Longitudinal Coordinate Research Articles

Interference analysis of radially polarized laser beams generated by ring optical elements with vortical phases at sharp focusing

We performed theoretical analysis of sharp focusing of radially polarized beams when there are annular apertures at vortex phase elements in the focusing system. We obtained analytical expressions for the field in the focal region in case of one and two annular apertures. We also present asymptotic expressions for the focal field near the optical axis and at a distance from it. We showed that for one narrow annular aperture with a vortex phase the focal distribution is proportional to a superposition of Bessel functions of different orders. In this case, the focal field is an axially symmetric and does not depend on the longitudinal coordinate. When two narrow annular apertures are used an interference pattern of two vector Bessel-type beams is generated in the focal region. In the case of equal vortex phases in both rings, the field in the focal region remains an axisymmetric one, but a periodic dependence on the longitudinal coordinate appears. If in each of the rings there are vortex phases of different orders, we obtain an interference pattern of more intricate type leading to formation of spiral beams.

Theory of ice-skating

Almost frictionless skating on ice relies on a thin layer of melted water insulating mechanically the blade of the skate from ice. Using the basic equations of fluid mechanics and Stefan law, we derive a set of two coupled equations for the thickness of the film and the length of contact, a length scale which cannot be taken as its value at rest. The analytical study of these equations allows to define a small a-dimensional parameter depending on the longitudinal coordinate which can be neglected everywhere except close to the contact points at the front and the end of the blade, where a boundary layer solution is given. This solution provides without any calculation the order of magnitude of the film thickness, and its dependence with respect to external parameters like the velocity and mass of the skater and the radius of profile and bite angle of the blade, in good agreement with the numerical study. Moreover this solution also shows that a lubricating water layer of macroscopic thickness always exists for standard values of ice skating data, contrary to what happens in the case of cavitation of droplets due to thermal heating (Leidenfrost effect).

Analysis of interference of radially polarized laser beams generated by ring optical elements with a vortex phase at sharp focusing

We theoretically analyze sharp focusing of radially polarized beams by a focusing system containing ring apertures and a vortex-phase optical element in the pupil. Analytic expressions for a field in the focal area for the radially polarized beams for one- and two-ring apertures are obtained. Asymptotic expressions for the focal field at a distance from the optical axis are also derived. It is shown that for a single vortex-phase narrow ring aperture, the field distribution in the focal area is proportional to the superposition of Bessel functions of different orders. The field is shown to possess the axial symmetry and be independent of the longitudinal coordinate. The structure of the interference field for the radially polarization is investigated. With two narrow ring apertures in the pupil of the sharp-focus system, the interference pattern of two vector Bessel-type beams is formed in the focal area. If both ring apertures have the same vortex phase, the field in the focal area remains axis-symmetric, although becoming periodically dependent on the longitudinal coordinate. If each ring has a different-order vortex phase, the interference is more complex and leads to the formation of rotating beams. The three-dimensional structure in the focal area can be controlled by varying the polarization and phase distribution in each of the rings.

Considerations on Acoustic Emissions in Ti Grade 5 During Fatigue Test

In this paper the behavior of Ti grade 5 specimens during fatigue tests, subjected to uniaxial sinusoidal load, was studied by using an Acoustic Emission (AE) detection system. A couple of detectors was placed on the sample in order to allow localization of the acoustic source. Slots were preliminary cut into the specimens in order to introduce a region of stress concentration. During the whole test all data characterizing the AE were collected, i.e. number of hits, amplitude of the recorded waveform, longitudinal coordinate of the acoustic source etc. Data were analyzed also applying different kinds of post-processing filters in order to isolate, for example, only events occurring in the higher stress region or having amplitude beyond a given selected levels. The system proved itself to have a good capability to localize the crack while, properly filtered cumulative graph of hits, display features strictly connected with the nucleation, and propagation of the cracks. Finally amplitude analysis of the recorded signal shows that two main bands of amplitude were recorded during the test.

D2cm³/DICRU ratio as a surrogate of bladder hotspots localizations during image-guided adaptive brachytherapy for cervical cancer: assessment and implications in late urinary morbidity analysis.

To evaluate the efficiency and potential implications of the lowest dose evaluated in the maximally exposed 2cm(3) of the bladder/dose evaluated at the International Commission for Radiation Units and Measurements (ICRU) bladder point (D2cm(3)/DICRU) ratio as surrogate to locate the D2cm(3) in patients treated with MRI-guided adaptive brachytherapy for cervical cancer. The D2cm(3) area of the bladder was located in 69 patients, using the Digital Imaging and Communications in Medicine coordinates of its barycenter, with respect to the ICRU bladder point. The D2cm(3)/DICRU ratio was correlated with the longitudinal coordinate of the D2cm(3). Afterward, the ratio was used in a retrospective cohort of 216 patients to evaluate its impact in dose-effect analyses for late urinary incontinence. The mean position of the D2cm(3) was 1.73±0.98 cm cranially, 0.59±0.65 cm backwardly, and 0.02±0.89 cm to the right of the ICRU point. It was located above the ICRU point in 95.7% of the patients. Its position was lower in patients with vaginal involvement at diagnosis (p=0.03). The D2cm(3)/DICRU ratio was correlated with the position of the D2cm(3) (R²=0.716, p<10(-6)). In speculating that a ratio greater than one would predict a D2cm(3) located above the ICRU point, the sensibility, specificity, positive, and negative predictive values were 95.2%, 100%, 100%, and 66.8%, respectively. Among the retrospective cohort, 85 patients had a ratio lower than 1.1, reflecting a D2cm(3) located in the lower bladder. In these patients, analyses showed significant dose relationship with Grade 2-4 incontinence (p=0.017), whereas no correlation was demonstrated in the remaining patients. The D2cm(3)/DICRU ratio is a relevant surrogate to estimate the localization of the D2cm(3). Significant dose-effect correlations for incontinence were established in patients with low values for this ratio.

The thermal entrance region in a porous medium saturated by a nanofluid: analysis of the Brinkman's model

The Darcy-Graetz problem for a channel filled by a nanofluid saturated porous medium is studied. The flow is assumed to be fully developed and described through Brinkman's model. For the model of the nanofluid, both thermophoresis and Brownian diffusion are taken into account. After an adiabatic preparation region, a boundary temperature linearly varying with the longitudinal coordinate is prescribed. A study of the thermal behaviour of the nanofluid is performed by solving numerically the fully-elliptic coupled equations, with reference both to the thermal entrance region and to the fully developed region. With reference to the fully developed region the solution has been obtained analytically, while for the thermal entrance region it has been obtained numerically, by a Galerkin finite element method implemented through the software package Comsol Multiphysics (© Comsol, Inc.). The analysis shows that, for physically interesting values of the Peclet number, the concentration field depends very weakly on the temperature distribution, for any given value assumed by the Darcy number. Indeed, since the effects of thermophoresis and Brownian diffusion are negligible, the homogeneous model could be employed effectively.

Generaleristics of unsteady MHD temperature boundary layer

Unsteady temperature magnetohydrodynamic (MHD) boundary layer on the arbitrary shape body which temperature is function of time and longitudinal coordinate has been studied. A generalized similarity method is applied to solve the governing non-linear differential equations. Universal partial differential equations of the discussed problem are obtained using the method by which the equations are transformed in such a way that neither the equations nor the boundary conditions depended on particular data of the considered problem. These equations are solved numerically and the integration results are given for different values of introduced parameters. Those solutions permit, before their application to the particular cases (assigned free stream velocity), a generalized analysis of the effects of certain pertinent parameters to the development of the boundary layer. Obtained results are discussed in detail for different values of introduced parameters. Based on the given universal solutions result it is possible to calculate any particular problem for defined free stream velocity and body temperature distribution.

Self-similar turbulent boundary layer with imposed pressure gradient. Four flow regimes

Self-similar flows of an incompressible fluid in a turbulent boundary layer, when the free-stream velocity is a power function (with the exponent m) of the longitudinal coordinate, have been studied. It has been shown that there are four different self-similar flow regimes corresponding to four individual similarity parameters one of which is the known Clauser parameter and the three other parameters have been established for the first time. At adverse pressure gradient, when the exponent m lies in a certain range depending on Reynolds number, the problem has two solutions with different values of the boundary-layer thickness and skin friction; consequently, hysteresis in a pre-separation flow is possible. Separation occurs not at the minimal value of m that corresponds to the strongest adverse pressure gradient, but at m = −0.216 −0.4 Rep−1/3 + O(Rep−2/3), where Rep is the Reynolds number based on longitudinal pressure gradient. The theoretical results are in good agreement with experimental data.

Modeling and Simulation of Solar Irradiance and Daylight Duration for a High-Power-Output Solar Module System

Solar energy is the largest available renewable energy for enhancing the endurance of a solar-powered unmanned aerial vehicle (UAV). However, harnessing solar energy is a great challenge because the power output efficiency of solar module systems is only 15% to 30%. A solar-powered UAV has the potential to outperform a battery-powered UAV, particularly in tasks involving a pseudo satellite that requires long operating hours. Atmospheric conditions and geographical location are the main causes of the poor performance of solar modules. Despite the improvements in solar cell efficiency over the years, solar module systems can still barely convert half of the sun’s power into electricity. This limitation hinders the use of current solar module systems for harvesting solar energy. Recent studies have focused not only on the type of solar cells but also on the positioning system. However, understanding and research on the solar irradiance intensity, as well as on the effect of daylight duration on the power output, remain lacking. A comprehensive model was developed to address this gap and investigate how the movement of the sun movement affects the performance of solar module systems. This simulation model found that daylight duration is more important than available solar irradiance. Higher solar irradiance and daylight duration corresponds to a higher power output of the solar module system. Daylight duration also depends on latitude where higher latitudes lead to longer daylight duration. On the other hand, longitudinal coordinates and elevation have minor effects on the estimation of daylight duration. Therefore, the northern hemisphere has more advantages than southern hemisphere during summer and vice versa.

Расчет закрученного неизотермического течения слоя двухфазной неньютоновской среды по конической поверхности

We consider the non-isothermic layer flow of two-phase non-Newtonian medium on the inner surface of the conical tube. The flow regime is laminar , axisymmetric and steady. The rheological state of the medium is described by the generalized law Ostwald de Ville. We also took into account the dependence of the temperature of medium consistency. The conservation equations of mass, momentum and energy mechanics of heterogeneous medium is used in quasi-homogeneous approximation. The recorded in biconical coordinate system equations are solved by method of equal costs surfaces. The provisions of equal costs surfaces are determined from the condition of the flow of the medium constancy between them. Conservation equations, written on the flow lines, are simplified and take the form of ordinary differential equations on the longitudinal coordinate. So that to calculate the partial derivatives on the transverse coordinate, which are present in the right part of the differential equations, the grid solutions are presented in the form of series expansion. The system of constructed ordinary differential equations is solved numerically.

Impact of Breast Cancer Patient Demographics and Treatment Type on Time From Diagnosis to Adjuvant Treatment at a Diverse Academic Medical Center

Impact of Breast Cancer Patient Demographics and Treatment Type on Time From Diagnosis to Adjuvant Treatment at a Diverse Academic Medical Center

A direct time measurement technique for determining the longitudinal coordinate in thin-walled drift tubes

Techniques for measuring the longitudinal coordinates in drift tubes are considered. It is shown that the use of the direct timing method to determine the longitudinal coordinates helps to obtain the longitudinal resolution several times better relative to the charge division method and is suitable for long tubes. The implementation of this method provides a means for designing coordinate detectors based on drift tubes with the two-dimensional readout and a high response speed, which will not be very complex.

Genetic diversity, population structure and phenotypic variation in European Salix viminalis L. (Salicaceae)

To investigate the potential of association genetics for willow breeding, Salix viminalis germplasm was assembled from UK and Swedish collections (comprising accessions from several European countries) and new samples collected from nature. A subset of the germplasm was planted at two sites (UK and Sweden), genotyped using 38 SSR markers and assessed for phenological and biomass traits. Population structure, genetic differentiation (F ST ) and quantitative trait differentiation (Q ST ) were investigated. The extent and patterns of trait adaptation were assessed by comparing F ST and Q ST parameters. Of the 505 genotyped diploid accessions, 27 % were not unique. Genetic diversity was high: 471 alleles was amplified; the mean number of alleles per locus was 13.46, mean observed heterozygosity was 0.55 and mean expected heterozygosity was 0.62. Bayesian clustering identified four subpopulations which generally corresponded to Western Russia, Western Europe, Eastern Europe and Sweden. All pairwise F ST values were highly significant (p < 0.001) with the greatest genetic differentiation detected between the Western Russian and the Western European subpopulations (F ST = 0.12), and the smallest between the Swedish and Eastern European populations (F ST = 0.04). The Swedish population also had the highest number of identical accessions, supporting the view that S. viminalis was introduced into this country and has been heavily influenced by humans. Q ST values were high for growth cessation and leaf senescence, and to some extent stem diameter, but low for bud burst time and shoot number. Overall negative clines between longitudinal coordinates and leaf senescence, bud burst and stem diameter were also found.

Study of gas-sheared liquid film in horizontal rectangular duct using high-speed LIF technique: Three-dimensional wavy structure and its relation to liquid entrainment

The flow of a liquid film sheared by high velocity gas stream in a horizontal rectangular duct was investigated using a high-speed laser-induced fluorescence technique. Measurements of local film thickness were resolved in both longitudinal and transverse coordinates with high spatial and temporal resolution. It was found that the generation of fast and slow ripples by the disturbance waves was qualitatively the same as it was observed earlier in completely different conditions. The transverse size and curvature of the disturbance waves and ripples were measured. A relationship between the three-dimensional structure of ripples on top of disturbance waves and the two mechanisms of liquid entrainment, known as ‘bag break-up’ and ‘ligament break-up’, is proposed.

KANTBP 3.0: New version of a program for computing energy levels, reflection and transmission matrices, and corresponding wave functions in the coupled-channel adiabatic approach

A FORTRAN program for calculating energy values, reflection and transmission matrices, and corresponding wave functions in a coupled-channel approximation of the adiabatic approach is presented. In this approach, a multidimensional Schrodinger equation is reduced to a system of the coupled second-order ordinary differential equations on a finite interval with the homogeneous boundary conditions of the third type at the left- and right-boundary points for continuous spectrum problem. The resulting system of these equations containing the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite element method. As a test desk, the program is applied to the calculation of the reflection and transmission matrices and corresponding wave functions for the two-dimensional problem with different barrier potentials.

Solution to the paradox of the linear stability of the Hagen-Poiseuille flow and the viscous dissipative mechanism of the emergence of turbulence in a boundary layer

It has been shown that the conclusion of the linear instability of the Hagen-Poiseuille flow at finite Reynolds numbers requires the refusal of the use of the traditional “normal” form of the representation of disturbances, which implies the possibility of separation of variables describing disturbances as functions of the radial and longitudinal (along the axis of a tube) coordinates. In the absence of such separation of variables in the developed linear theory, it has been proposed to use a modification of the Bubnov-Galerkin theory that makes it possible to take into account the difference between the periods of the longitudinal variability for different radial modes preliminarily determined by the standard application of the Galerkin-Kantorovich method to the evolution equation of extremely small axisymmetric disturbances of the tangential component of the velocity field. It has been shown that the consideration of even two linearly interacting radial modes for the Hagen-Poiseuille flow can provide linear instability only in the presence of the mentioned conditionally periodic longitudinal variability of disturbances along the axis of the tube, when the threshold Reynolds number Reth(p) is very sensitive to the ratio p of two longitudinal periods each describing longitudinal variability for its radial disturbance mode. In this case, the threshold Reynolds number can tend to infinity, Reth(p) → ∞, only at p = p k = k, p = p 1/k = 1/k, and $p = p_{\sqrt k } = [k + 1 \pm \sqrt {(k + 1)^2 - 4} ]/2$ , where k = 1, 2, 3, …. The minimum Reynolds number Reth(p) ≈ 448 (at which p ≈ 1.527) for the linear instability of the Hagen-Poiseuille flow quantitatively corresponds to the condition of the excitation of Tollmien-Schlichting waves in the boundary layer, where Reth = 420. Similarity of the mechanisms of linear viscous dissipative instability for the Hagen-Poiseuille flow and Tollmien-Schlichting waves has been discussed. Good quantitative agreement has been obtained between the phase velocities of the vortex disturbances and the experimental data on the velocities of the leading and trailing edges of turbulent “puffs” propagating along the axis of the tube.

A 1D higher gradient model derived from Koiter’s shell theory

A thin rectangular plate is modelled as an (initially flat) shell. Following Koiter, the two fundamental forms of the deformed middle surface are then used to define the strain measures of the body. On the middle surface of the plate two local coordinates are introduced: we will call them longitudinal and transversal, respectively. It is assumed that the components of the displacement field which characterize the middle surface kinematics can be expressed as a product of two functions: one defined along the longitudinal coordinate and one defined along the transversal coordinate. Given an explicit expression of the latter functions, the 2D plate fields are reduced to 1D ones. The functions of the transversal coordinate are chosen so that the stretch along it together with the membrane shear vanish. It is worth noting that the linearization of these constraints leads to the well-known Vlasov’s assumptions. It is shown that by modelling each side of a thin walled beam as a 1D continuum, the entire assembly can be reduced to a 1D model as well. This procedure gives rise to an hyperelastic 1D beam model in which at least the warping effect is taken into account. The main features of the model are shown by means of some simple applications.

Asymptotic solution of the diffusion equation in slender impermeable tubes of revolution. I. The leading-term approximation.

The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problem and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.

Analyzing ion distributions around DNA

We present a new method for analyzing ion, or molecule, distributions around helical nucleic acids and illustrate the approach by analyzing data derived from molecular dynamics simulations. The analysis is based on the use of curvilinear helicoidal coordinates and leads to highly localized ion densities compared to those obtained by simply superposing molecular dynamics snapshots in Cartesian space. The results identify highly populated and sequence-dependent regions where ions strongly interact with the nucleic and are coupled to its conformational fluctuations. The data from this approach is presented as ion populations or ion densities (in units of molarity) and can be analyzed in radial, angular and longitudinal coordinates using 1D or 2D graphics. It is also possible to regenerate 3D densities in Cartesian space. This approach makes it easy to understand and compare ion distributions and also allows the calculation of average ion populations in any desired zone surrounding a nucleic acid without requiring references to its constituent atoms. The method is illustrated using microsecond molecular dynamics simulations for two different DNA oligomers in the presence of 0.15 M potassium chloride. We discuss the results in terms of convergence, sequence-specific ion binding and coupling with DNA conformation.

Axial buckling analysis of vertically aligned ensembles of single-walled carbon nanotubes using nonlocal discrete and continuous models

Several novel models, based on the nonlocal stress theory, on the lateral buckling of two- and three-dimensional (2D and 3D) ensembles of vertically aligned single-walled carbon nanotubes (SWCNTs) are developed. The existing van der Waals forces between the constitutive atoms of the neighboring SWCNTs are modeled by an elastic layer, and each individual SWCNT is modeled using the nonlocal Rayleigh beam theory. The governing equations for lateral buckling of both 2D and 3D SWCNTs ensembles due to axial compressive loads are derived. These are called discrete models since the lateral deformations of each SWCNT only express in terms of the longitudinal coordinate of the SWCNT. It will be revealed that the lateral deformation of SWCNTs can be also stated in terms of two and three coordinates for 2D and 3D ensembles of SWCNTs, respectively. The resulting models are called continuous models. Based on both discrete and continuous models, the critical axial buckling loads for both 2D and 3D ensembles of SWCNTs for a special case, when the outer SWCNTs are prohibited from any lateral movement, are obtained. A reasonably good agreement between the results of the discrete model and those of the continuous model is reported. Subsequently, the roles of small-scale parameter, intertube distance, and number of SWCNTs on the critical buckling loads are examined. The obtained results and the proposed models in the present work would be very helpful in design and fabrication of 2D and 3D groups of vertically aligned SWCNTs, particularly those whose main duties are to transfer securely the applied axial forces.