70 research outputs found
Heat-Conducting, Compressible Mixtures with Multicomponent Diffusion: Construction of a Weak Solution
We investigate a coupling between the compressible Navier'stokes-Fourier system and the full Maxwell'stefan equations. This model describes the motion of a chemically reacting heat-conducting gaseous mixture. The viscosity coefficients are density-dependent functions vanishing in a vacuum and the internal pressure depends on species concentrations. By several levels of approximation we prove the global-in-time existence of weak solutions on the three-dimensional torus
Energy solutions to one-dimensional singular parabolic problems with data are viscosity solutions
We study one-dimensional very singular parabolic equations with periodic
boundary conditions and initial data in , which is the energy space. We
show existence of solutions in this energy space and then we prove that they
are viscosity solutions in the sense of Giga-Giga.Comment: 15 page
Multicomponent mixture model: The issue of existence via time discretization
We prove the existence of global-in-time weak solutions to a model of chemically reacting mixture. We consider a coupling between the compressible Navier-Stokes system and the reaction diffusion equations for chemical species when the thermal effects are neglected. We first prove the existence of weak solutions to the semi-discretization in time. Based on this, the existence of solutions to the evolutionary system is proven
Chemically reacting mixtures in terms of degenerated parabolic setting
The paper analyzes basic mathematical questions for a model of chemically reacting mixtures. We derive a model of several (finite) component compressible gas taking rigorously into account the thermodynamical regime. Mathematical description of the model leads to a degenerate parabolic equation with hyperbolic deviation. The thermodynamics implies that the diffusion terms are non-symmetric, not positively defined, and cross-diffusion effects must be strongly marked. The mathematical goal is to establish the existence of weak solutions globally in time for arbitrary number of reacting species. A key point is an entropy-like estimate showing possible renormalization of the system. © 2013 AIP Publishing LLC
Sharp conditions to avoid collisions in singular Cucker-Smale interactions
We consider the Cucker–Smale flocking model with a singular communication weight with . We provide a critical value of the exponent in the communication weight leading to global regularity of solutions or finite-time collision between particles. For , we show that there is no collision between particles in finite time if they are placed in different positions initially. For we investigate a version of the Cucker–Smale model with expanded singularity i.e. with weight , . For such model we provide a uniform with respect to the number of particles estimate that controls the -distance between particles. In case of it reduces to the estimate of collision avoidance
Statistical Inference for Valued-Edge Networks: Generalized Exponential Random Graph Models
Across the sciences, the statistical analysis of networks is central to the
production of knowledge on relational phenomena. Because of their ability to
model the structural generation of networks, exponential random graph models
are a ubiquitous means of analysis. However, they are limited by an inability
to model networks with valued edges. We solve this problem by introducing a
class of generalized exponential random graph models capable of modeling
networks whose edges are valued, thus greatly expanding the scope of networks
applied researchers can subject to statistical analysis
Theorems on existence and global dynamics for the Einstein equations
This article is a guide to theorems on existence and global dynamics of
solutions of the Einstein equations. It draws attention to open questions in
the field. The local-in-time Cauchy problem, which is relatively well
understood, is surveyed. Global results for solutions with various types of
symmetry are discussed. A selection of results from Newtonian theory and
special relativity that offer useful comparisons is presented. Treatments of
global results in the case of small data and results on constructing spacetimes
with prescribed singularity structure or late-time asymptotics are given. A
conjectural picture of the asymptotic behaviour of general cosmological
solutions of the Einstein equations is built up. Some miscellaneous topics
connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living
Rev. Rel. 5 (2002)
The Einstein-Vlasov System/Kinetic Theory
The main purpose of this article is to provide a guide to theorems on global
properties of solutions to the Einstein--Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades in which the main focus has
been on non-relativistic and special relativistic physics, i.e., to model the
dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In
1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-
Theorems on existence and global dynamics for the Einstein equations
This article is a guide to theorems on existence and global dynamics of
solutions of the Einstein equations. It draws attention to open questions in
the field. The local in time Cauchy problem, which is relatively well
understood, is surveyed. Global results for solutions with various types of
symmetry are discussed. A selection of results from Newtonian theory and
special relativity which offer useful comparisons is presented. Treatments of
global results in the case of small data and results on constructing spacetimes
with prescribed singularity structure are given. A conjectural picture of the
asymptotic behaviour of general cosmological solutions of the Einstein
equations is built up. Some miscellaneous topics connected with the main theme
are collected in a separate section.Comment: 54 pages, submitted to Living Reviews in Relativit
Observation of Two New Excited Ξb0 States Decaying to Λb0 K-π+
Two narrow resonant states are observed in the Λb0K-π+ mass spectrum using a data sample of proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the LHCb experiment and corresponding to an integrated luminosity of 6 fb-1. The minimal quark content of the Λb0K-π+ system indicates that these are excited Ξb0 baryons. The masses of the Ξb(6327)0 and Ξb(6333)0 states are m[Ξb(6327)0]=6327.28-0.21+0.23±0.12±0.24 and m[Ξb(6333)0]=6332.69-0.18+0.17±0.03±0.22 MeV, respectively, with a mass splitting of Δm=5.41-0.27+0.26±0.12 MeV, where the uncertainties are statistical, systematic, and due to the Λb0 mass measurement. The measured natural widths of these states are consistent with zero, with upper limits of Γ[Ξb(6327)0]<2.20(2.56) and Γ[Ξb(6333)0]<1.60(1.92) MeV at a 90% (95%) credibility level. The significance of the two-peak hypothesis is larger than nine (five) Gaussian standard deviations compared to the no-peak (one-peak) hypothesis. The masses, widths, and resonant structure of the new states are in good agreement with the expectations for a doublet of 1D Ξb0 resonances
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