Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport, and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold, and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models, and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.Comment: 38 pages, 16 figures. This version includes a much-expanded introduction, and a new section on nonlinear diffusion in addition to polish throughou

Non-linear models: applications in economics

The study concentrated on demonstrating how non-linear modelling can be useful to investigate the behavioural of dynamic economic systems. Using some adequate non-linear models could be a good way to find more refined solutions to actually unsolved problems or ambiguities in economics. Beginning with a short presentation of the simplest non-linear models, then we are demonstrating how the dynamics of complex systems, as the economic system is, could be explained on the base of some more advanced non-linear models and using specific techniques of simulation. We are considering the non-linear models only as an alternative to the stochastic linear models in economics. The conventional explanations of the behaviour of economic system contradict many times the empirical evidence. We are trying to demonstrate that small modifications in the standard linear form of some economic models make more complex and consequently more realistic the behaviour of system simulated on the base of the new non-linear models. Finally, few applications of non-linear models to the study of inflation-unemployment relationship, potentially useful for further empirical studies, are presented.non-linear model; continuous time map; strange attractor; fractal dimension; natural unemployment

Thick-walled composite tubes for offshore applications : an example of stress and failure analysis for filament-wound multi-layered pipes

Acknowledgements Financial support of the part of this research by The Royal Society, The Royal Academy of Engineering, and The Carnegie Trust for the Universities of Scotland is gratefully acknowledged.Peer reviewedPostprin

Global adaptation in networks of selfish components: emergent associative memory at the system scale

In some circumstances complex adaptive systems composed of numerous self-interested agents can self-organise into structures that enhance global adaptation, efficiency or function. However, the general conditions for such an outcome are poorly understood and present a fundamental open question for domains as varied as ecology, sociology, economics, organismic biology and technological infrastructure design. In contrast, sufficient conditions for artificial neural networks to form structures that perform collective computational processes such as associative memory/recall, classification, generalisation and optimisation, are well-understood. Such global functions within a single agent or organism are not wholly surprising since the mechanisms (e.g. Hebbian learning) that create these neural organisations may be selected for this purpose, but agents in a multi-agent system have no obvious reason to adhere to such a structuring protocol or produce such global behaviours when acting from individual self-interest. However, Hebbian learning is actually a very simple and fully-distributed habituation or positive feedback principle. Here we show that when self-interested agents can modify how they are affected by other agents (e.g. when they can influence which other agents they interact with) then, in adapting these inter-agent relationships to maximise their own utility, they will necessarily alter them in a manner homologous with Hebbian learning. Multi-agent systems with adaptable relationships will thereby exhibit the same system-level behaviours as neural networks under Hebbian learning. For example, improved global efficiency in multi-agent systems can be explained by the inherent ability of associative memory to generalise by idealising stored patterns and/or creating new combinations of sub-patterns. Thus distributed multi-agent systems can spontaneously exhibit adaptive global behaviours in the same sense, and by the same mechanism, as the organisational principles familiar in connectionist models of organismic learning

Describing the Flow Curve of Shear-Banding Fluids Through a Structural Minimal Model

Main characteristics of colloidal systems that develop fluid phases with different mechanical properties, namely shear-banding fluids, are briefly reviewed both from experimental and theoretical (modelling) point of view. A non-monotonic shear stress vs. shear rate constitutive relation is presented. This relation derives from a phenomenological model of a shear ratedependent viscosity describing structural changes and involves the possibility of multivalued shear rates under a given shear stress. In the case of a stress-dependent viscosity, the same model allows one to predict vorticity banding. Predictions of this model under controlled stress are discussed, namely occurrence of a kind of top- and bottom-jumping of the shear rate in response to stress increasing-decreasing. Applying this model to evaluation of the flow curve of such colloidal systems is performed. Particular emphasis is placed on the adequate computation of the shear rate function in cylindrical Couette cells in order to handle the corresponding flow curve which exhibits the well-known shear stress plateau. Indeed, as different fluid phases coexist in the flow domain, measured (torque vs. angular velocity) data cannot be directly converted into rheometric (shear stress vs. shear rate) functions. As the lacking non-local terms in the model prevents the direct determination of the stress-plateau, this value is included as an adjustable parameter. Thus model predictions satisfactorily match up experimental data of wormlike micellar solutions from the literature.Comment: 22 pages, 9 fi

Multi-Unit Auctions to Allocate Water Scarcity Simulating Bidding Behaviour with Agent Based Models

Multi-unit auctions are promising mechanisms for the reallocation of water. The main advantage of such auctions is to avoid the lumpy bid issue. However, there is great uncertainty about the best auction formats when multi-unit auctions are used. The theory can only supply the structural properties of equilibrium strategies and the multiplicity of equilibria makes comparisons across auction formats difficult. Empirical studies and experiments have improved our knowledge of multi- unit auctions but they remain scarce and most experiments are restricted to two bidders and two units. Moreover, they demonstrate that bidders have limited rationality and learn through experience. This paper constructs an agent-based model of bidders to compare the performance of alternative auction formats under circumstances where bidders submit continuous bid supply functions and learn over time to adjust their bids to improve their net incomes. We demonstrate that under the generalized Vickrey, simulated bids converge towards truthful bids as predicted by the theory and that bid shading is the rule for the uniform and discriminatory auctions. Our study allows us to assess the potential gains from agent-based modelling approaches in the assessment of the dynamic performance of multi-unit procurement auctions. Some recommendations on the desirable format of water auctions are provided.Multi-unit auctions, Learning, Multi-agent models, Water allocation

Asymmetric Price Impacts of Order Flow on Exchange Rate Dynamics

We generalize the portfolio shifts model advanced by Evans and Lyons (2002a; b), and develop the dynamic asymmetric portfolio shifts (DAPS) model by explicitly allowing for possible market under- and overreactions and for asymmetric pricing impacts of order flows. Using the Reuters D2000-1 daily trading data for eight currency markets over a four-month period from 1 May to 31 August 1996, we find strong evidence of a nonlinear cointegrating relationship between exchange rates and (cumulative) order flows: The price impact of negative order flows (selling pressure) is overwhelmingly stronger than that of the positive ones (buying pressure). Through the dynamic multiplier analysis, we find two typical patterns of the price discovery process. The markets following overreactions tend to display a delayed overshooting and a volatile but faster adjustment towards equilibrium whereas the markets following underreactions are generally characterized by a gradual but persistent adjustment. In our model, these heterogeneous adjustment patterns reflect different liquidity provisions associated with different market conditions following under- and overreactions. In addition, the larger is the mispricing, the faster is the overall adjustment speed, a finding consistent with Abreu and Brunnermeier (2002) and Cai et al. (2011). We also find that underreactions are followed mostly by positive feedback trading while overreactions are characterized by delayed overshooting in the short run but corrected by negative feedback trading at longer horizons, the finding is consistent with Barberis et al. (1998) who show that positive short-run autocorrelations (momentum) signal underreaction while negative long-run autocorrelations (reversal) signal overreaction.Exchange rate, order flow, under- and overreaction, asymmetric pricing impacts, asymmetric cointegrating relationship and dynamic multipliers