Efficiency at optimal work from finite reservoirs: a probabilistic perspective

We revisit the classic thermodynamic problem of maximum work extraction from two arbitrary sized hot and cold reservoirs, modelled as perfect gases. Assuming ignorance about the extent to which the process has advanced, which implies an ignorance about the final temperatures, we quantify the prior information about the process and assign a prior distribution to the unknown temperature(s). This requires that we also take into account the temperature values which are regarded to be unphysical in the standard theory, as they lead to a contradiction with the physical laws. Instead in our formulation, such values appear to be consistent with the given prior information and hence are included in the inference. We derive estimates of the efficiency at optimal work from the expected values of the final temperatures, and show that these values match with the exact expressions in the limit when any one of the reservoirs is very large compared to the other. For other relative sizes of the reservoirs, we suggest a weighting procedure over the estimates from two valid inference procedures, that generalizes the procedure suggested earlier in [J. Phys. A: Math. Theor. {\bf 46}, 365002 (2013)]. Thus a mean estimate for efficiency is obtained which agrees with the optimal performance to a high accuracy.Comment: 14 pages, 6 figure

Identification and stochastic control of helicopter dynamic modes

A general treatment of parameter identification and stochastic control for use on helicopter dynamic systems is presented. Rotor dynamic models, including specific applications to rotor blade flapping and the helicopter ground resonance problem are emphasized. Dynamic systems which are governed by periodic coefficients as well as constant coefficient models are addressed. The dynamic systems are modeled by linear state variable equations which are used in the identification and stochastic control formulation. The pure identification problem as well as the stochastic control problem which includes combined identification and control for dynamic systems is addressed. The stochastic control problem includes the effect of parameter uncertainty on the solution and the concept of learning and how this is affected by the control's duel effect. The identification formulation requires algorithms suitable for on line use and thus recursive identification algorithms are considered. The applications presented use the recursive extended kalman filter for parameter identification which has excellent convergence for systems without process noise

Tracking the Tracker from its Passive Sonar ML-PDA Estimates

Target motion analysis with wideband passive sonar has received much attention. Maximum likelihood probabilistic data-association (ML-PDA) represents an asymptotically efficient estimator for deterministic target motion, and is especially well-suited for low-observable targets; the results presented here apply to situations with higher signal to noise ratio as well, including of course the situation of a deterministic target observed via clean measurements without false alarms or missed detections. Here we study the inverse problem, namely, how to identify the observing platform (following a two-leg motion model) from the results of the target estimation process, i.e. the estimated target state and the Fisher information matrix, quantities we assume an eavesdropper might intercept. We tackle the problem and we present observability properties, with supporting simulation results.Comment: To appear in IEEE Transactions on Aerospace and Electronic System

Property (T)(T) for noncommutative universal lattices

We establish a new spectral criterion for Kazhdan's property $(T)$ which is applicable to a large class of discrete groups defined by generators and relations. As the main application, we prove property $(T)$ for the groups $EL_n(R)$, where $n\geq 3$ and $R$ is an arbitrary finitely generated associative ring. We also strengthen some of the results on property $(T)$ for Kac-Moody groups from a paper of Dymara and Januszkiewicz (Invent. Math 150 (2002)).Comment: 47 pages; final versio

Evaluation of the effect of vibration nonlinearity on convergence behavior of adaptive higher harmonic controllers

Effect of nonlinearity on convergence of the local linear and global linear adaptive controllers is evaluated. A nonlinear helicopter vibration model is selected for the evaluation which has sufficient nonlinearity, including multiple minimum, to assess the vibration reduction capability of the adaptive controllers. The adaptive control algorithms are based upon a linear transfer matrix assumption and the presence of nonlinearity has a significant effect on algorithm behavior. Simulation results are presented which demonstrate the importance of the caution property in the global linear controller. Caution is represented by a time varying rate weighting term in the local linear controller and this improves the algorithm convergence. Nonlinearity in some cases causes Kalman filter divergence. Two forms of the Kalman filter covariance equation are investigated

An investigation of adaptive controllers for helicopter vibration and the development of a new dual controller

An investigation of the properties important for the design of stochastic adaptive controllers for the higher harmonic control of helicopter vibration is presented. Three different model types are considered for the transfer relationship between the helicopter higher harmonic control input and the vibration output: (1) nonlinear; (2) linear with slow time varying coefficients; and (3) linear with constant coefficients. The stochastic controller formulations and solutions are presented for a dual, cautious, and deterministic controller for both linear and nonlinear transfer models. Extensive simulations are performed with the various models and controllers. It is shown that the cautious adaptive controller can sometimes result in unacceptable vibration control. A new second order dual controller is developed which is shown to modify the cautious adaptive controller by adding numerator and denominator correction terms to the cautious control algorithm. The new dual controller is simulated on a simple single-control vibration example and is found to achieve excellent vibration reduction and significantly improves upon the cautious controller

A Configurationally-Resolved-Super-Transition-Arrays method for calculation of the spectral absorption coefficient in hot plasmas

A new method, 'Configurationally-Resolved-Super-Transition-Arrays', for calculation of the spectral absorption coefficient in hot plasmas is presented. In the new method, the spectrum of each Super-Transition-Array is evaluated as the Fourier transform of a single Complex Pseudo Partition Function, which represents the exact analytical sum of the contributions of all constituting unresolved transition arrays sharing the same set of one-electron solutions. Thus, in the new method, the spectrum of each Super-Transition-Array is resolved down to the level of the (unresolved) transition arrays. It is shown that the corresponding spectrum, evaluated by the traditional Super-Transition-Arrays (STA) method [A. Bar Shalom, J. Oreg, W.H. Goldstein, D. Shvarts and A. Zigler, Phys. Rev. A 40, 3183 (1989)], is just the coarse grained Gaussian approximation of the Configurationally-Resolved-Super-Transition-Array. A new computer program is presented, capable of evaluating the absorption coefficient by both the new configurationally resolved and the traditional Gaussian Super-Transition-Arrays methods. A numerical example of gold at temperature 1keV and density 0.5 gr/cm^{3}, is presented, demonstrating the simplicity, efficiency and accuracy of the new method

Tuning spin-orbit coupling and superconductivity at the SrTiO3/LaAlO3 interface: a magneto-transport study

The superconducting transition temperature, Tc, of the SrTiO3/LaAlO3 interface was varied by the electric field effect. The anisotropy of the upper critical field and the normal state magneto-transport were studied as a function of gate voltage. The spin-orbit coupling energy is extracted. This tunable energy scale is used to explain the strong gate dependence of the mobility and of the anomalous Hall signal observed. The spin-orbit coupling energy follows Tc for the electric field range under study

Shubnikov-de Haas oscillations in SrTiO3\LaAlO3 interface

Quantum magnetic oscillations in SrTiO3/\LaAlO3 interface are observed. The evolution of their frequency and amplitude at various gate voltages and temperatures is studied. The data are consistent with the Shubnikov de-Haas theory. The Hall resistivity rho exhibits nonlinearity at low magnetic field. It is fitted assuming multiple carrier contributions. The comparison between the mobile carrier density inferred from the Hall data and the oscillation frequency suggests multiple valley and spin degeneracy. The small amplitude of the oscillations is discussed in the framework of the multiple band scenario