Lagrangian particle paths and ortho-normal quaternion frames

Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached to each Lagrangian fluid particle undergoing three-axis rotations, by using quaternions in combination with Ertel's theorem for frozen-in vorticity. The method is applicable to a wide range of Lagrangian flows including the three-dimensional Euler equations and its variants such as ideal MHD. The applicability of the quaterionic frame description to Lagrangian averaged velocity gradient dynamics is also demonstrated.Comment: 9 pages, one figure, revise

Development of an Optimization-Based Atomistic-to-Continuum Coupling Method

Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the efficiency of a continuum model. In this note we extend the optimization-based AtC, formulated in arXiv:1304.4976 for linear, one-dimensional problems to multi-dimensional settings and arbitrary interatomic potentials. We conjecture optimal error estimates for the multidimensional AtC, outline an implementation procedure, and provide numerical results to corroborate the conjecture for a 1D Lennard-Jones system with next-nearest neighbor interactions.Comment: 12 pages, 3 figure

On the well posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations

We give a well posed initial value formulation of the Baumgarte-Shapiro-Shibata-Nakamura form of Einstein's equations with gauge conditions given by a Bona-Masso like slicing condition for the lapse and a frozen shift. This is achieved by introducing extra variables and recasting the evolution equations into a first order symmetric hyperbolic system. We also consider the presence of artificial boundaries and derive a set of boundary conditions that guarantee that the resulting initial-boundary value problem is well posed, though not necessarily compatible with the constraints. In the case of dynamical gauge conditions for the lapse and shift we obtain a class of evolution equations which are strongly hyperbolic and so yield well posed initial value formulations

Effects of post metallization annealing on Al2O3 atomic layer deposition on n-GaN

The chemical, physical and electrical properties and the robustness of post metallization annealed Al2O3 atomic layers deposited on n-type GaN are investigated in this work. Planar metal insulator capacitors are used to demonstrate a gate-first with following ohmic contacts formation at elevated temperature up to 600 °C process flow. X-ray photoelectron spectroscopy indicates that no new bonds in the Al2O3 layer are formed due to exposure to the elevated annealing temperature. X-ray diffraction measurements show no crystallization of the oxide layer. Atomic force microscopy shows signs of degradation of the sample annealed at 600 °C. Electrical measurements indicate that the elevated annealing temperature results in an increase of the oxide depletion and the deep depletion capacitances simultaneously, that results in a reduction of the flat band voltage to zero, which is explained by fixed oxide charges curing. A forward bias step stress capacitance measurement shows that the total number of induced trapped charges are not strongly affected by the elevated annealing temperatures. Interface trap density of states analysis shows the lowest trapping concentration for the capacitor annealed at 500 °C. Above this temperature, the interface trap density of states increases. When all results are taken into consideration, we have found that the process thermal budget allows for an overlap between the gate oxide post metallization annealing and the ohmic contact formation at 500 °C

Control of Flow Structure on a Semi-Circular Planform Wing

Active flow control is used to modify the lift, drag and pitching moments on a semicircular wing with aspect ratio, AR = 2, and chord Reynolds number is 68,000. The wing is mounted on a pitch/plunge sting mechanism that responds to the instantaneous loads and moments acting on the wing. The leading edge of the airfoil contains 16 spatially localized actuators that can be independently controlled. Smoke wire visualization, surface pressure and six-component force balance measurements are used to characterize the effects of openloop forcing. The lift coefficients on the steady wing are enhanced with the actuation, similar to the effect of dynamic stall vortex lift enhancement that occurs during a pitch up maneuver. Surface pressure measurements are being used to construct a flow model for use in feedback control. Progress toward the goal of designing a feedback controller to stabilize the flight of the model in an oscillatory freestream is discussed

Increased C-reactive protein concentration and suicidal behavior in people with psychiatric disorders: A systematic review and meta-analysis

Objective: Suicide is a leading cause of death worldwide. Identifying factors associated with suicidality (suicidal ideation [SI]/suicidal behavior) could increase our understanding of the pathophysiological underpinnings of suicide and improve its prevention. Methods: We conducted a systematic review (PubMed/PsycInfo/Cochrane databases, up to September 2020) and random-effect meta-analysis including observational studies comparing peripheral C-reactive protein (CRP) levels in suicidal versus non-suicidal patients affected by any psychiatric disorder and healthy controls (HC). Primary outcome was the CRP standardized mean difference (SMD) between patients with high suicidality versus those with absent or low suicidality. Secondary outcomes were SMD of CRP levels between those with suicide attempt versus no suicide attempt, as well as between those with (high) versus low or absent SI. Quality of included studies was measured with Newcastle-Ottawa scale. Results: Out of initial 550 references, 21 observational studies involving 7682 subjects (7445 with mood disorders or first-episode psychosis, 237 HC) were included. A significant association of CRP levels with suicidality (SMD 0.688, 95% CI 0.476–0.9, p < 0.001) emerged. CRP levels were higher in individuals with high SI (SMD 1.145, 95% CI 0.273–2.018, p = 0.010) and in those with suicide attempt (SMD 0.549, 95%CI 0.363–0.735, p < 0.001) than non-suicidal individuals (either patients or HC). Main analyses were confirmed in sensitivity analysis (removing HC), and after adjusting for publication bias. The cross-sectional design of included studies, and the high heterogeneity of diagnosis and treatment limit the generalizability of these results. Median quality of included studies was high. Conclusion: CRP is associated with higher suicidality in patients with mental disorders. Large cohort studies longitudinally monitoring CRP levels are needed to explore its longitudinal association with suicidality

Renormalization group approach to multiscale modelling in materials science

Dendritic growth, and the formation of material microstructure in general, necessarily involves a wide range of length scales from the atomic up to sample dimensions. The phase field approach of Langer, enhanced by optimal asymptotic methods and adaptive mesh refinement, copes with this range of scales, and provides an effective way to move phase boundaries. However, it fails to preserve memory of the underlying crystallographic anisotropy, and thus is ill-suited for problems involving defects or elasticity. The phase field crystal (PFC) equation-- a conserving analogue of the Hohenberg-Swift equation --is a phase field equation with periodic solutions that represent the atomic density. It can natively model elasticity, the formation of solid phases, and accurately reproduces the nonequilibrium dynamics of phase transitions in real materials. However, the PFC models matter at the atomic scale, rendering it unsuitable for coping with the range of length scales in problems of serious interest. Here, we show that a computationally-efficient multiscale approach to the PFC can be developed systematically by using the renormalization group or equivalent techniques to derive appropriate coarse-grained coupled phase and amplitude equations, which are suitable for solution by adaptive mesh refinement algorithms

Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation

Hyperviscosity, Galerkin truncation and bottlenecks in turbulence

It is shown that the use of a high power $\alpha$ of the Laplacian in the dissipative term of hydrodynamical equations leads asymptotically to truncated inviscid \textit{conservative} dynamics with a finite range of spatial Fourier modes. Those at large wavenumbers thermalize, whereas modes at small wavenumbers obey ordinary viscous dynamics [C. Cichowlas et al. Phys. Rev. Lett. 95, 264502 (2005)]. The energy bottleneck observed for finite $\alpha$ may be interpreted as incomplete thermalization. Artifacts arising from models with $\alpha > 1$ are discussed.Comment: 4 pages, 2 figures, Phys. Rev. Lett. in pres