Complex dynamics in simple systems with periodic parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of ϵ-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

Tests of non-linearity using LIFFE futures transactions price data

This paper presents and implements a number of tests for non-linear dependence and a test for chaos using transactions prices on three LIFFE futures contracts: the Short Sterling interest rate contract, the Long Gilt government bond contract, and the FTSE 100 stock index futures contract. While previous studies of high frequency futures market data use only those transactions which involve a price change, we use all of the transaction prices on these contracts whether they involve a price change or not. Our results indicate irrefutable evidence of non-linearity in two of the three contracts, although we find no evidence of a chaotic process in any of the series. We are also able to provide some indications of the effect of the duration of the trading day on the degree of non-linearity of the underlying contract. The trading day for the Long Gilt contract was extended in August 1994, and prior to this date there is no evidence of any structure in the return series. However, after the extension of the trading day we do find evidence of a non-linear return structure.

Chaos in foreign exchange markets: a sceptical view

This paper tests directly for deterministic chaos in a set of ten daily Sterling-denominated exchange rates by calculating the largest Lyapunov exponent. Although in an earlier paper, strong evidence of nonlinearity has been shown, chaotic tendencies are noticeably absent from all series considered using this state-of-the-art technique. Doubt is cast on many recent papers which claim to have tested for the presence of chaos in economic data sets, based on what are argued here to be inappropriate techniques.

Systematic model forecast error in Rossby wave structure

Diabatic processes can alter Rossby wave structure; consequently errors arising from model processes propagate downstream. However, the chaotic spread of forecasts from initial condition uncertainty renders it difficult to trace back from root mean square forecast errors to model errors. Here diagnostics unaffected by phase errors are used, enabling investigation of systematic errors in Rossby waves in winter-season forecasts from three operational centers. Tropopause sharpness adjacent to ridges decreases with forecast lead time. It depends strongly on model resolution, even though models are examined on a common grid. Rossby wave amplitude reduces with lead time up to about five days, consistent with under-representation of diabatic modification and transport of air from the lower troposphere into upper-tropospheric ridges, and with too weak humidity gradients across the tropopause. However, amplitude also decreases when resolution is decreased. Further work is necessary to isolate the contribution from errors in the representation of diabatic processes.

Atmospheric circulation as a source of uncertainty in climate change projections

The evidence for anthropogenic climate change continues to strengthen, and concerns about severe weather events are increasing. As a result, scientific interest is rapidly shifting from detection and attribution of global climate change to prediction of its impacts at the regional scale. However, nearly everything we have any confidence in when it comes to climate change is related to global patterns of surface temperature, which are primarily controlled by thermodynamics. In contrast, we have much less confidence in atmospheric circulation aspects of climate change, which are primarily controlled by dynamics and exert a strong control on regional climate. Model projections of circulation-related fields, including precipitation, show a wide range of possible outcomes, even on centennial timescales. Sources of uncertainty include low-frequency chaotic variability and the sensitivity to model error of the circulation response to climate forcing. As the circulation response to external forcing appears to project strongly onto existing patterns of variability, knowledge of errors in the dynamics of variability may provide some constraints on model projections. Nevertheless, higher scientific confidence in circulation-related aspects of climate change will be difficult to obtain. For effective decision-making, it is necessary to move to a more explicitly probabilistic, risk-based approach.

Cultural policy, literature and readership in revolutionary Cuba: the view from the 21st century

This article presents a fresh perspective on cultural policy in revolutionary Cuba, focusing specifically on the centrality of dialogue with the general readership to the production, reception and regulation of literature. It first summarises the positions regarding revolutionary literature that have been asserted and essayed at various points along the sometimes chaotic trajectory of revolution in Cuba. It then examines reading-related policies and recent attempts within Cuba to re-orient reading practices in the aftermath of the Período Especial [Special Period], and ends by presenting current Cuban debates on the need to mitigate dialogic breakdown between literary text and readership.

A doubling of the sun's coronal magnetic field during the last 100 years

The solar wind is an extended ionized gas of very high electrical conductivity, and therefore drags some magnetic flux out of the Sun to fill the heliosphere with a weak interplanetary magnetic field(1,2). Magnetic reconnection-the merging of oppositely directed magnetic fields-between the interplanetary field and the Earth's magnetic field allows energy from the solar wind to enter the near-Earth environment. The Sun's properties, such as its luminosity, are related to its magnetic field, although the connections are still not well understood(3,4). Moreover, changes in the heliospheric magnetic field have been linked with changes in total cloud cover over the Earth, which may influence global climate(5), Here we show that measurements of the near-Earth interplanetary magnetic field reveal that the total magnetic flux leaving the Sun has risen by a factor of 1.4 since 1964: surrogate measurements of the interplanetary magnetic field indicate that the increase since 1901 has been by a factor of 2,3, This increase may be related to chaotic changes in the dynamo that generates the solar magnetic field. We do not yet know quantitatively how such changes will influence the global environment.

Fractal geometry and architecture design: case study review

The idea of buildings in harmony with nature can be traced back to ancient times. The increasing concerns on sustainability oriented buildings have added new challenges in building architectural design and called for new design responses. Sustainable design integrates and balances the human geometries and the natural ones. As the language of nature, it is, therefore, natural to assume that fractal geometry could play a role in developing new forms of aesthetics and sustainable architectural design. This paper gives a brief description of fractal geometry theory and presents its current status and recent developments through illustrative review of some fractal case studies in architecture design, which provides a bridge between fractal geometry and architecture design.

The error of representation: basic understanding

Representation error arises from the inability of the forecast model to accurately simulate the climatology of the truth. We present a rigorous framework for understanding this kind of error of representation. This framework shows that the lack of an inverse in the relationship between the true climatology (true attractor) and the forecast climatology (forecast attractor) leads to the error of representation. A new gain matrix for the data assimilation problem is derived that illustrates the proper approaches one may take to perform Bayesian data assimilation when the observations are of states on one attractor but the forecast model resides on another. This new data assimilation algorithm is the optimal scheme for the situation where the distributions on the true attractor and the forecast attractors are separately Gaussian and there exists a linear map between them. The results of this theory are illustrated in a simple Gaussian multivariate model.

The determinants of inward foreign direct investment in business services across European regions

The determinants of inward foreign direct investment in business services across European regions, Regional Studies. The role of forward linkages with manufacturing sectors and other service sectors as attractors of business services foreign direct investment (FDI) is studied at the regional level. Using data on 146 NUTS-2 regions, it is found that regions specialized in those (manufacturing) sectors that are high potential users of business services attract more FDI in the business services than other regions. Results are robust to the inclusion of the traditional determinants of foreign investments at the regional level as well as to controls for spatial dependence. The results suggest that regional policies aimed at attracting foreign investors in the business service industry might prove ineffective in the absence of a pre-existing local intermediate demand

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of ℝ d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

My generation(s): cycles, branding and renewal in E4’s 'Skins'

In an era of fragmenting audience and diversified viewing platforms, youth television needs to move fast and make a lot of noise in order to capture and maintain the attention of the teenage viewer. British ensemble youth drama Skins (E4, 2007-2013) calls attention to itself with its high doses of drugs, chaotic parties and casual attitudes towards sexuality. It also moves quickly, shedding its cast every two seasons as they graduate from school, then renewing itself with a fresh generation of 16 year old characters - three cycles in total. This essay will explore the challenges of maintaining audience connections whilst resetting the narrative clock with each cycle. I suggest that the development of the Skins brand was key to the programme’s success. Branding is particularly important for an audience demographic who increasingly consume their television outside of broadcast flow and essential for a programme which renews its cast every two years. The Skins brand operate as a framework, as the central audience draw, have the strength to maintain audience connections when it ‘graduates’ those characters they identify with at the close of each cycle and starts again from scratch. This essay will explore how the Skins brand constructs a cohesive identity across its multiple generations, yet also consider how the cyclic form poses challenges for the programme’s representations and narratives. This cyclic form allows Skins to repeatedly reach out to a new audience who comes of age alongside each new generation and to reflect shifts in British youth culture. Thus Skins remains ever-youthful, seeking to maintain an at times painfully hip identity. Yet the programme has a somewhat schizophrenic identity, torn between its roots in British realist drama and surrealist comedy and an escapist aspirational glamour that shows the influence of US Teen TV. This combination results in a tendency towards a heightened melodrama at odds with Skins claims for authenticity - its much vaunted teenage advisors and young writers - with the cyclic structure serving to amplify the programme’s excessive tendencies. Each cycle wrestles with a need for continuity and familiarity - partly maintained through brand, aesthetic and setting - yet a desire for freshness and originality, to assert difference from what has gone before. I suggest that the inevitable need for each cycle to ‘top’ what has gone before results in a move away from character-based intimacy and the everyday to high-stakes drama and violence which sits uncomfortably within British youth television.