Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.

Clustering behaviors in networks of integrate-and-fire oscillators

Clustering behavior is studied in a model of integrate-and-fire oscillators with excitatory pulse coupling. When considering a population of identical oscillators, the main result is a proof of global convergence to a phase-locked clustered behavior. The robustness of this clustering behavior is then investigated in a population of nonidentical oscillators by studying the transition from total clustering to the absence of clustering as the group coherence decreases. A robust intermediate situation of partial clustering, characterized by few oscillators traveling among nearly phase-locked clusters, is of particular interest. The analysis complements earlier studies of synchronization in a closely related model. © 2008 American Institute of Physics.

Multiple pitch estimation using non-homogeneous poisson processes

Novel statistical models are proposed and developed in this paper for automated multiple-pitch estimation problems. Point estimates of the parameters of partial frequencies of a musical note are modeled as realizations from a non-homogeneous Poisson process defined on the frequency axis. When several notes are combined, the processes for the individual notes combine to give a new Poisson process whose likelihood is easy to compute. This model avoids the data-association step of linking the harmonics of each note with the corresponding partials and is ideal for efficient Bayesian inference of unknown multiple fundamental frequencies in a signal. © 2011 IEEE.

The post-processed Galerkin method applied to non-linear shell vibrations

We present the results of a computational study of the post-processed Galerkin methods put forward by Garcia-Archilla et al. applied to the non-linear von Karman equations governing the dynamic response of a thin cylindrical panel periodically forced by a transverse point load. We spatially discretize the shell using finite differences to produce a large system of ordinary differential equations (ODEs). By analogy with spectral non-linear Galerkin methods we split this large system into a 'slowly' contracting subsystem and a 'quickly' contracting subsystem. We then compare the accuracy and efficiency of (i) ignoring the dynamics of the 'quick' system (analogous to a traditional spectral Galerkin truncation and sometimes referred to as 'subspace dynamics' in the finite element community when applied to numerical eigenvectors), (ii) slaving the dynamics of the quick system to the slow system during numerical integration (analogous to a non-linear Galerkin method), and (iii) ignoring the influence of the dynamics of the quick system on the evolution of the slow system until we require some output, when we 'lift' the variables from the slow system to the quick using the same slaving rule as in (ii). This corresponds to the post-processing of Garcia-Archilla et al. We find that method (iii) produces essentially the same accuracy as method (ii) but requires only the computational power of method (i) and is thus more efficient than either. In contrast with spectral methods, this type of finite-difference technique can be applied to irregularly shaped domains. We feel that post-processing of this form is a valuable method that can be implemented in computational schemes for a wide variety of partial differential equations (PDEs) of practical importance.

Enhanced integrated modelling approach to reconfiguring manufacturing enterprises

Dynamism and uncertainty are real challenges for present day manufacturing enterprises (MEs). Reasons include: an increasing demand for customisation, reduced time to market, shortened product life cycles and globalisation. MEs can reduce competitive pressure by becoming reconfigurable and change-capable. However, modern manufacturing philosophies, including agile and lean, must complement the application of reconfigurable manufacturing paradigms. Choosing and applying the best philosophies and techniques is very difficult as most MEs deploy complex and unique configurations of processes and resource systems, and seek economies of scope and scale in respect of changing and distinctive product flows. It follows that systematic methods of achieving model driven reconfiguration and interoperation of component based manufacturing systems are required to design, engineer and change future MEs. This thesis, titled Enhanced Integrated Modelling Approach to Reconfiguring Manufacturing Enterprises , introduces the development and prototyping a model-driven environment for the design, engineering, optimisation and control of the reconfiguration of MEs with an embedded capability to handle various types of change. The thesis describes a novel systematic approach, namely enhanced integrated modelling approach (EIMA), in which coherent sets of integrated models are created that facilitates the engineering of MEs especially their production planning and control (PPC) systems. The developed environment supports the engineering of common types of strategic, tactical and operational processes found in many MEs. The EIMA is centred on the ISO standardised CIMOSA process modelling approach. Early study led to the development of simulation models during which various CIMOSA shortcomings were observed, especially in its support for aspects of ME dynamism. A need was raised to structure and create semantically enriched models hence forming an enhanced integrated modelling environment. The thesis also presents three industrial case examples: (1) Ford Motor Company; (2) Bradgate Furniture Manufacturing Company; and (3) ACM Bearings Company. In order to understand the system prior to realisation of any PPC strategy, multiple process segments of any target organisation need to be modelled. Coherent multi-perspective case study models are presented that have facilitated process reengineering and associated resource system configuration. Such models have a capability to enable PPC decision making processes in support of the reconfiguration of MEs. During these case studies, capabilities of a number of software tools were exploited such as Arena®, Simul8®, Plant Simulation®, MS Visio®, and MS Excel®. Case study results demonstrated effectiveness of the concepts related to the EIMA. The research has resulted in new contributions to knowledge in terms of new understandings, concepts and methods in following ways: (1) a structured model driven integrated approach to the design, optimisation and control of future reconfiguration of MEs. The EIMA is an enriched and generic process modelling approach with capability to represent both static and dynamic aspects of an ME; and (2) example application cases showing benefits in terms of reduction in lead time, cost and resource load and in terms of improved responsiveness of processes and resource systems with a special focus on PPC; (3) identification and industrial application of a new key performance indicator (KPI) known as P3C the measuring and monitoring of which can aid in enhancing reconfigurability and responsiveness of MEs; and (4) an enriched modelling concept framework (E-MUNE) to capture requirements of static and dynamic aspects of MEs where the conceptual framework has the capability to be extended and modified according to the requirements. The thesis outlines key areas outlining a need for future research into integrated modelling approaches, interoperation and updating mechanisms of partial models in support of the reconfiguration of MEs.