Well-posedness and asymptotic behavior of a multidimensional model of morphogen transport

Morphogen transport is a biological process, occurring in the tissue of living organisms, which is a determining step in cell differentiation. We present rigorous analysis of a simple model of this process, which is a system coupling parabolic PDE with ODE. We prove existence and uniqueness of solutions for both stationary and evolution problems. Moreover we show that the solution converges exponentially to the equilibrium in $C^1\times C^0$ topology. We prove all results for arbitrary dimension of the domain. Our results improve significantly previously known results for the same model in the case of one dimensional domain

Internalization and end flux in morphogen gradient formation

AbstractTwo simple reaction–diffusion systems of partial differential equations and auxiliary conditions governing the activities of diffusible ligands such as Dpp in anterior–posterior axis of Drosophila wing imaginal discs were previously formulated and investigated by numerical simulations in [Developmental Cell 2 (2002) 785–796]. System B focuses on diffusion, reversible binding with receptors and ligand-mediated degradation for a fixed receptor concentration uniform in time and space. System C extended this basic but meaningful model to allow for endocytosis, exocytosis and receptor synthesis and degradation. The present paper provides a mathematical underpinning for the computational studies of these two systems and some insight gained from our analysis. We will see for instance that the two boundary value problems governing the steady state for the two systems are identical in form. This result will enable us to avoid dealing with internalization explicitly when we investigate other complex morphogen activities such as the effects of (1) feedback and (2) diffusible and non-diffusible molecules competing for ligands and receptors to inhibit cell signaling and pattern formation. The principal contribution of the present work pertains to the extension of System C to allow for a ligand flux at the source end. The more general model has many significant consequences including the removal of a limitation of previous models on ligand synthesis rate for the existence of steady state behavior. Linear stability of the corresponding steady state behavior is established. While the actual decay rate of transients is less accessible in this new model, it is possible to obtain tight upper and lower bounds for the decay rate in terms of the (effective) degradation rate of the receptors and that of the ligand-receptor complexes

A mechanism for morphogen-controlled domain growth

Many developmental systems are organised via the action of graded distributions of morphogens. In the Drosophila wing disc, for example, recent experimental evidence has shown that graded expression of the morphogen Dpp controls cell proliferation and hence disc growth. Our goal is to explore a simple model for regulation of wing growth via the Dpp gradient: we use a system of reaction-diffusion equations to model the dynamics of Dpp and its receptor Tkv, with advection arising as a result of the flow generated by cell proliferation. We analyse the model both numerically and analytically, showing that uniform domain growth across the disc produces an exponentially growing wing disc

Experimental investigation of high strain-rate, large-scale crack bridging behaviour of z-pin reinforced tapered laminates

Significant research exists on small-scale, quasi-static failure behaviour of Z-pinned composite laminates. However, little work has been conducted on large-scale, high strain-rate behaviour of Z-pinned composites at structural level. Small-scale testing is often at an insufficient scale to invoke the full crack bridging effects of the Z-pins. Full-scale testing on real components involves large length scales, complex geometries and resulting failure mechanisms that make it difficult to identify the specific effect of Z-pins on the component failure behaviour. A novel cantilever soft body impact test has been developed which is of sufficient scale to invoke large-scale delamination, such that behaviour in Z-pin arrays at high strain-rates can be studied. Laminates containing Z-pin arrays were subjected to soft-body gelatine impact in high-speed light gas-gun tests. Detailed fractographic investigation was carried out to investigate the dynamic failure behaviour of Z-pins at the microscopic scale

Experimental investigation of large-scale high-velocity soft-body impact on composite laminates

High-performance aerospace laminated composite structures manufactured from carbon-fibre prepreg are very susceptible to delamination failure under in-flight impact conditions. Much testing has been conducted at small length scales and quasi-static strain-rates to characterise the delamination performance of different material systems and loading scenarios. Testing at this scale and strain-rate is not representative of the failure conditions experienced by a laminate in a real impact event. Full-scale testing has also been conducted, but much of this is not in the open literature due to intellectual property constraints. Testing at this scale is also prohibitively expensive and involves complex failure mechanisms that cause difficulty in the analysis of associated failure behaviour. A novel test is presented which provides a simple, affordable alternative to full-scale testing but which invokes failure at sufficient scale and velocity to be representative of real component failure. This test design is experimentally validated through a series of soft-body gelatine impact tests using a light gas-gun facility. A fractographic analysis using scanning-electron microscopy was undertaken to examine microscopic failure behaviour, showing a possible reduction in crack mode-ratio during propagation

Study of phonons in irradiated epitaxial thin films of UO2

We report experiments to determine the effect of radiation damage on the phonon spectra of the most common nuclear fuel, UO2. We irradiated thin (∼300 nm) epitaxial films of UO2 with 2.1 MeV He2+ ions to 0.15 displacements per atom and a lattice swelling of Δa/a∼0.6% and then used grazing-incidence inelastic x-ray scattering to measure the phonon spectrum. We succeeded in observing the acoustic modes, both transverse and longitudinal, across the Brillouin zone. The phonon energies, in both the pristine and irradiated samples, are unchanged from those observed in bulk material. On the other hand, the phonon linewidths (inversely proportional to the phonon lifetimes) show a significant broadening when comparing the pristine and irradiated samples. This effect is shown to increase with phonon energy across the Brillouin zone. The decreases in the phonon lifetimes of the acoustic modes are roughly consistent with a 50% reduction in the thermal conductivity. © 2018 American Physical Society

Towards the first linkage map of the Didymella rabiei genome.

A genetic map was developed for the ascomycete Didymella rabiei (Kovachevski) v. Arx (anamorph: Ascochyta rabiei Pass. Labr.), the causal agent of Ascochyta blight in chickpea (Cicer arietinum L.). The map was generated with 77 F1 progeny derived from crossing an isolate from the U.S.A. and an isolate from Syria. A total of 232 DAF (DNA AmplificationFingerprinting) primers and 37 STMS (Sequence-Tagged Microsatellite Site) primer pairs were tested for polymorphism between the parental isolates; 50 markers were mapped, 36 DAFs and 14 STMSs. These markers cover 261.4cM in ten linkage groups. Nineteen markers remained unlinked. Significant deviation from the expected 1:1 segregation ratios was observed for only two markers (Prob. of x2 <0.05). The implications of our results on ploidy level of the asexual spores are discussed

Magnetic Field Generation in Stars

Enormous progress has been made on observing stellar magnetism in stars from the main sequence through to compact objects. Recent data have thrown into sharper relief the vexed question of the origin of stellar magnetic fields, which remains one of the main unanswered questions in astrophysics. In this chapter we review recent work in this area of research. In particular, we look at the fossil field hypothesis which links magnetism in compact stars to magnetism in main sequence and pre-main sequence stars and we consider why its feasibility has now been questioned particularly in the context of highly magnetic white dwarfs. We also review the fossil versus dynamo debate in the context of neutron stars and the roles played by key physical processes such as buoyancy, helicity, and superfluid turbulence,in the generation and stability of neutron star fields. Independent information on the internal magnetic field of neutron stars will come from future gravitational wave detections. Thus we maybe at the dawn of a new era of exciting discoveries in compact star magnetism driven by the opening of a new, non-electromagnetic observational window. We also review recent advances in the theory and computation of magnetohydrodynamic turbulence as it applies to stellar magnetism and dynamo theory. These advances offer insight into the action of stellar dynamos as well as processes whichcontrol the diffusive magnetic flux transport in stars.Comment: 41 pages, 7 figures. Invited review chapter on on magnetic field generation in stars to appear in Space Science Reviews, Springe

Viral capsids: Mechanical characteristics, genome packaging and delivery mechanisms

The main functions of viral capsids are to protect, transport and deliver their genome. The mechanical properties of capsids are supposed to be adapted to these tasks. Bacteriophage capsids also need to withstand the high pressures the DNA is exerting onto it as a result of the DNA packaging and its consequent confinement within the capsid. It is proposed that this pressure helps driving the genome into the host, but other mechanisms also seem to play an important role in ejection. DNA packaging and ejection strategies are obviously dependent on the mechanical properties of the capsid. This review focuses on the mechanical properties of viral capsids in general and the elucidation of the biophysical aspects of genome packaging mechanisms and genome delivery processes of double-stranded DNA bacteriophages in particular

Measurements of differential production cross sections for a Z boson in association with jets in pp collisions at root s=8 TeV

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