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Paula A Whitlock - One of the best experts on this subject based on the ideXlab platform.
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fluid solid demixing in four and five dimensional asymmetric binary hard hypersphere mixtures
Journal of Chemical Physics, 2019Co-Authors: Marvin Bishop, Paula A WhitlockAbstract:Additive asymmetric binary mixtures of hard Hyperspheres in four and five dimensions are investigated by Monte Carlo simulations. These investigations probe systems with diameter ratios of 0.4 and 0.5 in which the larger Hyperspheres are dominant at a mole fraction of 3/4. At the lower densities, the equations of state compare well with molecular dynamics data and a variety of theoretical predictions. When the mixture enters the metastable, two-phase regime, the smaller Hyperspheres exhibit unusual phenomena as the system density increases. To understand this behavior, the mean-square displacement at equilibrium from initial lattice positions, the various pair correlation functions, and occupancy numbers are calculated. In addition, the characteristics of an initially demixed system are studied.
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five dimensional binary hard hypersphere mixtures a monte carlo study
Journal of Chemical Physics, 2016Co-Authors: Marvin Bishop, Paula A WhitlockAbstract:Additive binary mixtures of five dimensional Hyperspheres were investigated by Monte Carlo simulations. Both equal packing fraction and equal mole fraction systems with diameter ratios of 0.4 and 0.5 were examined. A range of total densities were studied, spanning low to moderate density fluids. The pair correlation functions and the equations of state were determined and compared with molecular dynamics data and a variety of theoretical predictions. A significant result of the equal packing fraction simulations was the discovery of how quickly the larger Hyperspheres reorganized into a dense fluid after a random initial placement. In the equal mole fraction case, the pair correlation functions for the larger hypersphere agree with the pair correlation function of a pure fluid at an appropriately scaled density. The theoretical results for the equation of state compare well to the Monte Carlo calculations for all but the highest densities studied.
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phase transitions in four dimensional binary hard hypersphere mixtures
Journal of Chemical Physics, 2013Co-Authors: Marvin Bishop, Paula A WhitlockAbstract:Previous Monte Carlo investigations of binary hard Hyperspheres in four-dimensional mixtures are extended to higher densities where the systems may solidify. The ratios of the diameters of the Hyperspheres examined were 0.4, 0.5, and 0.6. Only the 0.4 system shows a clear two phase, solid-liquid transition and the larger component solidifies into a D4 crystal state. Its pair correlation function agrees with that of a one component fluid at an appropriately scaled density. The 0.5 systems exhibit states that are a mix of D4 and A4 regions. The 0.6 systems behave similarly to a jammed state rather than solidifying into a crystal. No demixing into two distinct fluid phases was observed for any of the simulations.
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monte carlo study of four dimensional binary hard hypersphere mixtures
Journal of Chemical Physics, 2012Co-Authors: Marvin Bishop, Paula A WhitlockAbstract:A multithreaded Monte Carlo code was used to study the properties of binary mixtures of hard Hyperspheres in four dimensions. The ratios of the diameters of the Hyperspheres examined were 0.4, 0.5, 0.6, and 0.8. Many total densities of the binary mixtures were investigated. The pair correlation functions and the equations of state were determined and compared with other simulation results and theoretical predictions. At lower diameter ratios the pair correlation functions of the mixture agree with the pair correlation function of a one component fluid at an appropriately scaled density. The theoretical results for the equation of state compare well to the Monte Carlo calculations for all but the highest densities studied.
Marvin Bishop - One of the best experts on this subject based on the ideXlab platform.
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fluid solid demixing in four and five dimensional asymmetric binary hard hypersphere mixtures
Journal of Chemical Physics, 2019Co-Authors: Marvin Bishop, Paula A WhitlockAbstract:Additive asymmetric binary mixtures of hard Hyperspheres in four and five dimensions are investigated by Monte Carlo simulations. These investigations probe systems with diameter ratios of 0.4 and 0.5 in which the larger Hyperspheres are dominant at a mole fraction of 3/4. At the lower densities, the equations of state compare well with molecular dynamics data and a variety of theoretical predictions. When the mixture enters the metastable, two-phase regime, the smaller Hyperspheres exhibit unusual phenomena as the system density increases. To understand this behavior, the mean-square displacement at equilibrium from initial lattice positions, the various pair correlation functions, and occupancy numbers are calculated. In addition, the characteristics of an initially demixed system are studied.
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five dimensional binary hard hypersphere mixtures a monte carlo study
Journal of Chemical Physics, 2016Co-Authors: Marvin Bishop, Paula A WhitlockAbstract:Additive binary mixtures of five dimensional Hyperspheres were investigated by Monte Carlo simulations. Both equal packing fraction and equal mole fraction systems with diameter ratios of 0.4 and 0.5 were examined. A range of total densities were studied, spanning low to moderate density fluids. The pair correlation functions and the equations of state were determined and compared with molecular dynamics data and a variety of theoretical predictions. A significant result of the equal packing fraction simulations was the discovery of how quickly the larger Hyperspheres reorganized into a dense fluid after a random initial placement. In the equal mole fraction case, the pair correlation functions for the larger hypersphere agree with the pair correlation function of a pure fluid at an appropriately scaled density. The theoretical results for the equation of state compare well to the Monte Carlo calculations for all but the highest densities studied.
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phase transitions in four dimensional binary hard hypersphere mixtures
Journal of Chemical Physics, 2013Co-Authors: Marvin Bishop, Paula A WhitlockAbstract:Previous Monte Carlo investigations of binary hard Hyperspheres in four-dimensional mixtures are extended to higher densities where the systems may solidify. The ratios of the diameters of the Hyperspheres examined were 0.4, 0.5, and 0.6. Only the 0.4 system shows a clear two phase, solid-liquid transition and the larger component solidifies into a D4 crystal state. Its pair correlation function agrees with that of a one component fluid at an appropriately scaled density. The 0.5 systems exhibit states that are a mix of D4 and A4 regions. The 0.6 systems behave similarly to a jammed state rather than solidifying into a crystal. No demixing into two distinct fluid phases was observed for any of the simulations.
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monte carlo study of four dimensional binary hard hypersphere mixtures
Journal of Chemical Physics, 2012Co-Authors: Marvin Bishop, Paula A WhitlockAbstract:A multithreaded Monte Carlo code was used to study the properties of binary mixtures of hard Hyperspheres in four dimensions. The ratios of the diameters of the Hyperspheres examined were 0.4, 0.5, 0.6, and 0.8. Many total densities of the binary mixtures were investigated. The pair correlation functions and the equations of state were determined and compared with other simulation results and theoretical predictions. At lower diameter ratios the pair correlation functions of the mixture agree with the pair correlation function of a one component fluid at an appropriately scaled density. The theoretical results for the equation of state compare well to the Monte Carlo calculations for all but the highest densities studied.
Xinjun Peng - One of the best experts on this subject based on the ideXlab platform.
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twin support vector hypersphere tsvh classifier for pattern recognition
Neural Computing and Applications, 2014Co-Authors: Xinjun PengAbstract:Motivated by the support vector data description, a classical one-class support vector machine, and the twin support vector machine classifier, this paper formulates a twin support vector hypersphere (TSVH) classifier, a novel binary support vector machine (SVM) classifier that determines a pair of Hyperspheres by solving two related SVM-type quadratic programming problems, each of which is smaller than that of a conventional SVM, which means that this TSVH is more efficient than the classical SVM. In addition, the TSVH successfully avoids matrix inversion compared with the twin support vector machine, which indicates learning algorithms of the SVM can be easily extended to this TSVH. Computational results on several synthetic as well as benchmark data sets indicate that the proposed TSVH is not only faster, but also obtains better generalization.
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a twin hypersphere support vector machine classifier and the fast learning algorithm
Information Sciences, 2013Co-Authors: Xinjun PengAbstract:This paper formulates a twin-hypersphere support vector machine (THSVM) classifier for binary recognition. Similar to the twin support vector machine (TWSVM) classifier, this THSVM determines two Hyperspheres by solving two related support vector machine (SVM)-type problems, each one is smaller than the classical SVM, which makes the THSVM be more efficient than the classical SVM. In addition, the THSVM avoids the matrix inversions in its two dual quadratic programming problems (QPPs) compared with the TWSVM. By considering the characteristics of the dual QPPs of THSVM, an efficient Gilbert's algorithm for the THSVM based on the reduced convex hull (RCH) instead of directly optimizing its pair of QPPs is further presented. Computational results on several synthetic as well as benchmark datasets indicate the significant advantages of the THSVM classifier in the computational time and test accuracy.
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least squares twin support vector hypersphere ls tsvh for pattern recognition
Expert Systems With Applications, 2010Co-Authors: Xinjun PengAbstract:The twin support vector hypersphere (TSVH) is a novel efficient pattern recognition tool, because it determines a pair of Hyperspheres by solving two related SVM-type problems, each of which is smaller than in a classical SVM. In this paper we formulate a least squares version for this classifier, termed as the least squares twin support vector hypersphere (LS-TSVH). This formulation leads to extremely simple and fast algorithm for generating binary classifier based on a pair of Hyperspheres. Due to equality type constraints in the formulation, the solution follows from solving two sets of nonlinear equations, instead of the two dual quadratic programming problems (QPPs) for TSVH. We show that the two sets of nonlinear equations are solved using the well-known Newton downhill algorithm. The effectiveness of proposed LS-TSVH is demonstrated by experimental results on several artificial and benchmark datasets.
Roland Hildebrand - One of the best experts on this subject based on the ideXlab platform.
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on the norm of the cubic form of complete hyperbolic affine Hyperspheres
Results in Mathematics, 2013Co-Authors: Roland HildebrandAbstract:Let \({M_n \subset \mathbb R^{n+1}}\) be a complete hyperbolic affine hypersphere with mean curvature H, \({H < 0}\), and let C be its cubic form. We derive a differential inequality and an upper bound on the scalar function \({||C||_{\infty}}\) defined by the fiber-wise maximum of the value of C on the unit sphere bundle of M. The bounds are attained for the affine Hyperspheres which are asymptotic to a simplicial cone. The results have applications in conic optimization.
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on the infinity norm of the cubic form of complete hyperbolic affine Hyperspheres
2013Co-Authors: Roland HildebrandAbstract:Let Mn⊂Rn+1 be a complete hyperbolic affine hypersphere with mean curvature H, H<0 , and let C be its cubic form. We derive a differential inequality and an upper bound on the scalar function ||C||∞ defined by the fiber-wise maximum of the value of C on the unit sphere bundle of M. The bounds are attained for the affine Hyperspheres which are asymptotic to a simplicial cone. The results have applications in conic optimization.
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centro affine hypersurface immersions with parallel cubic form
arXiv: Differential Geometry, 2012Co-Authors: Roland HildebrandAbstract:We consider non-degenerate centro-affine hypersurface immersions in R^n whose cubic form is parallel with respect to the Levi-Civita connection of the affine metric. There exists a bijective correspondence between homothetic families of proper affine Hyperspheres with center in the origin and with parallel cubic form, and K\"ochers conic omega-domains, which are the maximal connected sets consisting of invertible elements in a real semi-simple Jordan algebra. Every level surface of the omega function in an omega-domain is an affine complete, Euclidean complete proper affine hypersphere with parallel cubic form and with center in the origin. On the other hand, every proper affine hypersphere with parallel cubic form and with center in the origin can be represented as such a level surface. We provide a complete classification of proper affine Hyperspheres with parallel cubic form based on the classification of semi-simple real Jordan algebras. Centro-affine hypersurface immersions with parallel cubic form are related to the wider class of real unital Jordan algebras. Every such immersion can be extended to an affine complete one, whose conic hull is the connected component of the unit element in the set of invertible elements in a real unital Jordan algebra. Our approach can be used to study also other classes of hypersurfaces with parallel cubic form.
Koichi Ohno - One of the best experts on this subject based on the ideXlab platform.
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a scaled hypersphere interpolation technique for efficient construction of multidimensional potential energy surfaces
Chemical Physics Letters, 2005Co-Authors: Satoshi Maeda, Yu Watanabe, Koichi OhnoAbstract:Abstract An efficient interpolation technique was developed for constructing potential energy surfaces (PES) around equilibriums based on data sampling by the scaled hypersphere search (SHS) method. Energy functions on several sizes of hypersphere are interpolated using cosine functions expanded at the SHS path points located in directions having the largest anharmonicity. In an application to H 2 O molecule, wide range of PES including HOH inversion and OH dissociation channels could be constructed with only a Hessian matrix and energy values at 123 points. In vibrational state calculations, the present technique was found to be much more accurate than the fourth-order Taylor expansion.
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a new approach for finding a transition state connecting a reactant and a product without initial guess applications of the scaled hypersphere search method to isomerization reactions of hcn h2o 2 and alanine dipeptide
Chemical Physics Letters, 2005Co-Authors: Satoshi Maeda, Koichi OhnoAbstract:Abstract A new method for finding a transition state (TS) between a reactant and a product on the potential energy surface has been proposed. The scaled hypersphere search (SHS) method, in which reaction pathways are found as minima on the hypersphere, has been applied to finding TS. Starting from a hypersphere centered at the product with a radius just including the reactant on its surface, successive contraction of the sphere radii gives a pathway leading to the TS region. Applications of this method to isomerization of HCN, (H 2 O) 2 , and alanine dipeptide demonstrated highly accurate estimation of TS without any initial guess.
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a scaled hypersphere search method for the topography of reaction pathways on the potential energy surface
Chemical Physics Letters, 2004Co-Authors: Koichi Ohno, Satoshi MaedaAbstract:An algorithm for finding pathways to transition states (TS) or dissociation channels (DC) from equilibrium structures (EQ) on the potential energy surface (PES) is presented. The pathways around an EQ can be discovered at minima on the scaled hypersphere which would have a constant energy when the potentials are harmonic. Topographic maps including all TS, DC, and EQ were obtained for ab initio PES of H2O and HCHO in the MP2/3-21G level. The present scaled hypersphere search technique in combination with a downhill-walk algorithm enables us to make a topographic analysis of the PES for a given chemical composition.