Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. In this formulation the effective or eddy diffusivity depends on the entropy gradient, $\partial S/\partial r$, as well as entropy. First we present a simplified model with semi-analytical solutions, highlighting the large dynamic range of $\partial S/\partial r$, around 12 orders of magnitude, for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple, stable numerical scheme able to capture the large dynamic range of $\partial S/\partial r$ and provide a flexible and robust method for time-integrating the energy equation. We then consider a full model including energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using $\partial S/\partial r$ as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. Our computational framework is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations arising in other disciplines, particularly for non-linear functional forms of the diffusion coefficient

Linking the evolution of terrestrial interiors and an early outgassed atmosphere to astrophysical observations

A terrestrial planet is molten during formation and may remain so if subject to intense insolation or tidal forces. Observations continue to favour the detection and characterisation of hot planets, potentially with large outgassed atmospheres. We aim to determine the radius of hot Earth-like planets with large outgassed atmospheres and explore differences between molten and solid silicate planets and their influence on the mass-radius relationship and transmission and emission spectra. An interior-atmosphere model, combined with static structure calculations, tracks the evolving radius of a rocky mantle that is outgassing CO$_2$ and H$_2$O. Synthetic emission and transmission spectra are generated for CO$_2$ and H$_2$O dominated atmospheres. Atmospheres dominated by CO$_2$ suppress the outgassing of H$_2$O to a greater extent than previously realised, as previous studies have applied an erroneous relationship between volatile mass and partial pressure. We therefore predict more H$_2$O can be retained by the interior during the later stages of magma ocean crystallisation. Furthermore, formation of a lid at the surface can tie outgassing of H$_2$O to the efficiency of heat transport through the lid, rather than the atmosphere's radiative timescale. Contraction of the mantle as it solidifies gives $\sim5\%$ radius decrease, which can partly be offset by addition of a relatively light species to the atmosphere. We conclude that a molten silicate mantle can increase the radius of a terrestrial planet by around $5\%$ compared to its solid counterpart, or equivalently account for a $13\%$ decrease in bulk density. An outgassing atmosphere can perturb the total radius according to its speciation. Atmospheres of terrestrial planets around M-stars that are dominated by CO$_2$ or H$_2$O can be distinguished by observing facilities with extended wavelength coverage (e.g., JWST).Comment: 19 pages, published in A&A, abstract shortene

Phagosome-lysosome fusion is a calcium-independent event in macrophages.

Phagosome-lysosome membrane fusion is a highly regulated event that is essential for intracellular killing of microorganisms. Functionally, it represents a form of polarized regulated secretion, which is classically dependent on increases in intracellular ionized calcium ([Ca2+]i). Indeed, increases in [Ca2+]i are essential for phagosome-granule (lysosome) fusion in neutrophils and for lysosomal fusion events that mediate host cell invasion by Trypanosoma cruzi trypomastigotes. Since several intracellular pathogens survive in macrophage phagosomes that do not fuse with lysosomes, we examined the regulation of phagosome-lysosome fusion in macrophages. Macrophages (M phi) were treated with 12.5 microM bis-(2-amino-S-methylphenoxy) ethane-N,N,N',N',-tetraacetic acid tetraacetoxymethyl ester (MAPT/AM), a cell-permeant calcium chelator which reduced resting cytoplasmic [Ca2+]; from 80 nM to < or = 20 nM and completely blocked increases in [Ca2+]i in response to multiple stimuli, even in the presence of extracellular calcium. Subsequently, M phi phagocytosed serum-opsonized zymosan, staphylococci, or Mycobacterium bovis. Microbes were enumerated by 4',6-diamidino-2-phenylindole, dihydrochloride (DAPI) staining, and phagosome-lysosome fusion was scored using both lysosome-associated membrane protein (LAMP-1) as a membrane marker and rhodamine dextran as a content marker for lysosomes. Confirmation of phagosome-lysosome fusion by electron microscopy validated the fluorescence microscopy findings. We found that phagosome-lysosome fusion in M phi occurs noramlly at very low [Ca2+]i (< or = 20 nM). Kinetic analysis showed that in M phi none of the steps leading from particle binding to eventual phagosome-lysosome fusion are regulated by [Ca2+]i in a rate-limiting way. Furthermore, confocal microscopy revealed no difference in the intensity of LAMP-1 immunofluorescence in phagolysosome membranes in calcium-buffered vs. control macrophages. We conclude that neither membrane recognition nor fusion events in the phagosomal pathway in macrophages are dependent on or regulated by calcium

Circadian control of interferon-sensitive gene expression in murine skin.

The circadian clock coordinates a variety of immune responses with signals from the external environment to promote survival. We investigated the potential reciprocal relationship between the circadian clock and skin inflammation. We treated mice topically with the Toll-like receptor 7 (TLR7) agonist imiquimod (IMQ) to activate IFN-sensitive gene (ISG) pathways and induce psoriasiform inflammation. IMQ transiently altered core clock gene expression, an effect mirrored in human patient psoriatic lesions. In mouse skin 1 d after IMQ treatment, ISGs, including the key ISG transcription factor IFN regulatory factor 7 (Irf7), were more highly induced after treatment during the day than the night. Nuclear localization of phosphorylated-IRF7 was most prominently time-of-day dependent in epidermal leukocytes, suggesting that these cell types play an important role in the diurnal ISG response to IMQ. Mice lacking Bmal1 systemically had exacerbated and arrhythmic ISG/Irf7 expression after IMQ. Furthermore, daytime-restricted feeding, which affects the phase of the skin circadian clock, reverses the diurnal rhythm of IMQ-induced ISG expression in the skin. These results suggest a role for the circadian clock, driven by BMAL1, as a negative regulator of the ISG response, and highlight the finding that feeding time can modulate the skin immune response. Since the IFN response is essential for the antiviral and antitumor effects of TLR activation, these findings are consistent with the time-of-day-dependent variability in the ability to fight microbial pathogens and tumor initiation and offer support for the use of chronotherapy for their treatment

Timescales of chemical equilibrium between the convecting solid mantle and over- and underlying magma oceans

After accretion and formation, terrestrial planets go through at least one magma ocean episode. As the magma ocean crystallises, it creates the first layer of solid rocky mantle. Two different scenarios of magma ocean crystallisation involve that the solid mantle either (1) first appears at the core–mantle boundary and grows upwards or (2) appears at mid-mantle depth and grows in both directions. Regardless of the magma ocean freezing scenario, the composition of the solid mantle and liquid reservoirs continuously change due to fractional crystallisation. This chemical fractionation has important implications for the long-term thermo-chemical evolution of the mantle as well as its present-day dynamics and composition. In this work, we use numerical models to study convection in a solid mantle bounded at one or both boundaries by magma ocean(s) and, in particular, the related consequences for large-scale chemical fractionation. We use a parameterisation of fractional crystallisation of the magma ocean(s) and (re)melting of solid material at the interface between these reservoirs. When these crystallisation and remelting processes are taken into account, convection in the solid mantle occurs readily and is dominated by large wavelengths. Related material transfer across the mantle–magma ocean boundaries promotes chemical equilibrium and prevents extreme enrichment of the last-stage magma ocean (as would otherwise occur due to pure fractional crystallisation). The timescale of equilibration depends on the convective vigour of mantle convection and on the efficiency of material transfer between the solid mantle and magma ocean(s). For Earth, this timescale is comparable to that of magma ocean crystallisation suggested in previous studies (Lebrun et al., 2013), which may explain why the Earth's mantle is rather homogeneous in composition, as supported by geophysical constraints

In-clip Search Algorithm for Content-Based Audio Retrieval

Researchers are currently more interested in searching for fragments that are similar to a query, than a total data item that is similar to a query; the search interest is for contains , not is . The paper presents an O(logn) algorithm, called the generalized virtual node (GVN) algorithm; the GVN algorithm is a search algorithm for data fragments that have similar contents to that of a query. An example of the use of the GVN algorithm is in the search of a database of audio recordings for a few measures of a melody. Each audio clip is transformed into characteristic features and these features are stored in a hierarchical multidimensional structure, called a k-tree . The k-tree is exploited to build a unified retrieval model for any types of multimedia data. The experimental results of this in-clip search algorithm on an audio database demonstrate a search quality is qualitatively and quantitatively acceptable, with a retrieval time faster than other algorithms, such as brute-force and partial matching

Design, fabrication and control of soft robots

Conventionally, engineers have employed rigid materials to fabricate precise, predictable robotic systems, which are easily modelled as rigid members connected at discrete joints. Natural systems, however, often match or exceed the performance of robotic systems with deformable bodies. Cephalopods, for example, achieve amazing feats of manipulation and locomotion without a skeleton; even vertebrates such as humans achieve dynamic gaits by storing elastic energy in their compliant bones and soft tissues. Inspired by nature, engineers have begun to explore the design and control of soft-bodied robots composed of compliant materials. This Review discusses recent developments in the emerging field of soft robotics.National Science Foundation (U.S.) (Grant IIS-1226883

PETSc Users Manual

The Portable, Extensible Toolkit for Scientific Computation (PETSc), is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations. It supports MPI, and GPUs through CUDA or OpenCL, as well as hybrid MPI-GPU parallelism. PETSc (sometimes called PETSc/Tao) also contains the Tao optimization software library