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Computation, Volume 10, Issue 2 (February 2022) – 20 articles

Cover Story (view full-size image): Employing first-principles calculations based on density functional theory (DFT), we designed a novel two-dimensional (2D) elemental monolayer allotrope of carbon called hexatetra-carbon. In the hexatetra-carbon structure, each carbon atom bonds with its four neighboring atoms in a 2D double layer crystal structure, which is formed by a network of carbon hexagonal prisms, a semiconductor with an indirect band gap of 2.20 eV. This novel monolayer may be obtained from bilayer graphene under external mechanical strain. As a semiconductor with a moderate band gap in the visible light range, once synthesized, hexatetra-carbon shows promising applications in new opto-electronics technologies. View this paper.
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Article
On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks
Computation 2022, 10(2), 32; https://doi.org/10.3390/computation10020032 - 20 Feb 2022
Cited by 1 | Viewed by 798
Abstract
The problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the [...] Read more.
The problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the nodes where the capacitors will be installed. Simultaneously, the continuous variables are mainly associated with the power flow solution. The main contribution of this research is the reformulation of the exact MINLP model through a mixed-integer second-order cone programming model (MI-SOCP). This mixed-integer conic model maintains the nonlinearities of the original MINLP model; however, it can be solved efficiently with the branch & bound method combined with the interior point method adapted for conic programming models. The main advantage of the proposed MI-SOCP model is the possibility of finding the global optimum based on the convex nature of the power flow problem for each binary/integer variable combination in the branch & bound search tree. The numerical results in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness and robustness of the proposed MI-SOCP model compared to different metaheuristic approaches. The MI-SOCP model finds the final power losses of the IEEE 33- and IEEE 69-bus systems of 138.416kW and 145.397kW, which improves the best literature results reached with the flower pollination algorithm, i.e., 139.075 kW, and 145.860kW, respectively. The simulations are carried out in MATLAB software using its convex optimizer tool known as CVX with the Gurobi solver. Full article
(This article belongs to the Special Issue Recent Advances in Process Modeling and Optimisation)
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Article
Hierarchical Epidemic Model on Structured Population: Diffusion Patterns and Control Policies
Computation 2022, 10(2), 31; https://doi.org/10.3390/computation10020031 - 17 Feb 2022
Viewed by 688
Abstract
In the current study, we define a hierarchical epidemic model that helps to describe the propagation of a pathogen in a clustered human population. The estimation of a novel coronavirus spreading worldwide leads to the idea of the hierarchical structure of the epidemic [...] Read more.
In the current study, we define a hierarchical epidemic model that helps to describe the propagation of a pathogen in a clustered human population. The estimation of a novel coronavirus spreading worldwide leads to the idea of the hierarchical structure of the epidemic process. Thus, the propagation process is divided into three possible levels: a city, a country, and a worldwide. On each level, the pathogen propagation process is based on the susceptible-exposed-infected-recovered (SEIR) model. We thus formulate a modified transmission model of infected individuals between levels. The control of the pathogen’s spread can be seen as an optimal control problem. A trade-off exists between the cost of active virus propagation and the design of appropriate quarantine measures. Each level of the hierarchy is defined by its network. A series of numerical experiments was conducted to corroborate the obtained results. Full article
(This article belongs to the Section Computational Biology)
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Article
Kinetic Energy Density Functionals Based on a Generalized Screened Coulomb Potential: Linear Response and Future Perspectives
Computation 2022, 10(2), 30; https://doi.org/10.3390/computation10020030 - 15 Feb 2022
Cited by 1 | Viewed by 696
Abstract
We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations [...] Read more.
We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations (yGGA), are potentially efficient real-space semilocal methods that include significant non-local effects and can describe different important exact properties of the kinetic energy. In this work, we focus in particular on the linear response behavior for the homogeneous electron gas (HEG). We show that such functionals are able to reproduce the exact Lindhard function behavior with a very good accuracy, outperforming all other semilocal kinetic functionals. These theoretical advances allow us to perform a detailed analysis of a special class of yGGAs, namely the linear yGGA functionals. Thus, we show how the present approach can generalize the yGGA functionals improving the HEG linear behavior and leading to an extended formula for the kinetic functional. Moreover, testing on several jellium cluster model systems allows highlighting advantages and limitations of the linear yGGA functionals and future perspectives for the development of yGGA kinetic functionals. Full article
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Review
Science Mapping the Academic Knowledge on Business Improvement Districts
Computation 2022, 10(2), 29; https://doi.org/10.3390/computation10020029 - 13 Feb 2022
Viewed by 928
Abstract
Business Improvement Districts (BIDs) are a contemporary urban revitalization policy that has been set in motion through international policymaking circuits. They have been presented as a panacea to the economic and social challenges facing many cities and traditional shopping districts. However, a comprehensive [...] Read more.
Business Improvement Districts (BIDs) are a contemporary urban revitalization policy that has been set in motion through international policymaking circuits. They have been presented as a panacea to the economic and social challenges facing many cities and traditional shopping districts. However, a comprehensive overview of the academic literature on this form of local governance remains to be conducted. Drawing on bibliometric methods and bibliometrix R-tool, this paper maps and examines the state-of-the-art of academic knowledge on BIDs published between 1979 and 2021. Findings suggest that (i) scientific production has increased since the early 2000s, has crossed US borders but remains highly Anglo-Saxon-centered; (ii) academic knowledge on BIDs is multidisciplinary and has been published in high-impact journals; (iii) influential documents on BIDs have centered on three issues: urban governance/politics, policy mobilities–mutation and impacts assessment and criticisms; (iv) while author collaboration networks exist, the interaction between them is limited; (v) the conceptualization of BIDs has changed over time, both in thematic and geographical focus. These results constitute the first science mapping on the academic literature on BIDs, and we argue they should inform future scientific debates about the studying of this form of local governance. Full article
(This article belongs to the Special Issue Bibliometrics)
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Article
Accuracy and Precision in Electronic Structure Computation: Wien2k and FPLO
Computation 2022, 10(2), 28; https://doi.org/10.3390/computation10020028 - 11 Feb 2022
Cited by 1 | Viewed by 714
Abstract
Electronic structure calculations in the framework of density functional theory are based on complex numerical codes which are used in a multitude of applications. Frequently, existing experimental information is used as a gauge for the reliability of such codes. However, their results depend [...] Read more.
Electronic structure calculations in the framework of density functional theory are based on complex numerical codes which are used in a multitude of applications. Frequently, existing experimental information is used as a gauge for the reliability of such codes. However, their results depend both on the chosen exchange-correlation energy functional and on the specific numerical implementation of the Kohn-Sham equations. The only way to disentangle these two items is a direct comparison of two or more electronic structure codes. Here, we address the achievable numerical accuracy and numerical precision in the total energy computation of the two all-electron density-functional codes Wien2k and FPLO. Both codes are based on almost independent numerical implementations and largely differ in the representation of the Bloch wave function. Thus, it is a highly encouraging result that the total energy data obtained with both codes agree within less than 106. We here relate the term numerical accuracy to the value of the total energy E, while the term numerical precision is related to the numerical noise of E as observed in total energy derivatives. We find that Wien2k achieves a slightly higher accuracy than FPLO at the price of a larger numerical effort. Further, we demonstrate that the FPLO code shows somewhat higher precision, i.e., less numerical noise in E than Wien2k, which is useful for the evaluation of physical properties based on derivatives of E. Full article
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Article
Should We Gain Confidence from the Similarity of Results between Methods?
Computation 2022, 10(2), 27; https://doi.org/10.3390/computation10020027 - 11 Feb 2022
Cited by 1 | Viewed by 579
Abstract
Confirming the result of a calculation by a calculation with a different method is often seen as a validity check. However, when the methods considered are all subject to the same (systematic) errors, this practice fails. Using a statistical approach, we define measures [...] Read more.
Confirming the result of a calculation by a calculation with a different method is often seen as a validity check. However, when the methods considered are all subject to the same (systematic) errors, this practice fails. Using a statistical approach, we define measures for reliability and similarity, and we explore the extent to which the similarity of results can help improve our judgment of the validity of data. This method is illustrated on synthetic data and applied to two benchmark datasets extracted from the literature: band gaps of solids estimated by various density functional approximations, and effective atomization energies estimated by ab initio and machine-learning methods. Depending on the levels of bias and correlation of the datasets, we found that similarity may provide a null-to-marginal improvement in reliability and was mostly effective in eliminating large errors. Full article
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Article
Applying Bibliometric Techniques: Studying Interdisciplinarity in Higher Education Curriculum
Computation 2022, 10(2), 26; https://doi.org/10.3390/computation10020026 - 10 Feb 2022
Viewed by 731
Abstract
Bibliometric methods are relevant for a range of applications and disciplines. The majority of existing scholarship investigating citation and reference patterns focuses on studying research impact. This article presents a new approach to studying the curriculum using bibliometric methods. Through a review of [...] Read more.
Bibliometric methods are relevant for a range of applications and disciplines. The majority of existing scholarship investigating citation and reference patterns focuses on studying research impact. This article presents a new approach to studying the curriculum using bibliometric methods. Through a review of existing definitions and measures of interdisciplinary research and standardization procedures for comparing disciplinary citations, three measures were considered: variety, balance and dissimilarity. Bibliometric algorithms for assessing these measures were adopted and modified for a curriculum context, and three interdisciplinary programs were investigated that span undergraduate and graduate degrees. Data objects were course syllabi, and required references were coded for disciplinary affiliations. The results indicated that—despite purportedly pursuing a singular goal in the same academic unit—the programs employed distinct citation patterns. Variety was highest in the master’s program, and balance was highest in the doctoral program. Dissimilarity was highest in the doctoral program, yet a novel technique for disambiguating disciplinary composition was implemented to improve interpretation. The analysis yielded unexpected findings, which underscore the value of a systematic approach in advancing beyond discourse by harnessing bibliometric techniques to reveal underlying curricula structure. This study contributed a well-grounded bibliometric method that can be replicated in future studies. Full article
(This article belongs to the Special Issue Bibliometrics)
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Article
A Study on the Effect of Geometry and Operating Variables on Density Wave Oscillation in a Supercritical Natural Circulation Loop
Computation 2022, 10(2), 25; https://doi.org/10.3390/computation10020025 - 08 Feb 2022
Viewed by 672
Abstract
Nowadays, a prime technology in generation IV nuclear reactors, the supercritical water reactor (SCWR), is the main object of focus. The current article aims to develop a thermal hydraulic numerical model for predicting density wave oscillation (DWO) in a supercritical water natural circulation [...] Read more.
Nowadays, a prime technology in generation IV nuclear reactors, the supercritical water reactor (SCWR), is the main object of focus. The current article aims to develop a thermal hydraulic numerical model for predicting density wave oscillation (DWO) in a supercritical water natural circulation loop (SCWNCL). A one-dimensional thermal hydraulic mathematical model was developed. The numerical model consists of nonlinear mass, momentum, and energy conservation equations, which were discretized by applying the implicit finite difference technique. The numerical model was validated with experimental results, and numerical simulations were carried out to find the marginal stability boundary (MSB) and draw the stability map for the loop. Further, the effects of geometry (i.e., diameter and hot leg length) and operating parameters (i.e., inlet system pressure and friction factor) on the density wave oscillation of the SCWNCL were analyzed. Full article
(This article belongs to the Special Issue Computational Heat, Mass, and Momentum Transfer—III)
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Article
On the High-Resolution Discretization of the Maxwell Equations in a Composite Tape and the Heating Effects Induced by the Dielectric Losses
Computation 2022, 10(2), 24; https://doi.org/10.3390/computation10020024 - 29 Jan 2022
Viewed by 733
Abstract
Electromagnetic field propagation inside composite materials represents a challenge where fiber-scale simulation remains intractable using classical simulation methods. The present work proposes an original 3D simulation with a mesh resolution fine enough to resolve the fiber scale, thanks to the use of Proper [...] Read more.
Electromagnetic field propagation inside composite materials represents a challenge where fiber-scale simulation remains intractable using classical simulation methods. The present work proposes an original 3D simulation with a mesh resolution fine enough to resolve the fiber scale, thanks to the use of Proper Generalized Decomposition (PGD)-based space decomposition, which avoids the necessity of considering homogenized properties and considers the richest description of the involved physics from the solution of the Maxwell equations. This high-resolution simulation enables comparing the electromagnetic field propagation in a composite part, depending on the considered frequency and the fiber’s/wave polarization’s relative orientation. The electromagnetic fields are then post-processed to identify the heat generation terms and- the resulting induced thermal field. The results prove the ability of the PGD-based discretization to attain extremely high levels of resolution, the equivalent of 1010 finite-element degrees of freedom. The obtained results show an enhanced wave penetration when the electric field polarization coincides with the fiber orientation. On the contrary, when the electric field is polarized along the normal to the fiber orientation, both the penetration and the associated heating reduce significantly, compromising the use of homogenized models, rendering them unable to reproduce the observed behaviors. Full article
(This article belongs to the Section Computational Engineering)
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Article
Finite Mixture Models for Clustering Auto-Correlated Sales Series Data Influenced by Promotions
Computation 2022, 10(2), 23; https://doi.org/10.3390/computation10020023 - 28 Jan 2022
Viewed by 642
Abstract
The focus of the present paper is on clustering, namely the problem of finding distinct groups in a dataset so that each group consists of similar observations. We consider the finite mixtures of regression models, given their flexibility in modeling heterogeneous time series. [...] Read more.
The focus of the present paper is on clustering, namely the problem of finding distinct groups in a dataset so that each group consists of similar observations. We consider the finite mixtures of regression models, given their flexibility in modeling heterogeneous time series. Our study aims to implement a novel approach, which fits mixture models based on the spline and polynomial regression in the case of auto-correlated data, to cluster time series in an unsupervised machine learning framework. Given the assumption of auto-correlated data and the usage of exogenous variables in the mixture model, the usual approach of estimating the maximum likelihood parameters using the Expectation–Maximization (EM) algorithm is computationally prohibitive. Therefore, we provide a novel algorithm for model fitting combining auto-correlated observations with spline and polynomial regression. The case study of this paper consists of the task of clustering the time series of sales data influenced by promotional campaigns. We demonstrate the effectiveness of our method in a case study of 131 sales series data from a real-world company. Numerical outcomes demonstrate the efficacy of the proposed method for clustering auto-correlated time series. Despite the specific case study of this paper, the proposed method can be used in several real-world application fields. Full article
(This article belongs to the Section Computational Engineering)
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Article
Length-Gauge Optical Matrix Elements in WIEN2k
Computation 2022, 10(2), 22; https://doi.org/10.3390/computation10020022 - 26 Jan 2022
Cited by 1 | Viewed by 744
Abstract
Hybrid exchange-correlation functionals provide superior electronic structure and optical properties of semiconductors or insulators as compared to semilocal exchange-correlation potentials due to admixing a portion of the non-local exact exchange potential from a Hartree–Fock theory. Since the non-local potential does not commute with [...] Read more.
Hybrid exchange-correlation functionals provide superior electronic structure and optical properties of semiconductors or insulators as compared to semilocal exchange-correlation potentials due to admixing a portion of the non-local exact exchange potential from a Hartree–Fock theory. Since the non-local potential does not commute with the position operator, the momentum matrix elements do not fully capture the oscillator strength, while the length-gauge velocity matrix elements do. So far, length-gauge velocity matrix elements were not accessible in the all-electron full-potential WIEN2k package. We demonstrate the feasibility of computing length-gauge matrix elements in WIEN2k for a hybrid exchange-correlation functional based on a finite difference approach. To illustrate the implementation we determined matrix elements for optical transitions between the conduction and valence bands in GaAs, GaN, (CH3NH3)PbI3 and a monolayer MoS2. The non-locality of the Hartree–Fock exact exchange potential leads to a strong enhancement of the oscillator strength as noticed recently in calculations employing pseudopotentials (Laurien and Rubel: arXiv:2111.14772 (2021)). We obtained an analytical expression for the enhancement factor for the difference in eigenvalues not captured by the kinetic energy. It is expected that these results can also be extended to other non-local potentials, e.g., a many-body GW approximation. Full article
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Article
Analytic Solution to the Piecewise Linear Interface Construction Problem and Its Application in Curvature Calculation for Volume-of-Fluid Simulation Codes
Computation 2022, 10(2), 21; https://doi.org/10.3390/computation10020021 - 26 Jan 2022
Cited by 1 | Viewed by 889
Abstract
The plane–cube intersection problem has been discussed in the literature since 1984 and iterative solutions to it have been used as part of piecewise linear interface construction (PLIC) in computational fluid dynamics simulation codes ever since. In many cases, PLIC is the bottleneck [...] Read more.
The plane–cube intersection problem has been discussed in the literature since 1984 and iterative solutions to it have been used as part of piecewise linear interface construction (PLIC) in computational fluid dynamics simulation codes ever since. In many cases, PLIC is the bottleneck of these simulations regarding computing time, so a faster analytic solution to the plane–cube intersection would greatly reduce the computing time for such simulations. We derive an analytic solution for all intersection cases and compare it to the previous solution from Scardovelli and Zaleski (Scardovelli, R.; Zaleski, S. Analytical relations connecting linear interfaces and volume fractions in rectangular grids. J. Comput. Phys.2000, 164, 228–237), which we further improve to include edge cases and micro-optimize to reduce arithmetic operations and branching. We then extend our comparison regarding computing time and accuracy to include two different iterative solutions as well. We find that the best choice depends on the employed hardware platform: on the CPU, Newton–Raphson is fastest with compiler optimization enabled, while analytic solutions perform better than iterative solutions without. On the GPU, the fastest method is our optimized version of the analytic SZ solution. We finally provide details on one of the applications of PLIC—curvature calculation for the Volume-of-Fluid model used for free surface fluid simulations in combination with the lattice Boltzmann method. Full article
(This article belongs to the Section Computational Engineering)
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Editorial
Acknowledgment to Reviewers of Computation in 2021
Computation 2022, 10(2), 20; https://doi.org/10.3390/computation10020020 - 26 Jan 2022
Viewed by 633
Abstract
Rigorous peer-reviews are the basis of high-quality academic publishing [...] Full article
Article
Hexatetra-Carbon: A Novel Two-Dimensional Semiconductor Allotrope of Carbon
Computation 2022, 10(2), 19; https://doi.org/10.3390/computation10020019 - 25 Jan 2022
Cited by 1 | Viewed by 885
Abstract
Employing first-principles calculations based on density functional theory (DFT), we designed a novel two-dimensional (2D) elemental monolayer allotrope of carbon called hexatetra-carbon. In the hexatetra-carbon structure, each carbon atom bonds with its four neighboring atoms in a 2D double layer crystal structure, which [...] Read more.
Employing first-principles calculations based on density functional theory (DFT), we designed a novel two-dimensional (2D) elemental monolayer allotrope of carbon called hexatetra-carbon. In the hexatetra-carbon structure, each carbon atom bonds with its four neighboring atoms in a 2D double layer crystal structure, which is formed by a network of carbon hexagonal prisms. Based on our calculations, it is found that hexatetra-carbon exhibits a good structural stability as confirmed by its rather high calculated cohesive energy −6.86 eV/atom, and the absence of imaginary phonon modes in its phonon dispersion spectra. Moreover, compared with its hexagonal counterpart, i.e., graphene, which is a gapless material, our designed hexatetra-carbon is a semiconductor with an indirect band gap of 2.20 eV. Furthermore, with a deeper look at the hexatetra-carbon, one finds that this novel monolayer may be obtained from bilayer graphene under external mechanical strain conditions. As a semiconductor with a moderate band gap in the visible light range, once synthesized, hexatetra-carbon would show promising applications in new opto-electronics technologies. Full article
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Article
Impact of Charge-Resonance Excitations on CT-Mediated J-Type Aggregation in Singlet and Triplet Exciton States of Perylene Di-Imide Aggregates: A TDDFT Investigation
Computation 2022, 10(2), 18; https://doi.org/10.3390/computation10020018 - 25 Jan 2022
Cited by 1 | Viewed by 895
Abstract
The modulation of intermolecular interactions upon aggregation induces changes in excited state properties of organic molecules that can be detrimental for some optoelectronic applications but can be exploited for others. The time-dependent density functional theory (TDDFT) is a cost-effective approach to determining the [...] Read more.
The modulation of intermolecular interactions upon aggregation induces changes in excited state properties of organic molecules that can be detrimental for some optoelectronic applications but can be exploited for others. The time-dependent density functional theory (TDDFT) is a cost-effective approach to determining the exciton states of molecular aggregates, and it has been shown to provide reliable results when coupled with the appropriate choice of the functional. Here we apply a general procedure to analyze the aggregates’ exciton states derived from TDDFT calculations in terms of diabatic states chosen to coincide with local (LE) and charge-transfer (CT) excitations within a restricted orbital space. We apply the approach to study energy profiles, interstate couplings, and the charge-transfer character of singlet and triplet exciton states of perylene di-imide aggregates (PDI). We focus on the intermolecular displacement along the longitudinal translation coordinate, which mimics different amounts of slip-stacking observed in PDI crystals. The analysis, in terms of symmetry-adapted Frenkel excitations (FE) and charge-resonance (CR) states and their interactions, discloses how the interchange of the H/J character for small longitudinal shifts, previously reported for singlet exciton states, also occurs for triplet excitons. Full article
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Article
An Efficient Method for Comparing Numbers and Determining the Sign of a Number in RNS for Even Ranges
Computation 2022, 10(2), 17; https://doi.org/10.3390/computation10020017 - 24 Jan 2022
Viewed by 794
Abstract
Fully Homomorphic Encryption (FHE) permits processing information in the form of ciphertexts without decryption. It can ensure the security of information in common technologies used today, such as cloud computing, the Internet of Things, and machine learning, among others. A primary disadvantage for [...] Read more.
Fully Homomorphic Encryption (FHE) permits processing information in the form of ciphertexts without decryption. It can ensure the security of information in common technologies used today, such as cloud computing, the Internet of Things, and machine learning, among others. A primary disadvantage for its practical application is the low efficiency of sign and comparison operations. Several FHE schemes use the Residue Number System (RNS) to decrease the time complexity of these operations. Converting from the RNS to the positional number system and calculating the positional characteristic of a number are standard approaches for both operations in the RNS domain. In this paper, we propose a new method for comparing numbers and determining the sign of a number in RNS. We focus on the even ranges that are computationally simple due to their peculiarities. We compare the performance of several state-of-art algorithms based on an implementation in C++ and relatively simple moduli with a bit depth from 24 to 64 bits. The experimental analysis shows a better performance of our approach for all the test cases; it improves the sign detection between 1.93 and 15.3 times and the number comparison within 1.55–11.35 times with respect to all the methods and configurations. Full article
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Article
A Numerical Approach for Developing a Bearing-Bypass Design Criterion for Sizing Bolted Joints
Computation 2022, 10(2), 16; https://doi.org/10.3390/computation10020016 - 20 Jan 2022
Viewed by 609
Abstract
Bolted joints are widely used in composite aircraft structures, for their assembly. The appropriate bolted joint configuration (hole/bolt diameter, pitch, etc.) is carefully selected during the detail design phase, where high fidelity numerical models are required with substantial computational cost and time. This [...] Read more.
Bolted joints are widely used in composite aircraft structures, for their assembly. The appropriate bolted joint configuration (hole/bolt diameter, pitch, etc.) is carefully selected during the detail design phase, where high fidelity numerical models are required with substantial computational cost and time. This work presents a design criterion, which allows the selection of the bolted joint configuration during the preliminary design phase with less computational time. The developed design criterion is based on a fully parametric finite element (FE) model, built in ANSYS V19 (Canonsburg, PA, USA), of a bolted joint with progressive damage modelling (PDM) capabilities, so that the failure of the joint can be predicted. From the numerical analyses, the bearing load and the load that bypasses the hole are calculated, up to failure, for a variety of joint configurations and loading conditions. The results of each analysis are used for plotting the failure envelope for the investigated bolted-joint configuration. Consequently, a design criterion is generated for the bolted joint. The availability of these failure envelopes, as design criterion, permit the appropriate selection of the bolted-joint configuration in an earlier design phase saving valuable time and computational cost. Full article
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Article
Bayesian Instability of Optical Imaging: Ill Conditioning of Inverse Linear and Nonlinear Radiative Transfer Equation in the Fluid Regime
Computation 2022, 10(2), 15; https://doi.org/10.3390/computation10020015 - 19 Jan 2022
Viewed by 615
Abstract
For the inverse problem in physical models, one measures the solution and infers the model parameters using information from the collected data. Oftentimes, these data are inadequate and render the inverse problem ill-posed. We study the ill-posedness in the context of optical imaging, [...] Read more.
For the inverse problem in physical models, one measures the solution and infers the model parameters using information from the collected data. Oftentimes, these data are inadequate and render the inverse problem ill-posed. We study the ill-posedness in the context of optical imaging, which is a medical imaging technique that uses light to probe (bio-)tissue structure. Depending on the intensity of the light, the forward problem can be described by different types of equations. High-energy light scatters very little, and one uses the radiative transfer equation (RTE) as the model; low-energy light scatters frequently, so the diffusion equation (DE) suffices to be a good approximation. A multiscale approximation links the hyperbolic-type RTE with the parabolic-type DE. The inverse problems for the two equations have a multiscale passage as well, so one expects that as the energy of the photons diminishes, the inverse problem changes from well- to ill-posed. We study this stability deterioration using the Bayesian inference. In particular, we use the Kullback–Leibler divergence between the prior distribution and the posterior distribution based on the RTE to prove that the information gain from the measurement vanishes as the energy of the photons decreases, so that the inverse problem is ill-posed in the diffusive regime. In the linearized setting, we also show that the mean square error of the posterior distribution increases as we approach the diffusive regime. Full article
(This article belongs to the Special Issue Inverse Problems with Partial Data)
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Article
A Theoretical Survey of the UV–Visible Spectra of Axially and Peripherally Substituted Boron Subphthalocyanines
Computation 2022, 10(2), 14; https://doi.org/10.3390/computation10020014 - 18 Jan 2022
Cited by 1 | Viewed by 663
Abstract
The UV–visible spectra of a series of subphthalocyanines (SubPcs) characterized by three different axial substituents (An) in combination with H, F, NO2, SO2H and SO2CH3 peripheral substituents (Ri) were predicted and analyzed [...] Read more.
The UV–visible spectra of a series of subphthalocyanines (SubPcs) characterized by three different axial substituents (An) in combination with H, F, NO2, SO2H and SO2CH3 peripheral substituents (Ri) were predicted and analyzed by means of time-dependent DFT calculations, including chloroform as a solvent. In this analysis, we paid particular attention to the Q band, which remained almost unchanged regardless of the nature of the axial substituent. For the same axial substituent, changes in the Q band were also rather small when hydrogens at the periphery were replaced by R1 = SO2H and R1 = R2 = SO2H. However, the shifting of the Q band was almost 10 times larger when R1 = NO2 and R1 = R2 = NO2 due to the participation of this substituent in the π SubPc cloud. In most cases, the characteristics of the spectra can be explained considering only the transitions involving the HOMO-1, HOMO, LUMO and LUMO + 1 orbitals, where the Q band can be decomposed into two main contributions, leading to charge separation. Only for SubPc(A3,F,F,H) would one of the two contributions from the deepest orbital involved not lead to charge transfer. For this latter case, the HOMO-2 orbital must also be taken into account. In summary, the results obtained with the analysis of the MO indicate that the studied SubPcs are appropriate for photochemical devices. Full article
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Article
Organic Emitters Showing Excited-States Energy Inversion: An Assessment of MC-PDFT and Correlation Energy Functionals Beyond TD-DFT
Computation 2022, 10(2), 13; https://doi.org/10.3390/computation10020013 - 18 Jan 2022
Cited by 1 | Viewed by 739
Abstract
The lowest-energy singlet (S1) and triplet (T1) excited states of organic conjugated chromophores are known to be accurately calculated by modern wavefunction and Time-Dependent Density Functional Theory (TD-DFT) methods, with the accuracy of the latter heavily relying [...] Read more.
The lowest-energy singlet (S1) and triplet (T1) excited states of organic conjugated chromophores are known to be accurately calculated by modern wavefunction and Time-Dependent Density Functional Theory (TD-DFT) methods, with the accuracy of the latter heavily relying on the exchange-correlation functional employed. However, there are challenging cases for which this cannot be the case, due to the fact that those excited states are not exclusively formed by single excitations and/or are affected by marked correlation effects, and thus TD-DFT might fall short. We will tackle here a set of molecules belonging to the azaphenalene family, for which research recently documented an inversion of the relative energy of S1 and T1 excited states giving rise to a negative energy difference (ΔEST) between them and, thereby, contrary to most of the systems thus far treated by TD-DFT. Since methods going beyond standard TD-DFT are not extensively applied to excited-state calculations and considering how challenging this case is for the molecules investigated, we will prospectively employ here a set of non-standard methods (Multi-Configurational Pair Density Functional Theory or MC-PDFT) and correlation functionals (i.e., Lie–Clementi and Colle–Salvetti) relying not only on the electronic density but also on some modifications considering the intricate electronic structure of these systems. Full article
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