An analysis of the vertical structure equation for arbitrary thermal profiles

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations

A conservative pressure-correction scheme for transient simulations of reacting flows

AbstractAn algorithm is presented for numerical simulations of time-dependent low Mach number variable density flows with an arbitrary amount of scalar transport equations and a complex equation of state. The pressure-correction type algorithm is based on a segregated solution formalism. It is conservative and guarantees stable results, regardless of the difference in density between neighboring cells. Furthermore, states are predicted which exactly match the equation of state. In the one-dimensional example, considering non-premixed flames, a simplified flamesheet model is used to describe the combustion of fuel and oxidizer. We demonstrate that the predicted states exactly correspond to the equation of state. We illustrate the accuracy improvement due to higher order formulation and demonstrate grid convergence

Dimensional Effects on Densities of States and Interactions in Nanostructures

We consider electrons in the presence of interfaces with different effective electron mass, and electromagnetic fields in the presence of a high-permittivity interface in bulk material. The equations of motion for these dimensionally hybrid systems yield analytic expressions for Green’s functions and electromagnetic potentials that interpolate between the two-dimensional logarithmic potential at short distance, and the three-dimensional r−1 potential at large distance. This also yields results for electron densities of states which interpolate between the well-known two-dimensional and three-dimensional formulas. The transition length scales for interfaces of thickness L are found to be of order Lm/2m* for an interface in which electrons move with effective mass m*, and for a dielectric thin film with permittivity in a bulk of permittivity . We can easily test the merits of the formalism by comparing the calculated electromagnetic potential with the infinite series solutions from image charges. This confirms that the dimensionally hybrid models are excellent approximations for distances r ≳ L/2

Superheavy dark matter and ultrahigh energy cosmic rays

The phase of inflationary expansion in the early universe produces superheavy relics in a mass window between 10^{12} GeV and 10^{14} GeV. Decay or annihilation of these superheavy relics can explain the observed ultrahigh energy cosmic rays beyond the Greisen-Zatsepin-Kuzmin cutoff. We emphasize that the pattern of cosmic ray arrival directions with energies beyond 20 EeV will decide between the different proposals for the origin of ultrahigh energy cosmic rays.Comment: Based on an invited talk given by RD at Theory Canada 1, Vancouver, June 2-5, 200

Laser frequency stabilization to a single ion

A fundamental limit to the stability of a single-ion optical frequency standard is set by quantum noise in the measurement of the internal state of the ion. We discuss how the interrogation sequence and the processing of the atomic resonance signal can be optimized in order to obtain the highest possible stability under realistic experimental conditions. A servo algorithm is presented that stabilizes a laser frequency to the single-ion signal and that eliminates errors due to laser frequency drift. Numerical simulations of the servo characteristics are compared to experimental data from a frequency comparison of two single-ion standards based on a transition at 688 THz in 171Yb+. Experimentally, an instability sigma_y(100 s)=9*10^{-16} is obtained in the frequency difference between both standards.Comment: 15 pages, 5 figures, submitted to J. Phys.

Prevalence of Mental Health Disorder Symptoms and Rates of Help-seeking Among University-Enrolled, Black Men

Background. Black men in college represent a subgroup of emerging adults who are at increased risk of developing mental health disorders (MHDs), such as anxiety and depression. Such risk has been attributed to disproportionate experiences with everyday racial discrimination and high levels of psychological distress. Despite being at higher risk, university-enrolled, Black men are not utilizing mental health or health resources at optimal rates. The current evidence base describing prevalence of MHDs and health services utilization among Black men in college is limited. The present study addresses this by examining mental health prevalence among university-enrolled, Black men and their rates of health services utilization. Methods. We analyzed data (N ~ 2500) from a student survey, Spit for Science, a longitudinal, ongoing, research study at a mid-Atlantic, public university. Participants are given surveys in their freshman year and follow-up surveys every spring thereafter. Measures included: mental health disorders (depression and anxiety, as measured by the Symptom Checklist 90) and campus health service utilization (counseling center, health services, wellness center, and recreational sports). We conducted descriptive analyses to determine MHD symptom prevalence and utilization rates; Mann Whitney U tests to compare prevalence rates to White men and Black women; and, Chi-squared tests to compare rates of utilization among groups. Results. During their Freshman year, greater than 60% of students from each ethnic group reported at least one anxiety symptom and greater than 80% reported at least one depressive symptom. By senior year, reporting rates decreased significantly for Black men (49.6%) but remained high for White men (69.1%) and Black women (63%); p \u3c0.000. For depression, results were similar; however, only significant differences between Black men (72.7%) and Black women (87.1%); p\u3c0.000. Black men (20.4%), though reporting high levels of symptoms, still utilized counseling services at lower rates compared to White men (37.76%); p = 0.024. Conclusion. Findings suggest that Black men underutilize available campus health resources despite reporting one or more symptoms associated with anxiety and depression. Further research and prevention efforts are needed to improve help-seeking among this vulnerable population.https://scholarscompass.vcu.edu/gradposters/1077/thumbnail.jp

Hot new directions for quasi-Monte Carlo research in step with applications

This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first order QMC methods in the unit cube $[0,1]^s$ and in $\mathbb{R}^s$, and higher order QMC methods in the unit cube. One important feature is that their error bounds can be independent of the dimension $s$ under appropriate conditions on the function spaces. Another important feature is that good parameters for these QMC methods can be obtained by fast efficient algorithms even when $s$ is large. We outline three different applications and explain how they can tap into the different QMC theory. We also discuss three cost saving strategies that can be combined with QMC in these applications. Many of these recent QMC theory and methods are developed not in isolation, but in close connection with applications

The Dutch Symptom Checklist-90-Revised:Is the Use of the Subscales Justified?

The Symptom Checklist-90-Revised (SCL-90-R; Derogatis, 1977, 1994) was constructed to measure both general psychological distress and specific primary symptoms of distress. In this study, we evaluated to what extent the scale scores of the Dutch SCL-90-R reflect general and/or specific aspects of psychological distress in a psychiatric outpatients sample (N = 1,842), using a hierarchical factor model. The results revealed that the total scale score measures general psychological distress, with high reliability. The subscale scores Sleep Difficulties, Agoraphobia, Hostility, and Somatization reflect the specific primary symptoms reasonably well, with high reliability. The subscale score Depression hardly measures specific symptoms of distress, but instead a very common construct as is measured with the total scale of the SCL-90-R. The use of the Depression subscale score beyond the total scale score of the SCL-90-R appears therefore of limited value in clinical practice