We present a method for reconstructing the phonon relaxation time distribution τ ω = τ (ω) (including polarization) in a material from thermal spectroscopy data. The distinguishing feature of this approach is that it does not make use of the effective thermal conductivity concept and associated approximations. The reconstruction is posed as an optimization problem in which the relaxation times τ ω = τ (ω) are determined by minimizing the discrepancy between the experimental relaxation traces and solutions of the Boltzmann transport equation (BTE) for the same problem. The latter may be analytical, in which case the procedure is very efficient, or numerical. The proposed method is illustrated using Monte Carlo solutions of thermal grating relaxation as synthetic experimental data. The reconstruction is shown to agree very well with the relaxation times used to generate the synthetic Monte Carlo data and remains robust in the presence of uncertainty (noise).

We present a method for reconstructing the phonon relaxation-time function τ ω = τ (ω) (including polarization) and associated phonon free-path distribution from thermal spectroscopy data for systems featuring interfaces with unknown properties. Our method does not rely on the effective thermal-conductivity approximation or a particular physical model of the interface behavior. The reconstruction is formulated as an optimization problem in which the relaxation times are determined as functions of frequency by minimizing the discrepancy between the experimentally measured temperature profiles and solutions of the Boltzmann transport equation for the same system. Interface properties such as transmissivities are included as unknowns in the optimization; however, because for the thermal spectroscopy problems considered here the reconstruction is not very sensitive to the interface properties, the transmissivities are only approximately reconstructed and can be considered as byproducts of the calculation whose primary objective is the accurate determination of the relaxation times. The proposed method is validated using synthetic experimental data obtained from Monte Carlo solutions of the Boltzmann transport equation. The method is shown to remain robust in the presence of uncertainty (noise) in the measurement.

Abstract-In this paper, we consider the problem of designing in-vehicle driver-assist systems that warn or override the driver to prevent collisions with a guaranteed probability. The probabilistic nature of the problem naturally arises from many sources of uncertainty, among which the behavior of the surrounding vehicles and the response of the driver to on-board warnings. We formulate this problem as a control problem for uncertain systems under probabilistic safety specifications and leverage the structure of the application domain to reach computationally efficient implementations. Simulations using a naturalistic data set show that the empirical probability of safety is always within 5% of the theoretical value in the case of direct driver override, validating our models and algorithm. In the case of on-board warnings, the empirical value is more conservative due primarily to driver's decelerating more strongly than requested. But in all cases, the empirical value is greater than or equal to the theoretical value, demonstrating a clear safety benefit.Note to Practitioners: Abstract-Statistics show that a large percentage of vehicle crash fatalities and injuries happen in the proximity of intersections and stop signs. Many automotive companies have already released automated braking systems that warn drivers and reduce speed when approaching an obstacle. A major problem with the design of such driver-assist systems is to guarantee the absence of collisions even in the presence of uncertainty. In this work we present an approach using a probabilistic model for human driving behavior. The advantage of a probabilistic model is that it allows to distinguish between possible and probable scenarios. In particular, for any desired safety level P , our method guarantees safety as long as surrounding vehicles do not use behaviors from the 1 − P probability tail of their behavior distribution. Leveraging the monotone structure of the system we obtain an efficient algorithm that can compute warnings and overrides online. Moreover, simulations on a naturalistic data set show that the resulting override is considerably less conservative than one obtained when driver behavior is modeled through bounded uncertainty. There are a number of simplifying assumption made in this work, which limit the application mainly to prevention of rear-end collisions. We plan to generalize the method in order to be able to cover more general collision scenarios.

Phonon relaxation time and free path distributions are reconstructed from experimental measurements on a two-dimensional transient thermal grating and compared with density functional theory (DFT) results for silicon. The reconstruction is performed using the inverse problem formulation of Forghani et al. [Phys. Rev. B 94, 155439 (2016)]. The discrepancies observed between reconstructed and DFT results are analyzed in terms of the ability of each set of data to reproduce the experimental temperature relaxation profiles; the reconstructed data are found to predict temperature profiles in closer agreement with the experimental data than the DFT results, possibly due to discrepancies between the actual material and the idealized model studied in the DFT calculations. The reconstructed phonon properties accurately predict temperature relaxation profiles at grating length scales smaller than those spanned by the experimental data. This is a very important feature since in a variety of experimental setups, including the one providing the data in the present study, measurements are not available at all scales spanned by the material free paths.

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