Stochastic turbulence modeling in RANS simulations via Multilevel Monte Carlo

A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are considered to demonstrate the applicability of the MLMC method. The first approach is based on global perturbation of the baseline eddy viscosity field using a lognormal random field. A more general second extension is considered based on the work of [Xiao et al.(2017)], where the entire Reynolds Stress Tensor (RST) is perturbed while maintaining realizability. For two fundamental flows, we show that the MLMC method based on a hierarchy of meshes is asymptotically faster than plain Monte Carlo. Additionally, we demonstrate that for some flows an optimal multilevel estimator can be obtained for which the cost scales with the same order as a single CFD solve on the finest grid level.Comment: 40 page

Effect of polymer properties and adherend surfaces on adhesion

High temperature polymer surface characteristics associated with joint strength were evaluated. Selected samples represented composite adherends, aluminum filler and fiber glass carrier cloth. Detailed analysis of fractured joint surfaces revealed unique characteristics typical of the specific adhesive formulations and test conditions. A fracture mechanism model was developed for correlating macroscopic shear strength and microstructure of fracture surfaces. Applications were made to unpublished data on polyimides and fluoropolymers

A fundamental approach to adhesion: Synthesis, surface analysis, thermodynamics and mechanics

The effects of composites as adherends was studied. Several other variables were studied by fractography: aluminum powder adhesive filler, fiber glass cloth scrim or adhesive carrier, new adhesives PPQ-413 and LARC-13, and strength-test temperature. When the new results were juxtaposed with previous work, it appeared that complex interactions between adhesive, adherend, bonding, and testing conditions govern the observed strength and fracture-surface features. The design parameters likely to have a significant effect upon strength-test results are listed

Overdamped dynamics of a Brownian particle levitated in a Paul trap

We study the dynamics of the center of mass of a Brownian particle levitated in a Paul trap. We focus on the overdamped regime in the context of levitodynamics, comparing theory with our numerical simulations and experimental data from a nanoparticle in a Paul trap. We provide an exact analytical solution to the stochastic equation of motion, expressions for the standard deviation of the motion, and thermalization times by using the WKB method under two different limits. Finally, we prove the power spectral density of the motion can be approximated by that of an Ornstein-Uhlenbeck process and use the found expression to calibrate the motion of a trapped particle

Peter Julian Eymard, Saint of the Eucharist and Our Lady of the Most Blessed Sacrament

St. Peter Julian Eymard (1811-1868) founded the Congregation of the Blessed Sacrament in 1856 and is known as the “Saint of the Eucharist” (a title confirmed by Pope St. John XXIII in his canonization homily, Dec. 9, 1962). He explored many aspects of the great mystery of the Holy Eucharist in the conferences he delivered to his fellow religious over the years. These conferences have been published in nine separate volumes under different titles. One of the volumes—entitled “Our Lady of the Most Blessed Sacrament: Readings for the Month of May”— consists of thirty-one conferences, one for each day of the month. This article explores the theological underpinnings of the glorious title, Our Lady of the Blessed Sacrament, and it discusses St. Peter Julian Eymard’s marvelous insights regarding the Blessed Virgin and her relation to the Eucharist. In a special way, it highlights Our Lady as the most perfect adorer of Jesus in the Blessed Sacrament

A fundamental approach to adhesion: Synthesis, surface analysis, thermodynamics and mechanics

Various surface preparations for titanium 6-4 alloy were studied. An anodizing method was investigated, and compared with the results of other chemical treatments, namely, phosphate/fluoride, Pasa-Jell and Turco. The relative durability of the different surface treatments was assessed by monitoring changes in surface chemistry and morphology occasioned by aging at 505 K (450 F). Basic electron spectroscopic data were collected for polyimide and polyphenylquinoxaline adhesives and synthetic precursors. Fractographic studies were completed for several combinations of adherend, adhesive, and testing conditions

Theological Foundations for Eucharistic Reparation to the Heart of Jesus through the Heart of Mary in the Context of Messages Given to St. Margaret Mary and at Fatima

The private revelations associated with Fatima, Portugal, beginning with the messages of the Angel to the children in 1916, and then by Our Lady beginning in May of 1917, focus on making reparation for sins and for the conversion of sinners through prayer and penance. Notably, the messages specifically request reparation for sins which offend the Immaculate Heart of Mary, and link this reparation to the Holy Eucharist—and, by implication, to Christ’s Heart present therein. The Fatima revelations follow upon and complement those communicated by Our Lord to St. Margaret Mary Alacoque at Paray-le-Monial in the 1670s, in which Jesus asks for reparation to His Heart in the Eucharist. This complementarity is evident in light of the deep and inseparable union between the Hearts of Jesus and Mary—a union that is recognized in Tradition and confirmed in recent papal teaching, especially that of Pope St. John Paul II