Geometric frustration in compositionally modulated ferroelectrics

Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry1-7. Geometric frustration gives rise to new fundamental phenomena and is known to yield intriguing effects, such as the formation of exotic states like spin ice, spin liquids and spin glasses1-7. It has also led to interesting findings of fractional charge quantization and magnetic monopoles5,6. Geometric frustration related mechanisms have been proposed to understand the origins of relaxor behavior in some multiferroics, colossal magnetocapacitive coupling and unusual and novel mechanisms of high Tc superconductivity1-5. Although geometric frustration has been particularly well studied in magnetic systems in the last 20 years or so, its manifestation in the important class formed by ferroelectric materials (that are compounds exhibiting electric rather than magnetic dipoles) is basically unknown. Here, we show, via the use of a first-principles-based technique, that compositionally graded ferroelectrics possess the characteristic "fingerprints" associated with geometric frustration. These systems have a highly degenerate energy surface and exhibit original critical phenomena. They further reveal exotic orderings with novel stripe phases involving complex spatial organization. These stripes display spiral states, topological defects and curvature. Compositionally graded ferroelectrics can thus be considered as the "missing" link that brings ferroelectrics into the broad category of materials able to exhibit geometric frustration. Our ab-initio calculations allow a deep microscopic insight into this novel geometrically frustrated system.Comment: 14 pages, 5 Figures; http://www.nature.com/nature/journal/v470/n7335/full/nature09752.htm

Avalanches in self-organized critical neural networks: A minimal model for the neural SOC universality class

The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. The spin model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.Comment: 17 pages, 5 figure

The transition between stochastic and deterministic behavior in an excitable gene circuit

We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.Comment: PLoS ONE: Research Article, published 11 Apr 201

Correlation functions quantify super-resolution images and estimate apparent clustering due to over-counting

We present an analytical method to quantify clustering in super-resolution localization images of static surfaces in two dimensions. The method also describes how over-counting of labeled molecules contributes to apparent self-clustering and how the effective lateral resolution of an image can be determined. This treatment applies to clustering of proteins and lipids in membranes, where there is significant interest in using super-resolution localization techniques to probe membrane heterogeneity. When images are quantified using pair correlation functions, the magnitude of apparent clustering due to over-counting will vary inversely with the surface density of labeled molecules and does not depend on the number of times an average molecule is counted. Over-counting does not yield apparent co-clustering in double label experiments when pair cross-correlation functions are measured. We apply our analytical method to quantify the distribution of the IgE receptor (Fc{\epsilon}RI) on the plasma membranes of chemically fixed RBL-2H3 mast cells from images acquired using stochastic optical reconstruction microscopy (STORM) and scanning electron microscopy (SEM). We find that apparent clustering of labeled IgE bound to Fc{\epsilon}RI detected with both methods arises from over-counting of individual complexes. Thus our results indicate that these receptors are randomly distributed within the resolution and sensitivity limits of these experiments.Comment: 22 pages, 5 figure

Direct measurement of antiferromagnetic domain fluctuations

Measurements of magnetic noise emanating from ferromagnets due to domain motion were first carried out nearly 100 years ago and have underpinned much science and technology. Antiferromagnets, which carry no net external magnetic dipole moment, yet have a periodic arrangement of the electron spins extending over macroscopic distances, should also display magnetic noise, but this must be sampled at spatial wavelengths of order several interatomic spacings, rather than the macroscopic scales characteristic of ferromagnets. Here we present the first direct measurement of the fluctuations in the nanometre-scale spin- (charge-) density wave superstructure associated with antiferromagnetism in elemental Chromium. The technique used is X-ray Photon Correlation Spectroscopy, where coherent x-ray diffraction produces a speckle pattern that serves as a "fingerprint" of a particular magnetic domain configuration. The temporal evolution of the patterns corresponds to domain walls advancing and retreating over micron distances. While the domain wall motion is thermally activated at temperatures above 100K, it is not so at lower temperatures, and indeed has a rate which saturates at a finite value - consistent with quantum fluctuations - on cooling below 40K. Our work is important because it provides an important new measurement tool for antiferromagnetic domain engineering as well as revealing a fundamental new fact about spin dynamics in the simplest antiferromagnet.Comment: 19 pages, 4 figure

Modelling avalanches in martensites

Solids subject to continuous changes of temperature or mechanical load often exhibit discontinuous avalanche-like responses. For instance, avalanche dynamics have been observed during plastic deformation, fracture, domain switching in ferroic materials or martensitic transformations. The statistical analysis of avalanches reveals a very complex scenario with a distinctive lack of characteristic scales. Much effort has been devoted in the last decades to understand the origin and ubiquity of scale-free behaviour in solids and many other systems. This chapter reviews some efforts to understand the characteristics of avalanches in martensites through mathematical modelling.Comment: Chapter in the book "Avalanches in Functional Materials and Geophysics", edited by E. K. H. Salje, A. Saxena, and A. Planes. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-45612-6_

Anatomy of a microearthquake sequence on an active normal fault

The analysis of similar earthquakes, such as events in a seismic sequence, is an effective tool with which to monitor and study source processes and to understand the mechanical and dynamic states of active fault systems. We are observing seismicity that is primarily concentrated in very limited regions along the 1980 Irpinia earthquake fault zone in Southern Italy, which is a complex system characterised by extensional stress regime. These zones of weakness produce repeated earthquakes and swarm-like microearthquake sequences, which are concentrated in a few specific zones of the fault system. In this study, we focused on a sequence that occurred along the main fault segment of the 1980 Irpinia earthquake to understand its characteristics and its relation to the loading-unloading mechanisms of the fault system

Acoustic-Friction Networks and the Evolution of Precursory Rupture Fronts in Laboratory Earthquakes

We show that the mesoscopic and transport characteristics of networks follow the same trends for the same type of the shear ruptures in terms of rupture speed while also comparing the results of three different friction experiments.The classified fronts obtained from a saw cut Westerly granite fault regarding friction network parameters show a clear separation into two groups indicating two different rupture fronts. With respect to the scaling of local ruptures durations with the networks parameters we show that the gap is related to the possibility of a separation between slow and regular fronts

Critical Dynamics in Genetic Regulatory Networks: Examples from Four Kingdoms

The coordinated expression of the different genes in an organism is essential to sustain functionality under the random external perturbations to which the organism might be subjected. To cope with such external variability, the global dynamics of the genetic network must possess two central properties. (a) It must be robust enough as to guarantee stability under a broad range of external conditions, and (b) it must be flexible enough to recognize and integrate specific external signals that may help the organism to change and adapt to different environments. This compromise between robustness and adaptability has been observed in dynamical systems operating at the brink of a phase transition between order and chaos. Such systems are termed critical. Thus, criticality, a precise, measurable, and well characterized property of dynamical systems, makes it possible for robustness and adaptability to coexist in living organisms. In this work we investigate the dynamical properties of the gene transcription networks reported for S. cerevisiae, E. coli, and B. subtilis, as well as the network of segment polarity genes of D. melanogaster, and the network of flower development of A. thaliana. We use hundreds of microarray experiments to infer the nature of the regulatory interactions among genes, and implement these data into the Boolean models of the genetic networks. Our results show that, to the best of the current experimental data available, the five networks under study indeed operate close to criticality. The generality of this result suggests that criticality at the genetic level might constitute a fundamental evolutionary mechanism that generates the great diversity of dynamically robust living forms that we observe around us