Numerical Measurements of Scaling Relations in Two-Dimensional Conformal Fluid Turbulence

We present measurements of relativistic scaling relations in $(2+1)$-dimensional conformal fluid turbulence from direct numerical simulations, in the weakly compressible regime. These relations were analytically derived previously in Westernacher-Schneider, Lehner, Oz (2015) for a relativistic fluid; this work is a continuation of that study, providing further analytical insights together with numerical experiments to test the scaling relations and extract other important features characterizing the turbulent behavior. We first explicitly demonstrate that the non-relativistic limit of these scaling relations reduce to known results from the statistical theory of incompressible Navier-Stokes turbulence. In simulations of the inverse-cascade range, we find the relevant relativistic scaling relation is satisfied to a high degree of accuracy. We observe that the non-relativistic versions of this scaling relation underperform the relativistic one in both an absolute and relative sense, with a progressive degradation as the rms Mach number increases from $0.14$ to $0.19$. In the direct-cascade range, the two relevant relativistic scaling relations are satisfied with a lower degree of accuracy in a simulation with rms Mach number $0.11$. We elucidate the poorer agreement with further simulations of an incompressible Navier-Stokes fluid. Finally, as has been observed in the incompressible Navier-Stokes case, we show that the energy spectrum in the inverse-cascade of the conformal fluid exhibits $k^{-2}$ scaling rather than the Kolmogorov/Kraichnan expectation of $k^{-5/3}$, and that it is not necessarily associated with compressive effects. We comment on the implications for a recent calculation of the fractal dimension of a turbulent $(3+1)$-dimensional AdS black brane.Comment: 18 pages, 10 figures, 1 table. To be submitted to JHEP - comments welcome. V2 contains a technical edit for the JHEP compiler, as well as minor grammatical correction

How Big is Too Big? : The Potentially Coercive Effects of Plea Discount on Innocent Defendants

In the United States, approximately 95% of all criminal cases end in guilty pleas. Many scholars are concerned with plea bargaining’s potential to be coercive, and cite data on wrongful convictions as proof that an innocence problem exists. Estimates of false guilty pleas may range between 18 and 27 percent, though a true base rate is difficult to establish. Using vignettes, I examined the effects of guilt, trial penalty and plea discount size on plea decisions of adult participants recruited online through TurkPrime. Guilt was the strongest predictor of plea acceptance, but guilty plea rates increased for all participants with increasing discount and decreasing trial penalty, and the rate of false guilty pleas reached 18% in some conditions. Results are discussed in the context of the psychology of human decision making and in terms of their implications for public policy

Hecke Algebra Characters Evaluatedat Kazhdan-Lusztig Basis Elements Give the Betti Numbers of Hessenberg Varieties

From the Washington University Senior Honors Thesis Abstracts (WUSHTA), Spring 2018. Published by the Office of Undergraduate Research. Joy Zalis Kiefer, Director of Undergraduate Research and Associate Dean in the College of Arts & Sciences; Lindsey Paunovich, Editor; Helen Human, Programs Manager and Assistant Dean in the College of Arts and Sciences Mentor: John Shareshia

Dietary Patterns and Prostate Cancer Aggressiveness in African-American and European-American Men

Several foods and nutrients have been linked to prostate cancer risk, but the effect of overall diet on prostate cancer outcomes is not well understood. Previous research has primarily examined a posteriori dietary patterns in relation to prostate cancer; studies that have used a priori dietary patterns and their relationship with prostate cancer have been inconclusive. Furthermore, racial differences in prostate cancer incidence and aggressiveness are not well understood. Data from the case-only North Carolina-Louisiana Prostate Cancer Project (PCaP) was used to examine the association between overall dietary pattern, as measured by the Mediterranean Diet (MED) score and the Dietary Approaches to Stop Hypertension (DASH) score, and prostate cancer aggressiveness in African-American (AA) and European-American (EA) men. Dietary patterns were assessed using a modified NCI Diet History Questionnaire for a final sample of 1,899 participants. Higher MED scores were found to be inversely associated with high aggressive prostate cancer overall (OR: 92; 95% CI: 0.84-0.99; p trend: 0.03); and results were similar for AA men and EA men. DASH scores were not significantly associated with prostate cancer aggressiveness. These results suggest that following a Mediterranean diet may decrease the risk of developing high aggressive prostate cancer

Dynamical Thin Disks

Thin disk accretion is often modeled in highly dynamical settings using the two-dimensional equations of viscous hydrodynamics, with viscosity representing unresolved turbulence. These equations are supposed to arise after vertical integration of the full three-dimensional equations of hydrodynamics, under the assumption of a geometrically thin disk with mirror symmetry about the midplane. But in the dynamical context, vertical dynamics are neglected by incorrectly assuming instantaneous vertical hydrostatic equilibrium. The resulting errors in the local disk height couple to the horizontal dynamics through some viscosity prescriptions and gravitational softening models. Furthermore, the viscous terms in the horizontal equations are only complete if they are inserted after vertical integration, as if the system is actually two-dimensional. Since turbulence breaks mirror symmetry, it is more physically correct to insert a turbulence model at the three-dimensional level, and impose mirror symmetry only on average. Thus, some viscous terms are usually missing. We revisit the vertical integration procedure, restricting to the regime of a Newtonian, non-self-gravitating disk. We obtain six evolution equations with only horizontal dependence, which determine the local vertical position and velocity of the disk surface, in addition to the usual fluid variables. This "2.5-dimensional" formulation opens the door to efficiently study vertical oscillations of thin disks in dynamical settings, and to improve the treatment of unresolved turbulence. As a demonstration, by including viscous stress at the three-dimensional level, we recover missing viscous terms which involve the vertical variables. We also propose a resummation of the vertically integrated gravitational force, which has a strikingly similar form to a gravitational softening model advocated for in protoplanetary disk studies.Comment: Accepted to Physical Review