A novel scheme for human-friendly and time-delays robust neuropredictive teleoperation

A novel Neuropredictive Teleoperation (NPT) Scheme is presented. The design results from two key ideas: the exploitation of the measured or estimated neural input to the human arm or its electromyograph (EMG) as the system input and the employment of a predictor of the arm movement, based on this neural signal and an arm model, to compensate for time delays in the system. Although a multitude of such models, as well as measuring devices for the neural signals and the EMG, have been proposed, current telemanipulator research has only been considering highly simplified arm models. In the present design, the bilateral constraint that the master and slave are simultaneously compliant to each other's state (equal positions and forces) is abandoned, thus obtaining a simple to analyzesuccession of only locally controlled modules, and a robustness to time delays of up to 500 ms. The proposed designs were inspired by well established physiological evidence that the brain, rather than controlling the movement on-line, programs the arm with an action plan of a complete movement, which is then executed largely in open loop, regulated only by local reflex loops. As a model of the human arm the well-established Stark model is employed, whose mathematical representation is modified to make it suitable for an engineering application. The proposed scheme is however valid for any arm model. BIBO-stability and passivity results for a variety of local control laws are reported. Simulation results and comparisons with traditional designs also highlight the advantages of the proposed design.

Model inter-comparison between statistical and dynamic model assessments of the long-term stability of blanket peat in Great Britain (1940-2099)

We compared output from 3 dynamic process-based models (DMs: ECOSSE, MILLENNIA and the Durham Carbon Model) and 9 bioclimatic envelope models (BCEMs; including BBOG ensemble and PEATSTASH) ranging from simple threshold to semi-process-based models. Model simulations were run at 4 British peatland sites using historical climate data and climate projections under a medium (A1B) emissions scenario from the 11-RCM (regional climate model) ensemble underpinning UKCP09. The models showed that blanket peatlands are vulnerable to projected climate change; however, predictions varied between models as well as between sites. All BCEMs predicted a shift from presence to absence of a climate associated with blanket peat, where the sites with the lowest total annual precipitation were closest to the presence/absence threshold. DMs showed a more variable response. ECOSSE predicted a decline in net C sink and shift to net C source by the end of this century. The Durham Carbon Model predicted a smaller decline in the net C sink strength, but no shift to net C source. MILLENNIA predicted a slight overall increase in the net C sink. In contrast to the BCEM projections, the DMs predicted that the sites with coolest temperatures and greatest total annual precipitation showed the largest change in carbon sinks. In this model inter-comparison, the greatest variation in model output in response to climate change projections was not between the BCEMs and DMs but between the DMs themselves, because of different approaches to modelling soil organic matter pools and decomposition amongst other processes. The difference in the sign of the response has major implications for future climate feedbacks, climate policy and peatland management. Enhanced data collection, in particular monitoring peatland response to current change, would significantly improve model development and projections of future change.

A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.

Comments on “An ensemble cumulus convection parameterization with explicit cloud treatment”

Wagner and Graf (2010) derive a population evolution equation for an ensemble of convective plumes, an analogue with the Lotka–Volterra equation, from the energy equations for convective plumes provided by Arakawa and Schubert (1974). Although their proposal is interesting, as the present note shows, there are some problems with their derivation.

Environmental factors influencing the inactivation of Cronobacter sakazakii by high hydrostatic pressure

The effect of High Hydrostatic Pressure (HHP) on the survival of Cronobacter sakazakii was investigated. Deviations from linearity were found on the survival curves and the Mafart equation accurately described the kinetics of inactivation. Comparisons between strains and treatments were made based on the time needed for a 5-log10 reduction in viable count. The ability of C. sakazakii to tolerate high pressure was straindependent with a 26-fold difference in resistance among four strains tested. Pressure resistance was greatest in the stationary growth phase and at the highest growth temperatures tested (30 and 37 °C). Cells treated in neutral pH buffer were 5-fold more resistant than those treated at pH 4.0, and 8-fold more sensitive than those treated in buffer with sucrose added (aw=0.98). Pressure resistance data obtained in buffer at the appropriate pH adequately estimated the resistance of C. sakazakii in chicken and vegetables soups. In contrast, a significant protective effect against high pressure was conferred by rehydrated powdered milk. As expected, treatment efficacy improved as pressure increased. z values of 112, 136 and 156 MPa were obtained for pH 4.0, pH 7.0 and aw=0.98 buffers, respectively. Cells with sublethal injury to their outer and cytoplasmic membranes were detected after HHP under all the conditions tested. The lower resistance of C. sakazakii cells when treated in media of pH 4.0 seemed to be due to a decreased barostability of the bacterial envelopes. Conversely, the higher resistance displayed in media of reduced water activity may relate to a higher stability of bacterial envelopes.

Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Stability results for the time-harmonic Maxwell equations with impedance boundary conditions

We consider the time-harmonic Maxwell equations with constant coefficients in a bounded, uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak solutions. This result is pivotal for convergence proofs in numerical analysis and may be a tool in the analysis of electromagnetic boundary integral operators.

The effects of explicit versus parameterized convection on the MJO in a large-domain high-resolution tropical case study. Part I: Characterization of large-scale organization and propagation

High-resolution simulations over a large tropical domain (∼20◦S–20◦N and 42◦E–180◦E) using both explicit and parameterized convection are analyzed and compared to observations during a 10-day case study of an active Madden-Julian Oscillation (MJO) event. The parameterized convection model simulations at both 40 km and 12 km grid spacing have a very weak MJO signal and little eastward propagation. A 4 km explicit convection simulation using Smagorinsky subgrid mixing in the vertical and horizontal dimensions exhibits the best MJO strength and propagation speed. 12 km explicit convection simulations also perform much better than the 12 km parameterized convection run, suggesting that the convection scheme, rather than horizontal resolution, is key for these MJO simulations. Interestingly, a 4 km explicit convection simulation using the conventional boundary layer scheme for vertical subgrid mixing (but still using Smagorinsky horizontal mixing) completely loses the large-scale MJO organization, showing that relatively high resolution with explicit convection does not guarantee a good MJO simulation. Models with a good MJO representation have a more realistic relationship between lower-free-tropospheric moisture and precipitation, supporting the idea that moisture-convection feedback is a key process for MJO propagation. There is also increased generation of available potential energy and conversion of that energy into kinetic energy in models with a more realistic MJO, which is related to larger zonal variance in convective heating and vertical velocity, larger zonal temperature variance around 200 hPa, and larger correlations between temperature and ascent (and between temperature and diabatic heating) between 500–400 hPa.

The long-term stability of a possible aqueous ammonium sulfate ocean inside Titan

We model the thermal evolution of a subsurface ocean of aqueous ammonium sulfate inside Titan using a parameterized convection scheme. The cooling and crystallization of such an ocean depends on its heat flux balance, and is governed by the pressure-dependent melting temperatures at the top and bottom of the ocean. Using recent observations and previous experimental data, we present a nominal model which predicts the thickness of the ocean throughout the evolution of Titan; after 4.5 Ga we expect an aqueous ammonium sulfate ocean 56 km thick, overlain by a thick (176 km) heterogeneous crust of methane clathrate, ice I and ammonium sulfate. Underplating of the crust by ice I will give rise to compositional diapirs that are capable of rising through the crust and providing a mechanism for cryovolcanism at the surface. We have conducted a parameter space survey to account for possible variations in the nominal model, and find that for a wide range of plausible conditions, an ocean of aqueous ammonium sulfate can survive to the present day, which is consistent with the recent observations of Titan's spin state from Cassini radar data [Lorenz, R.D., Stiles, B.W., Kirk, R.L., Allison, M.D., del Marmo, P.P., Iess, L., Lunine, J.I., Ostro, S.J., Hensley, S., 2008. Science 319, 1649–1651].

Some numerical experiments on the effect of the variation of static stability in two-layer quasi-geostrophic models

A method to solve a quasi-geostrophic two-layer model including the variation of static stability is presented. The divergent part of the wind is incorporated by means of an iterative procedure. The procedure is rather fast and the time of computation is only 60–70% longer than for the usual two-layer model. The method of solution is justified by the conservation of the difference between the gross static stability and the kinetic energy. To eliminate the side-boundary conditions the experiments have been performed on a zonal channel model. The investigation falls mainly into three parts: The first part (section 5) contains a discussion of the significance of some physically inconsistent approximations. It is shown that physical inconsistencies are rather serious and for these inconsistent models which were studied the total kinetic energy increased faster than the gross static stability. In the next part (section 6) we are studying the effect of a Jacobian difference operator which conserves the total kinetic energy. The use of this operator in two-layer models will give a slight improvement but probably does not have any practical use in short periodic forecasts. It is also shown that the energy-conservative operator will change the wave-speed in an erroneous way if the wave-number or the grid-length is large in the meridional direction. In the final part (section 7) we investigate the behaviour of baroclinic waves for some different initial states and for two energy-consistent models, one with constant and one with variable static stability. According to the linear theory the waves adjust rather rapidly in such a way that the temperature wave will lag behind the pressure wave independent of the initial configuration. Thus, both models give rise to a baroclinic development even if the initial state is quasi-barotropic. The effect of the variation of static stability is very small, qualitative differences in the development are only observed during the first 12 hours. For an amplifying wave we will get a stabilization over the troughs and an instabilization over the ridges.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part I: gravity wave forcing

Parameterization schemes for the drag due to atmospheric gravity waves are discussed and compared in the context of a simple one-dimensional model of the quasi-biennial oscillation (QBO). A number of fundamental issues are examined in detail, with the goal of providing a better understanding of the mechanism by which gravity wave drag can produce an equatorial zonal wind oscillation. The gravity wave–driven QBOs are compared with those obtained from a parameterization of equatorial planetary waves. In all gravity wave cases, it is seen that the inclusion of vertical diffusion is crucial for the descent of the shear zones and the development of the QBO. An important difference between the schemes for the two types of waves is that in the case of equatorial planetary waves, vertical diffusion is needed only at the lowest levels, while for the gravity wave drag schemes it must be included at all levels. The question of whether there is downward propagation of influence in the simulated QBOs is addressed. In the gravity wave drag schemes, the evolution of the wind at a given level depends on the wind above, as well as on the wind below. This is in contrast to the parameterization for the equatorial planetary waves in which there is downward propagation of phase only. The stability of a zero-wind initial state is examined, and it is determined that a small perturbation to such a state will amplify with time to the extent that a zonal wind oscillation is permitted.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

Nonlinear stability of continuously stratified quasi-geostrophic flow

Nonlinear stability theorems analogous to Arnol'd's second stability theorem are established for continuously stratified quasi-geostrophic flow with general nonlinear boundary conditions in a vertically and horizontally confined domain. Both the standard quasi-geostrophic model and the modified quasi-geostrophic model (incorporating effects of hydrostatic compressibility) are treated. The results establish explicit upper bounds on the disturbance energy, the disturbance potential enstrophy, and the disturbance available potential energy on the horizontal boundaries, in terms of the initial disturbance fields. Nonlinear stability in the sense of Liapunov is also established.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 2. pseudoenergy-based theory

This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of disturbances to prescribed basic states, to SG dynamics. Part 1 was based on the pseudomomentum; Part 2 is based on the pseudoenergy. A pseudoenergy invariant is a conserved quantity, of second order in disturbance amplitude relative to a prescribed steady basic state, which is related to the time symmetry of the system. We derive such an invariant for the semi-geostrophic equations, and use it to obtain: (i) a linear stability theorem analogous to Arnol'd's ‘first theorem’; and (ii) a small-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. The results are derived for both the f-plane Boussinesq form of semi-geostrophic dynamics, and its extension to β-plane compressible flow by Magnusdottir & Schubert. Novel features particular to semi-geostrophic dynamics include apparently unnoticed lateral boundary stability criteria. Unlike the boundary stability criteria found in the first part of this study, however, these boundary criteria do not necessarily preclude the construction of provably stable basic states. The interior semi-geostrophic dynamics has an underlying Hamiltonian structure, which guarantees that symmetries in the system correspond naturally to the system's invariants. This is an important motivation for the theoretical approach used in this study. The connection between symmetries and conservation laws is made explicit using Noether's theorem applied to the Eulerian form of the Hamiltonian description of the interior dynamics.