Local Frustration Determines Molecular and Macroscopic Helix Structures

The effect of displaying cytochromes from an amyloid fibre is modelled as perturbation of -strands in a bilayer of helical -sheets, thereby explaining the spiral morphology of decorated amyloid and the dynamic response of morphology to cytochrome conformation. The morphology of the modelled fibre, which consists of minimal energy assemblies of rigid building blocks containing two anisotropic interacting units, depends primarily on the rigid constraints between units rather than the soft interactions between them. The framework is a discrete version of the bilayered frustration principle that drives morphology in Bauhinia seedpods. We show that self-assembly of frustrated long range structures can occur if the building blocks themselves are internally frustrated, e.g. amyloid morphology is governed by the conformation of the misfolded protein nucleating the fibre. Our model supports the idea that any peptide sequence can form amyloid if bilayers can form first, albeit stabilised by additional material such as chaperones or cytochromes. Analysis of experimentally derived amyloid structures supports our conclusions and suggests a range of frustration effects, which natural amyloid fibres may exploit. From this viewpoint, amyloid appears as a molecular example of a more general universal bilayered frustration principle, which may have profound implications for materials design using fibrous systems. Our model provides quantitative guidance for such applications. The relevance to longer length scales was proved by designing the morphology of a series of macroscopic magnetic stacks. Finally, this work leads to the idea of mixing controlled morphologically defined species to generate higher-order assembly and complex functional behaviour. The systematic kinking of decorated fibres and the nested frustration of the Bauhinia seed pod are two outstanding examples.

Predictive coding and the slowness principle: an information-theoretic approach.

Understanding the guiding principles of sensory coding strategies is a main goal in computational neuroscience. Among others, the principles of predictive coding and slowness appear to capture aspects of sensory processing. Predictive coding postulates that sensory systems are adapted to the structure of their input signals such that information about future inputs is encoded. Slow feature analysis (SFA) is a method for extracting slowly varying components from quickly varying input signals, thereby learning temporally invariant features. Here, we use the information bottleneck method to state an information-theoretic objective function for temporally local predictive coding. We then show that the linear case of SFA can be interpreted as a variant of predictive coding that maximizes the mutual information between the current output of the system and the input signal in the next time step. This demonstrates that the slowness principle and predictive coding are intimately related.

Local equilibrium of the Gibbs interface in two-phase systems

We analyze the local equilibrium assumption for interfaces from the perspective of gauge transformations, which are the small displacements of Gibbs' dividing surface. The gauge invariance of thermodynamic properties turns out to be equivalent to conditions for jumps of bulk densities across the interface. This insight strengthens the foundations of the local equilibrium assumption for interfaces and can be used to characterize nonequilibrium interfaces in a compact and consistent way, with a clear focus on gauge-invariant properties. Using the principle of gauge invariance, we show that the validity of Clapeyron equations can be extended to nonequilibrium interfaces, and an additional jump condition for the momentum density is recognized to be of the Clapeyron type. © 2012 Europhysics Letters Association.

On the two classes of global primary modal instability in laminar separation bubbles

The self-excited global instability mechanisms existing in flat-plate laminar separation bubbles are studied here, in order to shed light on the causes of unsteadiness and three- dimensionality of unforced, nominally two-dimensional separated flows. The presence of two known linear global mechanisms, namely an oscillator behavior driven by local regions of absolute inflectional instability and a centrifugal instability giving rise to a steady three- dimensionalization of the bubble, is studied in a series of model separation bubbles. Present results indicate that absolute instability, and consequently a global oscillator behavior, does not exist for two-dimensional bubbles with a peak reversed-flow velocity below 12% of the free-stream velocity. However, the three-dimensional instability becomes active for recirculation levels as low as urev ≈ 7%. These findings suggest a route to the three-dimensionality and unsteadiness observed in experiments and simulations substantially different from that usually found in the literature, in which two-dimensional vortex shedding is followed by three-dimensionalization.

Global linear stability of the boundary-layer flow over a rotating sphere

We consider the linear global stability of the boundary-layer flow over a rotating sphere. Our results suggest that a self-excited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°-65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotating-sphere flow may be different to that for the rotating disk. © 2014 Elsevier Masson SAS. All rights reserved.

Global modes with multiple saddle points

Significant progress has been made towards understanding the global stability of slowly-developing shear flows. The WKBJ theory developed by Patrick Huerre and his co-authors has proved absolutely central, with the result that both the linear and the nonlinear stability of a wide range of flows can now be understood in terms of their local absolute/convective instability properties. In many situations, the local absolute frequency possesses a single dominant saddle point in complex X-space (where X is the slow streamwise coordinate of the base flow), which then acts as a single wavemaker driving the entire global linear dynamics. In this paper we consider the more complicated case in which multiple saddles may act as the wavemaker for different values of some control parameter. We derive a frequency selection criterion in the general case, which is then validated against numerical results for the linearized third-order Ginzburg-Landau equation (which possesses two saddle points). We believe that this theory may be relevant to a number of flows, including the boundary layer on a rotating disk and the eccentric Taylor-Couette-Poiseuille flow. © 2014 Elsevier Masson SAS. All rights reserved.