Rigorous Computation Research Articles

Agent-Based simulation reveals localized isolation key to saving lives and resources

In the realm of pandemic dynamics, understanding the intricate interplay between disease transmission, interventions, and immunity is pivotal for effective control strategies. Through a rigorous agent-based computer simulation, we embarked on a comprehensive exploration, traversing unmitigated spread, lockdown scenarios, and the transformative potential of vaccination. we unveil that while quarantine unquestionably delays the pandemic peak, it does not act as an impenetrable barrier to halt the progression of infectious diseases. Vaccination factor revealed a potent weapon against outbreaks — higher vaccination percentage not only delayed infection peaks but also substantially curtailed their impact. Our investigation into bond dilution below the percolation threshold presents an additional dimension to pandemic control. We observed that localized isolation through bond dilution offers a more resource-efficient targeted control strategy than blanket lockdowns or large-scale vaccination campaigns.

PyArc: A python package for computing absorption and radiative coefficients from first principles

Light absorption and radiative recombination are two critical processes in optoelectronic materials that characterize the energy conversion efficiency. The absorption and radiative coefficients are thus key properties for device optimization and design. Here, we develop a python package named pyArc that allows rigorous computation of absorption and radiative coefficients from first principles. By integrating several interpolation strategies to augment k-point sampling in reciprocal space, our code is accurate yet highly efficient. In addition to evaluation of the coefficients, our code is capable of intuitive analysis of carrier distribution, facilitating a deeper understanding of the microscopic mechanisms underlying the radiative coefficients. Utilizing GaAs as a prototypical example, we demonstrate how to employ our package to compute absorption and radiative coefficients and to investigate the key features in the electronic structure that give rise to these coefficients. Program SummaryProgram title: PyArcCPC Library link to program files:https://doi.org/10.17632/5x9g9bvhcv.1Licensing provisions: MIT licenseProgramming language: Python 3Nature of problem: Light absorption and radiative recombination processes in semiconductors critically impact the energy conversion efficiency of optoelectronic devices. Developing a method to calculate coefficients of the two processes based on first-principles theory is essential, which not only can help to obtain the key properties of those semiconductor materials and guide the device design, but also can unveil the underlying microscopic mechanisms.Solution method: PyArc, written in the Python language, implements first-principles methodologies for the computation of absorption and radiative coefficients of semiconductors based on Fermi's golden rule. This package takes the electronic eigenvalues and dipole matrix elements of a material computed from first-principles codes such as VASP as input. Dense k-point sampling for the Brillouin zone is achieved through efficient interpolation schemes implemented in our code to acquire well converged results. The functionality of cross-sectional visualization of carrier distribution in our code provides intuitive insights into the fundamental mechanism beneath the charge-carrier radiative recombination process.

Rigorous Computation of Solutions of Semilinear PDEs on Unbounded Domains via Spectral Methods

Rigorous Computation of Solutions of Semilinear PDEs on Unbounded Domains via Spectral Methods

How to rule out (g − 2)μ in U1Lμ−Lτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{U}{(1)}_{L_{\\mu }-{L}_{\ au }} $$\\end{document} with white dwarf cooling

In recent years, the gauge group U1Lμ−Lτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{U}{(1)}_{L_{\\mu }-{L}_{\ au }} $$\\end{document} has received a lot of attention since it can, in principle, account for the observed excess in the anomalous muon magnetic moment (g − 2)μ, as well as the Hubble tension. Due to unavoidable, loop-induced kinetic mixing with the SM photon and Z, the U1Lμ−Lτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{U}{(1)}_{L_{\\mu }-{L}_{\ au }} $$\\end{document} gauge boson A′ can contribute to stellar cooling via decays into neutrinos. In this work, we perform for the first time an ab initio computation of the neutrino emissivities of white dwarf stars due to plasmon decay in a model of gauged U1Lμ−Lτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{U}{(1)}_{L_{\\mu }-{L}_{\ au }} $$\\end{document}. A key result is that current observations of the early-stage white dwarf neutrino luminosity at the 30% level exclude previously allowed regions of the parameter space favoured by a simultaneous explanation of the (g – 2)μ and H0 anomalies. In this work, we present the relevant white dwarf cooling limits over the entire A′ mass range. In particular, we have performed a rigorous computation of the luminosities in the resonant regime, where the A′ mass is comparable to the white dwarf plasma frequencies.

ADAS (Advanced Driver Assistance System)

Innovations in information technologies have resulted in more complex road safety applications. These systems offer numerous possibilities for improving road mobility. This study provides an integrated system that addresses two essential topics :safety and efficiency. To this end, the development and implementation of an integrated advanced driver assistance system (ADAS) for rural and intercity environments is proposed. Flexible autopilot with usage productivity, a surpassing support mechanism for single-carriageway pathways that considers the correct velocity expansion and acknowledges between the finest appropriate path extends for the movement, a junction support structure with speed regulation during approximate moves, and a crash prevention system with vague movement features are among the characteristics that were recently developed. To accomplish this, rigorous automotive kinematics computations were used to preserve equilibrium, and power system simulations were used to create optimal patterns. Computer vision and modeling were utilized to test and optimize the control module operations. Finally, the equipment is designed to notify a driver if an issue is detected and, if necessary, assume control of the vehicle. ADAS radar detectors identify vehicles and the surrounding area using electromagnetic radiation. The device measures the pace and direction of viewed objects, enabling autonomous vehicle systems to send safety notifications and govern operating procedures. Every single bit of evidence, including automobile position, accurate satellite imagery, and intricate map-matching computations, impacts the choice-making mechanisms for different ADAS structures

Factors That Influences Purchase Intention towards Co-Branded Local Cosmetics Mediated by Trust

In the pursuit of enlightenment, this scholarly investigation unfolded through the distribution of meticulously crafted questionnaires and rigorous data computation. Consequently, the yielded results transcend mere numbers, including quantitative and qualitative elements. This analytical inspection aims to uncover the deep implications of things such as brand awareness, social media marketing, brand image, e-WoM (electronic word of mouth), brand equity, and trust. These elements, seen as potential mediators, hold the potential to exert influence on the purchase intention of co-branded local cosmetics products. The data employed in this scholarly inquiry were gathered through the dissemination of questionnaires among consumers who had previously acquired Co-Branded local cosmetics within the confines of Batam City in Indonesia. The collected responses underwent meticulous analysis, facilitated by the technological prowess of SmartPLS. The distribution of the questionnaires was executed via Google Forms, skillfully designed to adhere to specific terms and conditions. The outreach strategy encompassed both online and offline channels, ensuring a comprehensive and diverse participant pool. In the contemporary landscape, research on local cosmetics has emerged as a popular and pertinent topic. Notwithstanding, prevailing studies in this domain have predominantly concentrated on generic cosmetic sales strategies. Consequently, a noticeable research gap exists. This prompted the conception of the present analysis, aimed at enriching our understanding of marketing dynamics achieved through collaborative efforts between distinct brands. The specific focus is on exploring the ramifications of co-branding and its intrinsic impact on purchase intention, thereby contributing valuable insights to the current body of knowledge in this domain.

Rigorous Computation of Linear Response for Intermittent Maps

Rigorous Computation of Linear Response for Intermittent Maps

Rigorous computation in dynamics based on topological methods for multivector fields

Motivated by the theoretical results of Mrozek et al. (Commun Nonlinear Sci Numer Simul 108:106–226, 2022) we present an algorithmic construction of a transversal cellular decomposition for a planar ODE. We then use the associated combinatorial multivector field to algorithmically detect the existence of an isolated invariant set with the Conley index of a periodic orbit and admitting a combinatorial Poincaré section. This construction combined with the theoretical results of Mrozek et al. (2022) leads to a method for automatized computer assisted proofs of the existence of periodic solutions in ODE’s.

Reduction in Degrees of Freedom for Large-Scale Nonlinear Systems in Computer-Assisted Proofs

In many physical systems, it is important to know the exact trajectory of a solution. Relevant applications include celestial mechanics, fluid mechanics, robotics, etc. For cases where analytical methods cannot be applied, one can use computer-assisted proofs or rigorous computations. One can obtain a guaranteed bound for the solution trajectory in the phase space. The application of rigorous computations poses few problems for low-dimensional systems of ordinary differential equations (ODEs) but is a challenging problem for large-scale systems, for example, systems of ODEs obtained from the discretization of the PDEs. A large-scale system size for rigorous computations can be as small as about a hundred ODE equations because computational complexity for rigorous algorithms is much larger than that for simple computations. We are interested in the application of rigorous computations to the problem of proving the existence of a periodic orbit in the Kolmogorov problem for the Navier–Stokes equations. One of the key issues, among others, is the computation complexity, which increases rapidly with the growth of the problem dimension. In previous papers, we showed that 79 degrees of freedom are needed in order to achieve convergence of the rigorous algorithm only for the system of ordinary differential equations. Here, we wish to demonstrate the application of the proper orthogonal decomposition (POD) in order to approximate the attracting set of the system and reduce the dimension of the active degrees of freedom.

Accurate inverse design for high-efficiency and broadband terahertz devices by co-simulation with genetic algorithms

In this study, we combined MATLAB with the rigorous electromagnetic field simulation software Computer Simulation Technology to perform a co-simulation method for inverse design of high-efficiency and broadband THz metasurface devices. In the proposed design method, genetic algorithm (GA) is embedded to realize automatic and inverse design. Aiming toward the different requirements of high-efficiency and broadband THz metasurface devices, different objective functions are set to optimize the design of different types of THz metasurface devices. Based on the rigorous electromagnetic simulation and genetic algorithm, the proposed design method can realize automatic and inverse design with high reliability, compared to the theoretical model based on catenary e-field theory. This study provides an important guiding role and an efficient method for designing and optimizing required metasurface devices with practical applied value.

Computing error bounds for asymptotic expansions of regular P-recursive sequences

Over the last several decades, improvements in the fields of analytic combinatorics and computer algebra have made determining the asymptotic behaviour of sequences satisfying linear recurrence relations with polynomial coefficients largely a matter of routine, under assumptions that hold often in practice. The algorithms involved typically take a sequence, encoded by a recurrence relation and initial terms, and return the leading terms in an asymptotic expansion up to a big-O error term. Less studied, however, are effective techniques giving an explicit bound on asymptotic error terms. Among other things, such explicit bounds typically allow the user to automatically prove sequence positivity (an active area of enumerative and algebraic combinatorics) by exhibiting an index when positive leading asymptotic behaviour dominates any error terms. In this article, we present a practical algorithm for computing such asymptotic approximations with rigorous error bounds, under the assumption that the generating series of the sequence is a solution of a differential equation with regular (Fuchsian) dominant singularities. Our algorithm approximately follows the singularity analysis method of Flajolet and Odlyzko [SIAM J. Discrete Math. 3 (1990), pp. 216–240], except that all big-O terms involved in the derivation of the asymptotic expansion are replaced by explicit error terms. The computation of the error terms combines analytic bounds from the literature with effective techniques from rigorous numerics and computer algebra. We implement our algorithm in the SageMath computer algebra system and exhibit its use on a variety of applications (including our original motivating example, solution uniqueness in the Canham model for the shape of genus one biomembranes).

Observed Polarized Scattered Light Phase Functions of Planet-forming Disks

Abstract Dust particles are the building blocks from which planetary bodies are made. A major goal of studies of planet-forming disks is to constrain the properties of dust particles and aggregates in order to trace their origin, structure, and the associated growth and mixing processes in the disk. Observations of the scattering and/or emission of dust in a location of the disk often lead to degenerate information about the kinds of particles involved, such as the size, porosity, or fractal dimensions of aggregates. Progress can be made by deriving the full (polarizing) scattering phase function of such particles at multiple wavelengths. This has now become possible by careful extraction from scattered light images. Such an extraction requires knowledge about the shape of the scattering surface in the disk, and we discuss how to obtain such knowledge as well as the associated uncertainties. We use a sample of disk images from observations with the Very Large Telescope/SPHERE to, for the first time, extract the phase functions of a whole sample of disks with broad phase-angle coverage. We find that polarized phase functions come in two categories. Comparing the extracted functions with theoretical predictions from rigorous T-Matrix computations of aggregates, we show that one category can be linked back to fractal, porous aggregates, while the other is consistent with more compact, less porous aggregates. We speculate that the more compact particles become visible in disks where embedded planets trigger enhanced vertical mixing.

Prediction of characteristic points of single-peak flow curve through statistical technique and artificial neural network

ABSTRACT Artificial neural network (ANN) is an input–output modeling technique that has been successfully implemented in the field of material science to predict material behavior in terms of constitutive models. The material behavior considered here is the stress–strain behavior of the material at elevated temperatures that is characterized by a single-peak flow curve consisting of characteristic points viz. critical stress, peak stress and steady-state stress. The present work focuses on predicting these stress values along with the corresponding strain values through statistical regression analysis (SRA), ANN, and multi-layer complex neural network (MLCNN) with reasonable accuracy. The flow curves obtained from the axisymmetric compression test of 304LN austenitic stainless steel, performed at constant temperatures and constant strain rates, are used to train the models. The MLCNN has performed best while SRA has performed relatively worst with the current dataset due to rigorous and thorough computation. Both MLCNN and ANN are observed to perform better than SRA because of their non-parametric nature of handling data.

High-Order Lohner-Type Algorithm for Rigorous Computation of Poincaré Maps in Systems of Delay Differential Equations with Several Delays

We present a Lohner-type algorithm for rigorous integration of systems of delay differential equations (DDEs) with multiple delays, and its application in computation of Poincaré maps, to study the dynamics of some bounded, eternal solutions. The algorithm is based on a piecewise Taylor representation of the solutions in the phase space, and it exploits the smoothing of solutions occurring in DDEs to produce enclosures of solutions of a high order. We apply the topological techniques to prove various kinds of dynamical behaviour, for example, existence of (apparently) unstable periodic orbits in Mackey–Glass equation (in the regime of parameters where chaos is numerically observed) and persistence of symbolic dynamics in a delay-perturbed chaotic ODE (the Rössler system).

On dynamics of double‐diffusive magneto‐convection in a non‐Newtonian fluid layer

This article concerns the dynamic transitions of a non‐Newtonian horizontal fluid layer with thermal and solute diffusion and in the presence of vertical magnetic field. First, a linear stability analysis is performed by deriving the principle of exchange of stability condition, which shows the system loses stability when the thermal Rayleigh number exceeds a threshold. Second, we consider the transition induced by real eigenvalues and complex eigenvalues, respectively, and two nonlinear transition theorems along with several transition numbers determining the transition types are obtained via the method of center manifold reduction. Finally, rigorous numerical computations are performed to offer examples of possible transition types. Our results show that both continuous and jump transitions can occur for certain parameters when the diffusivities from big to small are thermal, solute concentration and magnetic diffusion, but only continuous transition induced by real eigenvalues is observed when the diffusivities from big to small is the opposite of the previous case.

Lower bounds on the Hausdorff dimension of some Julia sets

We present an algorithm for a rigorous computation of lower bounds on the Hausdorff dimensions of Julia sets for a wide class of holomorphic maps. We apply this algorithm to obtain lower bounds on the Hausdorff dimension of the Julia sets of some infinitely renormalizable real quadratic polynomials, including the Feigenbaum polynomial . In addition to that, we construct a piecewise constant function on that provides rigorous lower bounds for the Hausdorff dimension of the Julia sets of all quadratic polynomials with . Finally, we verify the conjecture of Ludwik Jaksztas and Michel Zinsmeister that the Hausdorff dimension of the Julia set of a quadratic polynomial , is a C 1-smooth function of the real parameter c on the interval .

Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems

We confirm a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. The method of showing the main chaotic property, a positive Lyapunov exponent, is a computer-assisted proof. Using the recently developed theory of conditioned Lyapunov exponents on bounded domains and the modified Furstenberg-Khasminskii formula, the problem boils down to the rigorous computation of eigenfunctions of the Kolmogorov operators describing distributions of the underlying stochastic process.

Precision estimation of 3D objects using an observation distribution model in support of terrestrial laser scanner network design

First order geometric network design is an important quality assurance process for terrestrial laser scanning of complex built environments for the construction of digital as-built models. A key design task is the determination of a set of instrument locations or viewpoints that provide complete site coverage while meeting quality criteria. Although simplified point precision measures are often used in this regard, precision measures for common geometric objects found in the built environment—planes, cylinders and spheres—are arguably more relevant indicators of as-built model quality. The computation of such measures at the design stage—which is not currently done—requires generation of artificial observations by ray casting, which can be a dissuasive factor for their adoption. This paper presents models for the rigorous computation of geometric object precision without the need for ray casting. Instead, a model for the 2D distribution of angular observations is coupled with candidate viewpoint-object geometry to derive the covariance matrix of parameters. Three-dimensional models are developed and tested for vertical cylinders, spheres and vertical, horizontal and tilted planes. Precision estimates from real experimental data were used as the reference for assessing the accuracy of the predicted precision—specifically the standard deviation—of the parameters of these objects. Results show that the mean accuracy of the model-predicted precision was 4.3% (of the read data value) or better for the planes, regardless of plane orientation. The mean accuracy of the cylinders was up to 6.2%. Larger differences were found for some datasets due to incomplete object coverage with the reference data, not due to the model. Mean precision for the spheres was similar, up to 6.1%, following adoption of a new model for deriving the angular scanning limits. The computational advantage of the proposed method over precision estimates from simulated, high-resolution point clouds is also demonstrated. The CPU time required to estimate precision can be reduced by up to three orders of magnitude. These results demonstrate the utility of the derived models for efficiently determining object precision in 3D network design in support of scanning surveys for reality capture.

A Metastable Ketenyl Radical-Water Complex from UV Photolysis of the Carboxymethyl Radical.

The unpaired electron impacts the binding between radicals and ordinary closed-shell molecules in noncovalent complexes. Conversely, the complexation partner can enhance, decrease, or even control the reactivity of the interacting radical. Previously, such radical-molecule (and especially radical-water) complexes were studied by controlled assembly of the interacting partners which mostly leads to formation of the thermodynamically most stable species. Here, we show that UV photolysis of the resonance-stabilized carboxymethyl radical isolated in a cryogenic argon matrix at 4 K leads to the intermediary formation of a metastable, noncovalent complex of the ketenyl radical with a water molecule. In this complex, the ketenyl radical binds water at its terminal carbon atom, although a more stable isomer exists in which water interacts with the C-H bond of the radical. Rigorous W1 theory computations confirm that the ketenyl radical is a stronger donor in C-H···O interactions than ketene itself, while it performs comparably well as an acceptor. We propose that complex formation proceeds via an initial excited-state C-O bond breaking reaction in carboxymethyl under release of an OH radical, which is supported by multireference QD-NEVPT2 computations.

A general framework for the rigorous computation of invariant densities and the coarse-fine strategy

In this paper we present a general, axiomatical framework for the rigorous approximation of invariant densities and other important statistical features of dynamics. We approximate the system through a finite element reduction, by composing the associated transfer operator with a suitable finite dimensional projection (a discretization scheme) as in the well-known Ulam method.We introduce a general framework based on a list of properties (of the system and of the projection) that need to be verified so that we can take advantage of a so-called “coarse-fine” strategy. This strategy is a novel method in which we exploit information coming from a coarser approximation of the system to get useful information on a finer approximation, speeding up the computation. This coarse-fine strategy allows a precise estimation of invariant densities and also allows to estimate rigorously the speed of mixing of the system by the speed of mixing of a coarse approximation of it, which can easily be estimated by the computer.The estimates obtained her e are rigorous, i.e., they come with exact error bounds that are guaranteed to hold and take into account both the discretization and the approximations induced by finite-precision arithmetic.We apply this framework to several discretization schemes and examples of invariant density computation from previous works, obtaining a remarkable reduction in computation time.We have implemented the numerical methods described here in the Julia programming language, and released our implementation publicly as a Julia package.