Minimum Restraint Functions for unbounded dynamics: general and control-polynomial systems

We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family of admissible trajectories may lack important compactness properties. In the first part of the paper we show that the existence of a $p_0$-minimum restraint function provides not only global asymptotic controllability (despite non-transversality) but also a state-dependent upper bound for the value function (provided $p_0>0$). This extends to unbounded dynamics a former result which heavily relied on the compactness of the control set. In the second part of the paper we apply the general result to the case when the system is polynomial in the control variable. Some elementary, algebraic, properties of the convex hull of vector-valued polynomials' ranges allow some simplifications of the main result, in terms of either near-affine-control systems or reduction to weak subsystems for the original dynamics.Comment: arXiv admin note: text overlap with arXiv:1503.0344

Nonlinear dynamics of quantum dot nuclear spins

We report manifestly nonlinear dependence of quantum dot nuclear spin polarization on applied magnetic fields. Resonant absorption and emission of circularly polarized radiation pumps the resident quantum dot electron spin, which in turn leads to nuclear spin polarization due to hyperfine interaction. We observe that the resulting Overhauser field exhibits hysteresis as a function of the external magnetic field. This hysteresis is a consequence of the feedback of the Overhauser field on the nuclear spin cooling rate. A semi-classical model describing the coupled nuclear and electron spin dynamics successfully explains the observed hysteresis but leaves open questions for the low field behaviour of the nuclear spin polarization.Comment: 7 pages, 4 figure

Surface temperature distribution along a thin liquid layer due to thermocapillary convection

The surface temperature distributions due to thermocapillary convections in a thin liquid layer with heat fluxes imposed on the free surface were investigated. The nondimensional analysis predicts that, when convection is important, the characteristics length scale in the flow direction L, and the characteristic temperature difference delta T sub o can be represented by L and delta T sub o approx. (A2Ma)/1/4 delta T sub R, respectively, where L sub R and delta sub R are the reference scales used in the conduction dominant situations with A denoting the aspect ratio and Ma the Marangoni number. Having L and delta sub o defined, the global surface temperature gradient delta sub o/L, the global thermocapillary driving force, and other interesting features can be determined. Numerical calculations involving a Gaussian heat flux distribution are presented to justify these two relations

H3++H_3^{++} molecular ions can exist in strong magnetic fields

Using the variational method it is shown that for magnetic fields $B\geq 10^{11}$ G there can exist a molecular ion $H_3^{++}$.Comment: LaTeX, 7 pp, 1 table, 4 figures. Title modified. Consideration of the longitudinal size of the system was adde

Quantitative Kinematic Characterization of Reaching Impairments in Mice After a Stroke

Background and Objective. Kinematic analysis of reaching movements is increasingly used to evaluate upper extremity function after cerebrovascular insults in humans and has also been applied to rodent models. Such analyses can require time-consuming frame-by-frame inspections and are affected by the experimenter's bias. In this study, we introduce a semi-automated algorithm for tracking forepaw movements in mice. This methodology allows us to calculate several kinematic measures for the quantitative assessment of performance in a skilled reaching task before and after a focal cortical stroke. Methods. Mice were trained to reach for food pellets with their preferred paw until asymptotic performance was achieved. Photothrombosis was then applied to induce a focal ischemic injury in the motor cortex, contralateral to the trained limb. Mice were tested again once a week for 30 days. A high frame rate camera was used to record the movements of the paw, which was painted with a nontoxic dye. An algorithm was then applied off-line to track the trajectories and to compute kinematic measures for motor performance evaluation. Results. The tracking algorithm proved to be fast, accurate, and robust. A number of kinematic measures were identified as sensitive indicators of poststroke modifications. Based on end-point measures, ischemic mice appeared to improve their motor performance after 2 weeks. However, kinematic analysis revealed the persistence of specific trajectory adjustments up to 30 days poststroke, indicating the use of compensatory strategies. Conclusions. These results support the use of kinematic analysis in mice as a tool for both detection of poststroke functional impairments and tracking of motor improvements following rehabilitation. Similar studies could be performed in parallel with human studies to exploit the translational value of this skilled reaching analysis

Cusp-scaling behavior in fractal dimension of chaotic scattering

A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal dimension of the chaotic set for such a bifurcation. Our analysis and numerical computations in both two- and three-degrees-of-freedom systems suggest a striking feature associated with these subtle bifurcations: the dimension typically exhibits a sharp, cusplike local minimum at the bifurcation.Comment: 4 pages, 4 figures, Revte

FIR Filter Implementation by Efficient Sharing of Horizontal and Vertical Common Sub-expressions

No abstract availabl