Noether symmetries, energy-momentum tensors and conformal invariance in classical field theory

In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. Will this baggage on board, we next discuss in detail, for Poincar\'e invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of Poincar\'e symmetries and it is a basic ingredient of the generators of other eventual spacetime symmetries which may happen to exist. Instead, Hilbert tensors are the means to test whether a theory contains other spacetime symmetries beyond Poincar\'e. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincar\'e invariant Lagrangians, that the realization of scale invariance selects a unique Hilbert tensor which allows for an easy test as to whether conformal invariance is also realized. Finally we make some basic remarks on metric generally covariant theories and classical field theory in a fixed curved bakground.Comment: 31 pa

The wave-vector power spectrum of the local tunnelling density of states: ripples in a d-wave sea

A weak scattering potential imposed on a $CuO_2$ layer of a cuprate superconductor modulates the local density of states $N(x,\omega)$. In recently reported experimental studies scanning-tunneling maps of $N(x,\omega)$ have been Fourier transformed to obtain a wave-vector power spectrum. Here, for the case of a weak scattering potential, we discuss the structure of this power spectrum and its relationship to the quasi-particle spectrum and the structure factor of the scattering potential. Examples of quasi-particle interferences in normal metals and $s$- and d-wave superconductors are discussed.Comment: 22 pages, 21 figures; enlarged discussion of the d-wave response, to be published in Physical Review

Quantitative Assessment of the Anatomical Footprint of the C1 Pedicle Relative to the Lateral Mass: A Guide for C1 Lateral Mass Fixation

Study Design: Anatomic study. Objectives: To determine the relationship of the anatomical footprint of the C1 pedicle relative to the lateral mass (LM). Methods: Anatomic measurements were made on fresh frozen human cadaveric C1 specimens: pedicle width/height, LM width/height (minimum/maximum), LM depth, distance between LM’s medial aspect and pedicle’s medial border, distance between LM’s lateral aspect to pedicle’s lateral border, distance between pedicle’s inferior aspect and LM’s inferior border, distance between arch’s midline and pedicle’s medial border. The percentage of LM medial to the pedicle and the distance from the center of the LM to the pedicle’s medial wall were calculated. Results: A total of 42 LM were analyzed. The C1 pedicle’s lateral aspect was nearly confluent with the LM’s lateral border. Average pedicle width was 9.0 ± 1.1 mm, and average pedicle height was 5.0 ± 1.1 mm. Average LM width and depth were 17.0 ± 1.6 and 17.2 ± 1.6 mm, respectively. There was 6.9 ± 1.5 mm of bone medial to the medial C1 pedicle, which constituted 41% ± 9% of the LM’s width. The distance from C1 arch’s midline to the medial pedicle was 13.5 ± 2.0 mm. The LM’s center was 1.6 ± 1 mm lateral to the medial pedicle wall. There was on average 3.5 ± 0.6 mm of the LM inferior to the pedicle inferior border. Conclusions: The center of the lateral mass is 1.6 ± 1 mm lateral to the medial wall of the C1 pedicle and approximately 15 mm from the midline. There is 6.9 ± 1.5 mm of bone medial to the medial C1 pedicle. Thus, the medial aspect of C1 pedicle may be used as an anatomic reference for locating the center of the C1 LM for screw fixation

Growing and Marketing Elderberries in Missouri (2012)

The American elderberry (Sambucus canadensis, also known as Sambucus nigra subsp. canadensis) is native to much of eastern and midwestern North America. The plant is a medium to large multiple-stemmed shrub, bush or small tree. Elderberry is commonly found growing in a range of habitats throughout Missouri, but it prefers moist, well-drained, sunny sites and is often found along roadside ditches and streams.By Patrick L. Byers, Andrew L. Thomas, Mihaela M. Cernusca, Larry D. Godsey and Michael A. Gold (University of Missouri)Includes bibliographical reference

Water use and water availability constraints to decarbonised electricity systems

Analysis of numerous low carbon electricity strategies have been shown to have very divergent water requirements, normally needed for cooling of thermoelectric power stations. Our regional river-basin scale analysis of water use for future UK electricity strategies shows that, whilst in the majority of cases freshwater use is expected to decline, pathways with high levels of carbon capture and storage (CCS) will result in significantly elevated and concentrated water demands in a few key river basins. Furthermore, these growing demands are compared to both current water availability, and our expected regional water availability under the impacts of climate change. We identify key freshwater constraints to electricity strategies with high levels of CCS and show how these risks may be mitigated with higher levels of hybrid cooling and alternative cooling water sources

Permanent current from non-commutative spin algebra

We show that a spontaneous electric current is induced in a nano-scale conducting ring just by putting three ferromagnets. The current is a direct consequence of the non-commutativity of the spin algebra, and is proportional to the non-coplanarity (chirality) of the magnetization vectors. The spontaneous current gives a natural explanation to the chirality-driven anomalous Hall effect.Comment: 7 pages, 4 figures on separate pag

Josephson current through a Luttinger liquid

We study the Josephson effect through a one-dimensional system of interacting electrons, connected to two superconductors by tunnel junctions. The interactions are treated in the framework of the one-channel Luttinger model. At zero temperature, the Josephson critical current is found to decay algebraically with increasing distance between the junctions. The exponent is proportional to the strength of the Coulomb interaction. If the Luttinger liquid has a finite size, the Josephson current depends on the total number of electrons modulo 4. These parity effects are studied for the ring, coupled capacitively to a gate-voltage and threaded by a magnetic flux. The Josephson current changes continuously as a function of the gate voltage and {\em stepwise} as a function of the magnetic flux. The electron-electron interaction introduces {\em qualitatively} new features compared to the non-interacting case.Comment: 8 pages REVTEX , 4 figures available upon reques

Exact ground-state correlation functions of the one-dimensional strongly correlated electron models with the resonating-valence-bond ground state

We investigate the one-dimensional strongly correlated electron models which have the resonating-valence-bond state as the exact ground state. The correlation functions are evaluated exactly using the transfer matrix method for the geometric representations of the valence-bond states. In this method, we only treat matrices with small dimensions. This enables us to give analytical results. It is shown that the correlation functions decay exponentially with distance. The result suggests that there is a finite excitation gap, and that the ground state is insulating. Since the corresponding non-interacting systems may be insulating or metallic, we can say that the gap originates from strong correlation. The persistent currents of the present models are also investigated and found to be exactly vanishing.Comment: 59 pages, REVTeX 3.0, Figures are available on reques

Mapping midwifery and obstetric units in England

OBJECTIVE: to describe the configuration of midwifery units, both alongside&free-standing, and obstetric units in England. DESIGN: national survey amongst Heads of Midwifery in English Maternity Services SETTING: National Health Service (NHS) in England PARTICIPANTS: English Maternity Services Measurements descriptive statistics of Alongside Midwifery Units and Free-standing Midwifery Units and Obstetric Units and their annual births/year in English Maternity Services FINDINGS: alongside midwifery units have nearly doubled since 2010 (n = 53-97); free-standing midwifery units have increased slightly (n = 58-61). There has been a significant reduction in maternity services without either an alongside or free-standing midwifery unit (75-32). The percentage of all births in midwifery units has trebled, now representing 14% of all births in England. This masks significant differences in percentage of all births in midwifery units between different maternity services with a spread of 4% to 31%. KEY CONCLUSIONS: In some areas of England, women have no access to a local midwifery unit, despite the National Institute for Health&Clinical Excellence (NICE) recommending them as an important place of birth option for low risk women. The numbers of midwifery units have increased significantly in England since 2010 but this growth is almost exclusively in alongside midwifery units. The percentage of women giving birth in midwifery units varies significantly between maternity services suggesting that many midwifery units are underutilised. IMPLICATIONS FOR PRACTICE: Both the availability and utilisation of midwifery units in England could be improved

Possible retardation effects of quark confinement on the meson spectrum

The reduced Bethe-Salpeter equation with scalar confinement and vector gluon exchange is applied to quark-antiquark bound states. The so called intrinsic flaw of Salpeter equation with static scalar confinement is investigated. The notorious problem of narrow level spacings is found to be remedied by taking into consideration the retardation effect of scalar confinement. Good fit for the mass spectrum of both heavy and light quarkomium states is then obtained.Comment: 14 pages in LaTex for