Nonparametric identification of linearizations and uncertainty using Gaussian process models – application to robust wheel slip control

Gaussian process prior models offer a nonparametric approach to modelling unknown nonlinear systems from experimental data. These are flexible models which automatically adapt their model complexity to the available data, and which give not only mean predictions but also the variance of these predictions. A further advantage is the analytical derivation of derivatives of the model with respect to inputs, with their variance, providing a direct estimate of the locally linearized model with its corresponding parameter variance. We show how this can be used to tune a controller based on the linearized models, taking into account their uncertainty. The approach is applied to a simulated wheel slip control task illustrating controller development based on a nonparametric model of the unknown friction nonlinearity. Local stability and robustness of the controllers are tuned based on the uncertainty of the nonlinear models’ derivatives

Coherent adiabatic theory of two-electron quantum dot molecules in external spin baths

We derive an accurate molecular orbital based expression for the coherent time evolution of a two-electron wave function in a quantum dot molecule where the electrons interact with each other, with external time dependent electromagnetic fields and with a surrounding nuclear spin reservoir. The theory allows for direct numerical modeling of the decoherence in quantum dots due to hyperfine interactions. Calculations result in good agreement with recent singlet-triplet dephasing experiments by Laird et. al. [Phys. Rev. Lett. 97, 056801 (2006)], as well as analytical model calculations. Furthermore, it is shown that using a much faster electric switch than applied in these experiments will transfer the initial state to excited states where the hyperfine singlet-triplet mixing is negligible.Comment: 4 pages, 3 figure

Crystallization and phase-separation in non-additive binary hard-sphere mixtures

We calculate for the first time the full phase-diagram of an asymmetric non-additive hard-sphere mixture. The non-additivity strongly affects the crystallization and the fluid-fluid phase-separation. The global topology of the phase-diagram is controlled by an effective size-ratio y_{eff}, while the fluid-solid coexistence scales with the depth of the effective potential well.Comment: 4 pages, 4 figures, to appear in Phys. Rev.

Electronic magnification for astronomical camera tubes

Definitions, test schemes, and analyses used to provide variable magnification in the image section of the television sensor for large space telescopes are outlined. Experimental results show a definite form of magnetic field distribution is necessary to achieve magnification in the range 3X to 4X. Coil systems to establish the required field shapes were built, and both image intensifiers and camera tubes were operated at high magnification. The experiments confirm that such operation is practical and can provide satisfactory image quality. The main problem with such a system was identified as heating of the photocathode due to concentration of coil power dissipation in that vicinity. Suggestions for overcoming this disadvantage are included

The structure of colloid-polymer mixtures

We investigate the structure of colloid-polymer mixtures by calculating the structure factors for the Asakura-Oosawa model in the PY approximation. We discuss the role of potential range, polymer concentration and polymer-polymer interactions on the colloid-colloid structure. Our results compare reasonably well with the recent experiments of Moussa\"{i}d et. al. for small wavenumber $k$, but we find that the Hansen-Verlet freezing criterion is violated when the liquid phase becomes marginal.Comment: 7 pages, 4 figures, to appear in EuroPhys. Let

Relationship between Local Molecular Field Theory and Density Functional Theory for non-uniform liquids

The Local Molecular Field Theory (LMF) developed by Weeks and co-workers has proved successful for treating the structure and thermodynamics of a variety of non-uniform liquids. By reformulating LMF in terms of one-body direct correlation functions we recast the theory in the framework of classical Density Functional Theory (DFT). We show that the general LMF equation for the effective reference potential phi_R follows directly from the standard mean-field DFT treatment of attractive interatomic forces. Using an accurate (Fundamental Measures) DFT for the non-uniform hard-sphere reference fluid we determine phi_R for a hard-core Yukawa liquid adsorbed at a planar hard wall. In the approach to bulk liquid-gas coexistence we find the effective potentials exhibit rich structure that can include damped oscillations at large distances from the wall as well as the repulsive hump near the wall required to generate the low density 'gas' layer characteristic of complete drying. We argue that it would be difficult to obtain the same level of detail from other (non DFT based) implementations of LMF. LMF emphasizes the importance of making an intelligent division of the interatomic pair potential of the full system into a reference part and a remainder that can be treated in mean-field approximation. We investigate different divisions for an exactly solvable one- dimensional model where the pair potential has a hard-core plus a linear attractive tail. Results for the structure factor and the equation of state of the uniform fluid show that including a significant portion of the attraction in the reference system can be much more accurate than treating the full attractive tail in mean-field approximation. We discuss further aspects of the relationship between LMF and DFT.Comment: 35 pages, 10 Fig

Viscoelasticity of 2D liquids quantified in a dusty plasma experiment

The viscoelasticity of two-dimensional liquids is quantified in an experiment using a dusty plasma. An experimental method is demonstrated for measuring the wavenumber-dependent viscosity, $\eta(k)$, which is a quantitative indicator of viscoelasticity. Using an expression generalized here to include friction, $\eta(k)$ is computed from the transverse current autocorrelation function (TCAF), which is found by tracking random particle motion. The TCAF exhibits an oscillation that is a signature of elastic contributions to viscoelasticity. Simulations of a Yukawa liquid are consistent with the experiment.Comment: 5 pages text, 3 figures, 1 supplementary material, in press Physical Review Letters 201

Simple relationship between the virial-route hypernetted-chain and the compressibility-route Percus--Yevick values of the fourth virial coefficient

As is well known, approximate integral equations for liquids, such as the hypernetted chain (HNC) and Percus--Yevick (PY) theories, are in general thermodynamically inconsistent in the sense that the macroscopic properties obtained from the spatial correlation functions depend on the route followed. In particular, the values of the fourth virial coefficient $B_4$ predicted by the HNC and PY approximations via the virial route differ from those obtained via the compressibility route. Despite this, it is shown in this paper that the value of $B_4$ obtained from the virial route in the HNC theory is exactly three halves the value obtained from the compressibility route in the PY theory, irrespective of the interaction potential (whether isotropic or not), the number of components, and the dimensionality of the system. This simple relationship is confirmed in one-component systems by analytical results for the one-dimensional penetrable-square-well model and the three-dimensional penetrable-sphere model, as well as by numerical results for the one-dimensional Lennard--Jones model, the one-dimensional Gaussian core model, and the three-dimensional square-well model.Comment: 8 pages; 4 figures; v2: slight change of title; proof extended to multicomponent fluid