Simulation of a particle-laden turbulent channel flow using an improved stochastic Lagrangian model

The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift velocity in the limits of low and high particle inertia, is derived. It is also shown that some previously proposed stochastic models are not compatible with this transport equation in the limit of high particle inertia. The drift and diffusion parameters of these stochastic differential equations are then estimated using direct numerical simulation (DNS) data. It is observed that, contrary to the conventional modeling, they are highly space dependent and anisotropic. To investigate the performance of the present stochastic model, a comparison is made with DNS data as well as with two different stochastic models. A good prediction of the first and second order statistical moments of the particle and fluid seen velocities is obtained with the three models considered. Even for some components of the triple particle velocity correlations, an acceptable accordance is noticed. The performance of the three different models mainly diverges for the particle concentration and the drift velocity. The proposed model is seen to be the only one which succeeds in predicting the good evolution of these latter statistical quantities for the range of particle inertia studied

Spontaneous Raman scattering for simultaneous measurements of in-cylinder species

A technique for multi-species mole fraction measurement in internal combustion engines is described. The technique is based on the spontaneous Raman scattering. It can simultaneously provide the mole fractions of several species of N-2, O-2, H2O, CO2 and fuel. Using the system, simultaneous measurement of air/fuel ratio and burnt residual gas are carried out during the mixture process in a Controlled Auto Ignition (CAI) combustion engine. The accuracy and consistency of the measured results were confirmed by the measured air fuel ratio using an exhaust gas analyzer and independently calculated mole fraction values. Measurement of species mole fractions during combustion process has also been demonstrated. It shows that the SRS can provide valuable data on this process in a CAI combustion engine

Reducing RBM20 activity improves diastolic dysfunction and cardiac atrophy

Impaired diastolic filling is a main contributor to heart failure with preserved ejection fraction (HFpEF), a syndrome with increasing prevalence and no treatment. Both collagen and the giant sarcomeric protein titin determine diastolic function. Since titin's elastic properties can be adjusted physiologically, we evaluated titin-based stiffness as a therapeutic target. We adjusted RBM20-dependent cardiac isoform expression in the titin N2B knockout mouse with increased ventricular stiffness. A ~50 % reduction of RBM20 activity does not only maintain cardiac filling in diastole but also ameliorates cardiac atrophy and thus improves cardiac function in the N2B-deficient heart. Reduced RBM20 activity partially normalized gene expression related to muscle development and fatty acid metabolism. The adaptation of cardiac growth was related to hypertrophy signaling via four-and-a-half lim-domain proteins (FHLs) that translate mechanical input into hypertrophy signals. We provide a novel link between cardiac isoform expression and trophic signaling via FHLs and suggest cardiac splicing as a therapeutic target in diastolic dysfunction. KEY MESSAGE: Increasing the length of titin isoforms improves ventricular filling in heart disease. FHL proteins are regulated via RBM20 and adapt cardiac growth. RBM20 is a therapeutic target in diastolic dysfunction

Solidity of Viscous Liquids

Recent NMR experiments on supercooled toluene and glycerol by Hinze and Bohmer show that small rotation angles dominate with only few large molecular rotations. These results are here interpreted by assuming that viscous liquids are solid-like on short length scales. A characteristic length, the "solidity length", separates solid-like behavior from liquid-like behavior.Comment: Plain RevTex file, no figure

Crustal Composition and Moho Variations of the Central and Eastern United States: Improving Resolutionand Geologic Interpretation of EarthScope USArray Seismic Images Using Gravity

EarthScope\u27s USArray Transportable Array has shortcomings for the purpose of interpreting geologic features of wavelengths less than the Transportable Array station spacing, but these can be overcome by using higher spatial resolution gravity data. In this study, we exploit USArray receiver functions to reduce nonuniqueness in the interpretation of gravity anomalies. We model gravity anomalies from previously derived density variations of sedimentary basins, crustal Vp/Vs variation, Moho variation, and upper mantle density variation derived from body wave imaging informed by surface wave tomography to estimate Vp/Vs. Although average densities and density contrasts for these seismic variations can be derived, the gravity anomalies modeled from them do not explain the entire observed gravity anomaly field in the United States. We use the unmodeled gravity anomalies (residuals) to reconstruct local variations in densities of the crust associated with geologic sources. The approach uses velocity‐density relationships and differs from density computations that assume isostatic compensation. These intracrustal densities identify geologic sources not sampled by and, in some cases, aliased by the USArray station spacing. We show an example of this improvement in the vicinity of the Bloomfield Pluton, north of the bootheel of Missouri, in the central United States

Serum S100A8/A9 and S100A12 Levels in Children With Polyarticular Forms of Juvenile Idiopathic Arthritis: Relationship to Maintenance of Clinically Inactive Disease During Anti–Tumor Necrosis Factor Therapy and Occurrence of Disease Flare After Discontinuation of Therapy

© 2018, American College of Rheumatology Objective: To determine the relationship between serum levels of S100A8/A9 and S100A12 and the maintenance of clinically inactive disease during anti–tumor necrosis factor (anti-TNF) therapy and the occurrence of disease flare following withdrawal of anti-TNF therapy in patients with polyarticular forms of juvenile idiopathic arthritis (JIA). Methods: In this prospective, multicenter study, 137 patients with polyarticular-course JIA whose disease was clinically inactive while receiving anti-TNF therapy were enrolled. Patients were observed for an initial 6-month phase during which anti-TNF treatment was continued. For those patients who maintained clinically inactive disease over the 6 months, anti-TNF was withdrawn and they were followed up for 8 months to assess for the occurrence of flare. Serum S100 levels were measured at baseline and at the time of anti-TNF withdrawal. Spearman\u27s rank correlation test, Mann-Whitney U test, Kruskal-Wallis test, receiver operating characteristic (ROC) curve, and Kaplan-Meier survival analyses were used to assess the relationship between serum S100 levels and maintenance of clinically inactive disease and occurrence of disease flare after anti-TNF withdrawal. Results: Over the 6-month initial phase with anti-TNF therapy, the disease state reverted from clinically inactive to clinically active in 24 (18%) of the 130 evaluable patients with polyarticular-course JIA; following anti-TNF withdrawal, 39 (37%) of the 106 evaluable patients experienced a flare. Serum levels of S100A8/A9 and S100A12 were elevated in up to 45% of patients. Results of the ROC analysis revealed that serum S100 levels did not predict maintenance of clinically inactive disease during anti-TNF therapy nor did they predict disease flare after treatment withdrawal. Elevated levels of S100A8/A9 were not predictive of the occurrence of a disease flare within 30 days, 60 days, 90 days, or 8 months following anti-TNF withdrawal, and elevated S100A12 levels had a modest predictive ability for determining the risk of flare within 30, 60, and 90 days after treatment withdrawal. Serum S100A12 levels at the time of anti-TNF withdrawal were inversely correlated with the time to disease flare (r = −0.36). Conclusion: Serum S100 levels did not predict maintenance of clinically inactive disease or occurrence of disease flare in patients with polyarticular-course JIA, and S100A12 levels were only moderately, and inversely, correlated with the time to disease flare

Molecular mode-coupling theory applied to a liquid of diatomic molecules

We study the molecular mode coupling theory for a liquid of diatomic molecules. The equations for the critical tensorial nonergodicity parameters ${\bf F}_{ll'}^m(q)$ and the critical amplitudes of the $\beta$ - relaxation ${\bf H}_{ll'}^m(q)$ are solved up to a cut off $l_{co}$ = 2 without any further approximations. Here $l,m$ are indices of spherical harmonics. Contrary to previous studies, where additional approximations were applied, we find in agreement with simulations, that all molecular degrees of freedom vitrify at a single temperature $T_c$. The theoretical results for the non ergodicity parameters and the critical amplitudes are compared with those from simulations. The qualitative agreement is good for all molecular degrees of freedom. To study the influence of the cut off on the non ergodicity parameter, we also calculate the non ergodicity parameters for an upper cut off $l_{co}=4$. In addition we also propose a new method for the calculation of the critical nonergodicity parameterComment: 27 pages, 17 figure

The mean-squared displacement of a molecule moving in a glassy system

The mean-squared displacement (MSD) of a hard sphere and of a dumbbell molecule consisting of two fused hard spheres immersed in a dense hard-sphere system is calculated within the mode-coupling theory for ideal liquid-glass transitions. It is proven that the velocity correlator, which is the second time derivative of the MSD, is the negative of a completely monotone function for times within the structural-relaxation regime. The MSD is found to exhibit a large time interval for structural relaxation prior to the onset of the $\alpha$-process which cannot be described by the asymptotic formulas for the mode-coupling-theory-bifurcation dynamics. The $\alpha$-process for molecules with a large elongation is shown to exhibit an anomalously wide cross-over interval between the end of the von-Schweidler decay and the beginning of normal diffusion. The diffusivity of the molecule is predicted to vary non-monotonically as function of its elongation.Comment: 18 pages, 12 figures, Phys. Rev. E, in prin

Diffusion and viscosity in a supercooled polydisperse system

We have carried out extensive molecular dynamics simulations of a supercooled polydisperse Lennard-Jones liquid with large variations in temperature at a fixed pressure. The particles in the system are considered to be polydisperse both in size and mass. The temperature dependence of the dynamical properties such as the viscosity ($\eta$) and the self-diffusion coefficients ($D_i$) of different size particles is studied. Both viscosity and diffusion coefficients show super-Arrhenius temperature dependence and fit well to the well-known Vogel-Fulcher-Tammann (VFT) equation. Within the temperature range investigated, the value of the Angell's fragility parameter (D $\approx 1.4$) classifies the present system into a strongly fragile liquid. The critical temperature for diffusion ($T_o^{D_i}$) increases with the size of the particles. The critical temperature for viscosity ($T_o^{\eta}$) is larger than that for the diffusion and a sizeable deviations appear for the smaller size particles implying a decoupling of translational diffusion from viscosity in deeply supercooled liquid. Indeed, the diffusion shows markedly non-Stokesian behavior at low temperatures where a highly nonlinear dependence on size is observed. An inspection of the trajectories of the particles shows that at low temperatures the motions of both the smallest and largest size particles are discontinuous (jump-type). However, the crossover from continuous Brownian to large length hopping motion takes place at shorter time scales for the smaller size particles.Comment: Revtex4, 7 pages, 8 figure

Second order optimality conditions and their role in PDE control

If f : Rn R is twice continuously differentiable, f’(u) = 0 and f’’(u) is positive definite, then u is a local minimizer of f. This paper surveys the extension of this well known second order suffcient optimality condition to the case f : U R, where U is an infinite-dimensional linear normed space. The reader will be guided from the case of finite-dimensions via a brief discussion of the calculus of variations and the optimal control of ordinary differential equations to the control of nonlinear partial differential equations, where U is a function space. In particular, the following questions will be addressed: Is the extension to infinite dimensions straightforward or will unexpected difficulties occur? How second order sufficient optimality conditions must be modified, if simple inequality constraints are imposed on u? Why do we need second order conditions and how can they be applied? If they are important, are we able to check if they are fulfilled order sufficient optimality condition to the case f : U R, where U is an infinite-dimensional linear normed space. The reader will be guided from the case of finite-dimensions via a brief discussion of the calculus of variations and the optimal control of ordinary differential equations to the control of nonlinear partial differential equations, where U is a function space. In particular, the following questions will be addressed: Is the extension to infinite dimensions straightforward or will unexpected difficulties occur? How second order sufficient optimality conditions must be modified, if simple inequality constraints are imposed on u? Why do we need second order conditions and how can they be applied? If they are important, are we able to check if they are fulfilled? It turns out that infinite dimensions cause new difficulties that do not occur in finite dimensions. We will be faced with the surprising fact that the space, where f’’(u) exists can be useless to ensure positive definiteness of the quadratic form v f’’(u)v2. In this context, the famous two-norm discrepancy, its consequences, and techniques for overcoming this difficulty are explained. To keep the presentation simple, the theory is developed for problems in function spaces with simple box constraints of the form a = u = ß. The theory of second order conditions in the control of partial differential equations is presented exemplarily for the nonlinear heat equation. Different types of critical cones are introduced, where the positivity of f’’(u) must be required. Their form depends on whether a so-called Tikhonov regularization term is part of the functional f or not. In this context, the paper contains also new results that lead to quadratic growth conditions in the strong sense. As a first application of second-order sufficient conditions, the stability of optimal solutions with respect to perturbations of the data of the control problem is discussed. Second, their use in analyzing the discretization of control problems by finite elements is studied. A survey on further related topics, open questions, and relevant literature concludes the paper.The first author was partially supported by the Spanish Ministerio de Economía y Competitividad under project MTM2011-22711, the second author by DFG in the framework of the Collaborative Research Center SFB 910, project B6