The influence of anisotropic F region ion velocity distributions on ionospheric ion outflows into the magnetosphere

The contribution to the field-aligned ionospheric ion momentum equation, due to coupling between pressure anisotropy and the inhomogeneous geomagnetic field, is investigated. We term this contribution the “hydrodynamic mirror force” and investigate its dependence on the ion drift and the resulting deformations of the ion velocity distribution function from an isotropic form. It is shown that this extra upforce increases rapidly with ion drift relative to the neutral gas but is not highly dependent on the ion-neutral collision model employed. An example of a burst of flow observed by EISCAT, thought to be the ionospheric signature of a flux transfer event at the magnetopause, is studied in detail and it is shown that the nonthermal plasma which results is subject to a hydrodynamic mirror force which is roughly 10% of the gravitational downforce. In addition, predictions by the coupled University College London-Sheffield University model of the ionosphere and thermosphere show that the hydrodynamic mirror force in the auroral oval is up to 3% of the gravitational force for Kp of about 3, rising to 10% following a sudden increase in cross-cap potential. The spatial distribution of the upforce shows peaks in the cusp region and in the post-midnight auroral oval, similar to that of observed low-energy heavy ion flows from the ionosphere into the magnetosphere. We suggest the hydrodynamic mirror force may modulate these outflows by controlling the supply of heavy ions to regions of ion acceleration and that future simulations of the effects of Joule heating on ion outflows should make allowance for it.

Anharmonic force constant calculations

The relationship of the anharmonic force constants in curvilinear internal coordinates to the observed vibration-rotation spectrum of a molecule is reviewed. A simplified method of setting up the required non-linear coordinate transformations is described: this makes use of an / tensor, which is a straightforward generalization of the / matrix used in the customary description of harmonic force constant calculations. General formulae for the / tensor elements, in terms of the familiar L matrix elements, are presented. The use of non-linear symmetry coordinates and redundancies are described. Sample calculations on the water and ammonia molecules are reported.

Redundant coordinates in harmonic force-field calculations

Redundancy relations between vibrational coordinates may be linear (as for rectilinear coordinates used in deriving a G matrix), or non-linear (as for curvilinear coordinates used in formulating model force fields). It is shown that geometrically defined internal coordinates are necessarily curvilinear. Hence it is shown that linear force constants can occur in model force field calculations involving redundant coordinates, in disagreement with the recent proposal of Gussoni and Zerbi.

General derivative relations for anharmonic force fields

The brace notation, introduced by Allen and Csaszar (1993, J. chem. Phys., 98, 2983), provides a simple and compact way to deal with derivatives of arbitrary non-tensorial quantities. One of its main advantages is that it builds the permutational symmetry of the derivatives directly into the formalism. The brace notation is applied to formulate the general nth-order Cartesian derivatives of internal coordinates, and to provide closed forms for general, nth-order transformation equations of anharmonic force fields, expressed as Taylor series, from internal to Cartesian or normal coordinate spaces.

Implications of non-cylindrical flux ropes for magnetic cloud reconstruction techniques and the interpretation of double flux rope events

Magnetic clouds (MCs) are a subset of interplanetary coronal mass ejections (ICMEs) which exhibit signatures consistent with a magnetic flux rope structure. Techniques for reconstructing flux rope orientation from single-point in situ observations typically assume the flux rope is locally cylindrical, e.g., minimum variance analysis (MVA) and force-free flux rope (FFFR) fitting. In this study, we outline a non-cylindrical magnetic flux rope model, in which the flux rope radius and axial curvature can both vary along the length of the axis. This model is not necessarily intended to represent the global structure of MCs, but it can be used to quantify the error in MC reconstruction resulting from the cylindrical approximation. When the local flux rope axis is approximately perpendicular to the heliocentric radial direction, which is also the effective spacecraft trajectory through a magnetic cloud, the error in using cylindrical reconstruction methods is relatively small (≈ 10∘). However, as the local axis orientation becomes increasingly aligned with the radial direction, the spacecraft trajectory may pass close to the axis at two separate locations. This results in a magnetic field time series which deviates significantly from encounters with a force-free flux rope, and consequently the error in the axis orientation derived from cylindrical reconstructions can be as much as 90∘. Such two-axis encounters can result in an apparent ‘double flux rope’ signature in the magnetic field time series, sometimes observed in spacecraft data. Analysing each axis encounter independently produces reasonably accurate axis orientations with MVA, but larger errors with FFFR fitting.

Extracting force fields for disordered polymeric materials from neutron scattering data

We present a new approach that allows the determination of force-field parameters for the description of disordered macromolecular systems from experimental neutron diffraction data obtained over a large Q range. The procedure is based on a tight coupling between experimentally derived structure factors and computer modelling. We separate the molecular potential into non-interacting terms representing respectively bond stretching, angle bending and torsional rotation. The parameters for each of the potentials are extracted directly from experimental data through comparison of the experimental structure factor and those derived from atomistic level molecular models. The viability of these force fields is assessed by comparison of predicted large-scale features such as the characteristic ratio. The procedure is illustrated on molten poly(ethylene) and poly(tetrafluoroethylene).

The ocean's gravitational potential energy budget in a coupled climate model

This study examines, in a unified fashion, the budgets of ocean gravitational potential energy (GPE) and available gravitational potential energy (AGPE) in the control simulation of the coupled atmosphere–ocean general circulation model HadCM3. Only AGPE can be converted into kinetic energy by adiabatic processes. Diapycnal mixing supplies GPE, but not AGPE, whereas the reverse is true of the combined effect of surface buoyancy forcing and convection. Mixing and buoyancy forcing, thus, play complementary roles in sustaining the large scale circulation. However, the largest globally integrated source of GPE is resolved advection (+0.57 TW) and the largest sink is through parameterized eddy transports (-0.82 TW). The effect of these adiabatic processes on AGPE is identical to their effect on GPE, except for perturbations to both budgets due to numerical leakage exacerbated by non-linearities in the equation of state.

Impact of non-hydrostatic effects and trapped lee waves on mountain wave drag in directionally sheared flow

The orographic gravity wave drag produced in flow over an axisymmetric mountain when both vertical wind shear and non-hydrostatic effects are important was calculated using a semi-analytical two-layer linear model, including unidirectional or directional constant wind shear in a layer near the surface, above which the wind is constant. The drag behaviour is determined by partial wave reflection at the shear discontinuity, wave absorption at critical levels (both of which exist in hydrostatic flow), and total wave reflection at levels where the waves become evanescent (an intrinsically non-hydrostatic effect), which produces resonant trapped lee wave modes. As a result of constructive or destructive wave interference, the drag oscillates with the thickness of the constant-shear layer and the Richardson number within it (Ri), generally decreasing at low Ri and when the flow is strongly non-hydrostatic. Critical level absorption, which increases with the angle spanned by the wind velocity in the constant-shear layer, shields the surface from reflected waves, keeping the drag closer to its hydrostatic limit. While, for the parameter range considered here, the drag seldom exceeds this limit, a substantial drag fraction may be produced by trapped lee waves, particularly when the flow is strongly non-hydrostatic, the lower layer is thick and Ri is relatively high. In directionally sheared flows with Ri = O(1), the drag may be misaligned with the surface wind in a direction opposite to the shear, a behaviour which is totally due to non-trapped waves. The trapped lee wave drag, whose reaction force on the atmosphere is felt at low levels, may therefore have a distinctly different direction from the drag associated with vertically propagating waves, which acts on the atmosphere at higher levels.

Consent and the use of force: an examination of ‘intervention by invitation’ as a basis for US drone strikes in Pakistan, Somalia and Yemen

Drone strikes are becoming a key feature of the United States’ global military response to nonstate actors, and it has been widely adduced that these strikes have been carried out with the consent of the host states in which such non-state actors reside. This article examines the degree to which assertions of consent (or ‘intervention by invitation’), provided as a justification for drone strikes by the United States in Pakistan, Yemen and Somalia, can be said to accord with international law. First the article provides a broad sketch of the presence of consent in international law. It then analyses in detail the individual elements of consent as provided by Article 20 of the International Law Commission Draft Articles of State Responsibility. These require that consent should be ‘valid’, given by the legitimate government and expressed by an official empowered to do so. These elements will be dealt with individually, and each in turn will be applied to the cases of Pakistan, Yemen and Somalia. Finally, the article will examine the breadth of the exculpatory power of consent, and the extent to which it can preclude the wrongfulness of acts carried out in contravention of international law other than the prohibition of the use of force under Article 2(4) of the Charter of the United Nations.

Civilian casualties – do we really care? The failure of the revolution in military affairs of non-lethal weapons in the U.S., Russia and Israel

Causing civilian casualties during military operations has become a much politicised topic in international relations since the Second World War. Since the last decade of the 20th century, different scholars and political analysts have claimed that human life is valued more and more among the general international community. This argument has led many researchers to assume that democratic culture and traditions, modern ethical and moral issues have created a desire for a world without war or, at least, a demand that contemporary armed conflicts, if unavoidable, at least have to be far less lethal forcing the military to seek new technologies that can minimise civilian casualties and collateral damage. Non-Lethal Weapons (NLW) – weapons that are intended to minimise civilian casualties and collateral damage – are based on the technology that, during the 1990s, was expected to revolutionise the conduct of warfare making it significantly less deadly. The rapid rise of interest in NLW, ignited by the American military twenty five years ago, sparked off an entirely new military, as well as an academic, discourse concerning their potential contribution to military success on the 21st century battlefields. It seems, however, that except for this debate, very little has been done within the military forces themselves. This research suggests that the roots of this situation are much deeper than the simple professional misconduct of the military establishment, or the poor political behaviour of political leaders, who had sent them to fight. Following the story of NLW in the U.S., Russia and Israel this research focuses on the political and cultural aspects that have been supposed to force the military organisations of these countries to adopt new technologies and operational and organisational concepts regarding NLW in an attempt to minimise enemy civilian casualties during their military operations. This research finds that while American, Russian and Israeli national characters are, undoubtedly, products of the unique historical experience of each one of these nations, all of three pay very little regard to foreigners’ lives. Moreover, while it is generally argued that the international political pressure is a crucial factor that leads to the significant reduction of harmed civilians and destroyed civilian infrastructure, the findings of this research suggest that the American, Russian and Israeli governments are well prepared and politically equipped to fend off international criticism. As the analyses of the American, Russian and Israeli cases reveal, the political-military leaderships of these countries have very little external or domestic reasons to minimise enemy civilian casualties through fundamental-revolutionary change in their conduct of war. In other words, this research finds that employment of NLW have failed because the political leadership asks the militaries to reduce the enemy civilian casualties to a politically acceptable level, rather than to the technologically possible minimum; as in the socio-cultural-political context of each country, support for the former appears to be significantly higher than for the latter.