There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

流体力学杂志“Journal of Fluid Mechanics”由剑桥大学教授George Batchelor在1956年5月创办，在国际流体力学界享有很高的学术声望，被公认为是流体力学最著名的学术刊物之一，2005年的影响因子为2．061，雄居同类期刊之首．在它创刊50周年之际，2006年5月JFM出版了第554卷的纪念特刊，其中刊登了现任主编（美国西北大学S．H．Davis教授和英国剑桥大学T．J．Pedley教授）合写的述评：“Editorial：JFM at50”，以JFM为背景，从独特的视角对近50年来流体力学的发展进行了简明的回顾和展望，并归纳了一系列非常有启发性的有趣统计数字．2006年7月21日在剑桥大学应用数学和理论物理研究所（DAMTP）举行了创刊50周年的庆祝会．下午2点，JFM的新老编辑和来宾会聚一堂，Pedley教授致开幕词，其后是5个精彩的报告：The mysterious rattleback and its fluid counterpart（Keith Moffatt），Developments in shear instabilities（Patrick Huerre），Falling clouds（Elisabeth Guazzelli），Ecotectural fluid mechanics（Paul Linden），The success of JFM（Herbert Huppert），最后由Davis教授致闭幕词．

Journal of Fluid Mechanics创刊50周年

Magnetars are the strongest magnets in the present universe and the combination of extreme magnetic field, gravity and density makes them unique laboratories to probe current physical theories (from quantum electrodynamics to general relativity) in the strong field limit. Magnetars are observed as peculiar, burst-active x-ray pulsars, the anomalous x-ray pulsars (AXPs) and the soft gamma repeaters (SGRs); the latter emitted also three 'giant flares', extremely powerful events during which luminosities can reach up to 10(47) erg s(-1) for about one second. The last five years have witnessed an explosion in magnetar research which has led, among other things, to the discovery of transient, or 'outbursting', and 'low-field' magnetars. Substantial progress has been made also on the theoretical side. Quite detailed models for explaining the magnetars' persistent x-ray emission, the properties of the bursts, the flux evolution in transient sources have been developed and confronted with observations. New insight on neutron star asteroseismology has been gained through improved models of magnetar oscillations. The long-debated issue of magnetic field decay in neutron stars has been addressed, and its importance recognized in relation to the evolution of magnetars and to the links among magnetars and other families of isolated neutron stars. The aim of this paper is to present a comprehensive overview in which the observational results are discussed in the light of the most up-to-date theoretical models and their implications. This addresses not only the particular case of magnetar sources, but the more fundamental issue of how physics in strong magnetic fields can be constrained by the observations of these unique sources.

http://iopscience.iop.org/article/10.1088/0034-4885/78/11/116901/pdf

Magnetars: the physics behind observations. A review.

Magnetars are the strongest magnets in the present universe and the combination of extreme magnetic field, gravity and density makes them unique laboratories to probe current physical theories (from quantum electrodynamics to general relativity) in the strong field limit. Magnetars are observed as peculiar, burst--active X-ray pulsars, the Anomalous X-ray Pulsars (AXPs) and the Soft Gamma Repeaters (SGRs); the latter emitted also three "giant flares," extremely powerful events during which luminosities can reach up to 10^47 erg/s for about one second. The last five years have witnessed an explosion in magnetar research which has led, among other things, to the discovery of transient, or "outbursting," and "low-field" magnetars. Substantial progress has been made also on the theoretical side. Quite detailed models for explaining the magnetars' persistent X-ray emission, the properties of the bursts, the flux evolution in transient sources have been developed and confronted with observations. New insight on neutron star asteroseismology has been gained through improved models of magnetar oscillations. The long-debated issue of magnetic field decay in neutron stars has been addressed, and its importance recognized in relation to the evolution of magnetars and to the links among magnetars and other families of isolated neutron stars. The aim of this paper is to present a comprehensive overview in which the observational results are discussed in the light of the most up-to-date theoretical models and their implications. This addresses not only the particular case of magnetar sources, but the more fundamental issue of how physics in strong magnetic fields can be constrained by the observations of these unique sources.

Magnetars: the physics behind observations

: The final report covering the research performed under the Air Force Office of Scientific Research by the Dallas relativity group, summarizes information on personnel involved, on the scientific work done, and on the results obtained in the four years of the grant's duration. Topics investigated were in areas of General relativity, cosmology, and electrodynamics.

Exact Solutions of Einstein's Field Equations.

In this paper, we consider a simple two-fluid model for pulsar glitches. We derive the basic equations that govern the spin evolution of the system from two-fluid hydrodynamics, accounting for the vortex mediated mutual friction force that determines the glitch rise. This leads to a simple 'bulk' model that can be used to describe the main properties of a glitch event resulting from vortex unpinning. In order to model the long-term relaxation following the glitch, our model would require additional assumptions regarding the repinning of vortices, an issue that we only touch upon briefly. Instead, we focus on comparing the phenomenological model to results obtained from time-evolutions of the linearized two-fluid equations, i.e. a 'hydrodynamic' model for glitches. This allows us to study, for the first time, dynamics that was 'averaged' in the bulk model, i.e. consider the various neutron star oscillation modes that are excited during a glitch. The hydro-results are of some relevance for efforts to detect gravitational waves from glitching pulsars, although the conclusions drawn from our rather simple model are pessimistic as far as the detectability of these events is concerned.

The dynamics of pulsar glitches: contrasting phenomenology with numerical evolutions

We develop a new perturbative framework for studying the r modes of rotating superfluid neutron stars. Our analysis accounts for the centrifugal deformation of the star, and considers the two-fluid dynamics at linear order in the perturbed velocities. Our main focus is on a simple model system where the total density profile is that of an n= 1 polytrope. We derive a partially analytic solution for the superfluid analogue of the classical r mode. This solution is used to analyse the relevance of the vortex-mediated mutual friction damping, confirming that this dissipation mechanism is unlikely to suppress the gravitational-wave-driven instability in rapidly spinning superfluid neutron stars. Our calculation of the superfluid r modes is significantly simpler than previous approaches, because it decouples the r mode from all other inertial modes of the system. This leads to the results being clearer, but it also means that we cannot comment on the relevance of potential avoided crossings (and associated 'resonances') that may occur for particular parameter values. Our analysis of the mutual friction damping differs from previous studies in two important ways. First, we incorporate realistic pairing gaps which means that the regions of superfluidity in the star's core vary with temperature. Secondly, we allow the mutual friction parameters to take the whole range of permissible values rather than focusing on a particular mechanism. Thus, we consider not only the weak drag regime, but also the strong drag regime where the fluid dynamics are significantly different.

r modes and mutual friction in rapidly rotating superfluid neutron stars

This work is supported by the Spanish MINECO (grant AYA2015-66899-C2-1-P) and the Generalitat Valenciana (PROMETEOII-2014-069). AP acknowledges support from the European Union under the Marie Sklodowska Curie Actions Individual Fellowship, grant agreement no. 656370.

Towards asteroseismology of core-collapse supernovae with gravitational-wave observations – I. Cowling approximation

Improvements in ground-based, advanced gravitational wave (GW) detectors may allow in the near future to observe the GW signal of a nearby core-collapse supernova. For the most common type of progenitors, likely with slowly rotating cores, the dominant GW emission mechanisms are the post-bounce oscillations of the proto-neutron star (PNS) before the explosion. We present a new procedure to compute the eigenmodes of the system formed by the PNS and the stalled accretion shock in general relativity including spacetime perturbations. The new method improves on previous results by accounting for perturbations of both the lapse function and the conformal factor. We apply our analysis to two numerical core-collapse simulations and show that our improved method is able to obtain eigenfrequencies that accurately match the features observed in the GW signal and to predict the qualitative behaviour of quasi-radial oscillations. Our analysis is possible thanks to a newly developed algorithm to classify the computed eigenmodes in different classes (f-, p-, and g-modes), improving previous results which suffered from misclassification issues. We find that most of the GW energy is stored in the lowest order eigenmodes, in particular in the $^2g_1$ mode and in the $^2f$ mode. Our results also suggest that a low-frequency component of the GW signal attributed in previous works to the characteristic frequency of the Standing Accretion Shock Instability should be identified as the fundamental quadrupolar f-mode. We also develop a formalism to estimate the contribution of quasi-radial ($l=0$) modes to the quadrupolar component of the GW emission in the case of a deformed background, with application to rapidly rotating cores. This work provides further support for asteroseismology of core-collapse supernovae and the inference of PNS properties based on GW observations.

Towards asteroseismology of core-collapse supernovae with gravitational wave observations – II. Inclusion of space–time perturbations

The postbounce oscillations of newly-born relativistic stars are expected to lead to gravitational-wave emission through the excitation of nonradial oscillation modes. At the same time, the star is oscillating in its radial modes, with a central density variation that can reach several percent. Nonlinear couplings between radial oscillations and polar nonradial modes lead to the appearance of combination frequencies (sums and differences of the linear mode frequencies). We study such combination frequencies using a gauge-invariant perturbative formalism, which includes bilinear coupling terms between different oscillation modes. For typical values of the energy stored in each mode we find that gravitational waves emitted at combination frequencies could become detectable in galactic core-collapse supernovae with advanced interferometric or wideband resonant detectors.

Andrea Passamonti

Papers

The dynamics of pulsar glitches: contrasting phenomenology with numerical evolutions

r modes and mutual friction in rapidly rotating superfluid neutron stars

Towards asteroseismology of core-collapse supernovae with gravitational-wave observations – I. Cowling approximation

Towards asteroseismology of core-collapse supernovae with gravitational wave observations – II. Inclusion of space–time perturbations

Gravitational waves from nonlinear couplings of radial and polar nonradial modes in relativistic stars