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1
Feng, Y. T., and Yuanqiang Tan. "On Minkowski difference-based contact detection in discrete/discontinuous modelling of convex polygons/polyhedra." Engineering Computations 37, no. 1 (August 12, 2019): 54–72. http://dx.doi.org/10.1108/ec-03-2019-0124.
Анотація:
Purpose Contact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called entrance block of two polyhedra and reduces the contact to evaluate the distance between the reference point to the corresponding entrance block, but effective implementation is still lacking. Design/methodology/approach In this paper, the equivalence of the entrance block and the Minkowski difference of two polyhedra is emphasised and two well-known Minkowski difference-based contact detection and overlap computation algorithms, GJK and expanding polytope algorithm (EPA), are chosen as the possible numerical approaches to the 3D contact theory for DDA, and also as alternatives for computing polyhedral contact features in DEM. The key algorithmic issues are outlined and their important features are highlighted. Findings Numerical examples indicate that the average number of updates required in GJK for polyhedral contact is around 6, and only 1 or 2 iterations are needed in EPA to find the overlap and all the relevant contact features when the overlap between polyhedra is small. Originality/value The equivalence of the entrance block in DDA and the Minkowski difference of two polyhedra is emphasised; GJK- and EPA-based contact algorithms are applied to convex polyhedra in DEM; energy conservation is guaranteed for the contact theory used; and numerical results demonstrate the effectiveness of the proposed methodologies.
2
Fercoq, Olivier, Marianne Akian, Mustapha Bouhtou, and Stephane Gaubert. "Ergodic Control and Polyhedral Approaches to PageRank Optimization." IEEE Transactions on Automatic Control 58, no. 1 (January 2013): 134–48. http://dx.doi.org/10.1109/tac.2012.2226103.
3
Obikhod, Tetiana. "FORMATION OF MODERN MATHEMATICAL APPROACH TO SOLVING PROBLEMS OF PHYSICS." Physical and Mathematical Education 33, no. 1 (April 2, 2022): 26–29. http://dx.doi.org/10.31110/2413-1571-2022-033-1-004.
Анотація:
Formulation of the problem. Precision studies of the Higgs boson, supersymmetric particles, the magnetic moment of the muon, electric dipole moment of the electron, flavor anomalies demonstrate the deviation beyond Standard Model. They are connected with a new understanding of quantum field theory through the unification of gravity with particle physics in the framework of string theory - the powerful instrument, which has changed the theory picture. The article is devoted to the study of new physics through these two components. First, we considered particle physics in terms of the latest experimental data and then moved on to the mathematical apparatus of string theory. Materials and methods. The N = 2 Yang-Mills theory is the heterotic string analog determined in ten-dimensional space: four usual space-time coordinates and six extra dimensions, known as Calabi-Yau manifold in weighted projective space. We studied the Calabi-Yau manifold in terms of both differential forms and reflexive polyhedrа to extract the elementary particle information. For further work with Calabi-Yau manifolds, differential forms for calculation of cohomology groups and reflexive polyhedrа for calculation of Hodge numbers were used. We used two definitions of general properties of toric varieties: hypersurfaces in terms of differential forms and projective space in terms of reflexive polyhedral. Then we investigated lattice polyhedra ∆ which gives rise to families of Calabi-Yau hypersurfaces in weighted projective space, P∆. Such polyhedra admit a combinatorial characterization and are called reflexive polyhedra. Results. The comparison of two approaches to the description of Calabi-Yau manifold as a complex manifold and as weighted projective space led us to the conclusion about the equivalence of these two treatments in the context of calculation of the Euler characteristic. As Euler’s characteristic for elementary particle physics is the number of generations of quarks and leptons, the selection of Calabi-Yau manifolds with appropriate topological properties is one of the urgent problems of modern physics. It is necessary to stress that the important result of our paper is the coincidence of the value of the Euler characteristic, found in terms of Dolbeault cohomology and terms of reflexive polyhedral. The obtained information about topological invariants is necessary for predicting the number of generations in particle physics. Conclusions. Although a unified theory of all interactions has not yet been found, however, certain aspects related to the interpretation of the unified theory of all interactions in terms of modern mathematics give their significant results. Therefore, the use and development of the apparatus of algebraic geometry for finding topological invariants that have the value of observables in physics is an urgent task.
4
Colombi, Marco, Renata Mansini, and Martin Savelsbergh. "The generalized independent set problem: Polyhedral analysis and solution approaches." European Journal of Operational Research 260, no. 1 (July 2017): 41–55. http://dx.doi.org/10.1016/j.ejor.2016.11.050.
5
Carter, Paul. "Polyhedral: Recycling Boundary Ecologies." International Review of Information Ethics 11 (October 1, 2009): 45–51. http://dx.doi.org/10.29173/irie185.
Анотація:
Foregrounding the extent to which 'place' remains resistant to the politics and poetics of 'network culture', this essay approaches place as a boundary ecology rather than as an instance of cultural invariance. It calls on readers to think about attempts to actively recycle cultural 'debris' or 'waste' through an ethics of passage instead of the kind of instrumentalist statics that prevents the development of an ontology of mobility. Contending that such a capacity to inhabit passage is compromised by the eschatological language used to communicate the implications of environmental disaster, as well as by languages of consultation that (conceptually) empty place of any creative power to incubate alternatives – events, modes of relation –, the essay stresses the mythopoetic techniques that produce places as knots or nodal points within a network of passage. The designer's task is to create the hinge mechanisms that render such boundary ecologies inhabitable imaginatively, and by materialising the nexus between creativity and change to alter our position vis-a-vis our ethical responsibilities as citizens of a shared biosphere.
6
Mousavi, Seyedahmad, та Jinglai Shen. "Solution uniqueness of convex piecewise affine functions based optimization with applications to constrained ℓ1 minimization". ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 56. http://dx.doi.org/10.1051/cocv/2018061.
Анотація:
In this paper, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This class of problems incorporates many important polyhedral constrained ℓ1 recovery problems arising from sparse optimization, such as basis pursuit, LASSO, and basis pursuit denoising, as well as polyhedral gauge recovery. By leveraging the max-formulation of convex piecewise affine functions and convex analysis tools, we develop dual variables based necessary and sufficient uniqueness conditions via simple and yet unifying approaches; these conditions are applied to a wide range of ℓ1 minimization problems under possible polyhedral constraints. An effective linear program based scheme is proposed to verify solution uniqueness conditions. The results obtained in this paper not only recover the known solution uniqueness conditions in the literature by removing restrictive assumptions but also yield new uniqueness conditions for much broader constrained ℓ1-minimization problems.
7
Schreiber, Thomas, Guido Brunnett, and Frank lsselhard. "Two approaches for polyhedral reconstruction of 3D objects of arbitrary genus." International Journal of Vehicle Design 21, no. 2/3 (1999): 292. http://dx.doi.org/10.1504/ijvd.1999.005581.
8
Brimkov, Valentin E., and Reneta P. Barneva. "Graph-theoretic and polyhedral combinatorics issues and approaches in imaging sciences." Discrete Applied Mathematics 216 (January 2017): 321–22. http://dx.doi.org/10.1016/j.dam.2016.11.001.
9
Zheng, Fei, Yu-Yong Jiao, Xi Zhang, Jia-He Lv, and Fei Tan. "Improved contact approaches for irregular polygonal or polyhedral blocks and their applications." IOP Conference Series: Earth and Environmental Science 861, no. 3 (October 1, 2021): 032033. http://dx.doi.org/10.1088/1755-1315/861/3/032033.
10
Pringuey, Thibault, and R. Stewart Cant. "High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method." Communications in Computational Physics 12, no. 1 (July 2012): 1–41. http://dx.doi.org/10.4208/cicp.260511.050811a.
Анотація:
AbstractIn this article, we detail the methodology developed to construct arbitrarily high order schemes — linear and WENO — on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set.
11
Wang, Shaolei, Liangxiao Tan, Chengxin Zhang, Irshad Hussain, and Bien Tan. "Novel POSS-based organic–inorganic hybrid porous materials by low cost strategies." Journal of Materials Chemistry A 3, no. 12 (2015): 6542–48. http://dx.doi.org/10.1039/c4ta06963c.
Анотація:
Two kinds of POSS-based organic–inorganic hybrid porous materials have been synthesized via Friedel–Crafts and Scholl coupling reactions, for the first time, using low-cost building blocks i.e., octaphenylsilsesquioxanes and simple knitting approaches to obtain high Brunauer–Emmett–Teller (BET) surface area porous polyhedral oligomeric silsesquioxane (POSS)-based hybrid materials.
12
Brahimi, Nadjib, Stéphane Dauzere-Peres, and Laurence A. Wolsey. "Polyhedral and Lagrangian approaches for lot sizing with production time windows and setup times." Computers & Operations Research 37, no. 1 (January 2010): 182–88. http://dx.doi.org/10.1016/j.cor.2009.04.005.
13
Rathod, H. T., and H. S. Govinda Rao. "Integration of trivariate polynomials over linear polyhedra in Euclidean three-dimensional space." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 39, no. 3 (January 1998): 355–85. http://dx.doi.org/10.1017/s0334270000009450.
Анотація:
AbstractThis paper concerns with analytical integration of trivariate polynomials over linear polyhedra in Euclidean three-dimensional space. The volume integration of trivariate polynomials over linear polyhedra is computed as sum of surface integrals in R3 on application of the well known Gauss's divergence theorem and by using triangulation of the linear polyhedral boundary. The surface integrals in R3 over an arbitrary triangle are connected to surface integrals of bivariate polynomials in R2. The surface integrals in R2 over a simple polygon or over an arbitrary triangle are computed by two different approaches. The first algorithm is obtained by transforming the surface integrals in R2 into a sum of line integrals in a one-parameter space, while the second algorithm is obtained by transforming the surface integrals in R2 over an arbitrary triangle into a parametric double integral over a unit triangle. It is shown that the volume integration of trivariate polynomials over linear polyhedra can be obtained as a sum of surface integrals of bivariate polynomials in R2. The computation of surface integrals is proposed in the beginning of this paper and these are contained in Lemmas 1–6. These algorithms (Lemmas 1–6) and the theorem on volume integration are then followed by an example for which the detailed computational scheme has been explained. The symbolic integration formulas presented in this paper may lead to an easy and systematic incorporation of global properties of solid objects, for example, the volume, centre of mass, moments of inertia etc., required in engineering design processes.
14
TANGELDER, JOHAN W. H., and REMCO C. VELTKAMP. "POLYHEDRAL MODEL RETRIEVAL USING WEIGHTED POINT SETS." International Journal of Image and Graphics 03, no. 01 (January 2003): 209–29. http://dx.doi.org/10.1142/s021946780300097x.
Анотація:
Due to the recent improvements in laser scanning technology, 3D visualization and modeling, there is an increasing need for tools supporting the automatic search for 3D objects in archives. In this paper we describe a new geometric approach to 3D shape comparison and retrieval for arbitrary objects described by 3D polyhedral models that may contain gaps. In contrast with the existing approaches, our approach takes the overall relative spatial location into account by representing the 3D shape as a weighted point set. To compare two objects geometrically, we enclose each object by a 3D grid and generate a weighted point set, which represents a salient point for each non-empty grid cell. We compare three methods to obtain a salient point and a weight in each grid cell: (1) choosing the vertex in the cell with the highest Gaussian curvature, and choosing a measure as weight for that curvature, (2) choosing the area-weighted mean of the vertices in the cell, and choosing a measure as weight denoting the normal variation of the facets in the cell and (3) choosing the center of mass of all vertices in the cell, and choosing one as weight. Finally, we compute the similarity between two shapes by comparing their weighted point sets using a new shape similarity measure based on weight transportation that is a variation of the Earth Mover's Distance. Unlike the Earth Mover's Distance, the new shape similarity measure satisfies the triangle inequality. This property makes it suitable for use in indexing schemes, that depend on the triangle inequality, such as the one we introduce, based on the so-called vantage objects. The strength of our approach is proven through experimental results using a database consisting of 133 models such as mugs, cars and boats, and a database consisting of 512 models, mostly air planes, classified into conventional air planes, delta-jets, multi-fuselages, biplanes, helicopters and other models. The results show that the retrieval performance is better than related shape matching methods.
15
BHANDARKAR, SUCHENDRA M., and ANDREAS SIEBERT. "INTEGRA — AN INTEGRATED SYSTEM FOR RANGE IMAGE UNDERSTANDING." International Journal of Pattern Recognition and Artificial Intelligence 06, no. 05 (December 1992): 913–53. http://dx.doi.org/10.1142/s0218001492000461.
Анотація:
Segmentation, feature extraction, recognition and localization are the four stages in range image understanding. Conventional approaches to range image understanding have treated these stages in isolation with a largely bottom-up flow of control and data through these various stages. Strictly bottom-up approaches have proved to be fragile in the face of errors in segmentation due to noise and limitations on sensor resolution and accuracy. Synergetic interaction of these various stages is essential for an image understanding system to exhibit robust behavior. This paper describes the design and implementation of INTEGRA, a range image understanding system that attempts to exploit the synergy between the various stages in the image understanding process. The salient features of INTEGRA are: (i) A synergetic combination of edge- and surface-based segmentation processes that results in more accurate segmentation than would have been possible with either of them alone and (ii) the ability to correct errors made during segmentation in the matching and localization stages. INTEGRA at this time, is limited to recognition and localization of polyhedral objects and is in the process of being enhanced to handle objects with curved surfaces of quadratic order such as spherical, ellipsoidal, cylindrical, and conical surfaces. Experimental results on real range images containing single and multiple polyhedral objects are presented. Future enhancements to INTEGRA are discussed.
16
Cannella, Emanuele, Onur Derin, Paolo Meloni, Giuseppe Tuveri, and Todor Stefanov. "Adaptivity Support for MPSoCs Based on Process Migration in Polyhedral Process Networks." VLSI Design 2012 (March 4, 2012): 1–17. http://dx.doi.org/10.1155/2012/987209.
Анотація:
System adaptivity is becoming an important feature of modern embedded multiprocessor systems. To achieve the goal of system adaptivity when executing Polyhedral Process Networks (PPNs) on a generic tiled Network-on-Chip (NoC) MPSoC platform, we propose an approach to enable the run-time migration of processes among the available platform resources. In our approach, process migration is allowed by a middleware layer which comprises two main components. The first component concerns the inter-tile data communication between processes. We develop and evaluate a number of different communication approaches which implement the semantics of the PPN model of computation on a generic NoC platform. The presented communication approaches do not depend on the mapping of processes and have been implemented on a Network-on-Chip multiprocessor platform prototyped on an FPGA. Their comparison in terms of the introduced overhead is presented in two case studies with different communication characteristics. The second middleware component allows the actual run-time migration of PPN processes. To this end, we propose and evaluate a process migration mechanism which leverages the PPN model of computation to guarantee a predictable and efficient migration procedure. The efficiency and applicability of the proposed migration mechanism is shown in a real-life case study.
17
Lu, Fang, and Chun-Rong Chen. "Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/792364.
Анотація:
Various kinds of nonlinear scalarization functions play important roles in vector optimization. Among them, the one commonly known as the Gerstewitz function is good at scalarizing. In linear normed spaces, the globally Lipschitz property of such function is deduced via primal and dual spaces approaches, respectively. The equivalence of both expressions for globally Lipschitz constants obtained by primal and dual spaces approaches is established. In particular, when the ordering cone is polyhedral, the expression for calculating Lipschitz constant is given. As direct applications of the Lipschitz property, several sufficient conditions for Hölder continuity of both single-valued and set-valued solution mappings to parametric vector equilibrium problems are obtained using the nonlinear scalarization approach.
18
Zuo, Xin, Hong-Zhi Wei, and Chun-Rong Chen. "Continuity Results and Error Bounds on Pseudomonotone Vector Variational Inequalities via Scalarization." Journal of Function Spaces 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/7297854.
Анотація:
Continuity (both lower and upper semicontinuities) results of the Pareto/efficient solution mapping for a parametric vector variational inequality with a polyhedral constraint set are established via scalarization approaches, within the framework of strict pseudomonotonicity assumptions. As a direct application, the continuity of the solution mapping to a parametric weak Minty vector variational inequality is also discussed. Furthermore, error bounds for the weak vector variational inequality in terms of two known regularized gap functions are also obtained, under strong pseudomonotonicity assumptions.
19
Müller, Melanie, Robert E. Dinnebier, Naveed Z. Ali, Branton J. Campbell, and Martin Jansen. "Direct Access to the Order Parameter: Parameterized Symmetry Modes and Rigid Body Movements as a Function of Temperature." Materials Science Forum 651 (May 2010): 79–95. http://dx.doi.org/10.4028/www.scientific.net/msf.651.79.
Анотація:
The first order phase transition of CsFeO2 was investigated using synchrotron powder diffraction data as a function of temperature. Two alternative approaches were used to describe the deviation of the framework crystal structure relative to the high-symmetry parent structure: symmetry (a.k.a. distortion) modes and polyhedral-tilt parameters. In both cases, the relevant parameters were refined as a function of temperature using the method of parametric Rietveld refinement. We demonstrate a semi-automated and generally applicable method for the determination of spontaneous lattice strain variations, order parameters and power-law exponents as derived from Landau theory.
20
Quezada, Franco, Céline Gicquel, and Safia Kedad-Sidhoum. "Combining Polyhedral Approaches and Stochastic Dual Dynamic Integer Programming for Solving the Uncapacitated Lot-Sizing Problem Under Uncertainty." INFORMS Journal on Computing 34, no. 2 (March 2022): 1024–41. http://dx.doi.org/10.1287/ijoc.2021.1118.
Анотація:
We study the uncapacitated lot-sizing problem with uncertain demand and costs. The problem is modeled as a multistage stochastic mixed-integer linear program in which the evolution of the uncertain parameters is represented by a scenario tree. To solve this problem, we propose a new extension of the stochastic dual dynamic integer programming algorithm (SDDiP). This extension aims at being more computationally efficient in the management of the expected cost-to-go functions involved in the model, in particular by reducing their number and by exploiting the current knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. The algorithm is based on a partial decomposition of the problem into a set of stochastic subproblems, each one involving a subset of nodes forming a subtree of the initial scenario tree. We then introduce a cutting plane–generation procedure that iteratively strengthens the linear relaxation of these subproblems and enables the generation of an additional strengthened Benders’ cut, which improves the convergence of the method. We carry out extensive computational experiments on randomly generated large-size instances. Our numerical results show that the proposed algorithm significantly outperforms the SDDiP algorithm at providing good-quality solutions within the computation time limit. Summary of Contribution: This paper investigates a combinatorial optimization problem called the uncapacitated lot-sizing problem. This problem has been widely studied in the operations research literature as it appears as a core subproblem in many industrial production planning problems. We consider a stochastic extension in which the input parameters are subject to uncertainty and model the resulting stochastic optimization problem as a multistage stochastic integer program. To solve this stochastic problem, we propose a novel extension of the recently published stochastic dual dynamic integer programming (SDDiP) algorithm. The proposed extension relies on two main ideas: the use of a partial decomposition of the scenario tree and the exploitation of existing knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. We provide the results of extensive computational experiments carried out on large-size randomly generated instances. These results show that the proposed extended algorithm significantly outperforms the SDDiP at providing good-quality solutions for the stochastic uncapacitated lot-sizing problem. Although the paper focuses on a basic lot-sizing problem, the proposed algorithmic framework may be useful to solve more complex practical production planning problems.
21
OGRYCZAK, WŁODZIMIERZ, and TOMASZ ŚLIWIŃSKI. "ON DUAL APPROACHES TO EFFICIENT OPTIMIZATION OF LP COMPUTABLE RISK MEASURES FOR PORTFOLIO SELECTION." Asia-Pacific Journal of Operational Research 28, no. 01 (February 2011): 41–63. http://dx.doi.org/10.1142/s0217595911003041.
Анотація:
In the original Markowitz model for portfolio optimization the risk is measured by the variance. Several polyhedral risk measures have been introduced leading to Linear Programming (LP) computable portfolio optimization models in the case of discrete random variables represented by their realizations under specified scenarios. The LP models typically contain the number of constraints (matrix rows) proportional to the number of scenarios while the number of variables (matrix columns) proportional to the total of the number of scenarios and the number of instruments. They can effectively be solved with general purpose LP solvers provided that the number of scenarios is limited. However, real-life financial decisions are usually based on more advanced simulation models employed for scenario generation where one may get several thousands scenarios. This may lead to the LP models with huge number of variables and constraints thus decreasing their computational efficiency and making them hardly solvable by general LP tools. We show that the computational efficiency can be then dramatically improved by alternative models taking advantages of the LP duality. In the introduced models the number of structural constraints (matrix rows) is proportional to the number of instruments thus not affecting seriously the simplex method efficiency by the number of scenarios and therefore guaranteeing easy solvability.
22
SURTI, ANKIT, and N. V. REDDY. "NON-DISCRETIZED APPROACH TO VISIBILITY ANALYSIS FOR AUTOMATIC MOLD FEATURE RECOGNITION USING STEP PART MODEL." Journal of Advanced Manufacturing Systems 11, no. 01 (April 7, 2012): 1–16. http://dx.doi.org/10.1142/s0219686712500011.
Анотація:
Undercut feature recognition in automatic mold design requires analyzing the visibility/accessibility of the part along a known parting direction, the existing approaches for which are mostly restricted to polyhedral parts or a particular CAD platform or cannot handle partially accessible faces very well. The present work proposes a projection-based methodology to analyze the visibility of a part from a given parting direction without discretizing the part. An approach to further extract undercut features and generate corresponding side-cores is also presented. The implemented system uses STEP AP214/AP203 part files for input and output and has been successfully validated using parts geometrically similar to those used in literature as well as on a number of industrial parts of greater complexity.
23
Yannopapas, Vassilios. "An atomistic-electrodynamics theory for the optical response of periodic lattices of metallic nanoparticles in the quantum size regime." International Journal of Modern Physics B 31, no. 24 (September 30, 2017): 1740001. http://dx.doi.org/10.1142/s021797921740001x.
Анотація:
We present a new theoretical method for calculating the optical properties of periodic arrays of metallic nanoparticles whose dimensions are in the quantum-size limit and cannot, therefore, be described by macroscopic electrodynamic theory based on Maxwell’s equations. In the first stage, the method calculates the scattering matrix for a single metal nanoparticle described as a polyhedral cluster of atoms, via a discrete-dipole approximation/point-matching technique. The resulting scattering matrix is incorporated into a layer-multiple-scattering technique which allows the modeling of two- and three-dimensional nanostructures containing very small metal nanoparticles. The method is demonstrated for square arrays of silver nanoparticles with radii below 2 nm and the corresponding results are compared against classical local and nonlocal electrodynamic approaches.
24
Cuker, Adam, Joseph Marturano, Maria Carinato, Thomas Lowery, and Douglas Cines. "T2 Magnetic Resonance to Monitor Hemostasis." Seminars in Thrombosis and Hemostasis 45, no. 03 (August 17, 2018): 247–52. http://dx.doi.org/10.1055/s-0038-1667114.
Анотація:
AbstractThere is a clinical need for pragmatic approaches to measure integrated hemostatic reactions in whole blood rapidly, using small volumes of blood. The authors have applied T2 magnetic resonance (T2MR) to assess coagulation reactions based on partitioning of red blood cells and proteins that occurs during fibrin formation and platelet-mediated clot contraction. T2MR is amenable to measuring clotting times, individual coagulation factors, and platelet function. T2MR also revealed a novel “hypercoagulable” signature characterized by fibrin clots almost insusceptible to fibrinolysis that surround tessellated arrays of polyhedral erythrocytes (“third peak”). This signature, which develops under conditions associated with intense clot formation in vitro, may help identify patients at risk of developing thrombosis and for monitoring antithrombotic therapies in the future.
25
Hamp, Elyse, Rachel Gerber, Bora Pulatsu, Mario Santana Quintero, and Jeffrey Erochko. "Nonlinear Seismic Assessment of a Historic Rubble Masonry Building via Simplified and Advanced Computational Approaches." Buildings 12, no. 8 (July 29, 2022): 1130. http://dx.doi.org/10.3390/buildings12081130.
Анотація:
This research presents a comprehensive nonlinear quasi-static seismic assessment of an unreinforced rubble masonry building, Bytown Museum in Ottawa, Canada, using discontinuum-based analyses. In the proposed modeling approach, non-uniform geometrical properties of rubble masonry walls are replicated via a group of rigid polyhedral blocks interacting along their boundaries based on the discrete element method (DEM). Once the adopted modeling strategy is validated, the nonlinear quasi-static analysis of the South and North façades of the Bytown Museum is performed. Special attention is given to the irregular block generation within the discontinuum analysis framework, where discrete element models are generated from high-resolution site recording data, representing the masonry morphology at a high level of detail. Then, the predicted collapse mechanisms from advanced computational models are further utilized to generate pre-defined macro-blocks in kinematic limit analyses, providing a simple alternative solution for seismic assessment. The results reveal the significant effect of openings and the construction technique (morphology) in unreinforced rubble masonry buildings that can play an important role in the structural capacity and behavior. Moreover, it is noted that DEM-based solutions provide lower seismic capacity compared to kinematic limit analyses. Finally, a noticeable sensitivity to the input parameters in the discrete element models is noted; therefore, characterization of material properties is necessary for reliable predictions.
26
Bärmann, Andreas, Alexander Martin, and Oskar Schneider. "Efficient Formulations and Decomposition Approaches for Power Peak Reduction in Railway Traffic via Timetabling." Transportation Science 55, no. 3 (May 2021): 747–67. http://dx.doi.org/10.1287/trsc.2020.1021.
Анотація:
Over the last few years, optimization models for the energy-efficient operation of railway traffic have received more and more attention, particularly in connection with timetable design. In this work, we study the effect of load management via timetabling. The idea is to consider trains as time-flexible consumers in the railway power supply network and to use slight shifts in the departure times from the stations to avoid too many simultaneous departures. This limits peak consumption and can help to improve the stability of the power supply. To this end, we derive efficient formulations for the problem of an optimal timetable adjustment based on a given timetable draft, two of which even allow for totally unimodular polyhedral descriptions. The proper choice of the objective function allows the incorporation of the priorities of either the train operating companies or the infrastructure manager. These include the avoidance of large peaks in average or instantaneous consumption and the improved use of recuperated braking energy. To solve the arising optimization models efficiently, we develop specially tailored exact Benders decomposition schemes that allow for the computation of high-quality solutions within a very short time. In an extensive case study for German railway passenger traffic, we show that our methods are capable of solving the problem on a nationwide scale. We see that the optimal adjustment of timetables entails a tremendous potential for reducing energy consumption.
27
Chwatal, Andreas M., and Günther R. Raidl. "Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques." Advances in Operations Research 2011 (2011): 1–38. http://dx.doi.org/10.1155/2011/143732.
Анотація:
We present exact mixed integer programming approaches including branch-and-cut and branch-and-cut-and-price for the minimum label spanning tree problem as well as a variant of it having multiple labels assigned to each edge. We compare formulations based on network flows and directed connectivity cuts. Further, we show how to use odd-hole inequalities and additional inequalities to strengthen the formulation. Label variables can be added dynamically to the model in the pricing step. Primal heuristics are incorporated into the framework to speed up the overall solution process. After a polyhedral comparison of the involved formulations, comprehensive computational experiments are presented in order to compare and evaluate the underlying formulations and the particular algorithmic building blocks of the overall branch-and-cut- (and-price) framework.
28
Akgunduz, Ali, Prashant Banerjee, and Sanjay Mehrotra. "A Linear Programming Solution for Exact Collision Detection." Journal of Computing and Information Science in Engineering 5, no. 1 (March 1, 2005): 48–55. http://dx.doi.org/10.1115/1.1846053.
Анотація:
This paper addresses the issue of real-time collision detection between pairs of convex polyhedral objects undergoing fast rotational and translational motions. Accurate contact information between objects in virtual reality based simulations such as product design, assembly analysis, performance testing and ergonomic analysis of products are critical factors to explore when desired realism is to be achieved. For this purpose, fast, accurate and robust collision detection algorithms are required. The method described in the text models the exact collision detection problem between convex objects as a linear program. One of the strengths of the proposed methodology is its capability of addressing high speed interframe collision. In addition to the interframe collision detection, experimental data demonstrate that mathematical programming approaches offer promising results in terms of speed and robustness as well.
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RESHETOV, ALEXANDER. "A UNISTABLE POLYHEDRON WITH 14 FACES." International Journal of Computational Geometry & Applications 24, no. 01 (March 2014): 39–59. http://dx.doi.org/10.1142/s0218195914500022.
Анотація:
Unistable polyhedra are in equilibrium on only one of their faces. The smallest known homogeneous unistable polyhedron to date has 18 faces. Using a new optimization algorithm, we have found a unistable polyhedron with only 14 faces, which we believe to be a lower bound. Despite the simplicity of the formulation, computers were never successfully used for solving this problem due to the seemingly insurmountable dimensionality of the underlying mathematical apparatus. We introduce new optimization approaches designed to overcome the problem's intractability and discuss its significance to other application areas. We also mathematically prove the unistable property of the found bodies using rational arithmetic. Surprisingly enough, all of our computer-generated unistable polyhedra look similar to the human eye, providing important insights into the nature of the problem.
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Bartzis, Constantinos, and Tevfik Bultan. "Efficient Symbolic Representations for Arithmetic Constraints in Verification." International Journal of Foundations of Computer Science 14, no. 04 (August 2003): 605–24. http://dx.doi.org/10.1142/s0129054103001911.
Анотація:
In this paper we discuss efficient symbolic representations for infinite-state systems specified using linear arithmetic constraints. We give algorithms for constructing finite automata which represent integer sets that satisfy linear constraints. These automata can represent either signed or unsigned integers and have a lower number of states compared to other similar approaches. We present efficient storage techniques for the transition function of the automata and extend the construction algorithms to formulas on both boolean and integer variables. We also derive conditions which guarantee that the pre-condition computations used in symbolic verification algorithms do not cause an exponential increase in the automata size. We experimentally compare different symbolic representations by using them to verify non-trivial concurrent systems. Experimental results show that the symbolic representations based on our construction algorithms outperform the polyhedral representation used in Omega Library, and the automata representation used in LASH.
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Seraphin, Supapan, Dan Zhou, and Jun Jiao. "Insertion of yttrium carbide into carbon nanoclusters by vapor transport during growth." Proceedings, annual meeting, Electron Microscopy Society of America 51 (August 1, 1993): 758–59. http://dx.doi.org/10.1017/s0424820100149623.
Анотація:
Carbon nanoclusters have basic features in common, although they vary greatly in shapes. Concentric graphitic layers separated by 0.34 nm surround a hollow core a few nanometers in diameter. Encapsulating materials into this hollow core changes the physical properties drastically. The insertion offers the possibility to study materials of small dimensions in a closed-off environment. Technological promise is given for the production of nanowires, and other applications in which the nanoscale is of importance. Recent work takes a variety of approaches, inserting lead into nanotubes by capillary suction through open ends, or encapsulating microcrystals of LaC2 into the polyhedral cages. We report a method for filling carbon clusters of various shapes in situ through vapor transport from a composite anode of a graphite rod filled with yttrium oxide paste at a center hole.Both materials pass through the arc discharge, and grow as composite carbon nanoclusters at the pure graphite cathode.
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SILVEIRA, RODRIGO I., and RENÉ VAN OOSTRUM. "FLOODING COUNTRIES AND DESTROYING DAMS." International Journal of Computational Geometry & Applications 20, no. 03 (June 2010): 361–80. http://dx.doi.org/10.1142/s0218195910003347.
Анотація:
In many applications of terrain analysis, pits or local minima are considered artifacts that must be removed before the terrain can be used. Most of the existing methods for local minima removal work only for raster terrains. In this paper we consider algorithms to remove local minima from polyhedral terrains, by modifying the heights of the vertices. To limit the changes introduced to the terrain, we also try to minimize the total displacement of the vertices. Two approaches to remove local minima are analyzed: lifting vertices and lowering vertices. For the former we show that all local minima in a terrain with n vertices can be removed in the optimal way in [Formula: see text] time. For the latter we prove that the problem is NP-hard, and present an approximation algorithm with factor 2 ln k, where k is the number of local minima in the terrain.
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Zamora-Polo, Francisco, and Jesús Sánchez-Martín. "Teaching for a Better World. Sustainability and Sustainable Development Goals in the Construction of a Change-Maker University." Sustainability 11, no. 15 (August 5, 2019): 4224. http://dx.doi.org/10.3390/su11154224.
Анотація:
Sustainability, as a key concept in the education field, has submitted a relevant change during the last years. Thus, there is a growing debate about its meaning. It has undergone a crucial merging of significances from many fields: Ecology, environmental awareness, but also from politics, ethics or even spiritual approaches. All these fields have been co-involved in the building of such subject concept. In this sense, this article addresses the different ways of understanding sustainability as a polyhedral concept and how sustainability can be understood under the umbrella of the Sustainable Development Goals (SDGs). Furthermore, it is proposed a conceptual framework to teach this UN Program at Higher Education, contributing to the training of undergraduate and postgraduate students from both a professional and a personal point of view. This framework is applied in a case study—in particular, in a course of Primary Teacher Degree called Didactics of Matter and Energy. This article finishes with practical consideration to build a change-maker University.
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DE FARIAS, I. R., E. L. JOHNSON, and G. L. NEMHAUSER. "Branch-and-cut for combinatorial optimization problems without auxiliary binary variables." Knowledge Engineering Review 16, no. 1 (March 2001): 25–39. http://dx.doi.org/10.1017/s0269888901000030.
Анотація:
Many optimisation problems involve combinatorial constraints on continuous variables. An example of a combinatorial constraint is that at most one variable in a group of nonnegative variables may be positive. Traditionally, in the mathematical programming community, such problems have been modeled as mixed-integer programs by introducing auxiliary binary variables and additional constraints. Because the number of variables and constraints becomes larger and the combinatorial structure is not used to advantage, these mixed-integer programming models may not be solved satisfactorily, except for small instances. Traditionally, constraint programming approaches to such problems keep and use the combinatorial structure, but do not use linear programming bounds in the search for an optimal solution. Here we present a branch-and-cut approach that considers the combinatorial constraints without the introduction of binary variables. We review the development of this approach and show how strong constraints can be derived using ideas from polyhedral combinatorics. To illustrate the ideas, we present a production scheduling model that arises in the manufacture of fibre optic cables.
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Aminian, Minoo, David Couvin, Amina Shabbeer, Kane Hadley, Scott Vandenberg, Nalin Rastogi, and Kristin P. Bennett. "PredictingMycobacterium tuberculosisComplex Clades Using Knowledge-Based Bayesian Networks." BioMed Research International 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/398484.
Анотація:
We develop a novel approach for incorporating expert rules into Bayesian networks for classification ofMycobacterium tuberculosiscomplex (MTBC) clades. The proposed knowledge-based Bayesian network (KBBN) treats sets of expert rules as prior distributions on the classes. Unlike prior knowledge-based support vector machine approaches which require rules expressed as polyhedral sets, KBBN directly incorporates the rules without any modification. KBBN uses data to refine rule-based classifiers when the rule set is incomplete or ambiguous. We develop a predictive KBBN model for 69 MTBC clades found in the SITVIT international collection. We validate the approach using two testbeds that model knowledge of the MTBC obtained from two different experts and large DNA fingerprint databases to predict MTBC genetic clades and sublineages. These models represent strains of MTBC using high-throughput biomarkers called spacer oligonucleotide types (spoligotypes), since these are routinely gathered from MTBC isolates of tuberculosis (TB) patients. Results show that incorporating rules into problems can drastically increase classification accuracy if data alone are insufficient. The SITVIT KBBN is publicly available for use on the World Wide Web.
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DE LAZZER, A., and D. LANGBEIN. "Liquid surface in regular N-pods." Journal of Fluid Mechanics 358 (March 10, 1998): 203–21. http://dx.doi.org/10.1017/s0022112097008173.
Анотація:
The shape of liquid surfaces in regular N-pods in the absence of gravity is considered. A liquid volume in the vertex of a regular N-pod wets the adjacent faces if the sum of the liquid's contact angle γ with the faces and half the dihedral angle α between adjacent faces is smaller than π/2. A suggestion for why the surface shape in the wedge approaches its cylindrical shape at infinity exponentially is given. The range of this exponential decrease is related to the curvature of the meniscus and the angles α and γ: The decrement of the decrease generally shows a weak dependence on α+γ, predominantly depending on the liquid volume. Extremely close to the wetting limit, when α+γ approaches π/2, the decrement vanishes. The exponential meniscus shape leads to a similarity relation and allows small relative liquid volumes in polyhedrons to be split up into partial volumes ascribed to the corners and others ascribed to the wedges. The respective relations among volume, curvature, contact angle and corner geometry are obtained by numerical simulation and the limits of applicability are discussed. This greatly simplifies the calculation of liquid surfaces in the limit of small liquid volumes. The results obtained apply to liquid surfaces in a Space environment, e.g. to metallic melts in crucibles and to propellants and other technical fluids in tanks and reservoirs, as well as to liquid surfaces on Earth, e.g. to liquids trapped in polyhedral pores and to liquid foams, provided their characteristic length is sufficiently small compared to the capillary length.
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Falach, Harinda Nurril. "Perbandingan keefektifan pendekatan problem solving dan problem posing dalam pembelajaran matematika pada siswa SMP." PYTHAGORAS: Jurnal Pendidikan Matematika 11, no. 2 (December 6, 2016): 136. http://dx.doi.org/10.21831/pg.v11i2.10635.
Анотація:
Penelitian ini bertujuan untuk mendeskripsikan: 1) keefektifan pendekatan problem solving terhadap kemampuan pemahaman dan penalaran matematis; 2) keefektifan pendekatan problem posing terhadap kemampuan pemahaman dan penalaran matematis; 3) perbandingan keefektifan antara pendekatan pembelajaran problem solving dan problem posing terhadap kemampuan pemahaman dan penalaran matematis siswa SMP pada pembelajaran bangun ruang sisi datar. Penelitian ini merupakan penelitian eksperimen semu (quasi experiment). Data dianalisis menggunakan one sample t test, uji MANOVA rumus T2 Hotteling, dan uji t kriteria Bonferroni. Hasil penelitian menunjukkan bahwa: 1) pendekatan problem solving efektif terhadap kemampuan pemahaman dan penalaran matematis; 2) pendekatan problem posing efektif terhadap kemampuan pemahaman dan penalaran matematis; 3) pendekatan problem solving lebih efektif dibandingkan problem solving terhadap kemampuan pemahaman matematis tetapi pendekatan problem solving tidak lebih efektif dibandingkatn problem posingterhadap kemampuan penalaran matematis siswa SMP pada pembelajaran bangun ruang sisi datar.Kata kunci: pendekatan problem solving, pendekatan problem posing, kemampuan pemahaman matematis, dan kemampuan penalaran matematis. The effectiveness comparison of problem solving and problem posing approaches in mathematics learning towards junior high school students AbstractThe aim of this study is to describe: 1) the effectiveness of problem solving approach on mathematical understanding and reasoning ability; 2) the effectiveness of problem posing approach on mathematical understanding and reasoning ability; 3) the comparison effectiveness of polyhedral learning using problem solving approach and problem posing approach on mathematical understanding and reasoning ability of State Junior High School. This study was a quasi experiment. The data were analyzed using one-sample t test, MANOVA test with T2 Hotteling's formula, and t-test with Bonferroni criterion. The results of the study show that: 1) the problem solving approach has an effect on mathematical understanding and reasoning ability; 2) the problem posing approach has an effect on mathematical understanding and reasoning ability; and 3) the problem solving approach is more effective than the problem posing approach on mathematical understanding ability, but the problem solving approach is not more effective in polyhedral learning than the problem posing approach on mathematical reasoning ability of State Junior High.Keywords: problem solving approach, problem posing approach, mathematical understanding ability, and mathematical reasoning ability
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Ulmer, Benjamin, John Hall, and Faramarz Samavati. "General Method for Extending Discrete Global Grid Systems to Three Dimensions." ISPRS International Journal of Geo-Information 9, no. 4 (April 10, 2020): 233. http://dx.doi.org/10.3390/ijgi9040233.
Анотація:
Geospatial sensors are generating increasing amounts of three-dimensional (3D) data. While Discrete Global Grid Systems (DGGS) are a useful tool for integrating geospatial data, they provide no native support for 3D data. Several different 3D global grids have been proposed; however, these approaches are not consistent with state-of-the-art DGGSs. In this paper, we propose a general method that can extend any DGGS to the third dimension to operate as a 3D DGGS. This extension is done carefully to ensure any valid DGGS can be supported, including all refinement factors and non-congruent refinement. We define encoding, decoding, and indexing operations in a way that splits responsibility between the surface DGGS and the 3D component, which allows for easy transference of data between the 2D and 3D versions of a DGGS. As a part of this, we use radial mapping functions that serve a similar purpose as polyhedral projection in a conventional DGGS. We validate our method by creating three different 3D DGGSs tailored for three specific use cases. These use cases demonstrate our ability to quickly generate 3D global grids while achieving desired properties such as support for large ranges of altitudes, volume preservation between cells, and custom cell aspect ratio.
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Sánchez Dueñas, Blas. "Heterodoxia ideológica y acción política : Los Luchadores, de Esteban Beltrán." Epos : Revista de filología, no. 27 (January 1, 2011): 93. http://dx.doi.org/10.5944/epos.27.2011.10671.
Анотація:
Las panorámicas de la literatura finisecular fueron poliédricas, motivadas entre otras causas, por una problemática situación envuelta en una profunda crisis de las estructuras socio-políticas y económicas nacionales que propiciaron el advenimiento de nuevos planteamientos estéticos, resultado de una superposición de tendencias que venían desarrollándose desde años atrás. En medio de las múltiples corrientes que desde la literatura trataron de combatir los males nacionales, este trabajo aborda las consideraciones del escritor Esteban Beltrán a través de su obra Los luchadores con la que trataba de generar un nuevo clima social, aportar iniciativas de cambio social y acabar con la postración y subyugación de los colectivos proletarios.The polyhedral panoramic of literature at the turn of the century was motivated, among other reasons, by a troublesome situation wrapped up by a deep crisis of sociopolitical national structures. These structures favored the advent of new aesthetical approaches resulting from an overlap of tendencies that had been developed for years. Amid the various literary trends that attempted to face the national troubles, this contribution deals with the proposals presented by the writer Esteban Beltrán in his work Los luchadores. Like the rest of his production, this work intends to create a new social atmosphere, make proposals of social change and end up with prostration and subjugation of proletarian groups.
40
Chitsazan, Ali, Georg Klepp, and Birgit Glasmacher. "Numerical Prediction of the Second Peak in the Nusselt Number Distribution from an Impinging Round Jet." International Journal of Heat and Technology 39, no. 4 (August 31, 2021): 1243–52. http://dx.doi.org/10.18280/ijht.390422.
Анотація:
The results of numerical simulations of a single impinging round jet, using different numerical parameters are presented. To simulate the heat transfer in industrial drying with arrays of different jets the heat transfer for a single round jet (Re=23000 based on jet’s diameter and bulk velocity and the dimensionless jet’s outlet to target wall distance= 2) is used as a test case to validate the numerical model. The distribution of the Nusselt-number serves as a benchmark and the computational cost with regard to CPU-time and memory requirements should be minimal. To accurately predict the intensity and position of the secondary peak from an impinging flow, different approaches for turbulence modeling are considered and their results are compared with data from the literature. The influence of the grid size and the grid shape is analyzed and the grid-independent solution is determined. The results using different implementations of the SST k-omega model, as the best compromise between the computational cost and accuracy are compared. Low Re damping modification in the implementation of SST K-ω has an important role in the prediction of the secondary peak. Good results can be achieved with a coarse grid, as long as the boundary region is appropriately resolved. Polyhedral grids produce good quality results with lower memory requirements and cell numbers as well as shorter run times.
41
Kim, Young-Hee, Lawrence Barton, Nigam P. Rath, and John D. Kennedy. "Polyhedral ruthenaborane chemistry. Approaches to encapsulated boron cores. The isolation and characterisation of the partially encapsulated isocloso 10-vertex {RuB9} cluster compound [(PPh3)RuB9H9{RuCl2(PPh3)2}2]." Inorganic Chemistry Communications 8, no. 2 (February 2005): 147–50. http://dx.doi.org/10.1016/j.inoche.2004.09.006.
42
Skewis, Lynell R., Tatiana Lebedeva, Vyacheslav Papkov, Edward C. Thayer, Walter Massefski, Adam Cuker, Chandrasekaran Nagaswami, et al. "T2 Magnetic Resonance: A Diagnostic Platform for Studying Integrated Hemostasis in Whole Blood—Proof of Concept." Clinical Chemistry 60, no. 9 (September 1, 2014): 1174–82. http://dx.doi.org/10.1373/clinchem.2014.223735.
Анотація:
Abstract BACKGROUND Existing approaches for measuring hemostasis parameters require multiple platforms, can take hours to provide results, and generally require 1–25 mL of sample. We developed a diagnostic platform that allows comprehensive assessment of hemostatic parameters on a single instrument and provides results within 15 min using 0.04 mL of blood with minimal sample handling. METHODS T2 magnetic resonance (T2MR) was used to directly measure integrated reactions in whole blood samples by resolving multiple water relaxation times from distinct sample microenvironments. Clotting, clot contraction, and fibrinolysis stimulated by thrombin or tissue plasminogen activator, respectively, were measured. T2MR signals of clotting samples were compared with images produced by scanning electron microscopy and with standard reference methods for the following parameters: hematocrit, prothrombin time, clot strength, and platelet activity. RESULTS Application of T2MR methodology revealed conditions under which a unique T2MR signature appeared that corresponded with the formation of polyhedral erythrocytes, the dynamics and morphology of which are dependent on thrombin, fibrinogen, hematocrit, and platelet levels. We also showed that the T2MR platform can be used for precise and accurate measurements of hematocrit (%CV, 4.8%, R2 = 0.95), clotting time (%CV, 3.5%, R2 = 0.94), clot strength (R2 = 0.95), and platelet function (93% agreement with light transmission aggregometry). CONCLUSIONS This proof-of-concept study demonstrates that T2MR has the potential to provide rapid and sensitive identification of patients at risk for thrombosis or bleeding and to identify new biomarkers and therapeutic targets with a single, simple-to-employ analytic approach that may be suitable for routine use in both research and diverse clinical settings.
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da Fonseca, Guilherme Dias, André Luiz Moraes Alves, Marcos Felipe Braga da Costa, Mariana Sizenando Lyrio, Weslley L. S. Assis, and Paulo Rangel Rios. "Modeling and Simulation of Nucleation and Growth Transformations with Nucleation on Interfaces of Kelvin Polihedra Network." Materials Science Forum 930 (September 2018): 299–304. http://dx.doi.org/10.4028/www.scientific.net/msf.930.299.
Анотація:
Nucleation is a phenomenon associated to the start of the new phase, from a primary phase, named matrix. Growth is the increase in size of this new phase over time. In metallic materials, the nucleation may take place on the grain boundaries of the primary phase. A network of Kelvin polyhedra was used in this paper to represent the grains. A computer simulation was performed in which nucleation took places at the faces, edges and vertices of this polyhedral network. The Causal cone method was employed in the simulations. The results of the present computational simulations were compared with the classical Johnson Mehl-Avrami-Kolmogorov (JMAK) as well as with Cahn model for nucleation at the grain boundaries. JMAK theory considers nuclei to be uniform randomly located within the matrix. Cahn analytical model specifies that nucleation takes place on random planes. For a small number of nuclei, the simulations approached the JMAK model whereas as the number of nuclei increased the simulation results agree with Cahn's theory. Reasons for this are fully discussed.
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Beaude, L., R. Masson, S. Lopez, and P. Samier. "Combined face based and nodal based discretizations on hybrid meshes for non-isothermal two-phase Darcy flow problems." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 4 (July 2019): 1125–56. http://dx.doi.org/10.1051/m2an/2019014.
Анотація:
In the last 20 years many discretization schemes have been developed to approximate the Darcy fluxes on polyhedral cells in heterogeneous anisotropic porous media. Among them, we can distinguished cell based approaches like the Two Point Flux Approximation (TPFA) or the Multi Point Flux Approximation (MPFA) schemes, face based approaches like the Hybrid Finite Volume (HFV) scheme belonging to the family of Hybrid Mimetic Mixed methods and nodal based discretizations like the Vertex Approximate Gradient (VAG) scheme. They all have their own drawbacks and advantages which typically depend on the type of cells and on the anisotropy of the medium. In this work, we propose a new methodology to combine the VAG and HFV discretizations on arbitrary subsets of cells or faces in order to choose the best suited scheme in different parts of the mesh. In our approach the TPFA discretization is considered as an HFV discretization for which the face unknowns can be eliminated. The coupling strategy is based on a node to face interpolation operator at the interfaces which must be chosen to ensure the consistency, the coercivity and the limit conformity properties of the combined discretization. The convergence analysis is performed in the gradient discretization framework and convergence is proved for arbitrary cell or face partitions of the mesh. For face partitions, an additional stabilisation local to the cell is required to ensure the coercivity while for cell partitions no additional stabilisation is needed. The framework preserves at the interface the discrete conservation properties of the VAG and HFV schemes with fluxes based on local to each cell transmissibility matrices. This discrete conservative form allows to naturally extend the VAG and HFV discretizations of two-phase Darcy flow models to the combined VAG–HFV schemes. The efficiency of our approach is tested for single phase and immiscible two-phase Darcy flows on 3D meshes using a combination of the HFV and VAG discretizations as well as for non-isothermal compositional liquid gas Darcy flows on a vertical 2D cross-section of the Bouillante geothermal reservoir (Guadeloupe) using a combination of the TPFA and VAG discretizations.
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Ortiz, Carlos, Adriana Lara, Jesús González, and Ayse Borat. "A Randomized Greedy Algorithm for Piecewise Linear Motion Planning." Mathematics 9, no. 19 (September 23, 2021): 2358. http://dx.doi.org/10.3390/math9192358.
Анотація:
We describe and implement a randomized algorithm that inputs a polyhedron, thought of as the space of states of some automated guided vehicle R, and outputs an explicit system of piecewise linear motion planners for R. The algorithm is designed in such a way that the cardinality of the output is probabilistically close (with parameters chosen by the user) to the minimal possible cardinality.This yields the first automated solution for robust-to-noise robot motion planning in terms of simplicial complexity (SC) techniques, a discretization of Farber’s topological complexity TC. Besides its relevance toward technological applications, our work reveals that, unlike other discrete approaches to TC, the SC model can recast Farber’s invariant without having to introduce costly subdivisions. We develop and implement our algorithm by actually discretizing Macías-Virgós and Mosquera-Lois’ notion of homotopic distance, thus encompassing computer estimations of other sectional category invariants as well, such as the Lusternik-Schnirelmann category of polyhedra.
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Malakooti, Behnam. "Double Helix Value Functions, Ordinal/Cardinal Approach, Additive Utility Functions, Multiple Criteria, Decision Paradigm, Process, and Types (Z Theory I)." International Journal of Information Technology & Decision Making 14, no. 06 (November 2015): 1353–400. http://dx.doi.org/10.1142/s0219622014500412.
Анотація:
Z Utility Theory refers to a class of nonlinear utility functions for solving Risk and Multiple Criteria Decision-Making problems. Z utility functions are hybrids of additive and nonadditive (nonlinear) functions. This paper addresses the concepts and assessment methods for the additive part of Z-utility functions for multiple criteria problems that satisfy the efficiency (nondominancy) principle. We provide a decision paradigm and guidelines on how to approach, formulate, and solve decision-making problems. We, also, overview the modeling of decision process based on four types of decision-making styles. For multi-criteria problems, a new definition of convex efficiency is introduced. Also polyhedral efficiency is developed for presenting multi-criteria efficiency (nondominancy) graphically. New double helix quasi-linear value functions for multi-criteria are developed. Two types of double helix value functions for solving bi-criteria (Advantages versus Disadvantages) and also risk problems are introduced: Food–Fun curves for expected values and Fight-Flight curves for expected risk values. Ordinal/Cardinal Approach (OCA) for assessment of additive utility functions is developed. Simple consistency tests to determine whether the assessed utility function satisfies ordinal and/or cardinal properties are provided. We show that OCA can also be used to solve outranking problems. We provide a critique of Analytic Hierarchy Process (AHP) for assessing additive value functions and show that the developed Ordinal/Cardinal Approach overcomes the shortcomings of AHP. We also develop a unified/integrated approach for simultaneous assessment of nonlinear value and additive (multi-criteria) utility functions. These results in an additive utility function that can be concave, convex, or hybrid concave/convex based on the nonlinear value function. Finally, we show an interactive paired comparisons approach for solving nonadditive and nonlinear utility functions for bi-criteria decision-making problems. Several illustrative examples are provided. The paper provides reliable and robust approaches for modeling the utility preferences of heterogeneous economic agents in macro and micro-economics.
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Brinkmann, Gunnar, Pieter Goetschalckx, and Stan Schein. "Comparing the constructions of Goldberg, Fuller, Caspar, Klug and Coxeter, and a general approach to local symmetry-preserving operations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2206 (October 2017): 20170267. http://dx.doi.org/10.1098/rspa.2017.0267.
Анотація:
The use of operations on polyhedra possibly dates back to the ancient Greeks, who were the first to describe the Archimedean solids, which can be constructed from the Platonic solids by local symmetry-preserving operations (e.g. truncation) on the solid. By contrast, the results of decorations of polyhedra, e.g. by Islamic artists and by Escher, have been interpreted as decorated polyhedra—and not as new and different polyhedra. Only by interpreting decorations as combinatorial operations does it become clear how closely these two approaches are connected. In this article, we first sketch and compare the operations of Goldberg, Fuller, Caspar & Klug and Coxeter to construct polyhedra with icosahedral symmetry, where all faces are pentagons or hexagons and all vertices have three neighbours. We point out and correct an error in Goldberg’s construction. In addition, we transform the term symmetry-preserving into an exact requirement. This goal, symmetry-preserving, could also be obtained by taking global properties into account, e.g. the symmetry group itself, so we make precise the terms local and operation . As a result, we can generalize Goldberg’s approach to a systematic one that uses chamber operations to encompass all local symmetry-preserving operations on polyhedra.
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Hosseini, S. Ahmad, Güvenç Şahin, and Tonguç Ünlüyurt. "A Decomposition-Based Approach for the Multiperiod Multiproduct Distribution Planning Problem." Journal of Applied Mathematics 2014 (2014): 1–25. http://dx.doi.org/10.1155/2014/825058.
Анотація:
We address the most general case of multiperiod, multiproduct network planning problems, where we allow spoilage on arcs and storage at nodes. In our models, all network parameters change over time and products. The minimum-cost flow problem in the discrete-time model with varying network parameters is investigated when we allow storage and/or spoilage, and some reformulation techniques employing polyhedrals are developed to obtain optimal solutions for a predefined horizon. Our methods rely on appropriate definitions of polyhedrals and matrices that lead to LP problems comprising a set of sparse subproblems with special structures. Knowing that computational expenses of solving such a large-scale planning problem can be decreased by using decomposition techniques, the special structure of polyhedrals is utilized to develop algorithmic approaches based on decomposition techniques to handle the global problem aiming to save computational resources.
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Carpenter, Chris. "Finite-Volume Method Enables Simulation of Induced Seismicity." Journal of Petroleum Technology 74, no. 02 (February 1, 2022): 75–77. http://dx.doi.org/10.2118/0222-0075-jpt.
Анотація:
This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 203903, “A Collocated Finite-Volume Scheme for High-Performance Simulation of Induced Seismicity in Geoenergy Applications,” by A. Novikov, D.V. Voskov, SPE, and M. Khait, SPE, Delft University of Technology, et al. The paper has not been peer reviewed. In the complete paper, the authors develop a collocated finite-volume method (FVM) to study induced seismicity as a result of pore-pressure fluctuations. A discrete system is obtained based on a fully implicit coupled description of flow, elastic deformation, and contact mechanics at fault surfaces on a fully unstructured mesh. The cell-centered collocated scheme leads to convenient integration of the different physical equations because the unknowns share the same discrete locations on the mesh. Additionally, a multipoint flux approximation is formulated in a general procedure to treat heterogeneity, anisotropy, and cross-derivative terms for both flow and mechanics equations. Introduction The FVM has become an essential tool for flow and transport simulation because of its local conservation property. For mechanical deformation, however, the conservation property does not have the same importance. Nonetheless, the FVM is still an attractive choice because it represents conservation laws in integral form more naturally. Some authors in the literature use fixed-stress splitting algorithms to decouple mechanics and flow equations. These are a form of sequential implicit solution schemes and often lead to more-efficient simulations than fully implicit (FI) simulation. However, sequential schemes introduce certain restrictions on timestep sizes. On the other hand, FI schemes provide unconditionally convergent solutions and are more-robust and -convenient approaches for investigation of complex multiphysical problems. Although the FI approach does not imply any restriction on timestep size, it requires an efficient linear equation solution strategy for high-resolution models. In this study, the authors develop a collocated FI multipoint FVM scheme for poromechanics simulation of faulted reservoirs. The scheme can be used to solve poromechanics problems on unstructured polyhedral grids with minimal degrees of freedom per cell. It is also capable of considering material heterogeneity while preserving mass and momentum balances. This scheme is extended to consider discontinuities in displacements at faults. The developed algorithms have been embedded into the open-source Delft Advanced Research Terra Simulator (DARTS).
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Shapovalov, V. B. "USING THE ONTOLOGICAL MODEL OF THE STEM–CENTER IN THE EDUCATIONAL PROCESS." Scientific Notes of Junior Academy of Sciences of Ukraine, no. 1(20) (2021): 102–16. http://dx.doi.org/10.51707/2618-0529-2021-20-11.
Анотація:
The article is devoted to the practical aspects of using the ontological model of the STEM Center, which is built on the basis of cognitive information technology “Polyhedron”, in educational and research processes. Tools created using Microsoft and Google Spreadsheets are described. The application of the system of virtual museum Laboratories, a database of microorganisms, an ontological STEM classifier, a virtual laboratory of scientific publications, ontological virtual laboratories of expeditions, and a cognitive system for selecting research papers is analyzed. All tools of the CIT “Polyhedron” can be represented as a taxonomy, object-oriented, or prism. Approaches to data processing using ranking and auditing, which are elements of the CIT “Polyhedron”, have been developed. This approach is used in the selection of data by teachers and students, as well as in the processing of ontological knowledge bases, which is shown on the example of the microbial selection system. The database of a centralized information web-oriented educational environment consists of various types of educational programs. The ontologized program differs from the classical approaches to the interpretation of educational programs by a higher level of structured material and interactivity. Students and teachers can interact with structured curricula. Internal and external search tools are used to search for contexts based on the program’s terminology field. The ontological system of virtual museum laboratories provides a high level of structuring of information about objects and their virtualization. This allows you to use Museum ontologies during sightseeing classes. The database of microorganisms in the CIT “Polyhedron” system provided systematization of research knowledge in the educational process. CIT “Polyhedron” made it possible to identify the characteristics of research papers and systematize their processing in accordance with the user’s request.