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Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests.
Excitable solitons
(2020)
Excitable pulses are among the most widespread dynamical patterns that occur in many different systems, ranging from biological cells to chemical reactions and ecological populations. Traditionally, the mutual annihilation of two colliding pulses is regarded as their prototypical signature. Here we show that colliding excitable pulses may exhibit solitonlike crossover and pulse nucleation if the system obeys a mass conservation constraint. In contrast to previous observations in systems without mass conservation, these alternative collision scenarios are robustly observed over a wide range of parameters. We demonstrate our findings using a model of intracellular actin waves since, on time scales of wave propagations over the cell scale, cells obey conservation of actin monomers. The results provide a key concept to understand the ubiquitous occurrence of actin waves in cells, suggesting why they are so common, and why their dynamics is robust and long-lived.
Corona and the climate
(2020)
What is the optimal distribution of two types of crystalline phases on the surface of icosahedral shells, such as of many viral capsids? We here investigate the distribution of a thin layer of soft material on a crystalline convex icosahedral shell. We demonstrate how the shapes of spherical viruses can be understood from the perspective of elasticity theory of thin two-component shells. We develop a theory of shape transformations of an icosahedral shell upon addition of a softer, but still crystalline, material onto its surface. We show how the soft component "invades" the regions with the highest elastic energy and stress imposed by the 12 topological defects on the surface. We explore the phase diagram as a function of the surface fraction of the soft material, the shell size, and the incommensurability of the elastic moduli of the rigid and soft phases. We find that, as expected, progressive filling of the rigid shell by the soft phase starts from the most deformed regions of the icosahedron. With a progressively increasing soft-phase coverage, the spherical segments of domes are filled first (12 vertices of the shell), then the cylindrical segments connecting the domes (30 edges) are invaded, and, ultimately, the 20 flat faces of the icosahedral shell tend to be occupied by the soft material. We present a detailed theoretical investigation of the first two stages of this invasion process and develop a model of morphological changes of the cone structure that permits noncircular cross sections. In conclusion, we discuss the biological relevance of some structures predicted from our calculations, in particular for the shape of viral capsids.
The paper is motivated by some inconsistencies and contradictions present in the literature on the calculation of the so-called diffraction elastic constants. In an attempt at unifying the views that the two communities of Materials Science and Mechanics of Materials have on the subject, we revisit and define the terminology used in the field. We also clarify the limitations of the commonly used approaches and show that a unified methodology is also applicable to textured materials with a nearly arbitrary grain shape. We finally compare the predictions based on this methodology with experimental data obtained by in situ synchrotron radiation diffraction on additively manufactured Ti-6Al-4V alloy. We show that (a) the transverse isotropy of the material yields good agreement between the best-fit isotropy approximation (equivalent to the classic Kroner's model) and the experimental data and (b) the use of a general framework allows the calculation of all components of the tensor of diffraction elastic constants, which are not easily measurable by diffraction methods. This allows us to extend the current state-of-the-art with a predictive tool.
A very small fraction of (runaway) massive stars have masses exceeding 60-70 M-circle dot and are predicted to evolve as luminous blue variable and Wolf-Rayet stars before ending their lives as core-collapse supernovae. Our 2D axisymmetric hydrodynamical simulations explore how a fast wind (2000 km s(-1)) and high mass-loss rate (10(-5)M(circle dot) yr(-1)) can impact the morphology of the circumstellar medium. It is shaped as 100 pc-scale wind nebula that can be pierced by the driving star when it supersonically moves with velocity 20-40 km s(-1) through the interstellar medium (ISM) in the Galactic plane. The motion of such runaway stars displaces the position of the supernova explosion out of their bow shock nebula, imposing asymmetries to the eventual shock wave expansion and engendering Cygnus-loop-like supernova remnants. We conclude that the size (up to more than 200 pc) of the filamentary wind cavity in which the chemically enriched supernova ejecta expand, mixing efficiently the wind and ISM materials by at least 10 per cent in number density, can be used as a tracer of the runaway nature of the very massive progenitors of such 0.1Myr old remnants. Our results motivate further observational campaigns devoted to the bow shock of the very massive stars BD+43 degrees 3654 and to the close surroundings of the synchrotron-emitting Wolf-Rayet shell G2.4+1.4.
We study a distribution of times of the first arrivals to absorbing targets in turbulent diffusion, which is due to a multiplicative noise. Two examples of dynamical systems with a multiplicative noise are studied. The first one is a random process according to inhomogeneous diffusion, which is also known as a geometric Brownian motion in the Black-Scholes model. The second model is due to a random processes on a two-dimensional comb, where inhomogeneous advection is possible only along the backbone, while Brownian diffusion takes place inside the branches. It is shown that in both cases turbulent diffusion takes place as the one-dimensional random process with the log-normal distribution in the presence of absorbing targets, which are characterized by the Levy-Smirnov distribution for the first hitting times.
Whereas stable homogenous states of aqueous hydrocarbon solutions are typically observed at high temperatures and pressures far beyond the critical values corresponding to individual components, the stability of such system may be preserved upon transition into the region of metastable states at low temperatures and low pressures. This work is dedicated to the study of the thermal stability of a water-methane mixture formed by cryogenic vapor phase deposition. The obtained thin films were studied using vibrational spectroscopy in the temperature range of 16-180 K. During thermal annealing of the samples, characteristic vibrational C-H modes of methane were monitored alongside the chamber pressure to register both structural changes and desorption of the film material. The obtained results reveal that upon the co-deposition of methane and water, methane molecules appear both in non-bound and trapped states. The observed broadening of the characteristic C-H stretching mode at 3010 cm(-1) upon an increase in temperature of the sample from 16 to 90 K, followed by narrowing of the peak as the temperature is reduced back to 16 K, indicates localization of methane molecules within the water matrix at lower temperatures.
The Paris Climate Agreement aims to keep temperature rise well below 2 degrees C. This implies mitigation costs as well as avoided climate damages. Here we show that independent of the normative assumptions of inequality aversion and time preferences, the agreement constitutes the economically optimal policy pathway for the century. To this end we consistently incorporate a damage-cost curve reproducing the observed relation between temperature and economic growth into the integrated assessment model DICE. We thus provide an intertemporally optimizing cost-benefit analysis of this century's climate problem. We account for uncertainties regarding the damage curve, climate sensitivity, socioeconomic future, and mitigation costs. The resulting optimal temperature is robust as can be understood from the generic temperature-dependence of the mitigation costs and the level of damages inferred from the observed temperature-growth relationship. Our results show that the politically motivated Paris Climate Agreement also represents the economically favourable pathway, if carried out properly.