Two-dimensional Expansion Research Articles

Optical system design of the coded aperture imaging spectrometer

The coded aperture imaging spectrometer system based on the double-Amici-prism is designed in this paper, which includes the telescope objective, the coded template, the double-Amici-prism, the collimator lens and the imaging lens. This optical system can obtain a high diffraction efficiency. Compared to the imaging spectrometer system with a slit for this kind of system, the field of view is a two-dimensional spatial expansion, increasing the difficulty of design. For the subsequent data inversion algorithm, perfect imaging is needed, and based on this, the optical aberration of the system should be corrected carefully wildly. In this paper, we design and analyse the features of the imaging spectrometer system based on the double-Amici-prism, then the comple imaging spectrometer system. Telescope objective is designed to be telecentric, its MTF at 39 line pairs is 0.8, implying that good images can be obtained. Innovatively, an inverted telescope objective is used as a collimation system.The imaging spectrometer system's MTF at 39 line pairs is higher than 0.65. The imaging of the outdoor target scene, obtained by the coded aperture imaging spectrometer, proves that the design principle is feasible,the system is of high diffraction efficiency, the full-field imaging is of good quality, and the full spectrum of data is creditabe.

Rolling resistance of a rigid sphere with viscoelastic coatings

We present a novel three-dimensional boundary-element formulation that fully characterizes the mechanical behavior of the external boundary of a multi-layered viscoelastic coating attached to a hard rotating spherical core. The proposed formulation incorporates both, the viscoelastic, and the inertial effects of the steady-state rolling motion of the sphere, including the Coriolis effect. The proposed formulation is based on Fourier-domain expressions of all mechanical governing equations. It relates two-dimensional Fourier series expansions of surface displacements and stresses, which results in the formation of a compliance matrix for the outer boundary of the deformable coating, discretized into nodes. The computational cost of building such a compliance matrix is optimized, based on configurational similarities and symmetry. The proposed formulation is applied, in combination with a rolling contact solving strategy, to evaluate the viscoelastic rolling friction of a coated sphere on a rigid plane. Steady-state results generated by the proposed model are verified by comparison to those obtained from running dynamic simulations on a three-dimensional finite element model, beyond the transient. A detailed application example includes a verification of convergence and illustrates the dependence of rolling resistance on the applied load, the thickness of the coating, and the rolling velocity.

Controlling hiding capacity using image characteristics with a 2D-DE data hiding scheme

Reversible data hiding techniques have gained much attention during the last few years because of the losslessness requirements of critical applications in military and medical fields. Among the various reversible data hiding techniques, difference expansion (DE) technique is one of the most popular techniques. The most common thing between DE-based schemes is their dependence on one or more thresholds. The threshold is used in order to control the hiding capacity aiming at keeping high visual quality of the embedded image. However, there is no such automatic way to predict or determine those thresholds as they are usually predefined. In this paper, we study the possibility of utilizing image characteristics as thresholds with a block based two-dimensional difference expansion scheme (2D-DE). The experimental results show that a threshold based on standard deviation may be used to control the hiding capacity and this leads to enhance the visual quality.

Accurate 2d finite element calculations for hydrogen in magnetic fields of arbitrary strength

Recent observations of hundreds of hydrogen-rich magnetic white dwarf stars with magnetic fields up to 105 T (103 MG) have called for more comprehensive and accurate databases for wavelengths and oscillator strengths of the H atom in strong magnetic fields for all states evolving from the field-free levels with principal quantum numbers n≤10. We present a code to calculate the energy eigenvalues and wave functions of such states which is capable of covering the entire regime of field strengths B=0T to B∼109T. We achieve this high flexibility by using a two-dimensional finite element expansion of the wave functions in terms of B-splines in the directions parallel and perpendicular to the magnetic field, instead of using asymptotically valid basis expansions in terms of spherical harmonics or Landau orbitals. We have paid special attention to the automation of the program such that the data points for the magnetic field strengths at which the energy of a given state are calculated can be selected automatically. Furthermore, an elaborate method for varying the basis parameters is applied to ensure that the results reach a pre-selected precision, which also can be adjusted freely. Energies and wave functions are stored in a convenient format for further analysis, e.g. for the calculation of transition energies and oscillator strengths. The code has been tested to work for 300 states with an accuracy of better than 10−6 Rydberg across several symmetry subspaces over the entire regime of magnetic field strengths. Program summaryProgram title: H2dbCatalogue identifier: AERB_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERB_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 158867No. of bytes in distributed program, including test data, etc.: 322671Distribution format: tar.gzProgramming language: Fortran95.Computer: 1 HP Compaq dc5750.Operating system: Linux.RAM: At least 2 GBClassification: 2.1.External routines: Lapack (http://www.netlib.org/lapack/)Nature of problem:The hydrogen problem in the presence of a magnetic field of arbitrary strength shall be solved for all states up to a principal quantum number of n=10. We obtain the full energy vs. field strength function within a certain precision.Solution method:We expand the wave functions in a 2d B-spline basis, vary the corresponding energy functional for the B-spline coefficients and solve the resulting generalised eigenvalue problem. The B-spline basis parameters are adapted iteratively to ensure the overall precision of our results.Restrictions:Non-relativistic Hamiltonian, non-moving atom.Unusual features:Automated analysis of the states at magnetic field strengths from B=0T to B=109T.Running time:Seconds to minutes per single result; hours to days for a full analysis.

Efficient Rainbow Options Pricing Methods Based on Two-Dimensional Fourier Series Expansions

An efficient option pricing method based on two dimensional Fourier series expansions was proposed by Ruijter and Oosterlee in 2012, recently, this method was extended to modified two dimensional Fourier series expansions by Meng and Ding. In this paper, these methods are applied to deduce efficient pricing formulae for two bivariate assets rainbow options, so called as put-on-mini- mum and call-on-maximum. A series of numerical experiments for such options pricing is presen- ted to compare these methods, and some conclusions are then given based on those numerical results.

Efficient Rainbow Options Pricing Methods Based on Two-Dimensional Fourier Series Expansions

An efficient option pricing method based on two dimensional Fourier series expansions was proposed by Ruijter and Oosterlee in 2012, recently, this method was extended to modified two dimensional Fourier series expansions by Meng and Ding. In this paper, these methods are applied to deduce efficient pricing formulae for two bivariate assets rainbow options, so called as put-on-mini- mum and call-on-maximum. A series of numerical experiments for such options pricing is presen- ted to compare these methods, and some conclusions are then given based on those numerical results.

Two-dimensional Legendre wavelets for solving fractional Poisson equation with Dirichlet boundary conditions

Abstract In this paper, the two-dimensional Legendre wavelets are applied for numerical solution of the fractional Poisson equation with Dirichlet boundary conditions. In this way, a new operational matrix of fractional derivative for the Legendre wavelets is derived and then this operational matrix has been employed to obtain the numerical solution of the above-mentioned problem. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifies the problem. The convergence of the two-dimensional Legendre wavelets expansion is investigated. Also the power of this manageable method is illustrated.

Diel leaf growth of soybean: a novel method to analyze two-dimensional leaf expansion in high temporal resolution based on a marker tracking approach (Martrack Leaf).

BackgroundWe present a novel method for quantitative analysis of dicot leaf expansion at high temporal resolution. Image sequences of growing leaves were assessed using a marker tracking algorithm. An important feature of the method is the attachment of dark beads that serve as artificial landmarks to the leaf margin. The beads are mechanically constricted to the focal plane of a camera. Leaf expansion is approximated by the increase in area of the polygon defined by the centers of mass of the beads surrounding the leaf. Fluctuating illumination conditions often pose serious problems for tracking natural structures of a leaf; this problem is circumvented here by the use of the beads.ResultsThe new method has been used to assess leaf growth in environmental situations with different illumination conditions that are typical in agricultural and biological experiments: Constant illumination via fluorescent light tubes in a climate chamber, a mix of natural and artificial illumination in a greenhouse and natural illumination of the situation on typical summer days in the field. Typical features of diel (24h) soybean leaf growth patterns were revealed in all three conditions, thereby demonstrating the general applicability of the method. Algorithms are provided to the entire community interested in using such approaches.ConclusionsThe implementation Martrack Leaf presented here is a robust method to investigate diel leaf growth rhythms both under natural and artificial illumination conditions. It will be beneficial for the further elucidation of genotype x environment x management interactions affecting leaf growth processes.

Stiff, strong zero thermal expansion lattices via the Poisson effect

Abstract

Two-Dimensional Orthogonal DCT Expansion in Trapezoid and Triangular Blocks and Modified JPEG Image Compression

In the conventional JPEG algorithm, an image is divided into eight by eight blocks and then the 2-D DCT is applied to encode each block. In this paper, we find that, in addition to rectangular blocks, the 2-D DCT is also orthogonal in the trapezoid and triangular blocks. Therefore, instead of eight by eight blocks, we can generalize the JPEG algorithm and divide an image into trapezoid and triangular blocks according to the shapes of objects and achieve higher compression ratio. Compared with the existing shape adaptive compression algorithms, as we do not try to match the shape of each object exactly, the number of bytes used for encoding the edges can be less and the error caused from the high frequency component at the boundary can be avoided. The simulations show that, when the bit rate is fixed, our proposed algorithm can achieve higher PSNR than the JPEG algorithm and other shape adaptive algorithms. Furthermore, in addition to the 2-D DCT, we can also use our proposed method to generate the 2-D complete and orthogonal sine basis, Hartley basis, Walsh basis, and discrete polynomial basis in a trapezoid or a triangular block.

An efficient pricing method for rainbow options based on two-dimensional modified sine–sine series expansions

An efficient option pricing method based on the Fourier cosine series expansion was proposed by Fang and Oosterlee [A novel option pricing method based on Fourier-cosine series expansions, SIAM J. Sci. Comput. 31 (2008), pp. 826–848], and recently it has been used in two-dimensional cases by Ruijter and Oosterlee [Two-dimensional Fourier cosine series expansion method for pricing financial options, SIAM J. Sci. Comput. 34 (2012), pp. B642–B671]. In this paper, we consider a modification of the Fourier sine–sine expansion, whereby in [−1, 1] the sin(π nx) functions are replaced by sin(π(n−)x), n≥1, for pricing rainbow options. Feasible approaches for obtaining the pricing formulae are presented. A numerical comparison and a flexible and general error analysis are considered to prove the effectiveness of the method. Practical applications to basket options and correlation options under different models are also given. They indicate satisfactory convergence and efficiency as expected.

Time evolution of the two-dimensional expansion velocity distributions of the cathode plasma in pulsed high-power diodes

AbstractA combination of electrical and optical diagnostics has been used to investigate the time evolution of the two-dimensional expansion velocity distributions of the cathode plasma in pulsed high-power diodes. The perveance model based on the Child-Langmuir law was used to calculate the expansion velocity of the diode plasmas from voltage and current profiles. Additionally, a four-channel high speed framing camera was used to observe the formation and subsequent movement of the cathode plasma. More accurate and valuable information about the dynamics of the cathode plasma was also acquired by utilizing the digital image processing methods. Results from the experiments and theoretical analysis were compared. In this paper, the experiments have been performed using a high-voltage pulse generator with 200 kV output voltage and 110 ns pulse duration. Current densities up to 440 A/cm2were produced. The observation of the cathode plasma expansion in transverse direction indicated that the diode current was cathode-limited in the current rising stage (the first 60 ns of the current pulse). The perveance model should be modified taking in account the time dependent expanding plasma surface (i.e., not the whole cathode surface) for this period. The velocity in the direction parallel to the cathode surface (transverse velocity) was much larger than that in the direction perpendicular to the cathode surface (longitudinal velocity), and further, it dropped from 90 cm/μs to nearly 20 cm/μs rapidly. It was shown that, during the current flattop stage, the plasma filled out all the surface of cathode and the diode current was space-charge-limited. The values of the transverse velocity and longitudinal velocity were nearly the same and decreased relatively slowly. The satisfactory coincidence of experimental and calculated (both were in the range of 6–8 cm/μs) values of the cathode plasma expansion velocities was obtained.

Preparation of informational triage method in the disaster countermeasure headquarters using the two-dimensional expansion method

Preparation of informational triage method in the disaster countermeasure headquarters using the two-dimensional expansion method

Three-dimensional boundary element formulation of an incompressible viscoelastic layer of finite thickness applied to the rolling resistance of a rigid sphere

A three-dimensional boundary element formulation of an incompressible viscoelastic layer of finite thickness is proposed, in a moving frame of reference. The formulation is based on two-dimensional Fourier series expansions of relevant mechanical fields in the continuum of the layer. The linear viscoelastic material is characterized, in the most general way, by its frequency-domain master curves. The presented methodology results in a compliance matrix for the layer’s upper boundary, which includes the effects of steady-state motion and can be used in any contact problem-solving strategy. The proposed formulation is used, in combination with a contact solver, to build a full three-dimensional model for the steady-state rolling/sliding resistance incurred by a rigid sphere on the layer. Energy losses include viscoelastic damping and surface friction. The model is tested and its results are found to be consistent with existing solutions in limiting cases. An example is explored and the corresponding results are used to illustrate the influence of different parameters on the rolling resistance. General aspects of previously-described dependences are confirmed.

Expansion and differentiation of human primary osteoblasts in two- and three-dimensional culture

Despite the regenerative capability of bone, treatment of large defects often requires bone grafts. The challenge for bone grafting is to establish rapid and sufficient vascularization. Three-dimensional (3D) multicellular spheroids consisting of the relevant cell types can be used as “mini tissues” to study the complexity of angiogenesis. We investigated two-dimensional (2D) expansion, differentiation and characterization of primary osteoblasts as steps toward the establishment of 3D multicellular spheroids. Supplementation of cell culture medium with vitamin D3 induces the osteocalcin expression of osteoblasts. An increased osteocalcin concentration of 10.8 ± 0.58 ng/ml could be measured after 19 days in supplemented medium. Vitamin D3 has no influence on the expression of alkaline phosphatase or the deposition of calcium. Expression of these additional osteogenic markers requires addition of a cocktail of osteogenic factors that, conversely, have no influence on the expression of osteocalcin. Supplementation of the cell culture medium with both vitamin D3 and a cocktail of osteogenic factors is recommended to produce an osteoblast phenotype that secretes osteocalcin, expresses alkaline phosphatase and deposits calcium. In such a supplemented medium, a mean osteocalcin concentration of 11.63 ± 4.85 ng/ml was secreted by the osteoblasts. Distinguishing osteoblasts and fibroblasts remains a challenge. Neither differentiated nor undifferentiated osteoblasts can be distinguished from fibroblasts by the expression of CD90, ED-A-fibronectin or α-smooth muscle actin; however, these cell types exhibit clear differences in their growth characteristics. Osteoblasts can be arranged as 3D spheroids by coating the bottom of the cell culture device with agarose. The cellular composition of 3D multicellular spheroids can be evaluated quantitatively using vital fluorescence labeling techniques. Spheroids are a promising tool for studying angiogenic and osteogenic phenomena in vivo and in vitro.

Numerical Investigation on Laminar Flow Due to Sudden Expansion Using Nanofluid

Laminar two-dimensional sudden expansion flow of different nanofluids is studied numerically. The governing equations are solved using stream function-vorticity method. The effect of volume fraction of the nanoparticles and type of nanoparticles on flow behaviour is examined and found significant impact. The flow response to Reynolds number in the presence of nanoparticles is examined. The presence of nanoparticles decreases the flow bifurcation Reynolds number. The size and the reattachment length of the bottom wall recirculation increase with increasing volume fraction and particle density. The effect of volume fraction and density of nanoparticles on friction factor is reported. The bottom wall recirculation strongly respond to the variation in volume faction and type of particles. However, weak response is observed for top wall recirculation.

Bacterial Colony from Two-Dimensional Division to Three-Dimensional Development

On agar surface, bacterial daughter cells form a 4-cell array after the first two rounds of division, and this phenomenon has been previously attributed to a balancing of interactions among the daughter bacteria and the underneath agar. We studied further the organization and development of colony after additional generations. By confocal laser scanning microscopy and real-time imaging, we observed that bacterial cells were able to self-organize and resulted in a near circular micro-colony consisting of monolayer cells. After continuous dividing, bacteria transited from two-dimensional expansion into three-dimensional growth and formed two to multi-layers in the center but retained a monolayer in the outer ring of the circular colony. The transverse width of this outer ring appeared to be approximately constant once the micro-colony reached a certain age. This observation supports the notion that balanced interplays of the forces involved lead to a gross morphology as the bacteria divide into offspring on agar surface. In this case, the result is due to a balance between the expansion force of the dividing bacteria, the non-covalent force among bacterial offspring and that between bacteria and substratum.

Geographic Sampling Scheme as a Determinant of the Major Axis of Genetic Variation in Principal Components Analysis

Principal component (PC) maps, which plot the values of a given PC estimated on the basis of allele frequency variation at the geographic sampling locations of a set of populations, are often used to investigate the properties of past range expansions. Some studies have argued that in a range expansion, the axis of greatest variation (i.e., the first PC) is parallel to the axis of expansion. In contrast, others have identified a pattern in which the axis of greatest variation is perpendicular to the axis of expansion. Here, we seek to understand this difference in outcomes by investigating the effect of the geographic sampling scheme on the direction of the axis of greatest variation under a two-dimensional range expansion model. From datasets simulated using each of two different schemes for the geographic sampling of populations under the model, we create PC maps for the first PC. We find that depending on the geographic sampling scheme, the axis of greatest variation can be either parallel or perpendicular to the axis of expansion. We provide an explanation for this result in terms of intra- and interpopulation coalescence times.

MODE ANALYSIS AND SYSTEMATICAL DESIGN OF WIDE-BANDWIDTH PHOTONIC CRYSTAL 60° WAVEGUIDE BENDS WITH HIGH TRANSMISSION

We present a procedure to enhance the transmission efficiency of a photonic crystal slab waveguide bend by introducing an air hole with the same radius at the center of bend and optimizing the positions of three neighboring holes in the corner. The improvement relies only on the method of displacing holes which is technologically preferred to controlling variations in hole size or shape. We employ the effective refractive index approach and two-dimensional plane wave expansion method to analyze the guide modes of the straight waveguide and waveguide bend. The transmission character of bent waveguides is investigated using two-dimensional finite-difference time-domain method. Numerical studies demonstrate that the approximate method of mode analysis is unsuitable to our model. Alternatively, we systematically study the effect of different positions of the holes on the transmission. The optimized bends for the high transmission with broad bandwidth are proposed.

Wideband and low dispersion slow-light waveguide based on a photonic crystal with crescent-shaped air holes

We present a procedure to generate slow light with a large group index, wideband, and low dispersion in our suggested photonic crystal waveguide. By modulation of the declinations in the first two rows of air holes, the group index, the bandwidth, and the dispersion can be tuned effectively. Utilizing the two-dimensional plane wave expansion method (PWE) and the finite-difference time-domain method (FDTD), we demonstrate slow light with the group indices of 23, 35, and 45, respectively, while restricting the group-index variation within a 10% range. We accordingly attain an available bandwidth of 40.7, 23.7, and 5.1 nm, respectively. Meanwhile, the normalized delay-bandwidth product stays around 0.45, with minimal dispersion less than 0.2 (ps2/m) for all the cases.