Modelling heterogeneity of concrete using 2D lattice network for concrete fracture and comparison with AE study

In this paper, numerical modelling of fracture in concrete using two-dimensional lattice model is presented and also a few issues related to lattice modelling technique applicable to concrete fracture are reviewed. A comparison is made with acoustic emission (AE) events with the number of fractured elements. To implement the heterogeneity of the plain concrete, two methods namely, by generating grain structure of the concrete using Fuller's distribution and the concrete material properties are randomly distributed following Gaussian distribution are used. In the first method, the modelling of the concrete at meso level is carried out following the existing methods available in literature. The shape of the aggregates present in the concrete are assumed as perfect spheres and shape of the same in two-dimensional lattice network is circular. A three-point bend (TPB) specimen is tested in the experiment under crack mouth opening displacement (CMOD) control at a rate of 0.0004 mm/sec and the fracture process in the same TPB specimen is modelled using regular triangular 2D lattice network. Load versus crack mouth opening isplacement (CMOD) plots thus obtained by using both the methods are compared with experimental results. It was observed that the number of fractured elements increases near the peak load and beyond the peak load. That is once the crack starts to propagate. AE hits also increase rapidly beyond the peak load. It is compulsory here to mention that although the lattice modelling of concrete fracture used in this present study is very similar to those already available in literature, the present work brings out certain finer details which are not available explicitly in the earlier works.

2D-lattice distributed reflector laser

A single-contact, mode-hop-free, single longitudinal mode laser operating cw under large signal modulation at 2.5 Gbit/s at room temperature was created by introducing a short etched region around the ridge-waveguide of a Fabry-Perot laser. The device could be suitable for use in extended range data communications applications.

High coupling in novel 2D-lattice distributed reflector laser gratings

It is shown that 2D lattice gratings, despite being placed outside the waveguide region, exhibit sufficiently strong coupling coefficients that optical modes rapidly couple transversely into the etched grating region, yielding high coupling coefficients of 270cm-1. This performance allows mode-hop-free lasing operation in DBR structures.

Chaotic synchronization in 2D lattice for scene segmentation

Synchronization and chaos play important roles in neural activities and have been applied in oscillatory correlation modeling for scene and data analysis. Although it is an extensively studied topic, there are still few results regarding synchrony in locally coupled systems. In this paper we give a rigorous proof to show that large numbers of coupled chaotic oscillators with parameter mismatch in a 2D lattice can be synchronized by providing a sufficiently large coupling strength. We demonstrate how the obtained result can be applied to construct an oscillatory network for scene segmentation. (C) 2007 Elsevier B.V. All rights reserved.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

Hierarchical models for 2D presence/absence data having ambiguous zeroes: With a biogeographical case study on dingo behaviour

This dissertation is primarily an applied statistical modelling investigation, motivated by a case study comprising real data and real questions. Theoretical questions on modelling and computation of normalization constants arose from pursuit of these data analytic questions. The essence of the thesis can be described as follows. Consider binary data observed on a two-dimensional lattice. A common problem with such data is the ambiguity of zeroes recorded. These may represent zero response given some threshold (presence) or that the threshold has not been triggered (absence). Suppose that the researcher wishes to estimate the effects of covariates on the binary responses, whilst taking into account underlying spatial variation, which is itself of some interest. This situation arises in many contexts and the dingo, cypress and toad case studies described in the motivation chapter are examples of this. Two main approaches to modelling and inference are investigated in this thesis. The first is frequentist and based on generalized linear models, with spatial variation modelled by using a block structure or by smoothing the residuals spatially. The EM algorithm can be used to obtain point estimates, coupled with bootstrapping or asymptotic MLE estimates for standard errors. The second approach is Bayesian and based on a three- or four-tier hierarchical model, comprising a logistic regression with covariates for the data layer, a binary Markov Random field (MRF) for the underlying spatial process, and suitable priors for parameters in these main models. The three-parameter autologistic model is a particular MRF of interest. Markov chain Monte Carlo (MCMC) methods comprising hybrid Metropolis/Gibbs samplers is suitable for computation in this situation. Model performance can be gauged by MCMC diagnostics. Model choice can be assessed by incorporating another tier in the modelling hierarchy. This requires evaluation of a normalization constant, a notoriously difficult problem. Difficulty with estimating the normalization constant for the MRF can be overcome by using a path integral approach, although this is a highly computationally intensive method. Different methods of estimating ratios of normalization constants (N Cs) are investigated, including importance sampling Monte Carlo (ISMC), dependent Monte Carlo based on MCMC simulations (MCMC), and reverse logistic regression (RLR). I develop an idea present though not fully developed in the literature, and propose the Integrated mean canonical statistic (IMCS) method for estimating log NC ratios for binary MRFs. The IMCS method falls within the framework of the newly identified path sampling methods of Gelman & Meng (1998) and outperforms ISMC, MCMC and RLR. It also does not rely on simplifying assumptions, such as ignoring spatio-temporal dependence in the process. A thorough investigation is made of the application of IMCS to the three-parameter Autologistic model. This work introduces background computations required for the full implementation of the four-tier model in Chapter 7. Two different extensions of the three-tier model to a four-tier version are investigated. The first extension incorporates temporal dependence in the underlying spatio-temporal process. The second extensions allows the successes and failures in the data layer to depend on time. The MCMC computational method is extended to incorporate the extra layer. A major contribution of the thesis is the development of a fully Bayesian approach to inference for these hierarchical models for the first time. Note: The author of this thesis has agreed to make it open access but invites people downloading the thesis to send her an email via the 'Contact Author' function.

Dipolar Bose-Einstein condensate soliton on a two-dimensional optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

Electrochemical tuning and mechanical resilience of single-wall carbon nanotubes

Single-wall carbon nanotubes (SWNTs) are fascinating systems exhibiting many novel physical properties. In this paper, we give a brief review of the structural, electronic, vibrational, and mechanical properties of carbon nanotubes. In situ resonance Raman scattering of SWNTs investigated under electrochemical biasing demonstrates that the intensity of the radial breathing mode varies significantly in a nonmonotonic manner as a function of the cathodic bias voltage, but does not change appreciably under anodic bias. These results can be quantitatively understood in terms of the changes in the energy gaps between the 1 D van Hove singularities in the electron density of states, arising possibly due to the alterations in the overlap integral of pi bonds between the p-orbitals of the adjacent carbon atoms. In the second part of this paper, we review our high-pressure X-ray diffraction results, which show that the triangular lattice of the carbon nanotube bundles continues to persist up to similar to10 GPa. The lattice is seen to relax just before the phase transformation, which is observed at similar to10 GPa. Further, our results display the reversibility of the 2D lattice symmetry even after compression up to 13 GPa well beyond the 5 GPa value observed recently. These experimental results explicitly validate the predicted remarkable mechanical resilience of the nanotubes.

Interfacial self-assembly of a bacterial hydrophobin

The majority of bacteria in the natural environment live within the confines of a biofilm. The Gram-positive bacterium Bacillus subtilis forms biofilms that exhibit a characteristic wrinkled morphology and a highly hydrophobic surface. A critical component in generating these properties is the protein BslA, which forms a coat across the surface of the sessile community. We recently reported the structure of BslA, and noted the presence of a large surface-exposed hydrophobic patch. Such surface patches are also observed in the class of surface-active proteins known as hydrophobins, and are thought to mediate their interfacial activity. However, although functionally related to the hydrophobins, BslA shares no sequence nor structural similarity, and here we show that the mechanism of action is also distinct. Specifically, our results suggest that the amino acids making up the large, surface-exposed hydrophobic cap in the crystal structure are shielded in aqueous solution by adopting a random coil conformation, enabling the protein to be soluble and monomeric. At an interface, these cap residues refold, inserting the hydrophobic side chains into the air or oil phase and forming a three-stranded β-sheet. This form then self-assembles into a well-ordered 2D rectangular lattice that stabilizes the interface. By replacing a hydrophobic leucine in the center of the cap with a positively charged lysine, we changed the energetics of adsorption and disrupted the formation of the 2D lattice. This limited structural metamorphosis represents a previously unidentified environmentally responsive mechanism for interfacial stabilization by proteins.