On numerical solution of Fredholm and Hammerstein integral equations via Nystr\"{o}m method and Gaussian quadrature rules for splines

Nystr\"{o}m method is a standard numerical technique to solve Fredholm integral equations of the second kind where the integration of the kernel is approximated using a quadrature formula. Traditionally, the quadrature rule used is the classical polynomial Gauss quadrature. Motivated by the observation that a given function can be better approximated by a spline function of a lower degree than a single polynomial piece of a higher degree, in this work, we investigate the use of Gaussian rules for splines in the Nystr\"{o}m method. We show that, for continuous kernels, the approximate solution of linear Fredholm integral equations computed using spline Gaussian quadrature rules converges to the exact solution for $m \rightarrow \infty$, $m$ being the number of quadrature points. Our numerical results also show that, when fixing the same number of quadrature points, the approximation is more accurate using spline Gaussian rules than using the classical polynomial Gauss rules. We also investigate the non-linear case, considering Hammerstein integral equations, and present some numerical tests.RYC-2017-2264

Solving boundary value problems via the Nyström method using spline Gauss rules

We propose to use spline Gauss quadrature rules for solving boundary value problems (BVPs) using the Nyström method. When solving BVPs, one converts the corresponding partial differential equation inside a domain into the Fredholm integral equation of the second kind on the boundary in the sense of boundary integral equation (BIE). The Fredholm integral equation is then solved using the Nyström method, which involves the use of a particular quadrature rule, thus, converting the BIE problem to a linear system. We demonstrate this concept on the 2D Laplace problem over domains with smooth boundary as well as domains containing corners. We validate our approach on benchmark examples and the results indicate that, for a fixed number of quadrature points (i.e., the same computational effort), the spline Gauss quadratures return an approximation that is by one to two orders of magnitude more accurate compared to the solution obtained by traditional polynomial Gauss counterparts

Solving Boundary Value Problems Via the Nyström Method Using Spline Gauss Rules

We propose to use spline Gauss quadrature rules for solving boundary value problems (BVPs) using the Nyström method. When solving BVPs, one converts the corresponding partial differential equation inside a domain into the Fredholm integral equation of the second kind on the boundary in the sense of boundary integral equation (BIE). The Fredholm integral equation is then solved using the Nyström method, which involves a use of a particular quadrature rule, thus, converting the BIE problem to a linear system. We demonstrate this concept on the 2D Laplace problem over domains with smooth boundary as well as domains containing corners. We validate our approach on benchmark examples and the results indicate that, for a fixed number of quadrature points (i.e., the same computational effort), the spline Gauss quadratures return an approximation that is by one to two orders of magnitude more accurate compared to the solution obtained by traditional polynomial Gauss counterparts

VÍNCULO AFECTIVO DEL BINOMIO MADRE-HIJO EXPERIENCIA DE UNA MADRE ANTE LA SEPARACIÓN DE SU RECIÉN NACIDO POR PREMATURIDAD; UN ESTUDIO DE CASO

Se presenta el caso de una paciente puérpera de 20 años quien se encuentra en puerperio mediato de 28 horas. Objetivo: Aplicar los cuidados de enfermería que contribuyan a una recuperación satisfactoria en la paciente a través de una valoración obstétrica guiada desde el cuidado de enfermería Metodología: La presente investigación es de tipo cualitativa descriptiva aleatoria simple y se pretende obtener información objetiva acerca de la forma como se aplican las etapas del proceso de enfermería donde la práctica formativa del programa de enfermería servicio hospitalario de gineco-obstetricia del HUEM. Resultados: la paciente expresa satisfacción con los cuidados e intervenciones realizadas por enfermería, refiere que sintió compañía y apoyo en la situación que está viviendo. Conclusión: El puerperio es una etapa del ciclo vital de la mujer y la familia que requiere de una atención especial por parte de la enfermera ya que la mujer durante este proceso no solo esta sensible en la salud física si no también su parte psicológica ya que está pasando por un periodo trascendental y se interrelacionan muchos sentimientos y aspectos que cambian de alguna forma la vida de la mujer, y como enfermeras se debe ayudar a que todos estos cambios sean guiados a un buen desarrollo y a una excelente adopción del rol maternal, facilitando la vinculación madre-hijo

Negative thermal expansion of MgB2_{2} in the superconducting state and anomalous behavior of the bulk Gr\"uneisen function

The thermal expansion coefficient $\alpha$ of MgB$_2$ is revealed to change from positive to negative on cooling through the superconducting transition temperature $T_c$. The Gr\"uneisen function also becomes negative at $T_c$ followed by a dramatic increase to large positive values at low temperature. The results suggest anomalous coupling between superconducting electrons and low-energy phonons.Comment: 5 figures. submitted to Phys. Rev. Let

I-mode studies at ASDEX Upgrade: L-I and I-H transitions, pedestal and confinement properties

The I-mode is a plasma regime obtained when the usual L-H power threshold is high, e.g. with unfavourable ion B ∇ direction. It is characterised by the development of a temperature pedestal while the density remains roughly as in the L-mode. This leads to a confinement improvement above the L-mode level which can sometimes reach H-mode values. This regime, already obtained in the ASDEX Upgrade tokamak about two decades ago, has been studied again since 2009 taking advantage of the development of new diagnostics and heating possibilities. The I-mode in ASDEX Upgrade has been achieved with different heating methods such as NBI, ECRH and ICRF. The I-mode properties, power threshold, pedestal characteristics and confinement, are independent of the heating method. The power required at the L-I transition exhibits an offset linear density dependence but, in contrast to the L-H threshold, depends weakly on the magnetic field. The L-I transition seems to be mainly determined by the edge pressure gradient and the comparison between ECRH and NBI induced L-I transitions suggests that the ion channel plays a key role. The I-mode often evolves gradually over a few confinement times until the transition to H-mode which offers a very interesting situation to study the transport reduction and its link with the pedestal formation. Exploratory discharges in which n = 2 magnetic perturbations have been applied indicate that these can lead to an increase of the I-mode power threshold by flattening the edge pressure at fixed heating input power: more heating power is necessary to restore the required edge pressure gradient. Finally, the confinement properties of the I-mode are discussed in detail.European Commission (EUROfusion 633053

Effect of resonant magnetic perturbations on low collisionality discharges in MAST and a comparison with ASDEX Upgrade

Sustained ELM mitigation has been achieved on MAST and AUG using RMPs with a range of toroidal mode numbers over a wide region of low to medium collisionality discharges. The ELM energy loss and peak heat loads at the divertor targets have been reduced. The ELM mitigation phase is typically associated with a drop in plasma density and overall stored energy. In one particular scenario on MAST, by carefully adjusting the fuelling it has been possible to counteract the drop in density and to produce plasmas with mitigated ELMs, reduced peak divertor heat flux and with minimal degradation in pedestal height and confined energy. While the applied resonant magnetic perturbation field can be a good indicator for the onset of ELM mitigation on MAST and AUG there are some cases where this is not the case and which clearly emphasise the need to take into account the plasma response to the applied perturbations. The plasma response calculations show that the increase in ELM frequency is correlated with the size of the edge peeling-tearing like response of the plasma and the distortions of the plasma boundary in the X-point region.Comment: 31 pages, 28 figures. This is an author-created, un-copyedited version of an article submitted for publication in Nuclear Fusion. IoP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Giant room temperature piezoresistance in a metal/silicon hybrid

Metal/semiconductor hybrids are artificially created structures presenting novel properties not exhibited by either of the component materials alone. Here we present a giant piezoresistance effect in a hybrid formed from silicon and aluminum. The maximum piezoresistive gage factor (GF) of 843, measured at room temperature, compares with a GF of -93 measured in the bulk homogeneous silicon. This piezoresistance boost is not due to the silicon/aluminum interface, but results from a stress induced anisotropy in the silicon conductivity that acts to switch current away from the highly conductive aluminum for uniaxial tensile strains. Its magnitude is shown, via the calculation of hybrid resistivity weighting functions, to depend only on the geometrical arrangement of the component parts of the hybrid.Comment: 4 pages, 4 figures, accepted for publication in Physical Review Letter