Phase Mixing of Alfvén Waves Near a 2D Magnetic Null Point

The propagation of linear Alfvén wave pulses in an inhomogeneous plasma near a 2D coronal null point is investigated. When a uniform plasma density is considered, it is seen that an initially planar Alfvén wavefront remains planar, despite the varying equilibrium Alfvén speed, and that all the wave collects at the separatrices. Thus, in the non-ideal case, these Alfvénic disturbances preferentially dissipate their energy at these locations. For a non-uniform equilibrium density, it is found that the Alfvén wavefront is significantly distorted away from the initially planar geometry, inviting the possibility of dissipation due to phase mixing. Despite this however, we conclude that for the Alfvén wave, current density accumulation and preferential heating still primarily occur at the separatrices, even when an extremely non-uniform density profile is considered

State-dependence of climate sensitivity: attractor constraints and palaeoclimate regimes

Equilibrium climate sensitivity (ECS) is a key predictor of climate change. However, it is not very well constrained, either by climate models or by observational data. The reasons for this include strong internal variability and forcing on many time scales. In practise this means that the 'equilibrium' will only be relative to fixing the slow feedback processes before comparing palaeoclimate sensitivity estimates with estimates from model simulations. In addition, information from the late Pleistocene ice age cycles indicates that the climate cycles between cold and warm regimes, and the climate sensitivity varies considerably between regime because of fast feedback processes changing relative strength and time scales over one cycle. In this paper we consider climate sensitivity for quite general climate dynamics. Using a conceptual Earth system model of Gildor and Tziperman (2001) (with Milankovich forcing and dynamical ocean biogeochemistry) we explore various ways of quantifying the state-dependence of climate sensitivity from unperturbed and perturbed model time series. Even without considering any perturbations, we suggest that climate sensitivity can be usefully thought of as a distribution that quantifies variability within the 'climate attractor' and where there is a strong dependence on climate state and more specificially on the 'climate regime' where fast processes are approximately in equilibrium. We also consider perturbations by instantaneous doubling of CO$_2$ and similarly find a strong dependence on the climate state using our approach.Comment: 32 pages, 10 figure

Moving walls accelerate mixing

Mixing in viscous fluids is challenging, but chaotic advection in principle allows efficient mixing. In the best possible scenario,the decay rate of the concentration profile of a passive scalar should be exponential in time. In practice, several authors have found that the no-slip boundary condition at the walls of a vessel can slow down mixing considerably, turning an exponential decay into a power law. This slowdown affects the whole mixing region, and not just the vicinity of the wall. The reason is that when the chaotic mixing region extends to the wall, a separatrix connects to it. The approach to the wall along that separatrix is polynomial in time and dominates the long-time decay. However, if the walls are moved or rotated, closed orbits appear, separated from the central mixing region by a hyperbolic fixed point with a homoclinic orbit. The long-time approach to the fixed point is exponential, so an overall exponential decay is recovered, albeit with a thin unmixed region near the wall.Comment: 17 pages, 13 figures. PDFLaTeX with RevTeX 4-1 styl

Optimal mixing enhancement

We introduce a general-purpose method for optimising the mixing rate of advective fluid flows. An existing velocity field is perturbed in a $C^1$ neighborhood to maximize the mixing rate for flows generated by velocity fields in this neighborhood. Our numerical approach is based on the infinitesimal generator of the flow and is solved by standard linear programming methods. The perturbed flow may be easily constrained to preserve the same steady state distribution as the original flow, and various natural geometric constraints can also be simply applied. The same technique can also be used to optimize the mixing rate of advection-diffusion flow models by manipulating the drift term in a small neighborhood

Kinetics of binding and geometry of cells on molecular biochips

We examine how the shape of cells and the geometry of experiment affect the reaction-diffusion kinetics at the binding between target and probe molecules on molecular biochips. In particular, we compare the binding kinetics for the probes immobilized on surface of the semispherical and flat circular cells, the limit of thin slab of analyte solution over probe cell as well as hemispherical gel pads and cells printed in gel slab over a substrate. It is shown that hemispherical geometry provides significantly faster binding kinetics and ensures more spatially homogeneous distribution of local (from a pixel) signals over a cell in the transient regime. The advantage of using thin slabs with small volume of analyte solution may be hampered by the much longer binding kinetics needing the auxiliary mixing devices. Our analysis proves that the shape of cells and the geometry of experiment should be included to the list of essential factors at biochip designing.Comment: 10 pages, 1 figur

Autoignition in nonpremixed flow

The objective of this investigation has been to improve understanding of autoignition processes in nonpremixed flow fields of the types encountered in Diesel-engine ignition, through theoretical analyses that employ asymptotic methods of applied mathematics. The work was intended to develop formulas and equations that can be used in activities of applied research, such as code development, aimed at providing tools useful for the design of Diesel engines. The formulas may also be used directly for ignition estimates.Characteristic time scales were identified for these ignition problems. Their relative magnitudes were employed to define different regimes of ignition and to obtain simplified partial differential equations that describe ignition in these regimes. Effects of turbulence on ignition were addressed. Special attention was devoted to unsteady mixing layers, involving both variable strain and variable pressure, for which ignition-time formulas were derived. In addition, ignition analyses were completed for variable-volume chambers with arbitrary initial spatial variations of temperature and composition, to determine pressure histories produced by ignition-front propagation. These studies were based on one-step, Arrhenius approximations for the chemical kinetics and were restricted to ignition stages that precede ordinary flame propagation. Additional work considered triple-flame propagation that can odcur in mixing layers after ignition, with this same chemical-kinetic description, and asymptotic analysis of n-heptane ignition on the basis of a four-step, semi-empirical model for the chemical kinetics. In this latter study, the region of negative effective overall activation energy, between 800 K and 1100 K, was identified as exhibiting unusual ignition dynamics, and the asymptotic ignition-time formulas were shown to give good agreement with predictions of numerical integrations. This research has helped to strengthen the foundations of ignition theory for nonuniform media. It provided simplified descriptions of ignition processes that can be employed in studies of Diesel combustion that are oriented more towards development than are the present investigations. The asymptotic methods employed in this work thus appear capable of providing quite useful results

The Runaway Greenhouse: A History of Water on Venus

Radiative-convective equilibrium models of planetary atmospheres are discussed for the case when the infrared opacity is due to a vapor in equilibrium with its liquid or solid phase. For a grey gas, or for a gas which absorbs at all infrared wavelengths, equilibrium is impossible when the solar constant exceeds a critical value. Equilibrium therefore requires that the condensed phase evaporates into the atmosphere. Moist adiabatic and pseudoadiabatic atmospheres in which the condensing vapor is a major atmospheric constituent are considered. This situation would apply if the solar constant were supercritical with respect to an abundant substance such as water. It is shown that the condensing gas would be a major constituent at all levels in such an atmosphere. Photodissociation of water in the primordial Venus atmosphere is discussed in this context