Jacobi multipliers, non-local symmetries and nonlinear oscillators

Constants of motion, Lagrangians and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last multiplier allows us to find Lagrangian descriptions and constants of the motion. An application of the jet bundle formulation of symmetries of differential equations is presented in the second part of the paper. After a short review of the general formalism, the particular case of non-local symmetries is studied in detail by making use of an extended formalism. The theory is related to some results previously obtained by Krasil'shchi, Vinogradov and coworkers. Finally the existence of non-local symmetries for such two nonlinear oscillators is proved.Comment: 20 page

Multigap Superconductivity in Y2_2C3_3: A 13^{13}C-NMR Study

We report on the superconducting (SC) properties of Y$_2$C$_3$ with a relatively high transition temperature $T_{\rm c}=15.7$ K investigated by $^{13}$C nuclear-magnetic-resonance (NMR) measurements under a magnetic field. The $^{13}$C Knight shift has revealed a significant decrease below $T_{\rm c}$, suggesting a spin-singlet superconductivity. From an analysis of the temperature dependence of the nuclear spin-lattice relaxation rate $1/T_1$ in the SC state, Y$_2$C$_3$ is demonstrated to be a multigap superconductor that exhibits a large gap $2\Delta/k_{\rm B}T_{\rm c}=5$ at the main band and a small gap $2\Delta/k_{\rm B}T_{\rm c}=2$ at other bands. These results have revealed that Y$_2$C$_3$ is a unique multigap s-wave superconductor similar to MgB$_2$.Comment: 4 pages, 5 figure

Symmetries in Classical Field Theory

The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of infinitesimal symmetries, and to obtain the corresponding conservation laws.Comment: 70S05; 70H33; 55R10; 58A2

The emergence of altruism as a social norm

Expectations, exerting influence through social norms, are a very strong candidate to explain how complex societies function. In the Dictator game (DG), people expect generous behavior from others even when they cannot enforce any sharing of the pie. Here we assume that people donate following their expectations, and that they update their expectation after playing a DG by reinforcement learning to construct a model that explains the main experimental results in the DG. Full agreement with the experimental results is reached when some degree of mismatch between expectations and donations is added into the model. These results are robust against the presence of envious agents, but affected if we introduce selfish agents that do not update their expectations. Our results point to social norms being on the basis of the generous behavior observed in the DG and also to the wide applicability of reinforcement learning to explain many strategic interactions

Rotating Resonator-Oscillator Experiments to Test Lorentz Invariance in Electrodynamics

In this work we outline the two most commonly used test theories (RMS and SME) for testing Local Lorentz Invariance (LLI) of the photon. Then we develop the general framework of applying these test theories to resonator experiments with an emphasis on rotating experiments in the laboratory. We compare the inherent sensitivity factors of common experiments and propose some new configurations. Finally we apply the test theories to the rotating cryogenic experiment at the University of Western Australia, which recently set new limits in both the RMS and SME frameworks [hep-ph/0506074].Comment: Submitted to Lecture Notes in Physics, 36 pages, minor modifications, updated list of reference

Microfabricated Ion Traps

Ion traps offer the opportunity to study fundamental quantum systems with high level of accuracy highly decoupled from the environment. Individual atomic ions can be controlled and manipulated with electric fields, cooled to the ground state of motion with laser cooling and coherently manipulated using optical and microwave radiation. Microfabricated ion traps hold the advantage of allowing for smaller trap dimensions and better scalability towards large ion trap arrays also making them a vital ingredient for next generation quantum technologies. Here we provide an introduction into the principles and operation of microfabricated ion traps. We show an overview of material and electrical considerations which are vital for the design of such trap structures. We provide guidance in how to choose the appropriate fabrication design, consider different methods for the fabrication of microfabricated ion traps and discuss previously realized structures. We also discuss the phenomenon of anomalous heating of ions within ion traps, which becomes an important factor in the miniaturization of ion traps

Hanford Site ground-water monitoring for July through December 1987

The Pacific Northwest Laboratory monitors ground-water quality at the Hanford Site for the US Department of Energy to assess the impact of Site operations on the environment. Work undertaken between July and December 1987 included monitoring ground-water elevations across the Site, monitoring hazardous chemicals and radionuclides in ground water, geochemical evaluations of unconfined ground-water data, and calibration of ground-water flow and transport models. Water levels continued to rise in areas receiving increased recharge (e.g., beneath B Pond) and decline in areas where the release of water to disposal facilities has been terminated (e.g., U Pond). The major areas of ground-water contamination defined by monitoring activities are (1) carbon tetrachloride in the 200-West Area; (2) cyanide in and north of the 200-East and 200-West Areas; (3) hexavalent chromium contamination in the 100-B, 100-D, 100-F, 100-H, 100-K, and 200-West Areas; (4) chlorinated hydrocarbons in the vicinity of the Central Landfill and 300 Area; (5) uranium in the 100-F, 100-H, 200-West, and 300 Areas; and (6) tritium and nitrate across the Site. The MINTEQ geochemical code was used to identify chemical reactions that may be affecting the concentrations of dissolved hazardous chemicals in the unconfined ground water. Results indicate that many cations are present mainly as dissolved carbonate complexes and that a majority of the ground-water samples are in near equilibrium with carbonate minerals (e.g., calcite, dolomite, otavite)

From Classical Trajectories to Quantum Commutation Relations

In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian description because of the Noether theorem and because they are the starting point for the quantization. As a matter of fact many ambiguities arise in each step of such a reconstruction which must be solved by the ingenuity of the theoretician. In the present work we describe geometric structures emerging in Lagrangian, Hamiltonian and Quantum description of a dynamical system underlining how many of them are not really fixed only by the trajectories observed by the experimentalist.Comment: 25 pages. Comments are welcome

Magnetic Properties in Non-centrosymmetric Superconductors with and without Antiferromagnetic Order

The paramagnetic properties in non-centrosymmetric superconductors with and without antiferromagnetic (AFM) order are investigated with focus on the heavy Fermion superconductors, CePt_3Si, CeRhSi_3 and CeIrSi_3. First, we investigate the spin susceptibility in the linear response regime and elucidate the role of AFM order. The spin susceptibility at T=0 is independent of the pairing symmetry and increases in the AFM state. Second, the non-linear response to the magnetic field are investigated on the basis of an effective model for CePt_3Si which may be also applicable to CeRhSi_3 and CeIrSi_3. The role of antisymmetric spin-orbit coupling (ASOC), helical superconductivity, anisotropic Fermi surfaces and AFM order are examined in the dominantly s-, p- and d-wave states. We emphasize the qualitatively important role of the mixing of superconducting (SC) order parameters in the p-wave state which enhances the spin susceptibility and suppresses paramagnetic depairing effect in a significant way. Therefore, the dominantly p-wave superconductivity admixed with the s-wave order parameter is consistent with the paramagnetic properties of CePt_3Si at ambient pressure. We propose some experiments which can elucidate the novel pairing states in CePt_3Si as well as CeRhSi_3 and CeIrSi_3.Comment: To appear in J. Phys. Soc. Jpn. (2007) No.1

Evaluación de Parámetros de control obligatorio del agua potable proveniente del manantial Cuyuraya de la provincia de Huancané – Región Puno, 2019

El objetivo de este estudio fue el de evaluar los parámetros de control obligatorio de agua potable en la provincia de Huancané. Los puntos de monitoreo fueron seleccionados según la ubicación establecida por la Empresa Prestadora de Servicios “EPS NOR PUNO S.A.”; con los siguientes puntos: fuente principal de abastecimiento de agua (manantial Cuyuraya) y la red principal de abastecimiento (desde la primera vivienda, zona media y vivienda final) siendo un total de 6 puntos de monitoreo. Los parámetros evaluados según Reglamento de la Calidad del Agua para Consumo Humano DS N° 031 – 2010 – SA, fueron: pH, color, cloro residual, turbiedad, coliformes totales y termotolerantes, los cuales fueron analizados in-situ o en un laboratorio respectivamente, con un resultado de que solo 3 de los 6 parámetros evaluados cumplen con lo que indica el reglamento, debido a que Cloro Residual no llega al mínimo establecido de 0.5 mg/L, Coliformes Totales y Termotolerantes exceden en 16 UFC como máximo y <1.1 como mínimo, concluyendo que el agua que se distribuye en todo Huancané es directamente afectada por los niveles bajos de cloro residual, ocasionando que exista la presencia de coliformes (totales y termotolerantes), lo que afecta directamente a la calidad del agua que se distribuye en la provincia de Huancané.Trabajo de investigaciónJULIACAEscuela Profesional de Ingeniería AmbientalBiodiversidad y calidad ambienta