On Regularity of Abnormal Subriemannian Geodesics

We prove the smoothness of abnormal minimizers of subriemannian manifolds of step 3 with a nilpotent basis. We prove that rank 2 Carnot groups of step 4 admit no strictly abnormal minimizers. For any subriemannian manifolds of step less than 7, we show all abnormal minimizers have no corner type singularities, which partly generalize the main result of Leonardi-Monti.Comment: This paper has been withdrawn by the author due to a crucial computation error in (F_t^1)_sta

Anisotropic thermophoresis

Colloidal migration in temperature gradient is referred to as thermophoresis. In contrast to particles with spherical shape, we show that elongated colloids may have a thermophoretic response that varies with the colloid orientation. Remarkably, this can translate into a non-vanishing thermophoretic force in the direction perpendicular to the temperature gradient. Oppositely to the friction force, the thermophoretic force of a rod oriented with the temperature gradient can be larger or smaller than when oriented perpendicular to it. The precise anisotropic thermophoretic behavior clearly depends on the colloidal rod aspect ratio, and also on its surface details, which provides an interesting tunability to the devices constructed based on this principle. By means of mesoscale hydrodynamic simulations, we characterize this effect for different types of rod-like colloids.Comment: 8 pages, 10 figure

Adaptive reference model predictive control for power electronics

An adaptive reference model predictive control (ARMPC) approach is proposed as an alternative means of controlling power converters in response to the issue of steady-state residual errors presented in power converters under the conventional model predictive control (MPC). Differing from other methods of eliminating steady-state errors of MPC based control, such as MPC with integrator, the proposed ARMPC is designed to track the so-called virtual references instead of the actual references. Subsequently, additional tuning is not required for different operating conditions. In this paper, ARMPC is applied to a single-phase full-bridge voltage source inverter (VSI). It is experimentally validated that ARMPC exhibits strength in substantially eliminating the residual errors in environment of model mismatch, load change, and input voltage change, which would otherwise be present under MPC control. Moreover, it is experimentally demonstrated that the proposed ARMPC shows a consistent erasion of steady-state errors, while the MPC with integrator performs inconsistently for different cases of model mismatch after a fixed tuning of the weighting factor

Improved Pseudorandom Generators from Pseudorandom Multi-Switching Lemmas

We give the best known pseudorandom generators for two touchstone classes in unconditional derandomization: an $\varepsilon$-PRG for the class of size-$M$ depth-$d$ $\mathsf{AC}^0$ circuits with seed length $\log(M)^{d+O(1)}\cdot \log(1/\varepsilon)$, and an $\varepsilon$-PRG for the class of $S$-sparse $\mathbb{F}_2$ polynomials with seed length $2^{O(\sqrt{\log S})}\cdot \log(1/\varepsilon)$. These results bring the state of the art for unconditional derandomization of these classes into sharp alignment with the state of the art for computational hardness for all parameter settings: improving on the seed lengths of either PRG would require breakthrough progress on longstanding and notorious circuit lower bounds. The key enabling ingredient in our approach is a new \emph{pseudorandom multi-switching lemma}. We derandomize recently-developed \emph{multi}-switching lemmas, which are powerful generalizations of H{\aa}stad's switching lemma that deal with \emph{families} of depth-two circuits. Our pseudorandom multi-switching lemma---a randomness-efficient algorithm for sampling restrictions that simultaneously simplify all circuits in a family---achieves the parameters obtained by the (full randomness) multi-switching lemmas of Impagliazzo, Matthews, and Paturi [IMP12] and H{\aa}stad [H{\aa}s14]. This optimality of our derandomization translates into the optimality (given current circuit lower bounds) of our PRGs for $\mathsf{AC}^0$ and sparse $\mathbb{F}_2$ polynomials