On Arnol'd's second nonlinear stability theorem for two-dimensional quasi-geostrophic flow

Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.

High-latitude influence of the quasi-biennial oscillation

The interannual variability of the stratospheric winter polar vortex is correlated with the phase of the quasi-biennial oscillation (QBO) of tropical stratospheric winds. This dynamical coupling between high and low latitudes, often referred to as the Holton–Tan effect, has been the subject of numerous observational and modelling studies, yet important questions regarding its mechanism remain unanswered. In particular it remains unclear which vertical levels of the QBO exert the strongest influence on the winter polar vortex, and how QBO–vortex coupling interacts with the effects of other sources of atmospheric interannual variability such as the 11-year solar cycle or the El Nino Southern Oscillation. As stratosphere-resolving general circulation models begin to resolve the QBO and represent its teleconnections with other parts of the climate system, it seems timely to summarize what is currently known about the QBO’s high-latitude influence. In this review article, we offer a synthesis of the modelling and observational analyses of QBO–vortex coupling that have appeared in the literature, and update the observational record.

A numerical model of the ionospheric signatures of time-varying magnetic reconnection: III. Quasi-instantaneous convection responses in the Cowley-Lockwood paradigm

Using a numerical implementation of the Cowley and Lockwood (1992) model of flow excitation in the magnetosphere–ionosphere (MI) system, we show that both an expanding (on a _12-min timescale) and a quasiinstantaneous response in ionospheric convection to the onset of magnetopause reconnection can be accommodated by the Cowley–Lockwood conceptual framework. This model has a key feature of time dependence, necessarily considering the history of the coupled MI system. We show that a residual flow, driven by prior magnetopause reconnection, can produce a quasi-instantaneous global ionospheric convection response; perturbations from an equilibrium state may also be present from tail reconnection, which will superpose constructively to give a similar effect. On the other hand, when the MI system is relatively free of pre-existing flow, we can most clearly see the expanding nature of the response. As the open-closed field line boundary will frequently be in motion from such prior reconnection (both at the dayside magnetopause and in the cross-tail current sheet), it is expected that there will usually be some level of combined response to dayside reconnection.

On the quasi-periodic nature of magnetopause flux transfer events

The recurrence rate of flux transfer events (FTEs) observed near the dayside magnetopause is discussed. A survey of magnetopause observations by the ISEE satellites shows that the distribution of the intervals between FTE signatures has a mode value of 3 min, but is highly skewed, having upper and lower decile values of 1.5 min and 18.5 min, respectively. The mean value is found to be 8 min, consistent with previous surveys of magnetopause data. The recurrence of quasi-periodic events in the dayside auroral ionosphere is frequently used as evidence for an association with magnetopause FTEs, and the distribution of their repetition intervals should be matched to that presented here if such an association is to be confirmed. A survey of 1 year's 15-s data on the interplanetary magnetic field (IMF) suggests that the derived distribution could arise from fluctuations in the IMF Bz component, rather than from a natural oscillation frequency of the magnetosphere-ionosphere system.

Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model

We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen–Cahn/Cahn–Hilliard/Navier–Stokes–Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system.

Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities

We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a large deviation principle (LDP) for capacities for such Gaussian rough paths. Together with Lyons' universal limit theorem, our results yield immediately the corresponding results for pathwise solutions to stochastic differential equations driven by such Gaussian process in the sense of rough paths. Moreover, our LDP result implies the result of Yoshida on the LDP for capacities over the abstract Wiener space associated with such Gaussian process.

Generalized convective quasi-equilibrium principle

A generalization of Arakawa and Schubert's convective quasi-equilibrium principle is presented for a closure formulation of mass-flux convection parameterization. The original principle is based on the budget of the cloud work function. This principle is generalized by considering the budget for a vertical integral of an arbitrary convection-related quantity. The closure formulation includes Arakawa and Schubert's quasi-equilibrium, as well as both CAPE and moisture closures as special cases. The formulation also includes new possibilities for considering vertical integrals that are dependent on convective-scale variables, such as the moisture within convection. The generalized convective quasi-equilibrium is defined by a balance between large-scale forcing and convective response for a given vertically-integrated quantity. The latter takes the form of a convolution of a kernel matrix and a mass-flux spectrum, as in the original convective quasi-equilibrium. The kernel reduces to a scalar when either a bulk formulation is adopted, or only large-scale variables are considered within the vertical integral. Various physical implications of the generalized closure are discussed. These include the possibility that precipitation might be considered as a potentially-significant contribution to the large-scale forcing. Two dicta are proposed as guiding physical principles for the specifying a suitable vertically-integrated quantity.

The combined influences of westerly phase of the quasi biennial oscillation and 11-year solar maximum conditions on the Northern Hemisphere extratropical winter circulation

The combined influences of the westerly phase of the quasi-biennial oscillation (QBO-W) and solar maximum (Smax) conditions on the Northern Hemisphere extratropical winter circulation are investigated using reanalysis data and Center for Climate System Research/National Institute for Environmental Studies chemistry climate model (CCM) simulations. The composite analysis for the reanalysis data indicates strengthened polar vortex in December followed by weakened polar vortex in February–March for QBO-W during Smax (QBO-W/Smax) conditions. This relationship need not be specific to QBO-W/Smax conditions but may just require strengthened vortex in December, which is more likely under QBO-W/Smax. Both the reanalysis data and CCM simulations suggest that dynamical processes of planetary wave propagation and meridional circulation related to QBO-W around polar vortex in December are similar in character to those related to Smax; furthermore, both processes may work in concert to maintain stronger vortex during QBO-W/Smax. In the reanalysis data, the strengthened polar vortex in December is associated with the development of north–south dipole tropospheric anomaly in the Atlantic sector similar to the North Atlantic oscillation (NAO) during December–January. The structure of the north–south dipole anomaly has zonal wavenumber 1 (WN1) component, where the longitude of anomalous ridge overlaps with that of climatological ridge in the North Atlantic in January. This implies amplification of the WN1 wave and results in the enhancement of the upward WN1 propagation from troposphere into stratosphere in January, leading to the weakened polar vortex in February–March. Although WN2 waves do not play a direct role in forcing the stratospheric vortex evolution, their tropospheric response to QBO-W/Smax conditions appears to be related to the maintenance of the NAO-like anomaly in the high-latitude troposphere in January. These results may provide a possible explanation for the mechanisms underlying the seasonal evolution of wintertime polar vortex anomalies during QBO-W/Smax conditions and the role of troposphere in this evolution.

EXACT AND QUASI-EXACT MODELS OF STRANGE STARS

We construct and compare in this work a variety of simple models for strange stars, namely, hypothetical self-bound objects made of a cold stable version of the quark-gluon plasma. Exact, quasi-exact and numerical models are examined to find the most economical description for these objects. A simple and successful parametrization of them is given in terms of the central density, and the differences among the models are explicitly shown and discussed. In particular, we present a model starting with a Gaussian ansatz for the density profile that provides a very accurate and almost complete analytical integration of the problem, modulo a small difference for one of the metric potentials.

2-(4,5,6,7-tetrafluorobenzimidazol-2-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl, a hydrogen-bonded organic quasi-1D ferromagnet

The title radical (F4BlmNN) is a stable nitronylnitroxide that forms hydrogen-bonded NH center dot center dot center dot ON chains in the solid state. The chains assemble the F4BlmNN molecules to form stacked contacts between the radical groups, in a geometry that is expected to exhibit ferromagnetic (FM) exchange based on spin polarization (SP) models. The experimental magnetic susceptibility of F4BlmNN confirms the expectation, showing 1-D Heisenberg chain FM exchange behavior over 1.8-300 K with an intrachain exchange constant Of J(chain)/k = +22 K. At lower temperatures, ac magnetic susceptibility and variable field heat capacity measurements show that F4BlmNN acts as a quasi-1-D ferromagnet. The dominant ferromagnetic exchange interaction is attributable to overlap between spin orbitals of molecules within the hydrogen-bonded chains, consistent with the SP model expectations. The chains appear to be antiferromagnetically exchange coupled, giving cusps in the ac susceptibility and zero field heat capacity at lower temperatures. The results indicate that the sample orders magnetically at about 0.7 K. The magnetic heat capacity ordering cusp shifts to lower temperatures as external magnetic field increases, consistent with forming a bulk antiferromagnetic phase below a Neel temperature of T-N(0) = 0.72 K, with a critical field of H-c approximate to 1800 Oe. The interchain exchange is estimated to be zJ/k congruent to (-)0.1 K.

From decoherence-free channels to decoherence-free and quasi-free subspaces within bosonic dissipative networks

We present a technique to build, within a dissipative bosonic network, decoherence-free channels (DFCs): a group of normal-mode oscillators with null effective damping rates. We verify that the states protected within the DFC define the well-known decoherence-free subspaces (DFSs) when mapped back into the natural network oscillators. Therefore, our technique to build protected normal-mode channels turns out to be an alternative way to build DFSs, which offers advantages over the conventional method. It enables the computation of all the network-protected states at once, as well as leading naturally to the concept of the decoherence quasi-free subspace (DQFS), inside which a superposition state is quasi-completely protected against decoherence. The concept of the DQFS, weaker than that of the DFS, may provide a more manageable mechanism to control decoherence. Finally, as an application of the DQFSs, we show how to build them for quasi-perfect state transfer in networks of coupled quantum dissipative oscillators.

Quasi-perfect state transfer in a bosonic dissipative network

In this paper we propose a scheme for quasi-perfect state transfer in a network of dissipative harmonic oscillators. We consider ideal sender and receiver oscillators connected by a chain of nonideal transmitter oscillators coupled by nearest-neighbour resonances. From the algebraic properties of the dynamical quantities describing the evolution of the network state, we derive a criterion, fixing the coupling strengths between all the oscillators, apart from their natural frequencies, enabling perfect state transfer in the particular case of ideal transmitter oscillators. Our criterion provides an easily manipulated formula enabling perfect state transfer in the special case where the network nonidealities are disregarded. We also extend such a criterion to dissipative networks where the fidelity of the transferred state decreases due to the loss mechanisms. To circumvent almost completely the adverse effect of decoherence, we propose a protocol to achieve quasi-perfect state transfer in nonideal networks. By adjusting the common frequency of the sender and the receiver oscillators to be out of resonance with that of the transmitters, we demonstrate that the sender`s state tunnels to the receiver oscillator by virtually exciting the nonideal transmitter chain. This virtual process makes negligible the decay rate associated with the transmitter line at the expense of delaying the time interval for the state transfer process. Apart from our analytical results, numerical computations are presented to illustrate our protocol.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.