Angle Φ0 Research Articles

Study on the motion characteristics of Janus based on the squirmer model in the flow

The motion characteristics of Janus in the flow are studied numerically using the lattice Boltzmann method based on the squirmer model. The effects of velocity ratio J on the right and left hemisphere surface of Janus, particle Reynolds number Rep, flow Reynolds number Rec, initial orientation angle φ0 on Janus trajectory, and lateral equilibrium position yeq/H are analyzed. The results showed that, for the motion of Janus in stationary power-law fluids in a channel, Janus moves randomly in a small space in shear-thickening fluids when Rep is low and exhibits three motion modes at Rep = 5. The larger the J value, the easier it is for Janus to reach yeq/H. The higher the Rep, the closer the yeq/H is to the lower wall. In shear-thinning fluids, the motion of Janus exhibits significant randomness at Rep = 0.5 and 1, reaches the same yeq/H at Rep = 2 and 3, and tends toward yeq/H near the centerline and along the upper wall, respectively, at Rep = 4 and 5. For the motion of Janus particles in a channel flow of power-law fluids, in shear-thinning fluids, no matter what value J is, Janus reaches yeq/H on the centerline. The lower the Rep, the closer the yeq/H is to the wall. Two particles move toward yeq/H when Rep ≥ 1. The higher the Rep, the closer the yeq/H is to the centerline. The two particles will exhibit the upstream mode at Rep = 2. Two particles eventually reach yeq/H at different Rec. When φ0 > 0°, the two particles first eventually tend toward yeq/H = 0.2 and 0.8. When the value of φ0 is negative, the larger the absolute value of φ0 and higher the Rep, the more likely particles are to exhibit upstream mode.

Research on a safety evaluation system for railway-tunnel structures by fuzzy comprehensive evaluation theory

Long-term health detection of railway-tunnel is the development direction and trend of future railway tunnel research. Based on the actual engineering of a railway tunnel, this study developed a safety evaluation model for railway tunnel structures using a fuzzy comprehensive evaluation method and examined a health state evaluation method suitable for most railway tunnel structures. The results showed that the evaluation method comprehensively reflected the impact of various factors, which had strong practicality. The evaluation results were clear, accurate, and consistent with engineering practice. When using the safety factor index to study the stress of a railway tunnel structure, Midas/civil analysis showed that different levels of the surrounding rock structural vault in railway tunnels were in a tensile, control-bearing capacity state. When calculating safety factors, the range of a 60° central angle of a railway tunnel vault was calculated according to the tensile control-bearing capacity. Theoretical formulas of the range of the center angle φ0 of the vault tension zone were derived and then verified by experiments and numerical analysis.

A precision relation between Γ(K → μ+μ−)(t) and mathcal{B}left({K}_Lto {mu}^{+}{mu}^{-}right)/mathcal{B}left({K}_Lto gamma gamma right)

We find that the phase appearing in the unitarity relation between mathcal{B}left({K}_Lto {mu}^{+}{mu}^{-}right) and mathcal{B}left({K}_Lto gamma gamma right) is equal to the phase shift in the interference term of the time- dependent K → μ+μ− decay. A probe of this relation at future kaon facilities constitutes a Standard Model test with a theory precision of about 2%. The phase has further importance for sensitivity studies regarding the measurement of the time-dependent K → μ+μ− decay rate to extract the CKM matrix element combination mid {V}_{ts}{V}_{td}sin left(beta +{beta}_sright)mid approx {A}^2{lambda}^5overline{eta} . We find a model-independent theoretically clean prediction, cos2φ0 = 0.96 ± 0.03. The quoted error is a combination of the theoretical and experimental errors, and both of them are expected to shrink in the future. Using input from the large-NC limit within chiral perturbation theory, we find a theory preference towards solutions with negative cos φ0, reducing a four-fold ambiguity in the angle φ0 to a two-fold one.

О стабильности капель катализатора на границе контакта пар-жидкость-кристалл в процессе роста нитевидных нанокристаллов

The paper provides a physical justification for the wettability conditions for a crystalline surface of a limited area by a small-volume catalytic liquid at the end of a growing nanowires (NW) characterized by a contact angle β, which contributes to a fundamental understanding of the nature of the contact angle of catalyst drops at the top of the NW. It is shown that under the conditions of stationary growth of NWs with a transverse singular face, there are only values of the angles β and γ (the angle of inclination of the side surface of the crystal to this face), which correspond to the minimum increment of the free energy of the three-phase system αLVcosβ + αSL = αSVcosγ and determine the stability of the catalyst drop at the top of the NW. With the growth of cylindrical NWs, the conditions of indifferent equilibrium are realized at the drop wetting perimeter. A drop, due to the dissolution of a crystallizing substance or its separation from a liquid solution, can take an equilibrium shape with a contact angle β that does not satisfy the equilibrium contact angle condition θ in the Young equation. A concentric break (rib) at the NW tip should increase the observed wetting angle θ and lead to contact angle hysteresis. The restrictions imposed on the value of the contact angle of a stable catalyst drop at the top of the NW are determined. The catalyst drop will take an equilibrium shape if the hysteresis angle β is in the range θ < β ≤ θ' + γ (θ' is the wetting angle of the NW side walls). For the growth of semiconductor NWs in the form of a straight cylinder, γ = 90° and therefore always β > 90°. It is shown that the direction of displacement of the three-phase line relative to the droplet surface is determined by the growth angle φ0: for the nonwetting growth mode of NWs (with a transverse face) φ0 = β – γ; for the wetting growth mode (with the end surface curved near the three-phase line)

Magnetic phase diagram of helimagnetic Ba(Fe1−xScx)12O19 (0 ≤ x ≤ 0.2) hexagonal ferrite

Hexagonal ferrite Ba(Fe1−xScx)12O19 is an important magnetic oxide material in both science and engineering because it exhibits helimagnetism around room temperature (300 K). In this study, the magnetic phase diagram of Ba(Fe1−xScx)12O19 consisting of ferri-, heli-, antiferro-, and paramagnetic phases has been completed through magnetization and neutron diffraction measurements. The magnetic phase transition temperature to paramagnetism decreases with the increase in x, and the temperature at which the magnetization reaches a maximum, which corresponds to the magnetic phase transition from heli- to ferrimagnetism, is determined for low x crystals. The temperatures at which helimagnetism appears are precisely determined by observing the magnetic satellite reflection peaks in neutron diffraction at various temperatures, which characterize helimagnetism. Based on these results, the magnetic phase diagram of the Ba(Fe1−xScx)12O19 system is constructed in the T-x plane. Helimagnetism appears at x ≳ 0.06, and magnetism with antiferromagnetic components appears as the extension phase of helimagnetism at x ≳ 0.19 through the coexistence region. The turn angle ϕ0 of the helix for each x crystal is calculated from the relationship, ϕ0 = 2πδ, where δ is the incommensurability. The turn angle ϕ0 decreases with the increase in temperature for the same x crystal, and increases with the increase in x at the same temperature. Furthermore, it is found that there are clear thresholds at which ϕ0 cannot take values between 0°<ϕ0 ≲ 90° and 170° ≲ ϕ0< 180°.

О расчете аберрационных коэффициентов для цилиндрического зеркала

Angular аberration coefficients for a cylindrical mirror up to the fourth order in the vicinity of the azimuthal angle φ0 = 0 and in the vicinity of an arbitrary angle ϑ0 value are analytically obtained. A method is developed for calculating aberration coefficients of arbitrary order and in the vicinity of an arbitrary point based on the results of calculating several trajectories. Analytical and numerical methods for calculating aberration coefficients up to the fourth order are productive in the vicinity of the point (φ0 = 0, ϑ0) that coincide with high accuracy.

Numerical study of solidification of a drop with a growth angle difference

This study presents the direct numerical results of a drop solidifying on a plate, in which the difference between the growth angles is considered. The drop is two-dimensional with the presence of the left and right triple points, and the method used is a front-tracking technique. The growth angles at the right (ϕgr1) and left (ϕgr2) triple points are not equal, i.e. Δϕgr = ϕgr1–ϕgr2 ≠ 0°. Unlike the identical growth angles, the growth angle difference results in an asymmetric drop after complete solidification. In the presence of the solid-to-liquid density ratio ρsl < 1.0 (i.e. volume expansion), the tip of the solidified drop shifts more to the right as Δϕgr increases in the range of 0°–12°. In addition, the angle at the solidified drop top (i.e. tip angle) increases with Δϕgr. We also pay attention to the effects of some other parameters (such as the wetting angle ϕ0, the growth angle ϕgr1 and ρsl) on the solidification process with the growth angle difference. The results reveal that the growth angle varied in the range of 6°–24° has a minor effect on the movement of the tip to the right while the tip shift increases with an increase in ϕ0 in the range of 60°–130° or with a decrease in ρsl in the range of 0.8–1.1. The tip angle increases with an increase in ρsl or with a decrease in ϕgr1 or ϕ0. We also investigate the solidification process under the influence of the Bond number.

Numerical Simulation of Spear Motion as Game Items

Game development in 3D is mostly done by characters, items and the environment. Game items such as character weapons modeled in 3D will be the attraction of a game. In this paper, spear motion as a game items is modeled in 3D. Nonlinear Equations Six Degrees of Freedom (6 DOF) are used for mathematical models of spear motion. The parameters studied in the motion model are: geometry, mass and aerodynamics. Spear aerodynamic parameters were analyzed using the Datcom method. Numerical simulation of mathematical models of spear motion with variations in the initial velocity of the throw and the direction of the throw. From the results of numerical simulation, the maximum range R = 131.7 m at the initial velocity V0 = 40 m/s, the direction of throw (angle θ0 = 35 deg, angle φ0 = 10 deg, ψ0 = 0 deg). And the maximum height Hmax = 12.18 m is achieved at the initial velocity V0 = 20 m/s, direction of throw (angle θ0 = 35 deg, angle φ0 = 40 deg, angle ψ0 = 0 deg).

Numerical study of a liquid drop on an inclined surface with solidification

Drop deformation and solidification on an inclined surface appears in many engineered and industrial applications. In this paper, we thus present a front-tracking-based simulation of the deformation and solidification process of a liquid drop on a plate tilted at an angle ϕp in the range of 10°–80°. The plate temperature is kept fixed at a value below the liquid-solid phase change temperature of the drop liquid while the drop is assumed to stick to the surface. The drop experiences some oscillating deformation, and when it reaches almost a steady state shape the solidification process starts undergoing volume expansion (ρsl = 0.9). Increasing ϕp from 10° to 80° causes the liquid drop to experience more oscillations with larger amplitudes. The increase in ϕp makes the solidification process last longer and results in a more asymmetric solidified drop with an increase in the tip shift Δxt [i.e. Δxt/d = 0.1278(ϕp/ϕref) + 0.014 with d, apparent diameter of the liquid drop, and ϕref = 90°, reference angle]. However, varying ϕp in this range has a very minor effect on the height and the conical tip angle ϕt at the top of the solidified drop (i.e. Hs/d ≈ 0.784 and ϕt/ϕref ≈ 1.33). With the presence of the plate inclination (ϕp = 60°), the drop oscillates more strongly when increasing either the drop wetting angle ϕ0 (from 50° to 130°) or the Bond number Bo (from 0.1 to 3.2). These increases in ϕ0 and Bo also result in an increase in the solidification time τs and Δxt. In contrast, the tip angle is less affected by ϕ0 and Bo. Further investigations on ρsl and the growth angle ϕgr show that the solidified drop is more asymmetric with a decrease in ρsl from 1.0 to 0.8 while ϕgr varied from 0° to 28° induces no change in Δxt. Accordingly, the numerical results confirm that the plate angle and the initial liquid drop shape have strong impact on the asymmetry of the solidified drop, and volume expansion and the growth angle strongly affect the conical tip angle.

Polarimetry of photon echo on charged and neutral excitons in semiconductor quantum wells

Coherent optical spectroscopy such as four-wave mixing and photon echo generation deliver rich information on the energy levels involved in optical transitions through the analysis of polarization of the coherent response. In semiconductors, it can be applied to distinguish between different exciton complexes, which is a highly non-trivial problem in optical spectroscopy. We develop a simple approach based on photon echo polarimetry, in which polar plots of the photon echo amplitude are measured as function of the angle φ between the linear polarizations of the two exciting pulses. The rosette-like polar plots reveal a distinct difference between the neutral and charged exciton (trion) optical transitions in semiconductor nanostructures. We demonstrate this experimentally by photon echo polarimetry of a CdTe/(Cd, Mg)Te quantum well. The echoes of the trion and donor-bound exciton are linearly polarized at the angle 2φ with respect to the first pulse polarization and their amplitudes are weakly dependent on φ. While on the exciton the photon echo is co-polarized with the second exciting pulse and its amplitude scales as cosφ.

Analytical and numerical research of equivalent stabilizing force of stiffened truss chords

The aim of this paper is research of the equivalent stabilizing forces of the braced top flange of the truss. The study takes into account the initial bow imperfection e0 of the braced top flange and the im-perfection consisting in a twist of the roof girder’s principal plane by angle ϕ0(x). Moreover, axial force N3(x) in the top flange of the truss is assumed to be longitudinally parabolically variable. The values of the axial forces is: Nsupp in the support zone of the truss and Nspan in the central zone of truss. As part of this study parametric analyses of the equivalent stabilizing forces and the stress of the bracings depending on axial forces Nsupp and Nspan in the braced member were carried out. The results are compared with the results of numerical analyses of 3D models taking the geometric nonlinearity of the structure into account.

A numerical study of a liquid drop solidifying on a vertical cold wall

Solidification of a liquid drop on a vertical wall is a typical phase change heat transfer problem that exists widely in natural and engineering situations. In this study, we present the fully resolved two-dimensional simulations of such a problem by a front-tracking/finite difference method. Because of gravity, the liquid drop assumed stick to the cold wall shifts to the bottom during solidification. Numerical results show that the conical tip at the solidified drop top is still available with the presence of volume expansion, but the tip location is shifted downward, resulting in an asymmetric drop after complete solidification. The tip shift, height and shape of the solidified drop are investigated under the influences of various parameters such as the Prandtl number Pr, the Stefan number St, the Bond number, the Ohnesorge number Oh, and the density ratio of the solid to liquid phases ρsl. We also consider the effects of the growth angle ϕgr (at the triple point) and the initial drop shape (in terms of the contact angle ϕ0) on the solidification process. The most influent parameter is Bo whose increase in the range of 0.1–3.16 makes the drop more deformed with the tip shift linearly increasing with Bo. The tip shift also increases with an increase in ϕ0. However, increasing Oh (from 0.001 to 0.316), St (from 0.01 to 1.0) or ρsl (from 0.8 to 1.2) leads to a decrease in the tip shift. Concerning time for completing solidification, an increase in Bo, ϕgr or ϕ0, or a decrease in St, or ρsl results in an increase in the solidification time. The effects of these parameters on the drop height are also investigated.

Extracting structural information from MEH-PPV optical spectra.

The Frenkel-Holstein model in the Born-Oppenheimer regime is used to interpret temperature-dependent photoluminescence spectra of solutions made with the poly(p-phenylene vinylene) derivative MEH-PPV. Using our recently developed structural optimization method and assuming only intrachain electronic coupling, we predict the structure of emissive MEH-PPV chromophores in terms of a mean torsional angle ϕ0 and its static fluctuations σϕ, assuming no cis-trans defects. This allows us to fully account for the observed changes in spectra, and the chromophore structures obtained are consistent with the known phase transition at 180 K between a "red" and "blue" phase.

Acoustic Modes at the Twist Boundary in Piezoelectric Crystals

The transformations of the shear (SH and SV) and longitudinal (L) acoustic waves at the twist boundary in piezoelectrics of 62m and 42m the and classes have been investigated. This boundary is formed at a hard contact between two identical crystal half-spaces rotated relative to each other around the Z||6||4 axis by an angle 2ϕ. Propagation occurs along the bisector of this angle (х axis) in the (x, y) twist plane. Situations have been established in which the shear modes are localized at the twist boundary exclusively due to the combination of the piezoelectric effect and half-space rotation, as well as the joint effect of the elastic anisotropy and rotation. The cases of independence of a bulk wave of the half-space rotation and occurrence of leaky waves are described.

Direct Numerical Study of a Molten Metal Drop Solidifying on a Cold Plate with Different Wettability

This paper presents a direct numerical simulation of solidification of a molten metal drop on a cold plate with various wettability by an axisymmetric front-tracking method. Because of the plate kept at a temperature below the fusion value of the melt, a thin solid layer forms at the plate and evolves upwards. The numerical results show that the solidifying front is almost flat except near the triple point with a high solidification rate at the beginning and final stages of solidification. Two solid-to-liquid density ratios ρsl = 0.9 (volume change) and 1.0 (no change in volume), with two growth angles φ0 = 0° and 12° are considered. The presence of volume change and a non-zero growth angle results in a solidified drop with a conical shape at the top. The focusing issue is the effects of the wettability of the plate in terms of the contact angle φ0. Increasing the contact angle in the range of 45° to 120° increases time for completing solidification, i.e., solidification time. However, it has a minor effect on the conical angle at the top of the solidified drop and the difference between the initial liquid and final solidified heights of the drop. The effects of the density ratio and growth angle are also presented.

Focus shaping of cylindrically polarized Bessel–Gaussian beam modulated by Bessel gratings by a high numerical aperture objective

The focus-shaping technique of the cylindrically polarized Bessel–Gaussian-like beam, referred to the cylindrically polarized Bessel–Gaussian beam modulated by Bessel gratings, propagating through a high numerical-aperture lens is investigated theoretically and numerically in this paper, using the vector diffraction theory method. Results show that the intensity distribution in the focal region can be influenced considerably by: the beam topological charges (m, n), the beam parameter β and the polarization angle ϕ0. The intensity distribution in focal region can be tailored considerably by appropriately adjusting the polarization angle. Peak-centered, donut and flattop focal shapes with extended focal depth which are potentially useful in optical tweezers, material processing and laser printing can be obtained using this technique.

Anisotropic edge enhancement with spiral zone plate under femtosecond laser illumination.

Fractional and de-centered phase spiral zone plates (SZPs) are proposed for anisotropic edge enhancement using a femtosecond laser. The transmission functions of the two types of phase SZPs are deduced and the diffraction distributions are theoretically analyzed and simulated as well. By setting the fractional topological charge p and the orientation angle ϑ of a fractional SZP (FSZP), the intensity and the direction of the anisotropic edge enhancement can be controlled. A de-centered SZP (DSZP) can be obtained by shifting the coordinates of the traditional phase SZP while the topological charge equals to 1. The intensity and direction of the anisotropic edge enhancement can be controlled by setting the displacement distance r0 and the azimuthal angle φ0 of a DSZP. The anisotropic edge enhancement of the two phase SZPs was experimentally demonstrated with a phase pattern and living biological cells under femtosecond laser illumination.

Stress-Dilatancy for Soils. Part II: Experimental Validation for Triaxial Tests

Abstract Different forms of the stress-dilatancy relations obtained based on the frictional theory for the triaxial condition are presented. The analysed test data show that the shear resistance of many soils is purely frictional. The angle Φ0 represents the resistance of the soil as a combined effect of sliding and particle rolling on the macro-scale during shear at the critical frictional state. The stress-plastic dilatancy relations differ not only for triaxial compression and extension but also for drained and undrained conditions. The experiment investigated shows the correctness of the frictional state theory in the triaxial condition.

Spin-flip scattering of a half spin particle by a magnetic impurity in one dimension

In this article, the behavior of a half spin particle is studied. Specifically an electron with mass me, when passing through a magnetic field with fixed strength Bo is examined. A magnetic impurity is considered as a scatterer of a half spin particle in one dimension. This corresponds for example to a defect in the local magnetic structure inducing a magnetic field, e.g. as a result of strong spin-orbit coupling. From this set-up, the spin-flipping scattering processes are observed. Different profiles of Spin-Flip-Rate (SFR) against frequencies ω and amplitudes U are drawn respectively, for angle φ0=0, θ=π2 and different values of, μBB0, and radius R.

Fragment Velocity Distribution of Velocity Enhanced Warhead under Double Symmetric Initiations

AbstractCylindrical casing filled with charge under eccentric point initiation is a kind of velocity enhanced warhead (VEW). The initial velocity distribution of fragments from VEW is a key issue in the field of explosive technology. Most of the formulas existed can predict the fragment velocity distribution from VEW with a single eccentric initiation point, but the fragment velocity distribution of the VEWs with double symmetric eccentric initiation points is not studied well. In this paper, a new formula is established to predict the radial distribution of the fragment velocities from VEW under double symmetric initiation points. Not only the maximum velocity gains, but also the velocity gains with azimuth angle can be calculated using this formula. The formula applies a correctional function in consideration of both the angle 2ϕ between the two symmetric initiation points and the ratio of the mass charge to that of metal casing β. Finally, the X‐ray experiments were conducted to verify the formula established in this paper, and the predictions agree well with the experimental data. According to the comparisons between the calculated results from the formula and the published data, the formula also shows good agreement.