Browse
Submit Data
Databases
API
Help

Dataset Information

0 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Initial boundary-value problem for the spherically symmetric Einstein equations with fluids with tangential pressure.

ABSTRACT: We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial space-like hypersurface with a time-like boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.

SUBMITTER: Brito I

PROVIDER: S-EPMC5582177 | biostudies-literature | 2017 Aug

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Initial boundary-value problem for the spherically symmetric Einstein equations with fluids with tangential pressure.

Brito Irene I Mena Filipe C FC

Proceedings. Mathematical, physical, and engineering sciences 20170809 2204

We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial space-like hypersurface with a time-like boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior. ...[more]

PMID: 28878556

Similar Datasets

Analysis of tangential contact boundary value problems using potential functions.

Project description:This paper presents an analysis technique of high-order contact potential problems and its application to an elastic settlement analysis of a shallow foundation system subjected to a combined traction boundary condition. Closed-form solutions of potential functions are derived for an elastic half-space subjected to bilinear tangential traction boundary conditions over rectangular surface regions. Using the principle of superposition, the present solutions provide a means to form an approximate and continuous solution of elastic contact problems with higher-order tangential boundary conditions. As an application example, an elastic settlement analysis of a rigid footing founded on a dense granular soil is performed under a tangential traction boundary condition prescribed in an analogy with the stress equilibrium states of static sandpiles. A generalized solution approach to combined normal and tangential traction boundary value problems is discussed in the context of foundation engineering.

| S-EPMC6458418 | biostudies-literature

Solving the initial value problem of ordinary differential equations by Lie group based neural network method.

Project description:To combine a feedforward neural network (FNN) and Lie group (symmetry) theory of differential equations (DEs), an alternative artificial NN approach is proposed to solve the initial value problems (IVPs) of ordinary DEs (ODEs). Introducing the Lie group expressions of the solution, the trial solution of ODEs is split into two parts. The first part is a solution of other ODEs with initial values of original IVP. This is easily solved using the Lie group and known symbolic or numerical methods without any network parameters (weights and biases). The second part consists of an FNN with adjustable parameters. This is trained using the error back propagation method by minimizing an error (loss) function and updating the parameters. The method significantly reduces the number of the trainable parameters and can more quickly and accurately learn the real solution, compared to the existing similar methods. The numerical method is applied to several cases, including physical oscillation problems. The results have been graphically represented, and some conclusions have been made.

| S-EPMC8985966 | biostudies-literature

The Design and Synthesis of Highly Branched and Spherically Symmetric Fluorinated Macrocyclic Chelators.

Project description:Two novel, highly fluorinated macrocyclic chelators with highly branched and spherically symmetric fluorocarbon moieties have been designed and efficiently synthesized. This is achieved by conjugating a spherically symmetric fluorocarbon moiety to the macrocyclic chelator DOTA, with or without a flexible oligo-oxyethylene linker between these two parts. As a result of the spherical symmetry, all 27 fluorine atoms in each fluorinated chelator give a sharp singlet (19)F NMR signal. The hydrophilicity and the (19)F relaxation behavior of fluorinated chelators can be modulated by the insertion of a flexible linker between the fluorocarbon moiety and the macrocyclic linker. These chelators serve as prototypes for (1)H-(19)F dual-nuclei magnetic resonance imaging agents.

| S-EPMC2888522 | biostudies-literature

The Design and Synthesis of Highly Branched and Spherically Symmetric Fluorinated Oils and Amphiles.

Project description:A new emulsifier design principle, based on concepts borrowed from protein science, is proposed. Using this principle, a class of highly branched and spherically symmetric fluorinated oils and amphiles has been designed and synthesized, for potential applications in the construction of fluorocarbon nanoparticles. The Mitsunobu reaction was employed as the key step for introducing three perfluoro-tert-butoxyl groups into pentaerythritol derivatives with excellent yields and extremely simple isolation procedures. Due to the symmetric arrangement of the fluorine atoms, each fluorinated oil or amphile molecule gives one sharp singlet (19)F NMR signal.

| S-EPMC2083655 | biostudies-literature

Water-like solvation thermodynamics in a spherically symmetric solvent model with two characteristic lengths.

Project description:We examine by molecular dynamics simulation the solubility of small apolar solutes in a solvent whose particles interact via the Jagla potential, a spherically symmetric ramp potential with two characteristic lengths: an impenetrable hard core and a penetrable soft core. The Jagla fluid has been recently shown to possess water-like structural, dynamic, and thermodynamic anomalies. We find that the solubility exhibits a minimum with respect to temperature at fixed pressure and thereby show that the Jagla fluid also displays water-like solvation thermodynamics. We further find low-temperature swelling of a hard-sphere chain dissolved in the Jagla fluid and relate this phenomenon to cold unfolding of globular proteins. Our results are consistent with the possibility that the presence of two characteristic lengths in the Jagla potential is a key feature of water-like solvation thermodynamics. The penetrable core becomes increasingly important at low temperatures, which favors the formation of low-density, open structures in the Jagla solvent.

| S-EPMC2154404 | biostudies-literature

About positivity of green's functions for nonlocal boundary value problems with impulsive delay equations.

Project description:The impulsive delay differential equation is considered (Lx)(t) = x'(t) + ∑(i=1)(m) p(i)(t)x(t - τ(i) (t)) = f(t), t ∈ [a, b], x(t j) = β(j)x(t(j - 0)), j = 1,…, k, a = t0 < t1 < t2 < ⋯<t k < t k+1 = b, x(ζ) = 0, ζ ∉ [a, b], with nonlocal boundary condition lx = ∫(a)(b) φ(s)x'(s)ds + θx(a) = c, φ ∈ L ∞ [a, b]; θ, c ∈ R. Various results on existence and uniqueness of solutions and on positivity/negativity of the Green's functions for this equation are obtained.

| S-EPMC3956640 | biostudies-other

Transition from fractional to classical Stokes-Einstein behaviour in simple fluids.

Project description:An optical technique for tracking single particles has been used to evaluate the particle diameter at which diffusion transitions from molecular behaviour described by the fractional Stokes-Einstein relationship to particle behaviour described by the classical Stokes-Einstein relationship. The results confirm a prior prediction from molecular dynamic simulations that there is a particle size at which transition occurs and show it is inversely dependent on concentration and viscosity but independent of particle density. For concentrations in the range 5 × 10-3 to 5 × 10-6 mg ml-1 and viscosities from 0.8 to 150 mPa s, the transition was found to occur in the diameter range 150-300 nm.

| S-EPMC5749985 | biostudies-literature

Asymptotic analysis for dispersion relations and travel times in noise cross-correlations: spherically symmetric case

Project description:The cross-correlations of ambient noise or earthquake codas are massively used in seismic tomography to measure the dispersion curves of surface waves and the travel times of body waves. Such measurements are based on the assumption that these kinematic parameters in the cross-correlations of noise coincide with those in Green's functions. However, the relation between the cross-correlations of noise and Green's functions deserves to be studied more precisely. In this paper, we use the asymptotic analysis to study the dispersion relations of surface waves and the travel times of body waves, and come to the conclusion that for the spherically symmetric Earth model, when the distribution of noise sources is laterally uniform, the dispersion relations of surface waves and the travel times of SH body-wave phases in noise correlations should be exactly the same as those in Green's functions.

| S-EPMC6237510 | biostudies-literature

Multiple positive solutions to nonlinear boundary value problems of a system for fractional differential equations.

Project description:By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by -D(0+)(ν1)y1(t) = λ1a1(t)f(y1(t), y2(t)), - D(0+)(ν2)y2(t) = λ2a2(t)g(y1(t), y2(t)), where D(0+)(ν) is the standard Riemann-Liouville fractional derivative, ν1, ν2 ∈ (n - 1, n] for n > 3 and n ∈ N, subject to the boundary conditions y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = 0 = [D(0+ (α)y2(t)] t=1, for 1 ≤ α ≤ n - 2, or y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = ϕ1(y1), [D(0+)(α)y2(t)] t=1 = ϕ2(y2), for 1 ≤ α ≤ n - 2, ϕ1, ϕ2 ∈ C([0,1], R). Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result.

| S-EPMC3921945 | biostudies-other

Electrically induced transformations of defects in cholesteric layer with tangential-conical boundary conditions.

Project description:Electric-field-induced changes of the orientational structures of cholesteric liquid crystal layer with the tangential-conical boundary conditions have been investigated. The samples with the ratio of the cholesteric layer thickness d to the helix pitch p equalled to 0.57 have been considered. The perpendicularly applied electric field causes a decrease of the azimuthal director angle at the substrate with the conical surface anchoring. In the cells with d = 22 μm, the defect loops having the under-twisted and over-twisted areas are formed. At the defect loop the pair of point peculiarities is observed where the 180° jump of azimuthal angle of the director occurs. Under the action of electric field the loops shrink and disappear. In the cells with d = 13 μm, the over-twisted and under-twisted defect lines are formed. Applied voltage results in the shortening of lines or/and their transformation into a defect of the third type. The director field distribution near defect lines of three types has been investigated by the polarising microscopy techniques. It has been revealed that the length ratio between the over-twisted and third-type defect lines can be controlled by the electric field.

| S-EPMC7078221 | 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