Empirical evidence for a nonlinear effect of galactic cosmic rays on clouds

Galactic cosmic ray (GCR) changes have been suggested to affect weather and climate, and new evidence is presented here directly linking GCRs with clouds. Clouds increase the diffuse solar radiation, measured continuously at UK surface meteorological sites since 1947. The ratio of diffuse to total solar radiation-the diffuse fraction, (DF)-is used to infer cloud, and is compared with the daily mean neutron count rate measured at Climax; Colorado from 1951-2000, which provides a globally representative indicator of cosmic rays. Across the UK, oil days of high cosmic ray flux (above 3600 X 10(2) neutron counts h(-1), which occur 87% of the time on average) compared with low cosmic ray flux, (i) the chance of an overcast day increases by (19 +/- 4)%; and (ii) the diffuse fraction increases by (2 +/- 0.3)%. During sudden transient reductions in cosmic rays (e.g. Forbush events), simultaneous decreases occur in the diffuse fraction. The diffuse radiation changes are; therefore; unambiguously due to cosmic rays. Although the statistically significant nonlinear cosmic ray effect is small, it will have a considerably larger aggregate effect on longer timescale (e.g. centennial) climate variations when day-to-day variability averages out.

Linear and nonlinear microrheology of dense colloidal suspensions

The length and time scales accessible to optical tweezers make them an ideal tool for the examination of colloidal systems. Embedded high-refractive-index tracer particles in an index-matched hard sphere suspension provide 'handles' within the system to investigate the mechanical behaviour. Passive observations of the motion of a single probe particle give information about the linear response behaviour of the system, which can be linked to the macroscopic frequency-dependent viscous and elastic moduli of the suspension. Separate 'dragging' experiments allow observation of a sample's nonlinear response to an applied stress on a particle-by particle basis. Optical force measurements have given new data about the dynamics of phase transitions and particle interactions; an example in this study is the transition from liquid-like to solid-like behaviour, and the emergence of a yield stress and other effects attributable to nearest-neighbour caging effects. The forces needed to break such cages and the frequency of these cage breaking events are investigated in detail for systems close to the glass transition.

The two-dimensional anharmonic oscillator II: the microwave spectrum of silyl isocyanate, SiH3NCO

The J + 1 ← J transitions (J = 2, 3, 4, 5, and 6) in the microwave spectrum of SiH3NCO have been assigned for the vibrational ground state and for the vibrational states v10 = 1, 2, and 3. The results for v10 = 0 confirm earlier work. The vibration-rotation constants show a remarkable variation with v10 and l10. To a large extent the anomalous behavior of these constants has been explained in terms of a strongly anharmonic potential function for the ν10 vibrational mode.

The two-dimensional anharmonic oscillator III: the CCC bending mode of C3O2

Newly observed data on the rotational constants of carbon suboxide in excited vibrational states of the low-wavenumber bending vibration ν7 have been successfully interpreted in terms of the two-dimensional anharmonic oscillator wavefunctions associated with this vibration. By combining these results with published infrared and Raman spectra the vibrational assignment has been extended and a refined bending potential for ν7 has been derived: this has a minimum at a bending angle of about 24° at the central C atom, with an energy maximum at the linear configuration some 23 cm−1 above the minimum. From similar data on the combination and hot bands of ν7 with ν4 (1587 cm−1) and ν2 (786 cm−1) the effective ν7 bending potential has also been determined in the one-quantum excited states of ν4 and ν2. The effective ν7 potential shows significant changes from the ground vibrational state; the central hump in the ν7 potential surface is increased to about 50 cm−1 in the v4 = 1 state, and decreased to about 1 cm−1 in the v2 = 1 state. In the light of these results vibrational assignments are suggested for most of the observed bands in the infrared and Raman spectra of C3O2.

The two-dimensional anharmonic oscillator I: vibration-rotation constants of fulminic acid, HCNO

The lowest-wavenumber vibration of HCNO and DCNO, ν5, is known to involve a largeamplitude low-frequency anharmonic bending of the CH bond against the CNO frame. In this paper the anomalous vibrational dependence of the observed rotational constants B(v5, l5), and of the observed l-doubling interactions, is interpreted according to a simple effective vibration-rotation Hamiltonian in which the appropriate vibrational operators are averaged in an anharmonic potential surface over the normal coordinates (Q5x, Q5y). All of the data on both isotopes are interpreted according to a single potential surface having a minimum energy at a slightly bent configuration of the HCN angle ( 170°) with a maximum at the linear configuration about 2 cm−1 higher. The other coefficients in the Hamiltonian are also interpreted in terms of the structure and the harmonic and anharmonic force fields; the substitution structure at the “hypothetical linear configuration” determined in this way gives a CH bond length of 1.060 Å, in contrast to the value 1.027 Å determined from the ground-state rotational constants. We also discuss the difficulties in rationalizing our effective Hamiltonian in terms of more fundamental theory, as well as the success and limitations of its use in practice.

Two-dimensional anharmonic oscillator: application to 2,5-dihydrofuran

A program has been developed to calculate the energy levels and corresponding wavefunctions for a two‐dimensional anharmonic potential surface of at least C2v symmetry. This program has been employed to explain the high resolution splittings observed in the far infrared spectrum of 2,5‐dihydrofuran. The magnitude of the cross term connecting the ring‐twisting and ring‐puckering modes of 2,5‐dihydrofuran is sufficiently large to be significant. The potential surface determined also suggests that the ring‐twisting mode may be slightly anharmonic.

Initial boundary value problems for the nonlinear Schrödinger equation

A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.

Bayesian estimation and selection of nonlinear vector error correction models: The case of the sugar-ethanol-oil nexus in Brazil

Nonlinear adjustment toward long-run price equilibrium relationships in the sugar-ethanol-oil nexus in Brazil is examined. We develop generalized bivariate error correction models that allow for cointegration between sugar, ethanol, and oil prices, where dynamic adjustments are potentially nonlinear functions of the disequilibrium errors. A range of models are estimated using Bayesian Monte Carlo Markov Chain algorithms and compared using Bayesian model selection methods. The results suggest that the long-run drivers of Brazilian sugar prices are oil prices and that there are nonlinearities in the adjustment processes of sugar and ethanol prices to oil price but linear adjustment between ethanol and sugar prices.

Inclusion of nonlinear demand-supply relationships within large-scale partial equilibrium linear programming models

This paper presents a new method for the inclusion of nonlinear demand and supply relationships within a linear programming model. An existing method for this purpose is described first and its shortcomings are pointed out before showing how the new approach overcomes those difficulties and how it provides a more accurate and 'smooth' (rather than a kinked) approximation of the nonlinear functions as well as dealing with equilibrium under perfect competition instead of handling just the monopolistic situation. The workings of the proposed method are illustrated by extending a previously available sectoral model for the UK agriculture.