Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations

We define the concept of energy-variational solutions for the Ericksen--Leslie equations in three spatial dimensions. This solution concept is finer than dissipative solutions and satisfies the weak-strong uniqueness property. For a certain choice of the regularity weight, the existence of energy-variational solutions implies the existence of measure-valued solutions and for a different choice, we construct an energy-variational solution with the help of an implementable, structure-inheriting space-time discretization. Computational studies are performed in order to provide some evidence of the applicability of the proposed algorithm

Wall modes and the transition to bulk convection in rotating Rayleigh-B\'enard convection

We investigate states of rapidly rotating Rayleigh-B\'enard convection in a cylindrical cell over a range of Rayleigh number $3\times10^5\leq Ra \leq 5\times10^{9}$ and Ekman number $10^{-6} \leq Ek \leq 10^{-4}$ for Prandtl number $Pr = 0.8$ and aspect ratios $1/5 \leq \Gamma \leq 5$ using direct numerical simulations. We characterize, for perfectly insulating sidewall boundary conditions, the first transition to convection via wall mode instability and the nonlinear growth and instability of the resulting wall mode states including a secondary transition to time dependence. We show how the radial structure of the vertical velocity $u_z$ and the temperature $T$ is captured well by the linear eigenfunctions of the wall mode instability where the radial width of $u_z$ is $\delta_{u_z} \sim Ek^{1/3} r/H$ whereas $\delta_T \sim e^{-k r}$ ($k$ is the wavenumber of an laterally infinite wall mode state). The disparity in spatial scales for $Ek = 10^{-6}$ means that the heat transport is dominated by the radial structure of $u_z$ since $T$ varies slowly over the radial scale $\delta_{u_z}$. We further describe how the transition to a state of bulk convection is influenced by the presence of the wall mode states. We use temporal and spatial scales as measures of the local state of convection and the Nusselt number $Nu$ as representative of global transport. Our results elucidate the evolution of the wall state of rotating convection and confirm that wall modes are strongly linked with the boundary zonal flow (BZF) being the robust remnant of nonlinear wall mode states. We also show how the heat transport ($Nu$) contributions of wall modes and bulk modes are related and discuss approaches to disentangling their relative contributions

MR Spectroscopic Imaging of Peripheral Zone in Prostate Cancer Using a 3T MRI Scanner: Endorectal versus External Phased Array Coils.

Magnetic resonance spectroscopic imaging (MRSI) detects alterations in major prostate metabolites, such as citrate (Cit), creatine (Cr), and choline (Ch). We evaluated the sensitivity and accuracy of three-dimensional MRSI of prostate using an endorectal compared to an external phased array "receive" coil on a 3T MRI scanner. Eighteen patients with prostate cancer (PCa) who underwent endorectal MR imaging and proton (1H) MRSI were included in this study. Immediately after the endorectal MRSI scan, the PCa patients were scanned with the external phased array coil. The endorectal coil-detected metabolite ratio [(Ch+Cr)/Cit] was significantly higher in cancer locations (1.667 ± 0.663) compared to non-cancer locations (0.978 ± 0.420) (P < 0.001). Similarly, for the external phased array, the ratio was significantly higher in cancer locations (1.070 ± 0.525) compared to non-cancer locations (0.521 ± 0.310) (P < 0.001). The sensitivity and accuracy of cancer detection were 81% and 78% using the endorectal 'receive' coil, and 69% and 75%, respectively using the external phased array 'receive' coil

LiSc(BH_4)_4 as a Hydrogen Storage Material: Multinuclear High-Resolution Solid-State NMR and First-Principles Density Functional Theory Studies

A lithium salt of anionic scandium tetraborohydride complex, LiSc(BH_4)_4, was studied both experimentally and theoretically as a potential hydrogen storage medium. Ball milling mixtures of LiBH_4 and ScCl_3 produced LiCl and a unique crystalline hydride, which has been unequivocally identified via multinuclear solid-state nuclear magnetic resonance (NMR) to be LiSc(BH_4)_4. Under the present reaction conditions, there was no evidence for the formation of binary Sc(BH_4)_3. These observations are in agreement with our first-principles calculations of the relative stabilities of these phases. A tetragonal structure in space group I (#82) is predicted to be the lowest energy state for LiSc(BH_4)_4, which does not correspond to structures obtained to date on the crystalline ternary borohydride phases made by ball milling. Perhaps reaction conditions are resulting in formation of other polymorphs, which should be investigated in future studies via neutron scattering on deuterides. Hydrogen desorption while heating these Li−Sc−B−H materials up to 400 °C yielded only amorphous phases (besides the virtually unchanged LiCl) that were determined by NMR to be primarily ScB_2 and [B_(12)H_(12)]^(−2) anion containing (e.g., Li_2B_(12)H_(12)) along with residual LiBH_4. Reaction of a desorbed LiSc(BH_4)_4 + 4LiCl mixture (from 4LiBH_4/ScCl_3 sample) with hydrogen gas at 70 bar resulted only in an increase in the contents of Li_2B_(12)H_(12) and LiBH_4. Full reversibility to reform the LiSc(BH_4)_4 was not found. Overall, the Li−Sc−B−H system is not a favorable candidate for hydrogen storage applications

Human prostate sphere-forming cells represent a subset of basal epithelial cells capable of glandular regeneration in vivo.

BackgroundProstate stem/progenitor cells function in glandular development and maintenance. They may be targets for tumor initiation, so characterization of these cells may have therapeutic implications. Cells from dissociated tissues that form spheres in vitro often represent stem/progenitor cells. A subset of human prostate cells that form prostaspheres were evaluated for self-renewal and tissue regeneration capability in the present study.MethodsProstaspheres were generated from 59 prostatectomy specimens. Lineage marker expression and TMPRSS-ERG status was determined via immunohistochemistry and fluorescence in situ hybridization (FISH). Subpopulations of prostate epithelial cells were isolated by cell sorting and interrogated for sphere-forming activity. Tissue regeneration potential was assessed by combining sphere-forming cells with rat urogenital sinus mesenchyme (rUGSM) subcutaneously in immunocompromised mice.ResultsProstate tissue specimens were heterogeneous, containing both benign and malignant (Gleason 3-5) glands. TMPRSS-ERG fusion was found in approximately 70% of cancers examined. Prostaspheres developed from single cells at a variable rate (0.5-4%) and could be serially passaged. A basal phenotype (CD44+CD49f+CK5+p63+CK8-AR-PSA-) was observed among sphere-forming cells. Subpopulations of prostate cells expressing tumor-associated calcium signal transducer 2 (Trop2), CD44, and CD49f preferentially formed spheres. In vivo implantation of sphere-forming cells and rUGSM regenerated tubular structures containing discreet basal and luminal layers. The TMPRSS-ERG fusion was absent in prostaspheres derived from fusion-positive tumor tissue, suggesting a survival/growth advantage of benign prostate epithelial cells.ConclusionHuman prostate sphere-forming cells self-renew, have tissue regeneration capability, and represent a subpopulation of basal cells

Evidence and Ideology in Macroeconomics: The Case of Investment Cycles

The paper reports the principal findings of a long term research project on the description and explanation of business cycles. The research strongly confirmed the older view that business cycles have large systematic components that take the form of investment cycles. These quasi-periodic movements can be represented as low order, stochastic, dynamic processes with complex eigenvalues. Specifically, there is a fixed investment cycle of about 8 years and an inventory cycle of about 4 years. Maximum entropy spectral analysis was employed for the description of the cycles and continuous time econometrics for the explanatory models. The central explanatory mechanism is the second order accelerator, which incorporates adjustment costs both in relation to the capital stock and the rate of investment. By means of parametric resonance it was possible to show, both theoretically and empirically how cycles aggregate from the micro to the macro level. The same mathematical tool was also used to explain the international convergence of cycles. I argue that the theory of investment cycles was abandoned for ideological, not for evidential reasons. Methodological issues are also discussed

Science and Ideology in Economic, Political, and Social Thought

This paper has two sources: One is my own research in three broad areas: business cycles, economic measurement and social choice. In all of these fields I attempted to apply the basic precepts of the scientific method as it is understood in the natural sciences. I found that my effort at using natural science methods in economics was met with little understanding and often considerable hostility. I found economics to be driven less by common sense and empirical evidence, then by various ideologies that exhibited either a political or a methodological bias, or both. This brings me to the second source: Several books have appeared recently that describe in historical terms the ideological forces that have shaped either the direct areas in which I worked, or a broader background. These books taught me that the ideological forces in the social sciences are even stronger than I imagined on the basis of my own experiences. The scientific method is the antipode to ideology. I feel that the scientific work that I have done on specific, long standing and fundamental problems in economics and political science have given me additional insights into the destructive role of ideology beyond the history of thought orientation of the works I will be discussing