53 resultados para TOPOLOGY OF SINGULARITY
em Cambridge University Engineering Department Publications Database
Resumo:
We describe a method to explore the configurational phase space of chemical systems. It is based on the nested sampling algorithm recently proposed by Skilling (AIP Conf. Proc. 2004, 395; J. Bayesian Anal. 2006, 1, 833) and allows us to explore the entire potential energy surface (PES) efficiently in an unbiased way. The algorithm has two parameters which directly control the trade-off between the resolution with which the space is explored and the computational cost. We demonstrate the use of nested sampling on Lennard-Jones (LJ) clusters. Nested sampling provides a straightforward approximation for the partition function; thus, evaluating expectation values of arbitrary smooth operators at arbitrary temperatures becomes a simple postprocessing step. Access to absolute free energies allows us to determine the temperature-density phase diagram for LJ cluster stability. Even for relatively small clusters, the efficiency gain over parallel tempering in calculating the heat capacity is an order of magnitude or more. Furthermore, by analyzing the topology of the resulting samples, we are able to visualize the PES in a new and illuminating way. We identify a discretely valued order parameter with basins and suprabasins of the PES, allowing a straightforward and unambiguous definition of macroscopic states of an atomistic system and the evaluation of the associated free energies.
Resumo:
The paper presents a multiscale procedure for the linear analysis of components made of lattice materials. The method allows the analysis of both pin-jointed and rigid-jointed microtruss materials with arbitrary topology of the unit cell. At the macroscopic level, the procedure enables to determine the lattice stiffness, while at the microscopic level the internal forces in the lattice elements are expressed in terms of the macroscopic strain applied to the lattice component. A numeric validation of the method is described. The procedure is completely automated and can be easily used within an optimization framework to find the optimal geometric parameters of a given lattice material. © 2011 Elsevier Ltd. All rights reserved.
Resumo:
Genetic algorithms (GAs) have been used to tackle non-linear multi-objective optimization (MOO) problems successfully, but their success is governed by key parameters which have been shown to be sensitive to the nature of the particular problem, incorporating concerns such as the numbers of objectives and variables, and the size and topology of the search space, making it hard to determine the best settings in advance. This work describes a real-encoded multi-objective optimizing GA (MOGA) that uses self-adaptive mutation and crossover, and which is applied to optimization of an airfoil, for minimization of drag and maximization of lift coefficients. The MOGA is integrated with a Free-Form Deformation tool to manage the section geometry, and XFoil which evaluates each airfoil in terms of its aerodynamic efficiency. The performance is compared with those of the heuristic MOO algorithms, the Multi-Objective Tabu Search (MOTS) and NSGA-II, showing that this GA achieves better convergence.
Resumo:
We assume that the resistance matrix can be found in electrical impedance tomography from the assumption of linear dependence between the voltages and the currents and with the help of the resistance matrix and the transfer impedance between the electrodes, a directional algebraic reconstruction technique is proposed. The goal is to reconstruct the resistivity distribution by weighting the matrices that are obtained by calculating the orthogonal distance of the underlying mesh elements from the neighbouring port resistivity lines. These weighting matrices, which only depend on the topology of the underlying mesh, can be calculated offline and result in a computationally efficient online procedure with a reasonable image reconstruction performance. Simulation results are provided to validate this approach.
Resumo:
Considering some predictive mechanisms, we show that ultrafast average-consensus can be achieved in networks of interconnected agents. More specifically, by predicting the dynamics of the network several steps ahead and using this information in the design of the consensus protocol of each agent, drastic improvements can be achieved in terms of the speed of consensus convergence, without changing the topology of the network. Moreover, using these predictive mechanisms, the range of sampling periods leading to consensus convergence is greatly expanded compared with the routine consensus protocol. This study provides a mathematical basis for the idea that some predictive mechanisms exist in widely-spread biological swarms, flocks, and networks. From the industrial engineering point of view, inclusion of an efficient predictive mechanism allows for a significant increase in the speed of consensus convergence and also a reduction of the communication energy required to achieve a predefined consensus performance.
Resumo:
A group of mobile robots can localize cooperatively, using relative position and absolute orientation measurements, fused through an extended Kalman filter (ekf). The topology of the graph of relative measurements is known to affect the steady-state value of the position error covariance matrix. Classes of sensor graphs are identified, for which tight bounds for the trace of the covariance matrix can be obtained based on the algebraic properties of the underlying relative measurement graph. The string and the star graph topologies are considered, and the explicit form of the eigenvalues of error covariance matrix is given. More general sensor graph topologies are considered as combinations of the string and star topologies, when additional edges are added. It is demonstrated how the addition of edges increases the trace of the steady-state value of the position error covariance matrix, and the theoretical predictions are verified through simulation analysis.
Resumo:
A multi-objective design optimisation study has been carried out with the objectives to improve the overall efficiency of the device and to reduce the fuel consumption for the proposed micro-scale combustor design configuration. In a previous study we identified the topology of the combustion chamber that produced improved behaviour of the device in terms of the above design criteria. We now extend our design approach, and we propose a new configuration by the addition of a micro-cooling channel that will improve the thermal behaviour of the design as previously suggested in literature. Our initial numerical results revealed an improvement of 2.6% in the combustion efficiency when we applied the micro-cooling channel to an optimum design configuration we identified from our earlier multi-objective optimisation study, and under the same operating conditions. The computational modelling of the combustion process is implemented in the commercial computational fluid dynamics package ANSYS-CFX using Finite Rate Chemistry and a single step hydrogen-air reaction. With this model we try to balance good accuracy of the combustion solution and at the same time practicality within the context of an optimisation process. The whole design system comprises also the ANSYS-ICEM CFD package for the automatic geometry and mesh generation and the Multi-Objective Tabu Search algorithm for the design space exploration. We model the design problem with 5 geometrical parameters and 3 operational parameters subject to 5 design constraints that secure practicality and feasibility of the new optimum design configurations. The final results demonstrate the reliability and efficiency of the developed computational design system and most importantly we assess the practicality and manufacturability of the revealed optimum design configurations of micro-combustor devices. Copyright © 2013 by ASME.
Resumo:
Carbon fiber reinforced polymer (CFRP) composite sandwich panels with hybrid foam filled CFRP pyramidal lattice cores have been assembled from a carbon fiber braided net, 3D woven face sheets and various polymeric foams, and infused with an epoxy resin using a vacuum assisted resin transfer process. Sandwich panels with a fixed CFRP truss mass have been fabricated using a variety of closed cell polymer and syntactic foams, resulting in core densities ranging from 44-482kgm-3. The through thickness and in-plane shear modulus and strength of the cores increased with increasing foam density. The use of low compressive strength foams within the core was found to result in a significant reduction in the compressive strength contributed by the CFRP trusses. X-ray tomography led to the discovery that the trusses develop an elliptical cross-section shape during pressure assisted resin transfer. The ellipticity of the truss cross-sections increased, and the lattice contribution to the core strength decreased as the foam density was reduced. Micromechanical modeling was used to investigate the relationships between the mechanical properties and volume fractions of the core materials and truss topology of the hybrid core. The specific strength and moduli of the hybrid cores lay between those of the CFRP lattices and foams used to fabricate them. However, their volumetric and gravimetric energy absorptions significantly exceeded those of the materials from which they were fabricated. They compare favorably with other lightweight energy absorbing materials and structures. © 2013.