Article
Engineering, Marine
F. Perez-Arribas, A. Silva-Campillo, H. R. Diaz-Ojeda
Summary: This paper presents a practical method to define a quasi-developable surface by quantifying developability through the limit warp angle, which is beneficial for engineering applications and parametric definition of ship hulls during the initial design phases.
Article
Mathematics, Interdisciplinary Applications
P. Viswanathan
Summary: This paper describes a procedure for constructing a parameterized class of fractal functions that preserve the smoothness of the original function. The authors generalize the bicubic spline by introducing a two-parameter family of fractal functions, called bicubic fractal splines. Upper bounds for the interpolation error of the bicubic fractal spline and its derivatives are obtained under certain hypotheses. The paper also provides a detailed exposition of C-(2,C-2)-regular self-referential functions and their significance in the study of smoothness-preserving bivariate self-referential functions.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics
Aizeng Wang, Gang Zhao, Chuan He
Summary: This paper introduces a new theoretical tool, I-spline, which can transform different surfaces and/or curves into a unified form by introducing the definitions of naked knot and I-mesh. It is particularly effective in handling systems consisting of detached curves or surfaces, or systems having both curves and surfaces.
Article
Engineering, Multidisciplinary
Krunal Raval, Carla Manni, Hendrik Speleers
Summary: Tchebycheffian splines are smooth piecewise functions drawn from Tchebycheff spaces and possess properties similar to polynomial splines. Tchebycheffian B-splines (TB-splines), which are basis functions for Tchebycheffian splines, offer a flexible and robust environment. A subclass of Tchebycheffian splines with pieces in null-spaces of linear differential operators allows the combination of polynomials with exponential and trigonometric functions. This paper explores the use of TB-splines as an attractive alternative to standard polynomial B-splines and rational NURBS in isogeometric Galerkin methods.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Chemistry, Physical
Leroy L. Jia, Steven Pei, Robert A. Pelcovits, Thomas R. Powers
Summary: We use theory and numerical computation to study the shape of an axisymmetric fluid membrane with resistance to bending and constant area. Multiple branches of solutions are found, with catenoidal shape emerging as the maximal allowable separation. When the Gaussian curvature modulus is zero, additional cylindrical tether solutions are possible at large ring separations, while when it is non-zero, the force and the membrane tension diverge at maximum ring separation. Stabilities of different shapes are examined, showing that catenoidal membranes have distinct properties compared to their soap film counterparts.
Article
Computer Science, Artificial Intelligence
Jiapeng Tang, Xiaoguang Han, Mingkui Tan, Xin Tong, Kui Jia
Summary: This paper focuses on the challenging task of learning 3D object surface reconstructions from RGB images and proposes a method that learns and uses a topology-preserved skeletal shape representation to assist the surface reconstruction. Through experiments, the proposed method is shown to be effective and outperforms existing methods in the surface reconstruction task.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2022)
Article
Multidisciplinary Sciences
Helena Liu, Axel van de Walle
Summary: This study proposes a screening method to calculate the surface energy of crystals by simplifying the physical model. The method shows high accuracy in calculating the surface energy of crystal structures, and serves as a valuable tool for determining crystal shapes from first principles.
Article
Acoustics
Olavo M. Silva, Fernando Valentini, Eduardo L. Cardoso
Summary: This manuscript discusses shape and position preserving designs in harmonic vibration problems using topology optimization. The shape preserving designs consider the active input power as the objective function and the local time-averaged potential energy as constraint. A more stable solution procedure was found compared to the local dynamic compliance measure. A new formulation for position preserving design using local time-averaged kinetic energy as constraint is proposed, with examples presented to show the effectiveness of the approaches.
JOURNAL OF SOUND AND VIBRATION
(2021)
Article
Mathematics, Applied
Paul Castillo, Sergio Gomez
Summary: In this study, an optimal error estimate in the L-2 norm for a semi discrete method based on high order B-splines Galerkin spatial discretizations was derived and applied to a coupled nonlinear Schrodinger system with cubic nonlinearity. A fully discrete method based on a conservative nonlinear splitting Crank-Nicolson time step was proposed, with theoretical proof of conservation of mass and energy. Several numerical experiments using B-splines up to order 7 were conducted to validate the accuracy in space and time, as well as conservation properties of the method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Energy & Fuels
Jose A. Ruiz-Arias
Summary: Interpolation is a crucial process in solar resource assessment, and it plays a significant role in connecting consecutive components in the modeling chain. However, traditional interpolation methods often assume that the interpolating function must pass through interpolation points, which is not suitable for averaged datasets or variables that require consistency across the interpolation. To address this issue, the author introduces a mean-preserving splines method that can effectively interpolate one-dimensional data while conserving the interpolated field. This method utilizes second-order polynomial splines to minimize fluctuations in the interpolated field and restricts the interpolation results within user-provided limits. It also handles periodic boundary conditions and non-uniform averaging grids. The validity and performance of the method are demonstrated through relevant case examples in the solar resource assessment field.
Article
Automation & Control Systems
Gang Hu, Xiaoni Zhu, Guo Wei, Ching-Ter Chang
Summary: This paper presents the use of an improved marine predators algorithm (MPA) to optimize the shape of shape-adjustable generalized cubic developable Ball (SGCD-Ball) surfaces, solving shape adjustment and optimization issues with novel shape-adjustable generalized cubic Ball basis functions. The optimization of developable surfaces is effectively tackled through swarm intelligence algorithms, with the incorporation of a quasi-opposition strategy and a differential evolution algorithm into the MPA to develop an improved MPA known as ODMPA. The superiority of ODMPA is demonstrated through comparison with other algorithms on benchmark functions and engineering optimization problems, showing its effectiveness in precision and robustness.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2021)
Article
Computer Science, Software Engineering
Chris Yu, Caleb Brakensiek, Henrik Schumacher, Keenan Crane
Summary: This paper introduces a numerical framework for surface geometry optimization while avoiding collisions, utilizing tangent-point energy and a novel acceleration scheme based on fractional Sobolev inner product. By decomposing the preconditioner into two ordinary Poisson equations and a fractional differential operator, it avoids the complexity of building a multiresolution mesh hierarchy, and further accelerates the scheme through hierarchical approximation. The paper also explores potential applications in mathematical visualization, geometric modeling, and geometry processing.
ACM TRANSACTIONS ON GRAPHICS
(2021)
Article
Chemistry, Analytical
Bin Liu, Weiming Wang, Jun Zhou, Bo Li, Xiuping Liu
Summary: Extrinsic representations for non-rigid shapes with different poses are ideal in computer graphics applications, providing a pose invariant signature and reducing difficulties caused by varying poses. Existing methods often result in geometric distortions, but the proposed algorithm presents a novel approach that effectively preserves local structure and reduces distortion. The algorithm is simple, computationally efficient, and robust, with enhanced efficacy demonstrated in comparison to state-of-the-art methods on 3D shape unfolding.
Article
Chemistry, Physical
Tomas Rauch, Miguel A. L. Marques, Silvana Botti
Summary: Understanding the electronic properties of matter is crucial for proposing useful applications, as accurate approximations to the exchange-correlation functional of density functional theory may become computationally expensive for modeling hybrid organic/inorganic systems. The study of the local modified Becke-Johnson exchange-correlation potential for calculated ionization potentials is important for band alignment in composite systems. Demonstrating the potential's application in the electronic structure calculation of a composite semiconductor/molecule system shows its accuracy and usefulness.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2021)
Article
Multidisciplinary Sciences
Gudrun Albrecht, Esmeralda Mainar, Juan Manuel Pena, Beatriz Rubio
Summary: This paper proposes a new approach to define frequency trigonometric spline curves with shape preserving properties. The construction is based on the normalized B-basis and it is shown that it converges to the Bernstein polynomial basis. The obtained piecewise trigonometric curves also converge to uniform quartic B-Spline curves. This method has applications in CAM design, trajectory generation, data fitting, and solving interpolation problems.
Article
Mathematics
Goncalo Gutierres, Ricardo Mamede, Jose Luis Santos
Summary: We define a statistic on the graph of commutation classes of a permutation of the symmetric group, which allows us to show the ranked poset structure of these graphs with a minimum and maximum. This characterization also enables us to compute the diameter of the commutation graph for any permutation, leading to the results for the longest permutation and fully commutative permutations.
EUROPEAN JOURNAL OF COMBINATORICS
(2022)
Article
Chemistry, Physical
V. C. Mota, P. J. S. B. Caridade, A. J. C. Varandas, B. R. L. Galvao
Summary: An accurate potential energy surface (PES) for the HSiS system is presented, which is based on MRCI + Q calculations and extrapolated to the complete basis set limit. The PES accurately describes the long-range interactions and is used to predict the rate coefficients of the Si + SH -> SiS + H reaction. The reaction is shown to be dominated by long-range forces, with the mechanism Si + SH -> SiSH -> SSiH -> SiS + H being the most important one for all temperatures.
JOURNAL OF PHYSICAL CHEMISTRY A
(2022)
Article
Computer Science, Information Systems
Marco Silva, Andre Riker, Joel Torrado, Jose Santos, Marilia Curado
Summary: The advances made in sustainable energy technology have enabled the use of environmental friendly sources for powering IoT devices. Optimized approaches and distributed heuristic methods can be used to achieve and prolong energy neutral operation, ensuring efficient utilization of sustainable energy sources.
IEEE INTERNET OF THINGS JOURNAL
(2022)
Article
Chemistry, Physical
C. M. R. Rocha, H. Linnartz, A. J. C. Varandas
Summary: In this study, the first global potential energy surface (PES) for SiC2 is reported. The accurate ab initio energies were used in combination with a special approach to recover the spectroscopy of SiC2 while allowing for reaction dynamics studies. The results provide insights into the structural and chemical properties of SiC2 and its importance in circumstellar envelopes.
JOURNAL OF CHEMICAL PHYSICS
(2022)
Article
Mathematics
Ricardo Mamede, Jose Luis Santos, Diogo Soares
Summary: This article discusses the commutation classes and commutation graph of the signed symmetric group. By defining a rank function, the diameter and radius of the commutation graph for the longest signed permutation are computed. It is also proven that the commutation graph for the longest signed permutation is non-planar when n > 2.
DISCRETE MATHEMATICS
(2022)
Article
Chemistry, Physical
Antonio J. C. Varandas
Summary: In this study, the physical basis of the Periodic Table for the enumeration of Polyatomic Aromatic Hydrocarbons (PAH6) is commented on using the concept of quasi-molecules. The study utilizes mathematical lemma and quantum chemistry calculations to analyze the shared plane of quasi-molecules embedded on the parent molecule. Furthermore, novel planar molecules are presented, highlighting the difficulties in assessing planarity through common quantum chemistry calculations.
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
(2023)
Article
Chemistry, Physical
A. J. C. Varandas
Summary: This paper presents a nonempirical approach to reduce basis set error by splitting the vibrational frequencies into Hartree-Fock and electron correlation contributions and extrapolating them to the complete basis set (CBS) limit. The results demonstrate that the method performs well in calculating the vibrational frequencies of molecules.
JOURNAL OF CHEMICAL PHYSICS
(2022)
Article
Construction & Building Technology
Ana Aguiar, Paulo Fernandes, Andreia P. Guerreiro, Ricardo Tomas, Joao Agnelo, Jose Luis Santos, Filipe Araujo, Margarida C. Coelho, Carlos M. Fonseca, Pedro M. d'Orey, Miguel Luis, Susana Sargento
Summary: Eco-routing utilizes IoT technologies to distribute traffic in cities for improved mobility sustainability. This work presents a use case-oriented system design for an eco-routing service and demonstrates the potential reductions in carbon emissions and air pollutants.
SUSTAINABLE CITIES AND SOCIETY
(2022)
Article
Chemistry, Physical
A. J. C. Varandas
Summary: In this study, the researchers propose a new theory called the quasi-molecule theory and explain why carbon/n-triangulenes tend to be planar, while silicon-substituted/n-triangulenes show both planar and nonplanar configurations. The study also examines other polycyclic and sila-compounds.
JOURNAL OF PHYSICAL CHEMISTRY A
(2023)
Article
Chemistry, Physical
A. J. C. Varandas
Summary: This paper introduces the concept of partially hydrogenated graphenes as planar infinite benzenes and discusses their growth paths from benzene or coronene to graphene. The difficulty in performing ab initio calculations for large molecules is emphasized, and the use of MINI basis sets in probe calculations is justified. The 'attitudinal-green' approach advocated in this paper contrasts with the brute-force ('attitudinal-red') method.
CHEMICAL PHYSICS LETTERS
(2023)
Article
Chemistry, Physical
D. P. Freitas, F. N. N. Pansini, A. J. C. Varandas
Summary: The electronic structure, IR spectra, and Raman spectra of (HCN)(n) clusters were investigated using DFT calculations accounting for solvent effects. Both linear and cyclic structures were optimized and it was found that linear structures are local minima with or without solvent effects. Calculations with solvent effects showed faster convergence and the predicted spectra agreed well with previous theoretical and experimental results, especially when considering the solvent effects. Estimates of the IR spectrum for liquid HCN and the gas-phase Raman spectrum were also provided.
CHEMICAL PHYSICS LETTERS
(2023)
Article
Chemistry, Physical
Dandan Lu, Breno R. L. Galvao, Antonio J. C. Varandas, Hua Guo
Summary: The dynamics and kinetics of spin-forbidden transitions between N(D-2) and N(S-4) mediated by collisions with N-2 molecules were investigated using quantum wave packet (WP) method and semi-classical coherent switches with decay of mixing (CSDM) method. These transitions compete with exchange reaction channels on both doublet and quartet potential energy surfaces. The WP and CSDM quenching rate coefficients were in reasonable agreement with each other, reproducing previous theoretical results. For the excitation process, the agreement between the two approaches depended on the treatment of zero-point energy (ZPE) in the product, as the high endoergicity of this process led to severe violation of vibrational ZPE. The Gaussian-binning (GB) method improved the agreement with the quantum result. The excitation rate coefficients were two orders of magnitude smaller than those of the adiabatic exchange reaction, indicating inefficient intersystem crossing due to weak spin-orbit coupling between the two spin manifolds of the N-3 system.
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
(2023)
Article
Chemistry, Physical
Marcio O. Alves, Vinicius C. Mota, Joao P. Braga, Antonio J. C. Varandas, Hua Guo, Breno R. L. Galvao
Summary: In this study, an accurate potential energy surface (PES) for the lowest lying (4 )A '' state of the CNO system is presented. The energy terms are fitted using a theoretical framework, incorporating long-range interactions. The results show improved accuracy in predicting rate coefficients and highlight the importance of long-range interactions for low-temperature reactions.
JOURNAL OF CHEMICAL PHYSICS
(2023)
Article
Chemistry, Physical
A. J. C. Varandas
Summary: By tiling, it is shown that only three out of the thirteen title molecules are planar. The concept of quasi-molecule or its generalization is used to optimize the tiles at different spin-states and levels of theory. The shape-determining property of quasi-tetratomic tiles is demonstrated, while higher order terms are shape-preserving. The probabilistic nature of planarity is examined, and a planarity likelihood ratio is introduced. The planarity of borazine isomers is also predicted, but recent work suggests the possibility of errors in the predictions.
Article
Chemistry, Physical
A. J. C. Varandas
Summary: Ab initio molecular orbital theory is used to study the structures of pi-electron bare rings of group-XIV elements, including larger annulenes. The study provides explanations for the planarity or nonplanarity of these rings based on ab initio calculations and proposes a common rationale using a novel concept of quasi-molecules or the (3+4)-atom partition scheme.
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
(2022)
