Travelling, non-periodic patterns in nonlinear stability problems

In this short note we present results on the existence of several classes of travelling, non-periodic solutions of the complex Ginzburg-Landau equation. First we give a very short introduction to the G-L equation and show its importance in nonlinear stability theory. We then study the G-L equation with complex coefficients and establish the existence of a 2-parameter family of quasi-periodic solutions and two different types of one-parameter families of heteroclinic orbits; all members of these families travel with a well-defined wave-speed. The heteroclinic solutions correspond to (travelling) soliton-like localized structures which connect different (stable) periodic patterns. Mathematically, these families of travelling solutions (quasi-periodic and heteroclinic) are continuations into the complex case of the stationary solutions of the real G-L equation.     

Microstructural investigation of monoglyceride-water coagel systems by NMR and CryoSEM

Monoglyceride coagels consist of a network of plate-like crystals and are formed from a swollen gel state (alpha-gel). In order to resolve the transition mechanism, coagels were prepared with monoglycerides that differ in fatty acid composition (monomyristate and palmitate/stearate, respectively). Rheology provided information on kinetics of coagel formation and the strength of the resulting crystal network. From NMR measurements, the surface-to-volume ratio, tortuosity, and dimensionality of the network were obtained. These findings were in line with qualitative and quantitative structural information obtained from CryoSEM. As a model for the behaviour of non-monoglyceride species, the dynamics of (perdeuterated) palmitic acid was monitored in both alpha-gels and coagels. The experimental data support a two-stage mechanism. In the first stage, two-dimensional separation of D- and L-isomers in the monoglyceride bilayers of the alpha-gel occurs. This process depends primarily on lateral diffusion rate of the monoglycerides. Palmitic acid can be accommodated in the alpha-gel bilayer, but in the coagels it is separated into relative mobile and mechanically weak junction zones between the crystal plates. In the second stage of coagel formation, the crystal plates also grow in the third dimension. Both monoglyceride type and concentration determine the kinetics of this process.     

The Reclaim Screw in Mammoth Silos Operating on a Free Surface: Comparison Between Horizontal and Inclined Operation on Free Flowing Bulk Solids

Although the screw conveyor, operating on a free surface, has been used for years as reclaim and storage equipment in mammoth silos, there is no documented knowledge about its spill characteristics. Research at Delft University of Technology together with ESI Eurosilo B.V. on the inclined use of the reclaim screw to achieve homogenization in mammoth silos made this lack of knowledge apparent. This paper presents the results of experiments to gain insight into the spill during reclaiming. Experiments were conducted reclaiming a horizontal surface and up‐ and downwards along an inclined surface, using a free‐flowing bulk material. A relationship was found between the theoretical and effective fill ratio. This relationship shows a certain maximum effective fill ratio and a dependence on the reclaim‐depth. As expected, the effective fill ratio drops quickly when reclaiming upwards, mostly due to flow‐ and throwback: the fill is spilled behind the screw blades and over the axis. Unexpectedly, the effective fill ratio also decreases when reclaiming downwards due to a shift of material towards the non‐reclaiming side where it is left behind forming ridges on the surface. It is expected that all three mechanisms will cause less spill when reclaiming a cohesive material. The experiments provide the desired insight into spill mechanisms during reclaiming. Indeed, the inclined use of the reclaim screw to achieve homogenization is thought feasible when reclaiming downwards.     

Prognostic Metabolite Biomarkers for Soft Tissue Sarcomas Discovered by Mass Spectrometry Imaging

Metabolites can be an important read-out of disease. The identification and validation of biomarkers in the cancer metabolome that can stratify high-risk patients is one of the main current research aspects. Mass spectrometry has become the technique of choice for metabolomics studies, and mass spectrometry imaging (MSI) enables their visualization in patient tissues. In this study, we used MSI to identify prognostic metabolite biomarkers in high grade sarcomas; 33 high grade sarcoma patients, comprising osteosarcoma, leiomyosarcoma, myxofibrosarcoma, and undifferentiated pleomorphic sarcoma were analyzed. Metabolite MSI data were obtained from sections of fresh frozen tissue specimens with matrix-assisted laser/desorption ionization (MALDI) MSI in negative polarity using 9-aminoarcridine as matrix. Subsequent annotation of tumor regions by expert pathologists resulted in tumor-specific metabolite signatures, which were then tested for association with patient survival. Metabolite signals with significant clinical value were further validated and identified by high mass resolution Fourier transform ion cyclotron resonance (FTICR) MSI. Three metabolite signals were found to correlate with overall survival (m/z 180.9436 and 241.0118) and metastasis-free survival (m/z 160.8417). FTICR-MSI identified m/z 241.0118 as inositol cyclic phosphate and m/z 160.8417 as carnitine.

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Graphical Abstract ?

     

Homoclinic bifurcations at the onset of pulse self-replication

We establish a series of properties of symmetric, N-pulse, homoclinic solutions of the reduced Gray-Scott system: u^″=uv², v^″=v−uv², which play a pivotal role in questions concerning the existence and self-replication of pulse solutions of the full Gray-Scott model. Specifically, we establish the existence, and study properties, of solution branches in the (α,β)-plane that represent multi-pulse homoclinic orbits, where α and β are the central values of u(x) and v(x), respectively. We prove bounds for these solution branches, study their behavior as α→∞, and establish a series of geometric properties of these branches which are valid throughout the (α,β)-plane. We also establish qualitative properties of multi-pulse solutions and study how they bifurcate, i.e., how they change along the solution branches.     

Mathematical modelling and numerical simulation of the morphological development of neurons

Background

The morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other.

Methods

A variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described.

Results

Some comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development.

Conclusion

A unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity.