Wave chaotic behaviour generated by linear systems

It is shown that regimes with dynamical chaos are inherent not only to nonlinear system but they can be generated by initially linear systems and the requirements for chaotic dynamics and characteristics need further elaboration. Three simplest physical models are considered as examples. In the first, dynamic chaos in the interaction of three linear oscillators is investigated. Analogous process is shown in the second model of electromagnetic wave scattering in a double periodical inhomogeneous medium occupying half-space. The third model is a linear parametric problem for the electromagnetic field in homogeneous dielectric medium which permittivity is modulated in time. © 2008 Springer Science+Business Media, LLC.

Adding constrained discontinuities to Gaussian process models of wind fields

Gaussian Processes provide good prior models for spatial data, but can be too smooth. In many physical situations there are discontinuities along bounding surfaces, for example fronts in near-surface wind fields. We describe a modelling method for such a constrained discontinuity and demonstrate how to infer the model parameters in wind fields with MCMC sampling.

Improved multi-beam neural network scatterometer forward models

Current methods for retrieving near surface winds from scatterometer observations over the ocean surface require a foward sensor model which maps the wind vector to the measured backscatter. This paper develops a hybrid neural network forward model, which retains the physical understanding embodied in ¸mod, but incorporates greater flexibility, allowing a better fit to the observations. By introducing a separate model for the mid-beam and using a common model for the fore- and aft-beams, we show a significant improvement in local wind vector retrieval. The hybrid model also fits the scatterometer observations more closely. The model is trained in a Bayesian framework, accounting for the noise on the wind vector inputs. We show that adding more high wind speed observations in the training set improves wind vector retrieval at high wind speeds without compromising performance at medium or low wind speeds.

Adding constrained discontinuities to Gaussian process models of wind fields

Gaussian Processes provide good prior models for spatial data, but can be too smooth. In many physical situations there are discontinuities along bounding surfaces, for example fronts in near-surface wind fields. We describe a modelling method for such a constrained discontinuity and demonstrate how to infer the model parameters in wind fields with MCMC sampling.

Updating finite element models using measured vibration data

The modelling of mechanical structures using finite element analysis has become an indispensable stage in the design of new components and products. Once the theoretical design has been optimised a prototype may be constructed and tested. What can the engineer do if the measured and theoretically predicted vibration characteristics of the structure are significantly different? This thesis considers the problems of changing the parameters of the finite element model to improve the correlation between a physical structure and its mathematical model. Two new methods are introduced to perform the systematic parameter updating. The first uses the measured modal model to derive the parameter values with the minimum variance. The user must provide estimates for the variance of the theoretical parameter values and the measured data. Previous authors using similar methods have assumed that the estimated parameters and measured modal properties are statistically independent. This will generally be the case during the first iteration but will not be the case subsequently. The second method updates the parameters directly from the frequency response functions. The order of the finite element model of the structure is reduced as a function of the unknown parameters. A method related to a weighted equation error algorithm is used to update the parameters. After each iteration the weighting changes so that on convergence the output error is minimised. The suggested methods are extensively tested using simulated data. An H frame is then used to demonstrate the algorithms on a physical structure.

Equilibrium properties of disordered spin models with two-scale interactions

Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdös- Rényi graph structures above the percolation threshold and to Bethe lattices when appropriate boundary conditions apply. In this paper, we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model. The equilibrium properties are examined through the replica method, with exact analysis of the high-temperature paramagnetic, spin-glass, and ferromagnetic phases by perturbative schemes. We present results of replica symmetric variational approximations, where perturbative approaches fail at lower temperature. Results demonstrate re-entrant behaviors from spin glass to ferromagnetic phases as temperature is lowered, including transitions from replica symmetry broken to replica symmetric phases. The nature of high-temperature transitions is found to be sensitive to the connectivity profile in the sparse subgraph, with regular connectivity a discontinuous transition from the paramagnetic to ferromagnetic phases is apparent.

Improved neural network scatterometer forward models

Current methods for retrieving near-surface winds from scatterometer observations over the ocean surface require a forward sensor model which maps the wind vector to the measured backscatter. This paper develops a hybrid neural network forward model, which retains the physical understanding embodied in CMOD4, but incorporates greater flexibility, allowing a better fit to the observations. By introducing a separate model for the midbeam and using a common model for the fore and aft beams, we show a significant improvement in local wind vector retrieval. The hybrid model also fits the scatterometer observations more closely. The model is trained in a Bayesian framework, accounting for the noise on the wind vector inputs. We show that adding more high wind speed observations in the training set improves wind vector retrieval at high wind speeds without compromising performance at medium or low wind speeds. Copyright 2001 by the American Geophysical Union.

Development of multiphase and multiscale mathematical models for thermal spray process

High velocity oxyfuel (HVOF) thermal spraying is one of the most significant developments in the thermal spray industry since the development of the original plasma spray technique. The first investigation deals with the combustion and discrete particle models within the general purpose commercial CFD code FLUENT to solve the combustion of kerosene and couple the motion of fuel droplets with the gas flow dynamics in a Lagrangian fashion. The effects of liquid fuel droplets on the thermodynamics of the combusting gas flow are examined thoroughly showing that combustion process of kerosene is independent on the initial fuel droplet sizes. The second analysis copes with the full water cooling numerical model, which can assist on thermal performance optimisation or to determine the best method for heat removal without the cost of building physical prototypes. The numerical results indicate that the water flow rate and direction has noticeable influence on the cooling efficiency but no noticeable effect on the gas flow dynamics within the thermal spraying gun. The third investigation deals with the development and implementation of discrete phase particle models. The results indicate that most powder particles are not melted upon hitting the substrate to be coated. The oxidation model confirms that HVOF guns can produce metallic coating with low oxidation within the typical standing-off distance about 30cm. Physical properties such as porosity, microstructure, surface roughness and adhesion strength of coatings produced by droplet deposition in a thermal spray process are determined to a large extent by the dynamics of deformation and solidification of the particles impinging on the substrate. Therefore, is one of the objectives of this study to present a complete numerical model of droplet impact and solidification. The modelling results show that solidification of droplets is significantly affected by the thermal contact resistance/substrate surface roughness.

Modelling data and voice traffic over IP networks using continuous-time Markov models

Common approaches to IP-traffic modelling have featured the use of stochastic models, based on the Markov property, which can be classified into black box and white box models based on the approach used for modelling traffic. White box models, are simple to understand, transparent and have a physical meaning attributed to each of the associated parameters. To exploit this key advantage, this thesis explores the use of simple classic continuous-time Markov models based on a white box approach, to model, not only the network traffic statistics but also the source behaviour with respect to the network and application. The thesis is divided into two parts: The first part focuses on the use of simple Markov and Semi-Markov traffic models, starting from the simplest two-state model moving upwards to n-state models with Poisson and non-Poisson statistics. The thesis then introduces the convenient to use, mathematically derived, Gaussian Markov models which are used to model the measured network IP traffic statistics. As one of the most significant contributions, the thesis establishes the significance of the second-order density statistics as it reveals that, in contrast to first-order density, they carry much more unique information on traffic sources and behaviour. The thesis then exploits the use of Gaussian Markov models to model these unique features and finally shows how the use of simple classic Markov models coupled with use of second-order density statistics provides an excellent tool for capturing maximum traffic detail, which in itself is the essence of good traffic modelling. The second part of the thesis, studies the ON-OFF characteristics of VoIP traffic with reference to accurate measurements of the ON and OFF periods, made from a large multi-lingual database of over 100 hours worth of VoIP call recordings. The impact of the language, prosodic structure and speech rate of the speaker on the statistics of the ON-OFF periods is analysed and relevant conclusions are presented. Finally, an ON-OFF VoIP source model with log-normal transitions is contributed as an ideal candidate to model VoIP traffic and the results of this model are compared with those of previously published work.

Semantic linking through spaces for cyber-physical-socio intelligence:a methodology

Humans consciously and subconsciously establish various links, emerge semantic images and reason in mind, learn linking effect and rules, select linked individuals to interact, and form closed loops through links while co-experiencing in multiple spaces in lifetime. Machines are limited in these abilities although various graph-based models have been used to link resources in the cyber space. The following are fundamental limitations of machine intelligence: (1) machines know few links and rules in the physical space, physiological space, psychological space, socio space and mental space, so it is not realistic to expect machines to discover laws and solve problems in these spaces; and, (2) machines can only process pre-designed algorithms and data structures in the cyber space. They are limited in ability to go beyond the cyber space, to learn linking rules, to know the effect of linking, and to explain computing results according to physical, physiological, psychological and socio laws. Linking various spaces will create a complex space — the Cyber-Physical-Physiological-Psychological-Socio-Mental Environment CP3SME. Diverse spaces will emerge, evolve, compete and cooperate with each other to extend machine intelligence and human intelligence. From multi-disciplinary perspective, this paper reviews previous ideas on various links, introduces the concept of cyber-physical society, proposes the ideal of the CP3SME including its definition, characteristics, and multi-disciplinary revolution, and explores the methodology of linking through spaces for cyber-physical-socio intelligence. The methodology includes new models, principles, mechanisms, scientific issues, and philosophical explanation. The CP3SME aims at an ideal environment for humans to live and work. Exploration will go beyond previous ideals on intelligence and computing.

Self-sustained clusters and ergodicity breaking in spin models

Self-sustained spin clusters are analytically linked to ergodicity breaking in fully connected Ising and Sherrington-Kirkpatick (SK) models, relating the less understood spin space to the well understood state space. This correspondence is established through the absence of clusters in the paramagnetic phase, the presence of one dominant cluster in the Ising ferromagnet, and the formation of nontrivial clusters in SK spin glass. Yet unobserved phenomena are also revealed such as a first order phase transition in cluster sizes in the SK ferromagnet. The method could be adapted to investigate other spin models. © 2013 American Physical Society.

Role of fluctuations in membrane models:thermal versus nonthermal

We study the comparative importance of thermal to nonthermal fluctuations for membrane-based models in the linear regime. Our results, both in 1+1 and 2+1 dimensions, suggest that nonthermal fluctuations dominate thermal ones only when the relaxation time τ is large. For moderate to small values of τ, the dynamics is defined by a competition between these two forces. The results are expected to act as a quantitative benchmark for biological modeling in systems involving cytoskeletal and other nonthermal fluctuations. © 2011 American Physical Society.

The relation between physical properties of the anterior eye and ocular surface temperature

PURPOSE. To examine the relation between ocular surface temperature (OST) assessed by dynamic thermal imaging and physical parameters of the anterior eye in normal subjects. METHODS. Dynamic ocular thermography (ThermoTracer 7102MX) was used to record body temperature and continuous ocular surface temperature for 8 s after a blink in the right eyes of 25 subjects. Corneal thickness, corneal curvature, and anterior chamber depth (ACD) were assessed using Orbscan II; noninvasive tear break-up time (NIBUT) was assessed using the tearscope; slit lamp photography was used to record tear meniscus height (TMH) and objective bulbar redness. RESULTS. Initial OST after a blink was significantly correlated only with body temperature (r = 0.80, p < 0.0005), NIBUT (r = -0.68, p < 0.005) and corneal curvature (r = -0.40, p = 0.05). A regression model containing all the variables accounted for 70% (p = 0.002) of the variance in OST, of which NIBUT (29%, p = 0.004), and body temperature (18%, p = 0.005) contributed significantly. CONCLUSIONS. The results support previous theoretical models that OST radiation is principally related to the tear film; and demonstrate that it is less related to other characteristics such as corneal thickness, corneal curvature, and anterior chamber depth. © 2007 American Academy of Optometry.

Exploring the digital supply chain:implications and models for online software distribution

As a discipline, supply chain management (SCM) has traditionally been primarily concerned with the procurement, processing, movement and sale of physical goods. However an important class of products has emerged - digital products - which cannot be described as physical as they do not obey commonly understood physical laws. They do not possess mass or volume, and they require no energy in their manufacture or distribution. With the Internet, they can be distributed at speeds unimaginable in the physical world, and every copy produced is a 100% perfect duplicate of the original version. Furthermore, the ease with which digital products can be replicated has few analogues in the physical world. This paper assesses the effect of non-physicality on one such product – software – in relation to the practice of SCM. It explores the challenges that arise when managing the software supply chain and how practitioners are addressing these challenges. Using a two-pronged exploratory approach that examines the literature around software management as well as direct interviews with software distribution practitioners, a number of key challenges associated with software supply chains are uncovered, along with responses to these challenges. This paper proposes a new model for software supply chains that takes into account the non-physicality of the product being delivered. Central to this model is the replacement of physical flows with flows of intellectual property, the growing importance of innovation over duplication and the increased centrality of the customer in the entire process. Hybrid physical / digital supply chains are discussed and a framework for practitioners concerned with software supply chains is presented.

The role of pinning and instability in a class of non-equilibrium growth models

We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model is considered for the purpose. Following standard coarse graining procedures, it is shown that in the large time, long distance limit, the continuum model predicts a curvature independent KPZ phase, thereby suppressing all explicit effects of curvature and local pinning in the system, in the "perturbative" limit. A direct numerical integration of this growth equation, in 1+1 dimensions, supports this observation below a critical parametric range, above which generic instabilities, in the form of isolated pillared structures lead to deviations from standard scaling behaviour. Possibilities of controlling this instability by introducing statistically "irrelevant" (in the sense of renormalisation groups) higher ordered nonlinearities have also been discussed.