On the spectral gap of Brownian motion with jump boundary

In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one-dimensional case. Our methods are dierent and mainly probabilistic relying on coupling methods adapted to the special situation under investigation. Moreover we answer a question raised by Ben-Ari and Pinsky concerning the dependence of the spectral gap from the jump distribution in a multi-dimensional setting.

Decay to equilibrium for jump processes with heavy tails

The case is made for a more careful analysis of the large time asymptotic of infinite particle systems in the thermodynamic limit beyond zero density. The insufficiency of current analysis even in the model case of free particles is demonstrated. Recent advances based on more sophisticated analytical tools like functions of mean variation and Hardy spaces are sketched.

Jump and variance risk premia in the S&P 500

We analyze the risk premia embedded in the S&P 500 spot index and option markets. We use a long time-series of spot prices and a large panel of option prices to jointly estimate the diffusive stock risk premium, the price jump risk premium, the diffusive variance risk premium and the variance jump risk premium. The risk premia are statistically and economically significant and move over time. Investigating the economic drivers of the risk premia, we are able to explain up to 63 % of these variations.

A Tropospheric Assessment of the ERA-40, NCEP, and JRA-25 Global Reanalyses in the Polar Regions

The reliability of the global reanalyses in the polar regions is investigated. The overview stems from an April 2006 Scientific Committee on Antarctic Research (SCAR) workshop on the performance of global reanalyses in high latitudes held at the British Antarctic Survey. Overall, the skill is much higher in the Arctic than the Antarctic, where the reanalyses are only reliable in the summer months prior to the modern satellite era. In the Antarctic, large circulation differences between the reanalyses are found primarily before 1979, when vast quantities of satellite sounding data started to be assimilated. Specifically for ERA-40, this data discontinuity creates a marked jump in Antarctic snow accumulation, especially at high elevations. In the Arctic, the largest differences are related to the reanalyses depiction of clouds and their associated radiation impacts; ERA-40 captures the cloud variability much better than NCEP1 and JRA-25, but the ERA-40 and JRA-25 clouds are too optically thin for shortwave radiation. To further contrast the reanalyses skill, cyclone tracking results are presented. In the Southern Hemisphere, cyclonic activity is markedly different between the reanalyses, where there are few matched cyclones prior to 1979. In comparison, only some of the weaker cyclones are not matched in the Northern Hemisphere from 1958-2001, again indicating the superior skill in this hemisphere. Although this manuscript focuses on deficiencies in the reanalyses, it is important to note that they are a powerful tool for climate studies in both polar regions when used with a recognition of their limitations.

Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

The cumulus-capped boundary layer. II: Interface fluxes

This paper considers the relationship between the mean temperature and humidity profiles and the fluxes of heat and moisture at cloud base and the base of the inversion in the cumulus-capped boundary layer. The relationships derived are based on an approximate form of the scalar-flux budget and the scaling properties of the turbulent kinetic energy (TKE) budget. The scalar-flux budget gives a relationship between the change in the virtual potential temperature across either the cloud base transition zone or the inversion and the flux at the base of the layer. The scaling properties of the TKE budget lead to a relationship between the heat and moisture fluxes and the mean subsaturation through the liquid-water flux. The 'jump relation' for the virtual potential temperature at cloud base shows the close connection between the cumulus mass flux in the cumulus-capped boundary layer and the entrainment velocity in the dry-convective boundary layer. Gravity waves are shown to be an important feature of the inversion.

Cone model-based SEP event calculations for applications to multipoint observations

The problem of modeling solar energetic particle (SEP) events is important to both space weather research and forecasting, and yet it has seen relatively little progress. Most important SEP events are associated with coronal mass ejections (CMEs) that drive coronal and interplanetary shocks. These shocks can continuously produce accelerated particles from the ambient medium to well beyond 1 AU. This paper describes an effort to model real SEP events using a Center for Integrated Space weather Modeling (CISM) MHD solar wind simulation including a cone model of CMEs to initiate the related shocks. In addition to providing observation-inspired shock geometry and characteristics, this MHD simulation describes the time-dependent observer field line connections to the shock source. As a first approximation, we assume a shock jump-parameterized source strength and spectrum, and that scatter-free transport occurs outside of the shock source, thus emphasizing the role the shock evolution plays in determining the modeled SEP event profile. Three halo CME events on May 12, 1997, November 4, 1997 and December 13, 2006 are used to test the modeling approach. While challenges arise in the identification and characterization of the shocks in the MHD model results, this approach illustrates the importance to SEP event modeling of globally simulating the underlying heliospheric event. The results also suggest the potential utility of such a model for forcasting and for interpretation of separated multipoint measurements such as those expected from the STEREO mission.

The formation of large-scale current sheets within magnetic clouds

Magnetic clouds are a class of interplanetary coronal mass ejections (CME) predominantly characterised by a smooth rotation in the magnetic field direction, indicative of a magnetic flux rope structure. Many magnetic clouds, however, also contain sharp discontinuities within the smoothly varying magnetic field, suggestive of narrow current sheets. In this study we present observations and modelling of magnetic clouds with strong current sheet signatures close to the centre of the apparent flux rope structure. Using an analytical magnetic flux rope model, we demonstrate how such current sheets can form as a result of a cloud’s kinematic propagation from the Sun to the Earth, without any external forces or influences. This model is shown to match observations of four particular magnetic clouds remarkably well. The model predicts that current sheet intensity increases for increasing CME angular extent and decreasing CME radial expansion speed. Assuming such current sheets facilitate magnetic reconnection, the process of current sheet formation could ultimately lead a single flux rope becoming fragmented into multiple flux ropes. This change in topology has consequences for magnetic clouds as barriers to energetic particle propagation.

Magnetic cloud distortion resulting from propagation through a structured solar wind: Models and observations

Numerical simulations of magnetic clouds (MCs) propagating through a structured solar wind suggest that MC-associated magnetic flux ropes are highly distorted by inhomogeneities in the ambient medium. In particular, a solar wind configuration of fast wind from high latitudes and slow wind at low latitudes, common at periods close to solar minimum, should distort the cross section of magnetic clouds into concave-outward structures. This phenomenon has been reported in observations of shock front orientations, but not in the body of magnetic clouds. In this study an analytical magnetic cloud model based upon a kinematically distorted flux rope is modified to simulate propagation through a structured medium. This new model is then used to identify specific time series signatures of the resulting concave-outward flux ropes. In situ observations of three well studied magnetic clouds are examined with comparison to the model, but the expected concave-outward signatures are not present. Indeed, the observations are better described by the convex-outward flux rope model. This may be due to a sharp latitudinal transition from fast to slow wind, resulting in a globally concave-outward flux rope, but with convex-outward signatures on a local scale.

Intermittent release of transients in the slow solar wind: 1. Remote sensing observations

The Heliospheric Imager (HI) instruments on board the STEREO spacecraft are used to analyze the solar wind during August and September 2007. We show how HI can be used to image the streamer belt and, in particular, the variability of the slow solar wind which originates inside and in the vicinity of the streamer belt. Intermittent mass flows are observed in HI difference images, streaming out along the extension of helmet streamers. These flows can appear very differently in images: plasma distributed on twisted flux ropes, V‐shaped structures, or “blobs.” The variety of these transient features may highlight the richness of phenomena that could occur near helmet streamers: emergence of flux ropes, reconnection of magnetic field lines at the tip of helmet streamers, or disconnection of open magnetic field lines. The plasma released with these transient events forms part of the solar wind in the higher corona; HI observations show that these transients are frequently entrained by corotating interaction regions (CIRs), leading to the formation of larger, brighter plasma structures in HI images. This entrainment is used to estimate the trajectory of these plasma ejecta. In doing so, we demonstrate that successive transients can be entrained by the same CIR in the high corona if they emanate from the same corotating source. Some parts of the streamers are more effective sources of transients than others. Surprisingly, evidence is given for the outflow of a recurring twisted magnetic structure, suggesting that the emergence of flux ropes can be recurrent.

How soccer players head the ball: a test of optic acceleration cancellation theory with virtual reality

We measured the movements of soccer players heading a football in a fully immersive virtual reality environment. In mid-flight the ball’s trajectory was altered from its normal quasi-parabolic path to a linear one, producing a jump in the rate of change of the angle of elevation of gaze (α) from player to ball. One reaction time later the players adjusted their speed so that the rate of change of α increased when it had been reduced and reduced it when it had been increased. Since the result of the player’s movement was to regain a value of the rate of change close to that before the disturbance, the data suggest that the players have an expectation of, and memory for, the pattern that the rate of change of α will follow during the flight. The results support the general claim that players intercepting balls use servo control strategies and are consistent with the particular claim of Optic Acceleration Cancellation theory that the servo strategy is to allow α to increase at a steadily decreasing rate.

Modelling the cabling of rope systems

This paper presents a theoretical model of the torsional characteristics of parallel multi-part rope systems. In such systems, the ropes may cable, or wrap around each other, depending on the combination of applied torque, rope tension, length and spacing between the rope parts. Cabling constitutes a failure that might be retrievable but as such can seriously affect the performance of the rope system. The torsional characteristics of the system are very different before and after cabling, and theoretical models are given for both situations. Laboratory tests were performed on both two and four rope systems, with measurements being made of torque at rotations from 0 to 360 deg. Tests were run with different rope spacings, tensions and lengths and the results compared with predictions from the theoretical model. The conclusion from the test results was that the theoretical model predicts both the pre- and post-cabling torsional behaviour with an acceptable level of accuracy.

Torsional interactions between mooring line components

Six strand ropes generate torque under tension. This can lead to transfer of twist to other mooring line components, either permanently, or dynamically. The effects of this imposed twist can seriously affect strength and fatigue endurance. In order to predict the torsional interactions between components it is necessary to quantify the tension/torsion behavior of all the different categories of mooring line component, not just the six strand rope. This paper discusses the problems of torsional interaction and presents results of measurements of tension/torsion behavior of six strand rope, stud link chain and a PET fiber rope.

An analysis of arithmetic averaging in approximate Riemann solvers with an application to steady, supercritical flows

An analysis of various arithmetic averaging procedures for approximate Riemann solvers is made with a specific emphasis on efficiency and a jump capturing property. The various alternatives discussed are intended for future work, as well as the more immediate problem of steady, supercritical free-surface flows. Numerical results are shown for two test problems.