Why Two Renormalization Groups are Better than One

The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very difficult to calculate with an RG based on one flow parameter may be much more accessible using another; ii) using more than one RG requires less physical input in order to describe via RG methods the theory as a function of its parameters; iii) using more than one RG allows one to solve problems with more than one diverging length scale. The above points are illustrated concretely in the context of both particle physics and statistical physics using the techniques of environmentally friendly renormalization. Specifically, finite temperature $\lambda\phi^4$ theory, an Ising-type system in a film geometry, an Ising-type system in a transverse magnetic field, the QCD coupling constant at finite temperature and the crossover between bulk and surface critical behaviour in a semi-infinite geometry are considered.Comment: 17 pages LaTex; to be published in the Proceedings of RG '96, Dubn

Estimating drizzle drop size and precipitation rate using two-colour lidar measurements

A method to estimate the size and liquid water content of drizzle drops using lidar measurements at two wavelengths is described. The method exploits the differential absorption of infrared light by liquid water at 905 nm and 1.5 μm, which leads to a different backscatter cross section for water drops larger than ≈50 μm. The ratio of backscatter measured from drizzle samples below cloud base at these two wavelengths (the colour ratio) provides a measure of the median volume drop diameter D0. This is a strong effect: for D0=200 μm, a colour ratio of ≈6 dB is predicted. Once D0 is known, the measured backscatter at 905 nm can be used to calculate the liquid water content (LWC) and other moments of the drizzle drop distribution. The method is applied to observations of drizzle falling from stratocumulus and stratus clouds. High resolution (32 s, 36 m) profiles of D0, LWC and precipitation rate R are derived. The main sources of error in the technique are the need to assume a value for the dispersion parameter μ in the drop size spectrum (leading to at most a 35% error in R) and the influence of aerosol returns on the retrieval (≈10% error in R for the cases considered here). Radar reflectivities are also computed from the lidar data, and compared to independent measurements from a colocated cloud radar, offering independent validation of the derived drop size distributions

Gamble mode: Resonance contact mode in atomic force microscopy

Active noise reduction has been accomplished in atomic force microscopy by applying a high frequency, low amplitude vibration to the cantilever while it is in contact with a surface. The applied excitation (>~ 200 kHz; ~ 1 nm) is acoustically coupled to the tip and dampens the resonance Q factors of the system. The applied frequency is well above the bandwidth of the acquisition system (50 kHz). We call this mode "gamble mode" or "resonance contact.

Noise reduction in atomic force microscopy: Resonance contact mode

Noise reduction has been accomplished in atomic force microscopy by applying a high frequency, low amplitude vibration to the cantilever while it is in contact with a surface. The applied excitation (>~200 kHz; ~1 nm) is acoustically coupled to the tip and dampens the resonance Q factors of the system. The applied frequency is well above the bandwidth of the acquisition system (50 kHz). We call this mode "resonance contact" mode. The nonlinear behavior of the tip–sample interaction allows the high frequency excitation to effectively broaden the frequency response of the system resonances

The Specific Heat of a Ferromagnetic Film.

We analyze the specific heat for the $O(N)$ vector model on a $d$-dimensional film geometry of thickness $L$ using ``environmentally friendly'' renormalization. We consider periodic, Dirichlet and antiperiodic boundary conditions, deriving expressions for the specific heat and an effective specific heat exponent, \alpha\ef. In the case of $d=3$, for $N=1$, by matching to the exact exponent of the two dimensional Ising model we capture the crossover for \xi_L\ra\infty between power law behaviour in the limit {L\over\xi_L}\ra\infty and logarithmic behaviour in the limit {L\over\xi_L}\ra0 for fixed $L$, where $\xi_L$ is the correlation length in the transverse dimensions.Comment: 21 pages of Plain TeX. Postscript figures available upon request from [email protected]

Validation of the theoretical domains framework for use in behaviour change and implementation research

BACKGROUND: An integrative theoretical framework, developed for cross-disciplinary implementation and other behaviour change research, has been applied across a wide range of clinical situations. This study tests the validity of this framework. METHODS: Validity was investigated by behavioural experts sorting 112 unique theoretical constructs using closed and open sort tasks. The extent of replication was tested by Discriminant Content Validation and Fuzzy Cluster Analysis. RESULTS: There was good support for a refinement of the framework comprising 14 domains of theoretical constructs (average silhouette value 0.29): 'Knowledge', 'Skills', 'Social/Professional Role and Identity', 'Beliefs about Capabilities', 'Optimism', 'Beliefs about Consequences', 'Reinforcement', 'Intentions', 'Goals', 'Memory, Attention and Decision Processes', 'Environmental Context and Resources', 'Social Influences', 'Emotions', and 'Behavioural Regulation'. CONCLUSIONS: The refined Theoretical Domains Framework has a strengthened empirical base and provides a method for theoretically assessing implementation problems, as well as professional and other health-related behaviours as a basis for intervention development

The Influence of Thermal Pressure on Equilibrium Models of Hypermassive Neutron Star Merger Remnants

The merger of two neutron stars leaves behind a rapidly spinning hypermassive object whose survival is believed to depend on the maximum mass supported by the nuclear equation of state, angular momentum redistribution by (magneto-)rotational instabilities, and spindown by gravitational waves. The high temperatures (~5-40 MeV) prevailing in the merger remnant may provide thermal pressure support that could increase its maximum mass and, thus, its life on a neutrino-cooling timescale. We investigate the role of thermal pressure support in hypermassive merger remnants by computing sequences of spherically-symmetric and axisymmetric uniformly and differentially rotating equilibrium solutions to the general-relativistic stellar structure equations. Using a set of finite-temperature nuclear equations of state, we find that hot maximum-mass critically spinning configurations generally do not support larger baryonic masses than their cold counterparts. However, subcritically spinning configurations with mean density of less than a few times nuclear saturation density yield a significantly thermally enhanced mass. Even without decreasing the maximum mass, cooling and other forms of energy loss can drive the remnant to an unstable state. We infer secular instability by identifying approximate energy turning points in equilibrium sequences of constant baryonic mass parametrized by maximum density. Energy loss carries the remnant along the direction of decreasing gravitational mass and higher density until instability triggers collapse. Since configurations with more thermal pressure support are less compact and thus begin their evolution at a lower maximum density, they remain stable for longer periods after merger.Comment: 20 pages, 12 figures. Accepted for publication in Ap

Neutrino Breakup of A=3 Nuclei in Supernovae

We extend the virial equation of state to include 3H and 3He nuclei, and predict significant mass-three fractions near the neutrinosphere in supernovae. While alpha particles are often more abundant, we demonstrate that energy transfer cross-sections for muon and tau neutrinos at low densities are dominated by breakup of the loosely-bound 3H and 3He nuclei. The virial coefficients involving A=3 nuclei are calculated directly from the corresponding nucleon-3H and nucleon-3He scattering phase shifts. For the neutral-current inelastic cross-sections and the energy transfer cross sections, we perform ab-initio calculations based on microscopic two- and three-nucleon interactions and meson-exchange currents.Comment: 6 pages, 2 figures, minor additions, to appear in Phys. Rev.

Developing theory-informed interventions to implement evidence into practice: a systematic approach using the Theoretical Domains Framework

Background: There is little systematic operational guidance about how best to develop complex interventions to reduce the gap between practice and evidence. This article is one in a series of articles documenting the development and use of the Theoretical Domains Framework (TDF) to advance the science of implementation research. Methods: The intervention was developed considering three main components: theory, evidence, and practical issues. We used a four-step approach, consisting of guiding questions, to direct the choice of the most appropriate components of an implementation intervention: Who needs to do what, differently? Using a theoretical framework, which barriers and enablers need to be addressed? Which intervention components (behaviour change techniques and mode(s) of delivery) could overcome the modifiable barriers and enhance the enablers? And how can behaviour change be measured and understood? Results: A complex implementation intervention was designed that aimed to improve acute low back pain management in primary care. We used the TDF to identify the barriers and enablers to the uptake of evidence into practice and to guide the choice of intervention components. These components were then combined into a cohesive intervention. The intervention was delivered via two facilitated interactive small group workshops. We also produced a DVD to distribute to all participants in the intervention group. We chose outcome measures in order to assess the mediating mechanisms of behaviour change. Conclusions: We have illustrated a four-step systematic method for developing an intervention designed to change clinical practice based on a theoretical framework. The method of development provides a systematic framework that could be used by others developing complex implementation interventions. While this framework should be iteratively adjusted and refined to suit other contexts and settings, we believe that the four-step process should be maintained as the primary framework to guide researchers through a comprehensive intervention development process