Beam Boundaries Research Articles

Edge mode resonance in the dark state by a finite beam

We treat edge-mode resonance that may exist at boundaries of transversely finite beams illuminating a photonic lattice. The lattice is in the dark state signifying a perfect bound state in the continuum (BIC). The dark state is non-radiative in symmetric systems because lateral waves cannot couple to the lattice due to destructive interference between counter-propagating waves. However, if the incident beam is spatially finite, the balance is broken at beam boundaries, and edge modes are induced supporting local electromagnetic fields. Numerical studies illustrate key properties including coupled-wave near fields, spectral signatures at resonance, and local field profiles for representative beam geometries. The work contributes fundamentally to the understanding of resonant metasurfaces that are of high scientific interest worldwide.

Exact solutions for size-dependent bending of Timoshenko curved beams based on a modified nonlocal strain gradient model

Size-dependent bending analysis of Timoshenko curved beams is performed with a modified nonlocal strain gradient integral model, in which the integral constitutive equation is transformed into an equivalent differential form equipped with two constitutive boundary equations. The governing equations and boundary conditions are derived via the minimum total potential energy principle and solved analytically using the Laplace transformation technique and its inverse version. In numerical examples, the inconsistency of the nonlocal strain gradient model is examined extendedly under different boundary and loading conditions, while consistent softening and stiffening responses can be observed via the modified nonlocal strain gradient integral model. In addition, within the modified nonlocal strain gradient model, numerical examples also show that the increase of the opening angle can affect the total size effects of the combination of the two scale parameters (i.e., nonlocal and gradient), and these effects are inconsistent for different beam boundaries. Finally, by comparing with the results of the Euler–Bernoulli theory, an interesting finding is that as the nonlocal (or gradient length-scale) parameter increases, the shear deformations of simply supported-simply supported beams (or clamped-clamped/simply supported beams) become more significant.

Neutralization of ion beam by electron injection: Excitation and propagation of electrostatic solitary waves

The charge neutralization of an ion beam by electron injection is investigated using a two-dimensional electrostatic particle-in-cell code. The simulation results show that electrostatic solitary waves (ESWs) can be robustly generated in the neutralization process and last for a long time (for more than 30 μs) and therefore, ESWs can strongly affect the neutralization process. The ESWs propagate along the axis of the ion beam and reflect from the beam boundaries. The simulations clearly show that two ESWs can pass through each other with only small changes in amplitude. Partial exchange of trapped electrons in collisions of two ESWs is observed in the simulations and can explain interaction during collisions of two ESWs. Coalescence of two ESWs is also observed.

Simulations of Ion Thruster Beam Neutralization Using a Particle–Particle Model

A particle–particle (PP) model is developed to simulate ion thruster beam neutralization by thermal electrons emitted from a neutralizer located outside of the ion beam. Simulations are carried out using the real xenon to electron mass ratio. The results show that beam neutralization is initiated by an electron–ion mixing process in which the thermal electrons are trapped by the potential well in the ion beam and undergo an oscillation between the ion beam boundaries both along the beam direction and in the radial direction. The bouncing of the electrons in the radial direction generates transient oscillating perturbations inside the beam in both electron density and the electric field in the radial direction, which eventually dissipate when the electrons are thermalized and the ion beam is neutralized. The PP method directly uses Coulomb’s law to calculate the electrostatic force between particles and thus eliminates the constraints on mesh resolution and domain size of the particle-in-cell method. This method can be advantageous computationally when applied to simulations of very nonuniform, collisionless plasmas such as the plasma plume near ion thruster exit.

Refined sectional analysis with shear center prediction for nonhomogeneous anisotropic beams with nonuniform warping

A two-dimensional (2D) finite element (FE) sectional analysis system is developed for nonhomogeneous anisotropic beams established on a refined displacement-based elasticity theory. The classical effects due to elastic couplings, and nonclassical effects pertaining to three-dimensional (3D) warping displacements are incorporated in the formulation. The formulation allows for a generalized refined model with 12 × 12 stiffness matrix which subsequently encapsulates the Timoshenko model, Vlasov model for restrained torsion, and refined model for fully nonuniform warping (NUW). In addition, the shear center and tension center offsets are computed as cross-sectional properties based on the extended Trefftz’ theory for anisotropic beams. The accuracy of the sectional analysis is substantiated for isotropic as well as anisotropic, closed and open section beams with and without end restraints. The results indicate reliable predictions of the elastic properties for isotropic as well as anisotropic beams compared with the analytical solution, 3D FE solution, and other state-of-the-art methods. The static behavior of the beams is shown to be significantly influenced by the NUW effects especially in the vicinity of beam boundaries.

Exact theory for a linearly elastic interior beam

• Interior elasticity solution for a 2D plane beam is derived. • Kinematic central axis variables are formed from the 2D displacement field. • The 2D solution is presented as a 1D beam theory using the central axis variables. • Stresses do work on the lateral surfaces of the interior beam. • Exact 1D rod and beam finite elements are developed from the 2D solution. In this paper, an elasticity solution for a two-dimensional (2D) plane beam is derived and it is shown that the solution provides a complete framework for exact one-dimensional (1D) presentations of plane beams. First, an interior solution representing a general state of any 2D linearly elastic isotropic plane beam under a uniform distributed load is obtained by employing a stress function approach. The solution excludes the end effects of the beam and is valid sufficiently far away from the beam boundaries. Then, three kinematic variables defined at the central axis of the plane beam are formed from the 2D displacement field. Using these central axis variables, the 2D interior elasticity solution is presented in a novel manner in the form of a 1D beam theory. By applying the Clapeyron’s theorem, it is shown that the stresses acting as surface tractions on the lateral end surfaces of the interior beam need to be taken into account in all energy-based considerations related to the interior beam. Finally, exact 1D rod and beam finite elements are developed by the aid of the axis variables from the 2D solution.

Progressive collapse resistance of RC beams

The current guidelines for evaluating progressive collapse potential of existing and new buildings require analyzing and evaluating the structure for the case of an instantaneous loss of a primary vertical support, such as a column. In this paper, the response of a continuous beam bridging over a lost column is evaluated. A series of beam models are developed by changing structural characteristics such as lateral load design type (ordinary vs. special frames), axial stiffness at the beam boundaries, steel yield stress, amount of integrity reinforcement at bar cut-off locations and the beam span to study their effects on the performance of the beam. The modeling technique used for the analyses of the beams has been validated by comparing experimental and analytical results of an RC beam subjected to large deformations. Push-down analyses are carried out in order to study and characterize the full range of response and compare the behavior of the beams. For each case, the behavior of the critical sections are evaluated and used to describe load transfer mechanisms. The effects of different structural characteristics on the performance of the beam to resist progressive collapse are discussed by comparing the results of the analyses.

A padding method to reduce edge effects for enhanced damage identification using wavelet analysis

Vibration response based structural damage identification by spatial wavelet analysis is widely considered a powerful tool in Structural Health Monitoring (SHM). This work deals with the issue of border distortions in wavelet transform that can mask tiny damages close to the boundary of a structure. Since traditional padding methods (e.g., zero-padding, symmetric padding, linear padding) are often not satisfactory, a simple and computationally inexpensive signal extension method, based on fitting polynomial functions and continuity conditions at the extrema, is proposed. The method is applied to analyze noisy mode shapes and static deflection of cracked cantilever and simply supported beams. The effectiveness and the versatility of the method in localizing tiny damages close to clamped, free or hinged beam boundaries is demonstrated. Furthermore, an extensive comparison with the linear padding method and Messina׳s isomorphism methods is carried out.

Functional Interrogation of Adult Hypothalamic Neurogenesis with Focal Radiological Inhibition

The functional characterization of adult-born neurons remains a significant challenge. Approaches to inhibit adult neurogenesis via invasive viral delivery or transgenic animals have potential confounds that make interpretation of results from these studies difficult. New radiological tools are emerging, however, that allow one to noninvasively investigate the function of select groups of adult-born neurons through accurate and precise anatomical targeting in small animals. Focal ionizing radiation inhibits the birth and differentiation of new neurons, and allows targeting of specific neural progenitor regions. In order to illuminate the potential functional role that adult hypothalamic neurogenesis plays in the regulation of physiological processes, we developed a noninvasive focal irradiation technique to selectively inhibit the birth of adult-born neurons in the hypothalamic median eminence. We describe a method for Computer tomography-guided focal irradiation (CFIR) delivery to enable precise and accurate anatomical targeting in small animals. CFIR uses three-dimensional volumetric image guidance for localization and targeting of the radiation dose, minimizes radiation exposure to nontargeted brain regions, and allows for conformal dose distribution with sharp beam boundaries. This protocol allows one to ask questions regarding the function of adult-born neurons, but also opens areas to questions in areas of radiobiology, tumor biology, and immunology. These radiological tools will facilitate the translation of discoveries at the bench to the bedside.

Compressive behavior of dual-gusset-plate connections for buckling-restrained braced frames

This work conducts compression tests and finite element analyses for steel dual-gusset-plate connections used for buckling-restrained braced frames (BRBFs). Compared to a single-gusset-plate connection, dual gusset plates sandwiching a BRB core reduce gusset plate size, eliminate the need for splice plates, and enhance connection stability under compression. The experimental program investigated ultimate compression load by testing ten large dual-gusset-plate connections. Out-of-plane deformation of the gusset plate in the test resembled that of a buckled gusset plate with low bending rigidity provided by the BRB end. The general-purpose nonlinear finite element analysis program ABAQUS was applied for correlation analysis. A parametric study of the dual-gusset-plate connection was performed to study the effects of plate size, presence of centerline stiffeners, and beam and column boundaries on ultimate compression load. The ultimate compression load of the dual-gusset-plate connection could not be predicted based on the AISC-LRFD approach due to beam flange out-of-plane deformation. The ultimate compression load of the dual-gusset-plate connection was reasonably predicted using a column strip length from the Whitmore section to the workpoint of the beam and column centerlines and a buckling coefficient of K=2.

Assessment of scattered dose contribution to healthy tissue in radiation therapy using water phantom

In cancer therapy using gamma radiation one of the limiting factors in dose delivery is the safety of the healthy tissues and organs around the cancerous mass. Better collimation and dose fractionation are employed to achieve this. In the present paper results of scattered dose to healthy tissues around the incident beam cross-section or beam boundaries have been estimated using IAEA standard water phantom and Co-60 incident radiation. It has been observed that scattered dose to healthy tissues increases linearly from 4% to 7% of the incident dose of 185 cGy to 200 cGy at the centre of the beam, at 5 cm depth in water, as we increase the incident beam field size from 5 cm x 5 cm to 10 cm x 10 cm. Also the maximum unwanted scattered dose for any field size remains closer to the incident beam boundaries.

Scanning electron microscopy of dopant distribution in semiconductors

We show that, in scanning electron microscopy, it is possible to use the secondary electrons produced by the backscattered electrons to obtain chemical information on the dopant distribution in Sb-implanted silicon. Theoretical investigations and experimental data concur to point out that the resolution of the method is defined by the probe size—values of 1 nm or even lower are possible in the present instruments—while the contrast depends on the electron range and on the boundary conditions. A proper choice of beam energy and boundaries of the doped layer may allow a sensitivity below 1%, suitable to characterize the high-dose near-surface region of the ultrashallow junctions in cross-sectioned bulk specimens.

Analysis of laser-induced evaporation of Al target under conditions of vapour plasma formation

The plasma-controlled evaporation of the Al target induced by the laser pulse with intensity of 109 W/cm2 and wavelength of 1.06 μm is analysed with account for the two-dimensional effects. The self consistent model is applied, including the heat transfer equation in condensed medium, the equations of radiation gas dynamics in evaporated substance and the Knudsen layer model at the two media boundary. It is found that the phase transition at the target surface is controlled by the two factors: the surface temperature that depends on the transmitted radiation intensity, and the plasma pressure, governed by the expansion regime. The process comes through three characteristic stages, the sonic evaporation at the beginning, the condensation during the period of plasma formation and initial expansion, and finally, the re-start of evaporation in subsonic regime after the partial brightening of the plasma. During the subsonic evaporation stage the vapour flow and the mass removal rate are much higher near the beam boundaries than in the centre due to smaller plasma counter-pressure. The vapour plasma pattern is characterised by the dense hot zone near the surface where the absorption of laser energy occurs, and rapid decrease of density outside the zone due to three-dimensional expansion.

Analytical investigation and the design of the compressive strength of steel gusset plate connections

A parametric study of the inelastic compressive behaviour and strength of gusset plate connections is presented in this paper. The study is performed by the commercial finite element program ABAQUS. Based on the parametric study, general design guidelines are proposed. To increase the buckling strength of gusset plate connections efficiently and improve the energy absorption behaviour of the connections under cyclic loading, adding the centerline stiffener along the splice member as close to the beam and column boundaries as possible and/or adding free edge stiffeners are recommended. In addition, welded connection between the splice member and the gusset plate is recommended. The splice member with higher bending rigidity such as tee-sections and channel sections should always be used. Shaping the gusset plate according to 30° load dispersion angle may be recommended to reduce the size of the connection between the gusset plate and the beam and column boundaries provided that the splice member is sufficiently extended beyond the bending line. Finally, a design method accompanied by some design charts for rectangular type gusset plates subject to compression is proposed based on an inelastic plate buckling equation.

Automatic on-line electronic portal image analysis with a wavelet-based edge detector.

A fully automatic method for on-line electronic portal image analysis is proposed. The method uses multiscale edge detection with wavelets for both the field outline and the anatomical structures. An algorithm to extract and combine the information from different scales has been developed. The edges from the portal image are aligned with the edges from the reference image using chamfer matching. The reference is the first portal image of each treatment. The matching is applied first to the field and subsequently to the anatomy. The setup deviations are quantified as the displacement of the anatomical structures relative to the radiation beam boundaries. The performance of the algorithm was investigated for portal images with different contrast and noise level. The automatic analysis was used first to detect simulated displacements. Then the automatic procedure was tested on anterior-posterior and lateral portal images of a pelvic phantom. In both sets of tests the differences between the measured and the actual shifts were used to quantify the performance. Finally we applied the automatic procedure to clinical images of pelvic and lung regions. The output of the procedure was compared with the results of a manual match performed by a trained operator. The errors for the phantom tests were small: average standard deviation of 0.39 mm and 0.26 degrees and absolute mean error of 0.31 mm and 0.2 degrees were obtained. In the clinical cases average standard deviations of 1.32 mm and 0.6 degrees were found. The average absolute mean errors were 1.09 mm and 0.39 degrees. Failures were registered in 2% of the phantom tests and in 3% of the clinical cases. The algorithm execution is approximately 5 s on a 168 MHz Sun Ultra 2 workstation. The automatic analysis tool is considered to be a very useful tool for on-line setup corrections.

Ion separation in imperfect fields of the quadrupole mass analyzer Part II. Ion beam dynamics in the phase-space of the fringing field

The theoretical aspects of ion separation taking account of fringing fields in the quadrupole mass analyzer are analyzed by applying beam dynamics in phase-space. The mathematical simulation of fringing fields is developed by the principles of statistical mechanics. Numerical solutions of differential equations (the Hill equation) for ion motion in the fringing field are considered using matrix conversions with Galerkin-Slezkin's integral averaging in the iteration procedure. Analysis of beam dynamics in the phase-space where the law of phase volume conservation (Liouville's theorem) is valid indicates that, for stable ion motion, beam boundaries are described by a family of ellipses. The parameters of the ellipses are determined by the elements of the state transition matrix for an arbitrary set of initial conditions. Theoretical analysis indicates that beam divergence has a major influence on transmission. Transmission is an exponential function of relative transit time. The optimum time of transit through the fringing field has exponential dependences on the initial values of radial and angular envelopes of a beam with an asymptotic value of 1.77π.

Choice of optimum megavoltage for accelerators for photon beam treatment

Over three decades ago, the development of megavoltage accelerators revolutionized radiation oncology and provided the therapist with photons and electrons of any desired energy. The initial advantages cited for high energy photon therapy, listed below, have proved valid and accelerators have almost totally replaced orthovoltage units. Initially, it appeared that most of these cited advantages should continue to improve with increasing energy, and there has been an impetus for the production of ever higher megavoltage accelerators. Some of these advantages are reviewed in this paper. Also. recent investigations have indicated increasing diffuseness of the photon beam boundary with increasing energy because of lateral transport of electrons. The impact on treatment planning as a function of energy of the increase in volume dose due to the diffuseness of beam boundaries, “build-down” and “rebuild-up” effects in tissues at cavity and inhomogeneity interfaces, bone absorption, and photoneutron production are discussed. Consideration of the behavior of these parameters indicates that optimum photon energies have been achieved and that the impetus for higher megavoltages is unwarranted for most treatment. For many therapeutic applications, there are major advantages of 4 MV to 8 MV photon beams relative to 60Co gamma rays. For large lesions in the abdomen or pelvis there is an advantage to energies above those provided by 15 MV units. The various considerations above are discussed and summarized as a function of lesion site and megavoltage.

Assessment of Acute Radiation-Induced Pulmonary Changes Using Computed Tomography

In a prospective study of acute radiation-induced pulmonary changes, CT scans of 54 patients were performed before and at preselected times during the 6 months following fractionated radiation therapy of the thorax. The CT films were evaluated independently by three diagnostic radiologists and 36 patients were scored as having postirradiation pulmonary findings. The average interobserver agreement for this scoring was approximately 85%. The end point was observed as an increase in lung density within the irradiated volume on a follow-up CT examination. All 36 patients demonstrated lung opacities in an irregular, homogeneous, or nonhomogeneous pattern within the radiation beam boundaries. In addition, the following characteristics were observed at various frequencies in these 36 patients: extension of the changes across anatomic tissue boundaries (50%), air bronchograms (25%), loss of lung volume (15%), and pleural thickening (15%). Confinement of the findings within the irradiated volume was the only specific characteristic of postirradiation changes. In two patients the changes appeared as sharply defined, nodular opacities and were considered to be atypical of radiation damage. These were subsequently confirmed to be metastases. Prospective assessment of an adequate number of patients has helped to establish the CT appearance of acute radiation-induced pulmonary effects and, hence, to minimize its confusion with malignancies and other abnormalities.

Macro-element analysis of skewed and triangular orthotropic thin plates with beam boundaries

A generalized macro-flexibility analysis of stiffened orthotropic skewed and triangular thin plates with beam stiffened boundaries subjected to bending and stretching is presented. The proposed method accounts for minimized number of elements in a domain, i.e. the element size is independent of the final results. This is accomplished by satisfying the equilibrium and compatibility conditions along the nodal lines interconnecting contiguous elements. The solution form and shape functions of element shapes are a combination of Fourier series and polynomials with undetermined coefficients. To obtain a solution of a general domain, the orthotropic triangular and parallelogram macro-plate elements with edge beams, satisfying moment and shear equilibrium conditions along nodal lines, were assembled and analyzed by utilizing compatibility of deflection and slope. The results from the proposed methodology were compared to the ones from the finite element method. Also, the convergence was checked by increasing the number of harmonics. The study indicates that good convergence is observed within the first four harmonics.

Differential pencil beam dose computation model for photons

Differential pencil beam (DPB) is defined as the dose distribution relative to the position of the first collision, per unit collision density, for a monoenergetic pencil beam of photons in an infinite homogeneous medium of unit density. We have generated DPB dose distribution tables for a number of photon energies in water using the Monte Carlo method. The three-dimensional (3D) nature of the transport of photons and electrons is automatically incorporated in DPB dose distributions. Dose is computed by evaluating 3D integrals of DPB dose. The DPB dose computation model has been applied to calculate dose distributions for 60Co and accelerator beams. Calculations for the latter are performed using energy spectra generated with the Monte Carlo program. To predict dose distributions near the beam boundaries defined by the collimation system as well as blocks, we utilize the angular distribution of incident photons. Inhomogeneities are taken into account by attenuating the primary photon fluence exponentially utilizing the average total linear attenuation coefficient of intervening tissue, by multiplying photon fluence by the linear attenuation coefficient to yield the number of collisions in the scattering volume, and by scaling the path between the scattering volume element and the computation point by an effective density.