Two-dimensional Integration Research Articles

Photocycloaddition of Pt(II) Complexes in Supramolecular Composites for Three-dimensional + Two-dimensional Image Integration via Reaction Orthogonality

Photocycloaddition of Pt(II) Complexes in Supramolecular Composites for Three-dimensional + Two-dimensional Image Integration via Reaction Orthogonality

Theoretical study of differential cross sections for the ionization of helium by fast proton impact

Abstract We present the angular distribution of the ejected electron for single ionization of He by fast proton impact. A four-body formalism of the three-Coulomb wave is applied to calculate the triple differential cross sections at several impact energies in the scattering, perpendicular and azimuthal planes. Moreover, the three-body formalism of three-Coulomb, two-Coulomb and first Born approximation models has also been used to study the many-body effect on electron emission and the validity of the models. In the three-Coulomb wave model, the final state wave function incorporates distortion due to the three-body mutual Coulombic interaction. In this formalism, we use an uncorrelated and correlated Born initial state, which consists of a plane wave for the incoming projectile times a two-electron bound state wavefunction of the helium atom representing the 1s2(1S) state. But, in the case of the three-body formalism, the initial state wavefunction consists of a long-range Coulomb distortion for the incoming projectile and one active electron of the He atom described by the Roothaan–Hartree–Fock wavefunction. The structure with a single or two peaks with unequal intensity is observed in the angular distributions of the triple differential cross sections for the different kinematic conditions. In addition, the influence of static electron correlations is investigated using different bound state wavefunctions for the ground state of the He target. In the four-body formalism, the present computations are very fast by reducing a nine-dimensional integral to a two-dimensional real integral. Despite the simplicity and speed of the proposed quadrature, the comparison shows that the obtained results are in reasonable agreement with the experiment and are compatible with those of other theories.

Gaussian quadrature for certain two-dimensional hypersingular integrals

In this paper, the Gaussian quadrature formula is used to approximately calculate two-dimensional hypersingular integrals of the form ∬Sf(x,y)r3dS on the circular domain. The two-dimensional hypersingular integrals are changed into iterated integrals by polar transformation. The inner layer of the integral has singularity and Gaussian quadrature formula is constructed for this part. The outer layer without singularity is calculated by Gauss–Legendre quadrature formula of Riemann integral. The corresponding theoretical analysis is given. Furthermore, this type of two-dimensional hypersingular integral is extended to the form ∬Sf(x,y)rp+1dS(p>2) and an error estimate is also derived. Several numerical examples are presented to verify the effectiveness of the proposed algorithm, no matter the singularity is located at the center or near the boundary of the circular domain.

The effect of different edge conditions on the motion of a submerged elastic disc

The present study examines the effects of various edge conditions of a submerged flexible disc on wave propagation for infinite-depth water within the framework of linear water waves theory. Three types of edge conditions (namely Free edge, simply supported edge, and clamped edge) are taken into consideration for the analysis. The governing boundary value problem (BVP) has been solved by reducing it to a two-dimensional hypersingular integral equation. The notion of modal analysis has been adopted to examine the structural response of the disc on the propagation of waves. Later, the two-dimensional hypersingular integral has been transformed into a second kind one-dimensional Fredholm integral equation by applying Fourier series expansion. Finally, the Nystrom technique based on Gauss–Legendre quadrature nodes is used to obtain an approximate solution of the one-dimensional integral equation. The computed solution is used to evaluate the numerical estimates of the physical quantities such as added mass, damping coefficient, hydrodynamic force, and surface elevation for different edge conditions mentioned earlier.

Dynamics, quantum states and Compton scattering in nonlinear gravitational waves

The classical dynamics and the construction of quantum states in a plane wave curved spacetime are examined, paying particular attention to the similarities with the case of an electromagnetic plane wave in flat spacetime. A natural map connecting the dynamics of a particle in the Rosen metric and the motion of a charged particle in an electromagnetic plane wave is unveiled. We then discuss how this map can be translated into the quantum description by exploiting the large number of underlying symmetries. We examine the complete analogy between Volkov solutions and fermion states in the Rosen chart and properly extend this to massive vector bosons. We finally report the squared S-matrix element of Compton scattering in a sandwich plane wave spacetime in the form of a two-dimensional integral.

A (2+1)-dimensional domain wall at one-loop

We consider the domain wall in the (2+1)-dimensional ϕ4 double well model, created by extending the ϕ4 kink in an additional infinite direction. Classically, the tension is m3/3λ where λ is the coupling and m is the meson mass. At order O(λ0) all ultraviolet divergences can be removed by normal ordering, less trivial divergences arrive only at the next order. This allows us to easily quantize the domain wall, working at order O(λ0). We calculate the leading quantum correction to its tension as a two-dimensional integral over a function which is determined analytically. This integral is performed numerically, resulting in −0.0866m2. This correction has previously been computed twice in the literature, and the results of these two computations disagreed. Our result agrees with and so confirms that of Jaimunga, Semenoff and Zarembo. We also find, at this order, the excitation spectrum and a general expression for the one-loop tensions of domain walls in other scalar models.

Abstract 6244: MultiTME: A Bayesian method for integration and analysis of multimodal, multi-patient spatial profiling data

Abstract The role of the tumor microenvironment (TME) in cancer evolution and progression is complex and multi-faceted. Multiple cellular phenotypes and patterns of cell-cell communication have been implicated as drivers of drug resistance and metastasis. The spatial architecture of the TME is emerging as particularly important in characterizing the trajectory of tumor growth and response to therapy. Accordingly, there has been a rapid rise in technologies to spatially profile the TME. Each technology focuses on a different modality (e.g. transcriptomics, proteomics, metabolomics) and operates at a different granularity, from coarse-grained tissue spots aggregating dozens of cells to fine-grained subcellular resolution. There is currently no computational method capable of drawing unified inferences across modalities. We introduce MultiTME, a single, holistic generative model for jointly modeling multimodal data across multiple samples in a cohort. MultiTME addresses these challenges through a two-dimensional integration of both samples and multimodal data. MultiTME incorporates a cohort of tissue samples, enabling the joint modeling of different samples within a single analytical framework. This integration allows for a comprehensive analysis of the spatial distribution of cell types across multiple samples, enhancing the understanding of TME variability and the identification of robust biomarkers. MultiTME also integrates multimodal data with varying resolutions, such as Spatial Transcriptomics (ST), single-cell RNA sequencing (scRNA-seq), and Imaging Mass Cytometry (IMC), and provides a multi-layered understanding of the TME. This integration enables the modeling of TME at a finer scale and the discovery of cell types and subtypes that are not distinguishable using single-modal approaches. It also provides concurrent expression profiles across different modalities, leading to the identification of novel biomarkers. We demonstrate MultiTME's efficiency and scalability with a dataset of coupled ST, scRNA-seq, and IMC from a cohort of 8 lung cancer patients. MultiTME's capability to handle both intra-cohort and inter-modality variability offers a panoramic view of TME and helps identify biomarkers and therapeutic targets for cancer screening and treatment. MultiTME is open source. Citation Format: Haoran Zhang, Jeff Quinn, Liron Yoffe, Vivek Mittal, Wesley Tansey. MultiTME: A Bayesian method for integration and analysis of multimodal, multi-patient spatial profiling data [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 6244.

IRing: a program for two-dimensional powder diffraction image integration with automatic calibration

iRing is a processing program developed for the more convenient processing of two-dimensional diffraction images collected by image detectors. During the calibration process, iRing uses the Hough transform to achieve automatic peak finding and calibration. The speed of calibration is greatly improved and the difficulty of calibration is reduced. iRing also provides many supporting functions to help process data.

Thermal equation of state of rhodium to 191 GPa and 2700 K using double-sided flash laser heating in a diamond anvil cell

The phase behavior of rhodium (Rh) metal has been studied to 191 GPa and 2700 K using a combination of room-temperature isothermal compression and double-sided flash laser heating experiments. The isothermal compression data have been fitted with a second-order adapted polynomial of order L equation of state (EoS) with best-fitting parameters of V0=13.764(2)Å3/atom, K0=258(3)GPa, and K′=5.36(9). Two-dimensional maps of the uniaxial stress component t are presented for Rh at different pressures showing the spatial distribution of the local stress state of a relatively high-yield strength material encased in a Bi pressure medium. In addition, a simple, thermal pressure equation-of-state model, based on a single Einstein temperature, has been fitted to the high-pressure-temperature data up to 2700 K at 148 GPa and ambient-pressure thermal expansion data up to 1982 K. Also determined are the best-fitting parameters to reproduce the thermal EoS within the two-dimensional integration software. The optimized parameters are V0=13.764Å3/atom, K0=260.54GPa, K′=5.114, αT=2.99×10−5 K−1, ∂αT/∂T=1.27×10−9 K−2, ∂K0/∂T=−6.43×10−5GPa/K, and ∂K′/∂T=−9.3×10−10K−1. Published by the American Physical Society 2024

Two dimensional elastic dynamically focused beam migration in transversely isotropic (TI) media

The anisotropic ray tracing equations of elastic waves are derived for calculating the central ray's travel time, trajectory, and parameters P and Q. Based on the anisotropic ray tracing algorithm, we proposed a transversely isotropic elastic dynamically focused beam migration for two dimensional media. Based on the two dimensional Kirchhoff-Helmholtz integral of elastic waves, the elastic imaging weight coefficients are used to reduce the crosstalk noise. Then, based on the previous research, we introduced a sign function to eliminate the effect of polarity reversal in qPqSV wave migration. Through model tests, it can be found that the proposed method can process the multicomponent seismic data and image the complex structures for anisotropic media. The optimized dynamic ray tracing algorithm is superior to the conventional one in computational efficiency. Furthermore, the proposed method eliminates the limitations of the Gaussian beam imaging. This method not only does not affect the accuracy of shallow imaging, but also enhances the energy focusing and the amplitude of deep layers. The model tests have shown the accuracy and effectiveness of our proposed method.

A new distance transformation method of estimating domain integrals directly in boundary integral equation for transient heat conduction problems

Accurate estimation of domain integrals is of crucial importance for the pseudo-initial condition method applied in transient heat conduction analysis. When small time step is used, the integrand of the domain integral changes dramatically and is close to singular. A straightforward evaluation of the domain integrals using Gaussian quadrature may produce large errors. To improve the computational accuracy of two-dimensional domain integrals in boundary integral equation, a new distance transformation method is presented in this paper. The proposed method takes the time step as the transformation parameter, implementing the new transformation in the radial direction directly. With the new distance transformation method, the integrand of the domain integral can be smoother, thus more accurate results can be obtained. Numerical examples have demonstrated the efficiency and accuracy of the proposed method.

The 6 degrees of curriculum integration in medical education in the United States

Despite explicit expectations and accreditation requirements for integrated curriculum, there needs to be more clarity around an accepted common definition, best practices for implementation, and criteria for successful curriculum integration. To address the lack of consensus surrounding integration, we reviewed the literature and herein propose a definition for curriculum integration for the medical education audience. We further believe that medical education is ready to move beyond “horizontal” (1-dimensional) and “vertical” (2-dimensional) integration and propose a model of “6 degrees of curriculum integration” to expand the 2-dimensional concept for future designs of medical education programs and best prepare learners to meet the needs of patients. These 6 degrees include: interdisciplinary, timing and sequencing, instruction and assessment, incorporation of basic and clinical sciences, knowledge and skills-based competency progression, and graduated responsibilities in patient care. We encourage medical educators to look beyond 2-dimensional integration to this holistic and interconnected representation of curriculum integration.

Ground vehicle gravimetry system based on SINS and two-dimensional LDV integration: error analysis and verification

As an effective tool for refining local gravity data with mGal accuracy, vehicle gravimetry system usually consists of Strapdown Inertial Navigation System (SINS) and Global Navigation Satellite System (GNSS). However, the traditional system is unable to achieve gravimetry in an environment without GNSS signal dues to heavy dependence on GNSS signal. To solve this problem, this study proposed a gravimetry method specifically for the environment without GNSS signal, which consists of the high-precision Strapdown Inertial Navigation System (SINS) and Laser Doppler Velocimeter (LDV) developed by our unit. Based on the error analysis, the system index requirements were proposed, and the relevant indexes of the LDV are verified through simulation and vehicle experiment. The simulation results for different velocimeter accuracies show that the internal accord accuracy of the system is within 1mGal when the velocimeter accuracy is 1 ‰, and the internal accord accuracies of the system are more than 1mGal when the velocimeter accuracies are 5 ‰ and 10‰. The results of the vehicle experiment for different dimensional velocimeters show that when the spatial resolution is 1.7 km, the SINS/LDV (2D) and SINS/GNSS integrated systems have an internal accord accuracy of 0.68 mGal and 0.54 mGal, respectively, while the SINS/LDV (1D) integrated system has an internal accord accuracy of 1.50 mGal. The feasibility of the SINS/LDV system and the necessity of the SINS/LDV system for the dimension and accuracy of the velocimeter are illustrated.

Occurrence of structural color by assembling single-particle layers of organo-modified nanodiamond

Structural color was realized for the first time by using organo-modified nanodiamonds with a particle size of 5 nm and by the transferring their single particle layers to the substrate as multilayers. The occurrence of various gradations of structural colors was achieved by obtaining step-like multilayers in which the thickness of assembly of the single-particle layer was changed stepwise. It was found that the occurrence of structural color by organo-modified inorganic nanoparticles requires densification of particle packing in the plane by a process of two-dimensional particle integration. As a two-dimensional particle integration process, the method of "repeating compression-expansion" at the air/water interface was effective. In addition, the color tone of each layer was systematically changed by annealing the organo-modified nanodiamond multilayers. Annealing improved the layered regularity, pseudo-lattice distortion, and crystallite size; however, the direct cause of the color phase change was expected to be the uniformity of the mesoscopic particle layer thickness accompanied by defect reduction.

An Analytical Solution on Vibration Reduction and Shear Force Mitigation of Cantilever Mindlin Plates Using Orthogonal Ribs

Vibration of aircraft wings and the dynamic stress concentration at the clamped edge are important research topics due to concerns on the safety of aircrafts. To have a better understanding of the problem, the free and forced vibration response of a ribbed rectangular cantilever plate representing a section of an aircraft wing is investigated in this study. A new analytical solution is developed for the vibration analysis of rib stiffened cantilever plates using Mindlin plate and Timoshenko beam theories alongside the finite integral transform technique. The one- and two-dimensional integral transforms are applied to the governing equations of beams and plates, respectively, where the coupling force components at the interface between the base plate and the beam(s) can be automatically defined during the integral transform. Eventually, the partial differential equations are transformed into a system of linear algebraic equations in which its derivation is rigorous and easily implemented. Good agreements are found between the results of analytical solution, finite element analysis (FEA) and related literature. The solution is then employed to study the vibration suppression of cantilever plates and the shear force at the clamped edge. It is found that the insertion of a pair of orthogonal ribs in the plate can effectively reduce its vibration. An optimum orthogonal ribbing pattern is obtained using multi-objective particle swarm optimization (MOPSO) algorithm, taking into consideration both the vibration suppression of the plate and the maximum induced shear force at the corners of the clamped edge.

Two-dimensional radial integration displacement discontinuity method with high-order isoparametric elements

To improve the accuracy of Displacement Discontinuity Method and enhance its adaptivity, a general-purpose two-dimensional displacement discontinuity method with both linear and quadratic isoparametric elements has been developed to model engineering discontinuity problems where cracks or cavities are involved. Linear and quadratic isoparametric elements have linear and quadratic distributions of displacement discontinuity, respectively. Both of them belong to the discontinuous element type, in which the geometry shape functions are different from the interpolation shape functions. A new general formulation, based on the boundary integral functions, is given for displacement discontinuity problems with arbitrary boundary shapes. This formulation contains singular and strongly singular integrals which can be evaluated in the sense of Cauchy principal value and Hadamard principal value, respectively. The radial integration technique is applied to perform these singular integrals with sufficiently high accuracy. Five numerical examples, most of which have analytic solutions, are given to illustrate the improved accuracy of the proposed approach. Compared with the constant displacement discontinuity element, the numerical results by using the present isoparametric displacement discontinuity elements show better accuracy.

Numerical evaluation for two-dimensional integral using higher order Gaussian quadrature

Presented in this paper is a computational approach that uses higher order Gaussian quadrature to improve the accuracy of the evaluation of an integral. The transformation from ξη space (standard Gaussian) to st space (higher order Gaussian) were shown throughout this paper. Not even that, the efficacy of this higher order Gaussian quadrature were tested by implementing and comparing it with standard Gaussian quadrature over the same integral. Results shown that the evaluation of an integral by using higher order Gaussian quadrature provide accurate and converge results compared to an integral using standard Gaussian quadrature.

Axisymmetric elastic field in layered non-homogeneous and transversely isotropic geo-materials due to surface traction

This paper examines the axisymmetric problem of layered and non-homogeneous geo-material halfspaces with transverse isotropy. The halfspace is subjected to normal traction over a circular area of the boundary surface. A n-layered halfspace system approximates the arbitrary variation of the elastic parameters of non-homogeneous geo-materials with depth. The two-dimensional Fourier integral transforms in the cylindrical coordinate system and the backward transfer matrix method are used for the mathematical formulation and derivation. The solutions of the displacement, stress and strain fields are explicitly expressed in the matrix form in terms of classical improper Hankel transform integrals. The kernel functions of the Hankel transform integrals are explicitly expressed in the forms of backward transfer matrix. The singular terms associated with the improper Hankel transform integrals are analytically isolated and expressed in the exact closed-form. Numerical results indicate that there is no problem in the evaluation of the solutions of non-homogeneous halfspaces with arbitrarily variable elastic parameters and the inhomogeneity and transverse isotropy of layered geo-materials have significant effect on the elastic fields.

A Fourier cosine expansion method for pricing FX-TARN under Lévy processes

<abstract><p>In this paper, we extend the Fourier cosine expansion (COS) method to the pricing of {foreign exchange} target redemption note (FX-TARN), a popular exotic currency option. We take the FX spot rate and the cumulated positive cash flow as two state variables and factor the joint distribution by two marginals that can be approximated by Fourier cosine expansions. To recover the Fourier coefficients recursively, we approximate the two-dimensional integration by higher-order quadratures such as Gauss-Legendre or Clenshaw-Curtis quadrature for the integration over the spot rate. We derive the analytical formulas for the price under different knock-out types. We demonstrate that fast Fourier transform (FFT) can be employed to obtain the Fourier coefficients efficiently. We also evaluate the performance and accuracy of the method through a number of numerical experiments.</p></abstract>

Generalized Banach fixed-point theorem and numerical discretization for nonlinear Volterra–Fredholm equations

An investigation of two nonlinear mixed Volterra–Fredholm integral equations of the second kind is undertaken. The equations are constructed as fixed-point problems, under the condition of Lipschitz continuity, the Generalized Banach fixed-point theorem is used to prove the existence of a unique solution without any contraction assumption. A double numerical quadrature algorithm is constructed for the occurring two-dimensional integral. It is theoretically proved, under the existence of relevant partial derivatives, that the proposed numerical scheme has (i) first order of convergence if the nonlinear kernel is multi-variate, and (ii) second order of convergence if the kernel is uni-variate. A Newton–Raphson scheme is then designed and implemented for the resulting nonlinear algebraic system. Some numerical examples are used to demonstrate the accuracy and convergence of the method. The numerical results verify the theoretical results and show that the method performs well.