Presence Of Plane Research Articles

Interaction of a Sparce Particle Stratum with a Constantly Heated Plane in Presence of a Transverse Temperature Gradient

While modelling dispersions in containers or tubes it may be necessary to find distortions brought by the suspended particles in the temperature distribution in a vessel. Essential step of such a calculation is to determine of temperature field emerging when the particles are placed near the plane wall of the vessel. For simplicity one may suppose additionally that the carrying medium is stationary and that the particles are spherical. Solving this problem, the authors replace the plane by a fictitious particle that is mirror-positioned with respect to a given one. This allows to use multipole expansion for representation of the temperature that is a harmonic function in the case discussed. The obtained solution is used to find effective heat conduction coefficient of particles’ stratum placed in a half-space bounded by a plane with constant temperature. To do this, the authors average the temperature in the medium by the particles’ positions and compare the result with the solution of reference problem about temperature distribution in a half-space with a uniform stratum of other thermal conductance. The calculation is provided under the assumption that suspended spheres are placed rarely and therefore interact only with the plane but not with each other. A correction term is obtained that must be included in the expression for heat conduction coefficient if the total medium longitude in the direction orthogonal to the plane is finite.

Selected Features of Autonomous Underwater Robot Dynamics under Near-Bottom Equidistant Motion Control

Search and survey missions of an autonomous underwater robot are usually associated with motion along equidistant trajectories near the bottom. The most difficult problem here is to control motion in a vertical plane in presence of obstacles in the bottom relief along the motion route. When the obstacles are detected using a multi-channel front-viewing echolocation system, equidistant motion of the vehicle is provided with tracking of the bottom relief profile. The dynamic model of motion with specific requirements for the structure and control parameters is studied. Comparative analysis of the dynamic properties of control system depending on the design and functional features of the actuating elements and the range-measuring echolocation system is presented.

Analytical decomposition of Zernike and hexagonal modes over a hexagonal segmented optical aperture

Zernike polynomials are widely used to describe common optical aberrations of a wavefront as they are well suited to the circular geometry of various optical apertures. Non-conventional optical systems, such as future large optical telescopes with highly segmented primary mirrors or advanced wavefront control devices using segmented mirror membrane facesheets, exhibit a hexagonal geometry, making the hexagonal orthogonal polynomials a valued basis. A cost-benefit trade-off study for deriving practical upper limits in, e.g., polishing, phasing, alignment, and stability of hexagons imposes analytical calculation to avoid time-consuming end-to-end simulations, for the sake of exactness. It is important to include global modes over the pupil for Zernike decomposition over a hexagonal segmented optical aperture into the error budget. However, numerically calculated Zernike decomposition is not optimal due to the discontinuities at the segment boundaries that result in imperfect hexagon sampling. In this paper, we present a novel approach for a rigorous Zernike and hexagonal mode decomposition adapted to hexagonal segmented pupils by means of analytical calculations. By contrast to numerical approaches that are dependent on the sampling of the segment, the decomposition expressed analytically only relies on the number and positions of segments comprising the pupil. Our analytical method allows extremely quick results minimizing computational and memory costs. Further, the proposed formulae can be applied independently from the geometrical architecture of segmented optical apertures. Consequently, the method is universal and versatile per se. For instance, this work finds applications in optical metrology and active correction of phase aberrations. In modern astronomy with extremely large telescopes, it can contribute to sophisticated analytical specification of the contrast in the focal plane in presence of aberrations.

Multivariable Real-Time Control of Viscosity Curve for a Continuous Production Process of a Non-Newtonian Fluid

The application of a multivariable predictive controller to the mixing process for the production of a non-Newtonian fluid is discussed in this work. A data-driven model has been developed to describe the dynamic behaviour of the rheological properties of the fluid as a function of the operating conditions using experimental data collected in a pilot plant. The developed model provides a realistic process representation and it is used to test and verify the multivariable controller, which has been designed to maintain viscosity curves of the non-Newtonian fluid within a given region of the viscosity-vs-shear rate plane in presence of process disturbances occurring in the mixing process.

Locus of the apices of projectile trajectories under constant drag

Using the hodograph method, we present an analytical solution for projectile coplanar motion under constant drag, parametrised by the velocity angle. We find the locus formed by the apices of the projectile trajectories, and discuss its implementation for the motion of a particle on an inclined plane in presence of Coulomb friction. The range and time of flight are obtained numerically, and we find that the optimal launching angle is smaller than in the drag-free case. This is a good example of a problem with constant dissipation of energy that includes curvature; it is appropriate for intermediate courses of mechanics.

Virtually bloodless posterior midline exposure of the lumbar spine using the "para-midline" fatty plane.

The authors have developed a "para-midline" approach to the posterior lumbar spine using a virtually avascular surgical plane not previously described in the literature. It was their purpose to document consistent MRI presence of this plane and to prospectively evaluate its clinical use in terms of blood loss. Fifty consecutive patients undergoing primary lumbar surgery on 1-3 levels were prospectively enrolled from September 2014 to May 2015. The para-midline approach was used in all cases. The deep lumbar fascia is longitudinally incised on either side of the spinous processes instead of directly in the midline, which reveals the para-midline fatty plane. Blood loss during the approach and overall blood loss were recorded for all patients. MRIs from each patient were reviewed by an experienced neuroradiologist to determine the presence of the para-midline fatty plane. There was no recorded blood loss during the approach for all procedures. The average overall blood loss was 60 cc (20-200 cc). No patient required a transfusion intraoperatively or postoperatively. The fatty para-midline plane was noted on preoperative MRI at all operated levels in all patients. The average width of this plane was 6.5 mm (2-17 mm). The para-midline approach for lumbar surgery is associated with less blood loss than traditional, subperiosteal exposure techniques. The fatty interval through which this approach is made is universally present and identifiable on MRI. The authors offer this approach as a means of decreasing the risks associated with blood loss and transfusion with posterior lumbar surgery.

A Note on Hydromagnetic Flow of an Oldroyd-B Fluid near an Infinite Plate Induced by Half Rectified Sine Pulses

An initial value problem concerning the motion of an incompressible, electrically conducting, viscoelastic Oldroyd-B fluid bounded by an infinite rigid non-conducting plate is solved. The unsteady motion is generated impulsively from rest in the fluid due to half rectified sine pulses subjected on the plate in its own plane in presence of an external magnetic field. It is assumed that no external electric field is acting on the system and the magnetic Reynolds number is very small. The operational method is used to obtain exact solutions for the fluid velocity and the shear stress on the wall. Quantitative analysis of the results is presented with a view to disclose the simultaneous effects of the external magnetic field and the fluid elasticity on the flow and the wall shear stress for different periods of pulsation of the plate. It is also shown that the classical and hydromagnetic Rayleigh solutions appear as the limiting cases of the present analysis.

ExPlanes: exploring planes in triplet data.

Many methods for the analysis of gene expression-, protein- or metabolite-data focus on the investigation of binary relationships, while the underlying biological processes creating this data may generate relations of higher than bivariate complexity. We give a novel method ExPlanes that helps to explore certain types of ternary relationships in a statistically robust, Bayesian framework. To arrive at an characterization of the data structure contained in triplet data we investigate 2-dimensional planes being the only linear structures that cannot be inferred from projections of the data. The key part of our methodology is the definition of a robust, Bayesian plane posterior under the assumption of an invariant prior and a Gaussian error model. A numerical representation of the plane posterior can be explored interactively. Beyond this purely Bayesian approach we can use the plane posterior to construct a family of posterior-based test statistics that allow testing the data for different plane related hypotheses. To demonstrate practicability we queried triplets of metabolic data from a plant crossing experiment for the presence of plane-, line- and point-structures by using posterior-based test statistics and were able to show their distinctiveness.

Dynamics of chaotic magnetic lines: Intermittency and noble internal transport barriers in the tokamap

A purely magnetic approach is used to describe internal transport barriers (ITB’s) observed in tokamaks, generally “around” rational values of the safety factor q, and even in ohmic and positive shear situations. An Hamiltonian twist map “tokamap” is used to describe magnetic line section points in a poloidal (ψ,θ) plane in presence of a magnetic perturbation of strength L, inducing the appearance of magnetic islands and chaotic zones (“incomplete chaos”). For a low value of L<1, before breaking of the boundary circle on the plasma edge, a regular zone with robust magnetic surfaces is found in the plasma core, surrounded by two chaotic regions, separated by a transport barrier across which a magnetic line performs an intermittent motion. By using number theory and convergent rational island chains along Fibonacci series, the ITB is identified as composed of two permeable Cantori (broken Kolmogorov–Arnold–Moser surfaces) with “most noble” q values. No paradox however exists with experimental observations identifying the barriers as being “near” rational q values: this is also the case here for the two Cantori, but, more precisely, on neighboring most noble q values. Dispersion studies for an ensemble of magnetic lines in the large L regime where the boundary circle has been broken, shows an asymptotic radial subdiffusion, with different transient regimes. Comparison is performed with the flux diffusion in the standard map.

Active control of extended acoustic sources in a half-space

Many noise sources, such as an electronic transformer, are located on or near an acoustically rigid planar surface, such as a concrete floor. Thus far, however, most of the active noise control research has been based on the free-field assumption. The work presented here investigates the effect the presence of a rigid plane has on the active noise control of an acoustic source with characteristic dimensions comparable to the acoustic wavelength at the frequency of interest. It is shown that when the source is located a distance of one wavelength or more from the plane, the presence of the plane may be neglected. However, the minimum radiated power computed using a free space active analysis can be significantly greater than that predicted using a half space active analysis for distances less than one wavelength. As a result, using the simpler free space analysis techniques leads to less effective control for distances less than one wavelength.

Time-domain leaky modes on layered media: dispersion characteristics and synthesis of pulsed radiation

In a companion paper (see ibid., p.747-54, June 1993) studying short-pulse radiation from current elements in the presence of plane layered dielectric media, various alternatives for constructing the transient field in terms of spectral-domain wave functions are explored. Two distinctive synthesis options are structured around conventional time-harmonic and nonconventional time-dependent basis wave functions, respectively. To understand the characteristic properties of each, the frequency-wavenumber dispersion relation for the layered environment is explored here in detail. Especially interesting is the behavior of the nonconventional time-domain leaky modes, which exhibit anomalies not encountered in their conventional time-harmonic counterparts. An example is given of how these time-domain modal basis fields synthesize highly resolved short-pulse radiation from a source in a dielectric layer. >

Zinc Electrowinning under Periodical Reverse Current (PRC): Behavior of the Cathode and Effects of Lead Impurities

Laboratory‐scale experiments of zinc electrowinning under periodical reverse current (PRC) were carried out in acidic sulfate solutions. To study the effects of lead impurities on the zinc cathode, 0.3–15 mg/l of lead were added to the electrolyte. A square wave of current was used to produce the PRC. Current densities of 500 and 1500 A/m2 were investigated under both direct current and PRC. In the case of PRC, the direct and reverse pulses had respective durations of 100s and 0.1–1.0s. The current density of the reverse pulse was set at half the value of the direct pulse. Comparisons were made with conventional dc electrolysis. The presence of 5 mg/l of lead lowered the current efficiency in dc from 94.1 to 93.2%, while in PRC it raised it from 93.2 to 97.6%, using a reverse pulse duration of 0.1s. Correlation between the current efficiencies and the presence of the crystallographic plane (101) was also observed. It suggests that lead in the zinc deposit and the use of PRC influence the crystallographic growth of the zinc deposit. The presence of plane (101) increases the oyerpotential of hydrogen evolution on zinc, and this results in a higher current efficiency. A way of obtaining the beneficial plane is to use PRC and lead in the electrolyte together.

Motion of a string vibrating against a rigid fixed obstacle

We consider a string, fixed at both ends and moving in a plane in presence of a straight fixed obstacle placed on the equilibrium position of the string; the rebound of the string on the obstacle obeys the law of perfect reflection. The string being initially at rest in an arbitrary shape, we prove that the motion is periodic with the same period that the free oscillations.

On the two-baryon sector of soluble models with indefinite metric (I)

Systems containing two unphysical particles with complex energies are studied. It is shown that states which lie on the real axes, if one has no interaction between the two unphysical particles, go to the complex plane in presence of interaction.

Radiation and Scattering Problems in Compressible Plasmas. Part I. Solutions by Ray Optics

Ray‐optical concepts are introduced for propagation of electromagnetic and electroacoustic waves in an unbounded compressible plasma, and are then applied to the analysis of radiation in the presence of plane or curved interfaces and obstacles. The method involves tracing of the electromagnetic and acoustic rays through the medium, due account being taken of coupling in source regions, at boundaries, and at scattering centers. The formulas for reflected, refracted, and diffracted fields derived in this manner are verified for special cases by the rigorous treatment in part II, thereby providing confidence in the validity of the procedure.

Effects of Proton Bombardmemt on CaF2 Crystals

New features were observed in synthetic CaF 2 crystals which were colloidally colored by intense proton bombardmemt. There are (1) a surface of discontinuity at the end of the proton range, (2) a colloidally colored thin layer between the bombarded plane and the range end, and (3) the presence of plane where the dislocations were most decorated. These phenomena were explained to result from the inhomogeneous ionization and heat release during the proton penetration, and the atomic displacements and hydrogen introduction upon stopping of the protons in the crystal.