Acoustic emission source location in composite structure by Voronoi construction using geodesic curve evolution

Conventional analytical/numerical methods employing triangulation technique are suitable for locating acoustic emission (AE) source in a planar structure without structural discontinuities. But these methods cannot be extended to structures with complicated geometry, and, also, the problem gets compounded if the material of the structure is anisotropic warranting complex analytical velocity models. A geodesic approach using Voronoi construction is proposed in this work to locate the AE source in a composite structure. The approach is based on the fact that the wave takes minimum energy path to travel from the source to any other point in the connected domain. The geodesics are computed on the meshed surface of the structure using graph theory based on Dijkstra's algorithm. By propagating the waves in reverse virtually from these sensors along the geodesic path and by locating the first intersection point of these waves, one can get the AE source location. In this work, the geodesic approach is shown more suitable for a practicable source location solution in a composite structure with arbitrary surface containing finite discontinuities. Experiments have been conducted on composite plate specimens of simple and complex geometry to validate this method.

Deploy and search strategy for multi-agent systems using Voronoi partitions

In this paper we analyze a deploy and search strategy for multi-agent systems. Mobile agents equipped with sensors carry out search operation in the search space. The lack of information about the search space is modeled as an uncertainty density distribution over the space, and is assumed to be known to the agents a priori. In each step, the agents deploy themselves in an optimal way so as to maximize per step reduction in the uncertainty density. We analyze the proposed strategy for convergence and spatial distributedness. The control law moving the agents has been analyzed for stability and convergence using LaSalle's invariance principle, and for spatial distributedness under a few realistic constraints on the control input such as constant speed, limit on maximum speed, and also sensor range limits. The simulation experiments show that the strategy successfully reduces the average uncertainty density below the required level.

Variational calculation for the spin-(1/2 Heisenberg antiferromagnet on a square lattice

The ground-state properties of the spin-(1/2 Heisenberg antiferromagnet on a square lattice are studied by using a simple variational wave function that interpolates continuously between the Néel state and short-range resonating-valence-bond states. Exact calculations of the variational energy for small systems show that the state with the lowest energy has long-range antiferromagnetic order. The staggered magnetization in this state is approximately 70% of its maximum possible value. The variational estimate of the ground-state energy is substantially lower than the value obtained for the nearest-neighbor resonating-valence-bond wave function.

Combining Bayes Classification and Point Group Symmetry under Boolean Framework for Enhanced Protein Quaternary Structure Inference

Our ability to infer the protein quaternary structure automatically from atom and lattice information is inadequate, especially for weak complexes, and heteromeric quaternary structures. Several approaches exist, but they have limited performance. Here, we present a new scheme to infer protein quaternary structure from lattice and protein information, with all-around coverage for strong, weak and very weak affinity homomeric and heteromeric complexes. The scheme combines naive Bayes classifier and point group symmetry under Boolean framework to detect quaternary structures in crystal lattice. It consistently produces >= 90% coverage across diverse benchmarking data sets, including a notably superior 95% coverage for recognition heteromeric complexes, compared with 53% on the same data set by current state-of-the-art method. The detailed study of a limited number of prediction-failed cases offers interesting insights into the intriguing nature of protein contacts in lattice. The findings have implications for accurate inference of quaternary states of proteins, especially weak affinity complexes.

Automated Multi-Agent Search Using Centroidal Voronoi Configuration

This paper addresses the problem of automated multiagent search in an unknown environment. Autonomous agents equipped with sensors carry out a search operation in a search space, where the uncertainty, or lack of information about the environment, is known a priori as an uncertainty density distribution function. The agents are deployed in the search space to maximize single step search effectiveness. The centroidal Voronoi configuration, which achieves a locally optimal deployment, forms the basis for the proposed sequential deploy and search strategy. It is shown that with the proposed control law the agent trajectories converge in a globally asymptotic manner to the centroidal Voronoi configuration. Simulation experiments are provided to validate the strategy. Note to Practitioners-In this paper, searching an unknown region to gather information about it is modeled as a problem of using search as a means of reducing information uncertainty about the region. Moreover, multiple automated searchers or agents are used to carry out this operation optimally. This problem has many applications in search and surveillance operations using several autonomous UAVs or mobile robots. The concept of agents converging to the centroid of their Voronoi cells, weighted with the uncertainty density, is used to design a search strategy named as sequential deploy and search. Finally, the performance of the strategy is validated using simulations.

Variational principles in evolution

For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface-in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of the n-locus genetic system moves on the surface of the product space of n higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus.

Superconductivity from repulsion: a variational view

This letter presents a new class of variational wavefunctions for Fermi systems in any dimension. These wavefunctions introduce correlations between Cooper pairs in different momentum states and the relevant correlations can be computed analytically. At half filling we have a ground state with critical superconducting correlations, that causes negligible increase of the kinetic energy. We find large enhancements in a Cooper-pair correlation function caused purely by the interplay between the uncertainty principle, repulsion and the proximity of half filling. This is surprising since there is no accompanying signature in usual charge and spin response functions, and typifies a novel kind of many-body cooperative behaviour.

Variational Asymptotic Analysis of a Self-healing SMA Composite

A Shape Memory Alloy (SMA) wire reinforced composite shell structure is analyzed for self-healing characteristic using Variational Asymptotic Method (VAM). SMA behavior is modeled using a onedimensional constitutive model. A pre-notched specimen is loaded longitudinally to simulate crack propagation. The loading process is accompanied by martensitic phase transformation in pre-strained SMA wires, bridging the crack. To heal the composite, uniform heating is required to initiate reverse transformation in the wires and bringing the crack faces back into contact. The pre-strain in the SMA wires used for reinforcement, causes a closure force across the crack during reverse transformation of the wires under heating. The simulation can be useful in design of self-healing composite structures using SMA. Effect of various parameters, like composite and SMA material properties and the geometry of the specimen, on the cracking and self-healing can also be studied.

Multi-agent Search using Voronoi partitions

This paper addresses the problem of multiagent search in an unknown environment. The agents are autonomous in nature and are equipped with necessary sensors to carry out the search operation. The uncertainty, or lack of information about the search area is known a priori as a probability density function. The agents are deployed in an optimal way so as to maximize the one step uncertainty reduction. The agents continue to deploy themselves and reduce uncertainty till the uncertainty density is reduced over the search space below a minimum acceptable level. It has been shown, using LaSalle’s invariance principle, that a distributed control law which moves each of the agents towards the centroid of its Voronoi partition, modified by the sensor range leads to single step optimal deployment. This principle is now used to devise search trajectories for the agents. The simulations were carried out in 2D space with saturation on speeds of the agents. The results show that the control strategy per step indeed moves the agents to the respective centroid and the algorithm reduces the uncertainty distribution to the required level within a few steps.

Prediction of inter-laminar stresses in composite honeycomb sandwich panels under mechanical loading using Variational Asymptotic Method

This work focuses on the formulation of an asymptotically correct theory for symmetric composite honeycomb sandwich plate structures. In these panels, transverse stresses tremendously influence design. The conventional 2-D finite elements cannot predict the thickness-wise distributions of transverse shear or normal stresses and 3-D displacements. Unfortunately, the use of the more accurate three-dimensional finite elements is computationally prohibitive. The development of the present theory is based on the Variational Asymptotic Method (VAM). Its unique features are the identification and utilization of additional small parameters associated with the anisotropy and non-homogeneity of composite sandwich plate structures. These parameters are ratios of smallness of the thickness of both facial layers to that of the core and smallness of 3-D stiffness coefficients of the core to that of the face sheets. Finally, anisotropy in the core and face sheets is addressed by the small parameters within the 3-D stiffness matrices. Numerical results are illustrated for several sample problems. The 3-D responses recovered using VAM-based model are obtained in a much more computationally efficient manner than, and are in agreement with, those of available 3-D elasticity solutions and 3-D FE solutions of MSC NASTRAN. (c) 2012 Elsevier Ltd. All rights reserved.

Continuum theory of edge states of topological insulators: variational principle and boundary conditions

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.