Numerical solution of a long-term average control problem for singular stochastic processes

This paper analyzes numerically a long-term average stochastic control problem involving a controlled diffusion on a bounded region. The solution technique takes advantage of an infinite-dimensional linear programming formulation for the problem which relates the stationary measures to the generators of the diffusion. The restriction of the diffusion to an interval is accomplished through reflection at one end point and a jump operator acting singularly in time at the other end point. Different approximations of the linear program are obtained using finite differences for the differential operators (a Markov chain approximation to the diffusion) and using a finite element method to approximate the stationary density. The numerical results are compared with each other and with dynamic programming. This research has been supported in part by the U.S. National Security Agency under Grant Agreement Number H98230-05-1-0062. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation herein.     

Introduction to session 4

Applied Biochemistry and Biotechnology -     

Modeling the system of electrogasdynamic final-control elements

A system of electrogasdynamic final-control elements (plasma actuators) intended for increasing the stability of the boundary layer on a swept wing is considered. The actuators operate on the basis of dielectric barrier discharge. The physical model of the discharge in the air is formulated in the diffusion-drift approximation with account for three charged ionized-gas components, namely, electrons, positive nitrogen and oxygen ions, and negative oxygen ions. The boundary conditions on the dielectric surface are formulated with account for finite desorption and recombination rates of the charged particles. The numerical modeling for an actuator system of particular geometry shows a slight influence of the negative ions on the bulk force generated by each actuator. The main actuator parameters, such as the total longitudinal force and heat release, are shown to considerably depend on the dielectric permeabilities of insulation layers separating the external and internal electrodes. The expressions are derived that make it possible to estimate the gas velocity induced by the bulk force action of the dielectric barrier discharge on the gas flow.     

Torsional ultrasonic transducer computational design optimization

A torsional piezoelectric ultrasonic sensor design is proposed in this paper and computationally tested and optimized to measure shear stiffness properties of soft tissue. These are correlated with a number of pathologies like tumors, hepatic lesions and others. The reason is that, whereas compressibility is predominantly governed by the fluid phase of the tissue, the shear stiffness is dependent on the stroma micro-architecture, which is directly affected by those pathologies. However, diagnostic tools to quantify them are currently not well developed. The first contribution is a new typology of design adapted to quasifluids. A second contribution is the procedure for design optimization, for which an analytical estimate of the Robust Probability Of Detection, called RPOD, is presented for use as optimality criteria. The RPOD is formulated probabilistically to maximize the probability of detecting the least possible pathology while minimizing the effect of noise. The resulting optimal transducer has a resonance frequency of 28 [kHz].     

Beam properties of fully optimized,table-top,coherent source at 30 nm

We present results on development and experimental implementation of a 1-kHz, coherent extreme ultraviolet (XUV) radia- tion source based on high-order harmonic generation of the femtosecond, near-infrared laser pulses produced by the titanium-doped sapphire laser system (35 fs, 1.2 mJ, 810 nm) at the Institute of Physics AS CR / PALS Centre. The source comprises a low-density static gas cell filled with a conversion medium, typically argon. The comprehensive optimization of the XUV harmonic source has been performed with respect to major parameters such as gas pressure in the cell, cell length, position of the focus of the driving laser field with respect to the gas cell position, size of the driving near-infrared laser beam, chirp of the femtosecond pulse, and the focal length of the lens deployed in the experimental setup. Harmonic spectra were recorded using an XUV transmission grating spectrometer developed specifically for this purpose. Detailed characterization of the XUV source has been performed including measurement of the XUV beam profile, M² parameter of the beam, absolute energy, and spatial coherence.     

Distinctive Features of the Distributions of the Body Force Produced by a Plasma Actuator

Basing upon the assumption on the solenoidality of the field of the time-average body force produced by a surface dielectric barrier discharge analytical expressions for the spatial distributions of the components of this force are proposed. The calculations of the dischargegenerated near-surface jet are in good agreement with the experiment. The distinctive features of spatial distributions of the body force components calculated from the data of the velocity field measurements are physically explained.     

Characterization of collisionally pumped optical-field-ionization soft X-ray lasers

We give an overview of recent experimental results on optical-field-ionization collisional soft X-ray lasers developed at LOA. By focusing a 30-fs, circularly polarized Ti-sapphire laser pulse at an intensity of up to 8×10¹⁷ Wcm^-2 into a low-density gas cell containing Xe or Kr, we produced a few mm long plasma column for soft X-ray amplifier. Saturated amplification has been achieved on the 4d⁹5d(¹S₀)–4d⁹5p(¹P₁) transition at 41.8 nm in Xe⁸⁺, and on the 3d⁹4d(¹S₀)–3d⁹4p(¹P₁) transition in Kr⁸⁺ at 32.8 nm. Under optimum pumping conditions the Xe⁸⁺ laser provides about (5±2)×10⁹ photons per pulse whilst the Kr⁸⁺ laser delivers up to (2.5±1)×10⁹ photons per shot. The repetition rate of these soft X-ray lasers is 10 Hz. The beam wavefront of the Xe⁸⁺ laser has been measured by a Shack–Hartmann soft X-ray wavefront sensor, and the pulse duration by a cross-correlation technique. PACS 42.55.Vc; 32.30.Rj; 52.50.Jm     

Separation of isomers <Emphasis Type="Italic">L</Emphasis>-alanine and sarcosine in urine by electrospray ionization and tandem differential mobility analysis-mass spectrometry

Sarcosine, an isomer of L-alanine, has been proposed as a prostate cancer progression biomarker [1]. Both compounds are detected in urine, where the measured sarcosine/alanine ratio has been found to be higher in prostate biopsy-positive group versus controls. We present here preliminary evidence showing that urine samples spiked with sarcosine/alanine can be partially resolved in 3 min via tandem differential mobility analysis-mass spectrometry (DMA-MS). Based on the calibration curves obtained for two mobility peaks, we finally estimate their concentration ratio in urine.     

Towards a goldie theory for jordan pairs

A Goldie theory for Jordan pairs is started in this paper. We introduce a notion of order in linear Jordan pairs and study orders in nondegenerate linear Jordan pairs with descending chain condition on principal inner ideals. This work has been supported by DGICYT Grant PB93-0990 and by the “Convenio Marco de Cooperación Hispano-Marroquí”