Browse
Submit Data
Databases
API
Help

Dataset Information

0 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Global Stability of Minkowski Space for the Einstein-Vlasov System in the Harmonic Gauge.

ABSTRACT: Minkowski space is shown to be globally stable as a solution to the massive Einstein-Vlasov system. The proof is based on a harmonic gauge in which the equations reduce to a system of quasilinear wave equations for the metric, satisfying the weak null condition, coupled to a transport equation for the Vlasov particle distribution function. Central to the proof is a collection of vector fields used to control the particle distribution function, a function of both spacetime and momentum variables. The vector fields are derived using a general procedure, are adapted to the geometry of the solution and reduce to the generators of the symmetries of Minkowski space when restricted to acting on spacetime functions. Moreover, when specialising to the case of vacuum, the proof provides a simplification of previous stability works.

SUBMITTER: Lindblad H

PROVIDER: S-EPMC7010697 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Global Stability of Minkowski Space for the Einstein-Vlasov System in the Harmonic Gauge.

Lindblad Hans H Taylor Martin M

Archive for rational mechanics and analysis 20190724 1

Minkowski space is shown to be globally stable as a solution to the massive Einstein-Vlasov system. The proof is based on a harmonic gauge in which the equations reduce to a system of quasilinear wave equations for the metric, satisfying the weak null condition, coupled to a transport equation for the Vlasov particle distribution function. Central to the proof is a collection of vector fields used to control the particle distribution function, a function of both spacetime and momentum variables. ...[more]

PMID: 32103831

Similar Datasets

Protein signatures using electrostatic molecular surfaces in harmonic space.

Project description:We developed a novel method based on the Fourier analysis of protein molecular surfaces to speed up the analysis of the vast structural data generated in the post-genomic era. This method computes the power spectrum of surfaces of the molecular electrostatic potential, whose three-dimensional coordinates have been either experimentally or theoretically determined. Thus we achieve a reduction of the initial three-dimensional information on the molecular surface to the one-dimensional information on pairs of points at a fixed scale apart. Consequently, the similarity search in our method is computationally less demanding and significantly faster than shape comparison methods. As proof of principle, we applied our method to a training set of viral proteins that are involved in major diseases such as Hepatitis C, Dengue fever, Yellow fever, Bovine viral diarrhea and West Nile fever. The training set contains proteins of four different protein families, as well as a mammalian representative enzyme. We found that the power spectrum successfully assigns a unique signature to each protein included in our training set, thus providing a direct probe of functional similarity among proteins. The results agree with established biological data from conventional structural biochemistry analyses.

| S-EPMC3807749 | biostudies-literature

Gauge Theory on Projective Surfaces and Anti-self-dual Einstein Metrics in Dimension Four.

Project description:Given a projective structure on a surface \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document}N, we show how to canonically construct a neutral signature Einstein metric with non-zero scalar curvature as well as a symplectic form on the total space M of a certain rank 2 affine bundle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M \rightarrow N$$\end{document}M?N. The Einstein metric has anti-self-dual conformal curvature and admits a parallel field of anti-self-dual planes. We show that locally every such metric arises from our construction unless it is conformally flat. The homogeneous Einstein metric corresponding to the flat projective structure on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {RP}^2$$\end{document}RP2 is the non-compact real form of the Fubini–Study metric on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M=\mathrm {SL}(3, \mathbb {R})/\mathrm {GL}(2, \mathbb {R})$$\end{document}M=SL(3,R)/GL(2,R). We also show how our construction relates to a certain gauge-theoretic equation introduced by Calderbank.

| S-EPMC6294184 | biostudies-other

Direct evidence of spatial stability of Bose-Einstein condensate of magnons.

Project description:Bose-Einstein condensation of magnons is one of few macroscopic quantum phenomena observed at room temperature. Since its discovery, it became an object of intense research, which led to the observation of many exciting phenomena such as quantized vortices, second sound, and Bogolyubov waves. However, it remained unclear what physical mechanisms can be responsible for the spatial stability of the magnon condensate. Indeed, since magnons are believed to exhibit attractive interaction, it is generally expected that the condensate is unstable with respect to the real-space collapse, contrarily to experimental findings. Here, we provide direct experimental evidence that magnons in a condensate exhibit repulsive interaction resulting in the condensate stabilization and propose a mechanism, which is responsible for this interaction. Our experimental conclusions are additionally supported by the theoretical model based on the Gross-Pitaevskii equation. Our findings solve a long-standing problem, providing a new insight into the physics of magnon Bose-Einstein condensates.

| S-EPMC7125083 | biostudies-literature

Programming nonreciprocity and harmonic beam steering via a digitally space-time-coded metamaterial antenna.

Project description:Recent advancement in digital coding metasurfaces incorporating spatial and temporal modulation has enabled simultaneous control of electromagnetic (EM) waves in both space and frequency domains by manipulating incident EM waves in a transmissive or reflective fashion, resulting in time-reversal asymmetry. Here we show in theory and experiment that a digitally space-time-coded metamaterial (MTM) antenna with spatiotemporal modulation at its unit cell level can be regarded as a radiating counterpart of such digital metasurface, which will enable nonreciprocal EM wave transmission and reception via surface-to-leaky-wave transformation and harmonic frequency generation. Operating in the fast wave (radiation) region, the space-time-coded MTM antenna is tailored in a way such that the propagation constant of each programmable unit cell embedded with varactor diodes can toggle between positive and negative phases, which is done through providing digital sequences by using a field-programmable gate array (FPGA). Owing to the time-varying coding sequence, harmonic frequencies are generated with different main beam directions. Furthermore, the space time modulation of the digitally coded MTM antenna allows for nonreciprocal transmission and reception of EM waves by breaking the time-reversal symmetry, which may enable many applications, such as simultaneous transmitting and receiving, unidirectional transmission, radar sensing, and multiple-input and multiple-output (MIMO) beamformer.

| S-EPMC10163271 | biostudies-literature

Open-Source Strain Gauge System for Monitoring Pressure Distribution of Runner's Feet.

Project description:The objective of the research presented in this paper was to provide a novel open-source strain gauge system that shall enable the measurement of the pressure of a runner's feet on the ground and the presentation of the results of that measurement to the user. The system based on electronic shoe inserts with 16 built-in pressure sensors laminated in a transparent film was created, consisting of two parts: a mobile application and a wearable device. The developed system provides a number of advantages in comparison with existing solutions, including no need for calibration, an accurate and frequent measurement of pressure distribution, placement of electronics on the outside of a shoe, low cost, and an open-source approach to encourage enhancements and open collaboration.

| S-EPMC9959378 | biostudies-literature

Continuous Bose-Einstein condensation.

Project description:Bose-Einstein condensates (BECs) are macroscopic coherent matter waves that have revolutionized quantum science and atomic physics. They are important to quantum simulation1 and sensing2,3, for example, underlying atom interferometers in space4 and ambitious tests of Einstein's equivalence principle5,6. A long-standing constraint for quantum gas devices has been the need to execute cooling stages time-sequentially, restricting these devices to pulsed operation. Here we demonstrate continuous Bose-Einstein condensation by creating a continuous-wave (CW) condensate of strontium atoms that lasts indefinitely. The coherent matter wave is sustained by amplification through Bose-stimulated gain of atoms from a thermal bath. By steadily replenishing this bath while achieving 1,000 times higher phase-space densities than previous works7,8, we maintain the conditions for condensation. Our experiment is the matter wave analogue of a CW optical laser with fully reflective cavity mirrors. This proof-of-principle demonstration provides a new, hitherto missing piece of atom optics, enabling the construction of continuous coherent-matter-wave devices.

| S-EPMC9217748 | biostudies-literature

Harmonic oscillations in homeostatic controllers: Dynamics of the p53 regulatory system.

Project description:Homeostatic mechanisms are essential for the protection and adaptation of organisms in a changing and challenging environment. Previously, we have described molecular mechanisms that lead to robust homeostasis/adaptation under inflow or outflow perturbations. Here we report that harmonic oscillations occur in models of such homeostatic controllers and that a close relationship exists between the control of the p53/Mdm2 system and that of a homeostatic inflow controller. This homeostatic control model of the p53 system provides an explanation why large fluctuations in the amplitude of p53/Mdm2 oscillations may arise as part of the homeostatic regulation of p53 by Mdm2 under DNA-damaging conditions. In the presence of DNA damage p53 is upregulated, but is subject to a tight control by Mdm2 and other factors to avoid a premature apoptotic response of the cell at low DNA damage levels. One of the regulatory steps is the Mdm2-mediated degradation of p53 by the proteasome. Oscillations in the p53/Mdm2 system are considered to be part of a mechanism by which a cell decides between cell cycle arrest/DNA repair and apoptosis. In the homeostatic inflow control model, harmonic oscillations in p53/Mdm2 levels arise when the binding strength of p53 to degradation complexes increases. Due to the harmonic character of the oscillations rapid fluctuating noise can lead, as experimentally observed, to large variations in the amplitude of the oscillation but not in their period, a behavior which has been difficult to simulate by deterministic limit-cycle models. In conclusion, the oscillatory response of homeostatic controllers may provide new insights into the origin and role of oscillations observed in homeostatically controlled molecular networks.

| S-EPMC2830462 | biostudies-literature

A global representation of the protein fold space.

Project description:One of the principal goals of the structural genomics initiative is to identify the total repertoire of protein folds and obtain a global view of the "protein structure universe." Here, we present a 3D map of the protein fold space in which structurally related folds are represented by spatially adjacent points. Such a representation reveals a high-level organization of the fold space that is intuitively interpretable. The shape of the fold space and the overall distribution of the folds are defined by three dominant trends: secondary structure class, chain topology, and protein domain size. Random coil-like structures of small proteins and peptides are mapped to a region where the three trends converge, offering an interesting perspective on both the demography of fold space and the evolution of protein structures.

| S-EPMC151350 | biostudies-literature

Stability of healthy subgingival microbiome across space and time.

Project description:The subgingival microbiome is one of the most stable microbial ecosystems in the human body. Alterations in the subgingival microbiome have been associated with periodontal disease, but their variations over time and between different subgingival sites in periodontally healthy individuals have not been well described. We performed extensive, longitudinal sampling of the subgingival microbiome from five periodontally healthy individuals to define baseline spatial and temporal variations. A total of 251 subgingival samples from 5 subjects were collected over 6-12 months and deep sequenced. The overall microbial diversity and composition differed significantly between individuals. Within each individual, we observed considerable differences in microbiome composition between different subgingival sites. However, for a given site, the microbiome was remarkably stable over time, and this stability was associated with increased microbial diversity but was inversely correlated with the enrichment of putative periodontal pathogens. In contrast to microbiome composition, the predicted functional metagenome was similar across space and time, suggesting that periodontal health is associated with shared gene functions encoded by different microbiome consortia that are individualized. To our knowledge, this is one of the most detailed longitudinal analysis of the healthy subgingival microbiome to date that examined the longitudinal variability of different subgingival sites within individuals. These results suggest that a single measurement of the healthy subgingival microbiome at a given site can provide long term information of the microbial composition and functional potential, but sampling of each site is necessary to define the composition and community structure at individual subgingival sites.

| S-EPMC8671439 | biostudies-literature

Stability of silk and collagen protein materials in space.

Project description:Collagen and silk materials, in neat forms and as silica composites, were flown for 18 months on the International Space Station [Materials International Space Station Experiment (MISSE)-6] to assess the impact of space radiation on structure and function. As natural biomaterials, the impact of the space environment on films of these proteins was investigated to understand fundamental changes in structure and function related to the future utility in materials and medicine in space environments. About 15% of the film surfaces were etched by heavy ionizing particles such as atomic oxygen, the major component of the low-Earth orbit space environment. Unexpectedly, more than 80% of the silk and collagen materials were chemically crosslinked by space radiation. These findings are critical for designing next-generation biocompatible materials for contact with living systems in space environments, where the effects of heavy ionizing particles and other cosmic radiation need to be considered.

| S-EPMC3851920 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data