Exact, E=0, Solutions for General Power-Law Potentials. I. Classical Orbits

For zero energy, $E=0$, we derive exact, classical solutions for {\em all} power-law potentials, $V(r)=-\gamma/r^\nu$, with $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions lead to the orbits $\r(t)= [\cos \mu (\th(t)-\th_0(t))]^{1/\mu}$, for all $\mu \equiv \nu/2-1 \ne 0$. When $\nu>2$, the orbits are bound and go through the origin. This leads to discrete discontinuities in the functional dependence of $\th(t)$ and $\th_0(t)$, as functions of $t$, as the orbits pass through the origin. We describe a procedure to connect different analytic solutions for successive orbits at the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. Also, we explain why they all must violate the virial theorem. The unbound orbits are also discussed in detail. This includes the unusual orbits which have finite travel times to infinity and also the special $\nu = 2$ case.Comment: LaTeX, 27 pages with 12 figures available from the authors or can be generated from Mathematica instructions at end of the fil

A Relativistic Thomas-Fermi Description of Collective Modes in Droplets of Nuclear Matter

Isoscalar collective modes in a relativistic meson-nucleon system are investigated in the framework of the time-dependent Thomas-Fermi method. The energies of the collective modes are determined by solving consistently the dispersion relations and the boundary conditions. The energy weighted sum rule satisfied by the model allows the identification of the giant ressonances. The percentage of the energy weighted sum rule exhausted by the collective modes is in agreement with experimental data, but the energies come too high.Comment: 21 pages (RevTex) and 2 postscript figures as a compressed uuencode fil

Impact Evaluation of Wet-Weather Events on Influent Flow and Loadings of a Water Resource Recovery Facility

Since the introduction of environmental legislation anddirectives in Europe, the impact of combined sewer overflows (CSO) on receiving waterbodies has become a priority concern in water and wastewater treatment industry. Timeconsumingand expensive local sampling and monitoring campaigns have been carried outto estimate the characteristic flow and pollutant concentrations of CSO water. This studyfocused on estimating the frequency and duration of wet-weather events and their impactson influent flow and wastewater characteristics of the largest Italian water resource recoveryfacility (WRRF) in Castiglione Torinese. Eight years (viz. 2009-2016) of routinely collectedinfluent data in addition to the arithmetic mean daily precipitation rates (PI) of the plantcatchment area, were elaborated. Relationships between PI and volumetric influent flow rate(Qin), chemical oxygen demand (COD), ammonium concentration (N-NH4) and totalsuspended solids (TSS) are investigated. Time series data mining (TSDM) method isimplemented for segmentation of time series by use of sliding window algorithm to partitionthe available records associated with wet and dry weather events based on the dailyvariation of PI time series. Appling the methodology in conjunction with results obtained fromdata reduction techniques, a wet-weather definition is proposed for the plant. The resultsconfirm that applied methodology on routinely collected plant data can be considered as agood substitute for time-consuming and expensive sampling campaigns and plantmonitoring programs usually conducted for accurate emergency response and long-termpreparedness for extreme climate conditions

Tricritical Points in the Sherrington-Kirkpatrick Model in the Presence of Discrete Random Fields

The infinite-range-interaction Ising spin glass is considered in the presence of an external random magnetic field following a trimodal (three-peak) distribution. The model is studied through the replica method and phase diagrams are obtained within the replica-symmetry approximation. It is shown that the border of the ferromagnetic phase may present first-order phase transitions, as well as tricritical points at finite temperatures. Analogous to what happens for the Ising ferromagnet under a trimodal random field, it is verified that the first-order phase transitions are directly related to the dilution in the fields (represented by $p_{0}$). The ferromagnetic boundary at zero temperature also exhibits an interesting behavior: for $0<p_{0}<p_{0}^{*} \approx 0.30856$, a single tricritical point occurs, whereas if $p_{0}>p_{0}^{*}$ the critical frontier is completely continuous; however, for $p_{0}=p_{0}^{*}$, a fourth-order critical point appears. The stability analysis of the replica-symmetric solution is performed and the regions of validity of such a solution are identified; in particular, the Almeida-Thouless line in the plane field versus temperature is shown to depend on the weight $p_{0}$.Comment: 23pages, 7 ps figure

Nonlocal magnetization dynamics in ferromagnetic heterostructures

Two complementary effects modify the GHz magnetization dynamics of nanoscale heterostructures of ferromagnetic and normal materials relative to those of the isolated magnetic constituents: On the one hand, a time-dependent ferromagnetic magnetization pumps a spin angular-momentum flow into adjacent materials and, on the other hand, spin angular momentum is transferred between ferromagnets by an applied bias, causing mutual torques on the magnetizations. These phenomena are manifestly nonlocal: they are governed by the entire spin-coherent region that is limited in size by spin-flip relaxation processes. We review recent progress in understanding the magnetization dynamics in ferromagnetic heterostructures from first principles, focusing on the role of spin pumping in layered structures. The main body of the theory is semiclassical and based on a mean-field Stoner or spin-density--functional picture, but quantum-size effects and the role of electron-electron correlations are also discussed. A growing number of experiments support the theoretical predictions. The formalism should be useful to understand the physics and to engineer the characteristics of small devices such as magnetic random-access memory elements.Comment: 48 pages, 21 figures (3 in color

Wigner function for twisted photons

A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented, with special emphasis in the implications of rotational periodicity and angular-momentum discreteness.Comment: 6 pages, 4 figure

Biodiversity Loss and the Taxonomic Bottleneck: Emerging Biodiversity Science

Human domination of the Earth has resulted in dramatic changes to global and local patterns of biodiversity. Biodiversity is critical to human sustainability because it drives the ecosystem services that provide the core of our life-support system. As we, the human species, are the primary factor leading to the decline in biodiversity, we need detailed information about the biodiversity and species composition of specific locations in order to understand how different species contribute to ecosystem services and how humans can sustainably conserve and manage biodiversity. Taxonomy and ecology, two fundamental sciences that generate the knowledge about biodiversity, are associated with a number of limitations that prevent them from providing the information needed to fully understand the relevance of biodiversity in its entirety for human sustainability: (1) biodiversity conservation strategies that tend to be overly focused on research and policy on a global scale with little impact on local biodiversity; (2) the small knowledge base of extant global biodiversity; (3) a lack of much-needed site-specific data on the species composition of communities in human-dominated landscapes, which hinders ecosystem management and biodiversity conservation; (4) biodiversity studies with a lack of taxonomic precision; (5) a lack of taxonomic expertise and trained taxonomists; (6) a taxonomic bottleneck in biodiversity inventory and assessment; and (7) neglect of taxonomic resources and a lack of taxonomic service infrastructure for biodiversity science. These limitations are directly related to contemporary trends in research, conservation strategies, environmental stewardship, environmental education, sustainable development, and local site-specific conservation. Today’s biological knowledge is built on the known global biodiversity, which represents barely 20% of what is currently extant (commonly accepted estimate of 10 million species) on planet Earth. Much remains unexplored and unknown, particularly in hotspots regions of Africa, South Eastern Asia, and South and Central America, including many developing or underdeveloped countries, where localized biodiversity is scarcely studied or described. ‘‘Backyard biodiversity’’, defined as local biodiversity near human habitation, refers to the natural resources and capital for ecosystem services at the grassroots level, which urgently needs to be explored, documented, and conserved as it is the backbone of sustainable economic development in these countries. Beginning with early identification and documentation of local flora and fauna, taxonomy has documented global biodiversity and natural history based on the collection of ‘‘backyard biodiversity’’ specimens worldwide. However, this branch of science suffered a continuous decline in the latter half of the twentieth century, and has now reached a point of potential demise. At present there are very few professional taxonomists and trained local parataxonomists worldwide, while the need for, and demands on, taxonomic services by conservation and resource management communities are rapidly increasing. Systematic collections, the material basis of biodiversity information, have been neglected and abandoned, particularly at institutions of higher learning. Considering the rapid increase in the human population and urbanization, human sustainability requires new conceptual and practical approaches to refocusing and energizing the study of the biodiversity that is the core of natural resources for sustainable development and biotic capital for sustaining our life-support system. In this paper we aim to document and extrapolate the essence of biodiversity, discuss the state and nature of taxonomic demise, the trends of recent biodiversity studies, and suggest reasonable approaches to a biodiversity science to facilitate the expansion of global biodiversity knowledge and to create useful data on backyard biodiversity worldwide towards human sustainability

Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries

We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical systems possessing Lie-group symmetries. The concept of generalized coherent states and the method of harmonic analysis are used to construct explicitly a family of phase-space functions which are postulated to satisfy the Stratonovich-Weyl correspondence with a generalized traciality condition. The symbol calculus for the phase-space functions is given by means of the generalized twisted product. The phase-space formalism is used to study the problem of the reconstruction of quantum states. In particular, we consider the reconstruction method based on measurements of displaced projectors, which comprises a number of recently proposed quantum-optical schemes and is also related to the standard methods of signal processing. A general group-theoretic description of this method is developed using the technique of harmonic expansions on the phase space.Comment: REVTeX, 18 pages, no figure

Superintegrable systems with spin and second-order integrals of motion

We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems which allow additional integrals of motion that are second order matrix polynomials in the momenta. These integrals are assumed to be scalars, pseudoscalars, vectors or axial vectors. Among the superintegrable systems obtained, we mention a generalization of the Coulomb potential with scalar potential $V_0=\frac{\alpha}{r}+\frac{3\hbar^2}{8r^2}$ and spin orbital one $V_1=\frac{\hbar}{2r^2}$.Comment: 32 page

The Perceptions on Male Circumcision as a Preventive Measure Against HIV Infection and Considerations in Scaling up of the Services: A Qualitative Study Among Police Officers in Dar es Salaam, Tanzania.

\ud In recent randomized controlled trials, male circumcision has been proven to complement the available biomedical interventions in decreasing HIV transmission from infected women to uninfected men. Consequently, Tanzania is striving to scale-up safe medical male circumcision to reduce HIV transmission. However, there is a need to investigate the perceptions of male circumcision in Tanzania using specific populations. The purpose of the present study was to assess the perceptions of male circumcision in a cohort of police officers that also served as a source of volunteers for a phase I/II HIV vaccine (HIVIS-03) trial in Dar es Salaam, Tanzania. In-depth interviews with 24 men and 10 women were conducted. Content analysis informed by the socio-ecological model was used to analyze the data. Informants perceived male circumcision as a health-promoting practice that may prevent HIV transmission and other sexually transmitted infections. They reported male circumcision promotes sexual pleasure, confidence and hygiene or sexual cleanliness. They added that it is a religious ritual and a cultural practice that enhances the recognition of manhood in the community. However, informants were concerned about the cost involved in male circumcision and cleanliness of instruments used in medical and traditional male circumcision. They also expressed confusion about the shame of undergoing circumcision at an advanced age and pain that could emanate after circumcision. The participants advocated for health policies that promote medical male circumcision at childhood, specifically along with the vaccination program. The perceived benefit of male circumcision as a preventive strategy to HIV and other sexually transmitted infections is important. However, there is a need to ensure that male circumcision is conducted under hygienic conditions. Integrating male circumcision service in the routine childhood vaccination program may increase its coverage at early childhood. The findings from this investigation provide contextual understanding that may assist in scaling-up male circumcision in Tanzania.\u