Mixmaster Chaoticity as Semiclassical Limit of the Canonical Quantum Dynamics

Within a cosmological framework, we provide a Hamiltonian analysis of the Mixmaster Universe dynamics on the base of a standard Arnowitt-Deser-Misner approach, showing how the chaotic behavior characterizing the evolution of the system near the cosmological singularity can be obtained as the semiclassical limit of the canonical quantization of the model in the same dynamical representation. The relation between this intrinsic chaotic behavior and the indeterministic quantum dynamics is inferred through the coincidence between the microcanonical probability distribution and the semiclassical quantum one.Comment: 9 pages, 1 figur

Branching Interfaces with Infinitely Strong Couplings

A hierarchical froth model of the interface of a random $q$-state Potts ferromagnet in $2D$ is studied by recursive methods. A fraction $p$ of the nearest neighbour bonds is made inaccessible to domain walls by infinitely strong ferromagnetic couplings. Energetic and geometric scaling properties of the interface are controlled by zero temperature fixed distributions. For $p<p_c$, the directed percolation threshold, the interface behaves as for $p=0$, and scaling supports random Ising ($q=2$) critical behavior for all $q$'s. At $p=p_c$ three regimes are obtained for different ratios of ferro vs. antiferromagnetic couplings. With rates above a threshold value the interface is linear ( fractal dimension $d_f=1$) and its energy fluctuations, $\Delta E$ scale with length as $\Delta E\propto L^{\omega}$, with $\omega\simeq 0.48$. When the threshold is reached the interface branches at all scales and is fractal ($d_f\simeq 1.046$) with $\omega_c \simeq 0.51$. Thus, at $p_c$, dilution modifies both low temperature interfacial properties and critical scaling. Below threshold the interface becomes a probe of the backbone geometry (\df\simeq{\bar d}\simeq 1.305; $\bar d$ = backbone fractal dimension ), which even controls energy fluctuations ($\omega\simeq d_f\simeq\bar d$). Numerical determinations of directed percolation exponents on diamond hierarchical lattice are also presented.Comment: 16 pages, 3 Postscript figure

Exponential self-similar mixing and loss of regularity for continuity equations

We consider the mixing behaviour of the solutions of the continuity equation associated with a divergence-free velocity field. In this announcement we sketch two explicit examples of exponential decay of the mixing scale of the solution, in case of Sobolev velocity fields, thus showing the optimality of known lower bounds. We also describe how to use such examples to construct solutions to the continuity equation with Sobolev but non-Lipschitz velocity field exhibiting instantaneous loss of any fractional Sobolev regularity.Comment: 8 pages, 3 figures, statement of Theorem 11 slightly revise

Optimal welfare-to-work programs

A Welfare-to-Work (WTW) program is a mix of government expenditures on “passive” (unemployment insurance, social assistance) and “active” (job search monitoring, training, wage taxes/subsidies) labor market policies targeted to the unemployed. This paper provides a dynamic principal-agent framework suitable for analyzing the optimal sequence and duration of the different WTW policies, and the dynamic pattern of payments along the unemployment spell and of taxes/subsidies upon re-employment. First, we show that the optimal program endogenously generates an absorbing policy of last resort (that we call “social assistance”) characterized by a constant lifetime payment and no active participation by the agent. Second, human capital depreciation is a necessary condition for policy transitions to be part of an optimal WTW program. Whenever training is not optimally provided, we show that the typical sequence of policies is quite simple: the program starts with standard unemployment insurance, then switches into monitored search and, finally, into social assistance. Only the presence of an optimal training activity may generate richer transition patterns. Third, the optimal benefits are generally decreasing or constant during unemployment, but they must increase after a successful spell of training. In a calibration exercise based on the U.S. labor market and on the evidence from several evaluation studies, we use our model to analyze quantitatively the features of the optimal WTW program for the U.S. economy. With respect to the existing U.S. system, the optimal WTW scheme delivers sizeable welfare gains, by providing more insurance to skilled workers and more incentives to unskilled workers.

Exponential self-similar mixing by incompressible flows

We study the problem of the optimal mixing of a passive scalar under the action of an incompressible flow in two space dimensions. The scalar solves the continuity equation with a divergence-free velocity field, which satisfies a bound in the Sobolev space $W^{s,p}$, where $s \geq 0$ and $1\leq p\leq \infty$. The mixing properties are given in terms of a characteristic length scale, called the mixing scale. We consider two notions of mixing scale, one functional, expressed in terms of the homogeneous Sobolev norm $\dot H^{-1}$, the other geometric, related to rearrangements of sets. We study rates of decay in time of both scales under self-similar mixing. For the case $s=1$ and $1 \leq p \leq \infty$ (including the case of Lipschitz continuous velocities, and the case of physical interest of enstrophy-constrained flows), we present examples of velocity fields and initial configurations for the scalar that saturate the exponential lower bound, established in previous works, on the time decay of both scales. We also present several consequences for the geometry of regular Lagrangian flows associated to Sobolev velocity fields.Comment: To appear in Journal of the American Mathematical Society. Some results were announced in G. Alberti, G. Crippa, A. L. Mazzucato, "Exponential self-similar mixing and loss of regularity for continuity equations", C. R. Math. Acad. Sci. Paris, 352(11):901--906, 2014, arXiv:1407.2631v

Advanced Diagnostics of Position Sensors for the Actuation Systems of High-Speed Tilting Trains

Trains tilting permits a train to travel at a high speed while maintaining an acceptable passenger ride quality with respect to the lateral acceleration, and the consequent lateral force, received by the passengers when the train travels on a curved track at a speed in excess of the balance speed built into the curve geometry. The tilting of a train carbody is performed by a control and actuation system which operates as a closed servoloop accepting the commands from the train control system, generating the torque necessary to tilt the carbody with respect to the bogie and measuring the tilt angle to close the control loop. Measurement of the tilt angle of each train vehicle is performed by two sensors located in the front and rear part of the vehicle. Since a correct tilt angle measurement is vital for the system operation and for ensuring a safe ride, in case of discrepancy between the signals of the two tilt angle sensors of any vehicle, the tilting operation is disabled and the train speed is reduced. An innovative tilt angle sensors health management system is herein presented that makes intelligent use of all available information to allow detection of malfunctioning of an individual tilt angle sensor, thereby enabling a continued operation of the tilting system and a high speed travel after a sensor failure occurs