Optimal Boussinesq model for shallow-water waves interacting with a microstructure

In this paper, we consider the propagation of water waves in a long-wave asymptotic regime, when the bottom topography is periodic on a short length scale. We perform a multiscale asymptotic analysis of the full potential theory model and of a family of reduced Boussinesq systems parametrized by a free parameter that is the depth at which the velocity is evaluated. We obtain explicit expressions for the coefficients of the resulting effective Korteweg-de Vries (KdV) equations. We show that it is possible to choose the free parameter of the reduced model so as to match the KdV limits of the full and reduced models. Hence the reduced model is optimal regarding the embedded linear weakly dispersive and weakly nonlinear characteristics of the underlying physical problem, which has a microstructure. We also discuss the impact of the rough bottom on the effective wave propagation. In particular, nonlinearity is enhanced and we can distinguish two regimes depending on the period of the bottom where the dispersion is either enhanced or reduced compared to the flat bottom case. © 2007 The American Physical Society.

Air Fleet and Facility Planning via Optimal Control Models

A study is presented which is aimed at developing techniques suitable for effective planning and efficient operation of fleets of aircraft typical of the air force of a developing country. An important aspect of fleet management, the problem of resource allocation for achieving prescribed operational effectiveness of the fleet, is considered. For analysis purposes, it is assumed that the planes operate in a single flying-base repair-depot environment. The perennial problem of resource allocation for fleet and facility buildup that faces planners is modeled and solved as an optimal control problem. These models contain two "policy" variables representing investments in aircraft and repair facilities. The feasibility of decentralized control is explored by assuming the two policy variables are under the control of two independent decisionmakers guided by different and not often well coordinated objectives.

Air Fleet and Facility Planning via Optimal Control Models

A study is presented which is aimed at developing techniques suitable for effective planning and efficient operation of fleets of aircraft typical of the air force of a developing country. An important aspect of fleet management, the problem of resource allocation for achieving prescribed operational effectiveness of the fleet, is considered. For analysis purposes, it is assumed that the planes operate in a single flying-base repair-depot environment. The perennial problem of resource allocation for fleet and facility buildup that faces planners is modeled and solved as an optimal control problem. These models contain two "policy" variables representing investments in aircraft and repair facilities. The feasibility of decentralized control is explored by assuming the two policy variables are under the control of two independent decisionmakers guided by different and not often well coordinated objectives.

On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy

In this paper, the available potential energy (APE) framework of Winters et al. (J. Fluid Mech., vol. 289, 1995, p. 115) is extended to the fully compressible Navier– Stokes equations, with the aims of clarifying (i) the nature of the energy conversions taking place in turbulent thermally stratified fluids; and (ii) the role of surface buoyancy fluxes in the Munk & Wunsch (Deep-Sea Res., vol. 45, 1998, p. 1977) constraint on the mechanical energy sources of stirring required to maintain diapycnal mixing in the oceans. The new framework reveals that the observed turbulent rate of increase in the background gravitational potential energy GPEr , commonly thought to occur at the expense of the diffusively dissipated APE, actually occurs at the expense of internal energy, as in the laminar case. The APE dissipated by molecular diffusion, on the other hand, is found to be converted into internal energy (IE), similar to the viscously dissipated kinetic energy KE. Turbulent stirring, therefore, does not introduce a new APE/GPEr mechanical-to-mechanical energy conversion, but simply enhances the existing IE/GPEr conversion rate, in addition to enhancing the viscous dissipation and the entropy production rates. This, in turn, implies that molecular diffusion contributes to the dissipation of the available mechanical energy ME =APE +KE, along with viscous dissipation. This result has important implications for the interpretation of the concepts of mixing efficiency γmixing and flux Richardson number Rf , for which new physically based definitions are proposed and contrasted with previous definitions. The new framework allows for a more rigorous and general re-derivation from the first principles of Munk & Wunsch (1998, hereafter MW98)’s constraint, also valid for a non-Boussinesq ocean: G(KE) ≈ 1 − ξ Rf ξ Rf Wr, forcing = 1 + (1 − ξ )γmixing ξ γmixing Wr, forcing , where G(KE) is the work rate done by the mechanical forcing, Wr, forcing is the rate of loss of GPEr due to high-latitude cooling and ξ is a nonlinearity parameter such that ξ =1 for a linear equation of state (as considered by MW98), but ξ <1 otherwise. The most important result is that G(APE), the work rate done by the surface buoyancy fluxes, must be numerically as large as Wr, forcing and, therefore, as important as the mechanical forcing in stirring and driving the oceans. As a consequence, the overall mixing efficiency of the oceans is likely to be larger than the value γmixing =0.2 presently used, thereby possibly eliminating the apparent shortfall in mechanical stirring energy that results from using γmixing =0.2 in the above formula.

Testing optimal foraging theory models on benthic divers

Empirical testing of optimal foraging models on diving air-breathing animals is limited due to difficulties in quantifying the prey field through direct observations. Here we used accelerometers to detect rapid head movements during prey encounter events (PEE) of free-ranging benthic-divers, Australian fur seals, Arctocephalus pusillus doriferus. PEE signals from accelerometer data were validated by simultaneous video data. We then used PEEs as a measure of patch quality to test several optimal foraging model predictions. Seals had longer bottom durations in unfruitful dives (no PEE) than those with some foraging success (PEE. ≥. 1). However, when examined in greater detail, seals had longer bottom durations in dives with more PEEs, but shorter bottom durations in bouts (sequences of dives) with more PEEs. Our results suggest that seals were generally maximizing bottom durations in all foraging dives, characteristic of benthic divers. However, successful foraging dives might be more energetically costly (e.g. digestive costs), thus resulting in shorter bottom durations at the larger scale of bouts. Our study provides a case study of how the foraging behaviour of a central place forager foraging in a fairly homogeneous environment, with relatively high travel costs, may deviate from current foraging models under different situations. Future foraging models should aim to integrate other aspects (e.g. diet) of the foraging process for more accurate predictions.

Optimal control predicts human performance on objects with internal degrees of freedom.

On a daily basis, humans interact with a vast range of objects and tools. A class of tasks, which can pose a serious challenge to our motor skills, are those that involve manipulating objects with internal degrees of freedom, such as when folding laundry or using a lasso. Here, we use the framework of optimal feedback control to make predictions of how humans should interact with such objects. We confirm the predictions experimentally in a two-dimensional object manipulation task, in which subjects learned to control six different objects with complex dynamics. We show that the non-intuitive behavior observed when controlling objects with internal degrees of freedom can be accounted for by a simple cost function representing a trade-off between effort and accuracy. In addition to using a simple linear, point-mass optimal control model, we also used an optimal control model, which considers the non-linear dynamics of the human arm. We find that the more realistic optimal control model captures aspects of the data that cannot be accounted for by the linear model or other previous theories of motor control. The results suggest that our everyday interactions with objects can be understood by optimality principles and advocate the use of more realistic optimal control models for the study of human motor neuroscience.

Risk-sensitive optimal feedback control accounts for sensorimotor behavior under uncertainty.

Many aspects of human motor behavior can be understood using optimality principles such as optimal feedback control. However, these proposed optimal control models are risk-neutral; that is, they are indifferent to the variability of the movement cost. Here, we propose the use of a risk-sensitive optimal controller that incorporates movement cost variance either as an added cost (risk-averse controller) or as an added value (risk-seeking controller) to model human motor behavior in the face of uncertainty. We use a sensorimotor task to test the hypothesis that subjects are risk-sensitive. Subjects controlled a virtual ball undergoing Brownian motion towards a target. Subjects were required to minimize an explicit cost, in points, that was a combination of the final positional error of the ball and the integrated control cost. By testing subjects on different levels of Brownian motion noise and relative weighting of the position and control cost, we could distinguish between risk-sensitive and risk-neutral control. We show that subjects change their movement strategy pessimistically in the face of increased uncertainty in accord with the predictions of a risk-averse optimal controller. Our results suggest that risk-sensitivity is a fundamental attribute that needs to be incorporated into optimal feedback control models.

Risk-sensitive optimal feedback control accounts for sensorimotor behavior under uncertainty

Many aspects of human motor behavior can be understood using optimality principles such as optimal feedback control. However, these proposed optimal control models are risk-neutral; that is, they are indifferent to the variability of the movement cost. Here, we propose the use of a risk-sensitive optimal controller that incorporates movement cost variance either as an added cost (risk-averse controller) or as an added value (risk-seeking controller) to model human motor behavior in the face of uncertainty. We use a sensorimotor task to test the hypothesis that subjects are risk-sensitive. Subjects controlled a virtual ball undergoing Brownian motion towards a target. Subjects were required to minimize an explicit cost, in points, that was a combination of the final positional error of the ball and the integrated control cost. By testing subjects on different levels of Brownian motion noise and relative weighting of the position and control cost, we could distinguish between risk-sensitive and risk-neutral control. We show that subjects change their movement strategy pessimistically in the face of increased uncertainty in accord with the predictions of a risk-averse optimal controller. Our results suggest that risk-sensitivity is a fundamental attribute that needs to be incorporated into optimal feedback control models. © 2010 Nagengast et al.

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

Internal Models, Vestibular Cognition, and Mental Imagery: Conceptual Considerations

Vestibular cognition has recently gained attention. Despite numerous experimental and clinical demonstrations, it is not yet clear what vestibular cognition really is. For future research in vestibular cognition, adopting a computational approach will make it easier to explore the underlying mech- anisms. Indeed, most modeling approaches in vestibular science include a top-down or a priori component. We review recent Bayesian optimal observer models, and discuss in detail the conceptual value of prior assumptions, likelihood and posterior estimates for research in vestibular cognition. We then consider forward models in vestibular processing, which are required in order to distinguish between sensory input that is induced by active self-motion, and sensory input that is due to passive self-motion. We suggest that forward models are used not only in the service of estimating sensory states but they can also be drawn upon in an offline mode (e.g., spatial perspective transformations), in which interaction with sensory input is not desired. A computational approach to vestibular cogni- tion will help to discover connections across studies, and it will provide a more coherent framework for investigating vestibular cognition.

Optimal sequence of landfills in solid waste management

Given that landfills are depletable and replaceable resources, the right approach, when dealing with landfill management, is that of designing an optimal sequence of landfills rather than designing every single landfill separately. In this paper we use Optimal Control models, with mixed elements of both continuous and discrete time problems, to determine an optimal sequence of landfills, as regarding their capacity and lifetime. The resulting optimization problems involve splitting a time horizon of planning into several subintervals, the length of which has to be decided. In each of the subintervals some costs, the amount of which depends on the value of the decision variables, have to be borne. The obtained results may be applied to other economic problems such as private and public investments, consumption decisions on durable goods, etc.

Expert performance in sport and the dynamics of talent development

Research on expertise, talent identification and development has tended to be mono-disciplinary, typically adopting adopting neurogenetic deterministic or environmentalist positions, with an over-riding focus on operational issues. In this paper the validity of dualist positions on sport expertise is evaluated. It is argued that, to advance understanding of expertise and talent development, a shift towards a multi-disciplinary and integrative science focus is necessary, along with the development of a comprehensive multi-disciplinary theoretical rationale. Here we elucidate dynamical systems theory as a multi-disciplinary theoretical rationale for capturing how multiple interacting constraints can shape the development of expert performers. This approach suggests that talent development programmes should eschew the notion of common optimal performance models, emphasise the individual nature of pathways to expertise, and identify the range of interacting constraints that impinge on performance potential of individual athletes, rather than evaluating current performance on physical tests referenced to group norms.

A multidisciplinary examination of fast bowling talent development in cricket

Research on expertise, talent identification and development has tended to be mono-disciplinary, typically adopting geno-centric or environmentalist positions, with an overriding focus on operational issues. In this thesis, the validity of dualist positions on sport expertise is evaluated. It is argued that, to advance understanding of expertise and talent development, a shift towards a multidisciplinary and integrative science focus is necessary, along with the development of a comprehensive multidisciplinary theoretical rationale. Dynamical systems theory is utilised as a multidisciplinary theoretical rationale for the succession of studies, capturing how multiple interacting constraints can shape the development of expert performers. Phase I of the research examines experiential knowledge of coaches and players on the development of fast bowling talent utilising qualitative research methodology. It provides insights into the developmental histories of expert fast bowlers, as well as coaching philosophies on the constraints of fast bowling expertise. Results suggest talent development programmes should eschew the notion of common optimal performance models and emphasize the individual nature of pathways to expertise. Coaching and talent development programmes should identify the range of interacting constraints that impinge on the performance potential of individual athletes, rather than evaluating current performance on physical tests referenced to group norms. Phase II of this research comprises three further studies that investigate several of the key components identified as important for fast bowling expertise, talent identification and development extrapolated from Phase I of this research. This multidisciplinary programme of work involves a comprehensive analysis of fast bowling performance in a cross-section of the Cricket Australia high performance pathways, from the junior, emerging and national elite fast bowling squads. Briefly, differences were found in trunk kinematics associated with the generation of ball speed across the three groups. These differences in release mechanics indicated the functional adaptations in movement patterns as bowlers’ physical and anatomical characteristics changed during maturation. Second to the generation of ball speed, the ability to produce a range of delivery types was highlighted as a key component of expertise in the qualitative phase. The ability of athletes to produce consistent results on different surfaces and in different environments has drawn attention to the challenge of measuring consistency and flexibility in skill assessments. Examination of fast bowlers in Phase II demonstrated that national bowlers can make adjustments to the accuracy of subsequent deliveries during performance of a cricket bowling skills test, and perform a range of delivery types with increased accuracy and consistency. Finally, variability in selected delivery stride ground reaction force components in fast bowling revealed the degenerate nature of this complex multi-articular skill where the same performance outcome can be achieved with unique movement strategies. Utilising qualitative and quantitative methodologies to examine fast bowling expertise, the importance of degeneracy and adaptability in fast bowling has been highlighted alongside learning design that promotes dynamic learning environments.

社会形势预警的几种建模方法比较

Based on social survey data conducted by local research group in some counties executed in the nearly past five years in China, the author proposed and solved two kernel problems in the field of social situation forecasting: i) How can the attitudes’ data on individual level be integrated with social situation data on macrolevel; ii) How can the powers of forecasting models’ constructed by different statistic methods be compared? Five integrative statistics were applied to the research: 1) algorithm average (MEAN); 2) standard deviation (SD); 3) coefficient variability (CV); 4) mixed secondary moment (M2); 5) Tendency (TD). To solve the former problem, the five statistics were taken to synthesize the individual and mocrolevel data of social situations on the levels of counties’ regions, and form novel integrative datasets, from the basis of which, the latter problem was accomplished by the author: modeling methods such as Multiple Regression Analysis (MRA), Discriminant Analysis (DA) and Support Vector Machine (SVM) were used to construct several forecasting models. Meanwhile, on the dimensions of stepwise vs. enter, short-term vs. long-term forecasting and different integrative (statistic) models, meta-analysis and power analysis were taken to compare the predicting power of each model within and among modeling methods. Finally, it can be concluded from the research of the dissertation: 1) Exactly significant difference exists among different integrative (statistic) models, in which, tendency (TD) integrative models have the highest power, but coefficient variability (CV) ones have the lowest; 2) There is no significant difference of the power between stepwise and enter models as well as short-term and long-term forecasting models; 3) There is significant difference among models constructed by different methods, of which, support vector machine (SVM) has the highest statistic power. This research founded basis in all facets for exploring the optimal forecasting models of social situation’s more deeply, further more, it is the first time methods of meta-analysis and power analysis were immersed into the assessments of such forecasting models.

Does prey size matter? Novel observations of feeding in the leatherback turtle (Dermochelys coriacea) allow a test of predator–prey size relationships

Optimal foraging models predict that large predators should concentrate on large prey in order to maximize their net gain of energy intake. Here, we show that the largest species of sea turtle, Dermochelys coriacea, does not strictly adhere to this general pattern. Field observations combined with a theoretical model suggest that a 300 kg leatherback turtle would meet its energetic requirements by feeding for 3–4 h a day on 4 g jellyfish, but only if prey were aggregated in high-density patches. Therefore, prey abundance rather than prey size may, in some cases, be the overriding parameter for foraging leatherbacks. This is a classic example where the presence of small prey in the diet of a large marine predator may reflect profitable foraging decisions if the relatively low energy intake per small individual prey is offset by high encounter rates and minimal capture and handling costs. This study provides, to our knowledge, the first quantitative estimates of intake rate for this species.