Nonsymmetrical System Research Articles

Stereoscopic High-Speed Imaging For 3D Tracking Of Coughed Saliva Droplets In The Context Of COVID-19 Spreading

Droplets generated by talking and coughing play a major role in the spreading of COVID-19. There is thus a need for accurate measurements of the physical properties of exhaled droplets, including their number, speed and direction. Several challenges are associated with imaging coughed droplets such as high droplet speed near the mouth where both short exposure time to freeze droplet motion and kHz recording rate to resolve their displacement is required. In addition, as a highly non-symmetrical spray system is formed from a cough, three-dimensional visualization is necessary to faithfully capture coughing events. In this work, a 3D, high-speed imaging technique is presented that facilitates such challenging measurements. A laser beam with a probe volume 15 mm thick - 120 mm high is formed and illuminates droplets exiting the mouth imaged using two high-speed cameras. Data has been recorded for four different male subjects where 3D droplet speed and direction has been extracted for 10 coughs each. The maximum speed for a single cough has been estimated to vary between 11 and 45 m/s and the average droplet speed has been found to be in the range 6.5 - 8.7 m/s. These results will be used as input parameters to improve simulation models of droplet transport in the context of virus spreading.

Decarbonylative Reductive Coupling of Aromatic Esters by Nickel and Palladium Catalyst

Abstract Ni or Pd-catalyzed decarbonylative reductive couplings of aromatic esters were developed. A range of (hetero)aromatic esters was applicable to these reductive homocoupling reactions. Moreover, it was found that Pd-catalysis enables a reductive decarbonylative cross-coupling between two different aromatic esters to afford a nonsymmetrical biaryls system.

Synthesis, mesomorphic and geometrical approaches of new non-symmetrical system based on central naphthalene moiety

ABSTRACT New non-symmetrical homologues series based on central naphthalene moiety, (E)-4-(4-(hexyloxy phenyl diazenylnaphthalene-1-yl-4ʹ-alkoxybenzoate (I 6/n), were synthesised and their mesomorphic properties was investigated. The prepared group constitutes four homologues bearing two terminal alkoxy chains of different proportionation. Elemental analyses, FT-IR and NMR spectroscopy were carried out to elucidate their molecular structures. Examination of their mesomorphic properties, were conducted via differential scanning calorimetry (DSC) and polarised optical microscopy (POM). DSC and POM investigations indicated that all the synthesised homologues are monomorphic possessing the enantiotropic nematic (N) phase. A comparative study was conducted between the present investigated central naphthalene series (I 6/n) and their corresponding central benzene analogues (II 6/n). The results indicated that, the mesophase type and stability as well as the mesophase temperature are affected by the protrusion of the naphthalene group. Theoretical calculations are in accordance with the experimental values of the investigated series. Moreover, the location of naphthalene group in the centre of the molecular geometry, increases the rigidity of the molecule, thus affects their thermal and physical parameters. The experimentally determined nematic stability was correlated with the calculated parameters and the study reveals that there are many factors sharing together to different extents in the enhancement of the behaviour of the observed nematic phase, depending on the different proportionation of the terminal lengths.

Improved observer-based quadrature signal generator

In this paper, an improved quadrature signal generator (QSG) parameter tuning procedure is proposed, based on a modification of an existing adaptive observer QSG algorithm. Namely, in the existing solution an observer-based QSG is proposed with a parameter tuning procedure that results in a bandwidth frequency equal to the QSG input signal frequency, while in this paper, a modification of this parameter tuning procedure is proposed that enables the QSG to operate with increased bandwidths. A comparative analysis is presented, which evaluates both the existing solution and the solution based on the novel observer parameter tuning algorithm. Also, it is shown that when existing and proposed observer-based QSG operates with bandwidths that surpass the input signal angular frequency, the high-pass resulting observer frequency characteristics are obtained. By using frequency responses, and simulation and experimental tests, which include basic QSG operation and the PLL based on the proposed QSG, the resulting improvements are presented and compared. Also, the adaptive observer-based QSG with improved parameter tuning procedure is employed in the positive sequence component separation algorithm for the nonsymmetrical three-phase system, which represents an original application this type of QSG structure.

Improvement of a computer-aided alignment algorithm for the nonsymmetric off-axis reflective telescope

Due to complications of the off-axis three-mirror anastigmat (TMA) telescope, each optical element in the off-axis TMA telescope is introduced with theoretical eccentricity and tilt. Moreover, the introduction of freeform surfaces and other optical elements with complex surface features generally causes the initial alignment accuracy of the optical path to be low. A large initial alignment error amplifies the sensitivity of the misalignment calculation accuracy to the measurement error of the Zernike coefficient, resulting in difficulty obtaining convergence results for a computer-aided alignment algorithm. Considering the above issues, the alignment sensitivity of each component in the optical path is analyzed in this. The large conditional number of the sensitivity matrix results in poor algorithm robustness. Thus, an adaptive damping factor least-squares algorithm model is proposed and derived to improve the efficiency of the classical least-squares algorithm. A method for piecewise optimization of the damping factor is also deduced. Experiments based on a 0.6 m off-axis TMA telescope verify the effectiveness of the algorithm. Simulation and integration experiments show that the proposed method can reduce the accuracy requirements of the initial alignment and improve the adaptability of Zernike coefficient measurement noise. The alignment procedure is carried out for three iterations, and the average of the five field-of-view wave aberration values is enhanced from 2.1λ (RMS; λ=632.8nm) to 0.09λ (average). The improved algorithm can solve the large initial alignment error of a nonsymmetrical off-axis reflective optical system with a freeform surface as well as the problem of the low success rate of the misalignment value due to low Zernike coefficient measurement accuracy.

Optimization of Velocity Mode in Buslaev Two-Contour Networks via Competition Resolution Rules

<p>In computer networks based on the principle of packet switching, the important transmitting function is to maintain packet queues and suppress congestion. Therefore, the problems of optimal control of the communication networks are relevant. For example, there are users, and no more than a demand of one user can be served simultaneously. This paper considers a discrete dynamical system with two contours and two common points of the contours called the <em>nodes</em>. There are <em>n</em> cells and particles, located in the cells. At any discrete moment the particles of each contour occupy neighboring cells and form a cluster. The nodes divide each contour into two parts of length and (non-symmetrical system). The particles move in accordance with rule of the elementary cellular automaton 240 in the Wolfram classification. Delays in the particle movement are due to that more than one particle cannot move through the node simultaneously. A competition (conflict) occurs when two clusters come to the same node simultaneously. We have proved that the spectrum of velocities contains no more than two values for any fixed <em>n , d</em> and <em>l</em>. We have found an optimal rule which minimizes the average velocity of clusters. One of the competition clusters passes through the node first in accordance with a given competition rule. Two competition resolutions rules are introduced. The rules are called input priority and output priority resolution rules. These rules are Markovian, i.e., they takes into account only the present state of the system. For each set of parameters <em>n, d</em> and <em>l</em>, one of these two rules is optimal, i.e., this rule maximizes the average velocity of clusters. These rules are compared with the left-priority resolution rule, which was considered earlier. We have proved that the spectrum of velocities contains no more two values for any fixed <em>n, l,</em> and <em>d</em>. We have proved that the input priority rule is optimal if , and the output priority rule is optimal if .</p>

Effective length factor of a non-symmetrical cross-bracing system with a discontinuous diagonal

A non-rectangular frame panel usually contains an asymmetrical cross-bracing system with interrupted diagonals, leading to a more complicated buckling behavior than a symmetrical bracing system with continuous diagonals. There have been many studies of the stability theory of symmetrical cross-bracing systems, but few related to non-symmetrical systems. In this study, we analyzed elastic out-of-plane buckling of a general non-symmetrical cross-bracing system with a discontinuous diagonal. The discontinuous and continuous diagonals have different material and geometrical properties, and are not intersected at their mid-spans. A characteristic equation is presented to compute the critical loading of a non-symmetrical cross-bracing system when the supporting diagonal is under either compression or tension. The results show that the characteristic equation of a non-symmetrical bracing system can be transformed into a form the same as that of a geometrically mono-symmetrical system. To facilitate design applications, direct closed-form empirical equations of effective length factor are established for a general non-symmetrical cross-bracing case. The validity of the proposed empirical equations was verified by comparing predicted and theoretical results, and those from a stiffness approach.

Apparent efficiency of serially coupled columns in isocratic and gradient elution modes

The goal of this work was to understand the variation of apparent efficiency when serially coupling columns with identical stationary phase chemistries, but with differences in their kinetic performance. For this purpose, a mathematical treatment was developed both for isocratic and gradient modes to assess the change in plate numbers and peak widths when coupling arbitrary several columns. To validate the theory, experiments were also carried out using various mixtures of compounds, on columns packed with different particle sizes, to mimic highly efficient (new, not used) and poorly efficient columns (used one with many injections). Excellent agreement was found between measured and calculated peak widths. The average error in prediction was about 5% (which may be explained by the additional volume of the coupling tubes).In isocratic mode, the plate numbers are not additive when the coupled columns possess different efficiencies, and a limiting plate count value can be calculated depending on the efficiency and length of the individual columns. Theoretical efficiency limit can also be determined assuming one column in the row with infinite efficiency.In gradient elution mode, the columns’ order has a role (non-symmetrical system). When the last column has high enough efficiency, the gradient band compression effect may outperform the competing band broadening caused by dispersive and diffusive processes (peak sharpening). Therefore, in gradient mode, the columns should generally be sequentially placed according to their increasing efficiency.

On the Design of Sparse but Efficient Structures in Operations

It is widely believed that a little flexibility added at the right place can reap significant benefits for operations. Unfortunately, despite the extensive literature on this topic, we are not aware of any general methodology that can be used to guide managers in designing sparse (i.e., slightly flexible) and yet efficient operations. We address this issue using a distributionally robust approach to model the performance of a stochastic system under different process structures. We use the dual prices obtained from a related conic program to guide managers in the design process. This leads to a general solution methodology for the construction of efficient sparse structures for several classes of operational problems. Our approach can be used to design simple yet efficient structures for workforce deployment and for any level of sparsity requirement, to respond to deviations and disruptions in the operational environment. Furthermore, in the case of the classical process flexibility problem, our methodology can recover the k-chain structures that are known to be extremely efficient for this type of problem when the system is balanced and symmetric. We can also obtain the analog of 2-chain for nonsymmetrical system using this methodology. This paper was accepted by Yinyu Ye, optimization.

On the Design of Sparse But Efficient Structures in Operations

It is widely believed that little flexibility added at the right place can reap significant benefits for operations. Unfortunately, despite the extensive literature on this topic, we are not aware of any general methodology that can be used to guide managers to design sparse (i.e., slightly flexible) and yet efficient operations.We address this issue using a distributionally robust approach to model the performance of a stochastic system under different process structures. We use the dual prices obtained from a related conic program to guide managers in the design process. This leads to a general solution methodology for the construction of efficient sparse structures for several classes of operational problems.Our approach can be used to design simple yet efficient structures for workforce deployment and for any level of sparsity requirement, to respond to deviations and disruptions in the operational environment. Furthermore, in the case of the classical process flexibility problem, our methodology can recover the k-chain structures that are known to be extremely efficient for this type of problem when the system is balanced and symmetric. We can also obtain the analog of 2-chain for non-symmetrical system using this methodology.

HD +ortho-/para-H2rotational energy transfer non-reactive scattering at low astrophysical temperatures: 2 K ≲ T ≲ 300 K

State-resolved integral cross sections and corresponding thermal rate coefficients are computed for the HD + ortho -/ para -H 2 rotational energy transfer collision at low temperatures of astrophysical interest: 2 K ≲ T ≲ 300 K. A recent original full-dimensional H 2 -H2 potential energy surface (PES) was adopted and appropriately modified for the current non-symmetrical four-atomic system.

Effect of bifocal lens on propagation of Bessel beam

In this paper, we study the influence of the bifocal lens on the focusing properties of Bessel beam. Based on the generalized Huygens-Fresnel diffraction integral, a more general expression of the light intensity distribution of nonsymmetrical optical system which is described by 4×4 matrix is deduced. The optical field distribution of Bessel beam passing through bifocal lens is given and simulated numerically. The influence of the focal length of the bifocal lens on Bessel beam is analyzed in detail. The generalized expression of the light intensity distribution can involve three cases, i.e., ordinary lens, bifocal lens and cylindrical lens. The greater the astigmation, the poorer the bottle beam quality will be. The ability to imprison microscopic particles decreases.

Developments in excavation bracing systems

Modern bracing systems for retaining soil in excavations and their indications and differentiating features are summarized. A recent innovation in a widely used system, cast-in-drilled-hole concrete pile walls, is described. The innovation consists of the use of longitudinal reinforcement distributed non-uniformly around the perimeter of the pile section in order to more efficiently resist bending moment. This non-symmetrical distribution of reinforcement results in a significant reduction in the amount of steel required. Practical situations where the new system has advantages over existing bracing systems are described. Significant reductions in material costs, reduced transportation costs, and simpler site operations result with the innovative system. These benefits are ultimately associated with a reduction in total cost and an extension of the economical range of applicability of this pile wall system. Results of a full-scale experimental demonstration are described, in which a segment of cut-and-cover underground high-speed rail line was constructed using this non-symmetrical piling system. In this segment, conventional symmetrically reinforced and the new non-symmetrically reinforced piles were instrumented. The new system resulted in smaller deformations and did so with savings of longitudinal steel of 44%.

비대칭 오차요인이 있는 편심 광학계에서의 종수차 계산

줌렌즈에서 특정 렌즈군을 이동하여 손떨림 보정을 하는 광학적 방법에서는 광학계 설계단계에서 디센터(decenter)를 고려하여 설계한다. 이 때 여러 가지 광학설계 소프트웨어들은 디센터를 포함한 비대칭 오차요인이 있는 경우에 여러 가지 광학 성능들을 쉽게 계산할 수 있지만, 편심 광학계에 대한 정확한 분석이 부족하여 종수차 계산시에는 일부 계산오차가 생긴다. 특히 왜곡의 경우에는 비정상적으로 계산되는데, 이는 비대칭 오차요인이 있는 편심 광학계에서는 근축광선 추적이 제대로 되지 않기 때문이다. 본 논문에서는 이러한 손떨림으로 인한 디센터나 틸트(tilt)와 같은 비대칭 요인이 발생하는 줌렌즈에서 편심 광학계에 대한 근축광선 추적식을 새로이 유도하고, 이를 이용하여 비대칭 요인을 갖는 결상계의 종수차를 정확히 계산하는 방법을 제안한다. 이러한 편심 광학계에 대한 종수차 계산 방법은 줌렌즈의 손떨림 보정에 실제로 사용할 수 있다. When the optical image stabilization is implemented by moving one of the lens groups in a zoom system, decentration should be considered in the optical design process. Although it is partially possible to calibrate optical performances in an optical system with non-symmetrical elements by using a lot of commercial software, the results of calibrating longitudinal aberrations have some calibration errors because of the lack of precise consideration of decentered optical systems. In particular, the amount of distortion in paraxial ray tracing is different from the experimental value because paraxial ray tracing in the optical system is not useful. In this paper, in order to solve this problem being from various commercial lens design software, the set of equations of paraxial ray tracing in a zoom lens system with the non-symmetrical elements like decentration or tilt are theoretically induced. Then, the methods to calibrate the equations of longitudinal aberrations by using these equations in a non-symmetrical optical system are presented. The method of calibrating longitudinal aberrations can in practice be used to correct hand shaking effects in a zoom lens system.

Generalized formulas for stochastic electromagnetic beams on inverse propagation through nonsymmetrical optical systems

Generalized propagation formulas for the elements of the cross-spectral density matrix of stochastic electromagnetic beams on inverse propagation through an axially symmetrical or nonsymmetrical optical system are derived with the help of Fourier transform and inverse Fourier transform. As an example, we apply the formula to the inverse source problem of stochastic electromagnetic Gaussian Schell-model beams.

Cross-spectral density matrix of a random electromagnetic beam propagating through an apertured axially nonsymmetrical optical system

Using the fact that a hard-edged rectangular aperture function can be approximated by a two-dimensional multi-Gaussian series, analytic formulas for the elements of the cross-spectral density matrix of a random electromagnetic beam truncated by a rectangular aperture and passing through an axially nonsymmetrical optical system is derived. The analysis is illustrated by numerical examples relating to changes in the spectral degree of polarization of electromagnetic Gaussian Schell-model beams propagating through free space, focal system and dual-focus system. In particular, the effect of the size of the hard aperture on the spectral degree of polarization of the beam along its optical axis is discussed.

Elliptical Hermite-cosine-Gaussian beam and its propagation characteristics

A new kind of light beam named the elliptical Hermite-cosine-Gaussian beam (EHCosGB) is introduced in this paper by using a tensor method. An analytical propagation expression for an EHCosGB passing through an axially nonsymmetrical optical system is derived by using vector integration. By virtue of numerical simulations, the propagation properties of EHCosGBs through a free space and a focusing system are illustrated, respectively. The results indicate that an EHCosGB on the input plane can be regarded as the elliptical Hermite-Gaussian beam (EHGB) modulated by the cosine curves with certain oscillating frequency. Some of the neighboring lobes are combined and TEM-type Hermite-cosh-Gaussian beams are formed during the propagation.

Propagation of elliptical cosh-Gaussian beams and off-axial elliptical cosh-Gaussian beams in apertured optical systems

Based on the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical propagation expression for an elliptical cosh-Gaussian beam (EChGB) truncated by an elliptical aperture and passing through an axially nonsymmetrical optical system is obtained by use of vector integration. Furthermore, the analytical propagation expression for a truncated off-axial EChGB is derived as an application example. Some numerical simulations are given to illustrate the propagation properties of EChGBs and off-axial EChGBs passing through a free space with an elliptical aperture.

Decentred elliptical flat-topped light beams and their coherent and incoherent combinations

A new kind of laser beam called the decentred elliptical flat-topped light beam (DEFTB) is introduced in this paper by using a tensor method. Based on the generalized Collins integral, the propagation formula for a DEFTB passing through an axially nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be reduced to the formulae for the generalized decentred elliptical Gaussian beam and elliptical flat-topped light beam under certain conditions. As a typical application example of the derived formula, the propagation characteristics of a DEFTB in a thin lens system are calculated and discussed. Furthermore, the generalized laser beam arrays with rectangular symmetry and radial symmetry by using DEFTBs as fundamental modes are constructed and the propagation properties of both a coherent and an incoherent combination of DEFTBs in the thin lens system with numerical examples are investigated.

Focal shift and focal switch of focused truncated elliptical Gaussian beams

It is shown that when a generalized astigmatic elliptical Gaussian beam (EGB) propagates in a focusing optical system with an elliptical aperture, the effect of focal shift and focal switch can appear. An analytical propagation expression for an EGB through an axially nonsymmetrical optical system with a thin lens and an elliptical aperture is derived. Some numerical simulations are illustrated for its focal shift and focal switch, and some physical explanations are also given.