Narrow Results

Let R be a rectangle with given area a(R), height h(R) and width w(R), and r₁, r₂, …, r_n be n soft rectangles, where we mean by a soft rectangle a rectangle r whose area a(r) is prescribed but whose aspect ratio ρ(r) is allowed to be changed. In this paper, we consider the problem of packing n soft rectangles r₁, r₂, …, r_n into R. We prove that, if a(R) ≥ Σ_1≤i≤n a(r_i) + 0.10103a_max and a_max ≤ 3(min{h(R), w(R)})² hold for a a_max = max_1≤i≤n a(r_i), then these n soft rectangles can be packed inside R so that the apect ratio of each rectangle r_i is at most 3.

This study focuses on the characteristics of flow past three side-by-side rectangular cylinders under the effect of aspect ratios (AR) and Reynolds numbers (Re) at two different gap ratios ($g$) using the lattice Boltzmann method. For this purpose, AR is varied in the range of 0.25–4, the Re values are 100, 140 and 180 and the two different values of $g$ taken into account are $g=0.5$ and 3. The results are presented in the form of vorticity contours, temporal histories of drag and lift coefficients and power spectrum of lift coefficients. Also, the variation of physical parameters like mean drag coefficient, Strouhal number and the root-mean-square values of drag and lift coefficients with Re and AR is presented for $g=0.5$ and 3. The current numerical computations yield that for both gap ratios and all Re, there exist four different flow regimes depending on AR: (a) steady flow, (b) modulated flow, (c) symmetric flow and (d) periodic flow. At narrow gap ratios, the jet flow emerging within the gaps of cylinders altered the flow structures and fluid forces abruptly. The aspect ratio is found to have more influence on the flow characteristics of cylinders as compared to the Reynolds numbers at large gap ratios.

This paper contains natural convection of Ag–MgO/water micropolar hybrid nanofluid in a hollow hot square enclosure equipped by four cold obstacles on the walls. The simulations were performed by the lattice Boltzmann method (LBM). The influences of Rayleigh number and volume fraction of nanoparticle on the fluid flow and heat transfer performance were studied. Moreover, the effects of some geometric parameters, such as cold obstacle height and aspect ratio, were also considered in this study. The results showed that when the aspect ratio is not large ($\mathrm{\text{AR}}=0.2$ or 0.4), at low Rayleigh number (10³), the two secondary vortices are established in each main vortex and this kind of secondary vortex does not form at high Rayleigh number (10⁶). However, at $\mathrm{\text{Ra}}=10^6$, these secondary vortices occur again in the middle two vortices at $\mathrm{\text{AR}}=0.6$, which is similar to that at $\mathrm{\text{Ra}}=10^3$. At $\mathrm{\text{AR}}=0.2$, the critical Rayleigh number, when the dominated mechanism of heat transfer changes from conduction to convection, is 10⁴. However, the critical Rayleigh number becomes 10⁵ at $\mathrm{\text{AR}}=0.4$ or 0.6. When the cold obstacle height increases, the shape of the vortices inside the enclosure changes due to the different spaces. Besides, at $\mathrm{\text{Ra}}=10^6$, for different cold obstacle heights, the location of the thermal plume is different, owing to the different shapes of vortices. Accordingly, the average Nusselt number increases by increment of the Rayleigh number, nanoparticle volume fraction, cold obstacle height and aspect ratio.

This work is based on a numerical simulation to study the flow pattern and heat transfer characteristics inside a cavity in the form of an Islamic knot. The effect of height and length of the obstacle are investigated. Nine different obstacles with different lengths (a) and heights (b) are considered. It can be found that the variation in length and height of the hot obstacle leads to the obvious change in the flow field and temperature field. In addition, the small gap inside the cavity has a limited effect on the flow motion. Besides, the small gap between the cold and hot surfaces leads to higher conduction heat transport. For high Ra, the flow and heat transfer characteristics can be described in two situations. The first is included in the cases of $(a,b)=(10,1)$, (10, 2) and (10, 3), where the primary vortices are located on the top and bottom of the cavity. The second one consists of cases $(a,b)=(3,3)$, (4, 3), (5, 3), (6, 3), (7, 3) and (8, 3), where the primary flow circulations are established on the left and right sides. For all the cases, the average Nu increases by rising the Ra. By increasing the Ra, the average Nu in the second situation increases more significantly than that in the first one. The cases in the second situation always have better heat transfer performance than those in the first one, especially at higher Ra.

The sensitivity on shape and boundaries at the Curie point of the universal critical ratio L^dM²/χ for the Ising model is confirmed by a comparison of square and rectangular lattices. Tests with three different algorithms give the same results for the universal critical ratio on various lattice types and always the same dependence on the system's aspect ratio.

To predict the behavior of a dual plate composed of 5052-aluminum and 1002-cold rolled steel under ballistic impact, numerical and experimental approaches are attempted. For the accurate numerical simulation of the impact phenomena, the appropriate selection of the key parameter values based on numerical or experimental tests are critical. This study is focused on not only the optimization technique using the numerical simulation but also numerical and experimental procedures to obtain the required parameter values in the simulation. The Johnson-Cook model is used to simulate the mechanical behaviors, and the simplified experimental and the numerical approaches are performed to obtain the material properties of the model. The element erosion scheme for the robust simulation of the ballistic impact problem is applied by adjusting the element erosion criteria of each material based on numerical and experimental results. The adequate mesh size and the aspect ratio are chosen based on parametric studies. Plastic energy is suggested as a response representing the strength of the plate for the optimization under dynamic loading. Optimized thickness of the dual plate is obtained to resist the ballistic impact without penetration as well as to minimize the total weight.

A set of reduced MHD equations is derived using the equation of state including plasma compressibility. By applying assumption of pressure, i.e., R²P = const., a set of reduced magnetohydrodynamic equations for toroidal plasmas are obtained for large aspect ratio, high β tokamaks. These equations include all terms of the same order as the toroidal effect and only involve three variables, namely the flux, stream function and pressure.

In the present study, we measured velocity vector fields around hoop rings at each divided sections by using a particle image velocimetry method. The ring model used in this study was made of brass with two different aspect ratios and the experiment is carried out in a circulating water channel. As a result, we can observe two counter-rotating vortical flow structures around each hoop regime that is attributed to the interaction between direct pass through flow of hoop center and the shear flow separated from sharp-edged end of ring hoop.

Magnetic hysteresis behavior of isotropic permalloy elliptic nanorings of outer semi-major axis length $(a_{\mathrm{\text{out}}})$ 100 nm and thickness $(t)$ 20 nm were studied with respect to the variation of two parameters: outer semiminor axis length $(b_{\mathrm{\text{out}}})$ and the difference between outer and inner dimensions $(r)$. The outer semiminor axis length $(b_{\mathrm{\text{out}}})$ varied from 90 nm to 20 nm which covers from nearly circular nanoring to elliptic nanoring of high aspect ratio. The value of $r$ varied in steps of 10 nm. Micromagnetic simulation of in-plane hysteresis curve of these nanorings revealed that the remanent state of all of these elliptic rings are onion states if the magnetic field is applied along the longer side of the elliptic rings. If the magnetic field is applied along the shorter side, then the remanent states turn out to be vortex state. The hysteresis loss indicated by area of the hysteresis loop was found to be decreasing gradually with the increment of either $r$ or $b_{\mathrm{\text{out}}}$. On the other hand, the remanent magnetization increased with increment of $r$ but decreased with the increment of $b_{\mathrm{\text{out}}}$. The changes were attributed to three parameters mainly: inner curvature, exchange energy and demagnetization energy. The changes in loop area were discussed in light of variation of these three parameters.

Rectangular diaphragm is commonly used as a pressure sensitive component in MEMS pressure sensors. Its deformation under applied pressure directly determines the performance of micro-devices, accurately acquiring the pressure–deflection relationship, therefore, plays a significant role in pressure sensor design. This paper analyzes the deflection of an isotropic rectangular diaphragm under combined effects of loads. The model is regarded as a clamped plate with full surface uniform load and partially uniform load applied on its opposite sides. The full surface uniform load stands for the external measured pressure. The partial load is used to approximate the opposite reaction of the silicon island which is planted on the diaphragm to amplify the deformation displacement, thus to improve the sensitivity of the pressure sensor. Superposition method is proposed to calculate the diaphragm deflections. This method considers separately the actions of loads applied on the simple supported plate and moments distributed on edges. Considering the boundary condition of all edges clamped, the moments are constructed to eliminate the boundary rotations caused by lateral load. The diaphragm’s deflection is computed by superposing deflections which produced by loads applied on the simple supported plate and moments distributed on edges. This method provides higher calculation accuracy than Galerkin variational method, and it is used to analyze the influence factors of the diaphragm’s deflection, includes aspect ratio, thickness and the applied force area of the diaphragm.

In this paper, we propose a methodology for identifying typefaces of printed Chinese characters in documents. Three kinds of features, stroke width means, stroke width variations, and aspect ratio, are first used to classify character typefaces as: Black, Li, Kai-Round, or Ming-Song. Each of the last two groups contains two typefaces. Vertical/horizontal stroke width ratios are used to distinguish between the Ming and Song typefaces and accumulative pixel ratio to distinguish between the Kai and Round typefaces. Six different typeface feature distributions measured from 5401 printed Chinese characters are considered, and a trapezoid-shaped membership function is constructed for each distribution. Based on these membership functions, we determine what typeface each input character belongs to using a two-level decision tree. To increase the identification rate, the typeface of a certain character is adjusted according to the typeface identification results of the front and the next characters. In the character recognition system, we use two statistical features: crossing counts and contour directional counts. We achieved an 89.87% typeface identification rate in our experiments, and a 95.60% character recognition rate.

Mesh generation is a great example of inter-disciplinary research. Its development is built upon advances in computational and combinatorial geometry, data structures, numerical analysis, and scientific applications. Its success is justified not only by mathematical proofs about the quality and the numerical relevancy of geometry-based meshing algorithms, but also by the performance of meshing software in real applications. It embraces both provably good algorithms and practical heuristics. This paper presents a brief overview of algorithms, theorems, and software in mesh generation.

In colloidal suspensions containing large and small particles, a peculiar attractive force caused by entropy appears, this force can cause aggregation of large particles. With the concentration of small particles increasing, the large particles can be endocytosed by vesicle. A continuum model is developed to investigate the equilibrium mechanics between a biomembrane and an enveloped colloidal particle with different aspect ratios. The results show that the endocytosis of colloidal particle depends on the aspect ratio of colloidal particle. For a spherical colloidal particle (aspect ratio is zero), the entropy provides sufficient favorable energy to drive its engulfment; however, at a high aspect ratio, the entropy is not sufficient to overcome the resistance from the biomembrane and causes endocytosis.

The fractal dimensions of real world objects are commonly investigated using digital images. Unfortunately, these images are unable to represent an infinitesimal range of scales. In addition, a proper evaluation of the applied methods that encompass the image processing techniques is often missing. Several mathematical well-defined fractals with theoretically known fractal dimensions, represented by digital images, were investigated in this work. The very popular Box counting method was compared to a new image pyramid approach as well as to the Minkowski dilation method. Effects from noise and altered aspect ratios were also considered. The new Pyramid method is quite identical to the Box counting method, but it is easier to implement. Additionally, the calculation times are much shorter and memory requirements are almost comparable.

In the framework of passive control devices for the seismic protection of new and existing buildings, large attention is getting more focused on Steel Plate Shear Walls (SPSW). Such a system, which is characterized by the use of slender steel panels, has been largely adopted in the last few years both in the North America and Japan. The structural behavior of slender shear walls is strongly conditioned by buckling phenomena, which may have a significant influence also on the ultimate strength of the system, despite the development of stable post-critical behavior due to tension field mechanism. In order to assess the influence of the geometry on the structural behavior of shear plates, in this paper, the theoretical behavior of steel panels in shear, based on existing simplified methodologies (PFI method and strip model theory) is analyzed and then compared to the results obtained by an extensive numerical study carried out by means of accurate finite element models. The comparison between theoretical and numerical results has been developed with reference to different values of the thickness and by varying the aspect ratio of the plate. In addition, the influence of intermediate stiffeners is investigated. On the whole, the obtained results provide useful information for the correct design of slender steel plates in shear to be used as stiffening and strengthening devices in new and existing framed structures.

The transverse vibration control of a clamped, rectangular, isotropic plate by a vibratory flap subjected to harmonic excitation has been investigated by Finite Element Analysis (FEA) and experimental technique. The vibratory flap is a new plate-type dynamic vibration absorber, which can vibrate on the plate when attached as a cantilever plate. The study has been focused specifically on the influence of aspect ratio of vibratory flap on the dynamic response of the plate at constant mass ratio and constant tuning frequency ratio. The study has revealed that the dynamic response of the plate varies with respect to the aspect ratio for aforementioned conditions. An optimum aspect ratio has also been obtained by minimizing the mass ratio with maximum attenuation in the first and second target frequencies. The results have shown that the optimized flap can trim down the plate vibrations by up to 90–95% in the fundamental mode. Moreover, the dynamic response of the plate can be improved to a great extent due to the adoption of an optimal aspect ratio of the flap. Finally, the experimental outcomes have shown fairly good agreement with the results obtained from the finite element analysis.

The present study deals with numerical and experimental investigations on the vibration behavior of fiber-metal-laminated (FML) plates, a new aircraft material. A finite element (FE)-based formulation is established for the plate using the first-order Reissner–Mindlin theory, including both fibers and metals of different material properties in alternate layers. A four-node isoparametric quadratic element with five degrees of freedom per node is adopted in the analysis. Convergence studies and comparison with previous studies are made to validate the present FE formulation. A set of experiments was conducted to get natural frequencies of vibration for glass FML (GFML) plates using Bruel and Kjaer (B&K) Fast Fourier Transform (FFT) analyzer with PULSE platform. The effects of different parameters such as aspect ratio, side-to-thickness ratio, ply orientation, and boundary conditions on the dynamic behavior of the FMLs are studied. Good agreement is achieved between the numerical and experimental results. Both results indicate that increasing the aspect ratio can increase the natural frequency of the FML plate, while the increase in the side-to-thickness ratio decreases the natural frequency of vibration. The boundary conditions can significantly affect the natural frequency of the FML plates due to the restraint effect at the edges.

The purpose of this study is to investigate the flutter control scheme of super long-span bridges with various aspect ratios (e.g. width to height (B/H)) using passive aerodynamic countermeasures. Through a series of wind tunnel testing and theoretical analysis, three types of passive aerodynamic countermeasures, i.e. vertical central stabilizer (VCS), wind barrier and inspection rail, were investigated for five typical aspect ratios of a closed-box girder bridge. The results show that both the aspect ratio and flutter critical wind speed generally increase with the decrease of the ratio of torsional and vertical frequencies of the bridge. In the case of an aspect ratio of 8.9, a downward VCS (DVCS) has a much better flutter performance than that of an upward VCS (UVCS) because aerodynamic damping of Part A and Part D could produce a higher heaving degree of freedom (DOF) participation level. Furthermore, the position variation of wind barriers is superior to their shape variation for the bridge with an aspect ratio of 8.3, and the flutter performance of the girder with a combination of the wind barrier (WB3P3) and UDVCS with 0.3h/H DVCS appears to be better than that without countermeasures. In addition, the installation of an inspection rail near the bottom point of an inclined-web (IR3) has the best flutter control effect among four positions of inspection rails.

The effects of different percentages of multiwall carbon nanotube (MWCNT) on natural frequencies of polymer composite plates of varying edge-to-thickness ratio, aspect ratio and boundary conditions at ambient temperature are investigated experimentally and numerically. Conventional hand lay-up technique is used to prepare the MWCNT polymer composite plates with different percentages of carbon nanotubes (CNTs) mixed to the polymer. The elastic properties are determined experimentally by conducting uniaxial tensile test in the universal testing machine INSTRON 8862 as per ASTM D-3039. A set of experiments were conducted for the natural frequencies of vibration of MWCNT composite plates using the Bruel and Kjaer Fast Fourier Transform (FFT) analyzer with pulse platform. Detailed parametric studies are carried out to determine the effect of weight fraction of CNTs, aspect ratios, edge-to-thickness ratios and boundary conditions on the natural frequency of composite plates. Numerical solutions were obtained by the commercial finite element method (FEM) package ABAQUS. A simulation model is developed using the same geometrical and material properties determined experimentally from which the frequency responses are obtained. The simulation results are found to be consistent with the experimental ones. The results obtained showed an increase in elastic properties and natural frequencies up to 0.3 wt.% of MWCNT and decrease thereafter for all cases due to agglomeration of CNT in the polymer matrix. The morphology and dispersion of the CNTs in composites at micro level are investigated by using scanning electron microscopy (SEM) to further corroborate the behavior of specimens.

CFD simulations were performed for 60 human cerebral aneurysms (30 previously ruptured and 30 previously unruptured) to study the behavior of the time-averaged wall shear stress (TAWSS) with respect to the aspect ratio (AR), implementing a set of low, normal, and high-pressure differences between the inlet and the outlets of each artery. It is well known that there exists a direct relationship between TAWSS and the rupture. In this investigation, we presented an important result because the condition of the pressure among the branches and the AR may be measured in any patient, then a slope may be associated, and finally a TAWSS may be estimated. We found that when the pressure difference increased, the absolute slopes between TAWSS and AR increased as well. Also, the magnitude of the slope in the previously unruptured aneurysms was 4.7 times the slope in the previously ruptured aneurysms. On the other hand, TAWSS was higher in the previously unruptured aneurysm than previously ruptured aneurysms due to the unruptured aneurysms that have a smaller surface area. Furthermore, we analyzed the relationship between TAWSS and other geometric parameters of the aneurysm, such as bottleneck and non-sphericity index; however, no correlation was found for either cases.