Negative compressibility

Rearch financed by the Malta Council for Science and Technology and CHISMACOMB (an EU FP6 STREP project).Structures made up from bi-material elements which can exhibit negative properties, in particular negative compressibility (negative bulk modulus, i.e. expand in size when the external pressure is increased and shrink when the external pressure is decreased) are proposed. This anomalous behaviour is confirmed through finite element modelling.peer-reviewe

Auxetic behaviour from connected different-sized squares and rectangles

Auxetic materials exhibit the unusual property of becoming fatter when uniaxially stretched and thinner when uniaxially compressed (i.e. they exhibit a negative Poisson ratio; NPR), a property that may result in various enhanced properties. The NPR is the result of the manner in which particular geometric features in the micro- or nanostructure of the materials deform when they are subjected to uniaxial loads. Here, we propose and discuss a new model made from different-sized rigid rectangles, which rotate relative to each other. This new model has the advantage over existing models that it can be used to describe the properties of very different systems ranging from silicates and zeolites to liquid-crystalline polymers. We show that such systems can exhibit scale-independent auxetic behaviour for stretching in particular directions, with Poisson’s ratios being dependent on the shape and relative size of different rectangles in the model and the angle between them.peer-reviewe

Negative thermal expansion

Materials with a negative thermal expansion coefficient contract when heated and expand when cooled. This paper reviews mechanisms of how this unusual property can be achieved at the molecular and macroscopic level. Some applications of this unusual property are also discussed.peer-reviewe

Steady-state fluctuations of a genetic feedback loop:an exact solution

Genetic feedback loops in cells break detailed balance and involve bimolecular reactions; hence exact solutions revealing the nature of the stochastic fluctuations in these loops are lacking. We here consider the master equation for a gene regulatory feedback loop: a gene produces protein which then binds to the promoter of the same gene and regulates its expression. The protein degrades in its free and bound forms. This network breaks detailed balance and involves a single bimolecular reaction step. We provide an exact solution of the steady-state master equation for arbitrary values of the parameters, and present simplified solutions for a number of special cases. The full parametric dependence of the analytical non-equilibrium steady-state probability distribution is verified by direct numerical solution of the master equations. For the case where the degradation rate of bound and free protein is the same, our solution is at variance with a previous claim of an exact solution (Hornos et al, Phys. Rev. E {\bf 72}, 051907 (2005) and subsequent studies). We show explicitly that this is due to an unphysical formulation of the underlying master equation in those studies.Comment: 31 pages, 3 figures. Accepted for publication in the Journal of Chemical Physics (2012

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtolitres. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small sub-cellular compartment. This is achieved by applying a mesoscopic version of the quasi-steady state assumption to the exact Fokker-Planck equation associated with the Poisson Representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing sub-cellular volume, decreasing Michaelis-Menten constants and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.Comment: 13 pages, 4 figures; published in The Journal of Chemical Physic

Cálculo de los tiempos de circularvección en una población con patología vestibular. Influencia del estímulo visual

[corrected] To describe the results obtained for circularvection times (tCV) in a study of the phenomenon of visual-vestibular interaction for a population with vestibular pathology and to analyze differences in its calculation among patients reporting a worsening of their symptoms with visual stimuli. MATERIAL AND METHODS: A detailed case history was taken for all patients, followed by a sensory organization test using computerized dynamic posturography and the calculation of their tCV. RESULTS: The mean tCV results were: tCV2= 6.32+/-3.17 s; tCV3=6.57+/-3.68 s; tCVr=6.27+/-6.02 s. Significant differences were obtained in tCV2 (P=.046) and tCVr (P=.023). CONCLUSIONS: tCV is a diagnostic test using simple tools that can help differentiate patients in whom the visual stimulus is influenced

A novel mechanism for generating auxetic behaviour in reticulated foams : missing rib foam model

Foams have previously been fabricated with a negative Poisson's ratio (termed auxetic foams). A novel model is proposed to explain this and to describe the strain-dependent Poisson's function behaviour of honeycomb and foam materials. The model is two-dimensional and is based upon the observation of broken cell ribs in foams processed via the compression and heating technique usually employed to convert conventional foams to auxetic behaviour. The model has two forms: the “intact” form is a network of ribs with biaxial symmetry, and the “auxetic” form is a similar network but with a proportion of cell ribs removed. The model output is compared with that of an existing two-dimensional model and experimental data, and is found to be superior in predicting the Poisson's function and marginally better at predicting the stress–strain behaviour of the experimental data than the existing model, using realistic values for geometric parameters.peer-reviewe

How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order $\Omega^{-3/2}$ for reaction systems which do not obey detailed balance and at least accurate to order $\Omega^{-2}$ for systems obeying detailed balance, where $\Omega$ is the characteristic size of the system. Hence the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order $\Omega^{-1/2}$ and variance estimates accurate to order $\Omega^{-3/2}$. This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy

Sampling bias in systems with structural heterogeneity and limited internal diffusion

Complex systems research is becomingly increasingly data-driven, particularly in the social and biological domains. Many of the systems from which sample data are collected feature structural heterogeneity at the mesoscopic scale (i.e. communities) and limited inter-community diffusion. Here we show that the interplay between these two features can yield a significant bias in the global characteristics inferred from the data. We present a general framework to quantify this bias, and derive an explicit corrective factor for a wide class of systems. Applying our analysis to a recent high-profile survey of conflict mortality in Iraq suggests a significant overestimate of deaths

Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading

Finite Element models are developed for the in-plane linear elastic constants of a family of honeycombs comprising arrays of cylinders connected by ligaments. Honeycombs having cylinders with 3, 4 and 6 ligaments attached to them are considered, with two possible configurations explored for each of the 3- (trichiral and anti-trichiral) and 4- (tetrachiral and anti-tetrachiral) connected systems. Honeycombs for each configuration have been manufactured using rapid prototyping and subsequently characterised for mechanical properties through in-plane uniaxial loading to verify the models. An interesting consequence of the family of 'chiral' honeycombs presented here is the ability to produce negative Poisson's ratio (auxetic) response. The deformation mechanisms responsible for auxetic functionality in such honeycombs are discussed