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Comment on "Bias correction, quantile mapping, and downscaling: revisiting the inflation issue"
(2014)
In a recent paper, Maraun describes the adverse effects of quantile mapping on downscaling. He argues that when large-scale GCM variables are rescaled directly to small-scale fields or even station data, genuine small-scale covariability is lost and replaced by uniform variability inherited from the larger scales. This leads to a misrepresentation mainly of areal means and long-term trends. This comment acknowledges the former point, although the argument is relatively old, but disagrees with the latter, showing that grid-size long-term trends can be different from local trends. Finally, because it is partly incorrectly addressed, some clarification is added regarding the inflation issue, stressing that neither randomization nor inflation is free of unverified assumptions.
We argue that the theories of Volokitin and Persson (2014 New J. Phys. 16 118001), Dedkov and Kyasov (2008 J. Phys.: Condens. Matter 20 354006), and Pieplow and Henkel (2013 New J. Phys. 15 023027) agree on the electromagnetic force on a small, polarizable particle that is moving parallel to a planar, macroscopic body, as far as the contribution of evanescent waves is concerned. The apparent differences are discussed in detail and explained by choices of units and integral transformations. We point out in particular the role of the Lorentz contraction in the procedure used by Volokitin and Persson, where a macroscopic body is 'diluted' to obtain the force on a small particle. Differences that appear in the contribution of propagating photons are briefly mentioned.
Introducing the CTA concept
(2013)
The Cherenkov Telescope Array (CTA) is a new observatory for very high-energy (VHE) gamma rays. CTA has ambitions science goals, for which it is necessary to achieve full-sky coverage, to improve the sensitivity by about an order of magnitude, to span about four decades of energy, from a few tens of GeV to above 100 TeV with enhanced angular and energy resolutions over existing VHE gamma-ray observatories. An international collaboration has formed with more than 1000 members from 27 countries in Europe, Asia, Africa and North and South America. In 2010 the CTA Consortium completed a Design Study and started a three-year Preparatory Phase which leads to production readiness of CTA in 2014. In this paper we introduce the science goals and the concept of CTA, and provide an overview of the project.
Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook
A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The most unstable perturbation is the two-dimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode is followed up to a time-asymptotic steady state, which proves to be sensitive to three-dimensional perturbations even close to the point where the primary instability sets in. A comprehensive three-dimensional stability analysis of the two-dimensional steady tearing-mode state is performed by varying parameters of the sheet pinch. The instability with respect to three-dimensional perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the system parameters, the unstably perturbed state is followed up in its nonlinear evolution and is found to approach a three-dimensional steady state.
We investigate numerically the appearance of heteroclinic behavior in a three-dimensional, buoyancy-driven fluid layer with stress-free top and bottom boundaries, a square horizontal periodicity with a small aspect ratio, and rotation at low to moderate rates about a vertical axis. The Prandtl number is 6.8. If the rotation is not too slow, the skewed-varicose instability leads from stationary rolls to a stationary mixed-mode solution, which in turn loses stability to a heteroclinic cycle formed by unstable roll states and connections between them. The unstable eigenvectors of these roll states are also of the skewed-varicose or mixed-mode type and in some parameter regions skewed-varicose like shearing oscillations as well as square patterns are involved in the cycle. Always present weak noise leads to irregular horizontal translations of the convection pattern and makes the dynamics chaotic, which is verified by calculating Lyapunov exponents. In the nonrotating case, the primary rolls lose, depending on the aspect ratio, stability to traveling waves or a stationary square pattern. We also study the symmetries of the solutions at the intermittent fixed points in the heteroclinic cycle.
The nonlinear interaction of waves excited by the modified two-stream instability (Farley-Buneman instability) is considered. It is found that, during the linear stage of wave growth, the enhanced pressure of the high-frequency part of the waves locally generates a ponderomotive force. This force acts on the plasma particles and redistributes them. Thus an additional electrostatic polarization field occurs, which influences the low-frequency part of the waves. Then, the low-frequency waves also cause a redistribution of the high-frequency waves. In the paper, a self-consistent system of equations is obtained, which describes the nonlinear interaction of the waves. It is shown that the considered mechanism of wave interaction causes a nonlinear stabilization of the high-frequency waves’ growth and a formation of local density structures of the charged particles. The density modifications of the charged particles during the non-linear stage of wave growth and the possible interval of aspect angles of the high-frequency waves are estimated.
The aim of this paper is to describe an efficient strategy for descritizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips-regularization χ^δ α = (a * a + α I)^-1 A * y ^δ with a finite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing A n compared with standard methods.
We have numerically studied the bifurcations and transition to chaos in a two-dimensional fluid for varying values of the Reynolds number. These investigations have been motivated by experiments in fluids, where an array of vortices was driven by an electromotive force. In these experiments, successive changes leading to a complex motion of the vortices, due to increased forcing, have been explored [Tabeling, Perrin, and Fauve, J. Fluid Mech. 213, 511 (1990)]. We model this experiment by means of two-dimensional Navier-Stokes equations with a special external forcing, driving a linear chain of eight counter-rotating vortices, imposing stress-free boundary conditions in the vertical direction and periodic boundary conditions in the horizontal direction. As the strength of the forcing or the Reynolds number is raised, the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. Several steady states and periodic branches and a period doubling cascade appear on the route to chaos. For increasing values of the Reynolds number, shear flow develops, for which the spatial scale is large compared to the scale of the forcing. Furthermore, we have investigated the influence of the aspect ratio of the container as well as the effect of no-slip boundary conditions at the top and bottom, on the bifurcation scenario.
This paper deals with the electrical conductivity problem in geophysics. It is formulated as an elliptic boundary value problem of second order for a large class of bounded and unbounded domains. A special boundary condition, the so called "Complete Electrode Model", is used. Poincaré inequalities are formulated and proved in the context of weighted Sobolev spaces, leading to existence and uniqueness statements for the boundary value problem. In addition, a parameter-to-solution operator arising from the inverse conductivity problem in medicine (EIT) and geophysics is investigated mathematically and is shown to be smooth and analytic.
The stability of the quiescent ground state of an incompressible, viscous and electrically conducting fluid sheet, bounded by stress-free parallel planes and driven by an external electric field tangential to the boundaries, is studied numerically. The electrical conductivity varies as cosh–2(x1/a), where x1 is the cross-sheet coordinate and a is the half width of a current layer centered about the midplane of the sheet. For a <~ 0.4L, where L is the distance between the boundary planes, the ground state is unstable to disturbances whose wavelengths parallel to the sheet lie between lower and upper bounds depending on the value of a and on the Hartmann number. Asymmetry of the configuration with respect to the midplane of the sheet, modelled by the addition of an externally imposed constant magnetic field to a symmetric equilibrium field, acts as a stabilizing factor.
The bifurcations in a three-dimensional incompressible, electrically conducting fluid with an external forcing of the Roberts type have been studied numerically. The corresponding flow can serve as a model for the convection in the outer core of the Earth and is realized in an ongoing laboratory experiment aimed at demonstrating a dynamo effect. The symmetry group of the problem has been determined and special attention has been paid to symmetry breaking by the bifurcations. The nonmagnetic, steady Roberts flow loses stability to a steady magnetic state, which in turn is subject to secondary bifurcations. The secondary solution branches have been traced until they end up in chaotic states.
We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.
The stability of the quiescent ground state of an incompressible viscous fluid sheet bounded by two parallel planes, with an electrical conductivity varying across the sheet, and driven by an external electric field tangential to the boundaries is considered. It is demonstrated that irrespective of the conductivity profile, as magnetic and kinetic Reynolds numbers (based on the Alfvén velocity) are raised from small values, two-dimensional perturbations become unstable first.
Three-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at the top and bottom and periodic boundary conditions in the horizontal directions is investigated by means of numerical simulation and bifurcation-analysis techniques. The aspect ratio is fixed to a value of 2√2 and the Prandtl number to a value of 6.8. Two-dimensional convection rolls are found to be stable up to a Rayleigh number of 17 950, where a Hopf bifurcation leads to traveling waves. These are stable up to a Rayleigh number of 30 000, where a secondary Hopf bifurcation generates modulated traveling waves. We pay particular attention to the symmetries of the solutions and symmetry breaking by the bifurcations.