Boltzmann hierarchy for interacting neutrinos I: formalism

Starting from the collisional Boltzmann equation, we derive for the first time and from first principles the Boltzmann hierarchy for neutrinos including interactions with a scalar particle. Such interactions appear, for example, in majoron-like models of neutrino mass generation. We study two limits of the scalar mass: (i) An extremely massive scalar whose only role is to mediate an effective 4-fermion neutrino-neutrino interaction, and (ii) a massless scalar that can be produced in abundance and thus demands its own Boltzmann hierarchy. In contrast to, e.g., the first-order Boltzmann hierarchy for Thomson-scattering photons, our interacting neutrino/scalar Boltzmann hierarchies contain additional momentum-dependent collision terms arising from a non-negligible energy transfer in the neutrino-neutrino and neutrino-scalar interactions. This necessitates that we track each momentum mode of the phase space distributions individually, even if the particles were massless. Comparing our hierarchy with the commonly used $(c_{\rm eff}^2,c_{\rm vis}^2)$-parameterisation, we find no formal correspondence between the two approaches, which raises the question of whether the latter parameterisation even has an interpretation in terms of particle scattering. Lastly, although we have invoked majoron-like models as a motivation for our study, our treatment is in fact generally applicable to all scenarios in which the neutrino and/or other ultrarelativistic fermions interact with scalar particles.Comment: 44 pages, 14 figures; included scalar Boltzmann hierarchy in the massless case and plots of integral kernels; accepted by JCA

Anomalous Soft Photons in Hadron Production

Anomalous soft photons in excess of what is expected from electromagnetic bremsstrahlung have been observed in association with the production of hadrons, mostly mesons, in high-energy (K+)p, (pi+)p, (pi-)p, pp, and (e+)(e-) collisions. We propose a model for the simultaneous production of anomalous soft photons and mesons in quantum field theory, in which the meson production arises from the oscillation of color charge densities of the quarks of the underlying vacuum in the flux tube. As a quark carries both a color charge and an electric charge, the oscillation of the color charge densities will be accompanied by the oscillation of electric charge densities, which will in turn lead to the simultaneous production of soft photons during the meson production process. How the production of these soft photons may explain the anomalous soft photon data will be discussed. Further experimental measurements to test the model will be proposed.Comment: 19 pages, 2 figures, to be published in Physical Review

Inference and Optimization of Real Edges on Sparse Graphs - A Statistical Physics Perspective

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge-variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory.Comment: 21 pages, 10 figures, major changes: Sections IV to VII updated, Figs. 1 to 3 replace

Cascades of Dynamical Transitions in an Adaptive Population

In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to adapt their strategies together. This change in the environment results in dynamical transitions from vanishing to non-vanishing step sizes. When the diversity decreases further, we find a cascade of dynamical transitions for the different signal dimensions, supported by good agreement between simulations and theory. Besides, the signal of the largest step size at the steady state is likely to be the initial signal.Comment: 4 pages, 8 figure

Spectral multigrid methods for elliptic equations 2

A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included

Association of antihypertensive monotherapy with serum sodium and potassium levels in Chinese patients

<b>Background</b> International guidelines on management of hypertension recommend any major classes of antihypertensive drugs. However, the low prescribing rate of thiazides has been attributed to concerns about electrolyte disturbances and studies between antihypertensive drug classes and hyponatremia/hypokalemia among Chinese patients were scarce. <p></p> <b>Methods</b> From clinical databases we included 2,759 patients who received their first-ever antihypertensive monotherapy from January 2004 to June 2007 in a large territory of Hong Kong. We studied the plasma sodium and potassium levels 8 weeks after prescriptions and factors associated with hyponatremia and hypokalemia by multivariable regression analyses. <p></p> <b>Results</b> Among major antihypertensive drug classes, thiazide users had the lowest sodium level (139.6 mEq/l, 95% confidence interval (CI) 139.3, 140.0, P < 0.001) and patients-prescribed calcium channel blockers (CCBs; 3.92 mEq/l, 95% CI 3.89, 3.95) or thiazide diuretics (3.99 mEq/l, 95% CI 3.93, 4.04) had the lowest potassium levels (P < 0.001). Multivariate analysis reported that advanced age (>/=70 years, odds ratio (OR) 7.49, 95% CI 2.84, 19.8, P < 0.001), male gender (OR 2.38, 95% CI 1.45, 3.91, P < 0.001), and thiazide users (OR 2.42, 95% CI 1.29, 4.56, P = 0.006) were significantly associated with hyponatremia, while renin-angiotensin system (RAS) (OR 0.31, 95% CI 0.13, 0.73, P = 0.008) and beta-blockers (BBs) (OR 0.35, 95% CI 0.23, 0.54, P < 0.001) users were less likely to present with hypokalemia. However, the proportions having normonatremic (95.1%) and normokalemic (89.4%) levels were high. <p></p> <b>Conclusions</b> In view of the low prevalence of hyponatremia and hypokalemia associated with thiazides, physicians should not be deterred from prescribing thiazide diuretics as first-line antihypertensive agents as recommended by most international guidelines