Quantitative model for the kinetics of lyotropic phase transitions involving changes in monolayer curvature

We present a kinetic model for transformations between different self-assembled lipid structures. The model shows how data on the rates of phase transitions between mesophases of different geometries can be used to provide information on the mechanisms of the transformations and the transition states involved. This can be used, for example, to gain an insight into intermediate structures in cell membrane fission or fusion. In cases where the monolayer curvature changes on going from the initial to the final mesophase, we consider the phase transition to be driven primarily by the change in the relaxed curvature with pressure or temperature, which alters the relative curvature elastic energies of the two mesophase structures. Using this model, we have analyzed previously published kinetic data on the inter-conversion of inverse bicontinuous cubic phases in the 1-monoolein-30 wt% water system. The data are for a transition between QII(G) and QII(D) phases, and our analysis indicates that the transition state more closely resembles the QII(D) than the QII(G) phase. Using estimated values for the monolayer mean curvatures of the QII(G) and QII(D) phases of -0.123 nm(-1) and -0.133 nm(-1), respectively, gives values for the monolayer mean curvature of the transition state of between -0.131 nm(-1) and -0.132 nm(-1). Furthermore, we estimate that several thousand molecules undergo the phase transition cooperatively within one "cooperative unit", equivalent to 1-2 unit cells of QII(G) or 4-10 unit cells of QII(D).

On the initiation of surface waves by turbulent shear flow

An analytical model is developed for the initial stage of surface wave generation at an air-water interface by a turbulent shear flow in either the air or in the water. The model treats the problem of wave growth departing from a flat interface and is relevant for small waves whose forcing is dominated by turbulent pressure fluctuations. The wave growth is predicted using the linearised and inviscid equations of motion, essentially following Phillips [Phillips, O.M., 1957. On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417-445], but the pressure fluctuations that generate the waves are treated as unsteady and related to the turbulent velocity field using the rapid-distortion treatment of Durbin [Durbin, P.A., 1978. Rapid distortion theory of turbulent flows. PhD thesis, University of Cambridge]. This model, which assumes a constant mean shear rate F, can be viewed as the simplest representation of an oceanic or atmospheric boundary layer. For turbulent flows in the air and in the water producing pressure fluctuations of similar magnitude, the waves generated by turbulence in the water are found to be considerably steeper than those generated by turbulence in the air. For resonant waves, this is shown to be due to the shorter decorrelation time of turbulent pressure in the air (estimated as proportional to 1/Gamma), because of the higher shear rate existing in the air flow, and due to the smaller length scale of the turbulence in the water. Non-resonant waves generated by turbulence in the water, although being somewhat gentler, are still steeper than resonant waves generated by turbulence in the air. Hence, it is suggested that turbulence in the water may have a more important role than previously thought in the initiation of the surface waves that are subsequently amplified by feedback instability mechanisms.

Integrating control systems defined on the frame bundles of the space forms

This paper considers left-invariant control systems defined on the orthonormal frame bundles of simply connected manifolds of constant sectional curvature, namely the space forms Euclidean space E-3, the sphere S-3 and Hyperboloid H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1, 3). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. In the Euclidean case the elements of the Lie algebra se(3) are often referred to as twists. For constant twist motions, the corresponding curves g(t) is an element of SE(3) are known as screw motions, given in closed form by using the well known Rodrigues' formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

Threshold autoregressive and Markov switching models: an application to commercial real estate

Although financial theory rests heavily upon the assumption that asset returns are normally distributed, value indices of commercial real estate display significant departures from normality. In this paper, we apply and compare the properties of two recently proposed regime switching models for value indices of commercial real estate in the US and the UK, both of which relax the assumption that observations are drawn from a single distribution with constant mean and variance. Statistical tests of the models' specification indicate that the Markov switching model is better able to capture the non-stationary features of the data than the threshold autoregressive model, although both represent superior descriptions of the data than the models that allow for only one state. Our results have several implications for theoretical models and empirical research in finance.

Recent changes in solar outputs and the global mean surface temperature. III. Analysis of contributions to global mean air surface temperature rise

A multivariate fit to the variation in global mean surface air temperature anomaly over the past half century is presented. The fit procedure allows for the effect of response time on the waveform, amplitude and lag of each radiative forcing input, and each is allowed to have its own time constant. It is shown that the contribution of solar variability to the temperature trend since 1987 is small and downward; the best estimate is -1.3% and the 2sigma confidence level sets the uncertainty range of -0.7 to -1.9%. The result is the same if one quantifies the solar variation using galactic cosmic ray fluxes (for which the analysis can be extended back to 1953) or the most accurate total solar irradiance data composite. The rise in the global mean air surface temperatures is predominantly associated with a linear increase that represents the combined effects of changes in anthropogenic well-mixed greenhouse gases and aerosols, although, in recent decades, there is also a considerable contribution by a relative lack of major volcanic eruptions. The best estimate is that the anthropogenic factors contribute 75% of the rise since 1987, with an uncertainty range (set by the 2sigma confidence level using an AR(1) noise model) of 49–160%; thus, the uncertainty is large, but we can state that at least half of the temperature trend comes from the linear term and that this term could explain the entire rise. The results are consistent with the intergovernmental panel on climate change (IPCC) estimates of the changes in radiative forcing (given for 1961–1995) and are here combined with those estimates to find the response times, equilibrium climate sensitivities and pertinent heat capacities (i.e. the depth into the oceans to which a given radiative forcing variation penetrates) of the quasi-periodic (decadal-scale) input forcing variations. As shown by previous studies, the decadal-scale variations do not penetrate as deeply into the oceans as the longer term drifts and have shorter response times. Hence, conclusions about the response to century-scale forcing changes (and hence the associated equilibrium climate sensitivity and the temperature rise commitment) cannot be made from studies of the response to shorter period forcing changes.

ASYM20: a program for force constant and normal coordinate calculations, with a critical review of the theory involved

The theory of harmonic force constant refinement calculations is reviewed, and a general-purpose program for force constant and normal coordinate calculations is described. The program, called ASYM20. is available through Quantum Chemistry Program Exchange. It will work on molecules of any symmetry containing up to 20 atoms and will produce results on a series of isotopomers as desired. The vibrational secular equations are solved in either nonredundant valence internal coordinates or symmetry coordinates. As well as calculating the (harmonic) vibrational wavenumbers and normal coordinates, the program will calculate centrifugal distortion constants, Coriolis zeta constants, harmonic contributions to the α′s. root-mean-square amplitudes of vibration, and other quantities related to gas electron-diffraction studies and thermodynamic properties. The program will work in either a predict mode, in which it calculates results from an input force field, or in a refine mode, in which it refines an input force field by least squares to fit observed data on the quantities mentioned above. Predicate values of the force constants may be included in the data set for a least-squares refinement. The program is written in FORTRAN for use on a PC or a mainframe computer. Operation is mainly controlled by steering indices in the input data file, but some interactive control is also implemented.

OFDM joint data detection and phase noise cancellation for constant modulus modulations

This correspondence proposes a new algorithm for the OFDM joint data detection and phase noise (PHN) cancellation for constant modulus modulations. We highlight that it is important to address the overfitting problem since this is a major detrimental factor impairing the joint detection process. In order to attack the overfitting problem we propose an iterative approach based on minimum mean square prediction error (MMSPE) subject to the constraint that the estimated data symbols have constant power. The proposed constrained MMSPE algorithm (C-MMSPE) significantly improves the performance of existing approaches with little extra complexity being imposed. Simulation results are also given to verify the proposed algorithm.

An analytical model of mountain wave drag for wind profiles with shear and curvature

An analytical model is developed to predict the surface drag exerted by internal gravity waves on an isolated axisymmetric mountain over which there is a stratified flow with a velocity profile that varies relatively slowly with height. The model is linear with respect to the perturbations induced by the mountain, and solves the Taylor–Goldstein equation with variable coefficients using a Wentzel–Kramers–Brillouin (WKB) approximation, formally valid for high Richardson numbers, Ri. The WKB solution is extended to a higher order than in previous studies, enabling a rigorous treatment of the effects of shear and curvature of the wind profile on the surface drag. In the hydrostatic approximation, closed formulas for the drag are derived for generic wind profiles, where the relative magnitude of the corrections to the leading-order drag (valid for a constant wind profile) does not depend on the detailed shape of the orography. The drag is found to vary proportionally to Ri21, decreasing as Ri decreases for a wind that varies linearly with height, and increasing as Ri decreases for a wind that rotates with height maintaining its magnitude. In these two cases the surface drag is predicted to be aligned with the surface wind. When one of the wind components varies linearly with height and the other is constant, the surface drag is misaligned with the surface wind, especially for relatively small Ri. All these results are shown to be in fairly good agreement with numerical simulations of mesoscale nonhydrostatic models, for high and even moderate values of Ri.

Formulation and implementation of a residual-mean ocean circulation model

A parameterization of mesoscale eddies in coarse-resolution ocean general circulation models (GCM) is formulated and implemented using a residual-mean formalism. In that framework, mean buoyancy is advected by the residual velocity (the sum of the Eulerian and eddy-induced velocities) and modified by a residual flux which accounts for the diabatic effects of mesoscale eddies. The residual velocity is obtained by stepping forward a residual-mean momentum equation in which eddy stresses appear as forcing terms. Study of the spatial distribution of eddy stresses, derived by using them as control parameters to ‘‘fit’’ the residual-mean model to observations, supports the idea that eddy stresses can be likened to a vertical down-gradient flux of momentum with a coefficient which is constant in the vertical. The residual eddy flux is set to zero in the ocean interior, where mesoscale eddies are assumed to be quasi-adiabatic, but is parameterized by a horizontal down-gradient diffusivity near the surface where eddies develop a diabatic component as they stir properties horizontally across steep isopycnals. The residual-mean model is implemented and tested in the MIT general circulation model. It is shown that the resulting model (1) has a climatology that is superior to that obtained using the Gent and McWilliams parameterization scheme with a spatially uniform diffusivity and (2) allows one to significantly reduce the (spurious) horizontal viscosity used in coarse resolution GCMs.

Twentieth-century global-mean sea-level rise: is the whole greater than the sum of the parts?

Confidence in projections of global-mean sea level rise (GMSLR) depends on an ability to account for GMSLR during the twentieth century. There are contributions from ocean thermal expansion, mass loss from glaciers and ice sheets, groundwater extraction, and reservoir impoundment. Progress has been made toward solving the “enigma” of twentieth-century GMSLR, which is that the observed GMSLR has previously been found to exceed the sum of estimated contributions, especially for the earlier decades. The authors propose the following: thermal expansion simulated by climate models may previously have been underestimated because of their not including volcanic forcing in their control state; the rate of glacier mass loss was larger than previously estimated and was not smaller in the first half than in the second half of the century; the Greenland ice sheet could have made a positive contribution throughout the century; and groundwater depletion and reservoir impoundment, which are of opposite sign, may have been approximately equal in magnitude. It is possible to reconstruct the time series of GMSLR from the quantified contributions, apart from a constant residual term, which is small enough to be explained as a long-term contribution from the Antarctic ice sheet. The reconstructions account for the observation that the rate of GMSLR was not much larger during the last 50 years than during the twentieth century as a whole, despite the increasing anthropogenic forcing. Semiempirical methods for projecting GMSLR depend on the existence of a relationship between global climate change and the rate of GMSLR, but the implication of the authors' closure of the budget is that such a relationship is weak or absent during the twentieth century.