999 research outputs found
Convergence of finite volume scheme for degenerate parabolic problem with zero flux boundary condition
This note is devoted to the study of the finite volume methods used in the discretization of degenerate parabolic-hyperbolic equation with zero-flux boundary condition. The notion of an entropy-process solution, successfully used for the Dirichlet problem, is insufficient to obtain a uniqueness and convergence result because of a lack of regularity of solutions on the boundary. We infer the uniqueness of an entropy-process solution using the tool of the nonlinear semigroup theory by passing to the new abstract notion of integral-process solution. Then, we prove that numerical solution converges to the unique entropy solution as the mesh size tends to 0
A theory of -dissipative solvers for scalar conservation laws with discontinuous flux
We propose a general framework for the study of contractive semigroups
of solutions to conservation laws with discontinuous flux. Developing the ideas
of a number of preceding works we claim that the whole admissibility issue is
reduced to the selection of a family of "elementary solutions", which are
certain piecewise constant stationary weak solutions. We refer to such a family
as a "germ". It is well known that (CL) admits many different contractive
semigroups, some of which reflects different physical applications. We revisit
a number of the existing admissibility (or entropy) conditions and identify the
germs that underly these conditions. We devote specific attention to the
anishing viscosity" germ, which is a way to express the "-condition" of
Diehl. For any given germ, we formulate "germ-based" admissibility conditions
in the form of a trace condition on the flux discontinuity line (in the
spirit of Vol'pert) and in the form of a family of global entropy inequalities
(following Kruzhkov and Carrillo). We characterize those germs that lead to the
-contraction property for the associated admissible solutions. Our
approach offers a streamlined and unifying perspective on many of the known
entropy conditions, making it possible to recover earlier uniqueness results
under weaker conditions than before, and to provide new results for other less
studied problems. Several strategies for proving the existence of admissible
solutions are discussed, and existence results are given for fluxes satisfying
some additional conditions. These are based on convergence results either for
the vanishing viscosity method (with standard viscosity or with specific
viscosities "adapted" to the choice of a germ), or for specific germ-adapted
finite volume schemes
Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions
We introduce an iterative method for computing the first eigenpair
for the -Laplacian operator with homogeneous Dirichlet
data as the limit of as , where
is the positive solution of the sublinear Lane-Emden equation
with same boundary data. The method is
shown to work for any smooth, bounded domain. Solutions to the Lane-Emden
problem are obtained through inverse iteration of a super-solution which is
derived from the solution to the torsional creep problem. Convergence of
to is in the -norm and the rate of convergence of
to is at least . Numerical evidence is
presented.Comment: Section 5 was rewritten. Jed Brown was added as autho
Analysis on general meshes of a discrete duality finite volume method for subsurface flow problems
Observation of the Decay Λ0b→Λ+cτ−¯ν
The first observation of the semileptonic b-baryon decay Λb0→Λc+τ-ν¯τ, with a significance of 6.1σ, is reported using a data sample corresponding to 3 fb-1 of integrated luminosity, collected by the LHCb experiment at center-of-mass energies of 7 and 8 TeV at the LHC. The τ- lepton is reconstructed in the hadronic decay to three charged pions. The ratio K=B(Λb0→Λc+τ-ν¯τ)/B(Λb0→Λc+π-π+π-) is measured to be 2.46±0.27±0.40, where the first uncertainty is statistical and the second systematic. The branching fraction B(Λb0→Λc+τ-ν¯τ)=(1.50±0.16±0.25±0.23)% is obtained, where the third uncertainty is from the external branching fraction of the normalization channel Λb0→Λc+π-π+π-. The ratio of semileptonic branching fractions R(Λc+)B(Λb0→Λc+τ-ν¯τ)/B(Λb0→Λc+μ-ν¯μ) is derived to be 0.242±0.026±0.040±0.059, where the external branching fraction uncertainty from the channel Λb0→Λc+μ-ν¯μ contributes to the last term. This result is in agreement with the standard model prediction
A study of CP violation in the decays B±→[K+K-π+π-]Dh± (h= K, π) and B±→[π+π-π+π-]Dh±
The first study of CP violation in the decay mode B±→[K+K-π+π-]Dh± , with h= K, π , is presented, exploiting a data sample of proton–proton collisions collected by the LHCb experiment that corresponds to an integrated luminosity of 9 \,fb - 1 . The analysis is performed in bins of phase space, which are optimised for sensitivity to local CP asymmetries. CP -violating observables that are sensitive to the angle γ of the Unitarity Triangle are determined. The analysis requires external information on charm-decay parameters, which are currently taken from an amplitude analysis of LHCb data, but can be updated in the future when direct measurements become available. Measurements are also performed of phase-space integrated observables for B±→[K+K-π+π-]Dh± and B±→[π+π-π+π-]Dh± decays
Measurement of the photon polarization in decays
The photon polarization in transitions is measured for the
first time in radiative b-baryon decays exploiting the unique spin structure of
decays. A data sample corresponding to an
integrated luminosity of collected by the LHCb experiment in
collisions at a center-of-mass energy of is used. The photon
polarization is measured to be , where the first uncertainty is
statistical and the second systematic. This result is in agreement with the
Standard Model prediction and previous measurements in b-meson decays.
Charge-parity breaking effects are studied for the first time in this
observable and found to be consistent with symmetry.Comment: All figures and tables, along with machine-readable versions and any
supplementary material and additional information, are available at
https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2021-030.html (LHCb
public pages
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