Time minimal control of batch reactors

Abstract In this article we consider a control system modelling a batch reactor in which three species X

Nuclear DFT electromagnetic moments of intruder configurations calculated in heavy deformed open-shell odd nuclei with 63<=Z<=82 and 82<=N<=126

Within the nuclear DFT approach, we determined the magnetic dipole and electric quadrupole moments for paired nuclear states corresponding to the proton (neutron) quasiparticles blocked in the p11/2- (n13/2+) intruder configurations. We performed calculations for all deformed open-shell odd nuclei with 63<=Z<=82 and 82<=N<=126. Time-reversal symmetry was broken in the intrinsic reference frame and self-consistent shape and spin core polarizations were established. We determined spectroscopic moments of angular-momentum-projected wave functions and compared them with available experimental data. We obtained good agreement with data without using effective g-factors or effective charges in the dipole or quadrupole operators, respectively. We also showed that the intrinsic magnetic dipole moments, or those obtained for conserved intrinsic time-reversal symmetry, do not represent viable approximations of the spectroscopic ones.Comment: 11 RevTex pages, 9 figure

Monotonically convergent optimal control theory of quantum systems with spectral constraints on the control field

We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field is taken as a linear combination of the control field (computed by the standard algorithm) and the filtered field. The parameter of the linear combination is chosen to respect the monotonic behavior of the algorithm and to be as close to the filtered field as possible. We test the efficiency of this method on molecular alignment. Using band-pass filters, we show how to select particular rotational transitions to reach high alignment efficiency. We also consider spectral constraints corresponding to experimental conditions using pulse shaping techniques. We determine an optimal solution that could be implemented experimentally with this technique.Comment: 16 pages, 4 figures. To appear in Physical Review

Non Linearity of the Ball/Rubber Impact in Table Tennis: Experiments and Modeling

AbstractAlong with comfort, the speed is a key metric used to qualify the performance of a table tennis racket. The restitution coefficient which corresponds to the ratio between the velocities of the ball right before and after normally impacting the racket relates to the speed performance: the higher the restitution coefficient, the greater the speed. Thus, understanding the normal impact problem is key and suggests investigating the effects of the intrinsic properties and architectures of the constituents of the racket. In this work, both experimental and numerical studies were pursued. Experimentally, normal impact tests were performed for varying launching velocities on samples made of isolated or associated constituents of a table tennis racket and the restitution coefficients calculated. Numerically, 3D finite elements simulations were conducted to replicate the normal impact conditions while incorporating the time-dependent constitutive behavior of the polymeric elements contributing during the impact: the racket constituents (the foam and the compact) and the ball. The restitution coefficients are seen to decrease with increasing launching velocity, while being minimum when the two racket polymeric constituents are associated. A fair agreement is obtained with the FE simulations in which the sample/ball contact zone is identified as a ring with its mean radius increasing till the maximum crushing. Ultimately, additional FE calculations confirm that the friction plays a key role in the energy dissipation process, alongside with the rate-dependent behavior and architecture of the polymeric constituents

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya

Preliminaries Consider the local SR-geometry (U, D, g), where U is a neighborhood of 0 ∈ R 3 , D is a Martinet-type distribution, which can be taken in the normal form D = Ker ω, ω = dz − y 2 2 dx, and g is a C ω metric on D, which can be written (see Expanding F 1 and F 2 in Taylor series according to the previous weights and identifying at the order p two elements whose Taylor series are the same at the order p, we obtain the following normal forms of order −1 and 0: • Normal form of order −1: (flat case); • Normal form of order 0: 2 dx 2 + (1 + βx + γy) 2 dy 2 , α, β, γ ∈ R. 1.1. Geodesics equations. The energy minimization problem equivalent to the SR-problem is the following optimal control problem: from Pontryagin&apos;s maximum principle [9], minimizing solutions are solutions of the following equations: where H ν is the pseudo-Hamiltonian where ν is a constant normalized to 0 or 1/2. A solution of the previous equations is called an extremal; when ν = 1/2 (resp. ν = 0), the solutions are called normal (resp. abnormal), and their projections onto the state space are called the geodesics. They can be easily computed

Protein Kinase B Regulates T Lymphocyte Survival, Nuclear Factor κb Activation, and Bcl-XL Levels in Vivo

The serine/threonine kinase protein kinase B (PKB)/Akt mediates cell survival in a variety of systems. We have generated transgenic mice expressing a constitutively active form of PKB (gag-PKB) to examine the effects of PKB activity on T lymphocyte survival. Thymocytes and mature T cells overexpressing gag-PKB displayed increased active PKB, enhanced viability in culture, and resistance to a variety of apoptotic stimuli. PKB activity prolonged the survival of CD4+CD8+ double positive (DP) thymocytes in fetal thymic organ culture, but was unable to prevent antigen-induced clonal deletion of thymocytes expressing the major histocompatibility complex class I–restricted P14 T cell receptor (TCR). In mature T lymphocytes, PKB can be activated in response to TCR stimulation, and peptide-antigen–specific proliferation is enhanced in T cells expressing the gag-PKB transgene. Both thymocytes and T cells overexpressing gag-PKB displayed elevated levels of the antiapoptotic molecule Bcl-XL. In addition, the activation of peripheral T cells led to enhanced nuclear factor (NF)-κB activation via accelerated degradation of the NF-κB inhibitory protein IκBα. Our data highlight a physiological role for PKB in promoting survival of DP thymocytes and mature T cells, and provide evidence for the direct association of three major survival molecules (PKB, Bcl-XL, and NF-κB) in vivo in T lymphocytes

Saturation of a spin 1/2 particle by generalized Local control

We show how to apply a generalization of Local control design to the problem of saturation of a spin 1/2 particle by magnetic fields in Nuclear Magnetic Resonance. The generalization of local or Lyapunov control arises from the fact that the derivative of the Lyapunov function does not depend explicitly on the control field. The second derivative is used to determine the local control field. We compare the efficiency of this approach with respect to the time-optimal solution which has been recently derived using geometric methods.Comment: 12 pages, 4 figures, submitted to new journal of physics (2011