 pages, no figure

Efficient indexing of necklaces and irreducible polynomials over finite fields

We study the problem of indexing irreducible polynomials over finite fields, and give the first efficient algorithm for this problem. Specifically, we show the existence of poly(n, log q)-size circuits that compute a bijection between {1, ... , |S|} and the set S of all irreducible, monic, univariate polynomials of degree n over a finite field F_q. This has applications in pseudorandomness, and answers an open question of Alon, Goldreich, H{\aa}stad and Peralta[AGHP]. Our approach uses a connection between irreducible polynomials and necklaces ( equivalence classes of strings under cyclic rotation). Along the way, we give the first efficient algorithm for indexing necklaces of a given length over a given alphabet, which may be of independent interest

Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space

We solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that for a specific choice of the noncommutative parameters, the time reversal symmetry of the systems get restored since the energy spectrum becomes degenerate. This is in contrast to the noncommutative configuration space where the time reversal symmetry of the harmonic oscillator is always broken.Comment: 7 pages Late

Conformal Properties of Chern-Simons Vortices in External Fields

The construction and the symmetries of Chern-Simons vortices in harmonic and uniform magnetic force backgrounds found by Ezawa, Hotta and Iwazaki, and by Jackiw and Pi are generalized using the non-relativistic Kaluza-Klein-type framework presented in our previous paper. All Schrodinger-symmetric backgrounds are determined.Comment: 10 pages,CPT-94/p.3028, te

Assessment of Black Rail Status in Georgia, Breeding Season 2017 and 2018 Summaries

The Black Rail (Laterallus jamaicensis) is the most secretive and least understood marsh bird in North America with the Eastern Black Rail (L. j. jamaicensis), one of two subspecies that occur here, listed as endangered in six states along the Atlantic Coast and proposed for federal listing under the Endangered Species Act (USFWS–R4–ES–2018–0057, 2018). Black Rails require dense vegetation for cover during all stages of their life cycle. They require wetlands with minimal water coverage during the breeding season. Historic population size for the Eastern subspecies was likely in the tens of thousands (25,000 to 100,000; Delaney and Scott 2002) but is now believed to be in the hundreds to low thousands. Eastern Black Rails breed within three geographic areas within North America including the Atlantic Coast, the Gulf Coast, and the Midwest. The Atlantic Coast has generally been considered to support the largest breeding population throughout the range with pairs mostly confined to the highest elevations within tidal salt marshes. Breeding range along the Atlantic Coast has contracted south more than 450 kilometers and the population is estimated to be declining by 9% annually (Watts 2016). The primary driver of declines over the past three decades is believed to be sea-level rise and associated tidal inundation during the nesting season. Georgia is noticeably missing from most of the early descriptions of Eastern Black Rail distribution (e.g. Allen 1900, Bent 1926, Forbush 1929). Early authors describing Eastern Black Rail status in the state (Burleigh 1938, Greene et al. 1945, Burleigh 1958) indicate that the species was perhaps more common and widespread in previous decades. As in all states within the breeding range, the lack of status and distribution information is certainly facilitated by their secretive habits, but in Georgia this is also likely reflected in an extremely low population size, a lack of overlap between Black Rails and bird watchers, or both. Scattered historic occurrences along the outer coast suggested a presence of a potential breeding population (Sykes 2010). The Eastern Black Rail ranks as a species of high conservation concern (GA DNR Wildlife Action Plan 2015) and breeding season surveys ranked as one of the highest conservation action priorities within the plan. The 2016 population estimate for the state (based on available habitat) was 10 to 40 pairs though the uncertainty in this estimate was very high (Watts 2016). The only definitive breeding record in the state comes from Greene County (Sykes 2010), and this site has been the most consistently documented breeding area throughout the state in the past 25 years (Watts 2016). During the 2017 field season, 409 coastal points were surveyed, and during the 2018 field season 206 points were surveyed. All points surveyed in 2017 were along the outer coast in tidal or impounded wetlands. During the 2018 survey, 141 inland points and 65 coastal points were surveyed. Three rounds of surveys were conducted between 18 April and 17 July 2017 and between 1 May and 15 July 2018. All points were surveyed three times unless there were access issues during one of the survey rounds. A total of 1,827 individual play-back surveys were conducted, 1,213 in 2017, and 614 in 2018. We detected no Black Rails during either season

Rigorous Physicochemical Framework for Metal Ion Binding by Aqueous Nanoparticulate Humic Substances: Implications for Speciation Modeling by the NICA-Donnan and WHAM Codes

Latest knowledge on the reactivity of charged nanoparticulate complexants toward aqueous metal ions is discussed in mechanistic detail. We present a rigorous generic description of electrostatic and chemical contributions to metal ion binding by nanoparticulate complexants, and their dependence on particle size, particle type (i.e., reactive sites distributed within the particle body or confined to the surface), ionic strength of the aqueous medium, and the nature of the metal ion. For the example case of soft environmental particles such as fulvic and humic acids, practical strategies are delineated for determining intraparticulate metal ion speciation, and for evaluating intrinsic chemical binding affinities and heterogeneity. The results are compared with those obtained by popular codes for equilibrium speciation modeling (namely NICA-Donnan and WHAM). Physicochemical analysis of the discrepancies generated by these codes reveals the a priori hypotheses adopted therein and the inappropriateness of some of their key parameters. The significance of the characteristic time scales governing the formation and dissociation rates of metal−nanoparticle complexes in defining the relaxation properties and the complete equilibration of the metal− nanoparticulate complex dispersion is described. The dynamic features of nanoparticulate complexes are also discussed in the context of predictions of the labilities and bioavailabilities of the metal species