Growth dynamics of a Bose-Einstein condensate in a dimple trap without cooling

We study the formation of a Bose-Einstein condensate in a cigar-shaped three-dimensional harmonic trap, induced by the controlled addition of an attractive "dimple" potential along the weak axis. In this manner we are able to induce condensation without cooling due to a localized increase in the phase space density. We perform a quantitative analysis of the thermodynamic transformation in both the sudden and adiabatic regimes for a range of dimple widths and depths. We find good agreement with equilibrium calculations based on self-consistent semiclassical Hartree-Fock theory describing the condensate and thermal cloud. We observe there is an optimal dimple depth that results in a maximum in the condensate fraction. We also study the non-equilibrium dynamics of condensate formation in the sudden turn-on regime, finding good agreement for the observed time dependence of the condensate fraction with calculations based on quantum kinetic theory.Comment: v1: 9 pages, 7 figures, submitted to Phys. Rev. A; v2: 10 pages, 8 figures, fixed typos, added references, additional details on experimental procedure, values of phase-space density, new figure and discussion on effects of three-body loss in Appendix B (replaced with published version

Spikes from compound action potentials in simulated microelectrode recordings

In this paper we demonstrate by simulation, that the spike features apparent in low-impedance deep brain stimulation (DBS) targeting microelectrode recordings (MER) may not reflect the action potentials of individual neurons. Rather, they are more likely to be compound action potentials from a synchronized group of neurons local to the electrode. Initially we simulate the MER by combining the electric fields from a large number of independent neurons surrounding the microelectrode tip. When synchronization is introduced amongst neurons the resulting discernible spikes in an MER are far more likely to relate to compound action potentials from subsets of synchronized neurons than individual action potentials. Different sub-sets of neurons are then synchronized to see how well a conventional spike sorting algorithm can differentiate the compound action potentials from different groups of neurons. These simulations offer insight into the clinical interpretation of DBS MERs used to target deep brain structures.</p

Analysis of the non-Markov parameter in continuous-time signal processing

The use of statistical complexity metrics has yielded a number of successful methodologies to differentiate and identify signals from complex systems where the underlying dynamics cannot be calculated. The Mori-Zwanzig framework from statistical mechanics forms the basis for the generalized non-Markov parameter (NMP). The NMP has been used to successfully analyze signals in a diverse set of complex systems. In this paper we show that the Mori-Zwanzig framework masks an elegantly simple closed form of the first NMP, which, for C1 smooth autocorrelation functions, is solely a function of the second moment (spread) and amplitude envelope of the measured power spectrum. We then show that the higher-order NMPs can be constructed in closed form in a modular fashion from the lower-order NMPs. These results provide an alternative, signal processing-based perspective to analyze the NMP, which does not require an understanding of the Mori-Zwanzig generating equations. We analyze the parametric sensitivity of the zero-frequency value of the first NMP, which has been used as a metric to discriminate between states in complex systems. Specifically, we develop closed-form expressions for three instructive systems: band-limited white noise, the output of white noise input to an idealized all-pole filter,f and a simple harmonic oscillator driven by white noise. Analysis of these systems shows a primary sensitivity to the decay rate of the tail of the power spectrum. © 2014 American Physical Society

3D surface representation and trajectory optimization with a learning-based adaptive model predictive controller in incremental forming

In this work, a novel learning-based on-line adaptive shape predictive model is developed to represent the 3D surface of the formed shape after springback in single point incremental forming (SPIF). The model can be updated in each step to predict the forming shapes in future prediction horizons given a new potential tool path, with on-line collected historic geometrical data and their corresponding tool path in previous steps. Furthermore, this model is incorporated into a sequential coupled constrained model predictive control algorithm (MPC), to optimize the potential step-down and step-over sizes in future steps, to minimize the geometric error of the whole formed part in SPIF. Two different geometric shapes, a benchmark truncated cone (with only convex geometric feature) and a non-convex dog-bone (with varying convex and concave feature), are selected for the experimental testing of the new developed on-line adaptive model predictive control algorithm (AMPC). This paper presents the detailed data acquisition and modelling process, on-line feedback control algorithms and experimental validation. The experimental results indicated that the maximum geometric error in the concerned region for the benchmark truncated cone shape and the complex non-convex dog-bone shape can be successfully decreased from above 1.25 mm without control to below 0.75 mm with the current adaptive MPC controller, which cannot be achieved with our previous non-adaptive MPC controller. This is believed to be the first attempt to incorporate a learning-based nonlinear adaptive predictive model with a model predictive controller for tool path optimization in incremental forming. The adaptive model predictive controller (AMPC) demonstrated in this work may provide a powerful tool for geometric accuracy improvement for production of complex geometric shapes in varying forming conditions in incremental sheet forming in the future

A model predictive path control algorithm of single-point incremental forming for non-convex shapes

The geometrical error of the formed part is one of the most significant limitations that restricts the widespread application of incremental sheet forming (ISF) in aerospace industry. The geometry of ISF parts is dependent upon the tool path, so its correction can improve the part precision. Previous research has utilized model predictive control approach to achieve this, but the method was restricted to simple convex shapes. In this study, the tool path and the formed shape were parameterized and the analytical models of geometry responses relative to tool perturbations were proposed. Then, a model predictive control algorithm was developed, aiming at reducing the geometrical errors of the parts with complex non-convex shapes in the ISF process. Experimental validation of the developed control algorithm was carried out by forming a complex shape by single-point incremental forming. The results show that the developed control algorithm greatly reduced the geometrical error in the closed-loop process

A parametric simulation of neuronal noise from microelectrode recordings

In this paper we present an efficient model of microelectrode recordings (MER) from the subthalamic nucleus acquired during deep brain stimulation (DBS) surgery. The model shows how changes in the 'noise' relate to the neuronal spike time statistics. A top-down approach is used with analysis-by-synthesis of the MER power spectra. The model is built around a sum of filtered point processes consisting of thousands of neurons and including extracellular filtering. The quality of the model is demonstrated through comparisons to recordings from eight individuals (both hemispheres in six) who have undergone DBS implantation for the treatment of Parkinson's disease. The simulated recordings were compared using their voltage amplitude distributions, power spectral density estimates and phase synchrony while varying only one free parameter (the shape of the inter-spike interval distribution). Through this simple model, we show that the noise present in a DBS MER contains properties that match that of patient recordings when a Weibull distribution with shape parameter of 0.8 is used for the inter-spike interval