Diagonalization Method Research Articles

Symmetric Tridiagonal Eigenvalue Solver Across CPU Graphics Processing Unit (GPU) Nodes

In this work, an improved and scalable implementation of Cuppen’s algorithm for diagonalizing symmetric tridiagonal matrices is presented. This approach uses a hybrid-heterogeneous parallelization technique, taking advantage of GPU and CPU in a distributed hardware architecture. Cuppen’s algorithm is a theoretical concept and a powerful tool in various scientific and engineering applications. It is a key player in matrix diagonalization, finding its use in Functional Density Theory (FDT) and Spectral Clustering. This highly efficient and numerically stable algorithm computes eigenvalues and eigenvectors of symmetric tridiagonal matrices, making it a crucial component in many computational methods. One of the challenges in parallelizing algorithms for GPUs is their limited memory capacity. However, we overcome this limitation by utilizing multiple nodes with both CPUs and GPUs. This enables us to solve subproblems that fit within the memory of each device in parallel and subsequently combine these subproblems to obtain the complete solution. The hybrid-heterogeneous approach proposed in this work outperforms the state-of-the-art libraries and also maintains a high degree of accuracy in terms of orthogonality and quality of eigenvectors. Furthermore, the sequential version of the algorithm with our approach in this work demonstrates superior performance and potential for practical use. In the experiments carried out, it was possible to verify that the performance of the implementation that was carried out scales by 2× using two graphic cards in the same node. Notably, Symmetric Tridiagonal Eigenvalue Solvers are fundamental to solving more general eigenvalue problems. Additionally, the divide-and-conquer approach employed in this implementation can be extended to singular value solvers. Given the wide range of eigenvalue problems encountered in scientific and engineering domains, this work is essential in advancing computational methods for efficient and accurate matrix diagonalization.

A novel damage localization method of Circular Phased Array using Minimum Variance Distortionless Response Beamforming with Autocorrelation Matrix Diagonal Loading

Damage localization methods based on Acoustic Emission (AE) can be classified into time-based and waveform-based. However, the former requires a large number of sensors while the latter is limited to 2D plane localization. In order to address the challenge of achieving more accurate 3D localization using a reduced number of sensors, this paper proposes a Circular Phased Array using Minimum Variance Distortionless Response (MVDR) Beamforming with Autocorrelation Matrix Diagonal Loading (AMDL) method. Firstly, a sparse circular array is utilized to form multiple beamforming for coherent shear wave signals, decomposing the original 3D localization problem into Direction Of Arrival (DOA) estimation. Secondly, azimuth angle, elevation angle and autocorrelation matrix diagonal loading methods are introduced, working in conjunction with the MVDR beamforming algorithm. Finally, spatial integration is performed through matrix decomposition to solve geometric overdetermined equations. The effectiveness of the proposed method is validated through numerical simulations and experimental verifications under various damage conditions. Results indicate that estimation errors for azimuth and elevation angles are both less than 2 %, while 3D damage source localization errors remain within a range of less than 3 %. This proposed method extends beamforming technology from 2D plane localization to 3D localization, significantly reducing the complexity of sensor arrangement and lowering the cost of structural health monitoring systems by utilizing a small number of sensors.

Extraction of Spectra in the Shell Model MonteCarlo Method Using Imaginary-Time Correlation Matrices.

Nuclear energy levels are usually calculated using conventional diagonalization methods in the framework of the configuration-interaction (CI) shell model but these methods are prohibited in very large model spaces. The shell model MonteCarlo (SMMC) method is a powerful technique for calculating thermal and ground-state observables of nuclei in very large model spaces, but it is challenging to extract nuclear spectra in this approach. We present a novel method to extract within SMMC low-lying energy levels for given values of a set of good quantum numbers such as spin and parity. The method is based on imaginary-time correlation matrices (ITCMs) of one-body densities that satisfy asymptotically a generalized eigenvalue problem. We validate the method in a light nucleus that allows comparison with exact diagonalization results of the CI shell-model Hamiltonian. The method is broadly applicable to quantum many-body systems in other disciplines.

Electric-field-induced enhancement of exciton binding energy in one-dimensional phosphorene atomic chain

An electric field normally increases the separation between the electron and hole in an exciton without intrinsic polarization and suppresses their Coulombic interaction, resulting in the reduction of its binding energy. Our study of one-dimensional (1D) excitons in phosphorene atomic chains, by using the exact diagonalization method, however, reveals that an electric field applied along the chain axis actually increases the exciton binding energies. Further analysis shows that the electric field tends to enhance the long-range interaction between the electron and hole while suppressing their short-range interaction by inducing an alternating charge distribution along the atomic chain. The zigzag symmetry is believed to account for this unique excitonic phenomenon in the 1D system.

Quantitatively Deciphering the Local Structure and Luminescence Spectroscopy of Pr3+-Doped Yttrium Lithium Fluoride.

Praseodymium (Pr3+)-doped LiYF4 nanophosphors have garnered significant interest for their potential applications in lasers, phosphors, and quantum memories. However, there remains a lack of comprehensive research on the local coordination environment and luminescence spectroscopy of Pr3+:LiYF4 nanocrystals. This study presents the first investigation of the ground-state structure of Pr3+:LiYF4 crystals by employing the crystal structure prediction method, and a [PrF8]5- ligand complex with S4 local symmetry is determined. The complete energy levels of the Pr3+ ions in LiYF4 nanocrystals are unveiled by using our newly developed well-established parametrization matrix diagonalization method. A novel set of free-ion and crystal-field parameters is derived through a good simulation with 45 experimental energy levels. Many of the emissions of Pr3+-doped LiYF4 are successfully reproduced based on Judd-Ofelt theory, and these transitions are comparable to the experimental ones. Moreover, two new prominent emission bands with their peaks at 675 and 849 nm originating from 1I6 → 3F4 and 1I6 → 1G4 transitions, respectively, are predicted by us for the first time. This study could provide a feasible method to search for practical laser transition channels of solid-state lasers based on Pr3+: LiYF4 nanophosphors.

ScConfluence: single-cell diagonal integration with regularized Inverse Optimal Transport on weakly connected features

The abundance of unpaired multimodal single-cell data has motivated a growing body of research into the development of diagonal integration methods. However, the state-of-the-art suffers from the loss of biological information due to feature conversion and struggles with modality-specific populations. To overcome these crucial limitations, we here introduce scConfluence, a method for single-cell diagonal integration. scConfluence combines uncoupled autoencoders on the complete set of features with regularized Inverse Optimal Transport on weakly connected features. We extensively benchmark scConfluence in several single-cell integration scenarios proving that it outperforms the state-of-the-art. We then demonstrate the biological relevance of scConfluence in three applications. We predict spatial patterns for Scgn, Synpr and Olah in scRNA-smFISH integration. We improve the classification of B cells and Monocytes in highly heterogeneous scRNA-scATAC-CyTOF integration. Finally, we reveal the joint contribution of Fezf2 and apical dendrite morphology in Intra Telencephalic neurons, based on morphological images and scRNA.

Edge modes in finite-size systems with different edge terminals

Abstract We investigate the behavior of edge modes in the presence of different edge terminations and long-range (LR) hopping. Here, we mainly focus on such model crystals with two different types of structures (type I: “…–P–Q–P–Q–…” and type II: “… = P–Q = P–Q = …”), where P and Q represent crystal lines (CLs), while the symbols “–” and “=” denote the distance between the nearest neighbor (NN) CLs. Based on the lattice model Hamiltonian with LR hopping, the existence of edge modes is determined analytically by using the transfer matrix method (TMM) when different edge terminals are taken into consideration. Our findings are consistent with the numerical results obtained by the exact diagonalization method. We also notice that edge modes can exhibit different behaviors under different edge terminals. Our result is helpful in solving novel edge modes in honeycomb crystalline graphene and transition metal dichalcogenides with different edge terminals.

Two atoms in a harmonic trap with spin-orbital-angular-momentum coupling

We study the problem of two harmonically trapped atoms in the presence of spin-orbital-angular-momentum (SOAM) coupling. The two-body energy spectrum is numerically calculated by utilizing the exact diagonalization method. We analyze how the degeneracy of energy levels is lifted under the interplay between the interatomic interaction and SOAM coupling. The exact numerical results show excellent agreement with that of perturbation theory in the weak-interaction limit as well as that in the absence of SOAM coupling. The properties of correlations between the two atoms are also discussed with respect to the interaction strength. The findings in this paper may provide valuable insights into few-body physics subjected to SOAM coupling and the possible experimental detection of spectrum functions in many-body systems, such as radiofrequency spectroscopy. Published by the American Physical Society 2024

Investigating Spodoptera spp. diversity, percentage of attack, and control strategies in the West Java, Indonesia, corn cultivation

Abstract Corn, a crucial food crop in Indonesia, faces significant challenges from pests such as Spodoptera spp., impacting agricultural productivity and industrial applications. This study aimed to study the diversity and attack percentage of Spodoptera spp. on corn plants, along with the employed control techniques. The research was conducted using a survey method through field observation and farmer interviews. The insect sampling was carried out by purposive sampling, while the sampling of plants using the diagonal sampling method was done in three areas that were representative of the West Java province, Indonesia (Sumedang Regency, Cirebon Regency, and Bandung Regency). The results showed that Spodoptera frugiperda or fall armyworm has emerged as a dominant pest in all three areas. The diversity index (H′) of S. frugiperda across the Cirebon Regency, Bandung Regency, and Sumedang Regency was consistently low (<1). Varying infestation rates across districts, with the Cirebon Regency showing lower rates and Bandung and Sumedang Regencies exhibiting medium-level infestation. Farmers in Bandung and Sumedang Regencies are adopting a more diverse pest management strategy, including the regular monitoring and manual collection of larvae. In addition, the survey shows a positive relationship between the knowledge, skills, and attitude of farmers, suggesting that acquiring more information and understanding agricultural techniques contribute to effective task execution and foster positive mindsets. This comprehensive investigation sheds light on the regional variations in Spodoptera spp. dynamics, providing valuable insights for sustainable pest management in the corn cultivation of the West Java Province, Indonesia.

A Ramsey-Type Equilibrium Model with Spatially Dispersed Agents

AbstractWe present a spatial and time-continuous Ramsey-type equilibrium model for households and firms that interact on a spatial domain to model labor mobility in the presence of commuting costs. After discretization in space and time, we obtain a mixed complementarity problem that represents the spatial equilibrium model. We prove existence of equilibria using the theory of finite-dimensional variational inequalities and derive a tailored diagonalization method to solve the resulting large-scale instances. Finally, we present a case study that highlights the influence of commuting costs and show that the model allows to analyze transitory effects of industrial agglomeration that emerge and vanish over time as in the real economy.

Effects of hydrostatic pressure, temperature, and position-dependent mass on the nonlinear optical properties of triple delta-doped GaAs quantum well

In this study, we thoroughly investigate the impacts of hydrostatic pressure, temperature, and position-dependent mass (PDM) on the nonlinear optical properties of asymmetric triple δ-doped GaAs quantum wells. Our analysis covers total optical absorption coefficients, relative refractive index changes, nonlinear optical rectification, second harmonic generation, and third harmonic generation. Initially, we employ PDM to solve the time-independent Schrödinger equation using the diagonalization method under effective mass and parabolic band approaches, considering pressure and temperature dependencies. Utilizing the first four energy eigenvalues and eigenfunctions, we apply the compact density matrix method to compute the system’s nonlinear optical properties numerically. The results indicate a shift in optical property peak positions toward lower (higher) energy spectra with increasing hydrostatic pressure (temperature). Furthermore, the influence of PDM shifts the system’s optical properties toward the higher energy spectrum, resembling the effect of temperature. From an experimental and theoretical perspective, one of the topics that researchers work on most is GaAs-based δ-doped systems (δ-doped heterojunction bipolar transistors, δ-doped field effect transistors, δ-multiple independent gate field effect transistors, etc.). We believe these findings will provide valuable insights for the researchers involved in GaAs-based δ-doped optoelectronic device design.

Bound impurities in a one-dimensional Bose lattice gas: Low-energy properties and quench-induced dynamics

We study two mobile bosonic impurities immersed in a one-dimensional optical lattice and interacting with a bosonic bath. We employ the exact diagonalization method for small periodic lattices to study stationary properties and dynamics. We consider the branch of repulsive interactions that induce the formation of bound impurities, akin to the bipolaron problem. A comprehensive study of ground-state and low-energy properties is presented, including an examination of the interaction strengths which induce the formation of a bound dimer of impurities. We also study the dynamics induced after an interaction quench to examine the stability of the bound dimers. We reveal that after large interaction quenches from strong to weak interactions the system can show large oscillations over time with revivals of the dimer states. We find that the oscillations are driven by selected eigenstates with phase-separated configurations.

Electric field-induced electronic structure and intersubband transitions of a hydrogen molecular ion in a gaussian-type quantum ring

In this work, the influence of an external electric field on the electronic structure and intersubband transitions of a singly ionized double-donor system in a GaAs quantum ring defined by Gaussian-type potentials is investigated theoretically. Within the framework of the effective mass approach, the two-dimensional diagonalization method is used for the solution of the Schrödinger equation to obtain the eigen energies and corresponding wave functions. Numerical results reveal that the electronic energy spectrum and the linear optical absorption coefficient of the ring are remarkably affected by the strength of the lateral electric field, internuclear distance and parameters defining the confinement potential. Also, it has been shown that beyond the anti-crossing point, the wave functions exchange their symmetries without mixing, which is a characteristic feature of energy-level anti-crossing.

Twisted graphene superlattices: resonating valence bond states and magnetic properties

Resonating valence bond (RVB) states are fundamental for understanding quantum spin liquids in two-dimensional (2D) systems. The RVB state is a collective phenomenon in which spins are uncoupled. 2D lattices such as triangular, honeycomb, and dice lattices were investigated using the Hubbard model and exact diagonalization method. We analyzed the total spin, spin–spin correlation functions, local magnetic moments, and spin and charge gaps as a function of on-site Coulomb repulsion, electron concentration, and electronic hopping parameters. Phase diagrams showed that RVB states can live in half-filled and hole-doped anisotropic triangular lattices. We found two types of RVB states: one in the honeycomb sublattice and the other in the centered hexagons in the triangular lattices. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene and transition metal dichalcogenide systems, our results provide physical insights into the onset of magnetism and possible spin liquid states in these layered materials.

Correction of nonmonotone trust region algorithm based on a modified diagonal regularized quasi-Newton method

In this paper, a new appropriate diagonal matrix estimation of the Hessian is introduced by minimizing the Byrd and Nocedal function subject to the weak secant equation. The Hessian estimate is used to correct the framework of a nonmonotone trust region algorithm with the regularized quasi-Newton method. Moreover, to counteract the adverse effect of monotonicity, we introduce a new nonmonotone strategy. The global and superlinear convergence of the suggested algorithm is established under some standard conditions. The numerical experiments on unconstrained optimization test functions show that the new algorithm is efficient and robust.

The Nonlinear Optical Properties of Self-Assembled InAs/GaAs Quantum Dot: Effect of Hydrostatic Pressure and Temperature

In this study, we have investigated the effects of temperature (T) and hydrostatic pressure (P) on both the nonlinear and linear optical properties of an InAs/GaAs core/shell quantum dot (QD) system with a Screened-Modified Kratzer potential (SMKP). To achieve this objective, we calculated the energy levels and their corresponding wave functions of the structure using the diagonalization method within the framework of the effective mass approximation. Analytical expressions for the absorption coefficients (ACs) and relative refractive index changes (RRICs) were derived using the compact-density-matrix approach. In our numerical calculations, we first determined the variation of the SMKP dependence, the dipole transition matrix element, and the electron energies of the ground (1s) and first excited state (1p) over a range of hydrostatic pressure (P) and temperature (T). As a result, the obtained numerical calculations revealed that changes in P and T influence both the magnitude and position of the resonant peaks that define the ACs and RRICs

Nonlinear optical properties of GaAs/AlGaAs asymmetric triple quantum wells designed for quantum cascade lasers: Effect of externally applied electric and magnetic fields

We explore the impact of external fields on the absorption coefficients and relative refractive index changes in a quantum cascade laser profile-like heterostructure that consists of a triple asymmetric quantum well. Firstly, we solve numerically the time-independent Schrödinger equation by using the diagonalization method under the effective mass and parabolic band approaches, to obtain the energy levels and wavefunctions. Then, we evaluate the optical coefficients from the analytical expressions derived from the compact density matrix method. The obtained results put forth that the resonant peaks of optical coefficients shift to higher (lower) energies by increasing the value of the electric (magnetic) field. These results indicate that it would be possible to adjust the optical properties of these structures to the desired range with external fields. As a result, we hope that new optoelectronic devices based on asymmetric triple quantum wells can be developed using the features found here.

Nonlinear finite element analysis of shear defective reinforced concrete beam to column connections strengthened with three practical techniques

Extensive research efforts over the last decades have focused on the rehabilitation of vulnerable reinforced concrete (RC) beam to column moment resisting connections. Shear failure in the panel zone of the beam to column connections (BCCs) under the lateral seismic loads stands out as one of the main reasons of the vulnerability of moment resisting frames (MRFs), potentially resulting in severe consequences for the entire structure. The main aim of this study is to fairly investigate the effectiveness of three practical retrofitting methods to eliminate the joint shear failure in the RC beam to column connections which suffer from this undesirable brittle failure mode. To achieve this, a comprehensive review categorizing available retrofit techniques for shear-defective joints is first provided, outlining their advantages and limitations. The study then presents findings from a nonlinear three-dimensional (3D) finite element (FE) study on the performance of (RC) connections, characterized by predominant joint shear mode of failure and retrofitted using the three practical techniques. In this context, the FE model is validated through the monotonic simulation of quasi static cyclic tests conducted on connections strengthened by the three practical retrofitting methods from the literature. The selected methods were diagonal steel haunch method, RC planar joint expansion, and pre-tensioning of the joint core. The models, encompassing their precise geometric details, are applied to a full-scale exterior connection experiencing shear deficiencies to evaluate their effectiveness in real-world scenarios Additionally, a parametric study is conducted to assess the effects of various influential design variables on the effectiveness of these selected strengthening methods. These findings provide insights into the efficiency of retrofit techniques, thereby informing more robust design practices aimed at enhancing the performance and resilience of vulnerable shear defective RC BCCs retrofitted using the aforementioned strengthening techniques. The study has identified key design parameters crucial for the effectiveness of retrofit techniques in practical applications. These included haunch dimensions (thickness and length) for the haunch retrofit technique, additionally, the size of the added RC blocks for planar joint expansion technique and finally the enlargement size and the amount of applied prestressing bolt loads for pre-tensioning of the joint core retrofit technique.

Classical and quantum computing of shear viscosity for (2+1)D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for (2+1)-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density ηs is consistent with a well-known holographic result 14π at several temperatures on a 4×4 honeycomb lattice with the local electric representation truncated at jmax=12. We also find the ratio of the spectral function and frequency ρxy(ω)ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond jmax=12 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including jmax truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

Characterization of Physicochemical Properties and and Heavy Metals Content of Soils under Kratom (Mitragyna speciosa) Cultivation, Kapuas Hulu District, Indonesia

Background: Kapuas Hulu is a district in West Kalimantan Province, Indonesia, which is famous for its production of kratom (Mitragyna speciosa), a traditional medicinal plant. Kratom is the main cultivated plant carried out by farmers. However, data regarding the physicochemical properties of kratom plantation soil are still limited, especially regarding the heavy metal content. This research aimed to determine the physicochemical properties and heavy metal content of soil planted with kratom. Methods: This research was conducted on alluvial soil and peat planted with kratom. This research is survey of 2 fields where sampling from each land was carried out using the diagonal method, where 5 sub-samples were taken per land and composited, except for volume Weight. Result: Mineral land and peat land can be used as land for Kratom cultivation because the physicochemical properties of both lands support the growth of Kratom plus the heavy metal content is below the critical threshold.