Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory

The leading-order nucleon-nucleon (NN) potential derived from chiral perturbation theory consists of one-pion exchange plus a short-distance contact interaction. We show that in the 1S0 and 3S1-3D1 channels renormalization of the Lippmann-Schwinger equation for this potential can be achieved by performing one subtraction. This subtraction requires as its only input knowledge of the NN scattering lengths. This procedure leads to a set of integral equations for the partial-wave NN t-matrix which give cutoff-independent results for the corresponding NN phase shifts. This reformulation of the NN scattering equation offers practical advantages, because only observable quantities appear in the integral equation. The scattering equation may then be analytically continued to negative energies, where information on bound-state energies and wave functions can be extracted.Comment: 16 pages, 11 figure

Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves

We extend our subtractive-renormalization method in order to evaluate the 1S0 and 3S1-3D1 NN scattering phase shifts up to next-to-next-to-leading order (NNLO) in chiral effective theory. We show that, if energy-dependent contact terms are employed in the NN potential, the 1S0 phase shift can be obtained by carrying out two subtractions on the Lippmann-Schwinger equation. These subtractions use knowledge of the the scattering length and the 1S0 phase shift at a specific energy to eliminate the low-energy constants in the contact interaction from the scattering equation. For the J=1 coupled channel, a similar renormalization can be achieved by three subtractions that employ knowledge of the 3S1 scattering length, the 3S1 phase shift at a specific energy and the 3S1-3D1 generalized scattering length. In both channels a similar method can be applied to a potential with momentum-dependent contact terms, except that in that case one of the subtractions must be replaced by a fit to one piece of experimental data. This method allows the use of arbitrarily high cutoffs in the Lippmann-Schwinger equation. We examine the NNLO S-wave phase shifts for cutoffs as large as 5 GeV and show that the presence of linear energy dependence in the NN potential creates spurious poles in the scattering amplitude. In consequence the results are in conflict with empirical data over appreciable portions of the considered cutoff range. We also identify problems with the use of cutoffs greater than 1 GeV when momentum-dependent contact interactions are employed. These problems are ameliorated, but not eliminated, by the use of spectral-function regularization for the two-pion exchange part of the NN potentialComment: 40 pages, 21 figure

The near threshold N N -> d pi reaction in chiral perturbation theory

The near-threshold n p -> d pi0 cross section is calculated in chiral perturbation theory to next-to-leading order in the expansion parameter sqrt{M m_pi}/Lambda_chi. At this order irreducible pion loops contribute to the relevant pion-production operator. While their contribution to this operator is finite, considering initial-and final-state distortions produces a linear divergence in its matrix elements. We renormalize this divergence by introducing a counterterm, whose value we choose in order to reproduce the threshold n p -> d pi0 cross section measured at TRIUMF. The energy-dependence of this cross section is then predicted in chiral perturbation theory, being determined by the production of p-wave pions, and also by energy dependence in the amplitude for the production of s-wave pions. With an appropriate choice of the counterterm, the chiral prediction for this energy dependence converges well.Comment: 25 pages, REVTeX4, 5 eps figures, 1 reference added, 1 removed, changed cutoffs shown in Table III, some improvements in the text and figures, conclusions unaltered, accepted by PR

Subtractive renormalization of the chiral potentials up to next-to-next-to-leading order in higher NN partial waves

We develop a subtractive renormalization scheme to evaluate the P-wave NN scattering phase shifts using chiral effective theory potentials. This allows us to consider arbitrarily high cutoffs in the Lippmann-Schwinger equation (LSE). We employ NN potentials computed up to next-to-next-to-leading order (NNLO) in chiral effective theory, using both dimensional regularization and spectral-function regularization. Our results obtained from the subtracted P-wave LSE show that renormalization of the NNLO potential can be achieved by using the generalized NN scattering lengths as input--an alternative to fitting the constant that multiplies the P-wave contact interaction in the chiral effective theory NN force. However, in order to obtain a reasonable fit to the NN data at NNLO the generalized scattering lengths must be varied away from the values extracted from the so-called high-precision potentials. We investigate how the generalized scattering lengths extracted from NN data using various chiral potentials vary with the cutoff in the LSE. The cutoff-dependence of these observables, as well as of the phase shifts at $T_{lab} \approx 100$ MeV, suggests that for a chiral potential computed with dimensional regularization the highest LSE cutoff it is sensible to adopt is approximately 1 GeV. Using spectral-function regularization to compute the two-pion-exchange potentials postpones the onset of cutoff dependence in these quantities, but does not remove it.Comment: 27 pages, 14 figure

A study of resiliency among Chinese health care workers: Capacity to cope with workplace stress

This paper reports a study of resiliency to cope with workplace stress among Chinese health care workers. We adopted a qualitative-quantitative-biomarker approach to conduct interviews, focus group discussions, and a two-wave longitudinal survey. Wave 1 survey was conducted among health care workers in Hong Kong and Mainland China (N = 773). Amongst them, 287 took part in Wave 2 survey. A confirmatory factor analysis consistently supported a 9-item scale. A sub-sample's (N = 33) resiliency was positively related to salivary IgA levels (an immune marker). Results from hierarchical regressions demonstrated that resiliency measured in Wave 1 was positively related to job satisfaction, work-life balance, and quality of life; and negatively related to physical/psychological symptoms and injuries at work in Wave 2. © 2009 Elsevier Inc. All rights reserved.postprin

Street map analysis with excitable chemical medium

© 2018 American Physical Society. Belousov-Zhabotinsky (BZ) thin layer solution is a fruitful substrate for designing unconventional computing devices. A range of logical circuits, wet electronic devices, and neuromorphic prototypes have been constructed. Information processing in BZ computing devices is based on interaction of oxidation (excitation) wave fronts. Dynamics of the wave fronts propagation is programed by geometrical constraints and interaction of colliding wave fronts is tuned by illumination. We apply the principles of BZ computing to explore a geometry of street networks. We use two-variable Oregonator equations, the most widely accepted and verified in laboratory experiments BZ models, to study propagation of excitation wave fronts for a range of excitability parameters, with gradual transition from excitable to subexcitable to nonexcitable. We demonstrate a pruning strategy adopted by the medium with decreasing excitability when wider and ballistically appropriate streets are selected. We explain mechanics of streets selection and pruning. The results of the paper will be used in future studies of studying dynamics of cities and characterizing geometry of street networks

Cellular non-linear network model of microbial fuel cell

© 2017 Elsevier B.V. A cellular non-linear network (CNN) is a uniform regular array of locally connected continuous-state machines, or nodes, which update their states simultaneously in discrete time. A microbial fuel cell (MFC) is an electro-chemical reactor using the metabolism of bacteria to drive an electrical current. In a CNN model of the MFC, each node takes a vector of states which represent geometrical characteristics of the cell, like the electrodes or impermeable borders, and quantify measurable properties like bacterial population, charges produced and hydrogen ion concentrations. The model allows the study of integral reaction of the MFC, including temporal outputs, to spatial disturbances of the bacterial population and supply of nutrients. The model can also be used to evaluate inhomogeneous configurations of bacterial populations attached on the electrode biofilms