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Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response
Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using a numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2 , Be, N 2 , H 2 O, and C 2 H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.
Near equilibrium distributions for beams with space charge in linear and nonlinear periodic focusing systems
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Sequential double excitations from linear-response time-dependent density functional theory
Traditional UV/vis and X-ray spectroscopies focus mainly on the study of excitations starting exclusively from electronic ground states. However there are many experiments where transitions from excited states, both absorption and emission, are probed. In this work we develop a formalism based on linear-response time-dependent density functional theory to investigate spectroscopic properties of excited states. We apply our model to study the excited-state absorption of a diplatinum(II) complex under X-rays, and transient vis/UV absorption of pyrene and azobenzene.
Graph-based linear scaling electronic structure theory
We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.
Envelope Hamiltonian for charged-particle dynamics in general linear coupled systems
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ELM control optimization for various ITER scenarios based on linear and quasi-linear figures of merit
For the purpose of better understanding type-I edge localized mode (ELM) control in ITER with resonant magnetic perturbation (RMP) fields, the plasma response to RMP is computed by a resistive full magneto-hydrodynamic model in toroidal geometry. Five scenarios designed for ITER are considered, ranging from the pre-nuclear to nuclear phases. The plasma response to RMP is quantified by the plasma surface displacement near the X-point of the divertor plasma and at the outboard mid-plane. The optimal coil configurations between two high- Q deuterium-tritium (DT) scenarios (at the same plasma current of 15 MA and the same magnetic field of 5.3 T but different fusion gains, Q = 5 and 10) are predicted to be similar. For the other ITER scenarios with similar edge safety factor q 95 ~ 3 to that of the baseline scenario, the optimal coil phasing is also similar. The optimization results are different for a half-current full-field (7.5 MA/5.3 T) scenario, largely due to the difference in q 95 . The RMP coil currents are also optimized to tailor the core vs edge toroidal torques exerted by the 3D RMP fields on the plasma column. Torque optimization, with various objective functions proposed in the study, is useful for minimizing the side effects of RMP on the plasma core flow in ITER, while still maintaining the ELM control capability. Full utilization of three rows of ELM control coils in ITER is found to be essential to ensure both flexibility and robustness of ELM control, in terms of both linear and quasilinear plasma responses.
Linear-algebraic bath transformation for simulating complex open quantum systems
In studying open quantum systems, the environment is often approximated as a collection of non-interacting harmonic oscillators, a configuration also known as the star-bath model. It is also well known that the star-bath can be transformed into a nearest-neighbor interacting chain of oscillators. The chain-bath model has been widely used in renormalization group approaches. The transformation can be obtained by recursion relations or orthogonal polynomials. Based on a simple linear algebraic approach, we propose a bath partition strategy to reduce the system-bath coupling strength. As a result, the non-interacting star-bath is transformed into a set of weakly coupled multiple parallel chains. Furthermore, the transformed bath model allows complex problems to be practically implemented on quantum simulators, and it can also be employed in various numerical simulations of open quantum dynamics.
Integrating proteomic or transcriptomic data into metabolic models using linear bound flux balance analysis
Abstract Motivation Transcriptomics and proteomics data have been integrated into constraint-based models to influence flux predictions. However, it has been reported recently for Escherichia coli and Saccharomyces cerevisiae, that model predictions from parsimonious flux balance analysis (pFBA), which does not use expression data, are as good or better than predictions from various algorithms that integrate transcriptomics or proteomics data into constraint-based models. Results In this paper, we describe a novel constraint-based method called Linear Bound Flux Balance Analysis (LBFBA), which uses expression data (either transcriptomic or proteomic) to predict metabolic fluxes. The method uses expression data to place soft constraints on individual fluxes, which can be violated. Parameters in the soft constraints are first estimated from a training expression and flux dataset before being used to predict fluxes from expression data in other conditions. We applied LBFBA to E.coli and S.cerevisiae datasets and found that LBFBA predictions were more accurate than pFBA predictions, with average normalized errors roughly half of those from pFBA. For the first time, we demonstrate a computational method that integrates expression data into constraint-based models and improves quantitative flux predictions over pFBA. Availability and implementation Code is available in the Supplementary data available at Bioinformatics online. Supplementary information Supplementary data are available at Bioinformatics online.
Photoproduction of Λ and Σ 0 hyperons using linearly polarized photons
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Acoustic scaling of linear and mode-coupled anisotropic flow; implications for precision extraction of the specific shear viscosity
The n th -order linear flow coefficients v n L ( n = 2 , 3 , 4 , 5 ) , and the corresponding nonlinear mode-coupled ( mc ) coefficients v 4 , ( 2 , 2 ) mc , v 5 , ( 2 , 3 ) mc , v 6 , ( 3 , 3 ) mc , and v 6 , ( 2 , 2 , 2 ) mc , are studied for Pb+Pb collisions at s N N = 2.76 TeV. Both sets of coefficients suggest a common acoustic scaling pattern of exponential viscous modulation, with a rate proportional to the square of the harmonic numbers and the mean transverse momenta (respectively), and inversely proportional to the cube root of the charged particle multiplicity [ ( N ch ) 1 / 3 ] , which characterizes the dimensionless size of the systems produced in the collisions. These patterns and their associated scaling parameters offer new stringent constraints for eccentricity-independent estimates of the specific shear viscosity η s ( T ) and the viscous correction to the thermal distribution function for the matter produced in the collisions. They also give crucial constraints for extraction of the initial-state eccentricity spectrum.
Linear sigma model for multiflavor gauge theories
We consider a linear sigma model describing $2N_f^2$ bosons ($\sigma$, a 0 , $\eta$' and π) as an approximate effective theory for a $SU(3)$ local gauge theory with $N_f$ Dirac fermions in the fundamental representation. The model has a renormalizable U(N f ) L Ⓧ invariant part, which has an approximate $O(2N_f^2)$ symmetry, and two additional terms, one describing the effects of a $SU(N_f)_V$ invariant mass term and the other the effects of the axial anomaly. We calculate the spectrum for arbitrary $N_f$. Using preliminary and published lattice results from the LatKMI collaboration, we found combinations of the masses that vary slowly with the explicit chiral symmetry breaking and $N_f$. This suggests that the anomaly term plays a leading role in the mass spectrum and that simple formulas such as $M_\sigma^2\simeq (2/N_f-C_\sigma)M_{\eta'}^2$ should apply in the chiral limit. Lattice measurements of $M_{\eta'}^2$ and of approximate constants such as $C_\sigma$ could help locating the boundary of the conformal window. Here, we show that our calculation can be adapted for arbitrary representations of the gauge group and in particular to the minimal model with two sextets, where similar patterns are likely to apply.
Deterministic Linear Time for Maximal Poisson‐Disk Sampling using Chocks without Rejection or Approximation
Abstract We show how to sample uniformly within the three‐sided region bounded by a circle, a radial ray, and a tangent, called a “chock.” By dividing a 2D planar rectangle into a background grid, and subtracting Poisson disks from grid squares, we are able to represent the available region for samples exactly using triangles and chocks. Uniform random samples are generated from chock areas precisely without rejection sampling. This provides the first implemented algorithm for precise maximal Poisson‐disk sampling in deterministic linear time. We prove O(n · M(b) log b), where n is the number of samples, b is the bits of numerical precision and M is the cost of multiplication. Prior methods have higher time complexity, take expected time, are non‐maximal, and/or are not Poisson‐disk distributions in the most precise mathematical sense. We fill this theoretical lacuna.
Application of linear least squares to the analysis of Auger electron spectroscopy depth profiles of plutonium oxides [Application of linear least squares to the analysis of AES depth profiles of plutonium oxides]
In this paper, the application of the linear least squares (LLS) methodology allows for quantitative determination of variation in material composition with depth. LLS fits were applied to decompose and enhance the interpretation of spectra obtained by Auger electron spectroscopy during depth profiles of oxidized plutonium surfaces. By means of the LLS algorithm, chemical state assignments of the Pu P 1 VV/O 45 VV, O KLL, and C KLL Auger transitions were determined and the existence of a subsurface oxycarbide layer was identified, with confirmation of the oxide and metal components provided from comparison to previous measurements of standard samples.
Collocation Methods for Exploring Perturbations in Linear Stability Analysis
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid dynamics, there are examples where linear stability analysis predicts stability but transient simulations exhibit significant growth of infinitesimal perturbations. This behavior can be predicted by pseudospectral analysis. In this study, we show that an approach similar to pseudospectral analysis can be performed inexpensively using stochastic collocation methods and the results can be used to provide quantitative information about instability.In addition, we demonstrate that the results of the perturbation analysis provide insight into the behavior of unsteady flow simulations.
Starting dynamics of a linear-cavity femtosecond Mamyshev oscillator
Mamyshev oscillators can generate high-power femtosecond pulses, but starting a mode-locked state has remained a major challenge due to the suppression of continuous-wave lasing. Here, we study the starting dynamics of a linear Mamyshev oscillator designed to generate high-power femtosecond pulses while avoiding component damage. Reliable starting to stable mode-locking is achieved with a combination of modulation of the pump power and shifting of a filter passband. The starting process is automated, with full electronic control. The laser delivers 21-nJ pulses that are dechirped to 65 fs in duration outside the cavity.
Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations.
The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.
A failsafe analysis using NASTRAN's piecewise linear analysis and a nine node linear crack element
A two-dimensional crack element was implemented into NASTRAN as a user dummy element and used to study failsafe characteristics of the C5A fuselage. The element is formulated from Reitsner's functional requiring that it satisfy compatability with the linear boundary displacement elements in NASTRAN. Its accuracy is demonstrated by analyzing for the stress intensity factors of two simple crack configurations for which there are classic solutions.