Nonlinear transient waves in coupled phase oscillators with inertia

Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.Comment: 12 pages, 4 figure

Amplitude bounds for biochemical oscillators

We present a practical method to obtain bounds for the oscillation minima and maxima of large classes of biochemical oscillator models that generate oscillations through a negative feedback. These bounds depend on the feedback nonlinearity and are independent of explicit or effective feedback delays. For specific systems, we obtain explicit analytical expressions for the bounds and demonstrate their effectiveness in comparison with numerical simulations.Comment: 6 pages, 4 figure

Sequential pattern formation governed by signaling gradients

Rhythmic and sequential segmentation of the embryonic body plan is a vital developmental patterning process in all vertebrate species. However, a theoretical framework capturing the emergence of dynamic patterns of gene expression from the interplay of cell oscillations with tissue elongation and shortening and with signaling gradients, is still missing. Here we show that a set of coupled genetic oscillators in an elongating tissue that is regulated by diffusing and advected signaling molecules can account for segmentation as a self-organized patterning process. This system can form a finite number of segments and the dynamics of segmentation and the total number of segments formed depend strongly on kinetic parameters describing tissue elongation and signaling molecules. The model accounts for existing experimental perturbations to signaling gradients, and makes testable predictions about novel perturbations. The variety of different patterns formed in our model can account for the variability of segmentation between different animal species.Comment: 12 pages, 5 figure

Multi-Scale Entropy Analysis as a Method for Time-Series Analysis of Climate Data

Evidence is mounting that the temporal dynamics of the climate system are changing at the same time as the average global temperature is increasing due to multiple climate forcings. A large number of extreme weather events such as prolonged cold spells, heatwaves, droughts and floods have been recorded around the world in the past 10 years. Such changes in the temporal scaling behaviour of climate time-series data can be difficult to detect. While there are easy and direct ways of analysing climate data by calculating the means and variances for different levels of temporal aggregation, these methods can miss more subtle changes in their dynamics. This paper describes multi-scale entropy (MSE) analysis as a tool to study climate time-series data and to identify temporal scales of variability and their change over time in climate time-series. MSE estimates the sample entropy of the time-series after coarse-graining at different temporal scales. An application of MSE to Central European, variance-adjusted, mean monthly air temperature anomalies (CRUTEM4v) is provided. The results show that the temporal scales of the current climate (1960–2014) are different from the long-term average (1850–1960). For temporal scale factors longer than 12 months, the sample entropy increased markedly compared to the long-term record. Such an increase can be explained by systems theory with greater complexity in the regional temperature data. From 1961 the patterns of monthly air temperatures are less regular at time-scales greater than 12 months than in the earlier time period. This finding suggests that, at these inter-annual time scales, the temperature variability has become less predictable than in the past. It is possible that climate system feedbacks are expressed in altered temporal scales of the European temperature time-series data. A comparison with the variance and Shannon entropy shows that MSE analysis can provide additional information on the statistical properties of climate time-series data that can go undetected using traditional method

200years of European temperature variability: insights from and tests of the proxy surrogate reconstruction analog method

Spatially resolved climate reconstructions are commonly derived from long instrumental series and proxy data via linear regression based approaches that use the main modes of the climate system. Such reconstructions have been shown to underestimate climate variability and are based upon the assumption that the main modes of climate variability are stationary back in time. Climate models simulate physically consistent climate fields but cannot be taken to represent the real past climate trajectory because of their necessarily simplified scope and chaotic internal variability. Here, we present sensitivity tests of, and a 200-year temperature reconstruction from, the PSR (Proxy Surrogate Reconstruction) method. This method simultaneously capitalizes on the individual strengths of instrumental/proxy data based reconstructions and model simulations by selecting the model states (analogs) that are most similar with proxy/instrumental data available at specific places and specific moments of time. Sensitivity experiments reveal an optimal PSR configuration and indicate that 6,500 simulation years of existing climate models provide a sufficient pool of possible analogs to skillfully reconstruct monthly European temperature fields during the past 200years. Reconstruction verification based upon only seven instrumental stations indicates potential for extensions back in time using sparse proxy data. Additionally the PSR method allows evaluation of single time series, in this case the homogeneity of instrumental series, by identifying inconsistencies with the reconstructed climate field. We present an updated European temperature reconstruction including newly homogenized instrumental records performed with the computationally efficient PSR method that proves to capture the total variance of the targe

Three-dimensional submerged wall jets and their transition to density flows: Morphodynamics and implications for the depositional record

Jets that expand from an orifice into an ambient water body represent a basic flow model for depositional environments related to expanding flows. Momentum-dominated jets evolve into gravity-dominated density flows. To understand this transition and its sedimentological relevance, three-dimensional tank experiments with submerged wall jets were conducted, systematically varying parameters such as the initial density difference, bed slope, grain size and sediment supply. Bedform successions could be subdivided into those related to the jet and those related to the density flow. Jet deposits included early-stage bedforms, scours and mouth bars. Early-stage bedforms are asymmetrical dunes that spread concentrically from the orifice. Sediment entrainment by eddies from the expanding jets led to the formation of scours and mouth bars. Flows with lesser initial density difference produced more elongate scours. Conversely, scours became deeper for denser incoming flows. Coarser-grained sediment caused the formation of higher and steeper mouth bars and vice versa. The transition from momentum-dominated jets to gravity-dominated density flows occurred approximately at the mouth-bar crest. Hydraulic jumps were absent in the expanding jet regions and at the transitions to density flows. Instead, complex flow patterns and circulations were inferred from the velocity measurements within the scour and at the mouth-bar crests. Bedform trains related to the density flow were controlled by the grain size and sediment supply. Coarse-grained sediment and high supply rates caused strong mouth-bar aggradation and flow splitting, leading to the formation of bedform trains laterally adjacent to the mouth bar. Fine-grained sediment and low supply rates caused the formation of bedform trains downflow of the mouth bar. The symmetrical bedforms deposited by the density flows always displayed an in-phase relationship with the flow, indicating that they were antidunes. The experimental jet deposits resemble successions known from subaqueous ice-contact fans and deep water channel-lobe transition zones