Emergence and function of complex form in self-assembly and biological cells

This year, 2017, marks the centenary of the first publication of 'On Growth and Form', by the extraordinary Scottish classicist, biologist and part-time mathematician, D'Arcy Wentworth Thompson [1]..

Fast finite difference solvers for singular solutions of the elliptic Monge-Amp\`ere equation

The elliptic Monge-Ampere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail. In this article we build a finite difference solver for the Monge-Ampere equation, which converges even for singular solutions. Regularity results are used to select a priori between a stable, provably convergent monotone discretization and an accurate finite difference discretization in different regions of the computational domain. This allows singular solutions to be computed using a stable method, and regular solutions to be computed more accurately. The resulting nonlinear equations are then solved by Newton's method. Computational results in two and three dimensions validate the claims of accuracy and solution speed. A computational example is presented which demonstrates the necessity of the use of the monotone scheme near singularities.Comment: 23 pages, 4 figures, 4 tables; added arxiv links to references, added coment

Boundary driven zero-range processes in random media

The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the stationary state is found to be trivial in absence of boundary drive. Out of equilibrium, two further cases are distinguished according to the tail of the disorder distribution. For strong disorder, the fugacity profiles are found to be governed by the paths of normalized $\alpha$-stable subordinators. The expectations of integrated functions of the tagged particle position are calculated for three types of routes.Comment: 23 page

Accurate staging of chick embryonic tissues via deep learning of salient features

Recent work shows that the developmental potential of progenitor cells in the HH10 chick brain changes rapidly, accompanied by subtle changes in morphology. This demands increased temporal resolution for studies of the brain at this stage, necessitating precise and unbiased staging. Here, we investigated whether we could train a deep convolutional neural network to sub-stage HH10 chick brains using a small dataset of 151 expertly labelled images. By augmenting our images with biologically informed transformations and data-driven preprocessing steps, we successfully trained a classifier to sub-stage HH10 brains to 87.1% test accuracy. To determine whether our classifier could be generally applied, we re-trained it using images (269) of randomised control and experimental chick wings, and obtained similarly high test accuracy (86.1%). Saliency analyses revealed that biologically relevant features are used for classification. Our strategy enables training of image classifiers for various applications in developmental biology with limited microscopy data

Radiative Decay of a Long-Lived Particle and Big-Bang Nucleosynthesis

The effects of radiatively decaying, long-lived particles on big-bang nucleosynthesis (BBN) are discussed. If high-energy photons are emitted after BBN, they may change the abundances of the light elements through photodissociation processes, which may result in a significant discrepancy between the BBN theory and observation. We calculate the abundances of the light elements, including the effects of photodissociation induced by a radiatively decaying particle, but neglecting the hadronic branching ratio. Using these calculated abundances, we derive a constraint on such particles by comparing our theoretical results with observations. Taking into account the recent controversies regarding the observations of the light-element abundances, we derive constraints for various combinations of the measurements. We also discuss several models which predict such radiatively decaying particles, and we derive constraints on such models.Comment: Published version in Phys. Rev. D. Typos in figure captions correcte

Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder

We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each configuration, there is a unique jamming threshold, $\phi_c$, at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become non-zero. The distribution of $\phi_c$ values becomes narrower as the system size increases, so that essentially all configurations jam at the same $\phi$ in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. In fact, our results provide a well-defined meaning for "random close-packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, Point J, occurring at zero temperature and applied stress and at the random close-packing density, has properties reminiscent of an ordinary critical point. As Point J is approached from higher packing fractions, power-law scaling is found for many quantities. Moreover, near Point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, Point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. All of these results suggest that Point J may control behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure

Tomato: a crop species amenable to improvement by cellular and molecular methods

Tomato is a crop plant with a relatively small DNA content per haploid genome and a well developed genetics. Plant regeneration from explants and protoplasts is feasable which led to the development of efficient transformation procedures. In view of the current data, the isolation of useful mutants at the cellular level probably will be of limited value in the genetic improvement of tomato. Protoplast fusion may lead to novel combinations of organelle and nuclear DNA (cybrids), whereas this technique also provides a means of introducing genetic information from alien species into tomato. Important developments have come from molecular approaches. Following the construction of an RFLP map, these RFLP markers can be used in tomato to tag quantitative traits bred in from related species. Both RFLP's and transposons are in the process of being used to clone desired genes for which no gene products are known. Cloned genes can be introduced and potentially improve specific properties of tomato especially those controlled by single genes. Recent results suggest that, in principle, phenotypic mutants can be created for cloned and characterized genes and will prove their value in further improving the cultivated tomato.

Cracks in Martensite Plates as Hydrogen Traps in a Bearing Steel

It is demonstrated that a macroscopically homogeneous distribution of tiny cracks introduced into a martensitic bearing steel sample can provide powerful hydrogen traps. The phenomenon has been investigated through thermal desorption spectroscopy and hydrogen permeation measurements using both cracked and integral samples. The e↵ective hydrogen di↵usion coefficient through the cracked sample is found to be far less than in the uncracked one. Similarly, when samples are charged with hydrogen, and then subjected to thermal desorption analysis, the amount of hydrogen liberated from the cracked sample is smaller due to the trapping by the cracks. Theoretical analysis of the data shows that the traps due to cracks are so strong, that any hydrogen within the cracks can never in practice de-trap and cause harm by mechanisms that require the hydrogen to be mobile for the onset of embrittlement.W. Solano-Alvarez is very grateful for support from the Worshipful Company of Ironmongers, CONACyT, the Cambridge Overseas Trust, and the Roberto Rocca Education Programme.This is the accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s11661-014-2680-8

Ductile-Phase Toughening of Brazed Joints

A heat treatment is presented that uses ductile-phase toughening to mitigate the effect of brittle intermetallics in a Ni-based braze alloy. The fracture resistance has been enhanced by creating a microstructure containing elongated ductile γ-(Ni) domains that align, preferentially, across the joint. The development of this beneficial microstructure is based on an understanding of the transient dissolution, isothermal solidification, and coarsening phenomena. Due to slow kinetics, the elimination of intermetallics by diffusion is avoided in favor of ductile domain formation through solidification control. The toughening has been attributed to a combination of bridging and process zone dissipation, enabled by the ductile phase

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results