Opportunities for use of exact statistical equations

Exact structure function equations are an efficient means of obtaining asymptotic laws such as inertial range laws, as well as all measurable effects of inhomogeneity and anisotropy that cause deviations from such laws. "Exact" means that the equations are obtained from the Navier-Stokes equation or other hydrodynamic equations without any approximation. A pragmatic definition of local homogeneity lies within the exact equations because terms that explicitly depend on the rate of change of measurement location appear within the exact equations; an analogous statement is true for local stationarity. An exact definition of averaging operations is required for the exact equations. Careful derivations of several inertial range laws have appeared in the literature recently in the form of theorems. These theorems give the relationships of the energy dissipation rate to the structure function of acceleration increment multiplied by velocity increment and to both the trace of and the components of the third-order velocity structure functions. These laws are efficiently derived from the exact velocity structure function equations. In some respects, the results obtained herein differ from the previous theorems. The acceleration-velocity structure function is useful for obtaining the energy dissipation rate in particle tracking experiments provided that the effects of inhomogeneity are estimated by means of displacing the measurement location.Comment: accepted by Journal of Turbulenc

Modelling of the evolution of a droplet cloud in a turbulent flow

The effects of droplet inertia and turbulent mixing on the droplet number density distribution in a turbulent flow field are studied. A formulation of the turbulent convective diffusion equation for the droplet number density, based on the modified Fully Lagrangian Approach, is proposed. The Fully Lagrangian Approach for the dispersed phase is extended to account for the Hessian of transformation from Eulerian to Lagrangian variables. Droplets with moderate inertia are assumed to be transported and dispersed by large scale structures of a filtered field in the Large Eddy Simulation (LES) framework. Turbulent fluctuations, not visible in the filtered solution for the droplet velocity field, induce an additional diffusion mass flux and hence additional dispersion of the droplets. The Lagrangian formulation of the transport equation for the droplet number density and the modified Fully Lagrangian Approach (FLA) make it possible to resolve the flow regions with intersecting droplet trajectories in the filtered flow field. Thus, we can cope successfully with the problems of multivalued filtered droplet velocity regions and caustic formation. The spatial derivatives for the droplet number density are calculated by projecting the FLA solution on the Eulerian mesh, resulting in a hybrid Lagrangian–Eulerian approach to the problem. The main approximations for the method are supported by the calculation of droplet mixing in an unsteady one-dimensional flow field formed by large-scale oscillations with an imposed small-scale modulation. The results of the calculations for droplet mixing in decaying homogeneous and isotropic turbulence are validated by the results of Direct Numerical Simulations (DNS) for several values of the Stokes number

Meningioma of the pineal region

Meningiomas rarely occur in the pineal region, but they can reach huge diameters. We presented the case of a patient with a very large meningioma of the pineal region (6x5x4 cm). The tumor, developed from the falcotentorial junction, was totally removed via an occipital interhemispheric transtentorial approach with minimal postoperative neurological deficits. The postoperative course was complicated with an acute internal hydrocephalus that needed temporary placement of an external ventricular drainage. The supratentorial surgical corridors allow for increased exposure and are best suited for falcotentorial meningiomas

Longitudinal Structure Functions in Decaying and Forced Turbulence

In order to reliably compute the longitudinal structure functions in decaying and forced turbulence, local isotropy is examined with the aid of the isotropic expression of the incompressible conditions for the second and third order structure functions. Furthermore, the Karman-Howarth-Kolmogorov relation is investigated to examine the effects of external forcing and temporally decreasing of the second order structure function. On the basis of these investigations, the scaling range and exponents $\zeta_n$ of the longitudinal structure functions are determined for decaying and forced turbulence with the aid of the extended-self-similarity (ESS) method. We find that $\zeta_n$'s are smaller, for $n \geq 4$, in decaying turbulence than in forced turbulence. The reasons for this discrepancy are discussed. Analysis of the local slopes of the structure functions is used to justify the ESS method.Comment: 15 pages, 16 figure

Diffused vorticity approach to the oscillations of a rotating Bose-Einstein condensate confined in a harmonic plus quartic trap

The collective modes of a rotating Bose-Einstein condensate confined in an attractive quadratic plus quartic trap are investigated. Assuming the presence of a large number of vortices we apply the diffused vorticity approach to the system. We then use the sum rule technique for the calculation of collective frequencies, comparing the results with the numerical solution of the linearized hydrodynamic equations. Numerical solutions also show the existence of low-frequency multipole modes which are interpreted as vortex oscillations.Comment: 10 pages, 4 figure

Separation between coherent and turbulent fluctuations. What can we learn from the Empirical Mode Decomposition?

The performances of a new data processing technique, namely the Empirical Mode Decomposition, are evaluated on a fully developed turbulent velocity signal perturbed by a numerical forcing which mimics a long-period flapping. First, we introduce a "resemblance" criterion to discriminate between the polluted and the unpolluted modes extracted from the perturbed velocity signal by means of the Empirical Mode Decomposition algorithm. A rejection procedure, playing, somehow, the role of a high-pass filter, is then designed in order to infer the original velocity signal from the perturbed one. The quality of this recovering procedure is extensively evaluated in the case of a "mono-component" perturbation (sine wave) by varying both the amplitude and the frequency of the perturbation. An excellent agreement between the recovered and the reference velocity signals is found, even though some discrepancies are observed when the perturbation frequency overlaps the frequency range corresponding to the energy-containing eddies as emphasized by both the energy spectrum and the structure functions. Finally, our recovering procedure is successfully performed on a time-dependent perturbation (linear chirp) covering a broad range of frequencies.Comment: 23 pages, 13 figures, submitted to Experiments in Fluid

Solar Wind Turbulence and the Role of Ion Instabilities

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Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates

We consider a 2D rotating Bose gas described by the Gross-Pitaevskii (GP) theory and investigate the properties of the ground state of the theory for rotational speeds close to the critical speed for vortex nucleation. While one could expect that the vortex distribution should be homogeneous within the condensate we prove by means of an asymptotic analysis in the strongly interacting (Thomas-Fermi) regime that it is not. More precisely we rigorously derive a formula due to Sheehy and Radzihovsky [Phys. Rev. A 70, 063620(R) (2004)] for the vortex distribution, a consequence of which is that the vortex distribution is strongly inhomogeneous close to the critical speed and gradually homogenizes when the rotation speed is increased. From the mathematical point of view, a novelty of our approach is that we do not use any compactness argument in the proof, but instead provide explicit estimates on the difference between the vorticity measure of the GP ground state and the minimizer of a certain renormalized energy functional.Comment: 41 pages, journal ref: Communications in Mathematical Physics: Volume 321, Issue 3 (2013), Page 817-860, DOI : 10.1007/s00220-013-1697-

Carfilzomib and dexamethasone versus bortezomib and dexamethasone for patients with relapsed or refractory multiple myeloma (ENDEAVOR): And randomised, phase 3, open-label, multicentre study

Background: Bortezomib with dexamethasone is a standard treatment option for relapsed or refractory multiple myeloma. Carfilzomib with dexamethasone has shown promising activity in patients in this disease setting. The aim of this study was to compare the combination of carfilzomib and dexamethasone with bortezomib and dexamethasone in patients with relapsed or refractory multiple myeloma. Methods: In this randomised, phase 3, open-label, multicentre study, patients with relapsed or refractory multiple myeloma who had one to three previous treatments were randomly assigned (1:1) using a blocked randomisation scheme (block size of four) to receive carfilzomib with dexamethasone (carfilzomib group) or bortezomib with dexamethasone (bortezomib group). Randomisation was stratified by previous proteasome inhibitor therapy, previous lines of treatment, International Staging System stage, and planned route of bortezomib administration if randomly assigned to bortezomib with dexamethasone. Patients received treatment until progression with carfilzomib (20 mg/m2 on days 1 and 2 of cycle 1; 56 mg/m2 thereafter; 30 min intravenous infusion) and dexamethasone (20 mg oral or intravenous infusion) or bortezomib (1·3 mg/m2; intravenous bolus or subcutaneous injection) and dexamethasone (20 mg oral or intravenous infusion). The primary endpoint was progression-free survival in the intention-to-treat population. All participants who received at least one dose of study drug were included in the safety analyses. The study is ongoing but not enrolling participants; results for the interim analysis of the primary endpoint are presented. The trial is registered at ClinicalTrials.gov, number NCT01568866. Findings: Between June 20, 2012, and June 30, 2014, 929 patients were randomly assigned (464 to the carfilzomib group; 465 to the bortezomib group). Median follow-up was 11·9 months (IQR 9·3-16·1) in the carfilzomib group and 11·1 months (8·2-14·3) in the bortezomib group. Median progression-free survival was 18·7 months (95% CI 15·6-not estimable) in the carfilzomib group versus 9·4 months (8·4-10·4) in the bortezomib group at a preplanned interim analysis (hazard ratio [HR] 0·53 [95% CI 0·44-0·65]; p<0·0001). On-study death due to adverse events occurred in 18 (4%) of 464 patients in the carfilzomib group and in 16 (3%) of 465 patients in the bortezomib group. Serious adverse events were reported in 224 (48%) of 463 patients in the carfilzomib group and in 162 (36%) of 456 patients in the bortezomib group. The most frequent grade 3 or higher adverse events were anaemia (67 [14%] of 463 patients in the carfilzomib group vs 45 [10%] of 456 patients in the bortezomib group), hypertension (41 [9%] vs 12 [3%]), thrombocytopenia (39 [8%] vs 43 [9%]), and pneumonia (32 [7%] vs 36 [8%]). Interpretation: For patients with relapsed or refractory multiple myeloma, carfilzomib with dexamethasone could be considered in cases in which bortezomib with dexamethasone is a potential treatment option. Funding: Onyx Pharmaceuticals, Inc., an Amgen subsidiary