Reciprocal Root Research Articles

A comparison of tracking step inputs with a piezo stage using model predictive control and saturated linear quadratic Gaussian control

Compressed Sensing for Atomic Force Microscopy is a newer imaging mode that requires the piezo stage be driven rapidly between measurement locations. In contrast to raster scanning applications, this translates to a setpoint tracking problem. This paper considers the setpoint tracking performance of a piezo nano-positioning stage subject to rate-of-change limitations on the control signal, which is derived from the current limit of the power amplifier. To compensate the vibrational dynamics of the stage, a model predictive control scheme (MPC) and a linear quadratic Gaussian (LQG) controller which saturates the control increment are considered. In both cases, hysteresis and drift are compensated via dynamic inversion. To design the weighting matrices required by the MPC and linear feedback designs, an extension to classic reciprocal root locus ideas is proposed. The robustness of both schemes using classical methods like gain margin, phase margin, and gain of the sensitivity function at low frequencies is analyzed. The overall settle times achieved by both controllers (in both simulation and experiment) across a range of control weights where the reference input is a sequence of step inputs of varying amplitudes are compared. The results show that the best simulation settle time is achieved by MPC using the smallest control weight. However under experimental conditions, the best settle time is achieved by a much larger control weight and the performance of MPC becomes comparable with that of saturated linear feedback. This result is explained by showing that robustness increases with larger control weights. • Setpoint tracking controllers for a piezo stage with current limitation are compared. • Model predictive and saturated linear feedback controllers perform comparably. • Classical notions of robustness are useful in analyzing both controllers.

CYP720A1 function in roots is required for flowering time and systemic acquired resistance in the foliage of Arabidopsis

Systemic acquired resistance (SAR) is an inducible defense mechanism that systemically enhances resistance against pathogens in foliar tissues. SAR, which engages salicylic acid (SA) signaling, shares molecular components with the autonomous pathway, which is involved in controlling flowering time in Arabidopsis thaliana. FLOWERING LOCUS D (FLD) is one such autonomous pathway component that is required for flowering time and the systemic accumulation of SA during SAR. Here, we show that CYP720A1, a putative cytochrome P450 monoxygenase, controls FLD expression and is required for the timing of flowering and the manifestation of SAR. The delayed flowering time in the cyp720a1 mutant correlated with the elevated transcript level of the floral repressor FLC, while the SAR deficiency phenotype of the cyp720a1 mutant correlated with the inability to systemically accumulate SA. CYP720A1 transcript abundance in shoots is poor compared with roots. Reciprocal root-shoot grafting confirmed that CYP720A1 function in the roots is critical for flowering time and SAR. We therefore suggest that root to shoot communication involving a CYP720A1-dependent factor contributes to the timing of reproductive development and defense in the foliage.

Distinguished-root formulas for generalized Calabi–Yau hypersurfaces

By a "generalized Calabi-Yau hypersurface" we mean a hypersurface in ${\mathbb P}^n$ of degree $d$ dividing $n+1$. The zeta function of a generic such hypersurface has a reciprocal root distinguished by minimal $p$-divisibility. We study the $p$-adic variation of that distinguished root in a family and show that it equals the product of an appropriate power of $p$ times a product of special values of a certain $p$-adic analytic function ${\mathcal F}$. That function ${\mathcal F}$ is the $p$-adic analytic continuation of the ratio $F(\Lambda)/F(\Lambda^p)$, where $F(\Lambda)$ is a solution of the $A$-hypergeometric system of differential equations corresponding to the Picard-Fuchs equation of the family.

Three-dimensional alteration of constricted alveolar ridge affected by root thrusting with and without open-flap decortication.

To investigate the morphometric and histological alterations of the constricted alveolar ridge when affected by root thrusting with and without open-flap decortication. Eight beagles were divided into three groups: C, control without root thrusting; R, root thrusting only; RD, root thrusting with alveolar decortication. The ridge constriction model was prepared in 16 mandibular quadrants after extraction of the third premolars. Reciprocal root thrusting of the second and fourth premolars was performed toward the constricted ridge for 10 weeks, having a moment of 900 g-mm. Open-flap decortication was conducted on the constricted bone surface in group RD. Micro-CT-based histomorphometric analysis and trichrome-staining-based tissue fractional analysis were performed to evaluate morphometric and microstructural changes on the ridge. Group R revealed a higher percentage of bone volume (P < .001), lower bone mineral density (P < .01), and higher trabecular number (P < .001) than did group C, which was supported by a higher bone fraction woven to lamellar bone (P < .05) resulting from histologic fractional analysis. However, group RD showed no significant difference from group C. Root thrusting toward the constricted ridge induced hypertrophic bone modeling with a high trabecular fraction on the ridge. However, combined open-flap decortication with root thrusting did not improve the volume or quality of the constricted ridge.

Barkhausen noise characterisation during elastic bending and tensile-compression loading of case-hardened and tempered samples

This study examined the Barkhausen noise (BN) response of carburising case-hardened steel with varying tempering stages. The test material was loaded in bending and in alternating loading. The aim of the study was to obtain relevant multiparameter BN data from different loading conditions and to investigate the effect of applied stress on the BN response. The test bar series was made from case-hardened steel. Different tempering parameters were used to vary the surface hardness and the surface residual stresses of the studied series of test bars. In the bending tests, the samples were subjected to incrementally applied loading in the purely elastic deformation region. In addition, uniaxial stepwise loading with tensile and compressive stress was applied to selected samples simultaneously with the BN measurements. The BN measurements were performed under different loading conditions along with X-ray diffraction strain measurements in bending. The results revealed linear behaviour between the reciprocal root mean square value and the stress values obtained with strain gages and X-ray diffraction for the tempered samples.

Control of the surface morphology of solid electrolyte films during field-driven growth in a reactive plasma

Experiments on the generation of non-equilibrium surface patterns on ion-conducting thin films (AgCl, silver chloride) during field-driven growth in chlorine rf plasmas are reported. The growth experiments are performed in a vacuum flow reactor in the temperature range between 320 K and 450 K, at chlorine gas pressures in the order of 100 Pa, and by applying current densities in the order of 1 mA cm(-2). The surface morphology of product films is documented by scanning electron microscopy and analysed in terms of typical surface patterns. A large variety of different surface morphologies (often finger-like or dendritic) is prepared with a high lateral uniformity and good reproducibility. A theoretical stability criterion is derived on the basis of a linear stability analysis. The model-type experiments confirm this formal stability criterion: (a) The growth of the product surface is morphologically stable, if the plasma exhibits a higher conductivity than the growing solid. (b) The typical wavelength of the surface patterns that are formed during growth is proportional to the reciprocal root of the electric current. (c) The periodicity of the surface patterns decreases when the temperature is increased, and the growth rate of a surface instability grows with increasing temperature. All theoretical predictions are confirmed by corresponding experimental results.

High Cycle Thermal Fatigue Crack Initiation and Growth Behavior in Simulated BWR Environment

At a tee junction point of piping system, hot water and cold water is mixed with each other in a whirl. The vibrating mixing boundary between the hot and cold water causes a temperature fluctuation on an inside surface of the pipe just after the connection point. The temperature fluctuation yields a cyclic thermal stress near the pipe surface and results in the crack initiation. In this study the thermal fatigue tests using disk specimens in simulated BWR environment were performed and the thermal fatigue crack initiation strength was compared with the mechanical fatigue strength. Furthermore the thermal fatigue crack arrest depth was analyzed using the linear fracture mechanics, and the arrest depth was found to be in proportion to the reciprocal root of the frequency of temperature fluctuation, and the experimental results agreed well with the analytical ones.

HIGH LEVEL PATH COORDINATION FOR MULTIPLE VEHICLES AND RECIPROCAL ROOT LOCUS

Abstract This paper presents a method based on the reciprocal root locus (RRL) approach for solving the multiple vehicle path coordination problem. A high level planning assigns the tasks to each vehicle, specifying each mission, inside a structured workspace with known obstacles. The problem is solved in two steps: first the given workspace is mapped onto a semicircle, using the theory of conformal mappings, then the RRL method is applied. Examples involving multiple vehicles illustrate the proposed technique and its effectiveness.

High-Cycle Thermal Fatigue Crack Initiation and Growth Behavior in a Semi-Infinite Plate Model

At a T-junction in piping system, hot and cold water mixes in a whirl. The vibrating mixing boundary between the hot and cold water causes a temperature fluctuation on the inner surface of the pipe just after the connection point at the T-junction, and this temperature fluctuation yields a cyclic thermal stress near the pipe surface, resulting in crack initiation. In this study, the thermal stress distribution was analyzed for a semi-infinite plate model. The allowable water temperature range for the fatigue crack initiation was determined based on the mechanical fatigue test results. The thermal fatigue crack arrest behavior was analyzed based on the distributions of the stress intensity factor. The arrested crack depth is found to be in proportion to the reciprocal root of the frequency of the temperature fluctuation and is 3.8 mm for the frequency of 1 Hz.

High Cycle Thermal Fatigue Crack Initiation and Growth Behavior in Semi-infinite Plate Model.

At a tee junction point of piping system, hot water and cold water is mixed with each other in a whirl. The vibrating mixing boundary between the hot and cold water causes a temperature fluctuation on a inside surface of the pipe just after the connection point. The temperature fluctuation yields a cyclic thermal stress near the pipe surface and results in the crack initiation. In this study the thermal stress distribution was analyzed for a semi-infinite plate model and the fatigue crack growth behavior was examined. As a results, the thermal fatigue crack is arrested and the arrested crack depth is found to be in proportion to the reciprocal root of the frequency of temperature fluctuation.

Fracture toughness and hardness of zinc sulphide as a function of grain size

The erosion properties of brittle materials depend upon plastic deformation and crack generation at an impact or indented site. Vickers indentations have been used to investigate the plastic processes and crack systems in chemical vapour deposited zinc sulphide of different grain sizes. The hardness,H, and the “local” fracture toughnessKc, are dependent upon the grain size of the material. For small grain size material (<50 Μm) the Vickers hardness was found to increase with decreasing grain size in accord with the Petch mechanism, i.e.H=H0 +kd−1/2 wherek andH0 are constants andd is the grain diameter. A maximum hardness of ca. 4 GPa has been observed for material with an average 0.5 Μm grain diameter. In large grain size material, hardness anisotropy within the grains causes significant experimental scatter in the hardness measurements because the plastic impression formed by the indenter (load 10 N and 100 N) is smaller than the grain diameter. The values ofKc obtained using an indentation technique show that for grain sizes less than 8 ΜmKc decreases with decreasing grain size. For materials with a grain size in the range 500 Μm to 8 Μm, well developed median cracks were not observed, however, the radius of the fracture zone was measured in order to estimate an “effective”Kc. The “effective”Kc was found to increase approximately linearly with the reciprocal root of the grain size. Consideration of the models for elastic/plastic impact and micromechanics of crack nucleation in conjuction with the variation ofKc andH, indicate that zinc sulphide with a mean grain size of 8 Μm will give the optimum solid particle and rain erosion resistance.

Experimental determination of thermal and adhesion stress in particle filled thermoplasts

AbstractThe phenomena of dewetting in filled thermoplastics were studied by light microscopy and were correlated with variations in the slope of stress‐strain diagrams in constant strain rate tests. In such diagrams, kinks in the plots were found to correspond to the dewetting stress. The corresponding local stress at a filler particle is then equal to the sum of the thermal compressive stress and the adhesion stress. It was shown that the adhesion stress was proportional to the reciprocal root of the particle radius. Also, values of dewetting stress predicted for inorganic particles with radii smaller than 2–4 micrometers are higher than the stresses at which crazes and shear‐bands are formed near such particles, indicating that dewetting will not occur in those cases, and adhesion aids may be superfluous.

Use of macroporous polymeric high-performance liquid chromatographic columns in pharmaceutical analysis.

One of the advantages of polymeric HPLC packings over silica-based packings is chemical stability, particularly at elevated pH levels. This paper describes the application of polymeric (PLRP-S) columns to four typical pharmaceutical studies: the separation of Vigabatrin (4-aminohex-5-enoic acid), a novel GABA transaminase inhibitor, from its related compounds; the separation of Vigabatrin from a degradation product in a liquid formulation containing benzoic acid as a preservative; the determination of aminophylline in a tablet formulation; and the determination of sodium camphorsulphonate in a liquid formulation.This paper compares PLRP-S columns with silica-based columns and considers some theoretical parameters affecting chromatographic performance. The column efficiency of PLRP-S is shown to increase with temperature. Graphs of In k′ versus reciprocal temperature for LiChrosorb RP-18 and PLRP-S columns deviate slightly from linearity using methanol-water mobile phases. Graphs of reciprocal k′ versus reciprocal root ionic strength are linear for PLRP-S columns. The adsorption mechanism proposed to explain this phenomenon is the Stern-Gouy-Chapman theory of the electrical double layer.

The Teacher's Corner: A Note on the Expectation of the Reciprocal and Square Root of a Random Variable

In The American Statistician, February, 1966 (vol. 20, Number 1), [1] a well-known result, viz., the expectation of a positive random variable with a finite mean such that it is not identically equal to zero, is greater than the reciprocal of its expectation has been proved by a new simple method different from the conventional method depending on Schwarz's inequality [2] (which is also quite simple). There is however a still shorter method which the authors have been employing in statistics classes which might bear repetition although it should be well-known. It is as follows:

A Note on the Expectation of the Reciprocal and Square Root of a Random Variable

A Note on the Expectation of the Reciprocal and Square Root of a Random Variable