A transformation based method to design ultrasound array

In medical ultrasound imaging, the desired lateral field distribution at each focal distance can be obtained by optimal apodization. On the other hand, the lateral field is a function of focal distance. Hence, finding the optimal apodization is a very arduous process. To overcome this, we have introduced a suboptimal method by which optimal apodization can be calculated in any distance through a nonlinear transformation by the knowledge of the optimal one at a distance. This transformation is established on a fact that the lateral field distribution at focal distance can be expressed as the Fourier transform of a nonlinear function of the aperture weighting, instead of direct expression as the Fourier transform of the above. We have applied this method to map the apodization which obtains the desired beam pattern into the apodization which maintains the same properties on the lateral field distribution. For example, applying this method on a 50-elements λ/2 spaced linear array with length D has resulted in apodization that is optimal at distances D or D/2 by precision better than 9%. This method is useful especially in optimization problems, having no explicit constraint on the main lobe width, such as minimizing the sidelobe levels or minimizing main lobe width constrained to a predetermined value of sidelobe level. However, as the results show, this technique provides acceptable results in other cases.     

Optimal beam diameter for lateral optical forces on microspheres at a water-air interface

Optical tweezers with a low numerical aperture microscope objective is used to manipulate the microspheres at the water-air interface. In this letter, we determine the optimal optical trap for the lateral manipulation of microspheres at a water-air interface. The experimental results show that the trapping force is influenced by the expansion of the trapping beam at the back aperture of the objective. The optimal filling ratio of 0.65 is suggested for lateral optical manipulation at the water-air interface. The lateral trapping forces at the water-air interface are theoretically investigated with the ray-optics model. The numerical results show that the lateral trapping forces can be changed by shrinking the diameter of the trapping laser beam. The numerical results are in accordance with the experimental results.     

Displacements and deformations of a vortex light beam produced by the diffraction grating with embedded phase singularity

Properties of vortex light beams produced by a diffraction grating with groove bifurcation (“fork” structure) are studied in the case of small diffraction angles. Analytical expressions are derived for the amplitude distribution of a diffracted beam generated from an incident Gaussian beam with arbitrary radius and wavefront curvature, transversely shifted and inclined with respect to the nominal axis (normal to the grating crossing it at the bifurcation point). In such situations, the output beam becomes asymmetric; the optical vortex core and the intensity maximum displace orthogonally to the incident beam shift direction. The nearest vicinity of the vortex core preserves its circular symmetry and the optical vortex remains locally isotropic. The effects of misalignment depend on the incident beam characteristics, the diffraction order and the propagation distance behind the grating. Experimental measurements support the results of calculations.     

Buckling of coupled elastic rods

A simple physical system is studied which demonstrates the unfolding of a multiple bifurcation point. Two coupled elastic rods are subjected to a compressive load. The rods are joined such that their buckling directions are orthogonal. As the load is quasistatically increased from zero one of the two rods will buckle independently of the other. The “preferred” buckling mode is determined by two parameters, the length ratio and the stiffness ratio. The experimental system consists of two spring steel strips joined through a Teflon connector such that the buckling planes are orthogonal. The theoretical model consists of an analogous rigid rod and spring model which we assume retains the essential features of the continous system. Secondary bifurcation is essential to a continuous exchange of priority between the two buckling modes, and its role is examined for both imperfection-free and perturbed rod-spring systems. Our computational results are then compared with some experiments.     

定跨度变截面梁的弯曲问题

一.引言 在处理梁的弯曲问题时,人们经常利用函数级数来表示有关的各量,并后而得到各该量的近似值。胡海昌曾经指出:在横向载荷和轴向力同时作用下,适宜于用梁的屈曲的本徵函数展开式来表示梁的挠度;其中φ_n是满足所给的梁的支座情况的屈曲本徵函数,a_n是常数系数。他求得一个相当简单的公式以已知的本徵函数和本徵值表示诸系数     

A study of the effect of laser beam geometries on laser bending of sheet metal by buckling mechanism

Laser beam forming has emerged as a new and very promising technique to form sheet metal by thermal residual stresses. The objective of this work is to investigate numerically the effect of rectangular beam geometries, with different transverse width to length aspect ratio, on laser bending process of thin metal sheets, which is dominated by buckling mechanism. In this paper, a comprehensive thermal and structural finite element (FE) analysis is conducted to investigate the effect that these laser beam geometries have on the process and on the final product characteristics. To achieve this, temperature distributions, deformations, plastic strains, stresses, and residual stresses produced by different beam geometries are compared. The results suggest that beam geometries play an important role in the resulting temperature distributions on the workpiece. Longer beam dimensions in the scanning direction (in relation to its lateral dimension) produce higher temperatures due to longer beam–material interaction time. This affects the bending direction and the magnitude of the bending angles. Higher temperatures produce more plastic strains and hence higher deformation. This shows that the temperature-dependent yield stress plays a more dominant role in the deformation of the plate than the spread of the beam in the transverse direction. Also, longer beams have a tendency for the scanning line to curve away from its original position to form a concave shape. This is caused by buckling which develops tensile plastic strains along both ends of the scanning path. The buckling effect produces the opposite curve profile; convex along the tranverse direction and concave along the scanning path.     

Simultaneously Large and Opposite Lateral Beam Shifts for TE and TM Modes on a Double Metal-Cladding Slab

We report simultaneously large and opposite Goos-Hanchen shifts for TE and TM beams on a double metalcladding slab. Theoretical examination shows that both positive and negative lateral shifts are in two orders of the wavelength. It is also found that the magnitude of the lateral beam shift strongly depends on the thickness of the upper metal layer. The optimal thickness of the upper metal layer for zero reflection is found to be the critical thickness above which a negative beam shift occurs. Numerical calculations are in good agreement with the theoretical results.     

Motor-driven bacterial flagella and buckling instabilities

Many types of bacteria swim by rotating a bundle of helical filaments also called flagella. Each filament is driven by a rotary motor and a very flexible hook transmits the motor torque to the filament. We model it by discretizing Kirchhoff’s elastic-rod theory and develop a coarse-grained approach for driving the helical filament by a motor torque. A rotating flagellum generates a thrust force, which pushes the cell body forward and which increases with the motor torque. We fix the rotating flagellum in space and show that it buckles under the thrust force at a critical motor torque. Buckling becomes visible as a supercritical Hopf bifurcation in the thrust force. A second buckling transition occurs at an even higher motor torque. We attach the flagellum to a spherical cell body and also observe the first buckling transition during locomotion. By changing the size of the cell body, we vary the necessary thrust force and thereby obtain a characteristic relation between the critical thrust force and motor torque. We present a elaborate analytical model for the buckling transition based on a helical rod which quantitatively reproduces the critical force-torque relation. Real values for motor torque, cell body size, and the geometry of the helical filament suggest that buckling should occur in single bacterial flagella. We also find that the orientation of pulling flagella along the driving torque is not stable and comment on the biological relevance for marine bacteria.     

Conservative spatial chaos of buckled elastic linkages

Buckling of an elastic linkage under general loading is investigated. We show that buckling is related to an initial value problem, which is always a conservative, area-preserving mapping, even if the original static problem is nonconservative. In some special cases, we construct the global bifurcation diagrams, and argue that their complicated structure is a consequence of spatial chaos. We characterize spatial chaos by the associated initial value problem's topological entropy, which turns out to be related to the number of buckled configurations.     

COMPLEX DYNAMICS OF HIGH-SPEED AXIALLY MOVING SYSTEMS

In this paper, the dynamic response of a simply supported travelling beam subjected to a transverse load is investigated in the super-critical speed range. The well-known axially moving beam theory is considered and a simple viscous damping mechanism has been introduced. The displacement field is expanded in a series of the buckling modes, a sine series, and different techniques have been used in analyzing the response of the dynamical system. Periodic oscillations are studied by means of continuation techniques, while non-stationary dynamics are investigated through direct simulations. A comparison with the literature and a convergence test on the series expansion are performed. A sample case of a physical beam is developed and numerical results are presented concerning bifurcation analysis and stability, and direct simulations of global postcritical dynamics. A complex scenario of alternate regular and chaotic motions is found in a large range of the main parameters.     

Photothermal deflection microscopy for imaging sub-micronic defects in optical materials

Photothermal deflection is widely used to study defects in optical coatings and role of these defects in laser damage. Because defects responsible for laser damage are assumed to be nanometer-sized and lowly absorbing, both high spatial resolution and high sensitivity are required to detect them. In this work we theoretically and experimentally explore the capability of collinear photothermal deflection to give micronic resolution by reduction of the pump beam diameter. Thanks to a model describing temperature distribution and photothermal deflection, we have studied the effects of pump beam focusing on photothermal deflection. Then, we have developed a high resolution, high sensitivity microscope based on the photothermal deflection of a transmitted probe beam. The setup is characterized and the theoretical predictions are checked. We present a test of lateral spatial resolution obtained on specially prepared absorbing resolution targets and show that a lateral spatial resolution of 1 μm is reached on non-isolated defects. In case of single defects, we expect that 10 nm sized defects could be detected.     

Bifurcation in an inverted pendulum with tilted high-frequency excitation: analytical and experimental investigations on the symmetry-breaking of the bifurcation

In this study, we investigate the dynamics of an inverted pendulum subjected to high-frequency excitation. In particular, we focus on bifurcation phenomena in the dynamics and analyze the effect of the tilt of the excitation direction with respect to gravity direction on the bifurcation. It is analytically clarified that the tilt produces stable equilibrium states different from the directions of the gravity and the excitation. The stability of the stable equilibrium states under the effect of the tilt is discussed non-locally. Also, an analogy of the bifurcation of the inverted pendulum to that of the buckling phenomenon is presented. The theoretically predicted effects of the tilt are qualitatively confirmed by performing some experiments.     

图像复原式整形环形光横向超分辨共焦显微测量新方法

提出一种新的图像复原式整形环形光横向超分辨共焦显微测量法. 该方法首先利用二元光学器件，将高斯照明光束整形为环形光束，用于初步改善共焦显微镜的横向分辨力，然后利用基于最大似然估计法(maximum likelihood estimate, MLE)的单幅图像超分辨复原技术，重建测量图像的高频信息，来进一步改善共焦显微镜的横向分辨力. 实验表明,当λ=632.8nm，N.A. =0.85时，该方法能使共焦显微镜获得优于0.1μm的横向分辨力. 利用该方法建立的横向超分辨共焦显微系统除了具有显著的超分辨效果外 关键词： 超分辨 超分辨复原 最大似然估计 共焦成像     

Dynamic buckling and fragmentation in brittle rods

We present experiments on the dynamic buckling and fragmentation of slender rods axially impacted by a projectile. By combining the results of Saint-Venant and elastic beam theory, we derive a preferred wavelength lambda for the buckling instability, and experimentally verify the resulting scaling law for a range of materials including teflon, dry pasta, glass, and steel. For brittle materials, buckling leads to the fragmentation of the rod. Measured fragment length distributions show two peaks near lambda/2 and lambda/4. The nonmonotonic nature of the distributions reflect the influence of the deterministic buckling process on the more random fragmentation processes.     

发散型准直器限束孔应用于被动散射质子放疗可行性研究

被动散射质子放疗（Passive Scattering Proton Therapy,PSPT）是质子治疗的主要技术之一,束流通过准直器限束孔（Aperture）时因边缘散射效应导致患者体内剂量分布偏离理想状态。使用蒙特卡洛软件TOPAS（TOol for PArticle Simulation）对质子束流经过发散型与传统型准直器限束孔后进入水模体中的过程建模,分析两种准直器的边缘散射效应对剂量及中子能谱分布的影响,分别测试70,110,160,200,230,250 MeV能量下的质子束流,发现传统Aperture在70 MeV的质子束下边缘散射效应最明显,在距水箱表面0.5 cm深度处横向剂量曲线平坦度、均匀度分别达到4.63%,108.05%,随着深度增加边缘散射效应逐渐减弱,在布拉格峰位置处接近消失。使用发散型准直器限束孔后,在70 MeV下平坦度、均匀度分别降至1.28%,101.31%,对于100,160,200 MeV质子束均有不同程度改善。对于能量接近250 MeV的质子束,发散型准直器限束孔设置下横向剂量曲线并无优势。边缘散射效应导致的剂量不均随水深增加而减弱,对于各个能量质子,使用发散型准直器限束孔后次级中子减少。研究结果表明,发散型准直器限束孔应用于PSPT效果显著,为进一步应用于临床提供数据支撑。Passive Scattering Proton Therapy (PSPT) is one of the main technologies for proton radiation therapy. The dose distribution in the patient deviates from the ideal state due to the edge scattering effect when the beam passes through the aperture. In this paper, TOPAS, a Monte Carlo software, was used to simulate the passive scattering treatment head. The influence of the edge scattering effect of the two aperture sets on the dose distribution was compared. The proton beam at 70, 110, 160, 200, 230 and 250 MeV was tested respectively. We found that the scattering effect of the conventional aperture is most obvious at 70 MeV, and the flatness and hetergeneity of the lateral dose curve at the inlet of 0.5 cm of the tank reach 4.63%, 108.05%, respectively. The dose shift caused by the edge scattering effect decreases with increasing water depth and disappears at the Bragg peak. After using the divergent aperture, the flatness and uniformity at 70 MeV are reduced to 1.28% and 101.31%, respectively, and the 100, 160, and 200 MeV proton beams are improved in different extents. For a proton beam with an energy close to 250 MeV, there is no advantage in the lateral dose curve of the divergent aperture. For all energy protons, the secondary neutrons are reduced with divergent aperture. The results show that the divergent aperture is effective for PSPT and this study provides data support for further application in clinical practice.     

Solitons and collapse suppression due to parametric interaction in bulk Kerr media

We demonstrate that weak parametric interaction of a fundamental beam with its harmonic field in a Kerr medium can drastically modify the beam dynamics, giving rise to very complex bifurcation phenomena and quasi solitons. Most importantly, we reveal a novel physical mechanism of the collapse suppression in a bulk optical Kerr medium: parametric coupling to a weakly radiating harmonic field.     

Analysis of the positive or negative lateral shift of the reflected beam in Otto configuration under grazing incidence

We investigate the lateral shift of a TM-polarized light beam reflected from Otto configuration under grazing incidence. It is found that the lateral shift is strongly dependent on the thickness of the air-gap layer. By employing the pole-null representation, we demonstrate that the lateral shift is closely related to the null of the reflection function. The numerical simulations for a Gaussian beam are performed to demonstrate the validity of our theoretical analysis.     

Effect of coma on the focusing of an apertured singular beam

Effect of coma on the intensity distribution and encircled energy of a singular beam, at the focal plane of a lens, is evaluated numerically by using Fresnel–Kirchhoff diffraction integral for two different values of topological charge. Results show lateral shift and flattening of the dark core. It is noticed that the singular beam with double topological charge is affected more by comatic aberration in comparison to the beam with single topological charge. We also verified our results by using optical transfer function approach.     

Large positive and negative lateral optical beam shift due to long-range surface plasmon resonance

In this paper, we examine theoretically the beam shift at visible wavelengths on a long-range surface plasmon (LRSP) configuration by using the stationary-phase approach. We report that the lateral beam shift at the resonance of LRSP can be two orders of magnitude greater than a wavelength. It is also found that the sign of the lateral beam shift depends on the magnitude of the intrinsic damping relative to that of the radiative damping. Negative lateral beam shift occurs when the former is larger than the latter.     

Multiscale characterisation of diffuse granular failure

We study the evolution of structure inside a deforming, cohesionless granular material undergoing failure in the absence of strain localisation – so-called diffuse failure. The spatio-temporal evolution of the basic building blocks for self-organisation (i.e. force chains and minimal contact cycles) reveals direct insights into the structural origins of failure. Irrespective of failure mode, self-organisation is governed by the cooperative behaviour of truss-like 3-cycles providing lateral support to column-like force chains. The 3-cycles, which are initially in scarce supply, form a minority subset of the minimal contact cycle bases. At large length-scales (i.e. sample size), these structures are randomly dispersed, and remain as such while their population progressively falls as loading proceeds. Bereft of redundant constraints from the 3-cycles, the force chains are initially just above the isostatic state, a condition that progressively worsens as the sample dilates. This diminishing capacity for redistribution of forces without incurring physical rearrangements of member particles renders the force chains highly prone to buckling. A multiscale analysis of the spatial patterns of force chain buckling reveals no clustering or localisation with respect to the macroscopic scale. Temporal patterns of birth-and-death of 3-cycles and 3-force chains provide unambiguous evidence that significant structural reorganisations among these building blocks drive rheological behaviour at all stages of the loading history. The near-total collapse of all structural building blocks and the spatially random distribution of force chain buckling and 3-cycles hint at a possible signature of diffuse failure.