The Effect of Geocenter Motion on Jason-2 Orbits and the Mean Sea Level

We compute a series of Jason-2 GPS and SLR/DORIS-based orbits using ITRF2005 and the std0905 standards (Lemoine et al. 2010). Our GPS and SLR/DORIS orbit data sets span a period of 2 years from cycle 3 (July 2008) to cycle 74 (July 2010). We extract the Jason-2 orbit frame translational parameters per cycle by the means of a Helmert transformation between a set of reference orbits and a set of test orbits. We compare the annual terms of these time-series to the annual terms of two different geocenter motion models where biases and trends have been removed. Subsequently, we include the annual terms of the modeled geocenter motion as a degree-1 loading displacement correction to the GPS and SLR/DORIS tracking network of the POD process. Although the annual geocenter motion correction would reflect a stationary signal in time, under ideal conditions, the whole geocenter motion is a non-stationary process that includes secular trends. Our results suggest that our GSFC Jason-2 GPS-based orbits are closely tied to the center of mass (CM) of the Earth consistent with our current force modeling, whereas GSFC's SLR/DORIS-based orbits are tied to the origin of ITRF2005, which is the center of figure (CF) for sub-secular scales. We quantify the GPS and SLR/DORIS orbit centering and how this impacts the orbit radial error over the globe, which is assimilated into mean sea level (MSL) error, from the omission of the annual term of the geocenter correction. We find that for the SLR/DORIS std0905 orbits, currently used by the oceanographic community, only the negligence of the annual term of the geocenter motion correction results in a 4.67 plus or minus 3.40 mm error in the Z-component of the orbit frame which creates 1.06 plus or minus 2.66 mm of systematic error in the MSL estimates, mainly due to the uneven distribution of the oceans between the North and South hemisphere

Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

How Coupling Determines the Entrainment of Circadian Clocks

Autonomous circadian clocks drive daily rhythms in physiology and behaviour. A network of coupled neurons, the suprachiasmatic nucleus (SCN), serves as a robust self-sustained circadian pacemaker. Synchronization of this timer to the environmental light-dark cycle is crucial for an organism's fitness. In a recent theoretical and experimental study it was shown that coupling governs the entrainment range of circadian clocks. We apply the theory of coupled oscillators to analyse how diffusive and mean-field coupling affects the entrainment range of interacting cells. Mean-field coupling leads to amplitude expansion of weak oscillators and, as a result, reduces the entrainment range. We also show that coupling determines the rigidity of the synchronized SCN network, i.e. the relaxation rates upon perturbation. %(Floquet exponents). Our simulations and analytical calculations using generic oscillator models help to elucidate how coupling determines the entrainment of the SCN. Our theoretical framework helps to interpret experimental data

Circadian Rhythm and Sleep Disruption: Causes, Metabolic Consequences and Countermeasures.

Circadian (∼ 24 hour) timing systems pervade all kingdoms of life, and temporally optimize behaviour and physiology in humans. Relatively recent changes to our environments, such as the introduction of artificial lighting, can disorganize the circadian system, from the level of the molecular clocks that regulate the timing of cellular activities to the level of synchronization between our daily cycles of behaviour and the solar day. Sleep/wake cycles are intertwined with the circadian system, and global trends indicate that these too are increasingly subject to disruption. A large proportion of the world's population is at increased risk of environmentally-driven circadian rhythm and sleep disruption, and a minority of individuals are also genetically predisposed to circadian misalignment and sleep disorders. The consequences of disruption to the circadian system and sleep are profound and include myriad metabolic ramifications, some of which may be compounded by adverse effects on dietary choices. If not addressed, the deleterious effects of such disruption will continue to cause widespread health problems; therefore, implementation of the numerous behavioural and pharmaceutical interventions that can help restore circadian system alignment and enhance sleep will be important

Wave trains in an excitable FitzHugh Nagumo model Bistable dispersion relation and formation of isolas

We investigate the dispersion relations of nonlinear periodic wave trains in excitable systems which describe the dependence of the propagation velocity on the wavelength. Pulse interaction by oscillating pulse tails within a wave train leads to bistable wavelength bands, in which two stable and one unstable wave train coexist for the same wavelength. Essential spectra of the unstable wave trains exhibit a circle of eigenvalues with positive real parts. We describe the destruction of the bistable dispersion curve and the formation of isolas of wave trains in a sequence of transcritical bifurcations unfolding into pairs of saddle node bifurcations. It turns out that additional dispersion curves of unstable wave trains play an important role in the destruction of the bistable dispersion curv

Synchronization of cardiorhythm by weak external forcing

We study the possibility to synchronize cardiorhythm of a human by periodic and aperiodic sequences of light and sound pulses. Aperiodic forcing is defined by variation of RR intervals of another subject. Phase locking between cardiorhythm and weak external forcing is detected on finite time intervals. We observe the 1:1 synchronization for periodic forcing and n:m synchronization for aperiodic one