Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions

We study the Cauchy problem for general, nonlinear, strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of a nondegenerate (ND) system. This is the optimal condition guaranteeing, as we show it, that the Riemann problem can be solved with finitely many waves, only; we establish that the ND condition is generic in the sense of Baire (for the Whitney topology), so that any system can be approached by a ND system. Second, we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds. Third, we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the Cauchy problem; this provides a new existence proof as well as an approximation algorithm. As an application, we investigate the time-regularity of the graph solutions $(X,U)$ introduced by the second author, and propose a geometric version of our scheme; in turn, the spatial component $X$ of a graph solution can be chosen to be continuous in both time and space, while its component $U$ is continuous in space and has bounded variation in time.Comment: 74 page

Is the Blade Element Momentum theory overestimating wind turbine loads? – An aeroelastic comparison between OpenFAST's AeroDyn and QBlade's Lifting-Line Free Vortex Wake method

Abstract. Load calculations play a key role in determining the design loads of different wind turbine components. To obtain the aerodynamic loads for these calculations, the industry relies heavily on the Blade Element Momentum (BEM) theory. BEM methods use several engineering correction models to capture the aerodynamic phenomena present in Design Load Cases (DLCs) with turbulent wind. Because of this, BEM methods can overestimate aerodynamic loads under challenging conditions when compared to higher-order aerodynamic methods – such as the Lifting-Line Free Vortex Wake (LLFVW) method – leading to unnecessarily high design loads and component costs. In this paper, we give a quantitative answer to the question of load overestimation of a particular BEM implementation by comparing the results of aeroelastic load calculations done with the BEM-based OpenFAST code and the QBlade code, which uses a particular implementation of the LLFVW method. We compare extreme and fatigue load predictions from both codes using sixty-six 10 min load simulations of the Danish Technical University (DTU) 10 MW Reference Wind Turbine according to the IEC 61400-1 power production DLC group. Results from both codes show differences in fatigue and extreme load estimations for the considered sensors of the turbine. LLFVW simulations predict 9 % lower lifetime damage equivalent loads (DELs) for the out-of-plane blade root and the tower base fore–aft bending moments compared to BEM simulations. The results also show that lifetime DELs for the yaw-bearing tilt and yaw moments are 3 % and 4 % lower when calculated with the LLFVW code. An ultimate state analysis shows that extreme loads of the blade root out-of-plane bending moment predicted by the LLFVW simulations are 3 % lower than the moments predicted by BEM simulations. For the maximum tower base fore–aft bending moment, the LLFVW simulations predict an increase of 2 %. Further analysis reveals that there are two main contributors to these load differences. The first is the different way both codes treat the effect of the nonuniform wind field on the local blade aerodynamics. The second is the higher average aerodynamic torque in the LLFVW simulations. It influences the transition between operating modes of the controller and changes the aeroelastic behavior of the turbine, thus affecting the loads

Dichlorido{2-[(thio­phen-2-ylmeth­yl)imino­meth­yl]pyridine-κ2 N,N′}palladium(II)

In the title compound, [PdCl2(C11H10N2S)], the PdII ion is four-coordinated in a distorted square-planar environment by two N atoms of the chelating 2-[(thio­phen-2-ylmeth­yl)imino­meth­yl]pyridine ligand and two chloride anions. The thio­phene ring is rotationally disordered over two orientations in a 1:1 ratio. The crystal packing exhibits weak inter­molecular C—H⋯Cl and C—H⋯S hydrogen bonds

[Glucocorticoid induced TNFR-related protein (GITR) as marker of human regulatory T cells: expansion of the GITR(+)CD25⁻ cell subset in patients with systemic lupus erythematosus].

Objectives: Regulatory T cells (TREG) represent a T cell subset able to modulate immune response by suppressing autoreactive T-lymphocytes. The evidence of a reduced number and an impaired function of this cell population in autoimmune/ inflammatory chronic diseases led to the hypothesis of its involvement in the pathogenesis of these disorders. Glucocorticoid-induced TNFR-related protein (GITR) is a well known marker of murine TREG cells, but little is known in humans. The aim of this study was to investigate the characteristics of TREG cells in systemic lupus erythematosus (SLE) and the potential role of GITR as marker of human TREG. Methods: Nineteen SLE patients and 15 sex- and age-matched normal controls (NC) were enrolled. CD4+ T cells were magnetic sorted from peripheral blood by negative selection. Cell phenotype was analyzed through flow-cytometry using primary and secondary antibodies and real time polymerase-chain reaction (PCR) using TaqMan probes. Results: The CD25highGITRhigh subset was significantly decreased in SLE patients with respect to NC (0.37±0.21% vs 0.72±0.19%; p<0.05). On the opposite, the CD25-GITRhigh cell population was expanded in the peripheral blood of SLE patients (3.5±2.25 vs 0.70±0.32%, p<0.01). Interestingly, FoxP3 at mRNA level was expressed in both CD25- GITRhigh and CD25highGITRhigh cells, suggesting that both cell subsets have regulatory activity. Conclusions: CD4+CD25-GITRhigh cells are increased in SLE as compared to NC. The expression of high level of GITR, but not CD25, on FoxP3+ cells appears to point to a regulatory phenotype of this peculiar T cell subset

Needlet estimation of cross-correlation between CMB lensing maps and LSS

In this paper we develop a novel needlet-based estimator to investigate the crosscorrelation between cosmic microwave background (CMB) lensing maps and large-scale structure (LSS) data. We compare this estimator with its harmonic counterpart and, in particular, we analyze the bias effects of different forms of masking. In order to address this bias, we also implement a MASTER-like technique in the needlet case. The resulting estimator turns out to have an extremely good signal-to-noise performance. Our analysis aims at expanding and optimizing the operating domains in CMB-LSS cross-correlation studies, similarly to CMB needlet data analysis. It is motivated especially by next generation experiments (such as Euclid) which will allow us to derive much tighter constraints on cosmological and astrophysical parameters through cross-correlation measurements between CMB and LSS

A locally quadratic Glimm functional and sharp convergence rate of the Glimm scheme for nonlinear hyperbolic systems

Consider the Cauchy problem for a strictly hyperbolic, $N\times N$ quasilinear system in one space dimension u_t+A(u) u_x=0,\qquad u(0,x)=\bar u(x), \eqno (1) where $u \mapsto A(u)$ is a smooth matrix-valued map, and the initial data $\overline u$ is assumed to have small total variation. We investigate the rate of convergence of approximate solutions of (1) constructed by the Glimm scheme, under the assumption that, letting $\lambda_k(u)$, $r_k(u)$ denote the $k$-th eigenvalue and a corresponding eigenvector of $A(u)$, respectively, for each $k$-th characteristic family the linearly degenerate manifold $$\mathcal{M}_k \doteq \big\{u\in\Omega : \nabla\lambda_k(u)\cdot r_k(u)=0\big\}$$ is either the whole space, or it is empty, or it consists of a finite number of smooth, $N-1$-dimensional, connected, manifolds that are transversal to the characteristic vector field $r_k$. We introduce a Glimm type functional which is the sum of the cubic interaction potential defined in \cite{sie}, and of a quadratic term that takes into account interactions of waves of the same family with strength smaller than some fixed threshold parameter. Relying on an adapted wave tracing method, and on the decrease amount of such a functional, we obtain the same type of error estimates valid for Glimm approximate solutions of hyperbolic systems satisfying the classical Lax assumptions of genuine nonlinearity or linear degeneracy of the characteristic families.Comment: To appear on Archive for Rational Mechanics and Analysi

Entanglement entropy of non-unitary conformal field theory

Here we show that the Rényi entanglement entropy of a region of large size ℓ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as ceff(n+1)/2n log(L), where ceff=c-24Delta > 0 is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and Delta < 0 is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic, then there is an additional term proportional to $log(log(L)). These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models