Euler-Poincare reduction for discrete field theories

In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed.Comment: 24 pages, 3 figures (v2: simplified treatment

The pulsar spectral index distribution

The flux density spectra of radio pulsars are known to be steep and, to first order, described by a power-law relationship of the form S_{\nu} \propto \nu^{\alpha}, where S_{\nu} is the flux density at some frequency \nu and \alpha is the spectral index. Although measurements of \alpha have been made over the years for several hundred pulsars, a study of the intrinsic distribution of pulsar spectra has not been carried out. From the result of pulsar surveys carried out at three different radio frequencies, we use population synthesis techniques and a likelihood analysis to deduce what underlying spectral index distribution is required to replicate the results of these surveys. We find that in general the results of the surveys can be modelled by a Gaussian distribution of spectral indices with a mean of -1.4 and unit standard deviation. We also consider the impact of the so-called "Gigahertz-peaked spectrum" pulsars. The fraction of peaked spectrum sources in the population with significant turn-over at low frequencies appears to be at most 10%. We demonstrate that high-frequency (>2 GHz) surveys preferentially select flatter-spectrum pulsars and the converse is true for lower-frequency (<1 GHz) surveys. This implies that any correlations between \alpha and other pulsar parameters (for example age or magnetic field) need to carefully account for selection biases in pulsar surveys. We also expect that many known pulsars which have been detected at high frequencies will have shallow, or positive, spectral indices. The majority of pulsars do not have recorded flux density measurements over a wide frequency range, making it impossible to constrain their spectral shapes. We also suggest that such measurements would allow an improved description of any populations of pulsars with 'non-standard' spectra.Comment: 8 pages, 5 figures. Accepted by MNRA

Strong Exchange Couplings Drastically Slow Down Magnetization Relaxation in an Air‐Stable Cobalt(II)‐Radical Single‐Molecule Magnet (SMM)

The energy barrier leading to magnetic bistability in molecular clusters is determined by the magnetic anisotropy of the cluster constituents. By incorporating a highly anisotropic four‐coordinate cobalt(II) building block into a strongly coupled fully air‐ and moisture‐stable three‐spin system, it proved possible to suppress under‐barrier Raman processes leading to 350‐fold increase of magnetization relaxation time and pronounced hysteresis. Relaxation times of up to 9 hours at low temperatures were found

Model for the Scaling of Stresses and Fluctuations in Flows near Jamming

We probe flows of soft, viscous spheres near the jamming point, which acts as a critical point for static soft spheres. Starting from energy considerations, we find nontrivial scaling of velocity fluctuations with strain rate. Combining this scaling with insights from jamming, we arrive at an analytical model that predicts four distinct regimes of flow, each characterized by rational-valued scaling exponents. Both the number of regimes and values of the exponents depart from prior results. We validate predictions of the model with simulations.Comment: 4 pages, 5 figures (revised text and one new figure). To appear in Phys. Rev. Let