Comments about the paper entitled ``A generalized boundary integral equation for isotropic heat conduction with spatially varying thermal conductivity'' by A.J. Kassab and E. Divo.

An integral formulation for heat conduction problems in non-homogeneous media has recently been proposed by Kassab and Divo [Engineering Analysis with Boundary Elements 1996;18:273]. The goal of this communication is to revisit and clarify two key features of the formulation of Kassab and Divo. First, the contention that the integral equation formulation proposed by them does not possess the desired boundary-only character is made and substantiated; it is shown in particular that Eq. 10 therein does not hold owing to the fact that a crucial requirement for the fundamental solution, Eqs. (5c) and (5d) therein, is actually not met. Second, the limiting process associated with a vanishing neighbourhood in connection with the particular kernel function used therein is revisited

On the Identification of Machine Settings for Gear Surface Topography Corrections

In this paper we set out to investigate the performances of some algorithms proposed in the gear literature for identifying the machine-tool settings required to obtain predesigned gear tooth surface topographies, or needed to compensate for flank form deviations of real teeth. For ease of comparison, the problem is formulated as a nonlinear least squares problem, and the most widely employed algorithms are derived as special cases. The algorithms included in the analysis are: (i) one-step methods, (ii) iterative methods, (iii) iterative methods with step control. The performance index is devised in their ability of returning practical solutions in the presence of: (i) strong model nonlinearities, (ii) ill-conditioning of the sensitivity matrix, (iii) demanding topographic shapes. Instrumental here is an original classification of topographic modifications as either “simple” or “complex”, based on the SVD analysis of the sensitivity matrix. Some selected numerical examples demonstrate that iterative techniques with step control are the most convenient in terms of reliability and robustness of the obtained solutions. The generation process considered here is face-milling of hypoid gears, although the methodology is general enough to cope with any gear cutting/grinding method

Fixed-point implementation of a proximal Newton method for embedded model predictive control (I)

Extending the success of model predictive control (MPC) technologies in embedded applications heavily depends on the capability of improving quadratic programming (QP) solvers. Improvements can be done in two directions: better algorithms that reduce the number of arithmetic operations required to compute a solution, and more efficient architectures in terms of speed, power consumption, memory occupancy and cost. This paper proposes a fixed point implementation of a proximal Newton method to solve optimization problems arising in input-constrained MPC. The main advantages of the algorithm are its fast asymptotic convergence rate and its relatively low computational cost per iteration since it the solution of a small linear system is required. A detailed analysis on the effects of quantization errors is presented, showing the robustness of the algorithm with respect to finite-precision computations. A hardware implementation with specific optimizations to minimize computation times and memory footprint is also described, demonstrating the viability of low-cost, low-power controllers for high-bandwidth MPC applications. The algorithm is shown to be very effective for embedded MPC applications through a number of simulation experiments

Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars

This paper presents an adaptive high performance control method for autonomous miniature race cars. Racing dynamics are notoriously hard to model from first principles, which is addressed by means of a cautious nonlinear model predictive control (NMPC) approach that learns to improve its dynamics model from data and safely increases racing performance. The approach makes use of a Gaussian Process (GP) and takes residual model uncertainty into account through a chance constrained formulation. We present a sparse GP approximation with dynamically adjusting inducing inputs, enabling a real-time implementable controller. The formulation is demonstrated in simulations, which show significant improvement with respect to both lap time and constraint satisfaction compared to an NMPC without model learning

Collision Integrals for Cosmological Phase Transitions

The dynamics of the true-vacuum bubbles nucleated during a first-order phase transition is affected by the distribution functions of the particle species in the plasma, driven out-of-equilibrium by the travelling domain wall. An accurate modelling of this phenomenon is relevant for a quantitative description of phase transitions in the early universe and for the determination of the corresponding cosmic relics, such as, among the others, the stochastic background of gravitational waves. We address this problem by developing a new spectral method devised for a fast and reliable computation of the collision integral in the Boltzmann equations. In a scalar singlet extension of the Standard Model chosen as a benchmark scenario, we test our algorithm, determining the bubble speed and profile, and we asses the impact of the out-of-equilibrium dynamics.Comment: 18 pages, 3 figure

Towards T.R.I.C.K. 2.0 – A tool for the evaluation of the vehicle performance through the use of an advanced sensors system

In the last years, the tire technological development has played a fundamental role in motorsport and in automotive industry. The tire contact patch forces have a great influence on the vehicle behavior, so their correct estimation is a crucial task to understand how to improve the car performance. In order to identify the tire interaction characteristic, it is also necessary to use a procedure that allows the correct evaluation of the slip angles in the different operating conditions. This paper presents an evolution of the T.R.I.C.K. tool developed by the UniNa vehicle dynamics research group. In the first version of this tool an 8 degree of freedom vehicle model has been implemented and, starting from the experimental data acquired, the T.R.I.C.K. calculates the interaction forces and the tire slips using the equilibrium equations. Using more car parameters and further data obtained from track sessions and dedicated tests, in the presented release of the tool, new formulations have been developed for a more accurate calculation of the tire-road forces. The effectiveness of the treatments is assessed using experimental data and the simulator outputs. The new formulations introduced in this paper allows, depending on the availability of additional vehicle data and acquisition sensors, to estimate the interaction forces with different and more accurate methodologies than the equilibrium equations, while retaining very reduced simulation times. In this way it is possible to carry out a more precise study of vehicle dynamics with the possibility of investigating and significantly improving performance

Long-range and long-term interferometric tracking by static and dynamic force-clamp optical tweezers.

Optical tweezers are recognized single-molecule technique to resolve forces and motion on the molecular scale. Complex biological phenomena, such as cell differentiation and locomotion, require long range tracking capabilities with nanometer resolution over an extended period, to resolve molecular processes on the cellular scale. Here we introduce a real-time control of the microscope stage position to perform long-term tracking, with sub-millisecond resolution, of a bead attached to a neuron, preserving sub-nanometer sensitivity on a spatial range of centimeters, seven orders of magnitude larger. Moreover, the suitability of the system is tested by time- modulating the force-clamp condition to study the role of statically and dynamically applied forces in neuronal differentiation