Necrotic tumor growth: an analytic approach

The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium. Finally, we compute the solutions of the stationary linearized problem and comment on bifurcation.Comment: 14 pages, 3 figure

Robust Adaptive Control of an Uninhabited Surface Vehicle

In this paper, we develop a novel and robust adaptive autopilot for uninhabited surface vehicles (USV). In practice, usually asudden change in dynamics results in aborted missions and the USV has to be rescued to avoid possible damage to other marine crafts inthe vicinity. This problem has been investigated in our innovative design, which enables the autopilot to cope well with significant changes in the system dynamics and empowers USVs to accomplish their desired missions. The model predictivecontrol technique is employed which adopts an online adaptive nature by utilising three algorithms. Even with random initialisation,significant improvements over the gradient descent and least squares approaches have been achieved by the modified weightedleast squares (WLS) method, which periodically reinitialising the covariance matrix. Extensive simulation studies have been performed to test and verify the advantages of the proposed method

Spatially oriented plasmonic ‘nanograter’ structures

One of the key motivations in producing 3D structures has always been the realization of metamaterials with effective constituent properties that can be tuned in all propagation directions at various frequencies. Here, we report the investigation of spatially oriented “Nanograter” structures with orientation-dependent responses over a wide spectrum by focused-ion-beam based patterning and folding of thin film nanostructures. Au nano units of different shapes, standing along specifically designated orientations, were fabricated. Experimental measurements and simulation results show that such structures offer an additional degree of freedom for adjusting optical properties with the angle of inclination, in additional to the size of the structures. The response frequency can be varied in a wide range (8 μm–14 μm) by the spatial orientation (0°–180°) of the structures, transforming the response from magnetic into electric coupling. This may open up prospects for the fabrication of 3D nanostructures as optical interconnects, focusing elements and logic elements, moving toward the realization of 3D optical circuits

Atmospheric Ice‐Nucleating Particles in the Dusty Tropical Atlantic

Desert dust is one of the most important atmospheric ice-nucleating aerosol species around the globe. However, there have been very few measurements of ice-nucleating particle (INP) concentrations in dusty air close to desert sources. In this study we report the concentration of INPs in dust laden air over the tropical Atlantic within a few days' transport of one of the world's most important atmospheric sources of desert dust, the Sahara. These measurements were performed as part of the Ice in Clouds Experiment-Dust campaign based in Cape Verde, during August 2015. INP concentrations active in the immersion mode, determined using a droplet-on-filter technique, ranged from around 10² m⁻³ at -12°C to around 10⁵ m⁻³ at -23°C. There is about 2 orders of magnitude variability in INP concentration for a particular temperature, which is determined largely by the variability in atmospheric dust loading. These measurements were made at altitudes from 30 to 3,500 m in air containing a range of dust loadings. The ice active site density (n s ) for desert dust dominated aerosol derived from our measurements agrees with several laboratory-based parameterizations for ice nucleation by desert dust within 1 to 2 orders of magnitude. The small variability in n s values determined from our measurements (within about 1 order of magnitude) is striking given that the back trajectory analysis suggests that the sources of dust were geographically diverse. This is consistent with previous work, which indicates that desert dust's ice-nucleating activity is only weakly dependent on source

Surface electrons at plasma walls

In this chapter we introduce a microscopic modelling of the surplus electrons on the plasma wall which complements the classical description of the plasma sheath. First we introduce a model for the electron surface layer to study the quasistationary electron distribution and the potential at an unbiased plasma wall. Then we calculate sticking coefficients and desorption times for electron trapping in the image states. Finally we study how surplus electrons affect light scattering and how charge signatures offer the possibility of a novel charge measurement for dust grains.Comment: To appear in Complex Plasmas: Scientific Challenges and Technological Opportunities, Editors: M. Bonitz, K. Becker, J. Lopez and H. Thomse

Wdpcp, a PCP Protein Required for Ciliogenesis, Regulates Directional Cell Migration and Cell Polarity by Direct Modulation of the Actin Cytoskeleton

Planar cell polarity (PCP) regulates cell alignment required for collective cell movement during embryonic development. This requires PCP/PCP effector proteins, some of which also play essential roles in ciliogenesis, highlighting the long-standing question of the role of the cilium in PCP. Wdpcp, a PCP effector, was recently shown to regulate both ciliogenesis and collective cell movement, but the underlying mechanism is unknown. Here we show Wdpcp can regulate PCP by direct modulation of the actin cytoskeleton. These studies were made possible by recovery of a Wdpcp mutant mouse model. Wdpcp-deficient mice exhibit phenotypes reminiscent of Bardet-Biedl/Meckel-Gruber ciliopathy syndromes, including cardiac outflow tract and cochlea defects associated with PCP perturbation. We observed Wdpcp is localized to the transition zone, and in Wdpcp-deficient cells, Sept2, Nphp1, and Mks1 were lost from the transition zone, indicating Wdpcp is required for recruitment of proteins essential for ciliogenesis. Wdpcp is also found in the cytoplasm, where it is localized in the actin cytoskeleton and in focal adhesions. Wdpcp interacts with Sept2 and is colocalized with Sept2 in actin filaments, but in Wdpcp-deficient cells, Sept2 was lost from the actin cytoskeleton, suggesting Wdpcp is required for Sept2 recruitment to actin filaments. Significantly, organization of the actin filaments and focal contacts were markedly changed in Wdpcp-deficient cells. This was associated with decreased membrane ruffling, failure to establish cell polarity, and loss of directional cell migration. These results suggest the PCP defects in Wdpcp mutants are not caused by loss of cilia, but by direct disruption of the actin cytoskeleton. Consistent with this, Wdpcp mutant cochlea has normal kinocilia and yet exhibits PCP defects. Together, these findings provide the first evidence, to our knowledge, that a PCP component required for ciliogenesis can directly modulate the actin cytoskeleton to regulate cell polarity and directional cell migration

Drying-mediated patterns in colloid-polymer suspensions

Drying-mediated patterning of colloidal particles is a physical phenomenon that must be understood in inkjet printing technology to obtain crack-free uniform colloidal films. Here we experimentally study the drying-mediated patterns of a model colloid-polymer suspension and specifically observe how the deposit pattern appears after droplet evaporation by varying particle size and polymer concentration. We find that at a high polymer concentration, the ring-like pattern appears in suspensions with large colloids, contrary to suppression of ring formation in suspensions with small colloids thanks to colloidpolymer interactions. We attribute this unexpected reversal behavior to hydrodynamics and size dependence of colloid-polymer interactions. This finding would be very useful in developing control of drying-mediated self-assembly to produce crack-free uniform patterns from colloidal fluids.ope

Metamaterial bricks and quantization of meta-surfaces

Controlling acoustic fields is crucial in diverse applications such as loudspeaker design, ultrasound imaging and therapy or acoustic particle manipulation. The current approaches use fixed lenses or expensive phased arrays. Here, using a process of analogue-to-digital conversion and wavelet decomposition, we develop the notion of quantal meta-surfaces. The quanta here are small, pre-manufactured three-dimensional units—which we call metamaterial bricks—each encoding a specific phase delay. These bricks can be assembled into meta-surfaces to generate any diffraction-limited acoustic field. We apply this methodology to show experimental examples of acoustic focusing, steering and, after stacking single meta-surfaces into layers, the more complex field of an acoustic tractor beam. We demonstrate experimentally single-sided air-borne acoustic levitation using meta-layers at various bit-rates: from a 4-bit uniform to 3-bit non-uniform quantization in phase. This powerful methodology dramatically simplifies the design of acoustic devices and provides a key-step towards realizing spatial sound modulators

Controlling waves in space and time for imaging and focusing in complex media

In complex media such as white paint and biological tissue, light encounters nanoscale refractive-index inhomogeneities that cause multiple scattering. Such scattering is usually seen as an impediment to focusing and imaging. However, scientists have recently used strongly scattering materials to focus, shape and compress waves by controlling the many degrees of freedom in the incident waves. This was first demonstrated in the acoustic and microwave domains using time reversal, and is now being performed in the optical realm using spatial light modulators to address the many thousands of spatial degrees of freedom of light. This approach is being used to investigate phenomena such as optical super-resolution and the time reversal of light, thus opening many new avenues for imaging and focusing in turbid medi

High-throughput profiling of off-target DNA cleavage reveals RNA-programmed Cas9 nuclease specificity

The RNA-programmable Cas9 endonuclease cleaves double-stranded DNA at sites complementary to a 20-base-pair guide RNA. The Cas9 system has been used to modify genomes in multiple cells and organisms, demonstrating its potential as a facile genome-engineering tool. We used in vitro selection and high-throughput sequencing to determine the propensity of eight Cas9:guide RNA complexes to cleave each of 10^12 potential off-target DNA sequences. The selection results predicted five off-target sites in the human genome that were confirmed to undergo genome cleavage in HEK293T cells upon expression of one of two Cas9:guide RNA complexes. In contrast to previous models, our results show that Cas9:guide RNA specificity extends past a 7- to 12-base pair seed sequence. Our results also suggest a tradeoff between activity and specificity both in vitro and in cells as a shorter, less-active guide RNA is more specific then a longer, more-active guide RNA. High concentrations of Cas9:guide RNA complexes can cleave off-target sites containing mutations near or within the PAM that are not cleaved when enzyme concentrations are limiting