A note on reducing spurious pressure oscillations in fully conservative discontinuous Galerkin simulations of multicomponent flows

A well-known issue associated with the use of fully conservative schemes in multicomponent-flow simulations is the generation of spurious pressure oscillations at contact interfaces. These oscillations can rapidly lead to solver divergence even in the presence of smooth interfaces that are not fully resolved. In this note, we compare various strategies for reducing such oscillations that do not (a) introduce conservation error, (b) rely on artificial viscosity or limiting, or (c) degrade order of accuracy in smooth regions of the flow. The considered test case is one-dimensional advection of a high-pressure nitrogen/n-dodecane thermal bubble using the thermally perfect gas model. Several results are presented that contradict those corresponding to the more conventional hydrogen/oxygen thermal-bubble case

Manganese Oxide Thin Films Prepared by Nonaqueous Sol-Gel Processing: Preferential Formation of Birnessite

High quality manganese oxide thin films with smooth surfaces and even thicknesses have been prepared with a nonaqueous sol–gel process involving reduction of tetraethylammonium permanganate in methanol. Spin-coated films have been cast onto soft glass, quartz, and Ni foil substrates, with two coats being applied for optimum crystallization. The addition of alkali metal cations as dopants results in exclusive formation of the layered birnessite phase. By contrast, analogous reactions in bulk sol–gel reactions yield birnessite, tunneled, and spinel phases depending on the dopant cation. XRD patterns confirm the formation of well-crystallized birnessite. SEM images of Li-, Na-, and K–birnessite reveal extremely smooth films having uniform thickness of less than 0.5 μm. Thin films of Rb– and Cs–birnessite have more fractured and uneven surfaces as a result of some precipitation during the sol–gel transformation. All films consist of densely packed particles of about 0.1 μm. When tetrabutylammonium permanganate is used instead of tetraethylammonium permanganate, the sol–gel reaction yields amorphous manganese oxide as the result of diluted Mn sites in the xerogel film. Bilayer films have been prepared by casting an overcoat of K–birnessite onto an Na–birnessite film. However, Auger depth profiling indicates considerable mixing between the adjacent layers

Positivity-preserving and entropy-bounded discontinuous Galerkin method for the chemically reacting, compressible Navier-Stokes equations

This article concerns the development of a fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme for simulating the multicomponent, chemically reacting, compressible Navier-Stokes equations with complex thermodynamics. In particular, we extend to viscous flows the fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin method for the chemically reacting Euler equations that we previously introduced. An important component of the formulation is the positivity-preserving Lax-Friedrichs-type viscous flux function devised by Zhang [J. Comput. Phys., 328 (2017), pp. 301-343], which was adapted to multicomponent flows by Du and Yang [J. Comput. Phys., 469 (2022), pp. 111548] in a manner that treats the inviscid and viscous fluxes as a single flux. Here, we similarly extend the aforementioned flux function to multicomponent flows but separate the inviscid and viscous fluxes. This separation of the fluxes allows for use of other inviscid flux functions, as well as enforcement of entropy boundedness on only the convective contribution to the evolved state, as motivated by physical and mathematical principles. We also discuss in detail how to account for boundary conditions and incorporate previously developed pressure-equilibrium-preserving techniques into the positivity-preserving framework. Comparisons between the Lax-Friedrichs-type viscous flux function and more conventional flux functions are provided, the results of which motivate an adaptive solution procedure that employs the former only when the element-local solution average has negative species concentrations, nonpositive density, or nonpositive pressure. A variety of multicomponent, viscous flows is computed, ranging from a one-dimensional shock tube problem to multidimensional detonation waves and shock/mixing-layer interaction

Foxc1 is required by pericytes during fetal brain angiogenesis

Summary Brain pericytes play a critical role in blood vessel stability and blood–brain barrier maturation. Despite this, how brain pericytes function in these different capacities is only beginning to be understood. Here we show that the forkhead transcription factor Foxc1 is expressed by brain pericytes during development and is critical for pericyte regulation of vascular development in the fetal brain. Conditional deletion of Foxc1 from pericytes and vascular smooth muscle cells leads to late-gestation cerebral micro-hemorrhages as well as pericyte and endothelial cell hyperplasia due to increased proliferation of both cell types. Conditional Foxc1 mutants do not have widespread defects in BBB maturation, though focal breakdown of BBB integrity is observed in large, dysplastic vessels. qPCR profiling of brain microvessels isolated from conditional mutants showed alterations in pericyte-expressed proteoglycans while other genes previously implicated in pericyte–endothelial cell interactions were unchanged. Collectively these data point towards an important role for Foxc1 in certain brain pericyte functions (e.g. vessel morphogenesis) but not others (e.g. barriergenesis)

Single molecule force measurements of perlecan/HSPG2: A key component of the osteocyte pericellular matrix

Perlecan/HSPG2, a large, monomeric heparan sulfate proteoglycan (HSPG), is a key component of the lacunar canalicular system (LCS) of cortical bone, where it is part of the mechanosensing pericellular matrix (PCM) surrounding the osteocytic processes and serves as a tethering element that connects the osteocyte cell body to the bone matrix. Within the pericellular space surrounding the osteocyte cell body, perlecan can experience physiological fluid flow drag force and in that capacity function as a sensor to relay external stimuli to the osteocyte cell membrane. We previously showed that a reduction in perlecan secretion alters the PCM fiber composition and interferes with bone's response to a mechanical loading in vivo. To test our hypothesis that perlecan core protein can sustain tensile forces without unfolding under physiological loading conditions, atomic force microscopy (AFM) was used to capture images of perlecan monomers at nanoscale resolution and to perform single molecule force measurement (SMFMs). We found that the core protein of purified full-length human perlecan is of suitable size to span the pericellular space of the LCS, with a measured end-to-end length of 170 ± 20 nm and a diameter of 2–4 nm. Force pulling revealed a strong protein core that can withstand over 100 pN of tension well over the drag forces that are estimated to be exerted on the individual osteocyte tethers. Data fitting with an extensible worm-like chain model showed that the perlecan protein core has a mean elastic constant of 890 pN and a corresponding Young's modulus of 71 MPa. We conclude that perlecan has physical properties that would allow it to act as a strong but elastic tether in the LCS

Gravitational Waves from Core Collapse Supernovae

We present the gravitational wave signatures for a suite of axisymmetric core collapse supernova models with progenitors masses between 12 and 25 solar masses. These models are distinguished by the fact they explode and contain essential physics (in particular, multi-frequency neutrino transport and general relativity) needed for a more realistic description. Thus, we are able to compute complete waveforms (i.e., through explosion) based on non-parameterized, first-principles models. This is essential if the waveform amplitudes and time scales are to be computed more precisely. Fourier decomposition shows that the gravitational wave signals we predict should be observable by AdvLIGO across the range of progenitors considered here. The fundamental limitation of these models is in their imposition of axisymmetry. Further progress will require counterpart three-dimensional models.Comment: 10 pages, 5 figure

Radiative falloff in Schwarzschild-de Sitter spacetime

We consider the time evolution of a scalar field propagating in Schwarzschild-de Sitter spacetime. At early times, the field behaves as if it were in pure Schwarzschild spacetime; the structure of spacetime far from the black hole has no influence on the evolution. In this early epoch, the field's initial outburst is followed by quasi-normal oscillations, and then by an inverse power-law decay. At intermediate times, the power-law behavior gives way to a faster, exponential decay. At late times, the field behaves as if it were in pure de Sitter spacetime; the structure of spacetime near the black hole no longer influences the evolution in a significant way. In this late epoch, the field's behavior depends on the value of the curvature-coupling constant xi. If xi is less than a critical value 3/16, the field decays exponentially, with a decay constant that increases with increasing xi. If xi > 3/16, the field oscillates with a frequency that increases with increasing xi; the amplitude of the field still decays exponentially, but the decay constant is independent of xi.Comment: 10 pages, ReVTeX, 5 figures, references updated, and new section adde