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Spectral analysis of localized rotating waves in parabolic systems.

ABSTRACT: In this paper, we study the spectra and Fredholm properties of Ornstein-Uhlenbeck operators [Formula: see text]where [Formula: see text] is the profile of a rotating wave satisfying [Formula: see text] as [Formula: see text], the map [Formula: see text] is smooth and the matrix [Formula: see text] has eigenvalues with positive real parts and commutes with the limit matrix [Formula: see text] The matrix [Formula: see text] is assumed to be skew-symmetric with eigenvalues (?1,…,? d )=(±i?1,…,±i?k ,0,…,0). The spectra of these linearized operators are crucial for the nonlinear stability of rotating waves in reaction-diffusion systems. We prove under appropriate conditions that every [Formula: see text] satisfying the dispersion relation [Formula: see text]belongs to the essential spectrum [Formula: see text] in Lp For values Re?? to the right of the spectral bound for [Formula: see text], we show that the operator [Formula: see text] is Fredholm of index 0, solve the identification problem for the adjoint operator [Formula: see text] and formulate the Fredholm alternative. Moreover, we show that the set [Formula: see text]belongs to the point spectrum [Formula: see text] in Lp We determine the associated eigenfunctions and show that they decay exponentially in space. As an application, we analyse spinning soliton solutions which occur in the Ginzburg-Landau equation and compute their numerical spectra as well as associated eigenfunctions. Our results form the basis for investigating the nonlinear stability of rotating waves in higher space dimensions and truncations to bounded domains. This article is part of the themed issue 'Stability of nonlinear waves and patterns and related topics'.

SUBMITTER: Beyn WJ

PROVIDER: S-EPMC5869616 | biostudies-literature | 2018 Apr

REPOSITORIES: biostudies-literature

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Spectral analysis of localized rotating waves in parabolic systems.

Beyn Wolf-Jürgen WJ Otten Denny D

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 20180401 2117

In this paper, we study the spectra and Fredholm properties of Ornstein-Uhlenbeck operators [Formula: see text]where [Formula: see text] is the profile of a rotating wave satisfying [Formula: see text] as [Formula: see text], the map [Formula: see text] is smooth and the matrix [Formula: see text] has eigenvalues with positive real parts and commutes with the limit matrix [Formula: see text] The matrix [Formula: see text] is assumed to be skew-symmetric with eigenvalues (λ<sub>1</sub>,…,λ <sub>< ...[more]

PMID: 29507180

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Project description:PurposeCommercial parabolic flights accessible to customers with a wide range of health states will become more prevalent in the near future because of a growing private space flight sector. However, parabolic flights present the passengers' cardiovascular system with a combination of stressors, including a moderately hypobaric hypoxic ambient environment (HH) and repeated gravity transitions (GT). Thus, the aim of this study was to identify unique and combined effects of HH and GT on the human cardiovascular, pulmonary and fluid regulation systems.MethodsCardiac index was determined by inert gas rebreathing (CI(rb)), and continuous non-invasive finger blood pressure (FBP) was repeatedly measured in 18 healthy subjects in the standing position while they were in parabolic flight at 0 and 1.8 G(z). Plasma volume (PV) and fluid regulating blood hormones were determined five times over the flight day. Eleven out of the 18 subjects were subjected to an identical test protocol in a hypobaric chamber in ambient conditions comparable to parabolic flight.ResultsCI(rb) in 0 G(z) decreased significantly during flight (early, 5.139 ± 1.326 L/min; late, 4.150 ± 1.082 L/min) because of a significant decrease in heart rate (HR) (early, 92 ± 15 min(-1); late, 78 ± 12 min(-1)), even though the stroke volume (SV) remained the same. HH produced a small decrease in the PV, both in the hypobaric chamber and in parabolic flight, indicating a dominating HH effect without a significant effect of GT on PV (-52 ± 34 and -115 ± 32 ml, respectively). Pulmonary tissue volume decreased in the HH conditions because of hypoxic pulmonary vasoconstriction (0.694 ± 0.185 and 0.560 ± 0.207 ml) but increased at 0 and 1.8 G(z) in parabolic flight (0.593 ± 0.181 and 0.885 ± 0.458 ml, respectively), indicating that cardiac output and arterial blood pressure rather than HH are the main factors affecting pulmonary vascular regulation in parabolic flight.ConclusionHH and GT each lead to specific responses of the cardiovascular system in parabolic flight. Whereas HH seems to be mainly responsible for the PV decrease in flight, GT overrides the hypoxic pulmonary vasoconstriction induced by HH. This finding indicates the need for careful and individual medical examination and, if necessary, health status improvement for each individual considering a parabolic flight, given the effects of the combination of HH and GT in flight.

Project description:The organization of the eukaryotic cell into discrete membrane-bound organelles allows for the separation of incompatible biochemical processes, but the activities of these organelles must be coordinated. For example, lipid metabolism is distributed between the endoplasmic reticulum for lipid synthesis, lipid droplets for storage and transport, mitochondria and peroxisomes for ?-oxidation, and lysosomes for lipid hydrolysis and recycling. It is increasingly recognized that organelle contacts have a vital role in diverse cellular functions. However, the spatial and temporal organization of organelles within the cell remains poorly characterized, as fluorescence imaging approaches are limited in the number of different labels that can be distinguished in a single image. Here we present a systems-level analysis of the organelle interactome using a multispectral image acquisition method that overcomes the challenge of spectral overlap in the fluorescent protein palette. We used confocal and lattice light sheet instrumentation and an imaging informatics pipeline of five steps to achieve mapping of organelle numbers, volumes, speeds, positions and dynamic inter-organelle contacts in live cells from a monkey fibroblast cell line. We describe the frequency and locality of two-, three-, four- and five-way interactions among six different membrane-bound organelles (endoplasmic reticulum, Golgi, lysosome, peroxisome, mitochondria and lipid droplet) and show how these relationships change over time. We demonstrate that each organelle has a characteristic distribution and dispersion pattern in three-dimensional space and that there is a reproducible pattern of contacts among the six organelles, that is affected by microtubule and cell nutrient status. These live-cell confocal and lattice light sheet spectral imaging approaches are applicable to any cell system expressing multiple fluorescent probes, whether in normal conditions or when cells are exposed to disturbances such as drugs, pathogens or stress. This methodology thus offers a powerful descriptive tool and can be used to develop hypotheses about cellular organization and dynamics.

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Spectral analysis of localized rotating waves in parabolic systems.

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Spectral analysis of localized rotating waves in parabolic systems.

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