Making electromagnetic wavelets

Electromagnetic wavelets are constructed using scalar wavelets as superpotentials, together with an appropriate polarization. It is shown that oblate spheroidal antennas, which are ideal for their production and reception, can be made by deforming and merging two branch cuts. This determines a unique field on the interior of the spheroid which gives the boundary conditions for the surface charge-current density necessary to radiate the wavelets. These sources are computed, including the impulse response of the antenna.Comment: 29 pages, 4 figures; minor corrections and addition

A Weak Gravitational Lensing Analysis of Abell 2390

We report on the detection of dark matter in the cluster Abell 2390 using the weak gravitational distortion of background galaxies. We find that the cluster light and total mass distributions are quite similar over an angular scale of \simeq 7^\prime \;(1 \Mpc). The cluster galaxy and mass distributions are centered on the cluster cD galaxy and exhibit elliptical isocontours in the central \simeq 2^\prime \; (280 \kpc). The major axis of the ellipticity is aligned with the direction defined by the cluster cD and a ``straight arc'' located $\simeq 38^{\prime\prime}$ to the northwest. We determined the radial mass-to-light profile for this cluster and found a constant value of $(320 \pm 90) h\; M_\odot/L_{\odot V}$, which is consistent with other published determinations. We also compared our weak lensing azimuthally averaged radial mass profile with a spherical mass model proposed by the CNOC group on the basis of their detailed dynamical study of the cluster. We find good agreement between the two profiles, although there are weak indications that the CNOC density profile may be falling more steeply for $\theta\geq 3^\prime$ (420\kpc).Comment: 14 pages, latex file. Postscript file and one additional figure are available at ftp://magicbean.berkeley.edu/pub/squires/a2390/massandlight.ps.g

Induced pseudoscalar form factor of the nucleon at two-loop order in chiral perturbation theory

We calculate the imaginary part of the induced pseudoscalar form factor of the nucleon $G_P(t)$ in the framework of two-loop heavy baryon chiral perturbation theory. The effect of the calculated three-pion continuum on the pseudoscalar constant $g_P = (m_\mu/2M) G_P(t=-0.877m_\mu^2)$ measurable in ordinary muon capture $\mu^-p\to \nu_\mu n$ turns out to be negligibly small. Possible contributions from counterterms at two-loop order are numerically smaller than the uncertainty of the dominant pion-pole term proportional to the pion-nucleon coupling constant $g_{\pi N}= 13.2\pm 0.2$. We conclude that a sufficiently accurate representation of the induced pseudoscalar form factor of the nucleon at low momentum transfers $t$ is given by the sum of the pion-pole term and the Adler-Dothan-Wolfenstein term: $G_P(t) = 4g_{\pi N} M f_\pi/ (m_\pi^2 -t)- 2g_A M^2 /3$, with $= (0.44 \pm 0.02)$ fm$^2$ the axial mean square radius of the nucleon.Comment: 6 pages, 2 figures, accepted for publication in Physical Review

Microscopic optical potential from chiral nuclear forces

The energy- and density-dependent single-particle potential for nucleons is constructed in a medium of infinite isospin-symmetric nuclear matter starting from realistic nuclear interactions derived within the framework of chiral effective field theory. The leading-order terms from both two- and three-nucleon forces give rise to real, energy-independent contributions to the nucleon self-energy. The Hartree-Fock contribution from the two-nucleon force is attractive and strongly momentum dependent, in contrast to the contribution from the three-nucleon force which provides a nearly constant repulsive mean field that grows approximately linearly with the nuclear density. Together, the leading-order perturbative contributions yield an attractive single-particle potential that is however too weak compared to phenomenology. Second-order contributions from two- and three-body forces then provide the additional attraction required to reach the phenomenological depth. The imaginary part of the optical potential, which is positive (negative) for momenta below (above) the Fermi momentum, arises at second-order and is nearly inversion-symmetric about the Fermi surface when two-nucleon interactions alone are present. The imaginary part is strongly absorptive and requires the inclusion of an effective mass correction as well as self-consistent single-particle energies to attain qualitative agreement with phenomenology.Comment: 12 pages, 7 figures, added references, corrected typo

Three episodes of jet activity in the FRII radio galaxy B0925+420

We present Very Large Array images of a "Double-Double Radio Galaxy", a class of objects in which two pairs of lobes are aligned either side of the nucleus. In this object, B0925+420, we discover a third pair of lobes, close to the core and again in alignment with the other lobes. This first-known "Triple-Double" object strongly increases the likelihood that these lobes represent mutiple episodes of jet activity, as opposed to knots in an underlying jet. We model the lobes in terms of their dynamical evolution. We find that the inner pair of lobes is consistent with the outer pair having been displaced buoyantly by the ambient medium. The middle pair of lobes is more problematic - to the extent where an alternative model interpreting the middle and inner "lobes" as additional bow shocks within the outer lobes may be more appropriate - and we discuss the implications of this on our understanding of the density of the ambient medium.Comment: Accepted for publication in MNRAS. Figure 2 is best viewed in colou

Double-double radio galaxies: further insights into the formation of the radio structures

Double-double radio galaxies (DDRGs) offer a unique opportunity for us to study multiple episodes of jet activity in large-scale radio sources. We use radio data from the Very Large Array and the literature to model two DDRGs, B1450+333 and B1834+620, in terms of their dynamical evolution. We find that the standard Fanaroff-Riley II model is able to explain the properties of the two outer lobes of each source, whereby the lobes are formed by ram-pressure balance of a shock at the end of the jet with the surrounding medium. The inner pairs of lobes, however, are not well-described by the standard model. Instead we interpret the inner lobes as arising from the emission of relativistic electrons within the outer lobes, which are compressed and re-accelerated by the bow-shock in front of the restarted jets and within the outer lobes. The predicted rapid progression of the inner lobes through the outer lobes requires the eventual development of a hotspot at the edge of the outer lobe, causing the DDRG ultimately to resemble a standard Fanaroff-Riley II radio galaxy. This may suggest that DDRGs are a brief, yet normal, phase of the evolution of large-scale radio galaxies.Comment: Accepted for publication in MNRAS. 17 pages; 15 figures, 2 of which are in colou

Effective Fokker-Planck Equation for Birhythmic Modified van der Pol Oscillator

We present an explicit solution based on the phase-amplitude approximation of the Fokker-Planck equation associated with the Langevin equation of the birhythmic modified van der Pol system. The solution enables us to derive probability distributions analytically as well as the activation energies associated to switching between the coexisting different attractors that characterize the birhythmic system. Comparing analytical and numerical results we find good agreement when the frequencies of both attractors are equal, while the predictions of the analytic estimates deteriorate when the two frequencies depart. Under the effect of noise the two states that characterize the birhythmic system can merge, inasmuch as the parameter plane of the birhythmic solutions is found to shrink when the noise intensity increases. The solution of the Fokker-Planck equation shows that in the birhythmic region, the two attractors are characterized by very different probabilities of finding the system in such a state. The probability becomes comparable only for a narrow range of the control parameters, thus the two limit cycles have properties in close analogy with the thermodynamic phases

Wavelets and Quantum Algebras

Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation a non-linear, two parameter algebra. This structure can be mapped onto the quantum group $su_{q}(2)$ in one limit, and approaches a Fourier series generating algebra, in another limit. A duality between any scaling function and its corresponding non-linear algebra is obtained. Examples for the Haar and B-wavelets are worked out in detail.Comment: 27 pages Latex, 3 figure p

Global stability analysis of birhythmicity in a self-sustained oscillator

We analyze global stability properties of birhythmicity in a self-sustained system with random excitations. The model is a multi-limit cycles variation of the van der Pol oscillatorintroduced to analyze enzymatic substrate reactions in brain waves. We show that the two frequencies are strongly influenced by the nonlinear coefficients $\alpha$ and $\beta$. With a random excitation, such as a Gaussian white noise, the attractor's global stability is measured by the mean escape time $\tau$ from one limit-cycle. An effective activation energy barrier is obtained by the slope of the linear part of the variation of the escape time $\tau$ versus the inverse noise-intensity 1/D. We find that the trapping barriers of the two frequencies can be very different, thus leaving the system on the same attractor for an overwhelming time. However, we also find that the system is nearly symmetric in a narrow range of the parameters.Comment: 17 pages, 8 figures, to appear on Choas, 201