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

How much larger quantum correlations are than classical ones

Considering as distance between two two-party correlations the minimum number of half local results one party must toggle in order to turn one correlation into the other, we show that the volume of the set of physically obtainable correlations in the Einstein-Podolsky-Rosen-Bell scenario is (3 pi/8)^2 = 1.388 larger than the volume of the set of correlations obtainable in local deterministic or probabilistic hidden-variable theories, but is only 3 pi^2/32 = 0.925 of the volume allowed by arbitrary causal (i.e., no-signaling) theories.Comment: REVTeX4, 6 page

Coupling techniques for nonlinear hyperbolic equations. III. The well-balanced approximation of thick interfaces

We continue our analysis of the coupling between nonlinear hyperbolic problems across possibly resonant interfaces. In the first two parts of this series, we introduced a new framework for coupling problems which is based on the so-called thin interface model and uses an augmented formulation and an additional unknown for the interface location; this framework has the advantage of avoiding any explicit modeling of the interface structure. In the present paper, we pursue our investigation of the augmented formulation and we introduce a new coupling framework which is now based on the so-called thick interface model. For scalar nonlinear hyperbolic equations in one space variable, we observe that the Cauchy problem is well-posed. Then, our main achievement in the present paper is the design of a new well-balanced finite volume scheme which is adapted to the thick interface model, together with a proof of its convergence toward the unique entropy solution (for a broad class of nonlinear hyperbolic equations). Due to the presence of a possibly resonant interface, the standard technique based on a total variation estimate does not apply, and DiPerna's uniqueness theorem must be used. Following a method proposed by Coquel and LeFloch, our proof relies on discrete entropy inequalities for the coupling problem and an estimate of the discrete entropy dissipation in the proposed scheme.Comment: 21 page

Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon

A Comparison of Consistent Discretizations for Elliptic Problems on Polyhedral Grids

In this work, we review a set of consistent discretizations for second-order elliptic equations, and compare and contrast them with respect to accuracy, monotonicity, and factors affecting their computational cost (degrees of freedom, sparsity, and condition numbers). Our comparisons include the linear and nonlinear TPFA method, multipoint flux-approximation (MPFA-O), mimetic methods, and virtual element methods. We focus on incompressible flow and study the effects of deformed cell geometries and anisotropic permeability.acceptedVersio

Mutation update and genotype-phenotype correlations of novel and previously described mutations in TPM2 and TPM3 causing congenital myopathies

Mutations affecting skeletal muscle isoforms of the tropomyosin genes may cause nemaline myopathy, cap myopathy, core-rod myopathy, congenital fiber-type disproportion, distal arthrogryposes, and Escobar syndrome. We correlate the clinical picture of these diseases with novel (19) and previously reported (31) mutations of the TPM2 and TPM3 genes. Included are altogether 93 families: 53 with TPM2 mutations and 40 with TPM3 mutations. Thirty distinct pathogenic variants of TPM2 and 20 of TPM3 have been published or listed in the Leiden Open Variant Database (http://www.dmd.nl/). Most are heterozygous changes associated with autosomal-dominant disease. Patients with TPM2 mutations tended to present with milder symptoms than those with TPM3 mutations, DA being present only in the TPM2 group. Previous studies have shown that five of the mutations in TPM2 and one in TPM3 cause increased Ca2+ sensitivity resulting in a hypercontractile molecular phenotype. Patients with hypercontractile phenotype more often had contractures of the limb joints (18/19) and jaw (6/19) than those with nonhypercontractile ones (2/22 and 1/22), whereas patients with the non-hypercontractile molecular phenotype more often (19/22) had axial contractures than the hypercontractile group (7/19). Our in silico predictions show that most mutations affect tropomyosin–actin association or tropomyosin head-to-tail binding

Problems and Paradoxes in Economic and Social Policies of Modern Welfare States

Relationships between economic growth rates and the expansion of welfare expenditures in Western nations are examined. The point is made that real gross national product grew rapidly from about 1959 until about 1973, but that since 1973 it has either grown slowly or not at all, while welfare expenditures and entitlements have continued to escalate. Forecasts of a variety of important economic variables in these countries for the near term are presented and discussed, and it is concluded that despite the current modest economic improvement, difficulties in funding welfare states will continue throughout the remainder of the 1980s. Some consideration is given to problems in welfare states to the end of the century, and further difficulties in funding and managing these states are forecast for this period as well. Problems of welfare states are not regarded as short-term by-products of maladjustments experienced in the Western world in the last 10 years but rather as long-term characteristics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67103/2/10.1177_000271628547900102.pd

Assessment of diaphragm motion using ultrasonography in a patient with facio-scapulo-humeral dystrophy: A case report.

Diaphragm is the main inspiratory respiratory muscle and little is known about diaphragm ultrasound in facio-scapula-humeral muscular dystrophy, a neuromuscular disease characterized by an asymmetric skeletal muscle involvement. Diaphragm function evaluation DIAGNOSIS:: Diaphragm muscle weakness attested by the drop of vital capacity (VC) value from sitting position (74%) to supine position (46%). A diaphragm ultrasound was performed in supine position, from the anterior subcostal window OUTCOMES:: We found an opposite side to side hemi diaphragm displacement, either during sniff maneuver or during deep inspiration maneuver, showing a cranial abnormal reduced motion of the right hemi diaphragm whereas the left hemi diaphragm moved caudally. Diaphragm weakness may be present with an asymmetric pattern and an opposite motion during inspiration or sniff manoeuver in facio-scapula-humeral muscular dystrophy. A future study with a systematic evaluation of a greater number of FSHD1 patients will be necessary to characterize this population