Relevant bibliographies by topics / Mermin polynomials

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Mermin polynomials'

Author: Grafiati
Published: 1 February 2025

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Journal articles on the topic "Mermin polynomials"

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Garg, Anupam. "The discrete Chebyshev–Meckler–Mermin–Schwarz polynomials and spin algebra." Journal of Mathematical Physics 63, no. 7 (July 1, 2022): 072101. http://dx.doi.org/10.1063/5.0094575.

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The polynomials discovered by Chebyshev and subsequently related to spin transition probabilities by Meckler [Meckler, Phys. Rev. 111, 1447 (1958)] and Mermin and Schwarz [Found. Phys. 12, 101 (1982)] are studied, and their application to phase space representations of spin states and operators is examined. In particular, a formula relating the end-point value of the polynomials to scale factors relating different phase space representations of spherical harmonic operators is found. This formula is applied to illustrative calculations of Wigner functions for a single spin and the singlet state of a pair of spins.
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Morimae, Tomoyuki, Yuki Takeuchi, and Harumichi Nishimura. "Merlin-Arthur with efficient quantum Merlin and quantum supremacy for the second level of the Fourier hierarchy." Quantum 2 (November 15, 2018): 106. http://dx.doi.org/10.22331/q-2018-11-15-106.

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We introduce a simple sub-universal quantum computing model, which we call the Hadamard-classical circuit with one-qubit (HC1Q) model. It consists of a classical reversible circuit sandwiched by two layers of Hadamard gates, and therefore it is in the second level of the Fourier hierarchy. We show that output probability distributions of the HC1Q model cannot be classically efficiently sampled within a multiplicative error unless the polynomial-time hierarchy collapses to the second level. The proof technique is different from those used for previous sub-universal models, such as IQP, Boson Sampling, and DQC1, and therefore the technique itself might be useful for finding other sub-universal models that are hard to classically simulate. We also study the classical verification of quantum computing in the second level of the Fourier hierarchy. To this end, we define a promise problem, which we call the probability distribution distinguishability with maximum norm (PDD-Max). It is a promise problem to decide whether output probability distributions of two quantum circuits are far apart or close. We show that PDD-Max is BQP-complete, but if the two circuits are restricted to some types in the second level of the Fourier hierarchy, such as the HC1Q model or the IQP model, PDD-Max has a Merlin-Arthur system with quantum polynomial-time Merlin and classical probabilistic polynomial-time Arthur.
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CAI, JIN-YI, DENIS CHARLES, A. PAVAN, and SAMIK SENGUPTA. "ON HIGHER ARTHUR-MERLIN CLASSES." International Journal of Foundations of Computer Science 15, no. 01 (February 2004): 3–19. http://dx.doi.org/10.1142/s0129054104002273.

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We study higher Arthur-Merlin classes defined via several natural probabilistic operators BP, R and coR. We investigate the complexity classes they define, and a number of interactions between these operators and the standard polynomial time hierarchy. We prove a hierarchy theorem for these higher Arthur-Merlin classes involving interleaving operators, and a theorem giving non-trivial upper bounds to the intersection of the complementary classes in the hierarchy.
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Aharonov, Dorit, Michael Ben-Or, Fernando G. S. L. Brandão, and Or Sattath. "The Pursuit of Uniqueness: Extending Valiant-Vazirani Theorem to the Probabilistic and Quantum Settings." Quantum 6 (March 17, 2022): 668. http://dx.doi.org/10.22331/q-2022-03-17-668.

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Valiant-Vazirani showed in 1985 \cite{VV85} that solving NP with the promise that "yes" instances have only one witness is powerful enough to solve the entire NP class (under randomized reductions).We are interested in extending this result to the quantum setting. We prove extensions to the classes Merlin-Arthur MA and Quantum-Classical-Merlin-Arthur QCMA \cite{AN02}. Our results have implications for the complexity of approximating the ground state energy of a quantum local Hamiltonian with a unique ground state and an inverse polynomial spectral gap. We show that the estimation (to within polynomial accuracy) of the ground state energy of poly-gapped 1-D local Hamiltonians is QCMA-hard, under randomized reductions. This is in stark contrast to the case of constant gapped 1-D Hamiltonians, which is in NP \cite{Has07}. Moreover, it shows that unless QCMA can be reduced to NP by randomized reductions, there is no classical description of the ground state of every poly-gapped local Hamiltonian that allows efficient calculation of expectation values.Finally, we discuss a few of the obstacles to the establishment of an analogous result to the class Quantum-Merlin-Arthur (QMA). In particular, we show that random projections fail to provide a polynomial gap between two witnesses.
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Gharibian, Sevag, Jamie Sikora, and Sarvagya Upadhyay. "QMA variants with polynomially many provers." Quantum Information and Computation 13, no. 1&2 (January 2013): 135–57. http://dx.doi.org/10.26421/qic13.1-2-8.

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We study three variants of multi-prover quantum Merlin-Arthur proof systems. We first show that the class of problems that can be efficiently verified using polynomially many quantum proofs, each of logarithmic-size, is exactly \class{MQA} (also known as QCMA), the class of problems which can be efficiently verified via a classical proof and a quantum verifier. We then study the class $\class{BellQMA}(\poly)$, characterized by a verifier who first applies unentangled, nonadaptive measurements to each of the polynomially many proofs, followed by an arbitrary but efficient quantum verification circuit on the resulting measurement outcomes. We show that if the number of outcomes per nonadaptive measurement is a polynomially-bounded function, then the expressive power of the proof system is exactly \class{QMA}. Finally, we study a class equivalent to \class{QMA}($m$), denoted $\class{SepQMA}(m)$, where the verifier's measurement operator corresponding to outcome {\it accept} is a fully separable operator across the $m$ quantum proofs. Using cone programming duality, we give an alternate proof of a result of Harrow and Montanaro [FOCS, pp. 633--642 (2010)] that shows a perfect parallel repetition theorem for $\class{SepQMA}(m)$ for any $m$.
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de Boutray, Henri, Hamza Jaffali, Frédéric Holweck, Alain Giorgetti, and Pierre-Alain Masson. "Mermin polynomials for non-locality and entanglement detection in Grover’s algorithm and Quantum Fourier Transform." Quantum Information Processing 20, no. 3 (March 2021). http://dx.doi.org/10.1007/s11128-020-02976-z.

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Kuno, Yoshihito. "Study of quantum nonlocality by CHSH function and its extension in disordered fermions." Journal of Physics: Condensed Matter, September 18, 2024. http://dx.doi.org/10.1088/1361-648x/ad7cb4.

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Abstract Quantum nonlocality is an important concept in quantum physics. In this work, we study the quantum nonlocality in a fermion many-body system under quasi-periodic disorders. The Clauser-Horne-Shimony-Holt (CHSH) inequality is systematically investigated, which quantifies quantum nonlocality between two sites. We find particular behaviors of the quantifiers of quantum nonlocality around the extended and critical phase transitions in the system and further that the CHSH inequality is not broken in the globally averaged picture of the maximum value of the quantum nonlocality, but the violation probability of the CHSH inequality for two site pairs in the system becomes sufficiently finite in the critical phase and on a critical phase boundary. Further, we investigate an extension of the CHSH inequality, Mermin-Klyshko-Svetlichny (MKS) polynomials, which can characterize multipartite quantum nonlocality. We also find a similar behavior to the case of CHSH inequality. In particular, in the critical regime and on a transition point, the adjacent three-qubit MKS polynomial in a portion of the system exhibits a quantum nonlocal violation regime with a finite probability in the critical phase.
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Rethinasamy, Soorya, Margarite LaBorde, and Mark Wilde. "Quantum Computational Complexity and Symmetry." Canadian Journal of Physics, October 15, 2024. http://dx.doi.org/10.1139/cjp-2023-0260.

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Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the difficulty of symmetry-testing problems involving a unitary representation of a group and a state or a channel that is being tested. In particular, we prove that various such symmetry-testing problems are complete for BQP (bounded-error quantum polynomial time), QMA (quantum Merlin-Arthur), QSZK (quantum statistical zero-knowledge), QIP(2) (two-message quantum interactive proofs), QIP_EB(2) (two-message quantum interactive proofs restricted to entanglement-breaking provers), and QIP (quantum interactive proofs), thus spanning the prominent classes of the quantum interactive proof hierarchy and forging a non-trivial connection between symmetry and quantum computational complexity. Finally, we prove the inclusion of two Hamiltonian symmetry-testing problems in QMA and QAM, while leaving it as an intriguing open question to determine whether these problems are complete for these classes.
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Coblentz, Wayne K., and Michael J. Ottman. "Effects of harvest date and growth stage on triticale forages in the southwest USA: kinetics of in vitro disappearance of fiber and dry matter." Journal of Animal Science 100, no. 3 (February 5, 2022). http://dx.doi.org/10.1093/jas/skac020.

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Abstract Recently, there has been interest in including triticale (X Triticosecale Wittmack) within forage programs in the southwest USA. Our objectives were to evaluate in vitro disappearance kinetics of neutral detergent fiber (NDF) and dry matter (DM) for cultivars identified during 2019 as positively or negatively deviant from typical cultivars, based specifically on regressions of 48-h in vitro disappearance of NDF on growth stage (GRST). All NDF analyses included the use of heat-stable α-amylase and sodium sulfite, as well as correction for residual ash (asNDFom). Seven triticale cultivars were established on December 18, 2019 at the University of Arizona Maricopa Agricultural Center, located near Maricopa, AZ. Forage plots were arranged in a randomized complete block design with three complete blocks (replications), and then harvested on seven dates the following late-winter and spring (February 26, March 17, April 1, April 14, April 28, May 12, and May 26). Based on a linear model, GRST was highly variable among cultivars on March 17 (44 ± 10.6), April 1 (57 ± 12.1), April 14 (67 ± 8.9), and April 28 (79 ± 7.2) compared with other harvest dates (SD ≤ 1.7). For concentrations of asNDFom, all cultivars exhibited linear (P ≤ 0.042) and quadratic (P < 0.001) polynomial contrasts in response to harvest date, and all cultivars except Merlin Max (P ≥ 0.063) exhibited at least one additional cubic or quartic effect (P ≤ 0.015). A contributing factor to the unique response by Merlin Max was the numerically greater maximum canopy height (145 ± 9.8 cm) compared with the mean of all cultivars (107 ± 17.7 cm), which also was associated with greater percentages of stem, as well as reduced percentages of DM partitioned within the grain head. Regressions of asNDFom disappearance after 30- or 48-h incubations on GRST indicated this was an effective independent variable (R2 ≥ 0.927), and responses were most often linear in nature. Generally, relationships for DM disappearance were quadratic, ostensibly due to the complicating effect of grain fill, but GRST was again an effective predictor variable with R2 statistics ≥ 0.852 for 12 of 14 combinations of cultivar and incubation time. Predicted percentages of digestible DM attributed to asNDFom disappearance were ≥50.3% through the fully flowered stage of growth, but digestible contributions from nonfiber components following the onset of grain fill profoundly affected overall DM digestibility among cultivars harvested at later GRST.
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Coblentz, Wayne K., Michael J. Ottman, and Burney A. Kieke. "Effects of harvest date and growth stage on triticale forages in the southwest United States: agronomic characteristics, nutritive value, energy density, and in vitro disappearance of dry matter and fiber." Journal of Animal Science 100, no. 3 (February 5, 2022). http://dx.doi.org/10.1093/jas/skac021.

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Abstract Recently, there has been increased interest in including triticale (X Triticosecale Wittmack) or other winter cereals within forage programs throughout the southwest United States. Our objectives were to screen 14 diverse triticale cultivars for agronomic and nutritive characteristics with specific emphasis on identifying normal, as well as deviant, responses to the calendar date and plant maturity for forages seeded in December and harvested from late February throughout May at Maricopa, AZ. Fourteen cultivars were established in a randomized complete block design with each cultivar represented within each of three field blocks. Plots were clean tilled and established on December 18, 2018, and then harvested at 2-wk intervals beginning on February 27 and ending May 23, 2019. Across all harvest dates, forage (N = 315) energy density (NEL) exhibited strong negative correlations with growth stage (r = −0.879), plant height (r = −0.913), head weight (r = −0.814), and estimated dry matter (DM) yield (r = −0.886) but was positively associated with percentages of leaf (r = 0.949), and weakly associated with percentages of the stem (r = 0.138). Through April 10, similar correlations were observed within individual harvest dates (N = 45) for growth stage, leaf percentage, and plant height but not for stem or head-weight percentages. Within later harvest dates, only sporadic correlations with NEL were observed. Primarily cubic regression relationships for neutral detergent fiber, acid detergent lignin, 30- and 48-h in vitro disappearance of DM and fiber, and NEL were fit for the mean or typical cultivar using both days from February 1 and growth stage as independent variables. Coefficients of determination (R2 ≥ 0.860) in all cases indicated a good fit for the polynomial models. For NEL, deviation from the typical cultivar when days from February 1 was used as the independent regression variable was largely affected by cultivar maturation rate. When the growth stage was substituted as the independent variable, plant height, stem percentage beginning at anthesis, and low grain-head percentage were associated with the maximum negative deviant cultivar (Merlin Max). The 0.23 Mcal/kg difference between maximum positive and negative deviant cultivars at a common late-boot/early-heading stage of growth suggests that some attention should be placed on cultivar selection as well as forage inventory needs and overall cropping goals.
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Dissertations / Theses on the topic "Mermin polynomials"

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Amouzou, Grâce Dorcas Akpéné. "Etude de l’intrication par les polynômes de Mermin : application aux algorithmes quantiques." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2024. http://www.theses.fr/2024UBFCK063.

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Cette thèse explore la mesure de l'intrication dans certains états hypergraphiques, dans certains algorithmes quantiques tels que les algorithmes quantiques d'estimation de phase et de comptage, ainsi que dans les circuits d'agents réactifs, à l'aide de la mesure géométrique de l'intrication, d'outils issus des polynômes de Mermin et des matrices de coefficients. L'intrication est un concept présent en physique quantique qui n'a pas d'équivalent connu à ce jour en physique classique.Le coeur de notre recherche repose sur la mise en place de dispositifs de détection et de mesure de l'intrication afin d'étudier des états quantiques du point de vue de l'intrication.Dans cette optique, des calculs sont d'abord effectués numériquement puis sur simulateur et ordinateur quantiques. Effectivement, trois des outils exploités sont implémentables sur machine quantique, ce qui permet de comparer les résultats théoriques et "réels"
This thesis explores the measurement of entanglement in certain hypergraph states, in certain quantum algorithms like the Quantum Phase estimation and Counting algorithms as well as in reactive agent circuits, using the geometric measurement of entanglement, tools from Mermin polynomials and coefficient matrices. Entanglement is a concept present in quantum physics that has no known equivalent to date in classical physics.The core of our research is based on the implementation of entanglement detection and measurement devices in order to study quantum states from the point of view of entanglement.With this in mind, calculations are first carried out numerically and then on a quantum simulator and computer. Indeed, three of the tools used can be implemented on a quantum machine, which allows us to compare theoretical and "real" results
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Blier, Hugue. "Preuves interactives classiques." Thèse, 2006. http://hdl.handle.net/1866/16728.

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Mbakop, Guy Merlin [Verfasser]. "Effiziente Lösung reeller polynomialer Gleichungssysteme / Mbakop Guy Merlin." 1999. http://d-nb.info/958731624/34.

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Book chapters on the topic "Mermin polynomials"

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Ma, Jianbing, Weiru Liu, and Anthony Hunter. "The Non-archimedean Polynomials and Merging of Stratified Knowledge Bases." In Lecture Notes in Computer Science, 408–20. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02906-6_36.

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Valk, Jeroen, Mathijs de Weerdt, and Cees Witteveen. "Coordination in Multi-Agent Planning with an Application in Logistics." In Intelligent Techniques for Planning, 194–224. IGI Global, 2005. http://dx.doi.org/10.4018/978-1-59140-450-7.ch006.

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Multi-agent planning comprises planning in an environment with multiple autonomous actors. Techniques for multi-agent planning differ from conventional planning in that planning activities are distributed and the planning autonomy of the agents must be respected. We focus on approaches to coordinate the multi-agent planning process. While usually coordination is intertwined with the planning process, we distinguish a number of separate phases in the planning process to get a clear view on the different role(s) of coordination. In particular, we discuss the pre-planning coordination phase and post-planning coordination phase. In the pre-planning part, we view coordination as the process of managing (sub) task dependencies and we discuss a method that ensures complete planning autonomy by introducing additional (intra-agent) dependencies. In the post-planning part, we will show how agents can improve their plans through the exchange of resources. We present a plan merging algorithm that uses these resources to reduce the costs of independently developed plans. This (any-time) algorithm runs in polynomial time.
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Conference papers on the topic "Mermin polynomials"

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Shoup, Terry E. "An Improved Method for Predicting Minor-Axis Shear Stresses in Rectangular Shafts Under Torsion Using Optimization Polynomials." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86526.

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This paper presents four new approximation formulas for predicting the shear stress in rectangular members subjected to torque loading. The results are developed using a hybrid optimization method applied to a polynomial merit function to predict the maximum shear stress along the center of the shorter side of a rectangular cross section subjected to a torque. The results of this optimization process are shown to be highly accurate and easy to apply. It is believed that this is the first time that this approach has been applied to find this component of the shear stress. This paper includes an example application to illustrate the use of the approximate polynomials developed. The results are shown to be especially relevant to rectangular members that are subjected to combined torsion and bending.
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Mathew, Reji, and David S. Taubman. "Hierarchical and Polynomial Motion Modeling with Quad-Tree Leaf Merging." In 2006 International Conference on Image Processing. IEEE, 2006. http://dx.doi.org/10.1109/icip.2006.313103.

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Wang, Yongtian, Xingui Tang, and Lin Li. "Aberration polynomial fitting and MTF based optimization for general optical systems." In International Optical Design Conference. Washington, D.C.: Optica Publishing Group, 1998. http://dx.doi.org/10.1364/iodc.1998.lmc.4.

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Although there are different ways to implement MTF optimization1,2 in an optical design program, a common requirement of them is to express the wave-aberration as a polynomial in the exit pupil coordinates. While in-depth studies have been carried out for polynomial fitting for rotationally symmetric optical systems3,4, few publications can be found on the subject for general systems without symmetry. A simple scheme is developed for the efficient and accurate determination of the coefficients of a Zernike wave-aberration polynomial for a given object point and a general optical system. It enables rapid evaluations of MTF related image criteria such as the variance of the wave-aberration difference function, which is used as the merit function in damped-least-squares MTF optimization for nonsymmetric systems.
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Pauca, Ovidiu, Anca Maxim, and Constantin F. Caruntu. "Trajectory Planner based on Third-order Polynomials applied for Platoon Merging and Splitting." In 2021 29th Mediterranean Conference on Control and Automation (MED). IEEE, 2021. http://dx.doi.org/10.1109/med51440.2021.9480261.

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Shoup, T. E., and L. A. Sanchez. "An Improved Method for Predicting Shear Stress in Rectangular Shafts Based on Optimization Polynomials." In ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium collocated with the ASME 1995 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/cie1995-0777.

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Abstract This paper presents several new approximations for the coefficients associated with the shear stresses in rectangular shafts. The new results are developed using an optimization approach based on a polynomial merit function to predict the maximum shear stress along the center of the long side of the cross section. The results are shown to be more accurate than existing approximate methods that are now in the literature.
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Benferhat, Salem, Zied Bouraoui, Ma Thi Chau, Sylvain Lagrue, and Julien Rossit. "A Polynomial Algorithm for Merging Lightweight Ontologies in Possibility Theory Under Incommensurability Assumption." In 9th International Conference on Agents and Artificial Intelligence. SCITEPRESS - Science and Technology Publications, 2017. http://dx.doi.org/10.5220/0006120804150422.

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Gorguluarslan, Recep M., and Seung-Kyum Choi. "An Improved Stochastic Upscaling Method for Multiscale Engineering Systems." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34418.

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A stochastic multiscale modeling technique is proposed to construct coarse scale representation of a fine scale model for use in engineering design problems. The complexity of the fine scale heterogeneity under uncertainty is replaced with the homogenized coarse scale parameters by seeking agreement between the responses at both scales. Generalized polynomial chaos expansion is implemented to reduce the dimensionality of propagating uncertainty through scales and the computational costs of the upscaling method. It is integrated into a hybrid optimization procedure with the genetic algorithm and sequential quadratic programming. Two structural engineering problems that involve uncertainties in elastic material properties and geometric properties at fine scales are presented to demonstrate the applicability and merit of the proposed technique.
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Bernstein, N. S., and K. Preiss. "Representation of Tolerance Information in Solid Models." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0018.

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Abstract A set of tolerance constraints in solid models is represented as a constraint network over the degrees of freedom of the shape elements of the body. This approach is referred to as the constraint propagation approach to the representation of tolerance information. An evaluation of the resultant constraint network provides both an analysis of a specific dimension and tolerance scheme and figures of merit regarding the combinatorial and geometric/numeric computational complexity of a set of engineering spatial constraints. This paper discusses the representation needed to achieve that evaluation. The inherent computational complexity of spatial designs can then be explicitly evaluated and controlled. For many practical cases, semantic integrity and other evaluations may be conducted in low polynomial time, in the number of tolerance constraints. The representation is applicable also to assemblies.
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Peng, C., Y. Yan, X. Y. Wang, and Y. Z. Huo. "Analysis of Microstructure Evolution During Tensile Stress Induced Martensitic Transformations." In ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2008. http://dx.doi.org/10.1115/smasis2008-358.

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An image analysis technique was employed to document the layered parallel microstructures observed during tensile tests of CuAlNi single crystal shape memory alloys. The evolution of the microstructures during the stress induced martensitic transformation can be then well studied quantitatively by the evolution of the phase character function and its suitable averages. The results indicated clearly that the stress induced martensite transformation should consist three periods, initial formation, mixed formation and growth, merging due to growth. Euler-Lagrange equations for the minimizers of some one-dimensional energy functional were also studied for two types of two-well strain energy functions, the piecewise quadratic energy function and a smooth polynomial. The cell exclusive genetic algorithm was adapted to solve the nonlinear algebraic equations in the first case. The homotopy analysis method was used in the second case to find accurate series solutions. Multi-interface microstructures were obtained in both cases. The methods, especially the homotopy analysis seemed to be quite powerful to solve the nonlinear equations even with large number of interfaces.
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Vafaeesefat, Abbas, and Hoda A. ElMaraghy. "Data Reduction for Reverse Engineering of Free Form Surfaces." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/cie-9132.

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Abstract The large amount of irregular and unstructured data collected by the laser scanner, often refered to as “cloud data”, presents a serious challenge in reverse engineering applications. Data reduction is essential for simplifying the process of creating surface models in order to remove redundancy, save space, and speed up the display and recognition tasks. In this paper, an algorithm which effectively reduces the data collected by laser scanners is presented. Data points are first organized into a large regular grid of data points which is then interpolated using the linear polynominal dual Kriging technique to form the initial surface. Next, the algorithm generates a subset of this grid (within the specified deviation) by identifying the knots that play important role in the Kriging interpolation. Finally, additional reduction is done by merging the rectangles of the grid where the tangent variation between two rectangles is insignificant. Since the final surface is usually represented by a set of connected rectangles, the surface segmentation and fitting procedures can be accomplished in a short period of time. Examples are used to show the efficiency and validity of the proposed algorithms.
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