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Sample records for algebraic stress models

  1. A New Reynolds Stress Algebraic Equation Model

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.

    1994-01-01

    A general turbulent constitutive relation is directly applied to propose a new Reynolds stress algebraic equation model. In the development of this model, the constraints based on rapid distortion theory and realizability (i.e. the positivity of the normal Reynolds stresses and the Schwarz' inequality between turbulent velocity correlations) are imposed. Model coefficients are calibrated using well-studied basic flows such as homogeneous shear flow and the surface flow in the inertial sublayer. The performance of this model is then tested in complex turbulent flows including the separated flow over a backward-facing step and the flow in a confined jet. The calculation results are encouraging and point to the success of the present model in modeling turbulent flows with complex geometries.

  2. On explicit algebraic stress models for complex turbulent flows

    NASA Technical Reports Server (NTRS)

    Gatski, T. B.; Speziale, C. G.

    1992-01-01

    Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

  3. Prediction of Complex Aerodynamic Flows with Explicit Algebraic Stress Models

    NASA Technical Reports Server (NTRS)

    Abid, Ridha; Morrison, Joseph H.; Gatski, Thomas B.; Speziale, Charles G.

    1996-01-01

    An explicit algebraic stress equation, developed by Gatski and Speziale, is used in the framework of K-epsilon formulation to predict complex aerodynamic turbulent flows. The nonequilibrium effects are modeled through coefficients that depend nonlinearly on both rotational and irrotational strains. The proposed model was implemented in the ISAAC Navier-Stokes code. Comparisons with the experimental data are presented which clearly demonstrate that explicit algebraic stress models can predict the correct response to nonequilibrium flow.

  4. A Realizable Reynolds Stress Algebraic Equation Model

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.

    1993-01-01

    The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

  5. Assessment of an Explicit Algebraic Reynolds Stress Model

    NASA Technical Reports Server (NTRS)

    Carlson, Jan-Renee

    2005-01-01

    This study assesses an explicit algebraic Reynolds stress turbulence model in the in the three-dimensional Reynolds averaged Navier-Stokes (RANS) solver, ISAAC (Integrated Solution Algorithm for Arbitrary Con gurations). Additionally, it compares solutions for two select configurations between ISAAC and the RANS solver PAB3D. This study compares with either direct numerical simulation data, experimental data, or empirical models for several different geometries with compressible, separated, and high Reynolds number flows. In general, the turbulence model matched data or followed experimental trends well, and for the selected configurations, the computational results of ISAAC closely matched those of PAB3D using the same turbulence model.

  6. A Galilean Invariant Explicit Algebraic Reynolds Stress Model for Curved Flows

    NASA Technical Reports Server (NTRS)

    Girimaji, Sharath

    1996-01-01

    A Galilean invariant weak-equilbrium hypothesis that is sensitive to streamline curvature is proposed. The hypothesis leads to an algebraic Reynolds stress model for curved flows that is fully explicit and self-consistent. The model is tested in curved homogeneous shear flow: the agreement is excellent with Reynolds stress closure model and adequate with available experimental data.

  7. Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Models

    NASA Technical Reports Server (NTRS)

    Girimaji, Sharath S.

    1995-01-01

    A fully-explicit, self-consistent algebraic expression for the Reynolds stress, which is the exact solution to the Reynolds stress transport equation in the 'weak equilibrium' limit for two-dimensional mean flows for all linear and some quasi-linear pressure-strain models, is derived. Current explicit algebraic Reynolds stress models derived by employing the 'weak equilibrium' assumption treat the production-to-dissipation (P/epsilon) ratio implicitly, resulting in an effective viscosity that can be singular away from the equilibrium limit. In the present paper, the set of simultaneous algebraic Reynolds stress equations are solved in the full non-linear form and the eddy viscosity is found to be non-singular. Preliminary tests indicate that the model performs adequately, even for three dimensional mean flow cases. Due to the explicit and non-singular nature of the effective viscosity, this model should mitigate many of the difficulties encountered in computing complex turbulent flows with the algebraic Reynolds stress models.

  8. Predicting NonInertial Effects with Algebraic Stress Models which Account for Dissipation Rate Anisotropies

    NASA Technical Reports Server (NTRS)

    Jongen, T.; Machiels, L.; Gatski, T. B.

    1997-01-01

    Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coriolis-modified eddy-viscosity model, a realizable algebraic stress model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the turbulent model validation. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.

  9. Development of an algebraic stress/two-layer model for calculating thrust chamber flow fields

    NASA Technical Reports Server (NTRS)

    Chen, C. P.; Shang, H. M.; Huang, J.

    1993-01-01

    Following the consensus of a workshop in Turbulence Modeling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data, to account for the non-isotropic turbulence effects.

  10. Computation of turbulent rotating channel flow with an algebraic Reynolds stress model

    NASA Technical Reports Server (NTRS)

    Warfield, M. J.; Lakshminarayana, B.

    1986-01-01

    An Algebraic Reynolds Stress Model has been implemented to modify the Kolmogorov-Prandtl eddy viscosity relation to produce an anisotropic turbulence model. The eddy viscosity relation becomes a function of the local turbulent production to dissipation ratio and local turbulence/rotation parameters. The model is used to predict fully-developed rotating channel flow over a diverse range of rotation numbers. In addition, predictions are obtained for a developing channel flow with high rotation. The predictions are compared with the experimental data available. Good predictions are achieved for mean velocity and wall shear stress over most of the rotation speeds tested. There is some prediction breakdown at high rotation (rotation number greater than .10) where the effects of the rotation on turbulence become quite complex. At high rotation and low Reynolds number, the laminarization on the trailing side represents a complex effect of rotation which is difficult to predict with the described models.

  11. Development of an algebraic stress/two-layer model for calculating thrust chamber flow fields

    NASA Astrophysics Data System (ADS)

    Chen, C. P.; Shang, H. M.; Huang, J.

    1993-07-01

    Following the consensus of a workshop in Turbulence Modeling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data, to account for the non-isotropic turbulence effects.

  12. Computation of turbulent boundary layer flows with an algebraic stress turbulence model

    NASA Technical Reports Server (NTRS)

    Kim, Sang-Wook; Chen, Yen-Sen

    1986-01-01

    An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.

  13. Algebraic Reynolds stress modeling of turbulence subject to rapid homogeneous and non-homogeneous compression or expansion

    NASA Astrophysics Data System (ADS)

    Grigoriev, I. A.; Wallin, S.; Brethouwer, G.; Grundestam, O.; Johansson, A. V.

    2016-02-01

    A recently developed explicit algebraic Reynolds stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation," Phys. Fluids 25(10), 105112 (2013)] and the related differential Reynolds stress model (DRSM) are used to investigate the influence of homogeneous shear and compression on the evolution of turbulence in the limit of rapid distortion theory (RDT). The DRSM predictions of the turbulence kinetic energy evolution are in reasonable agreement with RDT while the evolution of diagonal components of anisotropy correctly captures the essential features, which is not the case for standard compressible extensions of DRSMs. The EARSM is shown to give a realizable anisotropy tensor and a correct trend of the growth of turbulence kinetic energy K, which saturates at a power law growth versus compression ratio, as well as retaining a normalized strain in the RDT regime. In contrast, an eddy-viscosity model results in a rapid exponential growth of K and excludes both realizability and high magnitude of the strain rate. We illustrate the importance of using a proper algebraic treatment of EARSM in systems with high values of dilatation and vorticity but low shear. A homogeneously compressed and rotating gas cloud with cylindrical symmetry, related to astrophysical flows and swirling supercritical flows, was investigated too. We also outline the extension of DRSM and EARSM to include the effect of non-homogeneous density coupled with "local mean acceleration" which can be important for, e.g., stratified flows or flows with heat release. A fixed-point analysis of direct numerical simulation data of combustion in a wall-jet flow demonstrates that our model gives quantitatively correct predictions of both streamwise and cross-stream components of turbulent density flux as well as their influence on the anisotropies. In summary, we believe that our approach, based on a proper

  14. Implementation of algebraic stress models in a general 3-D Navier-Stokes method (PAB3D)

    NASA Technical Reports Server (NTRS)

    Abdol-Hamid, Khaled S.

    1995-01-01

    A three-dimensional multiblock Navier-Stokes code, PAB3D, which was developed for propulsion integration and general aerodynamic analysis, has been used extensively by NASA Langley and other organizations to perform both internal (exhaust) and external flow analysis of complex aircraft configurations. This code was designed to solve the simplified Reynolds Averaged Navier-Stokes equations. A two-equation k-epsilon turbulence model has been used with considerable success, especially for attached flows. Accurate predicting of transonic shock wave location and pressure recovery in separated flow regions has been more difficult. Two algebraic Reynolds stress models (ASM) have been recently implemented in the code that greatly improved the code's ability to predict these difficult flow conditions. Good agreement with Direct Numerical Simulation (DNS) for a subsonic flat plate was achieved with ASM's developed by Shih, Zhu, and Lumley and Gatski and Speziale. Good predictions were also achieved at subsonic and transonic Mach numbers for shock location and trailing edge boattail pressure recovery on a single-engine afterbody/nozzle model.

  15. MODEL IDENTIFICATION AND COMPUTER ALGEBRA.

    PubMed

    Bollen, Kenneth A; Bauldry, Shawn

    2010-10-01

    Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods. PMID:21769158

  16. Teaching Modeling and Axiomatization with Boolean Algebra.

    ERIC Educational Resources Information Center

    De Villiers, Michael D.

    1987-01-01

    Presented is an alternative approach to the traditional teaching of Boolean algebra for secondary school mathematics. The main aim of the approach is to use Boolean algebra to teach pupils such mathematical processes as modeling and axiomatization. A course using the approach is described. (RH)

  17. One-Equation Algebraic Model Of Turbulence

    NASA Technical Reports Server (NTRS)

    Baldwin, B. S.; Barth, T. J.

    1993-01-01

    One-equation model of turbulence based on standard equations of k-epsilon model of turbulence, where k is turbulent energy and e is rate of dissipation of k. Derivation of one-equation model motivated partly by inaccuracies of flows computed by some Navier-Stokes-equations-solving algorithms incorporating algebraic models of turbulence. Satisfies need to avoid having to determine algebraic length scales.

  18. Algebraic operator approach to gas kinetic models

    NASA Astrophysics Data System (ADS)

    Il'ichov, L. V.

    1997-02-01

    Some general properties of the linear Boltzmann kinetic equation are used to present it in the form ∂ tϕ = - †Âϕ with the operators Âand† possessing some nontrivial algebraic properties. When applied to the Keilson-Storer kinetic model, this method gives an example of quantum ( q-deformed) Lie algebra. This approach provides also a natural generalization of the “kangaroo model”.

  19. Computational algebraic geometry of epidemic models

    NASA Astrophysics Data System (ADS)

    Rodríguez Vega, Martín.

    2014-06-01

    Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

  20. Algebraic models of flexible manufacturing systems

    NASA Astrophysics Data System (ADS)

    Leskin, Aleksei Alekseevich

    Various aspects of the use of mathematical methods in the development of flexible manufacturing systems are examined. Attention is given to dynamical and structural models of flexible manufacturing systems developed by using methods of algebraic and differential geometry, topology, polynomial algebra, and extreme value problem theory. The principles of model integration are discussed, and approaches are proposed for solving problems related to the selection of flexible manufacturing equipment, real-time modeling of the manufacturing process, and optimization of local automation systems. The discussion is illustrated by examples.

  1. Solving stochastic epidemiological models using computer algebra

    NASA Astrophysics Data System (ADS)

    Hincapie, Doracelly; Ospina, Juan

    2011-06-01

    Mathematical modeling in Epidemiology is an important tool to understand the ways under which the diseases are transmitted and controlled. The mathematical modeling can be implemented via deterministic or stochastic models. Deterministic models are based on short systems of non-linear ordinary differential equations and the stochastic models are based on very large systems of linear differential equations. Deterministic models admit complete, rigorous and automatic analysis of stability both local and global from which is possible to derive the algebraic expressions for the basic reproductive number and the corresponding epidemic thresholds using computer algebra software. Stochastic models are more difficult to treat and the analysis of their properties requires complicated considerations in statistical mathematics. In this work we propose to use computer algebra software with the aim to solve epidemic stochastic models such as the SIR model and the carrier-borne model. Specifically we use Maple to solve these stochastic models in the case of small groups and we obtain results that do not appear in standard textbooks or in the books updated on stochastic models in epidemiology. From our results we derive expressions which coincide with those obtained in the classical texts using advanced procedures in mathematical statistics. Our algorithms can be extended for other stochastic models in epidemiology and this shows the power of computer algebra software not only for analysis of deterministic models but also for the analysis of stochastic models. We also perform numerical simulations with our algebraic results and we made estimations for the basic parameters as the basic reproductive rate and the stochastic threshold theorem. We claim that our algorithms and results are important tools to control the diseases in a globalized world.

  2. Shapes and stability of algebraic nuclear models

    NASA Technical Reports Server (NTRS)

    Lopez-Moreno, Enrique; Castanos, Octavio

    1995-01-01

    A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes.

  3. A process algebra model of QED

    NASA Astrophysics Data System (ADS)

    Sulis, William

    2016-03-01

    The process algebra approach to quantum mechanics posits a finite, discrete, determinate ontology of primitive events which are generated by processes (in the sense of Whitehead). In this ontology, primitive events serve as elements of an emergent space-time and of emergent fundamental particles and fields. Each process generates a set of primitive elements, using only local information, causally propagated as a discrete wave, forming a causal space termed a causal tapestry. Each causal tapestry forms a discrete and finite sampling of an emergent causal manifold (space-time) M and emergent wave function. Interactions between processes are described by a process algebra which possesses 8 commutative operations (sums and products) together with a non-commutative concatenation operator (transitions). The process algebra possesses a representation via nondeterministic combinatorial games. The process algebra connects to quantum mechanics through the set valued process and configuration space covering maps, which associate each causal tapestry with sets of wave functions over M. Probabilities emerge from interactions between processes. The process algebra model has been shown to reproduce many features of the theory of non-relativistic scalar particles to a high degree of accuracy, without paradox or divergences. This paper extends the approach to a semi-classical form of quantum electrodynamics.

  4. An algebraic approach to the Hubbard model

    NASA Astrophysics Data System (ADS)

    de Leeuw, Marius; Regelskis, Vidas

    2016-02-01

    We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su (2 | 2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.

  5. Automorphism groups of composition algebras and quark models

    SciTech Connect

    Bjerregard, P.A.; Gonzalez, C.M.

    1996-12-01

    In this the authors study the automorphisms and derivations of real composition algebras with a view to its physical interpretations. They obtain canonical forms with a special stress in the four and eight dimensional cases. Also, using this description, they work with two mathematical models which describe some particles with certain observables in a surprising way. A first model, split g{sub 2}, describes two observables for three quarks, their antiquarks, and eight mesons combining the quarks involved. A second one, so(4,4) {circle_plus} so(2,2), describes all the observables for all quarks (u, d, s, c, b and t).

  6. Multi-Matrix Models and Noncommutative Frobenius Algebras Obtained from Symmetric Groups and Brauer Algebras

    NASA Astrophysics Data System (ADS)

    Kimura, Yusuke

    2015-07-01

    It has been understood that correlation functions of multi-trace operators in SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand, such algebras have been known to construct 2D topological field theories (TFTs). After reviewing the construction of 2D TFTs based on symmetric groups, we construct 2D TFTs based on walled Brauer algebras. In the construction, the introduction of a dual basis manifests a similarity between the two theories. We next construct a class of 2D field theories whose physical operators have the same symmetry as multi-trace operators constructed from some matrices. Such field theories correspond to non-commutative Frobenius algebras. A matrix structure arises as a consequence of the noncommutativity. Correlation functions of the Gaussian complex multi-matrix models can be translated into correlation functions of the two-dimensional field theories.

  7. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.

    1991-01-01

    A recently developed spatial operator algebra for manipulator modeling, control, and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics.

  8. Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra

    ERIC Educational Resources Information Center

    Jung, Hyunyi; Mintos, Alexia; Newton, Jill

    2015-01-01

    This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…

  9. Action Algebras and Model Algebras in Denotational Semantics

    NASA Astrophysics Data System (ADS)

    Guedes, Luiz Carlos Castro; Haeusler, Edward Hermann

    This article describes some results concerning the conceptual separation of model dependent and language inherent aspects in a denotational semantics of a programming language. Before going into the technical explanation, the authors wish to relate a story that illustrates how correctly and precisely posed questions can influence the direction of research. By means of his questions, Professor Mosses aided the PhD research of one of the authors of this article and taught the other, who at the time was a novice supervisor, the real meaning of careful PhD supervision. The student’s research had been partially developed towards the implementation of programming languages through denotational semantics specification, and the student had developed a prototype [12] that compared relatively well to some industrial compilers of the PASCAL language. During a visit to the BRICS lab in Aarhus, the student’s supervisor gave Professor Mosses a draft of an article describing the prototype and its implementation experiments. The next day, Professor Mosses asked the supervisor, “Why is the generated code so efficient when compared to that generated by an industrial compiler?” and “You claim that the efficiency is simply a consequence of the Object- Orientation mechanisms used by the prototype programming language (C++); this should be better investigated. Pay more attention to the class of programs that might have this good comparison profile.” As a result of these aptly chosen questions and comments, the student and supervisor made great strides in the subsequent research; the advice provided by Professor Mosses made them perceive that the code generated for certain semantic domains was efficient because it mapped to the “right aspect” of the language semantics. (Certain functional types, used to represent mappings such as Stores and Environments, were pushed to the level of the object language (as in gcc). This had the side-effect of generating

  10. A stochastic extension of the explicit algebraic subgrid-scale models

    SciTech Connect

    Rasam, A. Brethouwer, G.; Johansson, A. V.

    2014-05-15

    The explicit algebraic subgrid-scale (SGS) stress model (EASM) of Marstorp et al. [“Explicit algebraic subgrid stress models with application to rotating channel flow,” J. Fluid Mech. 639, 403–432 (2009)] and explicit algebraic SGS scalar flux model (EASFM) of Rasam et al. [“An explicit algebraic model for the subgrid-scale passive scalar flux,” J. Fluid Mech. 721, 541–577 (2013)] are extended with stochastic terms based on the Langevin equation formalism for the subgrid-scales by Marstorp et al. [“A stochastic subgrid model with application to turbulent flow and scalar mixing,” Phys. Fluids 19, 035107 (2007)]. The EASM and EASFM are nonlinear mixed and tensor eddy-diffusivity models, which improve large eddy simulation (LES) predictions of the mean flow, Reynolds stresses, and scalar fluxes of wall-bounded flows compared to isotropic eddy-viscosity and eddy-diffusivity SGS models, especially at coarse resolutions. The purpose of the stochastic extension of the explicit algebraic SGS models is to further improve the characteristics of the kinetic energy and scalar variance SGS dissipation, which are key quantities that govern the small-scale mixing and dispersion dynamics. LES of turbulent channel flow with passive scalar transport shows that the stochastic terms enhance SGS dissipation statistics such as length scale, variance, and probability density functions and introduce a significant amount of backscatter of energy from the subgrid to the resolved scales without causing numerical stability problems. The improvements in the SGS dissipation predictions in turn enhances the predicted resolved statistics such as the mean scalar, scalar fluxes, Reynolds stresses, and correlation lengths. Moreover, the nonalignment between the SGS stress and resolved strain-rate tensors predicted by the EASM with stochastic extension is in much closer agreement with direct numerical simulation data.

  11. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Kreutz, K.; Milman, M.

    1988-01-01

    A powerful new spatial operator algebra for modeling, control, and trajectory design of manipulators is discussed along with its implementation in the Ada programming language. Applications of this algebra to robotics include an operator representation of the manipulator Jacobian matrix; the robot dynamical equations formulated in terms of the spatial algebra, showing the complete equivalence between the recursive Newton-Euler formulations to robot dynamics; the operator factorization and inversion of the manipulator mass matrix which immediately results in O(N) recursive forward dynamics algorithms; the joint accelerations of a manipulator due to a tip contact force; the recursive computation of the equivalent mass matrix as seen at the tip of a manipulator; and recursive forward dynamics of a closed chain system. Finally, additional applications and current research involving the use of the spatial operator algebra are discussed in general terms.

  12. An algebraic cluster model based on the harmonic oscillator basis

    NASA Technical Reports Server (NTRS)

    Levai, Geza; Cseh, J.

    1995-01-01

    We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.

  13. Inverse Modelling Problems in Linear Algebra Undergraduate Courses

    ERIC Educational Resources Information Center

    Martinez-Luaces, Victor E.

    2013-01-01

    This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

  14. A Cognitive Model of Experts' Algebraic Solving Methods

    ERIC Educational Resources Information Center

    Cortes, Anibal

    2003-01-01

    We studied experts' solving methods and analyzed the nature of mathematical knowledge as well as their efficiency in algebraic calculations. We constructed a model of the experts cognitive functioning (notably teachers) in which the observed automatisms were modeled in terms of schemes and instruments. Mathematical justification of transformation…

  15. The Effects of the Content Enhancement Model in College Algebra

    ERIC Educational Resources Information Center

    VanCleave, Janet Milleret

    2010-01-01

    The purpose of this study was to investigate The Content Enhancement Model in the field of college algebra in a mid-western community college. The Content Enhancement Model is a teaching technique that teachers use to help students acquire the content information by helping them identify, organize, comprehend, and memorize material. This study…

  16. Optical linear algebra processors - Noise and error-source modeling

    NASA Technical Reports Server (NTRS)

    Casasent, D.; Ghosh, A.

    1985-01-01

    The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

  17. Cognitive Load and Modelling of an Algebra Problem

    ERIC Educational Resources Information Center

    Chinnappan, Mohan

    2010-01-01

    In the present study, I examine a modelling strategy as employed by a teacher in the context of an algebra lesson. The actions of this teacher suggest that a modelling approach will have a greater impact on enriching student learning if we do not lose sight of the need to manage associated cognitive loads that could either aid or hinder the…

  18. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Kreutz, Kenneth; Jain, Abhinandan

    1989-01-01

    A recently developed spatial operator algebra, useful for modeling, control, and trajectory design of manipulators is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus, the transition from an abstract problem formulation and solution to the detailed mechanizaton of specific algorithms is greatly simplified. The analytical formulation of the operator algebra, as well as its implementation in the Ada programming language are discussed.

  19. Algebraic approach to small-world network models

    NASA Astrophysics Data System (ADS)

    Rudolph-Lilith, Michelle; Muller, Lyle E.

    2014-01-01

    We introduce an analytic model for directed Watts-Strogatz small-world graphs and deduce an algebraic expression of its defining adjacency matrix. The latter is then used to calculate the small-world digraph's asymmetry index and clustering coefficient in an analytically exact fashion, valid nonasymptotically for all graph sizes. The proposed approach is general and can be applied to all algebraically well-defined graph-theoretical measures, thus allowing for an analytical investigation of finite-size small-world graphs.

  20. Generalization of Richardson-Gaudin models to rank-2 algebras

    SciTech Connect

    Errea, B; Lerma, S; Dukelsky, J; Dimitrova, S S; Pittel, S; Van Isacker, P; Gueorguiev, V G

    2006-07-20

    A generalization of Richardson-Gaudin models to the rank-2 SO(5) and SO(3,2) algebras is used to describe systems of two kinds of fermions or bosons interacting through a pairing force. They are applied to the proton-neutron neutron isovector pairing model and to the Interacting Boson Model 2, in the transition from vibration to gamma-soft nuclei, respectively. In both cases, the integrals of motion and their eigenvalues are obtained.

  1. Algebraic turbulence modeling for unstructured and adaptive meshes

    NASA Technical Reports Server (NTRS)

    Mavriplis, Dimitri J.

    1990-01-01

    An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.

  2. Highest weight representation for Sklyanin algebra sl(3)(u) with application to the Gaudin model

    SciTech Connect

    Burdik, C.; Navratil, O.

    2011-06-15

    We study the infinite-dimensional Sklyanin algebra sl(3)(u). Specifically we construct the highest weight representation for this algebra in an explicit form. Its application to the Gaudin model is mentioned.

  3. Boundary algebras and Kac modules for logarithmic minimal models

    NASA Astrophysics Data System (ADS)

    Morin-Duchesne, Alexi; Rasmussen, Jørgen; Ridout, David

    2015-10-01

    Virasoro Kac modules were originally introduced indirectly as representations whose characters arise in the continuum scaling limits of certain transfer matrices in logarithmic minimal models, described using Temperley-Lieb algebras. The lattice transfer operators include seams on the boundary that use Wenzl-Jones projectors. If the projectors are singular, the original prescription is to select a subspace of the Temperley-Lieb modules on which the action of the transfer operators is non-singular. However, this prescription does not, in general, yield representations of the Temperley-Lieb algebras and the Virasoro Kac modules have remained largely unidentified. Here, we introduce the appropriate algebraic framework for the lattice analysis as a quotient of the one-boundary Temperley-Lieb algebra. The corresponding standard modules are introduced and examined using invariant bilinear forms and their Gram determinants. The structures of the Virasoro Kac modules are inferred from these results and are found to be given by finitely generated submodules of Feigin-Fuchs modules. Additional evidence for this identification is obtained by comparing the formalism of lattice fusion with the fusion rules of the Virasoro Kac modules. These are obtained, at the character level, in complete generality by applying a Verlinde-like formula and, at the module level, in many explicit examples by applying the Nahm-Gaberdiel-Kausch fusion algorithm.

  4. Applications of algebraic image operators to model-based vision

    NASA Technical Reports Server (NTRS)

    Lerner, Bao-Ting; Morelli, Michael V.; Thomas, Hans J.

    1989-01-01

    A highly structured and compact algebraic representation of grey-level images is expanded. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, an innovative, efficient edge-detection scheme is devised. A robust method for linear feature extraction is developed by combining the techniques of a Hough transform and a line follower with this new edge detection scheme. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The feature extractor and model matcher are being incorporated into a distributed robot-control system.

  5. Integrability in three dimensions: Algebraic Bethe ansatz for anyonic models

    NASA Astrophysics Data System (ADS)

    Khachatryan, Sh.; Ferraz, A.; Klümper, A.; Sedrakyan, A.

    2015-10-01

    We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2 + 1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral parameters, in analogy with Yang-Baxter or tetrahedron equations. The basic ingredient of our models is the R-matrix, which describes the scattering of a pair of particles over another pair of particles, the quark-anti-quark (meson) scattering on another quark-anti-quark state. We show that the Kitaev model belongs to this class of models and its R-matrix fulfills well-defined equations for integrability.

  6. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Kreutz, K.; Jain, A.

    1989-01-01

    A spatial operator algebra for modeling the control and trajectory design of manipulation is discussed, with emphasis on its analytical formulation and implementation in the Ada programming language. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of the manipulator. Inversion is obtained using techniques of recursive filtering and smoothing. The operator alegbra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. Implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection, thus greatly simplifying the transition from an abstract problem formulation and solution to the detailed mechanization of a specific algorithm.

  7. Algebraic Turbulence-Chemistry Interaction Model

    NASA Technical Reports Server (NTRS)

    Norris, Andrew T.

    2012-01-01

    The results of a series of Perfectly Stirred Reactor (PSR) and Partially Stirred Reactor (PaSR) simulations are compared to each other over a wide range of operating conditions. It is found that the PaSR results can be simulated by a PSR solution with just an adjusted chemical reaction rate. A simple expression has been developed that gives the required change in reaction rate for a PSR solution to simulate the PaSR results. This expression is the basis of a simple turbulence-chemistry interaction model. The interaction model that has been developed is intended for use with simple one-step global reaction mechanisms and for steady-state flow simulations. Due to the simplicity of the model there is very little additional computational cost in adding it to existing CFD codes.

  8. An algebraic turbulence model for turbomachinery

    NASA Astrophysics Data System (ADS)

    Chima, Rodrick V.

    This paper presents a description and verification of RVC3D (rotor viscous code 3-D) which provides a Euler or Navier-Stokes analysis for steady three dimensional flows in turbomachinery. A motivation for this analysis is the calculation of turbine endwall heat transfer. Features of the turbulence model code include thin-layer formulation, Baldwin-Lomax or Cebeci-Smith turbulence models, node-centered finite difference formulation, and explicit four-stage Runge-Kutta time marching scheme. Results for flat plate, annular turbine cascade, turbine endwall heat transfer, and supersonic compressor blade test cases are presented.

  9. Applications Of Algebraic Image Operators To Model-Based Vision

    NASA Astrophysics Data System (ADS)

    Lerner, Bao-Ting; Morelli, Michael V.; Thomas, Hans J.

    1989-03-01

    This paper extends our previous research on a highly structured and compact algebraic representation of grey-level images. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, we have devised an innovative, efficient edge detection scheme.We have developed a robust method for linear feature extraction by combining the techniques of a Hough transform and a line follower with this new edge detection scheme. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The feature extractor and model matcher are being incorporated into a distributed robot control system. Model matching is accomplished using both top-down and bottom-up processing: a priori sensor and world model information are used to constrain the search of the image space for features, while extracted image information is used to update the model.

  10. A Frame Manipulation Algebra for ER Logical Stage Modelling

    NASA Astrophysics Data System (ADS)

    Furtado, Antonio L.; Casanova, Marco A.; Breitman, Karin K.; Barbosa, Simone D. J.

    The ER model is arguably today's most widely accepted basis for the conceptual specification of information systems. A further common practice is to use the Relational Model at an intermediate logical stage, in order to adequately prepare for physical implementation. Although the Relational Model still works well in contexts relying on standard databases, it imposes certain restrictions, not inherent in ER specifications, which make it less suitable in Web environments. This paper proposes frames as an alternative to move from ER specifications to logical stage modelling, and treats frames as an abstract data type equipped with a Frame Manipulation Algebra (FMA). It is argued that frames, with a long tradition in AI applications, are able to accommodate the irregularities of semi-structured data, and that frame-sets generalize relational tables, allowing to drop the strict homogeneity requirement. A prototype logic-programming tool has been developed to experiment with FMA. Examples are included to help describe the use of the operators.

  11. Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model

    NASA Astrophysics Data System (ADS)

    Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang

    2015-04-01

    In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.

  12. An Algebraic Spline Model of Molecular Surfaces for Energetic Computations

    PubMed Central

    Zhao, Wenqi; Bajaj, Chandrajit; Xu, Guoliang

    2009-01-01

    In this paper, we describe a new method to generate a smooth algebraic spline (AS) approximation of the molecular surface (MS) based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the PDB (Protein data bank). Our method first constructs a triangular prism scaffold covering the PDB structure, and then generates a piecewise polynomial F on the Bernstein-Bezier (BB) basis within the scaffold. An ASMS model of the molecular surface is extracted as the zero contours of F which is nearly C1 and has dual implicit and parametric representations. The dual representations allow us easily do the point sampling on the ASMS model and apply it to the accurate estimation of the integrals involved in the electrostatic solvation energy computations. Meanwhile comparing with the trivial piecewise linear surface model, fewer number of sampling points are needed for the ASMS, which effectively reduces the complexity of the energy estimation. PMID:21519111

  13. A Structural Model of Algebra Achievement: Computational Fluency and Spatial Visualisation as Mediators of the Effect of Working Memory on Algebra Achievement

    ERIC Educational Resources Information Center

    Tolar, Tammy Daun; Lederberg, Amy R.; Fletcher, Jack M.

    2009-01-01

    The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…

  14. Phases and phase transitions in the algebraic microscopic shell model

    NASA Astrophysics Data System (ADS)

    Georgieva, A. I.; Drumev, K. P.

    2016-01-01

    We explore the dynamical symmetries of the shell model number conserving algebra, which define three types of pairing and quadrupole phases, with the aim to obtain the prevailing phase or phase transition for the real nuclear systems in a single shell. This is achieved by establishing a correspondence between each of the pairing bases with the Elliott's SU(3) basis that describes collective rotation of nuclear systems. This allows for a complete classification of the basis states of different number of particles in all the limiting cases. The probability distribution of the SU(3) basis states within theirs corresponding pairing states is also obtained. The relative strengths of dynamically symmetric quadrupole-quadrupole interaction in respect to the isoscalar, isovector and total pairing interactions define a control parameter, which estimates the importance of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.

  15. An algebraic turbulence model for three-dimensional viscous flows

    NASA Technical Reports Server (NTRS)

    Chima, R. V.; Giel, P. W.; Boyle, R. J.

    1993-01-01

    An algebraic turbulence model is proposed for use with three-dimensional Navier-Stokes analyses. It incorporates features of both the Baldwin-Lomax and Cebeci-Smith models. The Baldwin-Lomax model uses the maximum of a function f(y) to determine length and velocity scales. An analysis of the Baldwin-Lomax model shows that f(y) can have a spurious maximum close to the wall, causing numerical problems and non-physical results. The proposed model uses integral relations to determine delta(*) u(sub e) and delta used in the Cebeci-Smith mode. It eliminates a constant in the Baldwin-Lomax model and determines the two remaining constants by comparison to the Cebeci-Smith formulation. Pressure gradient effects, a new wake model, and the implementation of these features in a three-dimensional Navier-Stokes code are also described. Results are shown for a flat plate boundary layer, an annular turbine cascade, and endwall heat transfer in a linear turbine cascade. The heat transfer results agree well with experimental data which shows large variations in endwall Stanton number contours with Reynolds number.

  16. Re"modeling" College Algebra: An Active Learning Approach

    ERIC Educational Resources Information Center

    Pinzon, D.; Pinzon, K.; Stackpole, M.

    2016-01-01

    In this paper, we discuss active learning in College Algebra at Georgia Gwinnett College. This approach has been used in more than 20 sections of College Algebra taught by the authors in the past four semesters. Students work in small, structured groups on guided inquiry activities after watching 15-20 minutes of videos before class. We discuss a…

  17. Analysis of DIRAC's behavior using model checking with process algebra

    NASA Astrophysics Data System (ADS)

    Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Graciani Diaz, Ricardo; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof

    2012-12-01

    DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.

  18. Dynamic Triggering Stress Modeling

    NASA Astrophysics Data System (ADS)

    Gonzalez-Huizar, H.; Velasco, A. A.

    2008-12-01

    It has been well established that static (permanent) stress changes can trigger nearby earthquakes, within a few fault lengths from the causative event, whereas triggering by dynamic (transient) stresses carried by seismic waves both nearby and at remote distances has not been as well documented nor understood. An analysis of the change in the local stress caused by the passing of surfaces waves is important for the understanding of this phenomenon. In this study, we modeled the change in the stress that the passing of Rayleigh and Loves waves causes on a fault plane of arbitrary orientation, and applied a Coulomb failure criteria to calculate the potential of these stress changes to trigger reverse, normal or strike-slip failure. We preliminarily test these model results with data from dynamically triggering earthquakes in the Australian Bowen Basin. In the Bowen region, the modeling predicts a maximum triggering potential for Rayleigh waves arriving perpendicularly to the strike of the reverse faults present in the region. The modeled potentials agree with our observations, and give us an understanding of the dynamic stress orientation needed to trigger different type of earthquakes.

  19. Nonlinear Reynolds stress models and the renormalization group

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Barton, J. Michael

    1990-01-01

    The renormalization group is applied to derive a nonlinear algebraic Reynolds stress model of anisotropic turbulence in which the Reynolds stresses are quadratic functions of the mean velocity gradients. The model results from a perturbation expansion that is truncated systematically at second order with subsequent terms contributing no further information. The resulting turbulence model applied to both low and high Reynolds number flows without requiring wall functions or ad hoc modifications of the equations. All constants are derived from the renormalization group procedure; no adjustable constants arise. The model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in noncircular ducts.

  20. Elliptic-blending second-moment turbulence closure using an algebraic anisotropic dissipation rate tensor model

    NASA Astrophysics Data System (ADS)

    Shin, Jong-Keun; Seo, Jeong-Sik; Choi, Young-Don

    2009-06-01

    This study describes the amendment of an algebraic anisotropic dissipation rate model (ADRM) and its application to various turbulent flows to test the model's performance. Modeling anisotropies for the turbulence dissipation rate is considered by an analysis of the exact transport equation for the dissipation rate tensor. The second-moment closure, which is based on the explicit amended ADRM, is proposed and it is closely linked to the elliptic-blending model that is used for the prediction of Reynolds stresses. To develop and calibrate the present elliptic-blending second-moment closure that uses the amended ADRM, firstly, the distributions of both the mean velocity and Reynolds stress are solved for flows in a fully developed non-rotating channel and a straight square duct. And then, the fully developed turbulent flows in a rotating channel and a rotating straight square duct are predicted to test the ability of the explicit amended ADRM that is combined with the rotation effect. The prediction results are directly compared with the DNS and the large-eddy simulation (LES) to assess the performance of the new model predictions and to show their reasonable agreement with the DNS and LES data for all the flow fields that are analyzed for the present study. This paper is a modified version of the original article from the Proceedings of the 5th International Symposium on Turbulence and Shear Flow Phenomena held in Munich, Germany on 27-29 August 2007.

  1. An abbreviated Reynolds stress turbulence model for airfoil flows

    NASA Technical Reports Server (NTRS)

    Gaffney, R. L., Jr.; Hassan, H. A.; Salas, M. D.

    1990-01-01

    An abbreviated Reynolds stress turbulence model is presented for solving turbulent flow over airfoils. The model consists of two partial differential equations, one for the Reynolds shear stress and the other for the turbulent kinetic energy. The normal stresses and the dissipation rate of turbulent kinetic energy are computed from algebraic relationships having the correct asymptotic near wall behavior. This allows the model to be integrated all the way to the wall without the use of wall functions. Results for a flat plate at zero angle of attack, a NACA 0012 airfoil and a RAE 2822 airfoil are presented.

  2. Clifford algebra-based spatio-temporal modelling and analysis for complex geo-simulation data

    NASA Astrophysics Data System (ADS)

    Luo, Wen; Yu, Zhaoyuan; Hu, Yong; Yuan, Linwang

    2013-10-01

    The spatio-temporal data simulating Ice-Land-Ocean interaction of Antarctic are used to demonstrate the Clifford algebra-based data model construction, spatio-temporal query and data analysis. The results suggest that Clifford algebra provides a powerful mathematical tool for the whole modelling and analysis chains for complex geo-simulation data. It can also help implement spatio-temporal analysis algorithms more clearly and simply.

  3. Algebraic multigrid preconditioner for the cardiac bidomain model.

    PubMed

    Plank, Gernot; Liebmann, Manfred; Weber dos Santos, Rodrigo; Vigmond, Edward J; Haase, Gundolf

    2007-04-01

    The bidomain equations are considered to be one of the most complete descriptions of the electrical activity in cardiac tissue, but large scale simulations, as resulting from discretization of an entire heart, remain a computational challenge due to the elliptic portion of the problem, the part associated with solving the extracellular potential. In such cases, the use of iterative solvers and parallel computing environments are mandatory to make parameter studies feasible. The preconditioned conjugate gradient (PCG) method is a standard choice for this problem. Although robust, its efficiency greatly depends on the choice of preconditioner. On structured grids, it has been demonstrated that a geometric multigrid preconditioner performs significantly better than an incomplete LU (ILU) preconditioner. However, unstructured grids are often preferred to better represent organ boundaries and allow for coarser discretization in the bath far from cardiac surfaces. Under these circumstances, algebraic multigrid (AMG) methods are advantageous since they compute coarser levels directly from the system matrix itself, thus avoiding the complexity of explicitly generating coarser, geometric grids. In this paper, the performance of an AMG preconditioner (BoomerAMG) is compared with that of the standard ILU preconditioner and a direct solver. BoomerAMG is used in two different ways, as a preconditioner and as a standalone solver. Two 3-D simulation examples modeling the induction of arrhythmias in rabbit ventricles were used to measure performance in both sequential and parallel simulations. It is shown that the AMG preconditioner is very well suited for the solution of the bidomain equation, being clearly superior to ILU preconditioning in all regards, with speedups by factors in the range 5.9-7.7. PMID:17405366

  4. Study of Transitions in the Atmospheric Boundary Layer Using Explicit Algebraic Turbulence Models

    NASA Astrophysics Data System (ADS)

    Lazeroms, W. M. J.; Svensson, G.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.

    2016-08-01

    We test a recently developed engineering turbulence model, a so-called explicit algebraic Reynolds-stress (EARS) model, in the context of the atmospheric boundary layer. First of all, we consider a stable boundary layer used as the well-known first test case from the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS1). The model is shown to agree well with data from large-eddy simulations (LES), and this agreement is significantly better than for a standard operational scheme with a prognostic equation for turbulent kinetic energy. Furthermore, we apply the model to a case with a (idealized) diurnal cycle and make a qualitative comparison with a simpler first-order model. Some interesting features of the model are highlighted, pertaining to its stronger foundation on physical principles. In particular, the use of more prognostic equations in the model is shown to give a more realistic dynamical behaviour. This qualitative study is the first step towards a more detailed comparison, for which additional LES data are needed.

  5. Excel Spreadsheets for Algebra: Improving Mental Modeling for Problem Solving

    ERIC Educational Resources Information Center

    Engerman, Jason; Rusek, Matthew; Clariana, Roy

    2014-01-01

    This experiment investigates the effectiveness of Excel spreadsheets in a high school algebra class. Students in the experiment group convincingly outperformed the control group on a post lesson assessment. The student responses, teacher observations involving Excel spreadsheet revealed that it operated as a mindtool, which formed the users'…

  6. From matrix models' topological expansion to topological string theories: counting surfaces with algebraic geometry

    NASA Astrophysics Data System (ADS)

    Orantin, N.

    2007-09-01

    The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links and extend them beyond the matrix models, following my work's evolution. First, I take care to define properly the hermitian 2 matrix model which gives rise to generating functions of discrete surfaces equipped with a spin structure. Then, I show how to compute all the terms in the topological expansion of any observable by using algebraic geometry tools. They are obtained as differential forms on an algebraic curve associated to the model: the spectral curve. In a second part, I show how to define such differentials on any algebraic curve even if it does not come from a matrix model. I then study their numerous symmetry properties under deformations of the algebraic curve. In particular, I show that these objects coincide with the topological expansion of the observable of a matrix model if the algebraic curve is the spectral curve of this model. Finally, I show that fine tuning the parameters ensure that these objects can be promoted to modular invariants and satisfy the holomorphic anomaly equation of the Kodaira-Spencer theory. This gives a new hint that the Dijkgraaf-Vafa conjecture is correct.

  7. Symmetric structure of field algebra of G-spin models determined by a normal subgroup

    SciTech Connect

    Xin, Qiaoling Jiang, Lining

    2014-09-15

    Let G be a finite group and H a normal subgroup. D(H; G) is the crossed product of C(H) and CG which is only a subalgebra of D(G), the double algebra of G. One can construct a C*-subalgebra F{sub H} of the field algebra F of G-spin models, so that F{sub H} is a D(H; G)-module algebra, whereas F is not. Then the observable algebra A{sub (H,G)} is obtained as the D(H; G)-invariant subalgebra of F{sub H}, and there exists a unique C*-representation of D(H; G) such that D(H; G) and A{sub (H,G)} are commutants with each other.

  8. Nonlinear Reynolds stress model for turbulent shear flows

    NASA Technical Reports Server (NTRS)

    Barton, J. Michael; Rubinstein, R.; Kirtley, K. R.

    1991-01-01

    A nonlinear algebraic Reynolds stress model, derived using the renormalization group, is applied to equilibrium homogeneous shear flow and fully developed flow in a square duct. The model, which is quadratically nonlinear in the velocity gradients, successfully captures the large-scale inhomogeneity and anisotropy of the flows studied. The ratios of normal stresses, as well as the actual magnitudes of the stresses are correctly predicted for equilibrium homogeneous shear flow. Reynolds normal stress anisotropy and attendant turbulence driven secondary flow are predicted for a square duct. Profiles of mean velocity and normal stresses are in good agreement with measurements. Very close to walls, agreement with measurements diminishes. The model has the benefit of containing no arbitrary constants; all values are determined directly from the theory. It seems that near wall behavior is influenced by more than the large scale anisotropy accommodated in the current model. More accurate near wall calculations may well require a model for anisotropic dissipation.

  9. A Comparison of Explicit Algebraic Turbulence Models and the Energy-Flux Budget (EFB) Closure in Gabls

    NASA Astrophysics Data System (ADS)

    Lazeroms, W. M.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.; Svensson, G.

    2014-12-01

    Turbulent flows with buoyancy effects occur in many situations, both in industry and in the atmosphere. It is challenging to correctly model such flows, especially in the case of stably stratified turbulence, where vertical motions are damped by buoyancy forces. For this purpose, we have derived a so-called explicit algebraic model for the Reynolds stresses and turbulent heat flux that gives accurate predictions in flows with buoyancy effects. Although inspired by turbulence models from engineering, the main aim of our work is to improve the parametrization of turbulence in the atmospheric boundary layer (ABL). Explicit algebraic turbulence models are a class of parametrizations that, on the one hand, are more advanced than standard eddy-diffusivity relations. On the other hand, they are signficantly easier to handle numerically than models that require the solution of the full flux-budget equations. To derive the algebraic model, we apply the assumption that transport terms of dimensionless fluxes can be neglected. Careful considerations of the algebra lead to a consistent formulation of the Reynolds stresses and turbulent heat flux, which is more general and robust than previous models of a similar kind. The model is shown to give good results compared to direct numerical simulations of engineering test cases, such as turbulent channel flow. Recent work has been aimed at testing the model in an atmospheric context. The first of these tests makes use of the GABLS1 case, in which a stable atmospheric boundary layer develops through a constant surface cooling rate. The model is able to give good predictions of this case compared to LES (see attached figure). Interestingly, the results are very close to the outcome of the recently developed Energy-Flux-Budget (EFB) closure by Zilitinkevich et al. (2013). A detailed discussion of the similarities and differences between these models will be given, which can give insight in the more general gap between engineering and

  10. Improving model-based diagnosis through algebraic analysis: The Petri net challenge

    SciTech Connect

    Portinale, L.

    1996-12-31

    The present paper describes the empirical evaluation of a linear algebra approach to model-based diagnosis, in case the behavioral model of the device under examination is described through a Petri net model. In particular, we show that algebraic analysis based on P-invariants of the net model, can significantly improve the performance of a model-based diagnostic system, while keeping the integrity of a general framework defined from a formal logical theory. A system called INVADS is described and experimental results, performed on a car fault domain and involving the comparison of different implementations of P-invariant based diagnosis, are then discussed.

  11. Performance of Renormalization Group Algebraic Turbulence Model on Boundary Layer Transition Simulation

    NASA Technical Reports Server (NTRS)

    Ahn, Kyung H.

    1994-01-01

    The RNG-based algebraic turbulence model, with a new method of solving the cubic equation and applying new length scales, is introduced. An analysis is made of the RNG length scale which was previously reported and the resulting eddy viscosity is compared with those from other algebraic turbulence models. Subsequently, a new length scale is introduced which actually uses the two previous RNG length scales in a systematic way to improve the model performance. The performance of the present RNG model is demonstrated by simulating the boundary layer flow over a flat plate and the flow over an airfoil.

  12. Algebraic turbulence models for the computation of two-dimensional high speed flows using unstructured grids

    NASA Technical Reports Server (NTRS)

    Rostand, Philippe

    1988-01-01

    The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practical way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.

  13. Designing Tasks for Math Modeling in College Algebra: A Critical Review

    ERIC Educational Resources Information Center

    Staats, Susan; Robertson, Douglas

    2014-01-01

    Over the last decade, the pedagogical approach known as mathematical modeling has received increased interest in college algebra classes in the United States. Math modeling assignments ask students to develop their own problem-solving tools to address non-routine, realistic scenarios. The open-ended quality of modeling activities creates dilemmas…

  14. AN ADA LINEAR ALGEBRA PACKAGE MODELED AFTER HAL/S

    NASA Technical Reports Server (NTRS)

    Klumpp, A. R.

    1994-01-01

    This package extends the Ada programming language to include linear algebra capabilities similar to those of the HAL/S programming language. The package is designed for avionics applications such as Space Station flight software. In addition to the HAL/S built-in functions, the package incorporates the quaternion functions used in the Shuttle and Galileo projects, and routines from LINPAK that solve systems of equations involving general square matrices. Language conventions in this package follow those of HAL/S to the maximum extent practical and minimize the effort required for writing new avionics software and translating existent software into Ada. Valid numeric types in this package include scalar, vector, matrix, and quaternion declarations. (Quaternions are fourcomponent vectors used in representing motion between two coordinate frames). Single precision and double precision floating point arithmetic is available in addition to the standard double precision integer manipulation. Infix operators are used instead of function calls to define dot products, cross products, quaternion products, and mixed scalar-vector, scalar-matrix, and vector-matrix products. The package contains two generic programs: one for floating point, and one for integer. The actual component type is passed as a formal parameter to the generic linear algebra package. The procedures for solving systems of linear equations defined by general matrices include GEFA, GECO, GESL, and GIDI. The HAL/S functions include ABVAL, UNIT, TRACE, DET, INVERSE, TRANSPOSE, GET, PUT, FETCH, PLACE, and IDENTITY. This package is written in Ada (Version 1.2) for batch execution and is machine independent. The linear algebra software depends on nothing outside the Ada language except for a call to a square root function for floating point scalars (such as SQRT in the DEC VAX MATHLIB library). This program was developed in 1989, and is a copyrighted work with all copyright vested in NASA.

  15. EPQ Models under Permissible Payment Delay: An Algebraic Approach

    NASA Astrophysics Data System (ADS)

    Huang, Yung-Fu; Hsu, Kuang-Hua

    The purpose of this research is to relax this assumption and establish the retailer`s inventory system as a cost minimization problem to determine the retailer`s optimal inventory cycle time. Then, an algebraic approach is provided and an easy-to-use theorem is derived to efficiently determine the optimal cycle time. From the final numerical examples, result implies that the retailer will order less quantity to take the benefits of the permissible delay in payments more frequently when the larger the differences between the unit selling price per item and the unit purchasing price per item.

  16. q-Deformation of symplectic dynamical symmetries in algebraic models of nuclear structure

    SciTech Connect

    Georgieva, A. I.; Sviratcheva, K. D.; Ivanov, M. I.; Draayer, J. P.

    2011-06-15

    With a view toward further nuclear structure applications of approaches based on quantum-deformed (or q-deformed) algebras, introduced to the authors by Yu.F. Smirnov, we construct a q analog of a boson realization of the symplectic noncompact sp(4, R) algebra together with a q analog of a fermion realization of the symplectic compact sp(4) algebra. The first study, on the q-deformed Sp(4,R) symmetry, is applied to the development of a q analog of the two-dimensional Interacting Boson Model with q-deformed SU(3) the underpinning dynamical symmetry group. An explicit realization in terms of q-tensor operators with respect to the standard su{sub q}(2) algebra is given. The group-subgroup structure of this framework yields the physical interpretation of the generators of the groups under consideration. The second symplectic algebra, the q-deformed sp(4), is applied to studying isovector pairing correlations in atomic nuclei. A specific q deformation of the sp(4) algebra is realized in terms of q deformed fermion creation and annihilation operators of the shell model. The generators of the algebra close on four distinct realizations of the u{sub q}(2) subalgebra. These reductions, which correspond to different types of pairing interactions, yield a complete classification of the basis states. An analysis of the role of the q deformation is based on a comparison of the results for energies of the lowest isovector-paired 0{sup +} states in the deformed and nondeformed cases.

  17. The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems

    ERIC Educational Resources Information Center

    Ng, Swee Fong; Lee, Kerry

    2009-01-01

    Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

  18. Development of an algebraic turbulence model for analysis of propulsion flows

    NASA Technical Reports Server (NTRS)

    Georgiadis, N. J.; Drummond, J. E.; Leonard, B. P.

    1992-01-01

    A simple turbulence model that will be applicable to propulsion flows having both wall bounded and unbounded regions was developed and installed within the PARC Navier-Stokes code by linking two existing algebraic turbulence models. The first is the Modified Mixing Length (MML) model which is optimized for wall bounded flows. The second is the Thomas model, the standard algebraic turbulence model in PARC which has been used to calculate both bounded and unbounded turbulent flows but was optimized for the latter. This paper discusses both models and the method employed to link them into one model (referred to as the MMLT model). The PARC code with the MMLT model was applied to two dimensional turbulent flows over a flat plate and over a backward facing step to validate and optimize the model and to compare its predictions to those obtained with the three turbulence models already available in PARC.

  19. A note on probabilistic models over strings: the linear algebra approach.

    PubMed

    Bouchard-Côté, Alexandre

    2013-12-01

    Probabilistic models over strings have played a key role in developing methods that take into consideration indels as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do inference on these probabilistic models, in which an important theoretical question is the complexity of computing the normalization of a class of string-valued graphical models. This question has been investigated using tools from combinatorics, dynamic programming, and graph theory, and has practical applications in Bayesian phylogenetics. In this work, we revisit this theoretical question from a different point of view, based on linear algebra. The main contribution is a set of results based on this linear algebra view that facilitate the analysis and design of inference algorithms on string-valued graphical models. As an illustration, we use this method to give a new elementary proof of a known result on the complexity of inference on the "TKF91" model, a well-known probabilistic model over strings. Compared to previous work, our proving method is easier to extend to other models, since it relies on a novel weak condition, triangular transducers, which is easy to establish in practice. The linear algebra view provides a concise way of describing transducer algorithms and their compositions, opens the possibility of transferring fast linear algebra libraries (for example, based on GPUs), as well as low rank matrix approximation methods, to string-valued inference problems. PMID:24135792

  20. Constructing and Modeling Algebraic Statements in the Multiplicative Domain: Investigating Fourth-Grade Student and Teacher Learning

    ERIC Educational Resources Information Center

    Grandau, Laura

    2013-01-01

    This study of fourth-grade students and teachers explores mathematics teaching and learning that focuses on discovering and modeling algebraic relationships. The study has two parts: an investigation of how students learn to construct algebraic statements and models for comparisons and measurement situations in the multiplicative domain, and an…

  1. Hyperbolic Kac-Moody algebras and chaos in Kaluza-Klein models

    NASA Astrophysics Data System (ADS)

    Damour, T.; Henneaux, M.; Julia, B.; Nicolai, H.

    2001-06-01

    Some time ago, it was found that the never-ending oscillatory chaotic behaviour discovered by Belinskii, Khalatnikov and Lifshitz (BKL) for the generic solution of the vacuum Einstein equations in the vicinity of a spacelike (``cosmological'') singularity disappears in spacetime dimensions /D≡d+1>10. Recently, a study of the generalization of the BKL chaotic behaviour to the superstring effective Lagrangians has revealed that this chaos is rooted in the structure of the fundamental Weyl chamber of some underlying hyperbolic Kac-Moody algebra. In this Letter we show that the same connection applies to pure gravity in any spacetime dimension />=4, where the relevant algebras are AEd. In this way the disappearance of chaos in pure gravity models in /D>=11 dimensions becomes linked to the fact that the Kac-Moody algebras AEd are no longer hyperbolic for /d>=10.

  2. Stress inoculation modeled in mice

    PubMed Central

    Brockhurst, J; Cheleuitte-Nieves, C; Buckmaster, C L; Schatzberg, A F; Lyons, D M

    2015-01-01

    Stress inoculation entails intermittent exposure to mildly stressful situations that present opportunities to learn, practice and improve coping in the context of exposure psychotherapies and resiliency training. Here we investigate behavioral and hormonal aspects of stress inoculation modeled in mice. Mice randomized to stress inoculation or a control treatment condition were assessed for corticosterone stress hormone responses and behavior during open-field, object-exploration and tail-suspension tests. Stress inoculation training sessions that acutely increased plasma levels of corticosterone diminished subsequent immobility as a measure of behavioral despair on tail-suspension tests. Stress inoculation also decreased subsequent freezing in the open field despite comparable levels of thigmotaxis in mice from both treatment conditions. Stress inoculation subsequently decreased novel-object exploration latencies and reduced corticosterone responses to repeated restraint. These results demonstrate that stress inoculation acutely stimulates glucocorticoid signaling and then enhances subsequent indications of active coping behavior in mice. Unlike mouse models that screen for the absence of vulnerability to stress or presence of traits that occur in resilient individuals, stress inoculation training reflects an experience-dependent learning-like process that resembles interventions designed to build resilience in humans. Mouse models of stress inoculation may provide novel insights for new preventive strategies or therapeutic treatments of human psychiatric disorders that are triggered and exacerbated by stressful life events. PMID:25826112

  3. CSOS models descending from chiral Potts models: degeneracy of the eigenspace and loop algebra

    NASA Astrophysics Data System (ADS)

    Au-Yang, Helen; Perk, Jacques H. H.

    2016-04-01

    Monodromy matrices of the {{\\boldsymbol{τ }}}2\\phantom{^{\\prime }} model are known to satisfy a Yang-Baxter equation with a six-vertex R-matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this R-matrix. We show the reason why in the superintegrable case the eigenspace is degenerate, but not in the general case. We then show that the eigenspaces of special CSOS models descending from the chiral Potts model are also degenerate. The existence of an L({{sl}}2) quantum loop algebra (or subalgebra) in these models is established by showing that the Serre relations hold for the generators. The highest weight polynomial (or the Drinfeld polynomial) of the representation is obtained by using the method of Baxter for the superintegrable case. As a byproduct, the eigenvalues of all such CSOS models are given explicitly.

  4. The Application of Boolean Algebra in Modelling of Leakage Condition of a Car Hydraulic Braking System

    NASA Astrophysics Data System (ADS)

    Idzikowski, A.; Salamon, S.

    2013-06-01

    A general characteristics of a car hydraulic braking system (CHBS) is presented in this publication. A graphical model of properties-component objects is developed for the above-mentioned system. Moreover, four mathematical models in terms of logic, the set theory and the Boolean algebra of Boolean functions are developed. The examination is ended with a general model of the CHBS for n - Boolean variables and the construction and mathematical-technical interpretation of this model is presented.

  5. Existence of standard models of conic fibrations over non-algebraically-closed fields

    SciTech Connect

    Avilov, A A

    2014-12-31

    We prove an analogue of Sarkisov's theorem on the existence of a standard model of a conic fibration over an algebraically closed field of characteristic different from two for three-dimensional conic fibrations over an arbitrary field of characteristic zero with an action of a finite group. Bibliography: 16 titles.

  6. The algebraic Bethe ansatz for scalar products in SU(3)-invariant integrable models

    NASA Astrophysics Data System (ADS)

    Belliard, S.; Pakuliak, S.; Ragoucy, E.; Slavnov, N. A.

    2012-10-01

    We study SU(3)-invariant integrable models solvable by a nested algebraic Bethe ansatz. We obtain a determinant representation for the particular case of scalar products of Bethe vectors. This representation can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.

  7. Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra

    ERIC Educational Resources Information Center

    Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

    2016-01-01

    Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…

  8. Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach

    NASA Astrophysics Data System (ADS)

    Pramanik, Souvik; Ghosh, Subir

    2013-10-01

    We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

  9. Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach

    NASA Astrophysics Data System (ADS)

    Pramanik, Souvik; Ghosh, Subir

    2013-08-01

    We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

  10. Teaching Algebra without Algebra

    ERIC Educational Resources Information Center

    Kalman, Richard S.

    2008-01-01

    Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…

  11. Interplay between the pairing and quadrupole interactions in the algebraic realization of the microscopic shell model

    NASA Astrophysics Data System (ADS)

    Drumev, Kalin; Georgieva, Ana

    2015-04-01

    We explore the algebraic realization of the Pairing-Plus-Quadrupole Model/PQM/ in the framework of the Elliott‘s SU(3) Model with the aim to obtain the complementary and competing features of the two interactions through the relation between the pairing and the SU(3) bases. First, we establish a correspondence between the SO(8) pairing basis and the Elliott's SU(3) basis. It is derived from their complementarity to the same LST coupling chain of the shell-model number-conserving algebra. The probability distribution of the SU(3) basis states within the SO(8) pairing states is also obtained and allows the investigation of the interplay between the pairing and quadrupole interactions in the Hamiltonian of the PQM, containing both of them as limiting cases. The description of some realistic N∼Z nuclear systems is investigated in a SU(3)-symmetry-adapted basis within a model space of one and two oscillator shells.

  12. Entanglement in a model for Hawking radiation: An application of quadratic algebras

    SciTech Connect

    Bambah, Bindu A.; Mukku, C.; Shreecharan, T.; Siva Prasad, K.

    2013-03-15

    Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: Black-Right-Pointing-Pointer We examine a toy model for Hawking radiation with quantized black hole modes. Black-Right-Pointing-Pointer We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. Black-Right-Pointing-Pointer We study the 'Dicke Superradiance' in black hole radiation using quadratically deformed su(2) algebras. Black-Right-Pointing-Pointer We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.

  13. A Model of Teacher Stress

    ERIC Educational Resources Information Center

    Kyriacou, Chris; Sutcliffe, John

    1978-01-01

    A definition and model of teacher stress is presented which conceptualizes teacher stress as a response syndrome (anger or depression) mediated by (1) an appraisal of threat to the teacher's self-esteem or well-being and (2) coping mechanisms activated to reduce the perceived threat. (Author)

  14. Intelligently deciphering unintelligible designs: algorithmic algebraic model checking in systems biology

    PubMed Central

    Mishra, Bud

    2009-01-01

    Systems biology, as a subject, has captured the imagination of both biologists and systems scientists alike. But what is it? This review provides one researcher's somewhat idiosyncratic view of the subject, but also aims to persuade young scientists to examine the possible evolution of this subject in a rich historical context. In particular, one may wish to read this review to envision a subject built out of a consilience of many interesting concepts from systems sciences, logic and model theory, and algebra, culminating in novel tools, techniques and theories that can reveal deep principles in biology—seen beyond mere observations. A particular focus in this review is on approaches embedded in an embryonic program, dubbed ‘algorithmic algebraic model checking’, and its powers and limitations. PMID:19364723

  15. Constraint algebra of general relativity from a formal continuum limit of canonical tensor model

    NASA Astrophysics Data System (ADS)

    Sasakura, Naoki; Sato, Yuki

    2015-10-01

    Canonical tensor model (CTM for short below) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. In the classical case, the constraints form a first-class constraint Poisson algebra with structures similar to that of the ADM formalism of general relativity, qualifying CTM as a possible discrete formalism for quantum gravity. In this paper, we show that, in a formal continuum limit, the constraint Poisson algebra of CTM with no cosmological constant exactly reproduces that of the ADM formalism. To this end, we obtain the expression of the metric tensor field in general relativity in terms of one of the dynamical rank-three tensors in CTM, and determine the correspondence between the constraints of CTM and those of the ADM formalism. On the other hand, the cosmological constant term of CTM seems to induce non-local dynamics, and is inconsistent with an assumption about locality of the continuum limit.

  16. Construction of linear models: A framework based on commutative Jordan algebras

    NASA Astrophysics Data System (ADS)

    Covas, R.; Carvalho, F.

    2016-06-01

    We show how to obtain the necessary structures for statistical analysis of the folllowing orthogonal models Y˜(1 μ +∑i Xiβi ,∑j σj2Mj+σ2I ) . These structures rely on the existence of Jordan algebras, in the sequence of [24], [8], [12], [9], [5] and [10].

  17. Closure of the algebra of constraints for a nonprojectable Horava model

    SciTech Connect

    Bellorin, Jorge; Restuccia, Alvaro

    2011-02-15

    We perform the Hamiltonian analysis for a nonprojectable Horava model whose potential is composed of R and R{sup 2} terms. We show that Dirac's algorithm for the preservation of the constraints can be done in a closed way, hence the algebra of constraints for this model is consistent. The model has an extra, odd, scalar mode whose decoupling limit can be seen in a linear-order perturbative analysis on weakly varying backgrounds. Although our results for this model point in favor of the consistency of the Horava theory, the validity of the full nonprojectable theory still remains unanswered.

  18. Modeling scalar dissipation and scalar variance in large eddy simulation: Algebraic and transport equation closures

    NASA Astrophysics Data System (ADS)

    Knudsen, E.; Richardson, E. S.; Doran, E. M.; Pitsch, H.; Chen, J. H.

    2012-05-01

    Scalar dissipation rates and subfilter scalar variances are important modeling parameters in large eddy simulations (LES) of reacting flows. Currently available models capture the general behavior of these parameters, but these models do not always perform with the degree of accuracy that is needed for predictive LES. Here, two direct numerical simulations (DNS) are used to analyze LES dissipation rate and variance models, and to propose a new model for the dissipation rate that is based on a transport equation. The first DNS that is considered is a non-premixed auto-igniting C2H4 jet flame simulation originally performed by Yoo et al. [Proc. Combust. Inst. 33, 1619-1627 (2011)], 10.1016/j.proci.2010.06.147. A LES of this case is run using algebraic models for the dissipation rate and subfilter variance. It is shown that the algebraic models fail to adequately reproduce the DNS results. This motivates the introduction of a transport equation model for the LES dissipation rate. Closure of the equation is addressed by formulating a new adapted dynamic approach. This approach borrows dynamically computed information from LES quantities that, unlike the dissipation rate, do not reside on the smallest flow length scales. The adapted dynamic approach is analyzed by considering a second DNS of scalar mixing in homogeneous isotropic turbulence. Data from this second DNS are used to confirm that the adapted dynamic approach successfully closes the dissipation rate equation over a wide range of LES filter widths. The first reacting jet case is then returned to and used to test the LES transport equation models. The transport equation model for the dissipation rate is shown to be more accurate than its algebraic counterpoint, and the dissipation rate is eliminated as a source of error in the transported variance model.

  19. A deformation of quantum affine algebra in squashed Wess-Zumino-Novikov-Witten models

    SciTech Connect

    Kawaguchi, Io; Yoshida, Kentaroh

    2014-06-01

    We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten models at the classical level. The target space is given by squashed S³ and the isometry is SU(2){sub L}×U(1){sub R}. It is known that SU(2){sub L} is enhanced to a couple of Yangians. We reveal here that an infinite-dimensional extension of U(1){sub R} is a deformation of quantum affine algebra, where a new deformation parameter is provided with the coefficient of the Wess-Zumino term. Then we consider the relation between the deformed quantum affine algebra and the pair of Yangians from the viewpoint of the left-right duality of monodromy matrices. The integrable structure is also discussed by computing the r/s-matrices that satisfy the extended classical Yang-Baxter equation. Finally, two degenerate limits are discussed.

  20. Teaching Algebra and Geometry Concepts by Modeling Telescope Optics

    ERIC Educational Resources Information Center

    Siegel, Lauren M.; Dickinson, Gail; Hooper, Eric J.; Daniels, Mark

    2008-01-01

    This article describes preparation and delivery of high school mathematics lessons that integrate mathematics and astronomy through The Geometer's Sketchpad models, traditional proof, and inquiry-based activities. The lessons were created by a University of Texas UTeach preservice teacher as part of a project-based field experience in which high…

  1. The addition of algebraic turbulence modeling to program LAURA

    NASA Technical Reports Server (NTRS)

    Cheatwood, F. Mcneil; Thompson, R. A.

    1993-01-01

    The Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) is modified to allow the calculation of turbulent flows. This is accomplished using the Cebeci-Smith and Baldwin-Lomax eddy-viscosity models in conjunction with the thin-layer Navier-Stokes options of the program. Turbulent calculations can be performed for both perfect-gas and equilibrium flows. However, a requirement of the models is that the flow be attached. It is seen that for slender bodies, adequate resolution of the boundary-layer gradients may require more cells in the normal direction than a laminar solution, even when grid stretching is employed. Results for axisymmetric and three-dimensional flows are presented. Comparison with experimental data and other numerical results reveal generally good agreement, except in the regions of detached flow.

  2. Algebraic approach to the projected deformed oscillator model

    NASA Astrophysics Data System (ADS)

    Asherova, R. M.; Smirnov, Yu. F.; Tolstoy, V. N.; Shustov, A. P.

    1981-03-01

    A new method of calculation in terms of the projected deformed oscillator model is proposed. The method involves expansion of its wave functions in terms of the wave functions of an isotropic oscillator potential. Only overlap integrals between projected wave functions and reduced probabilities B(E2) of E2 transitions are examined. B(E2) values are expressed as a series containing the corresponding values of the Elliott SU(3) scheme. The convergence of these expansions is shown to be fairly good. The expectation values of operators ( QQ) and ( QQQ), which characterize the effective internal non-sphericity and non-axiality of the nucleus, are also calculated and discussed.

  3. Extensions of algebraic image operators: An approach to model-based vision

    NASA Technical Reports Server (NTRS)

    Lerner, Bao-Ting; Morelli, Michael V.

    1990-01-01

    Researchers extend their previous research on a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, researchers devised an innovative, efficient edge detection scheme. An accurate method for deriving gradient component information from this edge detector is presented. Based upon this new edge detection system researchers developed a robust method for linear feature extraction by combining the techniques of a Hough transform and a line follower. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The algebraic operators are global operations which are easily reconfigured to operate on any size or shape region. This provides a natural platform from which to pursue dynamic scene analysis. A method for optimizing the linear feature extractor which capitalizes on the spatially reconfiguration nature of the edge detector/gradient component operator is discussed.

  4. Algebraic Construction of the Eigenstates for the Second Conserved Operator of the Quantum Calogero Model

    NASA Astrophysics Data System (ADS)

    Ujino, Hideaki; Wadati, Miki

    1996-03-01

    An algebraic construction of the eigenstates for the quantum Calogero modelis investigated. Extending the method of Lapointe and Vinet, weconstruct the eigenstates for the second conservedoperator of the quantum Calogero model.All the eigenstates can be factorizedinto symmetric polynomials which we call “Hi-Jack symmetric polynomials”and the ground state wave function.The conjectured formula for the eigenvalue of the second conserved operatoris confirmed.The Hi-Jack polynomials are strong candidates for the orthogonalbasis of the quantum Calogero model.

  5. A computer code for calculations in the algebraic collective model of the atomic nucleus

    NASA Astrophysics Data System (ADS)

    Welsh, T. A.; Rowe, D. J.

    2016-03-01

    A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1 , 1) × SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments qˆM and are at most quadratic in the corresponding conjugate momenta πˆN (- 2 ≤ M , N ≤ 2). The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators [ π ˆ ⊗ q ˆ ⊗ π ˆ ] 0 and [ π ˆ ⊗ π ˆ ] LM. The code is made efficient by use of an analytical expression for the needed SO(5)-reduced matrix elements, and use of SO(5) ⊃ SO(3)  Clebsch-Gordan coefficients obtained from precomputed data files provided with the code.

  6. Improvement of the second- and third-moment modeling of turbulence: A study of Reynolds-stress closure model

    NASA Technical Reports Server (NTRS)

    Amano, R. S.; Goel, P.

    1986-01-01

    Four parts of the Reynolds-stress closure modeling are reported: (1) improvement of the k and epsilon equaitons; (2) development of the third-moment transport equation; (3) formulation of the diffusion coefficient of the momentum equation by using the algebraic-stress model of turbulence; and (4) the application of the Reynolds-stress model to a heat exchanger problem. It was demonstrated that the third-moment transport model improved the prediction of the triple-velocity products in the recirculating and reattaching flow regions in comparison with the existing algebraic models for the triple-velocity products. Optimum values for empirical coefficients are obtained for the prediction of the backward-facing step flows. A functional expression is derived for the coefficient of the momentum diffusion by employing the algebraic-stress model. The second-moment closure is applied to a heat transfer problem. The computations for the flow in a corrugated-wall channel show that the second-moment closure improves the prediction of the heat transfer rates by 30% over the k - epsilon model.

  7. Thermoregulatory modeling for cold stress.

    PubMed

    Xu, Xiaojiang; Tikuisis, Peter

    2014-07-01

    Modeling for cold stress has generated a rich history of innovation, has exerted a catalytic influence on cold physiology research, and continues to impact human activity in cold environments. This overview begins with a brief summation of cold thermoregulatory model development followed by key principles that will continue to guide current and future model development. Different representations of the human body are discussed relative to the level of detail and prediction accuracy required. In addition to predictions of shivering and vasomotor responses to cold exposure, algorithms are presented for thermoregulatory mechanisms. Various avenues of heat exchange between the human body and a cold environment are reviewed. Applications of cold thermoregulatory modeling range from investigative interpretation of physiological observations to forecasting skin freezing times and hypothermia survival times. While these advances have been remarkable, the future of cold stress modeling is still faced with significant challenges that are summarized at the end of this overview. PMID:24944030

  8. Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

    NASA Astrophysics Data System (ADS)

    Cirilo António, N.; Manojlović, N.; Salom, I.

    2014-12-01

    We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.

  9. Modeling boyciana-fish-human interaction with partial differential algebraic equations.

    PubMed

    Jiang, Yushan; Zhang, Qingling; Wang, Haiyan

    2016-07-01

    Under the influence of human population distribution, the boyciana-fish ecological system is considered. First, the system can be described as a nonlinear partial differential algebraic equations system (PDAEs) with Neumann boundary conditions and ratio-dependent functional response. Second, we examine the system's persistence properties: the loacl stabilities of positive steady states, the absorbtion region and the global stability. And the proposed approach is illustrated by numerical simulation. Finally, by using the realistic data collected in the past fourteen years, the PDAEs parameter optimization model is built to predict the boyciana population. PMID:27155570

  10. Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions

    NASA Astrophysics Data System (ADS)

    Lavau, Sylvain; Samtleben, Henning; Strobl, Thomas

    2014-12-01

    We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six space-time dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge fields. We show that the algebraic consistency constraints governing this system permit to define a Lie 3-algebra, generalizing the structural Lie algebra of a standard Yang-Mills theory to the setting of a higher bundle. Reformulating the Lie 3-algebra in terms of a nilpotent degree 1 BRST-type operator Q, this higher bundle can be compactly described by means of a Q-bundle; its fiber is the shifted tangent of the Q-manifold corresponding to the Lie 3-algebra and its base the odd tangent bundle of space-time equipped with the de Rham differential. The generalized Bianchi identities can then be retrieved concisely from Q2 = 0, which encode all the essence of the structural identities. Gauge transformations are identified as vertical inner automorphisms of such a bundle, their algebra being determined from a Q-derived bracket.

  11. Algebraic turbulence models for the computation of two-dimensional high-speed flows using unstructured grids

    NASA Technical Reports Server (NTRS)

    Rostand, Philippe

    1989-01-01

    The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practial way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.

  12. Differential algebraic methods for space charge modeling and applications to the University of Maryland Electron Ring

    NASA Astrophysics Data System (ADS)

    Nissen, Edward W.

    2011-12-01

    The future of particle accelerators is moving towards the intensity frontier; the need to place more particles into a smaller space is a common requirement of nearly all applications of particle accelerators. Putting large numbers of particles in a small space means that the mutual repulsion of these charged particles becomes a significant factor, this effect is called space charge. In this work we develop a series of differential algebra based methods to simulate the effects of space charge in particle accelerators. These methods were used to model the University of Maryland Electron Ring, a small 3.8 meter diameter 10 KeV electron storage ring designed to observe the effects of space charge in a safe, cost effective manner. The methods developed here are designed to not only simulate the effects of space charge on the motions of the test particles in the system but to add their effects to the transfer map of the system. Once they have been added useful information about the beam, such as tune shifts and chromaticities, can be extracted directly from the map. In order to make the simulation self consistent, the statistical moments of the distribution are used to create a self consistent Taylor series representing the distribution function, which is combined with pre-stored integrals solved using a Duffy transformation to find the potential. This method can not only find the map of the system, but also advance the particles under most conditions. For conditions where it cannot be used to accurately advance the particles a differential algebra based fast multipole method is implemented. By using differential algebras to create local expansions, noticeable time savings are found.

  13. Realizable Closure Model for the Reynolds Stress in Rotating Frames

    NASA Astrophysics Data System (ADS)

    Petty, Charles; Benard, Andre

    2015-11-01

    The Reynolds-averaged Navier-Stokes equation for constant property Newtonian fluids is unclosed due to the explicit appearance of the normalized Reynolds stress and the turbulent kinetic energy. A non-negative algebraic mapping of the normalized Reynolds stress into itself provides a practical closure for a wide class of flows. Unlike eddy viscosity closure models, the theory predict the redistribution of the turbulent kinetic energy among the three components of the fluctuating velocity field for statistically stationary spanwise rotating channel flows as well as the Coriolis re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity field in rotating homogeneous decay. The results partially support the conjecture that the index-of-refraction of the troposphere is anisotropic at all scales.

  14. Multiobjective algebraic synthesis of neural control systems by implicit model following.

    PubMed

    Ferrari, Silvia

    2009-03-01

    The advantages brought about by using classical linear control theory in conjunction with neural approximators have long been recognized in the literature. In particular, using linear controllers to obtain the starting neural control design has been shown to be a key step for the successful development and implementation of adaptive-critic neural controllers. Despite their adaptive capabilities, neural controllers are often criticized for not providing the same performance and stability guarantees as classical linear designs. Therefore, this paper develops an algebraic synthesis procedure for designing dynamic output-feedback neural controllers that are closed-loop stable and meet the same performance objectives as any classical linear design. The performance synthesis problem is addressed by deriving implicit model-following algebraic relationships between model matrices, obtained from the classical design, and the neural control parameters. Additional linear matrix inequalities (LMIs) conditions for closed-loop exponential stability of the neural controller are derived using existing integral quadratic constraints (IQCs) for operators with repeated slope-restricted nonlinearities. The approach is demonstrated by designing a recurrent neural network controller for a highly maneuverable tailfin-controlled missile that meets multiple design objectives, including pole placement for transient tuning, H(infinity) and H(2) performance in the presence of parameter uncertainty, and command-input tracking. PMID:19203887

  15. Algebraic surface design and finite element meshes

    NASA Technical Reports Server (NTRS)

    Bajaj, Chandrajit L.

    1992-01-01

    Some of the techniques are summarized which are used in constructing C sup 0 and C sup 1 continuous meshes of low degree, implicitly defined, algebraic surface patches in three dimensional space. These meshes of low degree algebraic surface patches are used to construct accurate computer models of physical objects. These meshes are also used in the finite element simulation of physical phenomena (e.g., heat dissipation, stress/strain distributions, fluid flow characteristics) required in the computer prototyping of both the manufacturability and functionality of the geometric design.

  16. Early Childhood Teachers' Professional Learning in Early Algebraic Thinking: A Model that Supports New Knowledge and Pedagogy

    ERIC Educational Resources Information Center

    Warren, Elizabeth

    2009-01-01

    The implementation of a new mathematics syllabus in the elementary context is problematic, especially if it contains a new content area. A professional development model, Transformative Teaching in the Early Years Mathematics (TTEYM) was specifically developed to support the implementation of the new Patterns and Algebra strand. The model was…

  17. Comparing Cognitive Models of Domain Mastery and Task Performance in Algebra: Validity Evidence for a State Assessment

    ERIC Educational Resources Information Center

    Warner, Zachary B.

    2013-01-01

    This study compared an expert-based cognitive model of domain mastery with student-based cognitive models of task performance for Integrated Algebra. Interpretations of student test results are limited by experts' hypotheses of how students interact with the items. In reality, the cognitive processes that students use to solve each item may be…

  18. Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

    SciTech Connect

    Lin, Paul T. Shadid, John N.; Sala, Marzio; Tuminaro, Raymond S.; Hennigan, Gary L.; Hoekstra, Robert J.

    2009-09-20

    In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection-diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system is obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 10{sup 8} unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system.

  19. Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

    NASA Astrophysics Data System (ADS)

    Lin, Paul T.; Shadid, John N.; Sala, Marzio; Tuminaro, Raymond S.; Hennigan, Gary L.; Hoekstra, Robert J.

    2009-09-01

    In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection-diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system is obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 108 unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system.

  20. Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model

    NASA Astrophysics Data System (ADS)

    Chamseddine, Ali H.; Connes, Alain

    2007-11-01

    The purpose of this Letter is to remove the arbitrariness of the ad hoc choice of the algebra and its representation in the noncommutative approach to the standard model, which was begging for a conceptual explanation. We assume as before that space-time is the product of a four-dimensional manifold by a finite noncommmutative space F. The spectral action is the pure gravitational action for the product space. To remove the above arbitrariness, we classify the irreducible geometries F consistent with imposing reality and chiral conditions on spinors, to avoid the fermion doubling problem, which amounts to have total dimension 10 (in the K-theoretic sense). It gives, almost uniquely, the standard model with all its details, predicting the number of fermions per generation to be 16, their representations and the Higgs breaking mechanism, with very little input.

  1. Structure of 23Al from a multi-channel algebraic scattering model based on mirror symmetry

    NASA Astrophysics Data System (ADS)

    Fraser, P. R.; Kadyrov, A. S.; Massen-Hane, K.; Amos, K.; Canton, L.; Karataglidis, S.; van der Knijff, D.; Bray, I.

    2016-09-01

    The proton-rich nucleus 23Al has a ground state just 123 keV below the one-proton emission threshold, and as a result comparatively little is known experimentally about its properties, as with many such nuclei. Theoretical investigations have tended to model exclusively the ground and first one to three excited states known. In this paper, we theoretically model most of the known spectrum, and predict what states may as yet be unobserved. We use the multichannel algebraic scattering method to describe states as resonances of a valence proton coupled to a 22Mg rotor core. Six states with low-excitation energies and defined {J}π are matched, and we make the first prediction of the properties of four others and propound the possible existence of several more.

  2. Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model

    SciTech Connect

    Chamseddine, Ali H.; Connes, Alain

    2007-11-09

    The purpose of this Letter is to remove the arbitrariness of the ad hoc choice of the algebra and its representation in the noncommutative approach to the standard model, which was begging for a conceptual explanation. We assume as before that space-time is the product of a four-dimensional manifold by a finite noncommmutative space F. The spectral action is the pure gravitational action for the product space. To remove the above arbitrariness, we classify the irreducible geometries F consistent with imposing reality and chiral conditions on spinors, to avoid the fermion doubling problem, which amounts to have total dimension 10 (in the K-theoretic sense). It gives, almost uniquely, the standard model with all its details, predicting the number of fermions per generation to be 16, their representations and the Higgs breaking mechanism, with very little input.

  3. Algebraic geometry methods associated to the one-dimensional Hubbard model

    NASA Astrophysics Data System (ADS)

    Martins, M. J.

    2016-06-01

    In this paper we study the covering vertex model of the one-dimensional Hubbard Hamiltonian constructed by Shastry in the realm of algebraic geometry. We show that the Lax operator sits in a genus one curve which is not isomorphic but only isogenous to the curve suitable for the AdS/CFT context. We provide an uniformization of the Lax operator in terms of ratios of theta functions allowing us to establish relativistic like properties such as crossing and unitarity. We show that the respective R-matrix weights lie on an Abelian surface being birational to the product of two elliptic curves with distinct J-invariants. One of the curves is isomorphic to that of the Lax operator but the other is solely fourfold isogenous. These results clarify the reason the R-matrix can not be written using only difference of spectral parameters of the Lax operator.

  4. Validating Cognitive Models of Task Performance in Algebra on the SAT®. Research Report No. 2009-3

    ERIC Educational Resources Information Center

    Gierl, Mark J.; Leighton, Jacqueline P.; Wang, Changjiang; Zhou, Jiawen; Gokiert, Rebecca; Tan, Adele

    2009-01-01

    The purpose of the study is to present research focused on validating the four algebra cognitive models in Gierl, Wang, et al., using student response data collected with protocol analysis methods to evaluate the knowledge structures and processing skills used by a sample of SAT test takers.

  5. Stress induced obesity: lessons from rodent models of stress

    PubMed Central

    Patterson, Zachary R.; Abizaid, Alfonso

    2013-01-01

    Stress was once defined as the non-specific result of the body to any demand or challenge to homeostasis. A more current view of stress is the behavioral and physiological responses generated in the face of, or in anticipation of, a perceived threat. The stress response involves activation of the sympathetic nervous system and recruitment of the hypothalamic-pituitary-adrenal (HPA) axis. When an organism encounters a stressor (social, physical, etc.), these endogenous stress systems are stimulated in order to generate a fight-or-flight response, and manage the stressful situation. As such, an organism is forced to liberate energy resources in attempt to meet the energetic demands posed by the stressor. A change in the energy homeostatic balance is thus required to exploit an appropriate resource and deliver useable energy to the target muscles and tissues involved in the stress response. Acutely, this change in energy homeostasis and the liberation of energy is considered advantageous, as it is required for the survival of the organism. However, when an organism is subjected to a prolonged stressor, as is the case during chronic stress, a continuous irregularity in energy homeostasis is considered detrimental and may lead to the development of metabolic disturbances such as cardiovascular disease, type II diabetes mellitus and obesity. This concept has been studied extensively using animal models, and the neurobiological underpinnings of stress induced metabolic disorders are beginning to surface. However, different animal models of stress continue to produce divergent metabolic phenotypes wherein some animals become anorexic and lose body mass while others increase food intake and body mass and become vulnerable to the development of metabolic disturbances. It remains unclear exactly what factors associated with stress models can be used to predict the metabolic outcome of the organism. This review will explore a variety of rodent stress models and discuss the

  6. The Competent Use of the Analytic Method in the Solution of Algebraic Word Problems: A Didactical Model Based on a Numerical Approach with Junior High Students

    ERIC Educational Resources Information Center

    Rubio, Guillermo; del Valle, Rafael

    2004-01-01

    The study proves that a didactical model based in a method to solve word problems of increasing complexity which uses a numerical approach was essential to develop the analytical ability and the competent use of the algebraic language with students from three different performance levels in elementary algebra. It is shown that before using the…

  7. Virasoro algebra in the KN algebra; Bosonic string with fermionic ghosts on Riemann surfaces

    SciTech Connect

    Koibuchi, H. )

    1991-10-10

    In this paper the bosonic string model with fermionic ghosts is considered in the framework of the KN algebra. The authors' attentions are paid to representations of KN algebra and a Clifford algebra of the ghosts. The authors show that a Virasoro-like algebra is obtained from KN algebra when KN algebra has certain antilinear anti-involution, and that it is isomorphic to the usual Virasoro algebra. The authors show that there is an expected relation between a central charge of this Virasoro-like algebra and an anomaly of the combined system.

  8. Earth Algebra.

    ERIC Educational Resources Information Center

    Schaufele, Christopher; Zumoff, Nancy

    Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…

  9. Kiddie Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2009-01-01

    As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…

  10. Turbulence modeling of compound open-channel flows with and without vegetation on the floodplain using the Reynolds stress model

    NASA Astrophysics Data System (ADS)

    Kang, Hyeongsik; Choi, Sung-Uk

    2006-11-01

    A Reynolds stress model for the numerical simulation of compound open-channel flows with vegetation on the floodplain is described. The Reynolds stress model consists of various sub-models such as Speziale et al.'s model, Mellor and Herring's model, and Rotta's model for the pressure-strain correlation term, the turbulent diffusion term, and the dissipation term, respectively. For validation of the model, plain compound open-channel flows are simulated. The computed results were compared with measured data by [Tominaga A, Nezu I. Turbulent structure in compound open-channel flows. J Hydraul Eng, ASCE 1991;117(1):21-41] and the results show that the Reynolds stress model successfully simulates the mean flow and turbulence structure of plain compound channel flows. The model was then applied to compound open-channel flows with vegetated floodplains. Good agreement between the simulated results and data from an algebraic stress model by [Naot D, Nezu I, Nakagawa H. Hydrodynamic behavior of partly vegetated open channels. J Hydraul Eng, ASCE 1996;122(11):625-33] was found. However, it was shown that the RSM is capable of predicting the velocity dip and lateral shift in the maximum streamwise velocity, which were not observed in the data from algebraic stress modeling. Finally, a depth-averaged analysis of the streamwise momentum equation was performed to investigate the lateral momentum transfer in compound channel flows with vegetated floodplains. Compared with components by the secondary currents and Reynolds stress, the drag force due to the presence of vegetation appears to be a factor in reducing the bottom shear stress in both main channel and floodplain.

  11. A stress index model for balloon design

    NASA Technical Reports Server (NTRS)

    Smith, I. S.

    1987-01-01

    A NASA stress index model, SINDEX, is discussed which establishes the relative stress magnitudes along a balloon gore as a function of altitude. Application of the model to a data base of over 550 ballon flights demonstrates the effectiveness of the method. The results show a strong correlation between stress levels, failure rates, and the point of maximum stress coinciding with the observed failure locations. It is suggested that the model may be used during the balloon design process to lower the levels of stress in the balloon.

  12. Coherent States and Schwinger Models for Pseudo Generalization of the Heisenberg Algebra

    NASA Astrophysics Data System (ADS)

    Fakhri, H.; Mojaveri, B.; Dehghani, A.

    We show that the non-Hermitian Hamiltonians of the simple harmonic oscillator with {PT} and {C} symmetries involve a pseudo generalization of the Heisenberg algebra via two pairs of creation and annihilation operators which are {T}-pseudo-Hermiticity and {P}-anti-pseudo-Hermiticity of each other. The non-unitary Heisenberg algebra is represented by each of the pair of the operators in two different ways. Consequently, the coherent and the squeezed coherent states are calculated in two different approaches. Moreover, it is shown that the approach of Schwinger to construct the su(2), su(1, 1) and sp(4, ℝ) unitary algebras is promoted so that unitary algebras with more linearly dependent number of generators are made.

  13. Transient thermal stress recovery for structural models

    NASA Technical Reports Server (NTRS)

    Walls, William

    1992-01-01

    A method for computing transient thermal stress vectors from temperature vectors is described. The three step procedure involves the use of NASTRAN to generate an influence coefficient matrix which relates temperatures to stresses in the structural model. The transient thermal stresses are then recovered and sorted for maximum and minimum values. Verification data for the procedure is also provided.

  14. Application of a Reynolds Stress turbulence model to a supersonic hydrogen-air diffusion flame

    NASA Technical Reports Server (NTRS)

    Chandrasekhar, R.; Tiwari, S. N.

    1991-01-01

    A second-order differential Reynolds Stress turbulence model has been applied to the Favre-averaged Navier-Stokes equations for the study of supersonic flows undergoing hydrogen-air chemical reactions. An assumed Beta Probability Density Function is applied to account for the chemical source terms in the conservation equations. An algebraic Reynolds Flux model is used for the fluctuating density-velocity as well as the species mass fraction-velocity correlations. The variances of temperature and species fluctuations are also modelled using an algebraic flux technique. A seven-species, seven-reaction finite rate chemistry mechanism is used to simulate the combustion processes. The resulting formulation is validated by comparison with experimental data on reacting supersonic axisymmetric jets. Results obtained for specific conditions indicate that the effect of chemical reaction on the turbulence is significant.

  15. Stress analysis of Pathfinder-2 models

    NASA Technical Reports Server (NTRS)

    Mehrotra, S. C.; Mills, C. T. L.

    1984-01-01

    Stress analysis of the Pathfinder 2 fighter model was performed to determine a method for leading- and trailing-edge attachment that gives acceptable stress levels. Structural modeling of the wing was done using the finite element code SPAR. For the models studied, one ordinary lap joint was found to be satisfactory for the leading-edge flap, however, the alternating surface segmented lap joint method fo attachment was necessary for the trailing-edge flap to obtain acceptable stress levels.

  16. Image Sensor Model Using Geometric Algebra: From Calibration to Motion Estimation

    NASA Astrophysics Data System (ADS)

    Debaecker, Thibaud; Benosman, Ryad; Ieng, Sio H.

    In computer vision image sensors have universally been defined as the nonparametric association of projection rays in the 3D world to pixels in the images. If the pixels' physical topology can be often neglected in the case of perspective cameras, this approximation is no longer valid in the case of variant scale sensors, which are now widely used in robotics. Neglecting the nonnull pixel area and then the pixel volumic field of view implies that geometric reconstruction problems are solved by minimizing a cost function that combines the reprojection errors in the 2D images. This paper provides a complete and realistic cone-pixel camera model that equally fits constant or variant scale resolution together with a protocol to calibrate such a sensor. The proposed model involves a new characterization of pixel correspondences with 3D-cone intersections computed using convex hull and twists in Conformal Geometric Algebra. Simulated experiments show that standard methods and especially Bundle Adjustment are sometimes unable to reach the correct motion, because of their ray-pixel approach and the choice of reprojection error as a cost function which does not particularly fit the physical reality. This problem can be solved using a nonprojective cone intersection cost function as introduced below.

  17. Modifications of the law of the wall and algebraic turbulence modelling for separated boundary layers

    NASA Technical Reports Server (NTRS)

    Baldwin, B. S.; Maccormack, R. W.

    1976-01-01

    Various modifications of the conventional algebraic eddy viscosity turbulence model are investigated for application to separated flows. Friction velocity is defined in a way that avoids singular behavior at separation and reattachment but reverts to the conventional definition for flows with small pressure gradients. This leads to a modified law of the wall for separated flows. The effect on the calculated flow field of changes in the model that affect the eddy viscosity at various distances from the wall are determined by (1) switching from Prandtl's form to an inner layer formula due to Clauser at various distances from the wall, (2) varying the constant in the Van Driest damping factor, (3) using Clauser's inner layer formula all the way to the wall, and (4) applying a relaxation procedure in the evaluation of the constant in Clauser's inner layer formula. Numerical solutions of the compressible Navier-Stokes equations are used to determine the effects of the modifications. Experimental results from shock-induced separated flows at Mach numbers 2.93 and 8.45 are used for comparison. For these cases improved predictions of wall pressure distribution and positions of separation and reattachment are obtained from the relaxation version of the Clauser inner layer eddy viscosity formula.

  18. Super-Lie n-algebra extensions, higher WZW models and super-p-branes with tensor multiplet fields

    NASA Astrophysics Data System (ADS)

    Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs

    2015-12-01

    We formalize higher-dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature). We show generally how the intersection laws for such higher WZW-type σ-model branes (open brane ending on background brane) are encoded precisely in (super-)L∞-extension theory and how the resulting "extended (super-)space-times" formalize spacetimes containing σ-model brane condensates. As an application we prove in Lie n-algebra homotopy theory that the complete super-p-brane spectrum of superstring/M-theory is realized this way, including the pure σ-model branes (the "old brane scan") but also the branes with tensor multiplet worldvolume fields, notably the D-branes and the M5-brane. For instance the degree-0 piece of the higher symmetry algebra of 11-dimensional (11D) spacetime with an M2-brane condensate turns out to be the "M-theory super-Lie algebra". We also observe that in this formulation there is a simple formal proof of the fact that type IIA spacetime with a D0-brane condensate is the 11D sugra/M-theory spacetime, and of (prequantum) S-duality for type IIB string theory. Finally we give the non-perturbative description of all this by higher WZW-type σ-models on higher super-orbispaces with higher WZW terms in stacky differential cohomology.

  19. Kinematically consistent models of viscoelastic stress evolution

    NASA Astrophysics Data System (ADS)

    DeVries, Phoebe M. R.; Meade, Brendan J.

    2016-05-01

    Following large earthquakes, coseismic stresses at the base of the seismogenic zone may induce rapid viscoelastic deformation in the lower crust and upper mantle. As stresses diffuse away from the primary slip surface in these lower layers, the magnitudes of stress at distant locations (>1 fault length away) may slowly increase. This stress relaxation process has been used to explain delayed earthquake triggering sequences like the 1992 Mw = 7.3 Landers and 1999 Mw = 7.1 Hector Mine earthquakes in California. However, a conceptual difficulty associated with these models is that the magnitudes of stresses asymptote to constant values over long time scales. This effect introduces persistent perturbations to the total stress field over many earthquake cycles. Here we present a kinematically consistent viscoelastic stress transfer model where the total perturbation to the stress field at the end of the earthquake cycle is zero everywhere. With kinematically consistent models, hypotheses about the potential likelihood of viscoelastically triggered earthquakes may be based on the timing of stress maxima, rather than on any arbitrary or empirically constrained stress thresholds. Based on these models, we infer that earthquakes triggered by viscoelastic earthquake cycle effects may be most likely to occur during the first 50% of the earthquake cycle regardless of the assumed long-term and transient viscosities.

  20. A meteorologically driven maize stress indicator model

    NASA Technical Reports Server (NTRS)

    Taylor, T. W.; Ravet, F. W. (Principal Investigator)

    1981-01-01

    A maize soil moisture and temperature stress model is described which was developed to serve as a meteorological data filter to alert commodity analysts to potential stress conditions in the major maize-producing areas of the world. The model also identifies optimum climatic conditions and planting/harvest problems associated with poor tractability.

  1. A new model for algebraic Rossby solitary waves in rotation fluid and its solution

    NASA Astrophysics Data System (ADS)

    Chen, Yao-Deng; Yang, Hong-Wei; Gao, Yu-Fang; Yin, Bao-Shu; Feng, Xing-Ru

    2015-09-01

    A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space. Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves, the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves, the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon. Project supported by the Shandong Provincial Key Laboratory of Marine Ecology and Environment and Disaster Prevention and Mitigation Project, China (Grant No. 2012010), the National Natural Science Foundation of China (Grant Nos. 41205082 and 41476019), the Special Funds for Theoretical Physics of the National Natural Science Foundation of China (Grant No. 11447205), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China.

  2. Differential rotation and turbulent convection: A new Reynolds stress model and comparison with solar data

    NASA Technical Reports Server (NTRS)

    Canuto, V. M.; Minotti, F. O.; Schilling, O.

    1994-01-01

    In most hydrodynamic cases, the existence of a turbulent flow superimposed on a mean flow is caused by a shear instability in the latter. Boussinesq suggested the first model for the turbulent Reynolds stresses bar-(u(sub i)u(sub j)) in which the mean shear S(sub ij) is the cause (or source) of turbulence represented by the stress bar-(u(sub i)u(sub j)). In the case of solar differential rotation, exactly the reverse physical process occurs: turbulence (which must pre-exist) generates a mean flow which manifests itself in the form of differential rotation. Thus, the Boussinesq model is wholly inadequate because in the solar case, cause and effect are reversed. Since the Boussinesq model is inadequate, one needs an alternative model for the Reynolds stresses. We present a new dynamical model for the Reynolds stresses, convective fluxes, turbulent kinetic energy, and temperature fluctuations. The complete model requires the solution of 11 differential equations. We then introduce a set of simplifying assumptions which reduce the full dynamical model to a set of algebraic Reynolds stress models. We explicitly solve one of these models that entails only one differential equation. The overall agreement with the data is obtained with a model that is neither phenomenological nor one that requires a full numerical simulation, since it is algebraic in nature. The new model can play an important role in understanding the complex physics underlying the interplay between solar differential rotation and convection, as many physical processes can naturally be incorporated into the model.

  3. Modeling Residual Stresses in Ceramic Plates

    SciTech Connect

    Cantavella, V.; Moreno, A.; Mezquita, A.; Reig, Y.

    2008-02-15

    The generation of residual stresses during cooling of layered ceramic plates has been modeled. Each plate comprises a body and two thin layers (engobe and glaze). The model takes into account two types of stresses: thermal stresses, resulting from temperature gradients inside the plate during cooling, and the stresses produced by the mismatch of the coefficient of thermal expansion (CTE) of the layers. The body has been simulated using a linear viscoelastic constitutive equation. The engobe and the glaze layer have been considered as elastic solids below a certain temperature (setting temperature: T{sub a}). Above T{sub a} these two layers have no mechanical influence on the body.

  4. Modeling Residual Stresses in Ceramic Plates

    NASA Astrophysics Data System (ADS)

    Cantavella, V.; Moreno, A.; Mezquita, A.; Reig, Y.

    2008-02-01

    The generation of residual stresses during cooling of layered ceramic plates has been modeled. Each plate comprises a body and two thin layers (engobe and glaze). The model takes into account two types of stresses: thermal stresses, resulting from temperature gradients inside the plate during cooling, and the stresses produced by the mismatch of the coefficient of thermal expansion (CTE) of the layers. The body has been simulated using a linear viscoelastic constitutive equation. The engobe and the glaze layer have been considered as elastic solids below a certain temperature (setting temperature: Ta). Above Ta these two layers have no mechanical influence on the body.

  5. Solving multi-customer FPR model with quality assurance and discontinuous deliveries using a two-phase algebraic approach.

    PubMed

    Chiu, Yuan-Shyi Peter; Chou, Chung-Li; Chang, Huei-Hsin; Chiu, Singa Wang

    2016-01-01

    A multi-customer finite production rate (FPR) model with quality assurance and discontinuous delivery policy was investigated in a recent paper (Chiu et al. in J Appl Res Technol 12(1):5-13, 2014) using differential calculus approach. This study employs mathematical modeling along with a two-phase algebraic method to resolve such a specific multi-customer FPR model. As a result, the optimal replenishment lot size and number of shipments can be derived without using the differential calculus. Such a straightforward method may assist practitioners who with insufficient knowledge of calculus in learning and managing the real multi-customer FPR systems more effectively. PMID:27186457

  6. Magnetic resonance Spectroscopy with Linear Algebraic Modeling (SLAM) for higher speed and sensitivity

    NASA Astrophysics Data System (ADS)

    Zhang, Yi; Gabr, Refaat E.; Schär, Michael; Weiss, Robert G.; Bottomley, Paul A.

    2012-05-01

    Speed and signal-to-noise ratio (SNR) are critical for localized magnetic resonance spectroscopy (MRS) of low-concentration metabolites. Matching voxels to anatomical compartments a priori yields better SNR than the spectra created by summing signals from constituent chemical-shift-imaging (CSI) voxels post-acquisition. Here, a new method of localized Spectroscopy using Linear Algebraic Modeling (SLAM) is presented, that can realize this additional SNR gain. Unlike prior methods, SLAM generates spectra from C signal-generating anatomic compartments utilizing a CSI sequence wherein essentially only the C central k-space phase-encoding gradient steps with highest SNR are retained. After MRI-based compartment segmentation, the spectra are reconstructed by solving a sub-set of linear simultaneous equations from the standard CSI algorithm. SLAM is demonstrated with one-dimensional CSI surface coil phosphorus MRS in phantoms, the human leg and the heart on a 3T clinical scanner. Its SNR performance, accuracy, sensitivity to registration errors and inhomogeneity, are evaluated. Compared to one-dimensional CSI, SLAM yielded quantitatively the same results 4-times faster in 24 cardiac patients and healthy subjects. SLAM is further extended with fractional phase-encoding gradients that optimize SNR and/or minimize both inter- and intra-compartmental contamination. In proactive cardiac phosphorus MRS of six healthy subjects, both SLAM and fractional-SLAM (fSLAM) produced results indistinguishable from CSI while preserving SNR gains of 36-45% in the same scan-time. Both SLAM and fSLAM are simple to implement and reduce the minimum scan-time for CSI, which otherwise limits the translation of higher SNR achievable at higher field strengths to faster scanning.

  7. ALGEBRA v.1.27

    2005-04-11

    The ALGEBRA program allows the user to manipulate data from a finite element analysis before it is plotted. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database. The ALGEBRA program evaluates user-supplied functions of the data and writes the results to an output EXODUS II database that can be read by plot programs.

  8. Constructing a Coherent Problem Model to Facilitate Algebra Problem Solving in a Chemistry Context

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Yeung, Alexander Seeshing; Phan, Huy P.

    2015-01-01

    An experiment using a sample of 11th graders compared text editing and worked examples approaches in learning to solve dilution and molarity algebra word problems in a chemistry context. Text editing requires students to assess the structure of a word problem by specifying whether the problem text contains sufficient, missing, or irrelevant…

  9. Flipping an Algebra Classroom: Analyzing, Modeling, and Solving Systems of Linear Equations

    ERIC Educational Resources Information Center

    Kirvan, Rebecca; Rakes, Christopher R.; Zamora, Regie

    2015-01-01

    The present study investigated whether flipping an algebra classroom led to a stronger focus on conceptual understanding and improved learning of systems of linear equations for 54 seventh- and eighth-grade students using teacher journal data and district-mandated unit exam items. Multivariate analysis of covariance was used to compare scores on…

  10. Algebraic Bethe Ansatz for Open XXX Model with Triangular Boundary Matrices

    NASA Astrophysics Data System (ADS)

    Belliard, Samuel; Crampé, Nicolas; Ragoucy, Eric

    2013-05-01

    We consider an open XXX spin chain with two general boundary matrices whose entries obey a relation, which is equivalent to the possibility to put simultaneously the two matrices in a upper-triangular form. We construct Bethe vectors by means of a generalized algebraic Bethe ansatz. As usual, the method uses Bethe equations and provides transfer matrix eigenvalues.

  11. Prospective Mathematics Teachers' Sense Making of Polynomial Multiplication and Factorization Modeled with Algebra Tiles

    ERIC Educational Resources Information Center

    Caglayan, Günhan

    2013-01-01

    This study is about prospective secondary mathematics teachers' understanding and sense making of representational quantities generated by algebra tiles, the quantitative units (linear vs. areal) inherent in the nature of these quantities, and the quantitative addition and multiplication operations--referent preserving versus referent…

  12. Proposing and Testing a Model to Explain Traits of Algebra Preparedness

    ERIC Educational Resources Information Center

    Venenciano, Linda; Heck, Ronald

    2016-01-01

    Early experiences with theoretical thinking and generalization in measurement are hypothesized to develop constructs we name here as logical reasoning and preparedness for algebra. Based on work of V. V. Davydov (1975), the Measure Up (MU) elementary grades experimental mathematics curriculum uses quantities of area, length, volume, and mass to…

  13. Algebraic grid adaptation method using non-uniform rational B-spline surface modeling

    NASA Technical Reports Server (NTRS)

    Yang, Jiann-Cherng; Soni, B. K.

    1992-01-01

    An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique.

  14. Dynamics of gelling liquids: algebraic relaxation.

    PubMed

    Srivastava, Sunita; Kumar, C N; Tankeshwar, K

    2009-08-19

    The sol-gel system which is known, experimentally, to exhibit a power law decay of stress autocorrelation function has been studied theoretically. A second-order nonlinear differential equation obtained from Mori's integro-differential equation is derived which provides the algebraic decay of a time correlation function. Involved parameters in the expression obtained are related to exact properties of the corresponding correlation function. The algebraic model has been applied to Lennard-Jones and sol-gel systems. The model shows the behaviour of viscosity as has been observed in computer simulation and theoretical studies. The expression obtained for the viscosity predicts a logarithmic divergence at a critical value of the parameter in agreement with the prediction of other theories. PMID:21828600

  15. Higher level twisted Zhu algebras

    SciTech Connect

    Ekeren, Jethro van

    2011-05-15

    The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper, we consider the general setup of a vertex algebra V, graded by {Gamma}/Z for some subgroup {Gamma} of R containing Z, and with a Hamiltonian operator H having real (but not necessarily integer) eigenvalues. We construct the directed system of twisted level p Zhu algebras Zhu{sub p,{Gamma}}(V), and we prove the following theorems: For each p, there is a bijection between the irreducible Zhu{sub p,{Gamma}}(V)-modules and the irreducible {Gamma}-twisted positive energy V-modules, and V is ({Gamma}, H)-rational if and only if all its Zhu algebras Zhu{sub p,{Gamma}}(V) are finite dimensional and semisimple. The main novelty is the removal of the assumption of integer eigenvalues for H. We provide an explicit description of the level p Zhu algebras of a universal enveloping vertex algebra, in particular of the Virasoro vertex algebra Vir{sup c} and the universal affine Kac-Moody vertex algebra V{sup k}(g) at non-critical level. We also compute the inverse limits of these directed systems of algebras.

  16. Algebraic Squares: Complete and Incomplete.

    ERIC Educational Resources Information Center

    Gardella, Francis J.

    2000-01-01

    Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)

  17. Algebraic Thinking in Adult Education

    ERIC Educational Resources Information Center

    Manly, Myrna; Ginsburg, Lynda

    2010-01-01

    In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic…

  18. The Role and Modeling of Dispersive Stresses

    NASA Astrophysics Data System (ADS)

    Shavit, U.; Moltchanov, S.

    2012-12-01

    Dispersive stresses represent momentum fluxes that are induced by the spatial heterogeneity of flow environments such as forest canopies, river vegetation and coral reefs. When deriving the average momentum equation for such flow environments, these dispersive stresses resemble the Reynolds stresses but instead of correlations of temporal fluctuations they represent correlations of spatial fluctuations. Surprisingly, these stresses are ignored in flow models and very few studies attempted to provide a physical interpretation, let alone a closure model. Typical arguments that justify such modeling are that these stresses are small and negligible; however, recent studies have shown that they may be important. In a recent study we showed that dispersive stresses at the inlet to obstructed region (made of glass cylinders) are larger than the Reynolds stresses and their contribution to the momentum balance is as important as the pressure and the drag forces. In this presentation we will try to explain what they are, provide some intuitive physical interoperation and show that closure models can be developed. Our results are based on highly detailed particle image velocimeter (PIV) measurements that were obtained inside a canopy model made of vertical thin glass plates. Forty nine vertical cross sections were obtained 1000 times generating a huge dataset of more than 250 million data points for each flow conditions. A careful spatial averaging procedure was developed and both temporal and spatial correlations were obtained. An order of magnitude analysis will be presented and the role of each of the terms in the momentum equation will be evaluated. It will be shown that the dispersive stresses are large and significant within the area of the canopy leading edge. Since dispersive stresses do not exist upstream from the canopy they are expected to grow once the flow enters the canopy. Our PIV data shows an initial fast growth up to about one length scale into the patch

  19. Spatial-Operator Algebra For Robotic Manipulators

    NASA Technical Reports Server (NTRS)

    Rodriguez, Guillermo; Kreutz, Kenneth K.; Milman, Mark H.

    1991-01-01

    Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.

  20. A differential algebraic approach for the modeling of polycrystalline ferromagnetic hysteresis with minor loops and frequency dependence

    NASA Astrophysics Data System (ADS)

    Wang, Dan; Wang, Linxiang; Melnik, Roderick

    2016-07-01

    In the current paper, a nonlinear differential algebraic approach is proposed for the modeling of hysteretic dynamics of polycrystalline ferromagnetic materials. The model is constructed by employing a phenomenological theory to the magnetization orientation switching. For the modeling of hysteresis in polycrystalline ferromagnetic materials, the single crystal model is applied to each magnetic domain along its own principal axis. The overall dynamics of the polycrystalline materials is obtained by taking a weighted combination of the dynamics of all magnetic domains. The weight function for the combination is taken as the distribution function of the principal axes. Numerical simulations are performed and comparisons with its experimental counterparts are presented. The hysteretic dynamics caused by orientation switching processes is accurately captured by the proposed model. Minor hysteresis loops associated with partial-amplitude loadings are also captured. Rate dependence of the hysteresis loops are inherently incorporated into the model due to its differential nature.

  1. Thinking Visually about Algebra

    ERIC Educational Resources Information Center

    Baroudi, Ziad

    2015-01-01

    Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…

  2. The Effect of Scheduling Models for Introductory Algebra on 9th-Grade Students, Test Scores and Grades

    ERIC Educational Resources Information Center

    O'Hanlon, Angela L.

    2011-01-01

    The purpose of the study was to determine the effect of pacing and scheduling of algebra coursework on assigned 9th-grade students who traditionally would qualify for pre-algebra instruction and same course 9th-grade students who traditionally would qualify for standard algebra instruction. Students were selected based on completion of first-year…

  3. ANSYS Modeling of Hydrostatic Stress Effects

    NASA Technical Reports Server (NTRS)

    Allen, Phillip A.

    1999-01-01

    Classical metal plasticity theory assumes that hydrostatic pressure has no effect on the yield and postyield behavior of metals. Plasticity textbooks, from the earliest to the most modem, infer that there is no hydrostatic effect on the yielding of metals, and even modem finite element programs direct the user to assume the same. The object of this study is to use the von Mises and Drucker-Prager failure theory constitutive models in the finite element program ANSYS to see how well they model conditions of varying hydrostatic pressure. Data is presented for notched round bar (NRB) and "L" shaped tensile specimens. Similar results from finite element models in ABAQUS are shown for comparison. It is shown that when dealing with geometries having a high hydrostatic stress influence, constitutive models that have a functional dependence on hydrostatic stress are more accurate in predicting material behavior than those that are independent of hydrostatic stress.

  4. Turbulence Modeling: A NASA Perspective

    NASA Technical Reports Server (NTRS)

    Gatski, T. B.

    2001-01-01

    This paper presents turbulence modeling from NASA's perspective. The topics include: 1) Hierarchy of Solution Methods; 2) Turbulence Modeling Focus; 3) Linear Eddy Viscosity Models; and 4) Nonlinear Eddy Viscosity Algebraic Stress Models.

  5. Family Stress: A Coping Model for Intervention.

    ERIC Educational Resources Information Center

    Zeitlin, Shirley; Rosenblatt, William P.

    A support program was developed at the John F. Kennedy Medical Center in Edison, New Jersey for families of handicapped children (from birth to the age of 3) who are involved in an early intervention program. A cognitive-behavioral model (the Coping with Stress Model) was designed to help families assess coping effectiveness. The process, which…

  6. Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids.

    PubMed

    José, Marco V; Morgado, Eberto R; Guimarães, Romeu Cardoso; Zamudio, Gabriel S; de Farías, Sávio Torres; Bobadilla, Juan R; Sosa, Daniela

    2014-01-01

    Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state. PMID:25370377

  7. Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids

    PubMed Central

    José, Marco V.; Morgado, Eberto R.; Guimarães, Romeu Cardoso; Zamudio, Gabriel S.; de Farías, Sávio Torres; Bobadilla, Juan R.; Sosa, Daniela

    2014-01-01

    Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state. PMID:25370377

  8. Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method

    NASA Astrophysics Data System (ADS)

    Akbari, M. R.; Ganji, D. D.; Ahmadi, A. R.; Kachapi, Sayyid H. Hashemi

    2014-03-01

    In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.

  9. Distance geometry and geometric algebra

    NASA Astrophysics Data System (ADS)

    Dress, Andreas W. M.; Havel, Timothy F.

    1993-10-01

    As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)

  10. Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz

    NASA Astrophysics Data System (ADS)

    Belliard, Samuel; Crampé, Nicolas

    2013-11-01

    We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.

  11. Algebraic Bethe ansatz for the sℓ (2) Gaudin model with boundary

    NASA Astrophysics Data System (ADS)

    Cirilo António, N.; Manojlović, N.; Ragoucy, E.; Salom, I.

    2015-04-01

    Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. By defining the appropriate Bethe vectors which yield strikingly simple off shell action of the generating function, we fully implement the algebraic Bethe ansatz, obtaining the spectrum of the generating function and the corresponding Bethe equations.

  12. An Ada Linear-Algebra Software Package Modeled After HAL/S

    NASA Technical Reports Server (NTRS)

    Klumpp, Allan R.; Lawson, Charles L.

    1990-01-01

    New avionics software written more easily. Software package extends Ada programming language to include linear-algebra capabilities similar to those of HAL/S programming language. Designed for such avionics applications as Space Station flight software. In addition to built-in functions of HAL/S, package incorporates quaternion functions used in Space Shuttle and Galileo projects and routines from LINPAK solving systems of equations involving general square matrices. Contains two generic programs: one for floating-point computations and one for integer computations. Written on IBM/AT personal computer running under PC DOS, v.3.1.

  13. A stress-free model for residual stress assessment using thermoelastic stress analysis

    NASA Astrophysics Data System (ADS)

    Howell, Geoffrey; Dulieu-Barton, Janice M.; Achintha, Mithila; Robinson, Andrew F.

    2015-03-01

    Thermoelastic Stress Analysis (TSA) has been proposed as a method of obtaining residual stresses. The results of a preliminary study demonstrated that when Al-2024 plate containing holes that were plastically deformed by cold expansion process to 2% and 4% strain the thermoelastic response in the material around the hole was different to that obtained from a plate that had not experienced any plastic cold expansion (i.e. a reference specimen). This observation provides an opportunity for obtaining residual stresses based on TSA data. In many applications a reference specimen (i.e. residual stress free specimen) may not be available for comparison, so a synthetic, digital bitmap has been proposed as an alternative. An elastic finite element model is created using commercially available software Abaqus/Standard and the resultant stress field is extracted. The simulated stress field from the model is mapped onto a grid that matches the TSA pixel data from a physical reference specimen. This stress field is then converted to a ΔT/T field that can be compared to the full-field TSA data. When the reference experimental data is subtracted from the, bitmap dataset the resultant ΔT/T field is approximately zero. Further work proposes replacing the experimental reference data with that from specimens that have undergone cold expansion with the aim of revealing the regions affected by residual stress through a departure from zero in the resultant stress field. The paper demonstrates the first steps necessary for deriving the residual stresses from a general specimen using TSA.

  14. Flow stress model in metal cutting

    NASA Technical Reports Server (NTRS)

    Black, J. T.

    1978-01-01

    A model for the plastic deformation that occurs in metal cutting, based on dislocation mechanics, is presented. The model explains the fundamental deformation structure that develops during machining and is based on the well known Cottrell-Stokes Law, wherein the flow stress is partitioned into two parts; an athermal part which occurs in the shear fronts (or shear bands); and a thermal part which occurs in the lamella regions. The deformation envokes the presence of a cellular dislocation distribution which always exists in the material ahead of the shear process. This 'alien' dislocation distribution either exists in the metal prior to cutting or is produced by the compressive stress field which operates in front of the shear process. The magnitude of the flow stress and direction of the shear are shown to be correlated to the stacking fault energy of the metal being cut. The model is tested with respect to energy consumption rates and found to be consistent with observed values.

  15. A Deterministic Interfacial Cyclic Oxidation Spalling Model. Part 2; Algebraic Approximation, Descriptive Parameters, and Normalized Universal Curve

    NASA Technical Reports Server (NTRS)

    Smialek, James L.

    2002-01-01

    A cyclic oxidation interfacial spalling model has been developed in Part 1. The governing equations have been simplified here by substituting a new algebraic expression for the series (Good-Smialek approximation). This produced a direct relationship between cyclic oxidation weight change and model input parameters. It also allowed for the mathematical derivation of various descriptive parameters as a function of the inputs. It is shown that the maximum in weight change varies directly with the parabolic rate constant and cycle duration and inversely with the spall fraction, all to the 1/2 power. The number of cycles to reach maximum and zero weight change vary inversely with the spall fraction, and the ratio of these cycles is exactly 1:3 for most oxides. By suitably normalizing the weight change and cycle number, it is shown that all cyclic oxidation weight change model curves can be represented by one universal expression for a given oxide scale.

  16. Stress diffusion in models for shear banding

    NASA Astrophysics Data System (ADS)

    Masnada, Elian; Olmsted, Peter

    Understanding shear banding is of utmost importance from both theoretical and experimental point of view and consequently it has been studied for several decades. Despite this study numerous aspects of shear banding remains poorly understood. Because of the intrinsic inhomogeneity in the shear banded state, applicable constitutive models must be include spatial inhomogeneities, leading to a so-called 'diffusive' term in the equation of motion for the slow variables that carry stress. Such terms are also vital in describing the interaction of bulk shear banding flows with walls and incorporation of wall slip. In this work, we consider different sources of 'diffusion' in polymer models in which concentration degrees of freedom are negligible. The simplest models used are consistent with diffusive terms whose origin is intrinsically dissipative, such as due to hydrodynamic interactions. By contrast, models in which elastic effects such as finite chain stiffness contribute to stress diffusion are inconsistent with simple diffusive models, and we propose alternative consistent models

  17. Quantum solvable models with gl(2, c) Lie algebra symmetry embedded into the extension of unitary parasupersymmetry

    NASA Astrophysics Data System (ADS)

    Fakhri, H.; Chenaghlou, A.

    2007-05-01

    Introducing p - 1 new parameters into the multilinear relations, we extend the standard unitary parasupersymmetry algebra of order p so that by embedding the quantum solvable models possessing gl(2, c) Lie algebra symmetry into it, the partitions of integer numbers p - 1 and \\frac{1}{2}p(p-1) are established. These two partitions are performed by the new parameters and the product of new parameters with their labels, respectively. The former partition is just necessary for the real form h4; however, both of them are essential for the real forms u(2) and u(1, 1). By occupying these parameters with arbitrary values, the energy spectra are determined by the mean value of proposed parameters for the real form h4 with their label weight function as well as for the real forms u(2) and u(1, 1) with the weight function of their squared label. So for the given energies, the multilinear behaviour of parasupercharges is not specified uniquely by varying the new parameters continuously.

  18. Twisted Quantum Toroidal Algebras

    NASA Astrophysics Data System (ADS)

    Jing, Naihuan; Liu, Rongjia

    2014-09-01

    We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.

  19. Investigation and Modeling of Cranberry Weather Stress.

    NASA Astrophysics Data System (ADS)

    Croft, Paul Joseph

    Cranberry bog weather conditions and weather-related stress were investigated for development of crop yield prediction models and models to predict daily weather conditions in the bog. Field investigations and data gathering were completed at the Rutgers University Blueberry/Cranberry Research Center experimental bogs in Chatsworth, New Jersey. Study indicated that although cranberries generally exhibit little or no stomatal response to changing atmospheric conditions, the evaluation of weather-related stress could be accomplished via use of micrometeorological data. Definition of weather -related stress was made by establishing critical thresholds of the frequencies of occurrence, and magnitudes of, temperature and precipitation in the bog based on values determined by a review of the literature and a grower questionnaire. Stress frequencies were correlated with cranberry yield to develop predictive models based on the previous season's yield, prior season data, prior and current season data, current season data; and prior and current season data through July 31 of the current season. The predictive ability of the prior season models was best and could be used in crop planning and production. Further examination of bog micrometeorological data permitted the isolation of those weather conditions conducive to cranberry scald and allowed for the institution of a pilot scald advisory program during the 1991 season. The micrometeorological data from the bog was also used to develop models to predict daily canopy temperature and precipitation, based on upper air data, for grower use. Models were developed for each month for maximum and minimum temperatures and for precipitation and generally performed well. The modeling of bog weather conditions is an important first step toward daily prediction of cranberry weather-related stress.

  20. A Wave Equation including Leptons and Quarks for the Standard Model of Quantum Physics in Clifford Algebra

    NASA Astrophysics Data System (ADS)

    Daviau, Claude; Bertrand, Jacques

    A wave equation with mass term is studied for all particles and antiparticles of the first generation: electron and its neutrino, positron and antineutrino, quarks $u$ and $d$ with three states of color and antiquarks $\\overline{u}$ and $\\overline{d}$. This wave equation is form invariant under the $Cl_3^*$ group generalizing the relativistic invariance. It is gauge invariant under the $U(1)\\times SU(2) \\times SU(3)$ group of the standard model of quantum physics. The wave is a function of space and time with value in the Clifford algebra $Cl_{1,5}$. All features of the standard model, charge conjugation, color, left waves, Lagrangian formalism, are linked to the geometry of this extended space-time.

  1. Study of the “non-Abelian” current algebra of a non-linear σ-model

    NASA Astrophysics Data System (ADS)

    Ghosh, Subir

    2006-08-01

    A particular form of non-linear σ-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-Abelian nature of the invariance, with field dependent structure functions. Reduction of the field theory to a point particle framework yields a non-linear harmonic oscillator, which is a special case of similar models studied before in [J.F. Carinena et al., Nonlinearity 17 (2004) 1941, math-ph/0406002; J.F. Carinena et al., in: Proceedings of 10th International Conference in Modern Group Analysis, Larnaca, Cyprus, 2004, p. 39, arxiv:math-ph/0505028; J.F. Carinena et al., Rep. Math. Phys. 54 (2004) 285, arxiv:hep-th/0501106]. The connection with non-commutative geometry is also established.

  2. A Stage Model of Stress and Disease.

    PubMed

    Cohen, Sheldon; Gianaros, Peter J; Manuck, Stephen B

    2016-07-01

    In this article, we argued that the term stress has served as a valuable heuristic, helping researchers to integrate traditions that illuminate different stages of the process linking stressful life events to disease. We provided a short history of three traditions in the study of stress: the epidemiological, psychological, and biological. The epidemiological tradition focuses on defining which circumstances and experiences are deemed stressful on the basis of consensual agreement that they constitute threats to social or physical well-being. The psychological tradition focuses on individuals' perceptions of the stress presented by life events on the basis of their appraisals of the threats posed and the availability of effective coping resources. The biological tradition focuses on brain-based perturbations of physiological systems that are otherwise essential for normal homeostatic regulation and metabolic control. The foci of these three traditions have informed elements of a stage model of disease, wherein events appraised as stressful are viewed as triggering affective states that in turn engender behavioral and biological responses having possible downstream implications for disease. PMID:27474134

  3. Coverings of topological semi-abelian algebras

    NASA Astrophysics Data System (ADS)

    Mucuk, Osman; Demir, Serap

    2016-08-01

    In this work, we study on a category of topological semi-abelian algebras which are topological models of given an algebraic theory T whose category of models is semi-abelian; and investigate some results on the coverings of topological models of such theories yielding semi-abelian categories. We also consider the internal groupoid structure in the semi-abelian category of T-algebras, and give a criteria for the lifting of internal groupoid structure to the covering groupoids.

  4. Residual stresses and vector hysteresis modeling

    NASA Astrophysics Data System (ADS)

    Ktena, Aphrodite

    2016-04-01

    Residual stresses in magnetic materials, whether the result of processing or intentional loading, leave their footprint on macroscopic data, such hysteresis loops and differential permeability measurements. A Preisach-type vector model is used to reproduce the phenomenology observed based on assumptions deduced from the data: internal stresses lead to smaller and misaligned grains, hence increased domain wall pinning and angular dispersion of local easy axes, favouring rotation as a magnetization reversal mechanism; misaligned grains contribute to magnetostatic fields opposing the direction of the applied field. The model is using a vector operator which accounts for both reversible and irreversible processes; the Preisach concept for interactions for the role of stress related demagnetizing fields; and a characteristic probability density function which is constructed as a weighed sum of constituent functions: the material is modeled as consisting of various subsystems, e.g. reversal mechanisms or areas subject to strong/weak long range interactions and each subsystem is represented by a constituent probability density function. Our assumptions are validated since the model reproduces the hysteresis loops and differential permeability curves observed experimentally and calculations involving rotating inputs at various residual stress levels are consistent and in agreement with experimental evidence.

  5. Modular properties of doubly extended N = 4 superconformal algebras and their connection to rational torus models (I)

    NASA Astrophysics Data System (ADS)

    Petersen, Jens Lyng; Taormina, Anne

    1991-05-01

    The doubly extended N = 4 superconformal algebra, which contains all conventional extended superconformal algebras, is analyzed when one of the central extensions is set to 1. The modular transformations of the characters are derived, the relation between the characters and those of the N = 2 minimal is clarified, and in the process it is shown how rather simple extensions of the algebra based on rational torus theories, give rise to finite dimensional representations of the modular group.

  6. Algebraic vs physical N = 6 3-algebras

    SciTech Connect

    Cantarini, Nicoletta; Kac, Victor G.

    2014-01-15

    In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.

  7. Filiform Lie algebras of order 3

    SciTech Connect

    Navarro, R. M.

    2014-04-15

    The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.

  8. Priority in Process Algebras

    NASA Technical Reports Server (NTRS)

    Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.

    1999-01-01

    This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.

  9. Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows

    NASA Astrophysics Data System (ADS)

    Aratyn, Henrik; van de Leur, Johan

    2007-02-01

    We use a Grassmannian framework to define multi-component tau functions as expectation values of certain multi-component Fermi operators satisfying simple bilinear commutation relations on Clifford algebra. The tau functions contain both positive and negative flows and are shown to satisfy the 2n-component KP hierarchy. The hierarchy equations can be formulated in terms of pseudo-differential equations for n × n matrix wave functions derived in terms of tau functions. These equations are cast in form of Sato-Wilson relations. A reduction process leads to the AKNS, two-component Camassa-Holm and Cecotti-Vafa models and the formalism provides simple formulas for their solutions.

  10. A two-dimensional algebraic quantum liquid produced by an atomic simulator of the quantum Lifshitz model

    PubMed Central

    Po, Hoi Chun; Zhou, Qi

    2015-01-01

    Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems. PMID:26268154

  11. Hopf algebras and topological recursion

    NASA Astrophysics Data System (ADS)

    Esteves, João N.

    2015-11-01

    We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).

  12. Modeling DNA Thermodynamics under Torsional Stress

    PubMed Central

    Wang, Qian; Pettitt, B. Montgomery

    2014-01-01

    Negatively twisted DNA is essential to many biological functions. Due to torsional stress, duplex DNA can have local, sequence-dependent structural defects. In this work, a thermodynamic model of DNA was built to qualitatively predict the local sequence-dependent mechanical instabilities under torsional stress. The results were compared to both simulation of a coarse-grained model and experiment results. By using the Kirkwood superposition approximation, we built an analytical model to represent the free energy difference ΔW of a hydrogen-bonded basepair between the B-form helical state and the basepair opened (or locally melted) state, within a given sequence under torsional stress. We showed that ΔW can be well approximated by two-body interactions with its nearest-sequence-neighbor basepairs plus a free energy correction due to long-range correlations. This model is capable of rapidly predicting the position and thermodynamics of local defects in a given sequence. The result qualitatively matches with an in vitro experiment for a long DNA sequence (>4000 basepairs). The 12 parameters used in this model can be further quantitatively refined when more experimental data are available. PMID:24606942

  13. Modeling DNA thermodynamics under torsional stress.

    PubMed

    Wang, Qian; Pettitt, B Montgomery

    2014-03-01

    Negatively twisted DNA is essential to many biological functions. Due to torsional stress, duplex DNA can have local, sequence-dependent structural defects. In this work, a thermodynamic model of DNA was built to qualitatively predict the local sequence-dependent mechanical instabilities under torsional stress. The results were compared to both simulation of a coarse-grained model and experiment results. By using the Kirkwood superposition approximation, we built an analytical model to represent the free energy difference ΔW of a hydrogen-bonded basepair between the B-form helical state and the basepair opened (or locally melted) state, within a given sequence under torsional stress. We showed that ΔW can be well approximated by two-body interactions with its nearest-sequence-neighbor basepairs plus a free energy correction due to long-range correlations. This model is capable of rapidly predicting the position and thermodynamics of local defects in a given sequence. The result qualitatively matches with an in vitro experiment for a long DNA sequence (>4000 basepairs). The 12 parameters used in this model can be further quantitatively refined when more experimental data are available. PMID:24606942

  14. A Non-Econometric Analysis with Algebraic Models to Forecast the Numbers of Newly Hired and Retirement of Public Primary School Teachers in Taiwan

    ERIC Educational Resources Information Center

    Lung-Hsing, Kuo; Hung-Jen, Yang; Ying-Wen, Lin; Shang-Ming, Su

    2011-01-01

    In recent years, the "street teachers" issue has caused social concern in Taiwan. This study estimates the retirement of and needs for newly hired and public primary school teachers in 2010 using an algebraic model from the paper by Husssar (1999). This recursive methodology predicts the number of newly hired public primary school teachers due to…

  15. Residual Stresses Modeled in Thermal Barrier Coatings

    NASA Technical Reports Server (NTRS)

    Freborg, A. M.; Ferguson, B. L.; Petrus, G. J.; Brindley, W. J.

    1998-01-01

    Thermal barrier coating (TBC) applications continue to increase as the need for greater engine efficiency in aircraft and land-based gas turbines increases. However, durability and reliability issues limit the benefits that can be derived from TBC's. A thorough understanding of the mechanisms that cause TBC failure is a key to increasing, as well as predicting, TBC durability. Oxidation of the bond coat has been repeatedly identified as one of the major factors affecting the durability of the ceramic top coat during service. However, the mechanisms by which oxidation facilitates TBC failure are poorly understood and require further characterization. In addition, researchers have suspected that other bond coat and top coat factors might influence TBC thermal fatigue life, both separately and through interactions with the mechanism of oxidation. These other factors include the bond coat coefficient of thermal expansion, the bond coat roughness, and the creep behavior of both the ceramic and bond coat layers. Although it is difficult to design an experiment to examine these factors unambiguously, it is possible to design a computer modeling "experiment" to examine the action and interaction of these factors, as well as to determine failure drivers for TBC's. Previous computer models have examined some of these factors separately to determine their effect on coating residual stresses, but none have examined all the factors concurrently. The purpose of this research, which was performed at DCT, Inc., in contract with the NASA Lewis Research Center, was to develop an inclusive finite element model to characterize the effects of oxidation on the residual stresses within the TBC system during thermal cycling as well as to examine the interaction of oxidation with the other factors affecting TBC life. The plasma sprayed, two-layer thermal barrier coating that was modeled incorporated a superalloy substrate, a NiCrAlY bond coat, and a ZrO2-8 wt % Y2O3 ceramic top coat. We

  16. Animal Models of Stress Urinary Incontinence

    PubMed Central

    Jiang, Hai-Hong

    2011-01-01

    Stress urinary incontinence (SUI) is a common health problem significantly affecting the quality of life of women worldwide. Animal models that simulate SUI enable the assessment of the mechanism of risk factors for SUI in a controlled fashion, including childbirth injuries, and enable preclinical testing of new treatments and therapies for SUI. Animal models that simulate childbirth are presently being utilized to determine the mechanisms of the maternal injuries of childbirth that lead to SUI with the goal of developing prophylactic treatments. Methods of assessing SUI in animals that mimic diagnostic methods used clinically have been developed to evaluate the animal models. Use of these animal models to test innovative treatment strategies has the potential to improve clinical management of SUI. This chapter provides a review of the available animal models of SUI, as well as a review of the methods of assessing SUI in animal models, and potential treatments that have been tested on these models. PMID:21290221

  17. Comparing the Impact of Traditional and Modeling College Algebra Courses on Student Performance in Survey of Calculus

    ERIC Educational Resources Information Center

    West, Jerry G.

    2013-01-01

    Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to…

  18. New directions in algebraic dynamical systems

    NASA Astrophysics Data System (ADS)

    Schmidt, Klaus; Verbitskiy, Evgeny

    2011-02-01

    The logarithmic Mahler measure of certain multivariate polynomials occurs frequently as the entropy or the free energy of solvable lattice models (especially dimer models). It is also known that the entropy of an algebraic dynamical system is the logarithmic Mahler measure of the defining polynomial. The connection between the lattice models and the algebraic dynamical systems is still rather mysterious.

  19. Historical Topics in Algebra.

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, Inc., Reston, VA.

    This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…

  20. Algebraic Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Dankova, T. S.; Rosensteel, G.

    1998-10-01

    Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.

  1. Psychosomatic symptoms, stress, and modernization: a model.

    PubMed

    Dressler, W W

    1985-09-01

    The quantity of research on the effects of stress on disease has increased substantially in recent years, but little effort has been devoted to examining the effects of cultural influences in the stress process. A model is proposed in this paper in which cultural context exerts a modifying influence on the relationship between sociocultural stressors and psychosomatic symptoms, specifically in the context of modernization. In change situations involving increasing modernization there is increased differentiation in systems of social stratification within a community, due to increased potential for upward social mobility. The individuals who are upwardly mobile adopt a particular style of life, involving the acquisition of western consumer goods, as symbolic of their success. Lower class individuals strive to attain this same style of life as a claim to a higher status social identity, but their lower economic condition results in stressful incongruities and higher psychosomatic symptoms. Individuals who are successful in upward mobility are confronted by a different set of stressors that are primarily intrapsychic in nature. Events and circumstances perceived as threats to their self-identity are related to more psychosomatic symptoms. Thus, the meaning of specific stressors changes depending on the sociocultural context of the individual, and this meaning serves as a bridge between environmental circumstances and physiological outcomes. This model receives substantial empirical support in two field studies. Limitations of the model and implications for future research are discussed. PMID:4028786

  2. Deformations of 3-algebras

    SciTech Connect

    Figueroa-O'Farrill, Jose Miguel

    2009-11-15

    We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern-Simons theories with matter.

  3. Quantum cluster algebras and quantum nilpotent algebras

    PubMed Central

    Goodearl, Kenneth R.; Yakimov, Milen T.

    2014-01-01

    A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

  4. The algebras of large N matrix mechanics

    SciTech Connect

    Halpern, M.B.; Schwartz, C.

    1999-09-16

    Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.

  5. The Adaptive Calibration Model of stress responsivity

    PubMed Central

    Ellis, Bruce J.; Shirtcliff, Elizabeth A.

    2010-01-01

    This paper presents the Adaptive Calibration Model (ACM), an evolutionary-developmental theory of individual differences in the functioning of the stress response system. The stress response system has three main biological functions: (1) to coordinate the organism’s allostatic response to physical and psychosocial challenges; (2) to encode and filter information about the organism’s social and physical environment, mediating the organism’s openness to environmental inputs; and (3) to regulate the organism’s physiology and behavior in a broad range of fitness-relevant areas including defensive behaviors, competitive risk-taking, learning, attachment, affiliation and reproductive functioning. The information encoded by the system during development feeds back on the long-term calibration of the system itself, resulting in adaptive patterns of responsivity and individual differences in behavior. Drawing on evolutionary life history theory, we build a model of the development of stress responsivity across life stages, describe four prototypical responsivity patterns, and discuss the emergence and meaning of sex differences. The ACM extends the theory of biological sensitivity to context (BSC) and provides an integrative framework for future research in the field. PMID:21145350

  6. Matrix-algebra-based calculations of the time evolution of the binary spin-bath model for magnetization transfer

    NASA Astrophysics Data System (ADS)

    Müller, Dirk K.; Pampel, André; Möller, Harald E.

    2013-05-01

    Quantification of magnetization-transfer (MT) experiments are typically based on the assumption of the binary spin-bath model. This model allows for the extraction of up to six parameters (relative pool sizes, relaxation times, and exchange rate constants) for the characterization of macromolecules, which are coupled via exchange processes to the water in tissues. Here, an approach is presented for estimating MT parameters acquired with arbitrary saturation schemes and imaging pulse sequences. It uses matrix algebra to solve the Bloch-McConnell equations without unwarranted simplifications, such as assuming steady-state conditions for pulsed saturation schemes or neglecting imaging pulses. The algorithm achieves sufficient efficiency for voxel-by-voxel MT parameter estimations by using a polynomial interpolation technique. Simulations, as well as experiments in agar gels with continuous-wave and pulsed MT preparation, were performed for validation and for assessing approximations in previous modeling approaches. In vivo experiments in the normal human brain yielded results that were consistent with published data.

  7. Explicit stress integration of complex soil models

    NASA Astrophysics Data System (ADS)

    Zhao, Jidong; Sheng, Daichao; Rouainia, M.; Sloan, Scott W.

    2005-10-01

    In this paper, two complex critical-state models are implemented in a displacement finite element code. The two models are used for structured clays and sands, and are characterized by multiple yield surfaces, plastic yielding within the yield surface, and complex kinematic and isotropic hardening laws. The consistent tangent operators - which lead to a quadratic convergence when used in a fully implicit algorithm - are difficult to derive or may even not exist. The stress integration scheme used in this paper is based on the explicit Euler method with automatic substepping and error control. This scheme employs the classical elastoplastic stiffness matrix and requires only the first derivatives of the yield function and plastic potential. This explicit scheme is used to integrate the two complex critical-state models - the sub/super-loading surfaces model (SSLSM) and the kinematic hardening structure model (KHSM). Various boundary-value problems are then analysed. The results for the two models are compared with each other, as well with those from standard Cam-clay models. Accuracy and efficiency of the scheme used for the complex models are also investigated. Copyright

  8. Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley-Lieb algebras

    NASA Astrophysics Data System (ADS)

    Lykke Jacobsen, Jesper

    2015-11-01

    In previous work with Scullard, we have defined a graph polynomial P B (q, T) that gives access to the critical temperature T c of the q-state Potts model defined on a general two-dimensional lattice {L}. It depends on a basis B, containing n × m unit cells of {L}, and the relevant root T c(n, m) of P B (q, T) was observed to converge quickly to T c in the limit n,m\\to ∞ . Moreover, in exactly solvable cases there is no finite-size dependence at all. In this paper we show how to reformulate this method as an eigenvalue problem within the periodic Temperley-Lieb (TL) algebra. This corresponds to taking m\\to ∞ first, so that the bases B are semi-infinite cylinders of circumference n. The limit implies faster convergence in n, while maintaining the n-independence in exactly solvable cases. In this setup, T c(n) is determined by equating the largest eigenvalues of two topologically distinct sectors of the transfer matrix. Crucially, these two sectors determine the same critical exponent in the continuum limit, and the observed fast convergence is thus corroborated by results of conformal field theory. We obtain similar results for the dense and dilute phases of the O(N) loop model, using now a transfer matrix within the dilute periodic TL algebra. Compared with our previous study, the eigenvalue formulation allows us to double the size n for which T c(n) can be obtained, using the same computational effort. We study in details three significant cases: (i) bond percolation on the kagome lattice, up to n max = 14; (ii) site percolation on the square lattice, to n max = 21; and (iii) self-avoiding polygons on the square lattice, to n max = 19. Convergence properties of T c(n) and extrapolation schemes are studied in details for the first two cases. This leads to rather accurate values for the percolation thresholds: p c = 0.524 404 999 167 439(4) for bond percolation on the kagome lattice, and p c = 0.592 746 050 792 10(2) for site percolation on the square lattice.

  9. An algebraic model on the performance of a direct methanol fuel cell with consideration of methanol crossover

    NASA Astrophysics Data System (ADS)

    Yin, Ken-Ming

    An algebraic one-dimensional model on the membrane-electrode-assembly (MEA) of direct methanol fuel cell (DMFC) is proposed. Non-linear regression procedure was imposed on the model to retrieve important parameters: solid polymer electrolyte conductivity κ m, exchange current density of methanol electro-oxidation at anode catalyst surface i oM,ref, and mass diffusivity of methanol in aqueous phase within the porous electrode D a that correspond to the experimentally measured polarization curves. Although numerical iteration is required for a complete solution, the explicit relationships of methanol concentration, methanol crossover rate, oxygen concentration and cell discharge current density do provide a clear picture of the mass transport and electrochemical kinetics within the various porous media in the MEA. It is shown the cathode mixed potential induced by the parallel reactions of oxygen reduction and oxidation of crossover methanol elucidates the potential drop of the cathode and the decrease of the cell open circuit voltage (OCV). Methanol transport in the membrane is described by the diffusion, electro-osmosis, and pressure induced convection. Detailed accounts of the effects of anode methanol and cathode oxygen feed concentrations on the cell discharge performance are given with correlation to the physical structure and chemical compositions of the catalyst layers (CLs).

  10. The biopsychosocial model of stress in adolescence: self-awareness of performance versus stress reactivity.

    PubMed

    Rith-Najarian, Leslie R; McLaughlin, Katie A; Sheridan, Margaret A; Nock, Matthew K

    2014-03-01

    Extensive research among adults supports the biopsychosocial (BPS) model of challenge and threat, which describes relationships among stress appraisals, physiological stress reactivity, and performance; however, no previous studies have examined these relationships in adolescents. Perceptions of stressors as well as physiological reactivity to stress increase during adolescence, highlighting the importance of understanding the relationships among stress appraisals, physiological reactivity, and performance during this developmental period. In this study, 79 adolescent participants reported on stress appraisals before and after a Trier Social Stress Test in which they performed a speech task. Physiological stress reactivity was defined by changes in cardiac output and total peripheral resistance from a baseline rest period to the speech task, and performance on the speech was coded using an objective rating system. We observed in adolescents only two relationships found in past adult research on the BPS model variables: (1) pre-task stress appraisal predicted post-task stress appraisal and (2) performance predicted post-task stress appraisal. Physiological reactivity during the speech was unrelated to pre- and post-task stress appraisals and to performance. We conclude that the lack of association between post-task stress appraisal and physiological stress reactivity suggests that adolescents might have low self-awareness of physiological emotional arousal. Our findings further suggest that adolescent stress appraisals are based largely on their performance during stressful situations. Developmental implications of this potential lack of awareness of one's physiological and emotional state during adolescence are discussed. PMID:24491123

  11. The biopsychosocial model of stress in adolescence: self-awareness of performance versus stress reactivity

    PubMed Central

    Rith-Najarian, Leslie R.; McLaughlin, Katie A.; Sheridan, Margaret A.; Nock, Matthew K.

    2014-01-01

    Extensive research among adults supports the biopsychosocial (BPS) model of challenge and threat, which describes relationships among stress appraisals, physiological stress reactivity, and performance; however, no previous studies have examined these relationships in adolescents. Perceptions of stressors as well as physiological reactivity to stress increase during adolescence, highlighting the importance of understanding the relationships among stress appraisals, physiological reactivity, and performance during this developmental period. In this study, 79 adolescent participants reported on stress appraisals before and after a Trier Social Stress Test in which they performed a speech task. Physiological stress reactivity was defined by changes in cardiac output and total peripheral resistance from a baseline rest period to the speech task, and performance on the speech was coded using an objective rating system. We observed in adolescents only two relationships found in past adult research on the BPS model variables: (1) pre-task stress appraisal predicted post-task stress appraisal and (2) performance predicted post-task stress appraisal. Physiological reactivity during the speech was unrelated to pre- and post-task stress appraisals and to performance. We conclude that the lack of association between post-task stress appraisal and physiological stress reactivity suggests that adolescents might have low self-awareness of physiological emotional arousal. Our findings further suggest that adolescent stress appraisals are based largely on their performance during stressful situations. Developmental implications of this potential lack of awareness of one’s physiological and emotional state during adolescence are discussed. PMID:24491123

  12. Boundary Lax pairs from non-ultra-local Poisson algebras

    SciTech Connect

    Avan, Jean; Doikou, Anastasia

    2009-11-15

    We consider non-ultra-local linear Poisson algebras on a continuous line. Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or 'boundary' extensions. They are parametrized by a boundary scalar matrix and depend, in addition, on the choice of an antiautomorphism. The new algebras are the classical-linear counterparts of the known quadratic quantum boundary algebras. For any choice of parameters, the non-ultra-local contribution of the original Poisson algebra disappears. We also systematically construct the associated classical Lax pair. The classical boundary principal chiral model is examined as a physical example.

  13. Stress Management Model for the Elementary/Middle/High School.

    ERIC Educational Resources Information Center

    Matthews, Doris B.

    The Matthews Stress Management formula is a stress management model for use in schools. This effective, practical, and inexpensive model entails the awareness of the physiology of stress, perception of tangible bases of motivation for children, appropriate and simplified techniques, applicability to other areas, and full recognition of the…

  14. Stress Process Model for Individuals With Dementia

    PubMed Central

    Judge, Katherine S.; Menne, Heather L.; Whitlatch, Carol J.

    2010-01-01

    Purpose: Individuals with dementia (IWDs) face particular challenges in managing and coping with their illness. The experience of dementia may be affected by the etiology, stage, and severity of symptoms, preexisting and related chronic conditions, and available informal and formal supportive services. Although several studies have examined particular features of IWD’s illness experience, few draw upon a conceptual model that outlines the global illness experience and the resulting stressors that commence with symptom onset, proliferate over time, and continue through the later stages of cognitive loss. Building on the work of Pearlin and colleagues (1990, Caregiving and the stress process: An overview of concepts and their measures. The Gerontologist, 30, 583–594), this article proposes a stress process model (SPM) for IWDs that conceptualizes and examines the illness experience of IWDs. Implications: The proposed SPM for IWDs serves as a guide to (a) consider and understand the short- and long-term complexities of the illness experience for IWDs, (b) investigate specific hypotheses by outlining key stressors in the illness experience and by positing relationships among stressors and outcomes, and (c) help inform the development of interventions to prevent or reduce the negative stressors and enhance the positive experiences of living with a dementing illness. PMID:20022935

  15. Improved analytical model for residual stress prediction in orthogonal cutting

    NASA Astrophysics Data System (ADS)

    Qi, Zhaoxu; Li, Bin; Xiong, Liangshan

    2014-09-01

    The analytical model of residual stress in orthogonal cutting proposed by Jiann is an important tool for residual stress prediction in orthogonal cutting. In application of the model, a problem of low precision of the surface residual stress prediction is found. By theoretical analysis, several shortages of Jiann's model are picked out, including: inappropriate boundary conditions, unreasonable calculation method of thermal stress, ignorance of stress constraint and cyclic loading algorithm. These shortages may directly lead to the low precision of the surface residual stress prediction. To eliminate these shortages and make the prediction more accurate, an improved model is proposed. In this model, a new contact boundary condition between tool and workpiece is used to make it in accord with the real cutting process; an improved calculation method of thermal stress is adopted; a stress constraint is added according to the volumeconstancy of plastic deformation; and the accumulative effect of the stresses during cyclic loading is considered. At last, an experiment for measuring residual stress in cutting AISI 1045 steel is conducted. Also, Jiann's model and the improved model are simulated under the same conditions with cutting experiment. The comparisons show that the surface residual stresses predicted by the improved model is closer to the experimental results than the results predicted by Jiann's model.

  16. Improved analytical model for residual stress prediction in orthogonal cutting

    NASA Astrophysics Data System (ADS)

    Qi, Zhaoxu; Li, Bin; Xiong, Liangshan

    2014-09-01

    The analytical model of residual stress in orthogonal cutting proposed by Jiann is an important tool for residual stress prediction in orthogonal cutting. In application of the model, a problem of low precision of the surface residual stress prediction is found. By theoretical analysis, several shortages of Jiann's model are picked out, including: inappropriate boundary conditions, unreasonable calculation method of thermal stress, ignorance of stress constraint and cyclic loading algorithm. These shortages may directly lead to the low precision of the surface residual stress prediction. To eliminate these shortages and make the prediction more accurate, an improved model is proposed. In this model, a new contact boundary condition between tool and workpiece is used to make it in accord with the real cutting process; an improved calculation method of thermal stress is adopted; a stress constraint is added according to the volume-constancy of plastic deformation; and the accumulative effect of the stresses during cyclic loading is considered. At last, an experiment for measuring residual stress in cutting AISI 1045 steel is conducted. Also, Jiann's model and the improved model are simulated under the same conditions with cutting experiment. The comparisons show that the surface residual stresses predicted by the improved model is closer to the experimental results than the results predicted by Jiann's model.

  17. Learning Algebra in a Computer Algebra Environment

    ERIC Educational Resources Information Center

    Drijvers, Paul

    2004-01-01

    This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…

  18. Algebra in the Early Years? Yes!

    ERIC Educational Resources Information Center

    Taylor-Cox, Jennifer

    2003-01-01

    Suggests ways early years educators can begin teaching young children to think algebraically and prepare them for success in algebra. Focuses on ways to promote mathematical patterns, mathematical situations and structures, models of quantitative relationship, and change. Describes how first-graders used real object representations to better…

  19. Young Mathematicians at Work: Constructing Algebra

    ERIC Educational Resources Information Center

    Fosnot, Catherine Twomey; Jacob, Bill

    2010-01-01

    This book provides a landscape of learning that helps teachers recognize, support, and celebrate their students' capacity to structure their worlds algebraically. It identifies the models, contexts, and landmarks that facilitate algebraic thinking in young students and provides insightful and practical methods for teachers, math supervisors, and…

  20. Realizations of Galilei algebras

    NASA Astrophysics Data System (ADS)

    Nesterenko, Maryna; Pošta, Severin; Vaneeva, Olena

    2016-03-01

    All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by Shirokov. The varieties of the deformed Galilei algebras are discussed and families of one-parametric deformations are presented in explicit form. It is also shown that a number of well-known and physically interesting equations and systems are invariant with respect to the considered Galilei algebras or their deformations.

  1. Algebraic K-theory, K-regularity, and -duality of -stable C ∗-algebras

    NASA Astrophysics Data System (ADS)

    Mahanta, Snigdhayan

    2015-12-01

    We develop an algebraic formalism for topological -duality. More precisely, we show that topological -duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known isomorphism between twisted K-theories (up to a shift). In order to establish this result we model topological K-theory by algebraic K-theory. We also construct an E ∞ -operad starting from any strongly self-absorbing C ∗-algebra . Then we show that there is a functorial topological K-theory symmetric spectrum construction on the category of separable C ∗-algebras, such that is an algebra over this operad; moreover, is a module over this algebra. Along the way we obtain a new symmetric spectra valued functorial model for the (connective) topological K-theory of C ∗-algebras. We also show that -stable C ∗-algebras are K-regular providing evidence for a conjecture of Rosenberg. We conclude with an explicit description of the algebraic K-theory of a x+ b-semigroup C ∗-algebras coming from number theory and that of -stabilized noncommutative tori.

  2. A Theoretical Framework for Research in Algebra: Modification of Janvier's "Star" Model of Function Understanding.

    ERIC Educational Resources Information Center

    Bowman, Anita H.

    A pentagonal model, based on the star model of function understanding of C. Janvier (1987), is presented as a framework for the design and interpretation of research in the area of learning the concept of mathematical function. The five vertices of the pentagon correspond to five common representations of mathematical function: (1) graph; (2)…

  3. Algebraic multigrid preconditioning within parallel finite-element solvers for 3-D electromagnetic modelling problems in geophysics

    NASA Astrophysics Data System (ADS)

    Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María

    2014-06-01

    We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the

  4. Comparison of an algebraic multigrid algorithm to two iterative solvers used for modeling ground water flow and transport

    USGS Publications Warehouse

    Detwiler, R.L.; Mehl, S.; Rajaram, H.; Cheung, W.W.

    2002-01-01

    Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling.

  5. Comparison of an algebraic multigrid algorithm to two iterative solvers used for modeling ground water flow and transport.

    PubMed

    Detwiler, Russell L; Mehl, Steffen; Rajaram, Harihar; Cheung, Wendy W

    2002-01-01

    Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling. PMID:12019641

  6. A non-linear algebraic model for the turbulent scalar fluxes

    SciTech Connect

    Younis, B.A.; Speziale, C.G.; Clark, T.T.

    1995-09-01

    The need for a new approach to modelling the scalar fluxes stems from the lack of realism in the performance of the simple gradient-transport models and the inadequacy of many of the assumptions underlying the more complicated scalar-flux transport closures. The problems with the simple gradient-transport closures are well known. In models of this type, the scalar fluxes are related to the mean scalar field via a scalar turbulent diffusivity. The purpose of this paper is to report on a novel approach to the modelling of the turbulent scalar fluxes (u{sub i}{theta}) which arise as a consequence of time averaging the transport equation for a mean scalar ({Theta}). The focus of this paper will be on the case where {Theta} is a `passive` scalar; the extension of this approach to cases involving buoyancy and compressibility will be briefly discussed. Models of this type fail badly in complex and strongly-buoyant flows.

  7. Algebraic theory of molecules

    NASA Technical Reports Server (NTRS)

    Iachello, Franco

    1995-01-01

    An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.

  8. Orientation in operator algebras

    PubMed Central

    Alfsen, Erik M.; Shultz, Frederic W.

    1998-01-01

    A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457

  9. Developing Thinking in Algebra

    ERIC Educational Resources Information Center

    Mason, John; Graham, Alan; Johnson-Wilder, Sue

    2005-01-01

    This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…

  10. Connecting Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Darley, Joy W.; Leapard, Barbara B.

    2010-01-01

    Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…

  11. Applied Algebra Curriculum Modules.

    ERIC Educational Resources Information Center

    Texas State Technical Coll., Marshall.

    This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…

  12. Profiles of Algebraic Competence

    ERIC Educational Resources Information Center

    Humberstone, J.; Reeve, R.A.

    2008-01-01

    The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…

  13. Ternary Virasoro - Witt algebra.

    SciTech Connect

    Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham

    2008-01-01

    A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.

  14. Beyond Dirac - a Unified Algebra

    NASA Astrophysics Data System (ADS)

    Lundberg, Wayne R.

    2001-10-01

    A introductory insight will be shared regarding a 'separation of variables' approach to understanding the relationship between QCD and the origins of cosmological and particle mass. The discussion will then build upon work presented at DFP 2000, focussing on the formal basis for using 3x3x3 matrix algebra as it underlies and extends Dirac notation. A set of restrictions are established which break the multiple symmetries of the 3x3x3 matrix algebra, yielding Standard Model QCD objects and interactions. It will be shown that the 3x3x3 matrix representation unifies the algebra of strong and weak (and by extension, electromagnetic) interactions. A direct correspondence to string theoretic objects is established by considering the string to be partitioned in thirds. Rubik's cube is used as a graphical means of handling algebraic manipulation of 3x3x3 algebra. Further, its potential utility for advancing pedagogical methods through active engagement is discussed. A simulated classroom exercize will be conducted.

  15. Efficient Multi-Valued Bounded Model Checking for LTL over Quasi-Boolean Algebras

    NASA Astrophysics Data System (ADS)

    Andrade, Jefferson O.; Kameyama, Yukiyoshi

    Multi-valued Model Checking extends classical, two-valued model checking to multi-valued logic such as Quasi-Boolean logic. The added expressivity is useful in dealing with such concepts as incompleteness and uncertainty in target systems, while it comes with the cost of time and space. Chechik and others proposed an efficient reduction from multi-valued model checking problems to two-valued ones, but to the authors' knowledge, no study was done for multi-valued bounded model checking. In this paper, we propose a novel, efficient algorithm for multi-valued bounded model checking. A notable feature of our algorithm is that it is not based on reduction of multi-values into two-values; instead, it generates a single formula which represents multi-valuedness by a suitable encoding, and asks a standard SAT solver to check its satisfiability. Our experimental results show a significant improvement in the number of variables and clauses and also in execution time compared with the reduction-based one.

  16. Computational algebraic geometry for statistical modeling FY09Q2 progress.

    SciTech Connect

    Thompson, David C.; Rojas, Joseph Maurice; Pebay, Philippe Pierre

    2009-03-01

    This is a progress report on polynomial system solving for statistical modeling. This is a progress report on polynomial system solving for statistical modeling. This quarter we have developed our first model of shock response data and an algorithm for identifying the chamber cone containing a polynomial system in n variables with n+k terms within polynomial time - a significant improvement over previous algorithms, all having exponential worst-case complexity. We have implemented and verified the chamber cone algorithm for n+3 and are working to extend the implementation to handle arbitrary k. Later sections of this report explain chamber cones in more detail; the next section provides an overview of the project and how the current progress fits into it.

  17. SDG Fermion-Pair Algebraic SO(12) and Sp(10) Models and Their Boson Realizations

    NASA Astrophysics Data System (ADS)

    Navratil, P.; Geyer, H. B.; Dobes, J.; Dobaczewski, J.

    1995-11-01

    It is shown how the boson mapping formalism may be applied as a useful many-body tool to solve a fermion problem. This is done in the context of generalized Ginocchio models for which we introduce S-, D-, and G-pairs of fermions and subsequently construct the sdg-boson realizations of the generalized Dyson type. The constructed SO(12) and Sp(10) fermion models are solved beyond the explicit symmetry limits. Phase transitions to rotational structures are obtained also in situations where there is no underlying SU(3) symmetry.

  18. Algebraic expression for the diffuse irradiance reflectivity of water from the two-flow model.

    PubMed

    Jain, S C; Miller, J R

    1977-01-01

    A simple expression is obtained for the irradiance reflectance of the ocean based on a two-flow radiative transfer model. This expression is found to reproduce the Monte Carlo calculations to within 7% for scattering albedo values less than 0.8. On the basis of this expression, it is shown that the remotely sensed water color data can be interpreted with the help of iterative optimization techniques, provided that the variations of backscattering coefficient and absorption coefficient with wavelength can be modeled. PMID:20168452

  19. Computer algebra and operators

    NASA Technical Reports Server (NTRS)

    Fateman, Richard; Grossman, Robert

    1989-01-01

    The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

  20. Algebraic Lattices in QFT Renormalization

    NASA Astrophysics Data System (ADS)

    Borinsky, Michael

    2016-04-01

    The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.

  1. Algebraic Lattices in QFT Renormalization

    NASA Astrophysics Data System (ADS)

    Borinsky, Michael

    2016-07-01

    The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.

  2. Computational triadic algebras of signs

    SciTech Connect

    Zadrozny, W.

    1996-12-31

    We present a finite model of Peirce`s ten classes of signs. We briefly describe Peirce`s taxonomy of signs; we prove that any finite collection of signs can be extended to a finite algebra of signs in which all interpretants are themselves being interpreted; and we argue that Peirce`s ten classes of signs can be defined using constraints on algebras of signs. The paper opens the possibility of defining multimodal cognitive agents using Peirce`s classes of signs, and is a first step towards building a computational logic of signs based on Peirce`s taxonomies.

  3. Micromagnetic model for biaxial stress effects on magnetic properties

    NASA Astrophysics Data System (ADS)

    Sablik, M. J.; Riley, L. A.; Burkhardt, G. L.; Kwun, H.; Cannell, P. Y.; Watts, K. T.; Langman, R. A.

    1994-04-01

    A micromagnetic formulation has been developed for modeling the effect of biaxial stress on magnetoelastic processes in polycrystalline steels. The formulation uses a modified version of the Kashiwaya model for the effect of biaxial stress on magnetic properties and combines it with the Schneider-Cannell-Watts model for magnetoelastic processes in steels. In particular, the model involves use of an effective stress equal to one of the deviatoric (i.e. distortional) normal stress components, depending on whether the field is parallel to a tensile or compressive axis or to the third axis perpendicular to the plane of biaxial stress. Computer results are compared to experimental results on the effects of biaxial stress on magnetic properties in mild steel and in SAE-4130 steel. Good qualitative agreement is found in almost all cases, in that in going from one biaxial stress case to the next, the same kinds of changes are seen magnetically.

  4. A dynamic model of stress and sustained attention

    NASA Technical Reports Server (NTRS)

    Hancock, Peter A.; Warm, Joel S.

    2003-01-01

    This paper examines the effects of stress on sustained attention. With recognition of the task itself as the major source of cognitive stress, a dynamic model is presented that addresses the effects of stress on vigilance and, potentially, a wide variety of attention performance tasks.

  5. The Culture-Work-Health Model and Work Stress.

    ERIC Educational Resources Information Center

    Peterson, Michael; Wilson, John F.

    2002-01-01

    Examines the role of organizational culture in the etiology of workplace stress through the framework of the Culture-Work- Health model. A review of relevant business and health literature indicates that culture is an important component of work stress and may be a key to creating effective organizational stress interventions. (SM)

  6. Neotectonic stresses in Fennoscandia: field observations and modelling

    NASA Astrophysics Data System (ADS)

    Pascal, Christophe

    2013-04-01

    The present-day stress state of Fennoscandia is traditionally viewed as the combination of far field sources and residual glacial loading stresses. Investigations were conducted in different regions of Norway with the purpose of detecting and measuring stress-relief features and to derive from them valuable information on the crustal stress state. Stress-relief features are induced by blasting and sudden rock unloading in road construction and quarrying operations and are common in Norway and very likely in other regions of Fennoscandia. Stress relief at the Earth's surface is diagnostic of anomalously high stress levels at shallow depths in the crust and appears to be a characteristic of the formerly glaciated Baltic and Canadian Precambrian shields. The studied stress-relief features are, in general, indicative of NW-SE compression, suggesting ridge-push as the main source of stress. Our derived stress directions are also in excellent agreement with the ones derived from other kinds of stress indicators, including focal mechanisms from deep earthquakes, demonstrating that stress-relief features are valuable for neotectonic research. As a second step we applied numerical modelling techniques to simulate the neotectonic stress field in Fennoscandia with particular emphasis to southern Norway. A numerical method was used to reconstruct the structure of the Fennoscandian lithosphere. The numerical method involves classical steady-state heat equations to derive lithosphere thickness, geotherm and density distribution and, in addition, requires the studied lithosphere to be isostatically compensated at its base. The a priori crustal structure was derived from previous geophysical studies. Undulations of the geoid were used to calibrate the models. Once the density structure of the Fennoscandian lithosphere is reconstructed it is straightforward to quantify its stress state and compare modelling results with existing stress indicators. The modelling suggests that

  7. Modeling Genome-Scale mRNA Expression Datasets: From Matrix Algebra to Genetic Networks

    NASA Astrophysics Data System (ADS)

    Alter, Orly

    2003-03-01

    DNA microarray genome-wide expression data promise to enhance fundamental understanding of life on the molecular level, and may prove useful in medical diagnosis, treatment and drug design. Analysis of these new data requires mathematical tools that use large quantities of data and reduce the complexity of the data to make them comprehensible. These tools should provide predictive models, i.e., mathematical frameworks for the description of the data, in which the mathematical variables and operations may be assigned biological meaning. Such models will facilitate the unraveling of the cellular machineries that generate, sense and react to the expression signal. I will start with a description of the use of singular value decomposition (SVD) to construct the first model for genome-wide expression data. SVD is a unique data-driven linear transformation of the expression data from the genes × arrays space to the reduced ``eigengenes'' × ``eigenarrays'' space, where the eigengenes (eigenarrays) are unique orthonormal superpositions of the genes (arrays). Normalizing the data, by detecting and filtering out additive and multiplicative experimental artifacts and irrelevant biological processes, enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data, according to a chosen subset of eigengenes (and eigenarrays), rather than by overall expression, gives a global picture of gene expression in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. In some experiments, the significant eigengenes and eigenarrays can be associated with genome-wide effects of regulators, or with measured samples in which these regulators are overactive or underactive, respectively. I will then describe the use of generalized singular value decomposition (GSVD) to construct the first comparative model

  8. Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

    PubMed Central

    Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot

    2016-01-01

    Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate

  9. Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

    NASA Astrophysics Data System (ADS)

    Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot

    2016-01-01

    Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which is not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate

  10. Highly-accelerated quantitative 2D and 3D localized spectroscopy with linear algebraic modeling (SLAM) and sensitivity encoding

    NASA Astrophysics Data System (ADS)

    Zhang, Yi; Gabr, Refaat E.; Zhou, Jinyuan; Weiss, Robert G.; Bottomley, Paul A.

    2013-12-01

    Noninvasive magnetic resonance spectroscopy (MRS) with chemical shift imaging (CSI) provides valuable metabolic information for research and clinical studies, but is often limited by long scan times. Recently, spectroscopy with linear algebraic modeling (SLAM) was shown to provide compartment-averaged spectra resolved in one spatial dimension with many-fold reductions in scan-time. This was achieved using a small subset of the CSI phase-encoding steps from central image k-space that maximized the signal-to-noise ratio. Here, SLAM is extended to two- and three-dimensions (2D, 3D). In addition, SLAM is combined with sensitivity-encoded (SENSE) parallel imaging techniques, enabling the replacement of even more CSI phase-encoding steps to further accelerate scan-speed. A modified SLAM reconstruction algorithm is introduced that significantly reduces the effects of signal nonuniformity within compartments. Finally, main-field inhomogeneity corrections are provided, analogous to CSI. These methods are all tested on brain proton MRS data from a total of 24 patients with brain tumors, and in a human cardiac phosphorus 3D SLAM study at 3T. Acceleration factors of up to 120-fold versus CSI are demonstrated, including speed-up factors of 5-fold relative to already-accelerated SENSE CSI. Brain metabolites are quantified in SLAM and SENSE SLAM spectra and found to be indistinguishable from CSI measures from the same compartments. The modified reconstruction algorithm demonstrated immunity to maladjusted segmentation and errors from signal heterogeneity in brain data. In conclusion, SLAM demonstrates the potential to supplant CSI in studies requiring compartment-average spectra or large volume coverage, by dramatically reducing scan-time while providing essentially the same quantitative results.

  11. Tests of Predictions of the Algebraic Cluster Model: the Triangular D 3h Symmetry of 12C

    NASA Astrophysics Data System (ADS)

    Gai, Moshe

    2016-07-01

    A new theoretical approach to clustering in the frame of the Algebraic Cluster Model (ACM) has been developed. It predicts rotation-vibration structure with rotational band of an oblate equilateral triangular symmetric spinning top with a D 3h symmetry characterized by the sequence of states: 0+, 2+, 3-, 4±, 5- with a degenerate 4+ and 4- (parity doublet) states. Our measured new 2+ 2 in 12C allows the first study of rotation-vibration structure in 12C. The newly measured 5- state and 4- states fit very well the predicted ground state rotational band structure with the predicted sequence of states: 0+, 2+, 3-, 4±, 5- with almost degenerate 4+ and 4- (parity doublet) states. Such a D 3h symmetry is characteristic of triatomic molecules, but it is observed in the ground state rotational band of 12C for the first time in a nucleus. We discuss predictions of the ACM of other rotation-vibration bands in 12 C such as the (0+) Hoyle band and the (1-) bending mode with prediction of (“missing 3- and 4-”) states that may shed new light on clustering in 12C and light nuclei. In particular, the observation (or non observation) of the predicted (“missing”) states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.6542 MeV in 12C. We discuss proposed research programs at the Darmstadt S-DALINAC and at the newly constructed ELI-NP facility near Bucharest to test the predictions of the ACM in isotopes of carbon.

  12. Highly-accelerated quantitative 2D and 3D localized spectroscopy with linear algebraic modeling (SLAM) and sensitivity encoding

    PubMed Central

    Zhang, Yi; Gabr, Refaat E.; Zhou, Jinyuan; Weiss, Robert G.; Bottomley, Paul A.

    2013-01-01

    Noninvasive magnetic resonance spectroscopy (MRS) with chemical shift imaging (CSI) provides valuable metabolic information for research and clinical studies, but is often limited by long scan times. Recently, spectroscopy with linear algebraic modeling (SLAM) was shown to provide compartment-averaged spectra resolved in one spatial dimension with many-fold reductions in scan-time. This was achieved using a small subset of the CSI phase-encoding steps from central image k-space that maximized the signal-to-noise ratio. Here, SLAM is extended to two- and three-dimensions (2D, 3D). In addition, SLAM is combined with sensitivity-encoded (SENSE) parallel imaging techniques, enabling the replacement of even more CSI phase-encoding steps to further accelerate scan-speed. A modified SLAM reconstruction algorithm is introduced that significantly reduces the effects of signal nonuniformity within compartments. Finally, main-field inhomogeneity corrections are provided, analogous to CSI. These methods are all tested on brain proton MRS data from a total of 24 patients with brain tumors, and in a human cardiac phosphorus 3D SLAM study at 3T. Acceleration factors of up to 120-fold versus CSI are demonstrated, including speed-up factors of 5-fold relative to already-accelerated SENSE CSI. Brain metabolites are quantified in SLAM and SENSE SLAM spectra and found to be indistinguishable from CSI measures from the same compartments. The modified reconstruction algorithm demonstrated immunity to maladjusted segmentation and errors from signal heterogeneity in brain data. In conclusion, SLAM demonstrates the potential to supplant CSI in studies requiring compartment-average spectra or large volume coverage, by dramatically reducing scan-time while providing essentially the same quantitative results. PMID:24188921

  13. A dynamic model of stress and sustained attention

    NASA Technical Reports Server (NTRS)

    Hancock, P. A.; Warm, Joel S.

    1989-01-01

    Arguments are presented that an integrated view of stress and performance must consider the task demanding a sustained attention as a primary source of cognitive stress. A dynamic model is developed on the basis of the concept of adaptability in both physiological and psychological terms, that addresses the effects of stress on vigilance and, potentially, a wide variety of attention-demanding performance tasks. The model provides an insight into the failure of an operator under the driving influences of stress and opens a number of potential avenues through which solutions to the complex challenge of stress and performance might be posed.

  14. Effective Stress Management: A Model of Emotional Intelligence, Self-Leadership, and Student Stress Coping

    ERIC Educational Resources Information Center

    Houghton, Jeffery D.; Wu, Jinpei; Godwin, Jeffrey L.; Neck, Christopher P.; Manz, Charles C.

    2012-01-01

    This article develops and presents a model of the relationships among emotional intelligence, self-leadership, and stress coping among management students. In short, the authors' model suggests that effective emotion regulation and self-leadership, as mediated through positive affect and self-efficacy, has the potential to facilitate stress coping…

  15. Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution.

    PubMed

    Bratus, Alexander S; Novozhilov, Artem S; Semenov, Yuri S

    2014-10-01

    A particular case of the famous quasispecies model - the Crow-Kimura model with a permutation invariant fitness landscape - is investigated. Using the fact that the mutation matrix in the case of a permutation invariant fitness landscape has a special tridiagonal form, a change of the basis is suggested such that in the new coordinates a number of analytical results can be obtained. In particular, using the eigenvectors of the mutation matrix as the new basis, we show that the quasispecies distribution approaches a binomial one and give simple estimates for the speed of convergence. Another consequence of the suggested approach is a parametric solution to the system of equations determining the quasispecies. Using this parametric solution we show that our approach leads to exact asymptotic results in some cases, which are not covered by the existing methods. In particular, we are able to present not only the limit behavior of the leading eigenvalue (mean population fitness), but also the exact formulas for the limit quasispecies eigenvector for special cases. For instance, this eigenvector has a geometric distribution in the case of the classical single peaked fitness landscape. On the biological side, we propose a mathematical definition, based on the closeness of the quasispecies to the binomial distribution, which can be used as an operational definition of the notorious error threshold. Using this definition, we suggest two approximate formulas to estimate the critical mutation rate after which the quasispecies delocalization occurs. PMID:25149562

  16. Modeling of stresses at grain boundaries with respect to occurrence of stress corrosion cracking

    SciTech Connect

    Kozaczek, K.J.; Sinharoy, A.; Ruud, C.O.; McIlree, A.R.

    1995-12-31

    The distributions of elastic stresses/strains in the grain boundary regions were studied by the analytical and the finite element models. The grain boundaries represent the sites where stress concentration occurs as a result of discontinuity of elastic properties across the grain boundary and the presence of second phase particles elastically different from the surrounding matrix grains. A quantitative analysis of those stresses for steels and nickel based alloys showed that the stress concentrations in the grain boundary regions are high enough to cause a local microplastic deformation even when the material is in the macroscopic elastic regime. The stress redistribution as a result of such a plastic deformation was discussed.

  17. Modeling heat stress under different environmental conditions.

    PubMed

    Carabaño, M J; Logar, B; Bormann, J; Minet, J; Vanrobays, M-L; Díaz, C; Tychon, B; Gengler, N; Hammami, H

    2016-05-01

    Renewed interest in heat stress effects on livestock productivity derives from climate change, which is expected to increase temperatures and the frequency of extreme weather events. This study aimed at evaluating the effect of temperature and humidity on milk production in highly selected dairy cattle populations across 3 European regions differing in climate and production systems to detect differences and similarities that can be used to optimize heat stress (HS) effect modeling. Milk, fat, and protein test day data from official milk recording for 1999 to 2010 in 4 Holstein populations located in the Walloon Region of Belgium (BEL), Luxembourg (LUX), Slovenia (SLO), and southern Spain (SPA) were merged with temperature and humidity data provided by the state meteorological agencies. After merging, the number of test day records/cows per trait ranged from 686,726/49,655 in SLO to 1,982,047/136,746 in BEL. Values for the daily average and maximum temperature-humidity index (THIavg and THImax) ranges for THIavg/THImax were largest in SLO (22-74/28-84) and shortest in SPA (39-76/46-83). Change point techniques were used to determine comfort thresholds, which differed across traits and climatic regions. Milk yield showed an inverted U-shaped pattern of response across the THI scale with a HS threshold around 73 THImax units. For fat and protein, thresholds were lower than for milk yield and were shifted around 6 THI units toward larger values in SPA compared with the other countries. Fat showed lower HS thresholds than protein traits in all countries. The traditional broken line model was compared with quadratic and cubic fits of the pattern of response in production to increasing heat loads. A cubic polynomial model allowing for individual variation in patterns of response and THIavg as heat load measure showed the best statistical features. Higher/lower producing animals showed less/more persistent production (quantity and quality) across the THI scale. The

  18. Effectiveness of the Mind Research Institute's Algebra Readiness Curriculum on Student Achievement Implemented in a Tiered Response to Intervention Model

    ERIC Educational Resources Information Center

    Quick, Nancy

    2013-01-01

    Algebra is typically the gatekeeper for higher-level math coursework. Low math performance on standardized assessments impedes access to these higher-level math classes. Limited math progress in high school affects future career opportunities and quality of life. High school students who have historically struggled with math need interventions…

  19. Modeling the Effects of Stress: An Approach to Training

    NASA Technical Reports Server (NTRS)

    Cuper, Taryn

    2010-01-01

    Stress is an integral element of the operational conditions experienced by combat medics. The effects of stress can compromise the performance of combat medics who must reach and treat their comrades under often threatening circumstances. Examples of these effects include tunnel vision, loss of motor control, and diminished hearing, which can result in an inability to perceive further danger, satisfactorily treat the casualty, and communicate with others. While many training programs strive to recreate this stress to aid in the experiential learning process, stress inducement may not always be feasible or desired. In addition, live simulations are not always a practical, convenient, and repeatable method of training. Instead, presenting situational training on a personal computer is proposed as an effective training platform in which the effects of stress can be addressed in a different way. We explore the cognitive and motor effects of stress, as well as the benefits of training for mitigating these effects in real life. While many training applications focus on inducing stress in order to "condition" the stress response, the author explores the possibilities of modeling stress to produce a similar effect. Can presenting modeled effects of stress help prepare or inoculate soldiers for stressful situations in which they must perform at a high level? This paper investigates feasibility of modeling stress and describes the preliminary design considerations of a combat medic training system that utilizes this method of battlefield preparation.

  20. Application of reduced order modeling techniques to problems in heat conduction, isoelectric focusing and differential algebraic equations

    NASA Astrophysics Data System (ADS)

    Mathai, Pramod P.

    the uncertainty in the parameters of the differential equations. There is a clear need to design better experiments for IEF without the current overhead of expensive chemicals and labor. We show how with a simpler modeling of the underlying chemistry, we can still achieve the accuracy that has been achieved in existing literature for modeling small ranges of pH (hydrogen ion concentration) in IEF, but with far less computational time. We investigate a further reduction of time by modeling the IEF problem using the Proper Orthogonal Decomposition (POD) technique and show why POD may not be sufficient due to the underlying constraints. The final problem that we address in this thesis addresses a certain class of dynamics with high stiffness - in particular, differential algebraic equations. With the help of simple examples, we show how the traditional POD procedure will fail to model certain high stiffness problems due to a particular behavior of the vector field which we will denote as twist. We further show how a novel augmentation to the traditional POD algorithm can model-reduce problems with twist in a computationally cheap manner without any additional data requirements.

  1. ALGEBRA IIVer 1.22

    2003-06-03

    The ALGEBRA II program allows the user to manipulate data from a finite element analysis before it is plotted by evaluating algebraic expressions. The equation variables are dependent on the input database variable names. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database which can be read by plot programs. Code is written in a portable form as possible. Fortran codemore » is written in ANSI Standard FORTRAN-77. Machine-specific routines are limited in number and are grouped together to minimize the time required to adapt them to a new system. SEACAS codes has been ported to several Unix systems.« less

  2. A modular approach to modeling an isolated power system on a finite voltage bus using a differential algebraic equation solving routine

    NASA Astrophysics Data System (ADS)

    Kipps, Mark R.

    1994-03-01

    The modeling of power systems has been primarily driven by the commercial power utility industry. These models usually involve the assumption that system bus voltage and frequency are constant. However, in applications such as shipboard power systems this infinite bus assumption is not valid. This thesis investigates the modeling of a synchronous generator and various loads in a modular fashion on a finite bus. The simulation presented allows the interconnection of multiple state-space models via a bus voltage model. The major difficulty encountered in building a model which computes bus voltage at each time step is that bus voltage is a function of current and current derivative terms. Bus voltage is also an input to the state equations which produce the current and current derivatives. This creates an algebraic loop which is a form of implicit differential equation. A routine has been developed by Linda Petzold of Lawrence Livermore Laboratory for solving these types of equations. The routine, called Differential Algebraic System Solver (DASSL), has been implemented in a pre-release version of the software Advanced Continuous Simulation Language (ACSL) and has been made available to the Naval Postgraduate School on a trial basis. An isolated power system is modeled using this software and the DASSL routine. The system response to several dynamic situations is studied and the results are presented.

  3. A Richer Understanding of Algebra

    ERIC Educational Resources Information Center

    Foy, Michelle

    2008-01-01

    Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…

  4. On the computation of stress in affine versus nonaffine fibril kinematics within planar collagen network models.

    PubMed

    Pence, Thomas J; Monroe, Ryan J; Wright, Neil T

    2008-08-01

    Some recent analyses modeled the response of collagenous tissues, such as epicardium, using a hypothetical network consisting of interconnected springlike fibers. The fibers in the network were organized such that internal nodes served as the connection point between three such collagen springs. The results for assumed affine and nonaffine deformations are contrasted after a homogeneous deformation at the boundary. Affine deformation provides a stiffer mechanical response than nonaffine deformation. In contrast to nonaffine deformation, affine deformation determines the displacement of internal nodes without imposing detailed force balance, thereby complicating the simplest intuitive notion of stress, one based on free body cuts, at the single node scale. The standard notion of stress may then be recovered via average field theory computations based on large micromesh realizations. An alternative and by all indications complementary viewpoint for the determination of stress in these collagen fiber networks is discussed here, one in which stress is defined using elastic energy storage, a notion which is intuitive at the single node scale. It replaces the average field theory computations by an averaging technique over randomly oriented isolated simple elements. The analytical operations do not require large micromesh realizations, but the tedious nature of the mathematical manipulation is clearly aided by symbolic algebra calculation. For the example case of linear elastic deformation, this results in material stiffnesses that relate the infinitesimal strain and stress. The result that the affine case is stiffer than the nonaffine case is recovered, as would be expected. The energy framework also lends itself to the natural inclusion of changes in mechanical response due to the chemical, electrical, or thermal environment. PMID:18601451

  5. A meteorologically driven grain sorghum stress indicator model

    NASA Technical Reports Server (NTRS)

    Taylor, T. W.; Ravet, F. W. (Principal Investigator)

    1981-01-01

    A grain sorghum soil moisture and temperature stress model is described. It was developed to serve as a meteorological data filter to alert commodity analysts to potential stress conditions and crop phenology in selected grain sorghum production areas. The model also identifies optimum conditions on a daily basis and planting/harvest problems associated with poor tractability.

  6. Oxidative Stress in Genetic Mouse Models of Parkinson's Disease

    PubMed Central

    Varçin, Mustafa; Bentea, Eduard; Michotte, Yvette; Sarre, Sophie

    2012-01-01

    There is extensive evidence in Parkinson's disease of a link between oxidative stress and some of the monogenically inherited Parkinson's disease-associated genes. This paper focuses on the importance of this link and potential impact on neuronal function. Basic mechanisms of oxidative stress, the cellular antioxidant machinery, and the main sources of cellular oxidative stress are reviewed. Moreover, attention is given to the complex interaction between oxidative stress and other prominent pathogenic pathways in Parkinson's disease, such as mitochondrial dysfunction and neuroinflammation. Furthermore, an overview of the existing genetic mouse models of Parkinson's disease is given and the evidence of oxidative stress in these models highlighted. Taken into consideration the importance of ageing and environmental factors as a risk for developing Parkinson's disease, gene-environment interactions in genetically engineered mouse models of Parkinson's disease are also discussed, highlighting the role of oxidative damage in the interplay between genetic makeup, environmental stress, and ageing in Parkinson's disease. PMID:22829959

  7. Setting up virgin stress conditions in discrete element models

    PubMed Central

    Rojek, J.; Karlis, G.F.; Malinowski, L.J.; Beer, G.

    2013-01-01

    In the present work, a methodology for setting up virgin stress conditions in discrete element models is proposed. The developed algorithm is applicable to discrete or coupled discrete/continuum modeling of underground excavation employing the discrete element method (DEM). Since the DEM works with contact forces rather than stresses there is a need for the conversion of pre-excavation stresses to contact forces for the DEM model. Different possibilities of setting up virgin stress conditions in the DEM model are reviewed and critically assessed. Finally, a new method to obtain a discrete element model with contact forces equivalent to given macroscopic virgin stresses is proposed. The test examples presented show that good results may be obtained regardless of the shape of the DEM domain. PMID:27087731

  8. Connecting Algebra and Chemistry.

    ERIC Educational Resources Information Center

    O'Connor, Sean

    2003-01-01

    Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)

  9. Z 2-graded classical r-matrices and algebraic Bethe ansatz: applications to integrable models of quantum optics and nuclear physics

    NASA Astrophysics Data System (ADS)

    Skrypnyk, T.

    2016-09-01

    We consider quantum integrable models based on the Lie algebra gl(n) and non-skew-symmetric classical r-matrices associated with Z 2-gradings of gl(n) of the following type: {gl}(n)={gl}{(n)}\\bar{0}+{gl}{(n)}\\bar{1}, where {gl}{(n)}\\bar{0}={gl}({n}1)\\oplus {gl}(n-{n}1). Among the considered models are Gaudin-type models with an external magnetic field, used in nuclear physics to produce proton–neutron Bardeen–Cooper–Schrieer-type models, n-level many-mode Jaynes–Cummings–Dicke-type models of quantum optics, matrix generalization of Bose–Hubbard dimers, etc. We diagonalize the constructed models by means of the ‘generalized’ nested Bethe ansatz.

  10. A model analysis of static stress in the vestibular membranes

    PubMed Central

    Pender, Daniel J

    2009-01-01

    Background The scheme of the core vestibular membranes, consisting of serially connected utricle, ampulla and semicircular canal, first appeared hundreds of millions of years ago in primitive fish and has remained largely unchanged during the subsequent course of evolution. The labyrinths of higher organisms build on this core structure, with the addition of the phylogenetically newer membrane structures, namely, saccule, lagena and cochlea. An analysis of static stress in these core vestibular membranes may contribute to a better understanding of the role of stress in the evolution of derivative membrane structures over the long term as well as the short-term membrane distortions seen in Meniere's disease. Methods A model of these core vestibular membranes is proposed in order to analyze the distribution of stress in the walls of the component chambers. The model uses basic geometrical elements of hollow cylinders and spheres to emulate the actual structures. These model elements lend themselves to a mathematical analysis of static stress in their membranes. Results Hoop stress, akin to the stress in hoops used to reinforce barrel walls, is found to be the predominant stress in the model membranes. The level of hoop stress depends not only on pressure but as well on a geometric stress factor that incorporates membrane shape, thickness and curvature. This result implies that hoop stress may be unevenly distributed in the membranes of the several vestibular chambers due to variations in these dimensional parameters. These results provide a theoretical framework for appraising hoop stress levels in any vestibular labyrinth whose dimensions are known. Conclusion Static hoop stress disparities are likely to exist in the vestibular membranes given their complex physical configurations. Such stress disparities may contribute to the development of membrane pathologies as seen in Meniere's Disease. They may also factor in the evolutionary development of other derivative

  11. A simplified Reynolds stress model for unsteady turbulent boundary layers

    NASA Technical Reports Server (NTRS)

    Fan, Sixin; Lakshminarayana, Budugur

    1993-01-01

    A simplified Reynolds stress model has been developed for the prediction of unsteady turbulent boundary layers. By assuming that the net transport of Reynolds stresses is locally proportional to the net transport of the turbulent kinetic energy, the time dependent full Reynolds stress model is reduced to a set of ordinary differential equations. These equations contain only time derivatives and can be readily integrated in a time dependent boundary layer or Navier-Stokes code. The turbulent kinetic energy and dissipation rate needed for the model are obtained by solving the k-epsilon equations. This simplified Reynolds stress turbulence model (SRSM) does not use the eddy viscosity assumption, which may not be valid for unsteady turbulent flows. The anisotropy of both the steady and the unsteady turbulent normal stresses can be captured by the SRSM model. Through proper damping of the shear stresses, the present model can be used in the near wall region of turbulent boundary layers. This model has been validated against data for steady and unsteady turbulent boundary layers, including periodic turbulent boundary layers subjected to a mean adverse pressure gradient. For the cases tested, the predicted unsteady velocity and turbulent stress components agree well with the experimental data. Comparison between the predictions from the SRSM model and a k-epsilon model is also presented.

  12. Anisotropic stress and stability in modified gravity models

    SciTech Connect

    Saltas, Ippocratis D.; Kunz, Martin

    2011-03-15

    The existence of anisotropic stress of a purely geometrical origin seems to be a characteristic of higher order gravity models, and has been suggested as a probe to test these models observationally, for example, in weak lensing experiments. In this paper, we seek to find a class of higher order gravity models of f(R,G) type that would give us a zero anisotropic stress and study the consequences for the viability of the actual model. For the special case of a de Sitter background, we identify a subclass of models with the desired property. We also find a direct link between anisotropic stress and the stability of the model as well as the presence of extra degrees of freedom, which seems to be a general feature of higher order gravity models. Particularly, setting the anisotropic stress equal to zero for a de Sitter background leads to a singularity that makes it impossible to reach the de Sitter evolution.

  13. Fuzzy-algebra uncertainty assessment

    SciTech Connect

    Cooper, J.A.; Cooper, D.K.

    1994-12-01

    A significant number of analytical problems (for example, abnormal-environment safety analysis) depend on data that are partly or mostly subjective. Since fuzzy algebra depends on subjective operands, we have been investigating its applicability to these forms of assessment, particularly for portraying uncertainty in the results of PRA (probabilistic risk analysis) and in risk-analysis-aided decision-making. Since analysis results can be a major contributor to a safety-measure decision process, risk management depends on relating uncertainty to only known (not assumed) information. The uncertainties due to abnormal environments are even more challenging than those in normal-environment safety assessments; and therefore require an even more judicious approach. Fuzzy algebra matches these requirements well. One of the most useful aspects of this work is that we have shown the potential for significant differences (especially in perceived margin relative to a decision threshold) between fuzzy assessment and probabilistic assessment based on subtle factors inherent in the choice of probability distribution models. We have also shown the relation of fuzzy algebra assessment to ``bounds`` analysis, as well as a description of how analyses can migrate from bounds analysis to fuzzy-algebra analysis, and to probabilistic analysis as information about the process to be analyzed is obtained. Instructive examples are used to illustrate the points.

  14. Algebraic distance on graphs.

    SciTech Connect

    Chen, J.; Safro, I.

    2011-01-01

    Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.

  15. Severe Life Stress and Oxidative Stress in the Brain: From Animal Models to Human Pathology

    PubMed Central

    Jaquet, Vincent; Trabace, Luigia; Krause, Karl-Heinz

    2013-01-01

    Abstract Significance: Severe life stress (SLS), as opposed to trivial everyday stress, is defined as a serious psychosocial event with the potential of causing an impacting psychological traumatism. Recent Advances: Numerous studies have attempted to understand how the central nervous system (CNS) responds to SLS. This response includes a variety of morphological and neurochemical modifications; among them, oxidative stress is almost invariably observed. Oxidative stress is defined as disequilibrium between oxidant generation and the antioxidant response. Critical Issues: In this review, we discuss how SLS leads to oxidative stress in the CNS, and how the latter impacts pathophysiological outcomes. We also critically discuss experimental methods that measure oxidative stress in the CNS. The review covers animal models and human observations. Animal models of SLS include sleep deprivation, maternal separation, and social isolation in rodents, and the establishment of hierarchy in non-human primates. In humans, SLS, which is caused by traumatic events such as child abuse, war, and divorce, is also accompanied by oxidative stress in the CNS. Future Directions: The outcome of SLS in humans ranges from resilience, over post-traumatic stress disorder, to development of chronic mental disorders. Defining the sources of oxidative stress in SLS might in the long run provide new therapeutic avenues. Antioxid. Redox Signal. 18, 1475–1490. PMID:22746161

  16. Phase Boundaries in Algebraic Conformal QFT

    NASA Astrophysics Data System (ADS)

    Bischoff, Marcel; Kawahigashi, Yasuyuki; Longo, Roberto; Rehren, Karl-Henning

    2016-02-01

    We study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries. Phase boundaries are instances of a more general notion of boundaries that give rise to a variety of algebraic structures. These can be formulated in a common framework originating in Algebraic QFT, with the principle of Einstein Causality playing a prominent role. We classify the phase boundary conditions by the centre of a certain universal construction, which produces a reducible representation in which all possible boundary conditions are realized. For a large class of models, the classification reproduces results obtained in a different approach by Fuchs et al. before.

  17. SatStress: A Web-Accessible Model of Viscoelastic Tidal Stresses in Icy Satellites

    NASA Astrophysics Data System (ADS)

    Crawford, Z. A.; Mullen, M. E.; Pappalardo, R. T.

    2007-03-01

    We develop a viscoelastic treatment of the membrane stresses present on the surfaces of icy satellites, based on the gravitational potential, and describe the benefits of making the model and its source code publicly available via the WWW.

  18. Teaching Structure in Algebra

    ERIC Educational Resources Information Center

    Merlin, Ethan M.

    2013-01-01

    This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…

  19. Ready, Set, Algebra?

    ERIC Educational Resources Information Center

    Levy, Alissa Beth

    2012-01-01

    The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…

  20. Linear-Algebra Programs

    NASA Technical Reports Server (NTRS)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  1. Catching Up on Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2008-01-01

    A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…

  2. A study of Reynolds-stress closure model

    NASA Technical Reports Server (NTRS)

    Amano, R. S.; Goel, P.

    1985-01-01

    A hybrid model of the Reynolds stress closure was developed. This model was tested for various sizes of step flow, and the computed Reynolds stress behavior was compared with experimental data. The third order closure model was reviewed. Transport equations for the triple velocity correlation were developed and implemented in a numerical code to evaluate the behavior of the triple velocity products in various regions of the flow field including recirculating, reattaching, and redeveloping flow domains.

  3. A model of Barchan dunes including lateral shear stress.

    PubMed

    Schwämmle, V; Herrmann, H J

    2005-01-01

    Barchan dunes are found where sand availability is low and wind direction quite constant. The two dimensional shear stress of the wind field and the sand movement by saltation and avalanches over a barchan dune are simulated. The model with one dimensional shear stress is extended including surface diffusion and lateral shear stress. The resulting final shape is compared to the results of the model with a one dimensional shear stress and confirmed by comparison to measurements. We found agreement and improvements with respect to the model with one dimensional shear stress. Additionally, a characteristic edge at the center of the windward side is discovered which is also observed for big barchans. Diffusion effects reduce this effect for small dunes. PMID:15688141

  4. A finite element model for residual stress in repair welds

    SciTech Connect

    Feng, Z.; Wang, X.L.; Spooner, S.; Goodwin, G.M.; Maziasz, P.J.; Hubbard, C.R.; Zacharia, T.

    1996-03-28

    This paper describes a three-dimensional finite element model for calculation of the residual stress distribution caused by repair welding. Special user subroutines were developed to simulate the continuous deposition of filler metal during welding. The model was then tested by simulating the residual stress/strain field of a FeAl weld overlay clad on a 2{1/4}Cr-1 Mo steel plate, for which neutron diffraction measurement data of the residual strain field were available. It is shown that the calculated residual stress distribution was consistent with that determined with neutron diffraction. High tensile residual stresses in both the longitudinal and transverse directions were observed around the weld toe at the end of the weld. The strong spatial dependency of the residual stresses in the region around the weld demonstrates that the common two-dimensional cross-section finite element models should not be used for repair welding analysis.

  5. Incorporating Uncoupled Stress Effects into FEHM Modeling of HDR Reservoirs

    SciTech Connect

    Birdsell, Stephen A.

    1988-07-01

    Thermal and pressure-induced stress effects are extremely important aspects of modeling HDR reservoirs because these effects will control the transient behavior of reservoir flow impedance, water loss and flow distribution. Uncoupled stress effects will be added to the existing three-dimensional Finite Element Heat and Mass Transfer (FEHM) model (Birdsell, 1988) in order to more realistically simulate HDR reservoirs. Stress effects will be uncoupled in the new model since a fully-coupled code will not be available for some time.

  6. Emotional Stress and Cardiovascular Complications in Animal Models: A Review of the Influence of Stress Type

    PubMed Central

    Crestani, Carlos C.

    2016-01-01

    Emotional stress has been recognized as a modifiable risk factor for cardiovascular diseases. The impact of stress on physiological and psychological processes is determined by characteristics of the stress stimulus. For example, distinct responses are induced by acute vs. chronic aversive stimuli. Additionally, the magnitude of stress responses has been reported to be inversely related to the degree of predictability of the aversive stimulus. Therefore, the purpose of the present review was to discuss experimental research in animal models describing the influence of stressor stimulus characteristics, such as chronicity and predictability, in cardiovascular dysfunctions induced by emotional stress. Regarding chronicity, the importance of cardiovascular and autonomic adjustments during acute stress sessions and cardiovascular consequences of frequent stress response activation during repeated exposure to aversive threats (i.e., chronic stress) is discussed. Evidence of the cardiovascular and autonomic changes induced by chronic stressors involving daily exposure to the same stressor (predictable) vs. different stressors (unpredictable) is reviewed and discussed in terms of the impact of predictability in cardiovascular dysfunctions induced by stress. PMID:27445843

  7. Tectonic stressing in California modeled from GPS observations

    USGS Publications Warehouse

    Parsons, T.

    2006-01-01

    What happens in the crust as a result of geodetically observed secular motions? In this paper we find out by distorting a finite element model of California using GPS-derived displacements. A complex model was constructed using spatially varying crustal thickness, geothermal gradient, topography, and creeping faults. GPS velocity observations were interpolated and extrapolated across the model and boundary condition areas, and the model was loaded according to 5-year displacements. Results map highest differential stressing rates in a 200-km-wide band along the Pacific-North American plate boundary, coinciding with regions of greatest seismic energy release. Away from the plate boundary, GPS-derived crustal strain reduces modeled differential stress in some places, suggesting that some crustal motions are related to topographic collapse. Calculated stressing rates can be resolved onto fault planes: useful for addressing fault interactions and necessary for calculating earthquake advances or delays. As an example, I examine seismic quiescence on the Garlock fault despite a calculated minimum 0.1-0.4 MPa static stress increase from the 1857 M???7.8 Fort Tejon earthquake. Results from finite element modeling show very low to negative secular Coulomb stress growth on the Garlock fault, suggesting that the stress state may have been too low for large earthquake triggering. Thus the Garlock fault may only be stressed by San Andreas fault slip, a loading pattern that could explain its erratic rupture history.

  8. A hydrostatic stress-dependent anisotropic model of viscoplasticity

    NASA Technical Reports Server (NTRS)

    Robinson, D. N.; Tao, Q.; Verrilli, M. J.

    1994-01-01

    A hydrostatic stress-dependent, anisotropic model of viscoplasticity is formulated as an extension of Bodner's model. This represents a further extension of the isotropic Bodner model over that made to anisotropy by Robinson and MitiKavuma. Account is made of the inelastic deformation that can occur in metallic composites under hydrostatic stress. A procedure for determining the material parameters is identified that is virtually identical to the established characterization procedure for the original Bodner model. Characterization can be achieved using longitudinal/transverse tensile and shear tests and hydrostatic stress tests; alternatively, four off-axis tensile tests can be used. Conditions for a yield stress minimum under off-axis tension are discussed. The model is applied to a W/Cu composite; characterization is made using off-axis tensile data generated at NASA Lewis Research Center (LeRC).

  9. Thermal Residual Stress in Environmental Barrier Coated Silicon Nitride - Modeled

    NASA Technical Reports Server (NTRS)

    Ali, Abdul-Aziz; Bhatt, Ramakrishna T.

    2009-01-01

    When exposed to combustion environments containing moisture both un-reinforced and fiber reinforced silicon based ceramic materials tend to undergo surface recession. To avoid surface recession environmental barrier coating systems are required. However, due to differences in the elastic and thermal properties of the substrate and the environmental barrier coating, thermal residual stresses can be generated in the coated substrate. Depending on their magnitude and nature thermal residual stresses can have significant influence on the strength and fracture behavior of coated substrates. To determine the maximum residual stresses developed during deposition of the coatings, a finite element model (FEM) was developed. Using this model, the thermal residual stresses were predicted in silicon nitride substrates coated with three environmental coating systems namely barium strontium aluminum silicate (BSAS), rare earth mono silicate (REMS) and earth mono di-silicate (REDS). A parametric study was also conducted to determine the influence of coating layer thickness and material parameters on thermal residual stress. Results indicate that z-direction stresses in all three systems are small and negligible, but maximum in-plane stresses can be significant depending on the composition of the constituent layer and the distance from the substrate. The BSAS and REDS systems show much lower thermal residual stresses than REMS system. Parametric analysis indicates that in each system, the thermal residual stresses can be decreased with decreasing the modulus and thickness of the coating.

  10. Dynamic triggering: Stress modeling and a case study

    NASA Astrophysics Data System (ADS)

    Gonzalez-Huizar, Hector; Velasco, Aaron A.

    2011-02-01

    Changes in the static stress can trigger nearby earthquakes that occur within a few fault lengths from the causative event. Transient stresses caused by passage of surface waves commonly trigger events at remote distances, yet little is documented or understood about the processes and stresses necessary for remote triggering. To understand the causative stresses and environments behind remote, or dynamic, triggering, we must decipher the stresses caused by the passage of the surface waves in relation to the local stress field and fault conditions where the triggered events occur. In this study, we model the change in the stress field that the passing of Rayleigh and Love waves causes on a fault plane of arbitrary orientation relative to the direction of propagation of the waves, and we apply a Coulomb failure criterion to calculate the potential of these stress changes to trigger reverse, normal, or strike-slip failure. We compare these model results with data from dynamically triggered earthquakes in the Australian Bowen Basin, an area with low seismicity and mapped regional stress and that is at the margin of a stable continental craton. Our data analysis shows that for this region, surface waves arriving at 45° from the average strike direction are the most likely to trigger local seismicity. This agrees with our observations.

  11. Three-algebra for supermembrane and two-algebra for superstring

    NASA Astrophysics Data System (ADS)

    Lee, Kanghoon; Park, Jeong-Hyuck

    2009-04-01

    While string or Yang-Mills theories are based on Lie algebra or two-algebra structure, recent studies indicate that Script M-theory may require a one higher, three-algebra structure. Here we construct a covariant action for a supermembrane in eleven dimensions, which is invariant under global supersymmetry, local fermionic symmetry and worldvolume diffeomorphism. Our action is classically on-shell equivalent to the celebrated Bergshoeff-Sezgin-Townsend action. However, the novelty is that we spell the action genuinely in terms of Nambu three-brackets: All the derivatives appear through Nambu brackets and hence it manifests the three-algebra structure. Further the double dimensional reduction of our action gives straightforwardly to a type IIA string action featuring two-algebra. Applying the same method, we also construct a covariant action for type IIB superstring, leading directly to the IKKT matrix model.

  12. Stress field modelling from digital geological map data

    NASA Astrophysics Data System (ADS)

    Albert, Gáspár; Barancsuk, Ádám; Szentpéteri, Krisztián

    2016-04-01

    To create a model for the lithospheric stress a functional geodatabase is required which contains spatial and geodynamic parameters. A digital structural-geological map is a geodatabase, which usually contains enough attributes to create a stress field model. Such a model is not accurate enough for engineering-geological purposes because simplifications are always present in a map, but in many cases maps are the only sources for a tectonic analysis. The here presented method is designed for field geologist, who are interested to see the possible realization of the stress field over the area, on which they are working. This study presents an application which can produce a map of 3D stress vectors from a kml-file. The core application logic is implemented on top of a spatially aware relational database management system. This allows rapid and geographically accurate analysis of the imported geological features, taking advantage of standardized spatial algorithms and indexing. After pre-processing the map features in a GIS, according to the Type-Property-Orientation naming system, which was described in a previous study (Albert et al. 2014), the first stage of the algorithm generates an irregularly spaced point cloud by emitting a pattern of points within a user-defined buffer zone around each feature. For each point generated, a component-wise approximation of the tensor field at the point's position is computed, derived from the original feature's geodynamic properties. In a second stage a weighted moving average method calculates the stress vectors in a regular grid. Results can be exported as geospatial data for further analysis or cartographic visualization. Computation of the tensor field's components is based on the implementation of the Mohr diagram of a compressional model, which uses a Coulomb fracture criterion. Using a general assumption that the main principal stress must be greater than the stress from the overburden, the differential stress is

  13. Invariant differential operators for non-compact Lie algebras parabolically related to conformal Lie algebras

    NASA Astrophysics Data System (ADS)

    Dobrev, V. K.

    2013-02-01

    In the present paper we continue the project of systematic construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we call 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduce the new notion of parabolic relation between two non-compact semisimple Lie algebras G and G ' that have the same complexification and possess maximal parabolic subalgebras with the same complexification. Thus, we consider the exceptional algebra E 7(7) which is parabolically related to the CLA E 7(-25) , the parabolic subalgebras including E 6(6) and E 6(-26). Other interesting examples are the orthogonal algebras so(p, q) all of which are parabolically related to the conformal algebra so( n, 2) with p + q = n + 2, the parabolic subalgebras including the Lorentz subalgebra so( n - 1, 1) and its analogs so( p - 1, q - 1). We consider also E6(6) and E6(2) which are parabolically related to the hermitian symmetric case E6(-14) , the parabolic subalgebras including real forms of sl(6). We also give a formula for the number of representations in the main multiplets valid for CLAs and all algebras that are parabolically related to them. In all considered cases we give the main multiplets of indecomposable elementary representations including the necessary data for all relevant invariant differential operators. In the case of so( p, q) we give also the reduced multiplets. We should stress that the multiplets are given in the most economic way in pairs of shadow fields. Furthermore we should stress that the classification of all invariant differential operators includes as special cases all possible conservation laws and conserved currents, unitary or not.

  14. Semigroups and computer algebra in algebraic structures

    NASA Astrophysics Data System (ADS)

    Bijev, G.

    2012-11-01

    Some concepts in semigroup theory can be interpreted in several algebraic structures. A generalization fA,B,fA,B(X) = A(X')B of the complement operator (') on Boolean matrices is made, where A and B denote any rectangular Boolean matrices. While (') is an isomorphism between Boolean semilattices, the generalized complement operator is homomorphism in the general case. The map fA,B and its general inverse (fA,B)+ have quite similar properties to those in the linear algebra and are useful for solving linear equations in Boolean matrix algebras. For binary relations on a finite set, necessary and sufficient conditions for the equation αξβ = γ to have a solution ξ are proved. A generalization of Green's equivalence relations in semigroups for rectangular matrices is proposed. Relationships between them and the Moore-Penrose inverses are investigated. It is shown how any generalized Green's H-class could be constructed by given its corresponding linear subspaces and converted into a group isomorphic to a linear group. Some information about using computer algebra methods concerning this paper is given.

  15. Lie algebra extensions of current algebras on S3

    NASA Astrophysics Data System (ADS)

    Kori, Tosiaki; Imai, Yuto

    2015-06-01

    An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.

  16. Thermodynamic Modeling and Analysis of Human Stress Response

    NASA Technical Reports Server (NTRS)

    Boregowda, S. C.; Tiwari, S. N.

    1999-01-01

    A novel approach based on the second law of thermodynamics is developed to investigate the psychophysiology and quantify human stress level. Two types of stresses (thermal and mental) are examined. A Unified Stress Response Theory (USRT) is developed under the new proposed field of study called Engineering Psychophysiology. The USRT is used to investigate both thermal and mental stresses from a holistic (human body as a whole) and thermodynamic viewpoint. The original concepts and definitions are established as postulates which form the basis for thermodynamic approach to quantify human stress level. An Objective Thermal Stress Index (OTSI) is developed by applying the second law of thermodynamics to the human thermal system to quantify thermal stress or dis- comfort in the human body. The human thermal model based on finite element method is implemented. It is utilized as a "Computational Environmental Chamber" to conduct series of simulations to examine the human thermal stress responses under different environmental conditions. An innovative hybrid technique is developed to analyze human thermal behavior based on series of human-environment interaction simulations. Continuous monitoring of thermal stress is demonstrated with the help of OTSI. It is well established that the human thermal system obeys the second law of thermodynamics. Further, the OTSI is validated against the experimental data. Regarding mental stress, an Objective Mental Stress Index (OMSI) is developed by applying the Maxwell relations of thermodynamics to the combined thermal and cardiovascular system in the human body. The OMSI is utilized to demonstrate the technique of monitoring mental stress continuously and is validated with the help of series of experimental studies. Although the OMSI indicates the level of mental stress, it provides a strong thermodynamic and mathematical relationship between activities of thermal and cardiovascular systems of the human body.

  17. Micromagnetic modeling of the effects of stress on magnetic properties

    SciTech Connect

    Zhu, B.; Lo, C. C. H.; Lee, S. J.; Jiles, D. C.

    2001-06-01

    A micromagnetic model has been developed for investigating the effect of stress on the magnetic properties of thin films. This effect has been implemented by including the magnetoelastic energy term into the Landau{endash}Lifshitz{endash}Gilbert equation. Magnetization curves of a nickel film were calculated under both tensile and compressive stresses of various magnitudes applied along the field direction. The modeling results show that coercivity increased with increasing compressive stress while remanence decreased with increasing tensile stress. The results are in agreement with the experimental data in the literature and can be interpreted in terms of the effects of the applied stress on the irreversible rotation of magnetic moments during magnetization reversal under an applied field. {copyright} 2001 American Institute of Physics.

  18. Stress and Sleep Reactivity: A Prospective Investigation of the Stress-Diathesis Model of Insomnia

    PubMed Central

    Drake, Christopher L.; Pillai, Vivek; Roth, Thomas

    2014-01-01

    Study Objectives: To prospectively assess sleep reactivity as a diathesis of insomnia, and to delineate the interaction between this diathesis and naturalistic stress in the development of insomnia among normal sleepers. Design: Longitudinal. Setting: Community-based. Participants: 2,316 adults from the Evolution of Pathways to Insomnia Cohort (EPIC) with no history of insomnia or depression (46.8 ± 13.2 y; 60% female). Interventions: None. Measurements and Results: Participants reported the number of stressful events they encountered at baseline (Time 1), as well as the level of cognitive intrusion they experienced in response to each stressor. Stressful events (OR = 1.13; P < 0.01) and stress-induced cognitive intrusion (OR = 1.61; P < 0.01) were significant predictors of risk for insomnia one year hence (Time 2). Intrusion mediated the effects of stressful events on risk for insomnia (P < 0.05). Trait sleep reactivity significantly increased risk for insomnia (OR = 1.78; P < 0.01). Further, sleep reactivity moderated the effects of stress-induced intrusion (P < 0.05), such that the risk for insomnia as a function of intrusion was significantly higher in individuals with high sleep reactivity. Trait sleep reactivity also constituted a significant risk for depression (OR = 1.67; P < 0.01) two years later (Time 3). Insomnia at Time 2 significantly mediated this effect (P < 0.05). Conclusions: This study suggests that premorbid sleep reactivity is a significant risk factor for incident insomnia, and that it triggers insomnia by exacerbating the effects of stress-induced intrusion. Sleep reactivity is also a precipitant of depression, as mediated by insomnia. These findings support the stress-diathesis model of insomnia, while highlighting sleep reactivity as an important diathesis. Citation: Drake CL, Pillai V, Roth T. Stress and sleep reactivity: a prospective investigation of the stress-diathesis model of insomnia. SLEEP 2014;37(8):1295-1304. PMID:25083009

  19. Leibniz algebras associated with representations of filiform Lie algebras

    NASA Astrophysics Data System (ADS)

    Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.

    2015-12-01

    In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.

  20. Modeling Tidal Stresses on Planetary Bodies Using an Enhanced SatStress GUI

    NASA Astrophysics Data System (ADS)

    Patthoff, D. A.; Pappalardo, R. T.; Tang, L.; Kay, J.; Kattenhorn, S. A.

    2014-12-01

    Icy and rocky satellites of our solar system display a wide range of structural deformation on their surfaces. Some surfaces are old and heavily cratered showing little evidence for recent tectonism while other surfaces are sparsely cratered and young, with some moons showing geologically very recent or present-day activity. The young deformation can take the form of small cracks in the surface, large double ridges that can extend for thousands of km, and mountain ranges that can reach heights of several kilometers. Many of the potential sources of stress that can deform the surfaces are likely tied to the diurnal tidal deformation of the moons as they orbit their parent planets. Other secular sources of global-scale stress include: volume change induced by the melting or freezing of a subsurface liquid layer, change in the orbital parameters of the moon, or rotation of the outer shell of the satellite relative to the rest of the body (nonsynchronous rotation or true polar wander). We turn to computer modeling to correlate observed structural features to the possible stresses that created them. A variety of modeling programs exist and generally assume a thin ice shell and/or a multi-layered viscoelastic satellite. The program SatStress, which was developed by Zane Crawford and documented by Wahr et al. (2009), computes tidal and nonsynchronous rotation stresses on a satellite. It was later modified into a more user-friendly version with a graphical user interface (SatStress GUI) by Kay and Kattenhorn (2010). This implementation assumes a 4-layer viscoelastic body and is able to calculate stresses resulting from diurnal tides, nonsynchronous rotation, and ice shell thickening. Here we illustrate our recent enhancements to SatStress GUI and compare modeled stresses to example features observed on the surfaces of Ganymede, Europa, and Enceladus. Kay and Kattenhorn (2010) 41st LPSC, abs # 2046. Wahr et al. (2009) Icarus, 200, 188-206.

  1. An ambient agent model for analyzing managers' performance during stress

    NASA Astrophysics Data System (ADS)

    ChePa, Noraziah; Aziz, Azizi Ab; Gratim, Haned

    2016-08-01

    Stress at work have been reported everywhere. Work related performance during stress is a pattern of reactions that occurs when managers are presented with work demands that are not matched with their knowledge, skills, or abilities, and which challenge their ability to cope. Although there are many prior findings pertaining to explain the development of manager performance during stress, less attention has been given to explain the same concept through computational models. In such, a descriptive nature in psychological theories about managers' performance during stress can be transformed into a causal-mechanistic stage that explains the relationship between a series of observed phenomena. This paper proposed an ambient agent model for analyzing managers' performance during stress. Set of properties and variables are identified through past literatures to construct the model. Differential equations have been used in formalizing the model. Set of equations reflecting relations involved in the proposed model are presented. The proposed model is essential and can be encapsulated within an intelligent agent or robots that can be used to support managers during stress.

  2. Coreflections in Algebraic Quantum Logic

    NASA Astrophysics Data System (ADS)

    Jacobs, Bart; Mandemaker, Jorik

    2012-07-01

    Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.

  3. Modeling of grain boundary stresses in Alloy 600

    SciTech Connect

    Kozaczek, K.J.; Sinharoy, A.; Ruud, C.O.; Mcllree, A.R.

    1995-04-01

    Corrosive environments combined with high stress levels and susceptible microstructures can cause intergranular stress corrosion cracking (IGSCC) of Alloy 600 components on both primary and secondary sides of pressurized water reactors. One factor affecting the IGSCC is intergranular carbide precipitation controlled by heat treatment of Alloy 600. This study is concerned with analysis of elastic stress fields in vicinity of M{sub 7}C{sub 3} and M{sub 23}C{sub 6} carbides precipitated in the matrix and at a grain boundary triple point. The local stress concentration which can lead to IGSCC initiation was studied using a two-dimensional finite element model. The intergranular precipitates are more effective stress raisers than the intragranular precipitates. The combination of the elastic property mismatch and the precipitate shape can result in a local stress field substantially different than the macroscopic stress. The maximum local stresses in the vicinity of the intergranular precipitate were almost twice as high as the applied stress.

  4. Thermomechanical Modeling of Stress Relaxation in Shape Memory Alloy Wires

    NASA Astrophysics Data System (ADS)

    Zare, Fateme; Kadkhodaei, Mahmoud; Salafian, Iman

    2015-04-01

    When a shape memory alloy (SMA) is subjected to a mechanical load, especially at high strain rates, its temperature varies due to thermomechanical coupling in the response of these materials. Thus, if strain is kept constant during the transformation, temperature change will cause stress to decrease during loading and to increase during unloading. A decrease in stress under constant strain indicates stress relaxation, and an increase in stress indicates stress recovery, i.e., reverse stress relaxation. In this paper, a fully coupled thermomechanical model is developed in a continuum framework to study stress relaxation and stress recovery in SMA wires. Numerical simulations at different ambient temperatures, applied strain rates, wire radii, and relaxation intervals are done to show the abilities of the proposed model in predicting relaxation phenomena in various conditions where strain remains constant during loading or unloading. Relaxation experiments were also performed on NiTi wires, and the numerical and empirical results are shown to be in a good agreement.

  5. Models and Methods to Investigate Acute Stress Responses in Cattle

    PubMed Central

    Chen, Yi; Arsenault, Ryan; Napper, Scott; Griebel, Philip

    2015-01-01

    There is a growing appreciation within the livestock industry and throughout society that animal stress is an important issue that must be addressed. With implications for animal health, well-being, and productivity, minimizing animal stress through improved animal management procedures and/or selective breeding is becoming a priority. Effective management of stress, however, depends on the ability to identify and quantify the effects of various stressors and determine if individual or combined stressors have distinct biological effects. Furthermore, it is critical to determine the duration of stress-induced biological effects if we are to understand how stress alters animal production and disease susceptibility. Common stress models used to evaluate both psychological and physical stressors in cattle are reviewed. We identify some of the major gaps in our knowledge regarding responses to specific stressors and propose more integrated methodologies and approaches to measuring these responses. These approaches are based on an increased knowledge of both the metabolic and immune effects of stress. Finally, we speculate on how these findings may impact animal agriculture, as well as the potential application of large animal models to understanding human stress. PMID:26633525

  6. Third-moment closure of turbulence for predictions of separating and reattaching shear flows: A study of Reynolds-stress closure model

    NASA Technical Reports Server (NTRS)

    Amano, R. S.; Goel, P.

    1986-01-01

    A numerical study of computations in backward-facing steps with flow separation and reattachment, using the Reynolds stress closure is presented. The highlight of this study is the improvement of the Reynold-stress model (RSM) by modifying the diffusive transport of the Reynolds stresses through the formulation, solution and subsequent incorporation of the transport equations of the third moments, bar-u(i)u(j)u(k), into the turbulence model. The diffusive transport of the Reynolds stresses, represented by the gradients of the third moments, attains greater significance in recirculating flows. The third moments evaluated by the development and solution of the complete transport equations are superior to those obtained by existing algebraic correlations. A low-Reynolds number model for the transport equations of the third moments is developed and considerable improvement in the near-wall profiles of the third moments is observed. The values of the empirical constants utilized in the development of the model are recommended. The Reynolds-stress closure is consolidated by incorporating the equations of k and e, containing the modified diffusion coefficients, and the transport equations of the third moments into the Reynolds stress equations. Computational results obtained by the original k-e model, the original RSM and the consolidated and modified RSM are compared with experimental data. Overall improvement in the predictions is seen by consolidation of the RMS and a marked improvement in the profiles of bar-u(i)u(j)u(k) is obtained around the reattachment region.

  7. Creep and stress relaxation modeling of polycrystalline ceramic fibers

    NASA Technical Reports Server (NTRS)

    Dicarlo, James A.; Morscher, Gregory N.

    1994-01-01

    A variety of high performance polycrystalline ceramic fibers are currently being considered as reinforcement for high temperature ceramic matrix composites. However, under mechanical loading about 800 C, these fibers display creep related instabilities which can result in detrimental changes in composite dimensions, strength, and internal stress distributions. As a first step toward understanding these effects, this study examines the validity of a mechanism-based empirical model which describes primary stage tensile creep and stress relaxation of polycrystalline ceramic fibers as independent functions of time, temperature, and applied stress or strain. To verify these functional dependencies, a simple bend test is used to measure stress relaxation for four types of commercial ceramic fibers for which direct tensile creep data are available. These fibers include both nonoxide (SCS-6, Nicalon) and oxide (PRD-166, FP) compositions. The results of the Bend Stress Relaxation (BSR) test not only confirm the stress, time, and temperature dependencies predicted by the model, but also allow measurement of model empirical parameters for the four fiber types. In addition, comparison of model tensile creep predictions based on the BSR test results with the literature data show good agreement, supporting both the predictive capability of the model and the use of the BSR text as a simple method for parameter determination for other fibers.

  8. Creep and stress relaxation modeling of polycrystalline ceramic fibers

    NASA Technical Reports Server (NTRS)

    Dicarlo, James A.; Morscher, Gregory N.

    1991-01-01

    A variety of high performance polycrystalline ceramic fibers are currently being considered as reinforcement for high temperature ceramic matrix composites. However, under mechanical loading above 800 C, these fibers display creep-related instabilities which can result in detrimental changes in composite dimensions, strength, and internal stress distributions. As a first step toward understanding these effects, this study examines the validity of mechanistic-based empirical model which describes primary stage tensile creep and stress relaxation of polycrystalline ceramic fibers as independent functions of time, temperature, and applied stress or strain. To verify these functional dependencies, a simple bend test is used to measure stress relaxation for four types of commercial ceramic fibers for which direct tensile creep data are available. These fibers include both nonoxide (SCS-6, Nicalon) and oxide (PRD-166, FP) compositions. The results of the bend stress relaxation (BSR) test not only confirm the stress, time, and temperature dependencies predicted by the model but also allow measurement of model empirical parameters for the four fiber types. In addition, comparison of model predictions and BSR test results with the literature tensile creep data show good agreement, supporting both the predictive capability of the model and the use of the BSR test as a simple method for parameter determination for other fibers.

  9. Modelling of the Global Geopotential Energy & Stress Field

    NASA Astrophysics Data System (ADS)

    Schiffer, C.; Nielsen, S. B.

    2012-04-01

    Lateral density and topography variations yield in and important contribution to the lithospheric stress field. The leading quantity is the Geopotential Energy, the integrated lithostatic pressure in a rock column. The horizontal gradient of this quantity is related to horizontal stresses through the Equations of equilibrium of stresses. The Geopotential Energy furthermore can be linearly related to the Geoid under assumption of local isostasy. Satellite Geoid measurements contain, however, also non-isostatic deeper mantle responses of long wavelength. Unfortunately, high-pass filtering of the Geoid does not suppress only the deeper sources. The age-dependent signal of the oceanic lithosphere, for instance, is of long wave length and a prominent representative of in-plane stress, derived from the horizontal gradient of isostatic Geoid anomalies and responsible for the ridge push effect. Therefore a global lithospheric density model is required in order to isolate the shallow Geoid signal and calculate the stress pattern from isostatically compensated lithospheric sources. We use a linearized inverse method to fit a lithospheric reference model to observations such as topography and surface heat flow in the presence of local isostasy and a steady state geotherm. Subsequently we use a FEM code to solve the Equations of equilibrium of stresses for a three dimensional elastic shell. The modelled results are shown and compared with the global stress field and other publications.

  10. Developing Algebraic Thinking.

    ERIC Educational Resources Information Center

    Alejandre, Suzanne

    2002-01-01

    Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)

  11. Algebraic integrability: a survey.

    PubMed

    Vanhaecke, Pol

    2008-03-28

    We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863

  12. Algebraic Semantics for Narrative

    ERIC Educational Resources Information Center

    Kahn, E.

    1974-01-01

    This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)

  13. FAST TRACK COMMUNICATION: Kac Moody algebras and controlled chaos

    NASA Astrophysics Data System (ADS)

    Wesley, Daniel H.

    2007-02-01

    Compactification can control chaotic Mixmaster behaviour in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac Moody algebras. We show that different compactifications define 'mutations' of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems determined by Lorentzian (but not hyperbolic) algebras. Cosmological models with a smooth pre-big bang phase require that chaos is absent: we show that compactification alone cannot eliminate chaos in the simplest compactifications of the heterotic string on a Calabi Yau, or M theory on a manifold of G2 holonomy.

  14. Aprepro - Algebraic Preprocessor

    2005-08-01

    Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.

  15. Geometric Algebra for Physicists

    NASA Astrophysics Data System (ADS)

    Doran, Chris; Lasenby, Anthony

    2007-11-01

    Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.

  16. Covariant deformed oscillator algebras

    NASA Technical Reports Server (NTRS)

    Quesne, Christiane

    1995-01-01

    The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.

  17. Boolean modeling and fault diagnosis in oxidative stress response

    PubMed Central

    2012-01-01

    Background Oxidative stress is a consequence of normal and abnormal cellular metabolism and is linked to the development of human diseases. The effective functioning of the pathway responding to oxidative stress protects the cellular DNA against oxidative damage; conversely the failure of the oxidative stress response mechanism can induce aberrant cellular behavior leading to diseases such as neurodegenerative disorders and cancer. Thus, understanding the normal signaling present in oxidative stress response pathways and determining possible signaling alterations leading to disease could provide us with useful pointers for therapeutic purposes. Using knowledge of oxidative stress response pathways from the literature, we developed a Boolean network model whose simulated behavior is consistent with earlier experimental observations from the literature. Concatenating the oxidative stress response pathways with the PI3-Kinase-Akt pathway, the oxidative stress is linked to the phenotype of apoptosis, once again through a Boolean network model. Furthermore, we present an approach for pinpointing possible fault locations by using temporal variations in the oxidative stress input and observing the resulting deviations in the apoptotic signature from the normally predicted pathway. Such an approach could potentially form the basis for designing more effective combination therapies against complex diseases such as cancer. Results In this paper, we have developed a Boolean network model for the oxidative stress response. This model was developed based on pathway information from the current literature pertaining to oxidative stress. Where applicable, the behaviour predicted by the model is in agreement with experimental observations from the published literature. We have also linked the oxidative stress response to the phenomenon of apoptosis via the PI3k/Akt pathway. Conclusions It is our hope that some of the additional predictions here, such as those pertaining to the

  18. Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen-like ions

    NASA Astrophysics Data System (ADS)

    Surzhykov, Andrey; Koval, Peter; Fritzsche, Stephan

    2005-01-01

    Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in the design of semiconductor devices. Therefore, the analytical as well as numerical solutions of the hydrogen-like ions are frequently required both, for analyzing experimental data and for carrying out quite advanced theoretical studies. In order to support a fast and consistent access to these (Coulomb-field) solutions, here we present the DIRAC program which has been developed originally for studying the properties and dynamical behavior of the (hydrogen-like) ions. In the present version, a set of MAPLE procedures is provided for the Coulomb wave and Green's functions by applying the (wave) equations from both, the nonrelativistic and relativistic theory. Apart from the interactive access to these functions, moreover, a number of radial integrals are also implemented in the DIRAC program which may help the user to construct transition amplitudes and cross sections as they occur frequently in the theory of ion-atom and ion-photon collisions. Program summaryTitle of program:DIRAC Catalogue number: ADUQ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUQ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Computer for which the program is designed and has been tested: All computers with a license of the computer algebra package MAPLE [1] Program language used: Maple 8 and 9 No. of lines in distributed program, including test data, etc.:2186 No. of bytes in distributed program, including test data, etc.: 162 591 Distribution format: tar gzip file CPC Program Library subprograms required: None Nature of the physical problem: Analytical solutions of the hydrogen atom are widely used in very different fields of physics [2,3]. Despite of the rather simple structure

  19. The Algebraic Way

    NASA Astrophysics Data System (ADS)

    Hiley, B. J.

    In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.

  20. DG Poisson algebra and its universal enveloping algebra

    NASA Astrophysics Data System (ADS)

    Lü, JiaFeng; Wang, XingTing; Zhuang, GuangBin

    2016-05-01

    In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.

  1. Quantum walks, deformed relativity and Hopf algebra symmetries.

    PubMed

    Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo

    2016-05-28

    We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras-the usual Poincaré and theκ-Poincaré algebras. PMID:27091171

  2. Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

    NASA Technical Reports Server (NTRS)

    Jongen, T.; Gatski, T. B.

    1997-01-01

    The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

  3. Residual stresses and damage in unidirectional model composites

    SciTech Connect

    Chatterjee, A.; Moschler, J.W.; Mall, S.; Kerans, R.J.; Pagano, N.J.

    1989-10-01

    Unidirectional model composites were fabricated with SiC fibers and different borosilicate glasses to study the effect of residual stress states on the damage progression in these composites. A specially designed straining stage was employed to study the failure modes in these materials under stepwise loading. Although both fiber and matrix cracks were observed in all specimens, the mechanisms of failure were found to be different and strongly dependent on the residual stress state in these materials. 15 refs.

  4. Modeling of Stress Triggered Faulting at Agenor Linea, Europa

    NASA Astrophysics Data System (ADS)

    Nahm, A. L.; Cameron, M. E.; Smith-Konter, B. R.; Pappalardo, R. T.

    2012-04-01

    To better understand the role of tidal stress sources and implications for faulting on Europa, we investigate the relationship between shear and normal stresses at Agenor Linea (AL), a ~1500 km long, E-W trending, 20-30 km wide zone of geologically young deformation located in the southern hemisphere of Europa which forks into two branches at its eastern end. The orientation of AL is consistent with tensile stresses resulting from long-term decoupled ice shell rotation (non-synchronous rotation [NSR]) as well as dextral shear stresses due to diurnal flexure of the ice shell. Its brightness and lack of cross-cutting features make AL a candidate for recent or current activity. Several observations indicate that right-lateral strike-slip faulting has occurred, such as left-stepping en echelon fractures in the northern portion of AL and the presence of an imbricate fan or horsetail complex at AL's western end. To calculate tidal stresses on Europa, we utilize SatStress, a numerical code that calculates tidal stresses at any point on the surface of a satellite for both diurnal and NSR stresses. We adopt SatStress model parameters appropriate to a spherically symmetric ice shell of thickness 20 km, underlain by a global subsurface ocean: shear modulus G = 3.5 GPa, Poisson ratio ν = 0.33, gravity g= 1.32 m/s2, ice density ρ = 920 kg/m3, satellite radius R= 1.56 x 103 km, satellite mass M= 4.8 x 1022 kg, semimajor axis a= 6.71 x 105 km, and eccentricity e= 0.0094. In this study we assume a coefficient of friction μ = 0.6 and consider a range of vertical fault depths zto 6 km. To assess shear failure at AL, we adopt a model based on the Coulomb failure criterion. This model balances stresses that promote and resist the motion of a fault, simultaneously accounting for both normal and shear tidal and NSR stresses, the coefficient of friction of ice, and additional stress at depth due to the overburden pressure. In this model, tidal shear stresses drive strike-slip motions

  5. Modelling of of hydraulic fractures trajectories in inhomogeneous stress field

    NASA Astrophysics Data System (ADS)

    Andreev, A. A.; Galybin, A.

    2013-05-01

    The paper examines an actual problem of oil and gas production -- modelling of the hydro-fracture trajectories depending on ihomogeneous distributions of pore pressure. The results could serve for improvement of the design of hydraulic fracturing in the oil/gas fields. The methods of the plane elasticity theory and fracture mechanics are employed. It is assumed, that in addition to the homogeneous field of natural stress the reservoir is also subjected to additional stresses caused by technological reasons, which makes the total stress field to be inhomogeneous. Therefore, the objective is to model a curvilinear crack path in an elastic inhomogeneous-loaded plane depending on the different mechanical parameters that control the stress state of the reservoir. For the simulation of the trajectory of a crack the method of boundary integral equation is used. The algorithms of step-by-step determination of the crack's trajectory development using the criterion of maximum tensile stresses at the end of the cracks have been developed. For the numerical realization of the solution we used a special modification of the method of mechanical quadratures providing effective and fast solution of the corresponding system of singular integral equation. The solution for the hydro-fracture path have been simulated for the case of inhomogeneous stress field due to presence of injection well for several physical models.

  6. Comparison of algebraic and analytical approaches to the formulation of the statistical model-based reconstruction problem for X-ray computed tomography.

    PubMed

    Cierniak, Robert; Lorent, Anna

    2016-09-01

    The main aim of this paper is to investigate properties of our originally formulated statistical model-based iterative approach applied to the image reconstruction from projections problem which are related to its conditioning, and, in this manner, to prove a superiority of this approach over ones recently used by other authors. The reconstruction algorithm based on this conception uses a maximum likelihood estimation with an objective adjusted to the probability distribution of measured signals obtained from an X-ray computed tomography system with parallel beam geometry. The analysis and experimental results presented here show that our analytical approach outperforms the referential algebraic methodology which is explored widely in the literature and exploited in various commercial implementations. PMID:27289536

  7. Career Vitalization and Stress among Professors: An Attributional Model.

    ERIC Educational Resources Information Center

    Bumpus, J. Frank

    A model that conceptualizes career stress for faculty members and that suggests options for enhancing career vitality is considered. The model draws upon attribution theory, the locus of control in work of Julian Rotter and the literature of depression by Martin E. P. Seligman. It suggests that perceived causes, or attributions, are directly…

  8. Simulating canopy temperature for modelling heat stress in cereals

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Crop models must be improved to account for the large effects of heat stress effects on crop yields. To date, most approaches in crop models use air temperature despite evidence that crop canopy temperature better explains yield reductions associated with high temperature events. This study presents...

  9. A Multimodular Tensegrity Model of an Actin Stress Fiber

    PubMed Central

    Luo, Yaozhi; Xu, Xian; Lele, Tanmay; Kumar, Sanjay; Ingber, Donald E.

    2008-01-01

    Stress fibers are contractile bundles in the cytoskeleton that stabilize cell structure by exerting traction forces on extracellular matrix. Individual stress fibers are molecular bundles composed of parallel actin and myosin filaments linked by various actin-binding proteins, which are organized end-on-end in a sarcomere-like pattern within an elongated three-dimensional network. While measurements of single stress fibers in living cells show that they behave like tensed viscoelastic fibers, precisely how this mechanical behavior arises from this complex supramolecular arrangement of protein components remains unclear. Here we show that computationally modeling a stress fiber as a multi-modular tensegrity network can predict several key behaviors of stress fibers measured in living cells, including viscoelastic retraction, fiber splaying after severing, non-uniform contraction, and elliptical strain of a puncture wound within the fiber. The tensegrity model also can explain how they simultaneously experience passive tension and generate active contraction forces; in contrast, a tensed cable net model predicts some, but not all, of these properties. Thus, tensegrity models may provide a useful link between molecular and cellular scale mechanical behaviors, and represent a new handle on multi-scale modeling of living materials. PMID:18632107

  10. Understanding lithospheric stresses in Arctic: constraints and models

    NASA Astrophysics Data System (ADS)

    Medvedev, Sergei; Minakov, Alexander; Lebedeva-Ivanova, Nina; Gaina, Carmen

    2016-04-01

    This pilot project aims to model stress patterns and analyze factors controlling lithospheric stresses in Arctic. The project aims to understand the modern stresses in Arctic as well as to define the ways to test recent hypotheses about Cenozoic evolution of the region. The regions around Lomonosov Ridge and Barents Sea are of particular interest driven by recent acquisition of high-resolution potential field and seismic data. Naturally, the major contributor to the lithospheric stress distribution is the gravitational potential energy (GPE). The study tries to incorporate available geological and geophysical data to build reliable GPE. In particular, we use the recently developed integrated gravity inversion for crustal thickness which incorporates up-to-date compilations of gravity anomalies, bathymetry, and sedimentary thickness. The modelled lithosphere thermal structure assumes a pure shear extension and the ocean age model constrained by global plate kinematics for the last ca. 120 Ma. The results of this approach are juxtaposed with estimates of the density variation inferred from the upper mantle S-wave velocity models based on previous surface wave tomography studies. Although new data and interpretations of the Arctic lithosphere structure become available now, there are areas of low accuracy or even lack of data. To compensate for this, we compare two approaches to constrain GPE: (1) one that directly integrates density of modelled lithosphere and (2) one that uses geoid anomalies which are filtered to account for density variations down to the base of the lithosphere only. The two versions of GPE compared to each other and the stresses calculated numerically are compared with observations. That allows us to optimize GPE and understand density structure, stress pattern, and factors controlling the stresses in Arctic.

  11. C-Graded vertex algebras and conformal flow

    SciTech Connect

    Laber, Rob; Mason, Geoffrey

    2014-01-15

    We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by “lowest weight vectors.” We show that such vertex algebras have a “good” representation theory in the sense that there is a Zhu algebra A(V) and a bijection between simple admissible V-modules and simple A(V)-modules. We also consider pseudo vertex operator algebras (PVOAs), which are C-graded vertex algebras with a conformal vector such that the homogeneous subspaces of V are generalized eigenspaces for L(0); essentially, these are VOAs that lack any semisimplicity or integrality assumptions on L(0). As a motivating example, we show that deformation of the conformal structure (conformal flow) of a strongly regular VOA (e.g., a lattice theory, or Wess-Zumino-Witten model) is a path in a space whose points are PVOAs.

  12. Spatial-Operator Algebra For Flexible-Link Manipulators

    NASA Technical Reports Server (NTRS)

    Jain, Abhinandan; Rodriguez, Guillermo

    1994-01-01

    Method of computing dynamics of multiple-flexible-link robotic manipulators based on spatial-operator algebra, which originally applied to rigid-link manipulators. Aspects of spatial-operator-algebra approach described in several previous articles in NASA Tech Briefs-most recently "Robot Control Based on Spatial-Operator Algebra" (NPO-17918). In extension of spatial-operator algebra to manipulators with flexible links, each link represented by finite-element model: mass of flexible link apportioned among smaller, lumped-mass rigid bodies, coupling of motions expressed in terms of vibrational modes. This leads to operator expression for modal-mass matrix of link.

  13. Model of cellular mechanotransduction via actin stress fibers.

    PubMed

    Gouget, Cecile L M; Hwang, Yongyun; Barakat, Abdul I

    2016-04-01

    Mechanical stresses due to blood flow regulate vascular endothelial cell structure and function and play a key role in arterial physiology and pathology. In particular, the development of atherosclerosis has been shown to correlate with regions of disturbed blood flow where endothelial cells are round and have a randomly organized cytoskeleton. Thus, deciphering the relation between the mechanical environment, cell structure, and cell function is a key step toward understanding the early development of atherosclerosis. Recent experiments have demonstrated very rapid ([Formula: see text]100 ms) and long-distance ([Formula: see text]10 [Formula: see text]m) cellular mechanotransduction in which prestressed actin stress fibers play a critical role. Here, we develop a model of mechanical signal transmission within a cell by describing strains in a network of prestressed viscoelastic stress fibers following the application of a force to the cell surface. We find force transmission dynamics that are consistent with experimental results. We also show that the extent of stress fiber alignment and the direction of the applied force relative to this alignment are key determinants of the efficiency of mechanical signal transmission. These results are consistent with the link observed experimentally between cytoskeletal organization, mechanical stress, and cellular responsiveness to stress. Based on these results, we suggest that mechanical strain of actin stress fibers under force constitutes a key link in the mechanotransduction chain. PMID:26081725

  14. Stress Rupture Fracture Model and Microstructure Evolution for Waspaloy

    NASA Astrophysics Data System (ADS)

    Yao, Zhihao; Zhang, Maicang; Dong, Jianxin

    2013-07-01

    Stress rupture behavior and microstructure evolution of nickel-based superalloy Waspaloy specimens from tenon teeth of an as-received 60,000-hour service-exposed gas turbine disk were studied between 923 K and 1088 K (650 °C and 815 °C) under initial applied stresses varying from 150 to 840 MPa. Good microstructure stability and performance were verified for this turbine disk prior to stress rupture testing. Microstructure instability, such as the coarsening and dissolution of γ' precipitates at the varying test conditions, was observed to be increased with temperature and reduced stress. Little microstructure variation was observed at 923 K (650 °C). Only secondary γ' instability occurred at 973 K (700 °C). Four fracture mechanisms were obtained. Transgranular creep fracture was exhibited up to 923 K (650 °C) and at high stress. A mixed mode of transgranular and intergranular creep fracture occurred with reduced stress as a transition to intergranular creep fracture (ICF) at low stress. ICF was dominated by grain boundary sliding at low temperature and by the nucleation and growth of grain boundary cavities due to microstructure instability at high temperature. The fracture mechanism map and microstructure-related fracture model were constructed. Residual lifetime was also evaluated by the Larson-Miller parameter method.

  15. Unconditionally stable time marching scheme for Reynolds stress models

    NASA Astrophysics Data System (ADS)

    Mor-Yossef, Y.

    2014-11-01

    Progress toward a stable and efficient numerical treatment for the compressible Favre-Reynolds-averaged Navier-Stokes equations with a Reynolds-stress model (RSM) is presented. The mean-flow and the Reynolds stress model equations are discretized using finite differences on a curvilinear coordinates mesh. The convective flux is approximated by a third-order upwind biased MUSCL scheme. The diffusive flux is approximated using second-order central differencing, based on a full-viscous stencil. The novel time-marching approach relies on decoupled, implicit time integration, that is, the five mean-flow equations are solved separately from the seven Reynolds-stress closure equations. The key idea is the use of the unconditionally positive-convergent implicit scheme (UPC), originally developed for two-equation turbulence models. The extension of the UPC scheme for RSM guarantees the positivity of the normal Reynolds-stress components and the turbulence (specific) dissipation rate for any time step. Thanks to the UPC matrix-free structure and the decoupled approach, the resulting computational scheme is very efficient. Special care is dedicated to maintain the implicit operator compact, involving only nearest neighbor grid points, while fully supporting the larger discretized residual stencil. Results obtained from two- and three-dimensional numerical simulations demonstrate the significant progress achieved in this work toward optimally convergent solution of Reynolds stress models. Furthermore, the scheme is shown to be unconditionally stable and positive.

  16. Atomistic modelling of residual stress at UO2 surfaces.

    PubMed

    Arayro, Jack; Tréglia, Guy; Ribeiro, Fabienne

    2016-01-13

    Modelling oxide surface behaviour is of both technological and fundamental interest. In particular, in the case of the UO2 system, which is of major importance in the nuclear industry, it is essential to account for the link between microstructure and macroscopic mechanical properties. Indeed micromechanical models at the mesoscale need to be supplied by the energetic and stress data calculated at the nanoscale. In this framework, we present a theoretical study, coupling an analytical model and thermostatistical simulation to investigate the modifications induced by the presence of a surface regarding atomic relaxation and energetic and stress profiles. In particular, we show that the surface effective thickness as well as the stress profile, which are required by micromechanical approaches, are strongly anisotropic. PMID:26648246

  17. Using thermal stress to model aspects of disease states.

    PubMed

    Wilson, Thad E; Klabunde, Richard E; Monahan, Kevin D

    2014-07-01

    Exposure to acute heat or cold stress elicits numerous physiological responses aimed at maintaining body temperatures. Interestingly, many of the physiological responses, mediated by the cardiovascular and autonomic nervous systems, resemble aspects of, or responses to, certain disease states. The purpose of this Perspective is to highlight some of these areas in order to explore how they may help us better understand the pathophysiology underlying aspects of certain disease states. The benefits of using this human thermal stress approach are that (1) no adjustments for inherent comparative differences in animals are needed, (2) non-medicated healthy humans with no underlying co-morbidities can be studied in place of complex patients, and (3) more mechanistic perturbations can be safely employed without endangering potentially vulnerable populations. Cold stress can be used to induce stable elevations in blood pressure. Cold stress may also be used to model conditions where increases in myocardial oxygen demand are not met by anticipated increases in coronary blood flow, as occurs in older adults. Lower-body negative pressure has the capacity to model aspects of shock, and the further addition of heat stress improves and expands this model because passive-heat exposure lowers systemic vascular resistance at a time when central blood volume and left-ventricular filling pressure are reduced. Heat stress can model aspects of heat syncope and orthostatic intolerance as heat stress decreases cerebral blood flow and alters the Frank-Starling mechanism resulting in larger decreases in stroke volume for a given change in left-ventricular filling pressure. Combined, thermal perturbations may provide in vivo paradigms that can be employed to gain insights into pathophysiological aspects of certain disease states. PMID:24956954

  18. A PROGRESSIVE RUPTURE MODEL OF SOFT TISSUE STRESS RELAXATION

    PubMed Central

    Bates, Jason H.T.; Ma, Baoshun

    2013-01-01

    A striking feature of stress relaxation in biological soft tissue is that it frequently follows a power law in time with an exponent that is independent of strain even when the elastic properties of the tissue are highly nonlinear. This kind of behavior is an example of quasi-linear viscoelasticity, and is usually modeled in a purely empirical fashion. The goal of the present study was to account for quasi-linear viscoelasticity in mechanistic terms based on our previously developed hypothesis that it arises as a result of isolated micro-yield events occurring in sequence throughout the tissue, each event passing the stress it was sustaining on to other regions of the tissue until they themselves yield. We modeled stress relaxation computationally in a collection of stress-bearing elements. Each element experiences a stochastic sequence of either increases in elastic equilibrium length or decreases in stiffness according to the stress imposed upon it. This successfully predicts quasi-linear viscoelastic behavior, and in addition predicts power-law stress relaxation that proceeds at the same slow rate as observed in real biological soft tissue. PMID:23508634

  19. Modelling of residually stressed materials with application to AAA.

    PubMed

    Ahamed, T; Dorfmann, L; Ogden, R W

    2016-08-01

    Residual stresses are generated in living tissues by processes of growth and adaptation and they significantly influence the mechanical behaviour of the tissues. Thus, to effectively model the elastic response of the tissues relative to a residually stressed configuration the residual stresses need to be incorporated into the constitutive equations. The purposes of this paper are (a) to summarise a general elastic constitutive formulation that includes residual stress, (b) to specify the tensors needed for the three-dimensional implementation of the theory in a nonlinear finite element code, and (c) to use the theory and its implementation to evaluate the wall stress distribution in an abdominal aortic aneurysm (AAA) using patient specific geometry and material model parameters. The considered material is anisotropic with two preferred directions indicating the orientation of the collagen fibres in the aortic tissue. The method described in this paper is general and can be used, by specifying appropriate energy functions, to investigate other residually stressed biological systems. PMID:26874252

  20. Sex differences in the chronic mild stress model of depression.

    PubMed

    Franceschelli, Anthony; Herchick, Samantha; Thelen, Connor; Papadopoulou-Daifoti, Zeta; Pitychoutis, Pothitos M

    2014-09-01

    A large volume of clinical and experimental evidence documents sex differences in brain anatomy, chemistry, and function, as well as in stress and drug responses. The chronic mild stress model (CMS) is one of the most extensively investigated animal models of chronic stress. However, only a limited number of studies have been conducted in female rodents despite the markedly higher prevalence of major depression among women. Herein, we review CMS studies conducted in rats and mice of both sexes and further discuss intriguing sex-dependent behavioral and neurobiological findings. The PubMed literature search engine was used to find and collect all relevant articles analyzed in this review. Specifically, a multitermed search was performed with 'chronic mild stress', 'chronic unpredictable stress' and 'chronic variable stress' as base terms and 'sex', 'gender', 'females' and 'depression' as secondary terms in various combinations. Male and female rodents appear to be differentially affected by CMS application, depending on the behavioral, physiological, and neurobiological indices that are being measured. Importantly, the CMS paradigm, despite its limitations, has been successfully used to assess a constellation of interdisciplinary research questions in the sex differences field and has served as a 'silver bullet' in assessing the role of sex in the neurobiology of major depression. PMID:25025701

  1. A review of Reynolds stress models for turbulent shear flows

    NASA Technical Reports Server (NTRS)

    Speziale, Charles G.

    1995-01-01

    A detailed review of recent developments in Reynolds stress modeling for incompressible turbulent shear flows is provided. The mathematical foundations of both two-equation models and full second-order closures are explored in depth. It is shown how these models can be systematically derived for two-dimensional mean turbulent flows that are close to equilibrium. A variety of examples are provided to demonstrate how well properly calibrated versions of these models perform for such flows. However, substantial problems remain for the description of more complex turbulent flows where there are large departures from equilibrium. Recent efforts to extend Reynolds stress models to nonequilibrium turbulent flows are discussed briefly along with the major modeling issues relevant to practical naval hydrodynamics applications.

  2. On Griess Algebras

    NASA Astrophysics Data System (ADS)

    Roitman, Michael

    2008-08-01

    In this paper we prove that for any commutative (but in general non-associative) algebra A with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra V = V0 Å V2 Å V3 Å ¼, such that dim V0 = 1 and V2 contains A. We can choose V so that if A has a unit e, then 2e is the Virasoro element of V, and if G is a finite group of automorphisms of A, then G acts on V as well. In addition, the algebra V can be chosen with a non-degenerate invariant bilinear form, in which case it is simple.

  3. Adaptive Algebraic Multigrid Methods

    SciTech Connect

    Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J

    2004-04-09

    Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.

  4. Gender Differences in Animal Models of Posttraumatic Stress Disorder

    PubMed Central

    Cohen, Hagit; Yehuda, Rachel

    2011-01-01

    Epidemiological studies report higher prevalence rates of stress-related disorders such as acute stress disorder and post-traumatic stress disorder (PTSD) in women than in men following exposure to trauma. It is still not clear whether this greater prevalence in woman reflects a greater vulnerability to stress-related psychopathology. A number of individual and trauma-related characteristics have been hypothesized to contribute to these gender differences in physiological and psychological responses to trauma, differences in appraisal, interpretation or experience of threat, coping style or social support. In this context, the use of an animal model for PTSD to analyze some of these gender-related differences may be of particular utility. Animal models of PTSD offer the opportunity to distinguish between biological and socio-cultural factors, which so often enter the discussion about gender differences in PTSD prevalence. In this review, we present and discuss sex-differences in behavioral, neurochemical, neurobiological and pharmacological findings that we have collected from several different animal studies related to both basal conditions and stress responses. These models have used different paradigms and have elicited a range of behavioral and physiological manifestations associated with gender. The overall data presented demonstrate that male animals are significantly more vulnerable to acute and chronic stress, whereas females are far more resilient. The stark contradiction between these findings and contemporary epidemiological data regarding human subjects is worthy of further study. The examination of these gender-related differences can deepen our understanding of the risk or the pathophysiology of stress-related disorders. PMID:21508518

  5. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  6. Effective stress model for partially and fully saturated rocks

    SciTech Connect

    Dey, T.N.

    1989-01-01

    An effective stress model which calculates the pressure-volume (P-V) and deviatoric stress response of partially and fully saturated rocks is described here. The model includes pore pressure effects on pore crushing and shear strength as well as effects of shear enhanced void collapse and shear caused dilatancy. The model can directly use tabular data for the P-V behavior of the rock solids and the water, and for the drained pore crushing behavior and shear strength, which simplifies model fitting. Phase transitions in the solids and vaporization of the water are also allowed. Use of the model is illustrated by an example of wave propagation in limestone. 6 refs., 4 figs.

  7. Computer Program For Linear Algebra

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.; Hanson, R. J.

    1987-01-01

    Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.

  8. Stressors, stress and stress consequences during long-duration manned space missions: a descriptive model

    NASA Astrophysics Data System (ADS)

    Geuna, Stefano; Brunelli, Francesco; Perino, Maria A.

    Keeping crew members in good health is a major factor in the success or failure of long-duration manned space missions. Among the many possible agents that can affect the crew's general well-being, stress is certainly one of the most critical because of its implications on human health and performance, both physical and mental. Nevertheless, very few studies have been performed on this fundamental issue and none of them has addressed it in its entirity, considering its diverse physical and psychological aspects. In this work, a descriptive model is proposed to expound the mechanism and sequence of events which mediate stress. A critical analysis of the information provided by past manned spaceflights and by dedicated research performed in analogous environments is presented, and an extrapolation of the available data on human stress in such extreme conditions is proposed. Both internal and external stressors have been identified, at physical and psychosocial levels, thus providing the basis for their early detection and preventive reduction. The possible negative consequences of stress that may lead to disease in crewmembers are described. Finally, the most effective instruments which may be of help in reducing space-related human stress and treating its negative consequences are suggested.

  9. Algebraic geometric codes

    NASA Technical Reports Server (NTRS)

    Shahshahani, M.

    1991-01-01

    The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.

  10. Extended conformal algebras

    NASA Astrophysics Data System (ADS)

    Bouwknegt, Peter

    1988-06-01

    We investigate extensions of the Virasoro algebra by a single primary field of integer or halfinteger conformal dimension Δ. We argue that for vanishing structure constant CΔΔΔ, the extended conformal algebra can only be associative for a generic c-value if Δ=1/2, 1, 3/2, 2 or 3. For the other Δ<=5 we compute the finite set of allowed c-values and identify the rational solutions. The case CΔΔΔ≠0 is also briefly discussed. I would like to thank Kareljan Schoutens for discussions and Sander Bais for a careful reading of the manuscript.

  11. Depression, Stress, and Anhedonia: Toward a Synthesis and Integrated Model

    PubMed Central

    Pizzagalli, Diego A.

    2014-01-01

    Depression is a significant public health problem, but its etiology and pathophysiology remain poorly understood. Such incomplete understanding likely arises from the fact that depression encompasses a heterogeneous set of disorders. To overcome these limitations, renewed interest in intermediate phenotypes (endophenotypes) has resurfaced, and anhedonia has emerged as one of the most promising endophenotypes of depression. Here, a heuristic model is presented postulating that anhedonia arises from dysfunctional interactions between stress and brain reward systems. To this end, we review and integrate three bodies of independent literature investigating the role of (1) anhedonia, (2) dopamine, and (3) stress in depression. In a fourth section, we summarize animal data indicating that stress negatively affect mesocorticolimbic dopaminergic pathways critically implicated in incentive motivation and reinforcement learning. In the last section, we provide a synthesis of these four literatures, present initial evidence consistent with our model, and discuss directions for future research. PMID:24471371

  12. Computer-Intensive Algebra and Students' Conceptual Knowledge of Functions.

    ERIC Educational Resources Information Center

    O'Callaghan, Brian R.

    1998-01-01

    Describes a research project that examined the effects of the Computer-Intensive Algebra (CIA) and traditional algebra curricula on students' (N=802) understanding of the function concept. Results indicate that CIA students achieved a better understanding of functions and were better at the components of modeling, interpreting, and translating.…

  13. Martian sub-crustal stress from gravity and topographic models

    NASA Astrophysics Data System (ADS)

    Tenzer, Robert; Eshagh, Mehdi; Jin, Shuanggen

    2015-09-01

    The latest Martian gravity and topographic models derived from the Mars Orbiter Laser Altimeter and the Mars Global Surveyor spacecraft tracking data are used to compute the sub-crustal stress field on Mars. For this purpose, we apply the method for a simultaneous determination of the horizontal sub-crustal stress component and the crustal thickness based on solving the Navier-Stokes problem and incorporating the Vening Meinesz-Moritz inverse problem of isostasy. Results reveal that most of the Martian sub-crustal stress is concentrated in the Tharsis region, with the most prominent signatures attributed to a formation of Tharsis major volcanoes followed by crustal loading. The stress distribution across the Valles Marineris rift valleys indicates extensional tectonism. This finding agrees with more recent theories of a tectonic origin of Valles Marineris caused, for instance, by a crustal loading of the Tharsis bulge that resulted in a regional trusting and folding. Aside from these features, the Martian stress field is relatively smooth with only a slightly enhanced pattern of major impact basins. The signatures of active global tectonics and polar ice load are absent. Whereas the signature of the hemispheric dichotomy is also missing, the long-wavelength spectrum of the stress field comprises the signature of additional dichotomy attributed to the isostatically uncompensated crustal load of Tharsis volcanic accumulations. These results suggest a different origin of the Earth's and Martian sub-crustal stress. Whereas the former is mainly related to active global tectonics, the latter is generated by a crustal loading and regional tectonism associated with a volcanic evolution on Mars. The additional sub-crustal stress around major impact basins is likely explained by a crustal extrusion after impact followed by a Moho uplift.

  14. Uncertainties in obtaining high reliability from stress-strength models

    NASA Technical Reports Server (NTRS)

    Neal, Donald M.; Matthews, William T.; Vangel, Mark G.

    1992-01-01

    There has been a recent interest in determining high statistical reliability in risk assessment of aircraft components. The potential consequences are identified of incorrectly assuming a particular statistical distribution for stress or strength data used in obtaining the high reliability values. The computation of the reliability is defined as the probability of the strength being greater than the stress over the range of stress values. This method is often referred to as the stress-strength model. A sensitivity analysis was performed involving a comparison of reliability results in order to evaluate the effects of assuming specific statistical distributions. Both known population distributions, and those that differed slightly from the known, were considered. Results showed substantial differences in reliability estimates even for almost nondetectable differences in the assumed distributions. These differences represent a potential problem in using the stress-strength model for high reliability computations, since in practice it is impossible to ever know the exact (population) distribution. An alternative reliability computation procedure is examined involving determination of a lower bound on the reliability values using extreme value distributions. This procedure reduces the possibility of obtaining nonconservative reliability estimates. Results indicated the method can provide conservative bounds when computing high reliability. An alternative reliability computation procedure is examined involving determination of a lower bound on the reliability values using extreme value distributions. This procedure reduces the possibility of obtaining nonconservative reliability estimates. Results indicated the method can provide conservative bounds when computing high reliability.

  15. Sex Differences in Adolescent Depression: Stress Exposure and Reactivity Models

    ERIC Educational Resources Information Center

    Hankin, Benjamin L.; Mermelstein, Robin; Roesch, Linda

    2007-01-01

    Stress exposure and reactivity models were examined as explanations for why girls exhibit greater levels of depressive symptoms than boys. In a multiwave, longitudinal design, adolescents' depressive symptoms, alcohol usage, and occurrence of stressors were assessed at baseline, 6, and 12 months later (N=538; 54.5% female; ages 13-18, average…

  16. Teaching Arithmetic and Algebraic Expressions

    ERIC Educational Resources Information Center

    Subramaniam, K.; Banerjee, Rakhi

    2004-01-01

    A teaching intervention study was conducted with sixth grade students to explore the interconnections between students' growing understanding of arithmetic expressions and beginning algebra. Three groups of students were chosen, with two groups receiving instruction in arithmetic and algebra, and one group in algebra without arithmetic. Students…

  17. Assessing Elementary Algebra with STACK

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.

    2007-01-01

    This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

  18. Spinors in the hyperbolic algebra

    NASA Astrophysics Data System (ADS)

    Ulrych, S.

    2006-01-01

    The three-dimensional universal complex Clifford algebra Cbar3,0 is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.

  19. Algebraic Artful Aids.

    ERIC Educational Resources Information Center

    Glick, David

    1995-01-01

    Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)

  20. From Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott

    2007-01-01

    Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…

  1. Computer Algebra versus Manipulation

    ERIC Educational Resources Information Center

    Zand, Hossein; Crowe, David

    2004-01-01

    In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…

  2. The Power of Algebra.

    ERIC Educational Resources Information Center

    Boiteau, Denise; Stansfield, David

    This document describes mathematical programs on the basic concepts of algebra produced by Louisiana Public Broadcasting. Programs included are: (1) "Inverse Operations"; (2) "The Order of Operations"; (3) "Basic Properties" (addition and multiplication of numbers and variables); (4) "The Positive and Negative Numbers"; and (5) "Using Positive…

  3. Pre-Algebra.

    ERIC Educational Resources Information Center

    Kennedy, John

    This text provides information and exercises on arithmetic topics which should be mastered before a student enrolls in an Elementary Algebra course. Section I describes the fundamental properties and relationships of whole numbers, focusing on basic operations, divisibility tests, exponents, order of operations, prime numbers, greatest common…

  4. Computers in Abstract Algebra

    ERIC Educational Resources Information Center

    Nwabueze, Kenneth K.

    2004-01-01

    The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…

  5. Modeling of residual stresses by HY-100 weldments

    SciTech Connect

    Zacharia, T.; Taljat, B.; Radhakrishnan, B.

    1997-02-01

    Residual stress distribution in a HY-100 steel disk, induced by GTA spot welding, was analyzed by finite element (FE) formulations and measured by neutron diffraction (ND). Computations used temperature- dependent thermophysical and mechanical properties. FE model predictions are in good agreement with ND data in far heat affected zone (HAZ) and in base metal. Predicted residual stresses in fusion zone and near HAZ were higher than those measured by ND. This discrepancy was attributed to microstructural changes and associated material properties in the HAZ and fusion zone due to phase transformations during the weld thermal cycle.

  6. Permutation centralizer algebras and multimatrix invariants

    NASA Astrophysics Data System (ADS)

    Mattioli, Paolo; Ramgoolam, Sanjaye

    2016-03-01

    We introduce a class of permutation centralizer algebras which underly the combinatorics of multimatrix gauge-invariant observables. One family of such noncommutative algebras is parametrized by two integers. Its Wedderburn-Artin decomposition explains the counting of restricted Schur operators, which were introduced in the physics literature to describe open strings attached to giant gravitons and were subsequently used to diagonalize the Gaussian inner product for gauge invariants of two-matrix models. The structure of the algebra, notably its dimension, its center and its maximally commuting subalgebra, is related to Littlewood-Richardson numbers for composing Young diagrams. It gives a precise characterization of the minimal set of charges needed to distinguish arbitrary matrix gauge invariants, which are related to enhanced symmetries in gauge theory. The algebra also gives a star product for matrix invariants. The center of the algebra allows efficient computation of a sector of multimatrix correlators. These generate the counting of a certain class of bicoloured ribbon graphs with arbitrary genus.

  7. Modelling Of Residual Stresses Induced By High Speed Milling Process

    NASA Astrophysics Data System (ADS)

    Desmaison, Olivier; Mocellin, Katia; Jardin, Nicolas

    2011-05-01

    Maintenance processes used in heavy industries often include high speed milling operations. The reliability of the post-process material state has to be studied. Numerical simulation appears to be a very interesting way to supply an efficient residual stresses (RS) distribution prediction. Because the adiabatic shear band and the serrated chip shaping are features of the austenitic stainless steel high speed machining, a 2D high speed orthogonal cutting model is briefly presented. This finite element model, developed on Forge® software, is based on data taken from Outeiro & al.'s paper [1]. A new behaviour law fully coupling Johnson-Cook's constitutive law and Latham and Cockcroft's damage model is detailed in this paper. It ensures results that fit those found in literature. Then, the numerical tools used on the 2D model are integrated to a 3D high speed milling model. Residual stresses distribution is analysed, on the surface and into the depth of the material. Various revolutions and passes of the two teeth hemispheric mill on the workpiece are simulated. Thus the sensitivity of the residual stresses generation to the cutting conditions can be discussed. In order to validate the 3D model, a comparison of the cutting forces measured by EDF R&D to those given by numerical simulations is achieved.

  8. Modelling Of Residual Stresses Induced By High Speed Milling Process

    SciTech Connect

    Desmaison, Olivier; Mocellin, Katia; Jardin, Nicolas

    2011-05-04

    Maintenance processes used in heavy industries often include high speed milling operations. The reliability of the post-process material state has to be studied. Numerical simulation appears to be a very interesting way to supply an efficient residual stresses (RS) distribution prediction.Because the adiabatic shear band and the serrated chip shaping are features of the austenitic stainless steel high speed machining, a 2D high speed orthogonal cutting model is briefly presented. This finite element model, developed on Forge registered software, is based on data taken from Outeiro and al.'s paper [1]. A new behaviour law fully coupling Johnson-Cook's constitutive law and Latham and Cockcroft's damage model is detailed in this paper. It ensures results that fit those found in literature.Then, the numerical tools used on the 2D model are integrated to a 3D high speed milling model. Residual stresses distribution is analysed, on the surface and into the depth of the material. Various revolutions and passes of the two teeth hemispheric mill on the workpiece are simulated. Thus the sensitivity of the residual stresses generation to the cutting conditions can be discussed. In order to validate the 3D model, a comparison of the cutting forces measured by EDF R and D to those given by numerical simulations is achieved.

  9. Yield Stress Modeling of Electrorheological Fluids Using Neural Network

    NASA Astrophysics Data System (ADS)

    Wei, Kexiang; Meng, Guang

    Electrorheological (ER) fluids are a kind of smart materials whose rheological properties can be rapidly changed by applied electric fields. Many potential industrial applications of ER technology have been proposed. In order to formulate better ER fluids and design ER devices, it is important to predict the yield stress of ER fluids based on the ER fluids components and the operating conditions. This paper proposes a new method for predicting the yield stress of ER fluids with neural network (NN). A multilayer perceptron with a single hidden layer of neurons is used to model the ER effect. The data for training and test were produced from the simulation of previous proposed mathematical models. The Levernberg-Marquardt back propagation algorithm was selected for fast learning. The results show the neural network model can well approximate the previous theoretical model, and the predicted outputs of NN agree nearly with the theoretical model values under the same input, all of which demonstrate that it is possible to generate a robust NN model for rapidly predicting the yield stress of ER fluids under different input parameters.

  10. ALGEBRA: a computer program that algebraically manipulates finite element output data. [In extended FORTRAN for CDC 7600 or CYBER 76 only

    SciTech Connect

    Richgels, M A; Biffle, J H

    1980-09-01

    ALGEBRA is a program that allows the user to process output data from finite-element analysis codes before they are sent to plotting routines. These data take the form of variable values (stress, strain, and velocity components, etc.) on a tape that is both the output tape from the analyses code and the input tape to ALGEBRA. The ALGEBRA code evaluates functions of these data and writes the function values on an output tape that can be used as input to plotting routines. Convenient input format and error detection capabilities aid the user in providing ALGEBRA with the functions to be evaluated. 1 figure.

  11. Formal Formality of the Hypercommutative Algebras of Low Dimensional Calabi-Yau Varieties

    NASA Astrophysics Data System (ADS)

    Drummond-Cole, Gabriel C.

    2014-04-01

    There is a homotopy hypercommutative algebra structure on the cohomology of a Calabi-Yau variety. The truncation of this homotopy hypercommutative algebra to a strict hypercommutative algebra is well-known as a mathematical realization of the genus zero B-model. It is shown that this truncation loses no information for some cases, including all Calabi-Yau 3-folds.

  12. Modeling of thermal stresses in elastic multilayer coating systems

    NASA Astrophysics Data System (ADS)

    Gao, Chunxue; Zhao, Zhiwei; Li, Xuehua

    2015-02-01

    The performance and reliability of multilayer coating systems are strongly influenced by thermal stresses. The present study develops an alternative analytical model to predict the thermal stresses in elastic multilayer coating systems. An exact closed-form solution is obtained which is independent of the number of coating layers. In addition, with the definition of the coordinate system, the closed-form solution is concisely formulated. Specific results are calculated for thermal stresses in HfO2/SiO2 multilayer optical coatings, and a finite element analysis is performed to confirm the analytical results. The two results agree fairly well with each other. Also, when the thicknesses of the coating layers are much less than the substrate thickness, the approximate solution is obtained based on the exact closed-form solution, and its accuracy is examined.

  13. XML algebras for data mining

    NASA Astrophysics Data System (ADS)

    Zhang, Ming; Yao, JingTao

    2004-04-01

    The XML is a new standard for data representation and exchange on the Internet. There are studies on XML query languages as well as XML algebras in literature. However, attention has not been paid to research on XML algebras for data mining due to partially the fact that there is no widely accepted definition of XML mining tasks. This paper tries to examine the XML mining tasks and provide guidelines to design XML algebras for data mining. Some summarization and comparison have been done to existing XML algebras. We argue that by adding additional operators for mining tasks, XML algebras may work well for data mining with XML documents.

  14. An algebra of discrete event processes

    NASA Technical Reports Server (NTRS)

    Heymann, Michael; Meyer, George

    1991-01-01

    This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.

  15. Optical systolic solutions of linear algebraic equations

    NASA Technical Reports Server (NTRS)

    Neuman, C. P.; Casasent, D.

    1984-01-01

    The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.

  16. Fock representations of exchange algebras with involution

    SciTech Connect

    Liguori, A.; Mintchev, M.; Rossi, M.

    1997-06-01

    An associative algebra scr(A){sub R} with exchange properties generalizing the canonical (anti)commutation relations is considered. We introduce a family of involutions in scr(A){sub R} and construct the relative Fock representations, examining the positivity of the metric. As an application of the general results, we rigorously prove unitarity of the scattering operator of integrable models in 1+1 space-time dimensions. In this context the possibility of adopting various involutions in the Zamolodchikov{endash}Faddeev algebra is also explored. {copyright} {ital 1997 American Institute of Physics.}

  17. A rabbit ear model for cold stress testing.

    PubMed

    Smith, T L; Gordon, S; Holden, M B; Smith, B P; Russell, G B; Koman, L A

    1994-01-01

    A rabbit ear model resembling the human digit was studied to determine the vascular response of the rabbit ear to a cold stress. Following moderate cooling (10 minutes at 5 degrees - 8 degrees C), auricular blood flow and cutaneous perfusion were reduced. This decrease was reversed by 30 minutes of warming. The response in the rabbit ear to cold stress is similar to that of normal human digits. The similarities between the control of the circulation in human digits and rabbit ears may result from the similarities in digital and auricular vascular receptors and receptor subtypes. Verification of the rabbit model provides an experimental method for obtaining important data regarding digital pathophysiology and the treatment of cold intolerance. Further study with this model will provide clinically relevant information regarding the pathophysiology of digital thermoregulatory abnormalities. PMID:7830538

  18. Modeling the Stress Strain Behavior of Woven Ceramic Matrix Composites

    NASA Technical Reports Server (NTRS)

    Morscher, Gregory N.

    2006-01-01

    Woven SiC fiber reinforced SiC matrix composites represent one of the most mature composite systems to date. Future components fabricated out of these woven ceramic matrix composites are expected to vary in shape, curvature, architecture, and thickness. The design of future components using woven ceramic matrix composites necessitates a modeling approach that can account for these variations which are physically controlled by local constituent contents and architecture. Research over the years supported primarily by NASA Glenn Research Center has led to the development of simple mechanistic-based models that can describe the entire stress-strain curve for composite systems fabricated with chemical vapor infiltrated matrices and melt-infiltrated matrices for a wide range of constituent content and architecture. Several examples will be presented that demonstrate the approach to modeling which incorporates a thorough understanding of the stress-dependent matrix cracking properties of the composite system.

  19. Single prolonged stress: toward an animal model of posttraumatic stress disorder.

    PubMed

    Yamamoto, Shigeto; Morinobu, Shigeru; Takei, Shiro; Fuchikami, Manabu; Matsuki, Aya; Yamawaki, Shigeto; Liberzon, Israel

    2009-01-01

    Although selective serotonin reuptake inhibitors (SSRIs) are reported to be effective in decreasing posttraumatic stress disorder (PTSD) symptoms, a subgroup of PTSD patients remain chronically symptomatic and maintain conditioned fear responses to traumatic stimuli. In this context, the establishment of an appropriate animal model of PTSD is necessary to promote better understanding of the mechanisms of the disorder and to facilitate the development of more effective therapeutic alternatives to SSRIs. Although no single widely accepted animal model of PTSD has been established to date, the single prolonged stress (SPS) animal model has been partially validated as a model for PTSD. SPS rats mimic the pathophysiological abnormalities and behavioral characteristics of PTSD, such as enhanced anxiety-like behavior and glucocorticoid negative feedback, and they exhibit the expected therapeutic response to paroxetine on enhanced fear memory. In addition, SPS rats exhibit enhanced freezing in response to contextual fear conditioning, and impaired extinction of fear memory, which is alleviated by D-cycloserine. The enhanced consolidation and impaired extinction of fear memory found in SPS rats suggests that this model has additional value because recent studies of PTSD indicate that memory abnormalities are a central feature. In this study, we summarize the behavioral and pathophysiological PTSD-like symptoms in SPS, focusing on memory abnormalities, and evaluate the validity of SPS as an animal model of PTSD. PMID:19918929

  20. Stress models of depression: forming genetically vulnerable strains.

    PubMed

    Henn, Fritz A; Vollmayr, Barbara

    2005-01-01

    Among the most useful models for depressive disorders are those, which involve a stress induced change in behaviour. Learned helplessness is one such model and is induced through exposure to uncontrollable and unpredictable aversive events. Learned helplessness as induced in rats using foot shock is well characterized and has good face validity and predictive validity as a model of depression, including alterations in HPA axis activity and REM sleep characteristic of depression. The data concerning the validity will be briefly reviewed. The model can also be used to look at the role of genetics through selective breeding. These studies will be reviewed and the utility of the genetic strains for understanding the interaction of stress and affect will be examined. A second model of depression using exposure to chronic stress also has high face and predictive validity. A new form of this approach, recently described, also is suitable for the examination of genetic factors leading to depressive like behaviour and this will be presented. PMID:15925700

  1. Thermal Indices and Thermophysiological Modeling for Heat Stress.

    PubMed

    Havenith, George; Fiala, Dusan

    2015-01-01

    The assessment of the risk of human exposure to heat is a topic as relevant today as a century ago. The introduction and use of heat stress indices and models to predict and quantify heat stress and heat strain has helped to reduce morbidity and mortality in industrial, military, sports, and leisure activities dramatically. Models used range from simple instruments that attempt to mimic the human-environment heat exchange to complex thermophysiological models that simulate both internal and external heat and mass transfer, including related processes through (protective) clothing. This article discusses the most commonly used indices and models and looks at how these are deployed in the different contexts of industrial, military, and biometeorological applications, with focus on use to predict related thermal sensations, acute risk of heat illness, and epidemiological analysis of morbidity and mortality. A critical assessment is made of tendencies to use simple indices such as WBGT in more complex conditions (e.g., while wearing protective clothing), or when employed in conjunction with inappropriate sensors. Regarding the more complex thermophysiological models, the article discusses more recent developments including model individualization approaches and advanced systems that combine simulation models with (body worn) sensors to provide real-time risk assessment. The models discussed in the article range from historical indices to recent developments in using thermophysiological models in (bio) meteorological applications as an indicator of the combined effect of outdoor weather settings on humans. PMID:26756633

  2. On Dunkl angular momenta algebra

    NASA Astrophysics Data System (ADS)

    Feigin, Misha; Hakobyan, Tigran

    2015-11-01

    We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.

  3. Algebraic connectivity and graph robustness.

    SciTech Connect

    Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.

    2009-07-01

    Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.

  4. Modeling grain-scale thermoelastic stresses on airless bodies

    NASA Astrophysics Data System (ADS)

    Molaro, J.; Byrne, S.

    2013-12-01

    Thermal stress weathering is the mechanical breakdown of rock from expansion and contraction caused by changes in temperature. Damage occurs in the form of microscopic cracks that result from a thermal cycle or thermal shock. This process may play an important role in the evolution of airless landscapes, by contributing to regolith production and crater degradation. Without the presence of an atmosphere, rock surfaces experience very dramatic temperature changes that induce high thermoelastic stresses in the near sub-surface. The thermoelastic behavior of each surface is primarily controlled by its distance to the sun and its solar day length, providing a unique experience on each body. For example, slowly rotating bodies that are close to the sun (such as Mercury) experience a very wide diurnal temperature range. Bodies further from the sun (such as NEAs) have a much smaller range, but rotate quickly and experience rapid temperature 'shocks' during sunrise/set. While many studies suggest stresses induced by these temperature changes may cause rock breakdown, the extent of the damage produced as a result is unknown. In this study, we modeled thermoelastic stresses produced on airless surfaces at the mineral grain scale. Finite Element Analysis of Microstructures (OOF2) is a 2-D finite element modeling program, developed at NIST and designed to help scientists calculate macroscopic properties of real or simulated microstructures. This allows us to model thermal behavior of microstructures with varying grain sizes and thermophysical properties, and to explore the relationship between the spatial and temporal temperature gradients and stress. Using OOF2, we imposed the solar and conductive fluxes calculated by our 1-D thermal model at the surface and at 5mm depth on a microstructure. The microstructure has bulk properties typical of a basalt, and a grain size of ~0.3 mm. We assigned 20% and 80% of the grains a thermal conductivity of 1 and 3 W/mK, respectively. The

  5. A probabilistic model of intergranular stress corrosion cracking

    SciTech Connect

    Bourcier, R.J.; Jones, W.B. ); Scully, J.R. )

    1991-01-01

    We have developed a model which utilizes a probabilistic failure criterion to describe intergranular stress corrosion cracking (IGSCC). A two-dimensional array of elements representing a section of a pipe wall is analyzed, with each element in the array representing a segment of grain boundary. The failure criterion is applied repetitively to each element of the array that is exposed to the interior of the pipe (i.e. the corrosive fluid) until that element dissolves, thereby exposing the next element. A number of environmental, mechanical, and materials factors have been incorporated into the model, including: (1) the macroscopic applied stress profile, (2) the stress history, (3) the extent and grain-to- grain distribution of carbide sensitization levels, which can be applied to a subset of elements comprising a grain boundary, and (4) a data set containing IGSCC crack growth rates as function of applied stress intensity and sensitization level averaged over a large population of grains. The latter information was obtained from the literature for AISI 304 stainless steel under light water nuclear reactor primary coolant environmental conditions. The resulting crack growth simulations are presented and discussed. 14 refs., 10 figs.

  6. An Evaluation of Saxon's Algebra Test.

    ERIC Educational Resources Information Center

    Johnson, Dale M.; Smith, Blaine

    1987-01-01

    John Saxon's incremental development model has been proclaimed as a superior teaching strategy for mathematics. This study evaluated the Saxon approach and textbook using 276 Algebra I students in experimental and control groups. The groups were compared in cognitive and affective areas. Results are presented. (Author/MT)

  7. Digital Maps, Matrices and Computer Algebra

    ERIC Educational Resources Information Center

    Knight, D. G.

    2005-01-01

    The way in which computer algebra systems, such as Maple, have made the study of complex problems accessible to undergraduate mathematicians with modest computational skills is illustrated by some large matrix calculations, which arise from representing the Earth's surface by digital elevation models. Such problems are often considered to lie in…

  8. Using Technology to Balance Algebraic Explorations

    ERIC Educational Resources Information Center

    Kurz, Terri L.

    2013-01-01

    In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…

  9. The geometric semantics of algebraic quantum mechanics.

    PubMed

    Cruz Morales, John Alexander; Zilber, Boris

    2015-08-01

    In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. PMID:26124252

  10. An Application of Boolean Algebra to Biology

    ERIC Educational Resources Information Center

    McConnell, John W.

    1971-01-01

    Examines the model of interacting nerve systems based on a switching theory, which uses a mathematical structure familiar to many high school students and requires little knowledge of biology. Reviews the basic operation of nerves, and demonstrates how Boolean algebraic statements are applied to synaptic interactions. (PR)

  11. Reynolds stress closure modeling in wall-bounded flows

    NASA Technical Reports Server (NTRS)

    Durbin, Paul A.

    1993-01-01

    This report describes two projects. Firstly, a Reynolds stress closure for near-wall turbulence is described. It was motivated by the simpler k-epsilon-(v-bar(exp 2)) model described in last year's annual research brief. Direct Numerical Simulation of three-dimensional channel flow shows a curious decrease of the turbulent kinetic energy. The second topic of this report is a model which reproduces this effect. That model is described and used to discuss the relevance of the three dimensional channel flow simulation to swept wing boundary layers.

  12. Animal models of post-traumatic stress disorder: face validity

    PubMed Central

    Goswami, Sonal; Rodríguez-Sierra, Olga; Cascardi, Michele; Paré, Denis

    2013-01-01

    Post-traumatic stress disorder (PTSD) is a debilitating condition that develops in a proportion of individuals following a traumatic event. Despite recent advances, ethical limitations associated with human research impede progress in understanding PTSD. Fortunately, much effort has focused on developing animal models to help study the pathophysiology of PTSD. Here, we provide an overview of animal PTSD models where a variety of stressors (physical, psychosocial, or psychogenic) are used to examine the long-term effects of severe trauma. We emphasize models involving predator threat because they reproduce human individual differences in susceptibility to, and in the long-term consequences of, psychological trauma. PMID:23754973

  13. Animal models of post-traumatic stress disorder: face validity.

    PubMed

    Goswami, Sonal; Rodríguez-Sierra, Olga; Cascardi, Michele; Paré, Denis

    2013-01-01

    Post-traumatic stress disorder (PTSD) is a debilitating condition that develops in a proportion of individuals following a traumatic event. Despite recent advances, ethical limitations associated with human research impede progress in understanding PTSD. Fortunately, much effort has focused on developing animal models to help study the pathophysiology of PTSD. Here, we provide an overview of animal PTSD models where a variety of stressors (physical, psychosocial, or psychogenic) are used to examine the long-term effects of severe trauma. We emphasize models involving predator threat because they reproduce human individual differences in susceptibility to, and in the long-term consequences of, psychological trauma. PMID:23754973

  14. Neural models on temperature regulation for cold-stressed animals

    NASA Technical Reports Server (NTRS)

    Horowitz, J. M.

    1975-01-01

    The present review evaluates several assumptions common to a variety of current models for thermoregulation in cold-stressed animals. Three areas covered by the models are discussed: signals to and from the central nervous system (CNS), portions of the CNS involved, and the arrangement of neurons within networks. Assumptions in each of these categories are considered. The evaluation of the models is based on the experimental foundations of the assumptions. Regions of the nervous system concerned here include the hypothalamus, the skin, the spinal cord, the hippocampus, and the septal area of the brain.

  15. Stress corrosion cracking of metal matrix composites: Modeling and experiment

    SciTech Connect

    Jones, R.H.

    1990-10-01

    The stress corrosion crack growth ate of metal matrix composites has been described by a model which is dependent on the length-to- diameter ({ell}/d) ratio and volume fraction of the reinforcing phase and matrix creep component. The model predicts a large dependence of the stress corrosion crack growth rate of a metal matrix composite on {ell}/d and matrix creep component and a small dependence on the volume fraction of reinforcement. Experimentally determined crack growth rates for 7090 Al/SiC tested in 3.5% NcCl solution, 6061 Al/SiC tested in moist air with NaCl and immersed in NaCl solution, and Mg/Al{sub 2}0{sub 3} tested in a chloride/chromate solution are all consistent with the model. The close correspondence between the model and experiment for a matrix creep stress exponent of 3 suggest that there is little corrosion damage to the reinforcing phase in these systems. 16 refs., 5 figs.

  16. Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras

    SciTech Connect

    Marquette, Ian

    2013-07-15

    We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.

  17. Dynamics of urban heat stress events in climate models

    NASA Astrophysics Data System (ADS)

    Yang, David

    2016-04-01

    Extreme heat stress events as measured by the wet-bulb temperature require extraordinarily high air temperatures coupled with high humidity. These conditions are rare, as relative humidity rapidly falls with rising air temperature, and this effect often results in decreasing heat stress as temperature rises. However, in certain coastal locations in the Middle East recent heat waves have resulted in wet-bulb temperatures of 33-35 degrees C, which approach the theoretical limits of human tolerance. These conditions result from the combination of extreme desert heat and humid winds off of the warm ocean waters. It is unclear if climate models properly simulate these dynamics. This study will analyse the ability of the CMIP5 model suite to replicate observed dynamics during extreme heat events in major urban areas.

  18. Mathematical Modeling of Intravascular Blood Coagulation under Wall Shear Stress

    PubMed Central

    Rukhlenko, Oleksii S.; Dudchenko, Olga A.; Zlobina, Ksenia E.; Guria, Georgy Th.

    2015-01-01

    Increased shear stress such as observed at local stenosis may cause drastic changes in the permeability of the vessel wall to procoagulants and thus initiate intravascular blood coagulation. In this paper we suggest a mathematical model to investigate how shear stress-induced permeability influences the thrombogenic potential of atherosclerotic plaques. Numerical analysis of the model reveals the existence of two hydrodynamic thresholds for activation of blood coagulation in the system and unveils typical scenarios of thrombus formation. The dependence of blood coagulation development on the intensity of blood flow, as well as on geometrical parameters of atherosclerotic plaque is described. Relevant parametric diagrams are drawn. The results suggest a previously unrecognized role of relatively small plaques (resulting in less than 50% of the lumen area reduction) in atherothrombosis and have important implications for the existing stenting guidelines. PMID:26222505

  19. An Integrated Model of Posttraumatic Stress and Growth.

    PubMed

    Lancaster, Steven L; Klein, Keith R; Nadia, Cyrus; Szabo, Lisa; Mogerman, Ben

    2015-01-01

    A number of recent models have examined cognitive predictors of posttraumatic stress and posttraumatic growth (S. Barton, A. Boals, & L. Knowles, 2013; J. Groleau, L. Calhoun, A. Cann, & G. Tedeschi, 2013; K. N. Triplett, R. G. Tedeschi, A. Cann, L. G. Calhoun, & C. L. Reeve, 2012). The current study examined an integrated model of predictors of distress and perceived growth in 194 college undergraduates. Domains covered included the roles of core belief challenge, event centrality, posttrauma cognitions, and event-related rumination. Negative cognitions about the self and the centrality of the event directly predicted both growth and distress, although intrusive rumination predicted only posttraumatic stress disorder symptoms, and deliberate rumination predicted only posttraumatic growth. Future research should continue to examine the shared and unique predictors of postevent growth and distress. PMID:26011515

  20. Computational modeling of cardiovascular response to orthostatic stress

    NASA Technical Reports Server (NTRS)

    Heldt, Thomas; Shim, Eun B.; Kamm, Roger D.; Mark, Roger G.

    2002-01-01

    The objective of this study is to develop a model of the cardiovascular system capable of simulating the short-term (< or = 5 min) transient and steady-state hemodynamic responses to head-up tilt and lower body negative pressure. The model consists of a closed-loop lumped-parameter representation of the circulation connected to set-point models of the arterial and cardiopulmonary baroreflexes. Model parameters are largely based on literature values. Model verification was performed by comparing the simulation output under baseline conditions and at different levels of orthostatic stress to sets of population-averaged hemodynamic data reported in the literature. On the basis of experimental evidence, we adjusted some model parameters to simulate experimental data. Orthostatic stress simulations are not statistically different from experimental data (two-sided test of significance with Bonferroni adjustment for multiple comparisons). Transient response characteristics of heart rate to tilt also compare well with reported data. A case study is presented on how the model is intended to be used in the future to investigate the effects of post-spaceflight orthostatic intolerance.

  1. Computational modeling of cardiovascular response to orthostatic stress.

    PubMed

    Heldt, Thomas; Shim, Eun B; Kamm, Roger D; Mark, Roger G

    2002-03-01

    The objective of this study is to develop a model of the cardiovascular system capable of simulating the short-term (< or = 5 min) transient and steady-state hemodynamic responses to head-up tilt and lower body negative pressure. The model consists of a closed-loop lumped-parameter representation of the circulation connected to set-point models of the arterial and cardiopulmonary baroreflexes. Model parameters are largely based on literature values. Model verification was performed by comparing the simulation output under baseline conditions and at different levels of orthostatic stress to sets of population-averaged hemodynamic data reported in the literature. On the basis of experimental evidence, we adjusted some model parameters to simulate experimental data. Orthostatic stress simulations are not statistically different from experimental data (two-sided test of significance with Bonferroni adjustment for multiple comparisons). Transient response characteristics of heart rate to tilt also compare well with reported data. A case study is presented on how the model is intended to be used in the future to investigate the effects of post-spaceflight orthostatic intolerance. PMID:11842064

  2. Stress

    MedlinePlus

    ... sudden negative change, such as losing a job, divorce, or illness Traumatic stress, which happens when you ... stress, so you can avoid more serious health effects. NIH: National Institute of Mental Health

  3. Survey of Turbulence Models for the Computation of Turbulent Jet Flow and Noise

    NASA Technical Reports Server (NTRS)

    Nallasamy, N.

    1999-01-01

    The report presents an overview of jet noise computation utilizing the computational fluid dynamic solution of the turbulent jet flow field. The jet flow solution obtained with an appropriate turbulence model provides the turbulence characteristics needed for the computation of jet mixing noise. A brief account of turbulence models that are relevant for the jet noise computation is presented. The jet flow solutions that have been directly used to calculate jet noise are first reviewed. Then, the turbulent jet flow studies that compute the turbulence characteristics that may be used for noise calculations are summarized. In particular, flow solutions obtained with the k-e model, algebraic Reynolds stress model, and Reynolds stress transport equation model are reviewed. Since, the small scale jet mixing noise predictions can be improved by utilizing anisotropic turbulence characteristics, turbulence models that can provide the Reynolds stress components must now be considered for jet flow computations. In this regard, algebraic stress models and Reynolds stress transport models are good candidates. Reynolds stress transport models involve more modeling and computational effort and time compared to algebraic stress models. Hence, it is recommended that an algebraic Reynolds stress model (ASM) be implemented in flow solvers to compute the Reynolds stress components.

  4. Stress monitoring in a maxilla model and dentition

    NASA Astrophysics Data System (ADS)

    Milczewski, Maura S.; Kalinowski, Hypolito J.; da Silva, Jean C. C.; Abe, Ilda; Simões, José A.; Saga, Armando

    2011-05-01

    Fiber Bragg gratings were used to measure stress caused by the orthodontic appliance in an experimental model reproducing the maxilla and dentition. This study brings light to the understanding of the way forces are dissipated on the dentition and propagate to the adjacent bone. Results show deformations on the order of 4 μɛ and a linear relationship between strain and the applied load in the incisor, canine and molar teeth.

  5. Prediction of Plate Motions and Stresses from Global Dynamic Models

    NASA Astrophysics Data System (ADS)

    Ghosh, A.; Holt, W. E.

    2011-12-01

    Predicting plate motions correctly has been a challenge for global dynamic models. In addition to predicting plate motions, a successful model must also explain the following features: plate rigidity, plate boundary zone deformation, as well as intraplate stress patterns and deformation. In this study we show that, given constraints from shallow lithosphere structure, history of subduction, and first order features from whole mantle tomography, it is possible to achieve a high level of accuracy in predicting plate motions and lithosphere deformation within plate boundary zones. Best-fit dynamic models presently provide an RMS velocity misfit of global surface motions (compared at 63,000 spaced points in the GSRM NNR model [Kreemer et al., 2006]) of order 1 cm/yr. We explore the relative contribution of shallow lithosphere structure vs. whole mantle convection in affecting surface deformation as well as plate motions. We show that shallow lithosphere structure that includes topography and lateral density variations in the lithosphere is an integral part of global force balance. Its inclusion in geodynamic models is essential in order to match observations of surface motions and stresses, particularly within continental zones of deformation. We also argue that stiff slabs may not be as important as has been previously claimed in controlling plate motion and lithosphere deformation. An important result of this study is the calibration of absolute stress magnitudes in the lithosphere, verified through benchmarking using whole mantle convection models. Given additional constraints of the matching of surface motions, we also calibrate the absolute effective lithosphere viscosities. Best-fit models require plates with effective viscosities of order 1023 Pa-s, with plate boundary zones possessing effective viscosities 1-3 orders of magnitude weaker. Given deviatoric stress magnitudes within the lithosphere of order 10 - 60 MPa, our global models predict less than 2 mm

  6. Clifford Algebra Cℓ 3(ℂ) for Applications to Field Theories

    NASA Astrophysics Data System (ADS)

    Panicaud, B.

    2011-10-01

    The multivectorial algebras present yet both an academic and a technological interest. Difficulties can occur for their use. Indeed, in all applications care is taken to distinguish between polar and axial vectors and between scalars and pseudo scalars. Then a total of eight elements are often considered even if they are not given the correct name of multivectors. Eventually because of their simplicity, only the vectorial algebra or the quaternions algebra are explicitly used for physical applications. Nevertheless, it should be more convenient to use directly more complex algebras in order to have a wider range of application. The aim of this paper is to inquire into one particular Clifford algebra which could solve this problem. The present study is both didactic concerning its construction and pragmatic because of the introduced applications. The construction method is not an original one. But this latter allows to build up the associated real algebra as well as a peculiar formalism that enables a formal analogy with the classical vectorial algebra. Finally several fields of the theoretical physics will be described thanks to this algebra, as well as a more applied case in general relativity emphasizing simultaneously its relative validity in this particular domain and the easiness of modeling some physical problems.

  7. The Algebra Artist

    ERIC Educational Resources Information Center

    Beigie, Darin

    2014-01-01

    Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…

  8. Algebraic Multigrid Benchmark

    SciTech Connect

    2013-05-06

    AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.

  9. Vertex Algebras, Kac-Moody Algebras, and the Monster

    NASA Astrophysics Data System (ADS)

    Borcherds, Richard E.

    1986-05-01

    It is known that the adjoint representation of any Kac-Moody algebra A can be identified with a subquotient of a certain Fock space representation constructed from the root lattice of A. I define a product on the whole of the Fock space that restricts to the Lie algebra product on this subquotient. This product (together with a infinite number of other products) is constructed using a generalization of vertex operators. I also construct an integral form for the universal enveloping algebra of any Kac-Moody algebra that can be used to define Kac-Moody groups over finite fields, some new irreducible integrable representations, and a sort of affinization of any Kac-Moody algebra. The ``Moonshine'' representation of the Monster constructed by Frenkel and others also has products like the ones constructed for Kac-Moody algebras, one of which extends the Griess product on the 196884-dimensional piece to the whole representation.

  10. Inflammatory Stress and Idiosyncratic Hepatotoxicity: Hints from Animal Models

    PubMed Central

    Deng, Xiaomin; Luyendyk, James P.; Ganey, Patricia E.

    2009-01-01

    Adverse drug reactions (ADRs) present a serious human health problem. They are major contributors to hospitalization and mortality throughout the world (Lazarou et al., 1998; Pirmohamed et al., 2004). A small fraction (less than 5%) of ADRs can be classified as “idiosyncratic.” Idiosyncratic ADRs (IADRs) are caused by drugs with diverse pharmacological effects and occur at various times during drug therapy. Although IADRs affect a number of organs, liver toxicity occurs frequently and is the primary focus of this review. Because of the inconsistency of clinical data and the lack of experimental animal models, how IADRs arise is largely undefined. Generation of toxic drug metabolites and induction of specific immunity are frequently cited as causes of IADRs, but definitive evidence supporting either mechanism is lacking for most drugs. Among the more recent hypotheses for causation of IADRs is that inflammatory stress induced by exogenous or endogenous inflammagens is a susceptibility factor. In this review, we give a brief overview of idiosyncratic hepatotoxicity and the inflammatory response induced by bacterial lipopolysaccharide. We discuss the inflammatory stress hypothesis and use as examples two drugs that have caused IADRs in human patients: ranitidine and diclofenac. The review focuses on experimental animal models that support the inflammatory stress hypothesis and on the mechanisms of hepatotoxic response in these models. The need for design of epidemiological studies and the potential for implementation of inflammation interaction studies in preclinical toxicity screening are also discussed briefly. PMID:19805476

  11. A heuristic model for MRI turbulent stresses in Hall MHD

    NASA Astrophysics Data System (ADS)

    Lingam, Manasvi; Bhattacharjee, Amitava

    2016-07-01

    Although the Shakura-Sunyaev α viscosity prescription has been highly successful in characterizing myriad astrophysical environments, it has proven to be partly inadequate in modelling turbulent stresses driven by the magnetorotational instability (MRI). Hence, we adopt the approach employed by Ogilvie, but in the context of Hall magnetohydrodynamics (MHD), to study MRI turbulence. We utilize the exact evolution equations for the stresses, and the non-linear terms are closed through the invocation of dimensional analysis and physical considerations. We demonstrate that the inclusion of the Hall term leads to non-trivial results, including the modification of the Reynolds and Maxwell stresses, as well as the (asymptotic) non-equipartition between the kinetic and magnetic energies; the latter issue is also addressed via the analysis of non-linear waves. The asymptotic ratio of the kinetic to magnetic energies is shown to be independent of the choice of initial conditions, but it is governed by the Hall parameter. We contrast our model with an altered version of the Kazantsev prescription from small-scale dynamo theory, and the Hall term does not generally contribute in the latter approach, illustrating the limitations of this formalism. We indicate potential astrophysical applications of our model, including the solar wind where a lack of equipartition has been observed.

  12. Model for how retrograde actin flow regulates adhesion traction stresses.

    PubMed

    Li, Ying; Bhimalapuram, Prabhakar; Dinner, Aaron R

    2010-05-19

    Cells from animals adhere to and exert mechanical forces on their surroundings. Cells must control these forces for many biological processes, and dysfunction can lead to pathologies. How the actions of molecules within a cell are coordinated to regulate the adhesive interaction with the extracellular matrix remains poorly understood. It has been observed that cytoplasmic proteins that link integrin cell-surface receptors with the actin cytoskeleton flow with varying rates from the leading edge toward the center of a cell. Here, we explore theoretically how measurable subcellular traction stresses depend on the local speed of retrograde actin flow. In the model, forces result from the stretching of molecular complexes in response to the drag from the flow; because these complexes break with extension-dependent kinetics, the flow results in a decrease in their number when sufficiently large. Competition between these two effects naturally gives rise to a clutch-like behavior and a nonmonotonic trend in the measured stresses, consistent with recent data for epithelial cells. We use this basic framework to evaluate slip and catch bond mechanisms for integrins; better fits of experimental data are obtained with a catch bond representation. Extension of the model to one comprising multiple molecular interfaces shifts the peak stress to higher speeds. Connections to other models and cell movement are discussed. PMID:21386439

  13. A new ply model for interlaminar stress analysis

    NASA Technical Reports Server (NTRS)

    Rao Valisetty, R.; Rehfield, L. W.

    1985-01-01

    An accurate estimate of interlaminar stresses is crucial to understanding, as well as predicting, many delamination-related failures in composite materials. A new model for ply-level sublaminate analysis is presented and applied. The homogeneous plate theory developed earlier by the authors (Valisetty and Rehfield, 1983) is further refined, and the equations are reduced appropriately for the classical finite-width free-edge laminate elasticity problem and a related delamination crack growth problem. It is applied to the laminate on a ply-by-ply basis. This theory incorporates all the essential physical effects and appears to be an adequate model for predicting the behavior of individual layers in equilibrium. On the basis of the number of equations and boundary conditions required for the implementation of layer equilibrium, this theory also appears to be the simplest of its kind presented so far. The stress induced in the free-edge region of a (0,90,90,0) laminate in uniform extension and the energy release rates for the delamination between the -30 deg and 90 deg plies of a (+, -30,+, -30, 90,90)s laminate are computed using the new analysis. The results are in excellent agreement with the existing numerical solutions. The new ply behavioral model appears to be very promising; it yields stresses and displacements that are statically and kinematically compatible at interlaminar surfaces.

  14. Modeling the effects of torsional stress on hysteretic magnetization

    SciTech Connect

    Sablik, M.J.; Jiles, D.C.

    1999-01-01

    Opposite torques applied axially to a polycrystalline ferromagnetic rod result in tensile and compressive stresses acting perpendicularly at the rod surface at 45{degree} to the rod axis. These stresses affect the magnetization of the rod when a magnetic field is applied parallel to the rod axis. It is shown how one can formulate the magnetomechanical hysteresis model so as to treat this special case of biaxial stress and take into account the effect of opposite torques on the magnetic properties of the rod. Variation of hysteresis parameters such as coercive field, remanent flux density, differential permeability at the coercive field, and hysteresis loss as a function of applied torque are determined from the model. In the model, the torque is applied first and then the field is cycled to give hysteresis loops. It is found that the torque dependence of the magnetic properties is different, depending on what is chosen for H{sub max}, the maximum value of the applied magnetic field H. The best parameter to use for tracking the torque is found to be H{sub c} at saturation or near saturation, since that parameter shows an almost linear decrease with the applied torque.

  15. A heuristic model for MRI turbulent stresses in Hall MHD

    NASA Astrophysics Data System (ADS)

    Lingam, Manasvi; Bhattacharjee, Amitava

    2016-04-01

    Although the Shakura-Sunyaev α viscosity prescription has been highly successful in characterizing myriad astrophysical environments, it has proven to be partly inadequate in modelling turbulent stresses driven by the MRI. Hence, we adopt the approach employed by Ogilvie (2003), but in the context of Hall magnetohydrodynamics (MHD), to study MRI turbulence. We utilize the exact evolution equations for the stresses, and the non-linear terms are closed through the invocation of dimensional analysis and physical considerations. We demonstrate that the inclusion of the Hall term leads to non-trivial results, including the modification of the Reynolds and Maxwell stresses, as well as the (asymptotic) non-equipartition between the kinetic and magnetic energies; the latter issue is also addressed via the analysis of non-linear waves. The asymptotic ratio of the kinetic and magnetic energies is shown to be independent of the choice of initial conditions, but it is governed by the Hall parameter. We contrast our model with the Kazantsev prescription from small-scale dynamo theory, and the Hall term does not generally contribute in the latter approach, illustrating the limitations of the Kazantsev formalism. We indicate potential astrophysical applications of our model, including the solar wind where a lack of equipartition has been observed.

  16. Inflammatory stress and idiosyncratic hepatotoxicity: hints from animal models.

    PubMed

    Deng, Xiaomin; Luyendyk, James P; Ganey, Patricia E; Roth, Robert A

    2009-09-01

    Adverse drug reactions (ADRs) present a serious human health problem. They are major contributors to hospitalization and mortality throughout the world (Lazarou et al., 1998; Pirmohamed et al., 2004). A small fraction (less than 5%) of ADRs can be classified as "idiosyncratic." Idiosyncratic ADRs (IADRs) are caused by drugs with diverse pharmacological effects and occur at various times during drug therapy. Although IADRs affect a number of organs, liver toxicity occurs frequently and is the primary focus of this review. Because of the inconsistency of clinical data and the lack of experimental animal models, how IADRs arise is largely undefined. Generation of toxic drug metabolites and induction of specific immunity are frequently cited as causes of IADRs, but definitive evidence supporting either mechanism is lacking for most drugs. Among the more recent hypotheses for causation of IADRs is that inflammatory stress induced by exogenous or endogenous inflammagens is a susceptibility factor. In this review, we give a brief overview of idiosyncratic hepatotoxicity and the inflammatory response induced by bacterial lipopolysaccharide. We discuss the inflammatory stress hypothesis and use as examples two drugs that have caused IADRs in human patients: ranitidine and diclofenac. The review focuses on experimental animal models that support the inflammatory stress hypothesis and on the mechanisms of hepatotoxic response in these models. The need for design of epidemiological studies and the potential for implementation of inflammation interaction studies in preclinical toxicity screening are also discussed briefly. PMID:19805476

  17. The tensor hierarchy algebra

    NASA Astrophysics Data System (ADS)

    Palmkvist, Jakob

    2014-01-01

    We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D - 2 - p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.

  18. The tensor hierarchy algebra

    SciTech Connect

    Palmkvist, Jakob

    2014-01-15

    We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.

  19. Stress Management Affects Outcomes in the Pathophysiology of an Endometriosis Model

    PubMed Central

    Cruz, Myrella L.; Hernández, Siomara; Thompson, Kenira J.; Bayona, Manuel; Flores, Idhaliz

    2014-01-01

    We have previously shown detrimental effects of stress in an animal model of endometriosis. We now investigated whether the ability to control stress can affect disease parameters. Endometriosis was surgically induced in female Sprague-Dawley rats before exposing animals to a controllable (submerged platform) or uncontrollable (no platform) swim stress protocol. Corticosterone levels and fecal pellet numbers were measured as an indicator of stress. Uncontrollable stress increased the number and size of the endometriotic cysts. Rats receiving uncontrollable stress had higher anxiety than those exposed to controllable stress or no stress and higher corticosterone levels. Uncontrollable stressed rats had more colonic damage and uterine cell infiltration compared to no stress, while controllable stress rats showed less of an effect. Uncontrollable stress also increased both colonic and uterine motility. In summary, the level of stress controllability appears to modulate the behavior and pathophysiology of endometriosis and offers evidence for evaluating therapeutic interventions. PMID:25015902

  20. Modeling Diffusion Induced Stresses for Lithium-Ion Battery Materials

    NASA Astrophysics Data System (ADS)

    Chiu Huang, Cheng-Kai

    Advancing lithium-ion battery technology is of paramount importance for satisfying the energy storage needs in the U.S., especially for the application in the electric vehicle industry. To provide a better acceleration for electric vehicles, a fast and repeatable discharging rate is required. However, particle fractures and capacity loss have been reported under high current rate (C-rate) during charging/discharging and after a period of cycling. During charging and discharging, lithium ions extract from and intercalate into electrode materials accompanied with the volume change and phase transition between Li-rich phase and Li-poor phase. It is suggested that the diffusion-induced-stress is one of the main reasons causing capacity loss due to the mechanical degradation of electrode particles. Therefore, there is a fundamental need to provide a mechanistic understanding by considering the structure-mechanics-property interactions in lithium-ion battery materials. Among many cathode materials, the olivine-based lithium-iron-phosphate (LiFePO4) with an orthorhombic crystal structure is one of the promising cathode materials for the application in electric vehicles. In this research we first use a multiphysic approach to investigate the stress evolution, especially on the phase boundary during lithiation in single LiFePO4 particles. A diffusion-controlled finite element model accompanied with the experimentally observed phase boundary propagation is developed via a finite element package, ANSYS, in which lithium ion concentration-dependent anisotropic material properties and volume misfits are incorporated. The stress components on the phase boundary are used to explain the Mode I, Mode II, and Mode III fracture propensities in LiFePO4 particles. The elastic strain energy evolution is also discussed to explain why a layer-by-layer lithium insertion mechanism (i.e. first-order phase transformation) is energetically preferred. Another importation issue is how current

  1. The determination of the surface stress in an atmospheric model

    SciTech Connect

    Janseen, P.A.E.M. ); Beljaars, A.C.M.; Simmons, A.; Viterbo, P. )

    1992-12-01

    By forcing a third-generation wave-prediction model with surface stresses from the European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric model, it was discovered that lower wave heights were generated than by forcing with the ECMWF surface winds. The apparent inconsistency between surface stresses and surface winds in the atmospheric model turns out to be time-step dependent. A similar conclusion may be inferred from results of the WAMDI group. Apparently, a number of atmospheric models have inaccuracies in the boundary-layer scheme near the surface. In this paper it is argued that the reason for the inaccuracies is related to the numerical integration scheme that is used in these models. It is shown that a numerical scheme that treats physics and dynamics separately has an equilibrium that is time-step dependent. An alternative scheme-namely, simultaneous, implicit treatment of both physics and dynamics-removes this deficiency. Possible consequences for atmospheric-, wave-, and ocean-circulation models are briefly discussed.

  2. Deterministic Stress Modeling of Hot Gas Segregation in a Turbine

    NASA Technical Reports Server (NTRS)

    Busby, Judy; Sondak, Doug; Staubach, Brent; Davis, Roger

    1998-01-01

    Simulation of unsteady viscous turbomachinery flowfields is presently impractical as a design tool due to the long run times required. Designers rely predominantly on steady-state simulations, but these simulations do not account for some of the important unsteady flow physics. Unsteady flow effects can be modeled as source terms in the steady flow equations. These source terms, referred to as Lumped Deterministic Stresses (LDS), can be used to drive steady flow solution procedures to reproduce the time-average of an unsteady flow solution. The goal of this work is to investigate the feasibility of using inviscid lumped deterministic stresses to model unsteady combustion hot streak migration effects on the turbine blade tip and outer air seal heat loads using a steady computational approach. The LDS model is obtained from an unsteady inviscid calculation. The LDS model is then used with a steady viscous computation to simulate the time-averaged viscous solution. Both two-dimensional and three-dimensional applications are examined. The inviscid LDS model produces good results for the two-dimensional case and requires less than 10% of the CPU time of the unsteady viscous run. For the three-dimensional case, the LDS model does a good job of reproducing the time-averaged viscous temperature migration and separation as well as heat load on the outer air seal at a CPU cost that is 25% of that of an unsteady viscous computation.

  3. Glacial Atlantic overturning increased by wind stress in climate models

    NASA Astrophysics Data System (ADS)

    Muglia, Juan; Schmittner, Andreas

    2015-11-01

    Previous Paleoclimate Model Intercomparison Project (PMIP) simulations of the Last Glacial Maximum (LGM) Atlantic Meridional Overturning Circulation (AMOC) showed dissimilar results on transports and structure. Here we analyze the most recent PMIP3 models, which show a consistent increase (on average by 41 ± 26%) and deepening (663 ± 550 m) of the AMOC with respect to preindustrial simulations, in contrast to some reconstructions from proxy data. Simulations run with the University of Victoria (UVic) ocean circulation model suggest that this is caused by changes in the Northern Hemisphere wind stress, brought about by the presence of ice sheets over North America in the LGM. When forced with LGM wind stress anomalies from PMIP3 models, the UVic model responds with an increase of the northward salt transport in the North Atlantic, which strengthens North Atlantic Deep Water formation and the AMOC. These results improve our understanding of the LGM AMOC's driving forces and suggest that some ocean mechanisms may not be correctly represented in PMIP3 models or some proxy data may need reinterpretation.

  4. (I,q)-graded Lie algebraic extensions of the Poincaré algebra, constraints on I and q

    NASA Astrophysics Data System (ADS)

    Wills Toro, Luis Alberto

    1995-04-01

    The constraints on the index set I and on the function q of the (I,q)-graded Lie algebras over K containing the Poincaré Lie algebra are studied. By using the single-grading model, particular choices for I and q consistent with the found constraints are determined for K=C. Gradings are then found for which I⊆I=Z2×(Z4N×Z4N)×Gre, with N∈N and Gre an Abelian group. These gradings provide a way for algebraic extensions of the Poincaré Lie algebra beyond the Z2-gradings of supersymmetry and supergravity. In these algebraic extensions, each other commuting space-time parameter can either commute or anticommute with the further parameters of the (I,q)-graded (super) manifold. Different field representations can have—with each other—generalized commutative behavior beyond commutativity and anticommutativity.

  5. Application and improvement of Raupach's shear stress partitioning model

    NASA Astrophysics Data System (ADS)

    Walter, B. A.; Lehning, M.; Gromke, C.

    2012-12-01

    Aeolian processes such as the entrainment, transport and redeposition of sand, soil or snow are able to significantly reshape the earth's surface. In times of increasing desertification and land degradation, often driven by wind erosion, investigations of aeolian processes become more and more important in environmental sciences. The reliable prediction of the sheltering effect of vegetation canopies against sediment erosion, for instance, is a clear practical application of such investigations to identify suitable and sustainable counteractive measures against wind erosion. This study presents an application and improvement of a theoretical model presented by Raupach (Boundary-Layer Meteorology, 1992, Vol.60, 375-395 and Journal of Geophysical Research, 1993, Vol.98, 3023-3029) which allows for quantifying the sheltering effect of vegetation against sediment erosion. The model predicts the shear stress ratios τS'/τ and τS''/τ. Here, τS is the part of the total shear stress τ that acts on the ground beneath the plants. The spatial peak τS'' of the surface shear stress is responsible for the onset of particle entrainment whereas the spatial mean τS' can be used to quantify particle mass fluxes. The precise and accurate prediction of these quantities is essential when modeling wind erosion. Measurements of the surface shear stress distributions τS(x,y) on the ground beneath live vegetation canopies (plant species: lolium perenne) were performed in a controlled wind tunnel environment to determine the model parameters and to evaluate the model performance. Rigid, non-porous wooden blocks instead of the plants were additionally tested for the purpose of comparison, since previous wind tunnel studies used exclusively artificial plant imitations for their experiments on shear stress partitioning. The model constant c, which is needed to determine the total stress τ for a canopy of interest and which remained rather unspecified to date, was found to be c ≈ 0

  6. Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras

    NASA Astrophysics Data System (ADS)

    Paseka, Jan; Riečanová, Zdenka

    2010-12-01

    We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.

  7. Symmetric linear systems - An application of algebraic systems theory

    NASA Technical Reports Server (NTRS)

    Hazewinkel, M.; Martin, C.

    1983-01-01

    Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

  8. Isoflurane Suppresses Stress-Enhanced Fear Learning in a Rodent Model of Posttraumatic Stress Disorder

    PubMed Central

    Rau, Vinuta; Oh, Irene; Laster, Michael; Eger, Edmond I; Fanselow, Michael S.

    2009-01-01

    Background A minority of patients who experience awareness and/or pain during surgery subsequently develop posttraumatic stress disorder. In a rodent model of posttraumatic stress disorder, stress-enhanced fear learning (SEFL), rats are pre-exposed to a stressor of 15 footshocks. Subsequent exposure to a single footshock produces an enhanced fear response. This effect is akin to sensitized reactions shown by some posttraumatic stress disorder patients to cues previously associated with the traumatic event. Methods We studied the effect of isoflurane and nitrous oxide on SEFL. Rats were exposed to the inhaled anesthetic during or after a 15-footshock stressor. Then rats were given a single footshock in a different environment. Their fear response was quantified in response to the 15-footshock and single-footshock environments. SEFL longevity was tested by placing a 90-day period between the 15 footshocks and the single footshock. In addition, the intensity of the footshock was increased to evaluate treatment effectiveness. Results Increasing isoflurane concentrations decreased SEFL when given during, but not after, the stressor. At 0.40 minimum alveolar concentration, isoflurane given during the stressor blocked SEFL 90 days later. A three-fold increase in the stressor intensity increased the isoflurane concentration required to block SEFL to no more than 0.67 minimum alveolar concentration. As with isoflurane, nitrous oxide suppressed SEFL at a similar minimum alveolar concentration fraction. Conclusions These results suggest that sufficient concentrations (perhaps 0.67 minimum alveolar concentration or less) of an inhaled anesthetic may prevent SEFL. PMID:19212264

  9. The interaction of acute and chronic stress impairs model-based behavioral control.

    PubMed

    Radenbach, Christoph; Reiter, Andrea M F; Engert, Veronika; Sjoerds, Zsuzsika; Villringer, Arno; Heinze, Hans-Jochen; Deserno, Lorenz; Schlagenhauf, Florian

    2015-03-01

    It is suggested that acute stress shifts behavioral control from goal-directed, model-based toward habitual, model-free strategies. Recent findings indicate that interindividual differences in the cortisol stress response influence model-based decision-making. Although not yet investigated in humans, animal studies show that chronic stress also shifts decision-making toward more habitual behavior. Here, we ask whether acute stress and individual vulnerability factors, such as stress reactivity and previous exposure to stressful life events, impact the balance between model-free and model-based control systems. To test this, 39 male participants (21-30 years old) were exposed to a potent psychosocial stressor (Trier Social Stress Test) and a control condition in a within-subjects design before they performed a sequential decision-making task which evaluates the balance between the two systems. Physiological and subjective stress reactivity was assessed before, during, and after acute stress exposure. By means of computational modeling, we demonstrate that interindividual variability in stress reactivity predicts impairments in model-based decision-making. Whereas acute psychosocial stress did not alter model-based behavioral control, we found chronic and acute stress to interact in their detrimental effect on decision-making: subjects with high but not low chronic stress levels as indicated by stressful life events exhibited reduced model-based control in response to acute psychosocial stress. These findings emphasize that stress reactivity and chronic stress play an important role in mediating the relationship between stress and decision-making. Our results might stimulate new insights into the interplay between chronic and acute stress, attenuated model-based control, and the pathogenesis of various psychiatric diseases. PMID:25662093

  10. Deformed Maxwell Algebras and their Realizations

    SciTech Connect

    Gomis, Joaquim; Kamimura, Kiyoshi; Lukierski, Jerzy

    2009-12-15

    We study all possible deformations of the Maxwell algebra. In D = d+1not =3 dimensions there is only one-parameter deformation. The deformed algebra is isomorphic to so(d+1, 1)+so(d, 1) or to so(d, 2)+so(d, 1) depending on the signs of the deformation parameter. We construct in the dS(AdS) space a model of massive particle interacting with Abelian vector field via nonlocal Lorentz force. In D = 2+1 the deformations depend on two parameters b and k. We construct a phase diagram, with two parts of the (b, k) plane with so(3, 1)+so(2, 1) and so( 2, 2)+so(2, 1) algebras separated by a critical curve along which the algebra is isomorphic to Iso(2, 1)+so(2, 1). We introduce in D = 2+1 the Volkov-Akulov type model for a Abelian Goldstone-Nambu vector field described by a non-linear action containing as its bilinear term the free Chern-Simons Lagrangean.

  11. Locally finite dimensional Lie algebras

    NASA Astrophysics Data System (ADS)

    Hennig, Johanna

    We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L. Then we prove two structure theorems for simple, locally finite dimensional Lie algebras over an algebraically closed field of characteristic p which give sufficient conditions for the algebras to be of the form [K(R, *), K( R, *)] / (Z(R) ∩ [ K(R, *), K(R, *)]) for a simple, locally finite dimensional associative algebra R with involution *. Lastly, we explore the noncommutative geometry of locally simple representations of the diagonal locally finite Lie algebras sl(ninfinity), o( ninfinity), and sp(n infinity).

  12. Quantum computation using geometric algebra

    NASA Astrophysics Data System (ADS)

    Matzke, Douglas James

    This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.

  13. Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

    PubMed

    Verburgt, Lukas M

    2016-01-01

    This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s. PMID:26806075

  14. On the cohomology of Leibniz conformal algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Jiao

    2015-04-01

    We construct a new cohomology complex of Leibniz conformal algebras with coefficients in a representation instead of a module. The low-dimensional cohomology groups of this complex are computed. Meanwhile, we construct a Leibniz algebra from a Leibniz conformal algebra and prove that the category of Leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution Leibniz algebras.

  15. Assessing Algebraic Solving Ability: A Theoretical Framework

    ERIC Educational Resources Information Center

    Lian, Lim Hooi; Yew, Wun Thiam

    2012-01-01

    Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

  16. Analytical Model for Thermal Elastoplastic Stresses of Functionally Graded Materials

    SciTech Connect

    Zhai, P. C.; Chen, G.; Liu, L. S.; Fang, C.; Zhang, Q. J.

    2008-02-15

    A modification analytical model is presented for the thermal elastoplastic stresses of functionally graded materials subjected to thermal loading. The presented model follows the analytical scheme presented by Y. L. Shen and S. Suresh [6]. In the present model, the functionally graded materials are considered as multilayered materials. Each layer consists of metal and ceramic with different volume fraction. The ceramic layer and the FGM interlayers are considered as elastic brittle materials. The metal layer is considered as elastic-perfectly plastic ductile materials. Closed-form solutions for different characteristic temperature for thermal loading are presented as a function of the structure geometries and the thermomechanical properties of the materials. A main advance of the present model is that the possibility of the initial and spread of plasticity from the two sides of the ductile layers taken into account. Comparing the analytical results with the results from the finite element analysis, the thermal stresses and deformation from the present model are in good agreement with the numerical ones.

  17. DEM Modelling of Non-linear Viscoelastic Stress Waves

    NASA Astrophysics Data System (ADS)

    Wang, Wenqiang; Tang, Zhiping; Horie, Yasuyuki

    2001-06-01

    A DEM(Discrete Element Method) simulation of nonlinear viscoelastic stress wave problems is carried out. The interaction forces among elements are described using a model in which neighbor elements are linked by a nonlinear spring and a certain number of Maxwell components in parallel. By making use of exponential relaxation moduli, it is shown that numerical computation of the convolution integral does not require storing and repeatedly calculating strain history, and can reduce the computational cost dramatically. To validate the viscoelastic DM2 code, stress wave propagation in a Maxwell rod with one end subjected to a constant stress loading is simulated. Results excellently fit those from the characteristics calculation. Satisfactory results are also obtained in the simulation of one-dimensional plane wave in a plastic bonded explosive. The code is then used to investigate the problem of meso-scale damage in this explosive under shock loading. Results not only show "compression damage", but also reveal a complex damage evolution. They demonstrate a unique capability of DEM in modeling heterogeneous materials.

  18. Modeling the stress dependence of Barkhausen phenomena for stress axis linear and noncollinear with applied magnetic field (abstract)

    SciTech Connect

    Sablik, M.J.; Augustyniak, B.; Chmielewski, M.

    1996-04-01

    The almost linear dependence of the maximum Barkhausen noise signal amplitude on stress has made it a tool for nondestructive evaluation of residual stress. Recently, a model has been developed to account for the stress dependence of the Barkhausen noise signal. The model uses the development of Alessandro {ital et} {ital al}. who use coupled Langevin equations to derive an expression for the Barkhausen noise power spectrum. The model joins this expression to the magnetomechanical hysteresis model of Sablik {ital et} {ital al}., obtaining both a hysteretic and stress-dependent result for the magnetic-field-dependent Barkhausen noise envelope and obtaining specifically the almost linear stress dependence of the Barkhausen noise maximum experimentally. In this paper, we extend the model to derive the angular dependence observed by Kwun of the Barkhausen noise amplitude when stress axis is taken at different angles relative to magnetic field. We also apply the model to the experimental observation that in XC10 French steel, there is an apparent almost linear correlation with stress of hysteresis loss and of the integral of the Barkhausen noise signal over applied field {ital H}. Further, the two quantities, Barkhausen noise integral and hysteresis loss, are linearly correlated with each other. The model shows how that behavior is to be expected for the measured steel because of its sharply rising hysteresis curve. {copyright} {ital 1996 American Institute of Physics.}

  19. Thermal mechanical stress modeling of GCtM seals

    SciTech Connect

    Dai, Steve Xunhu; Chambers, Robert

    2015-09-01

    Finite-element thermal stress modeling at the glass-ceramic to metal (GCtM) interface was conducted assuming heterogeneous glass-ceramic microstructure. The glass-ceramics were treated as composites consisting of high expansion silica crystalline phases dispersed in a uniform residual glass. Interfacial stresses were examined for two types of glass-ceramics. One was designated as SL16 glass -ceramic, owing to its step-like thermal strain curve with an overall coefficient of thermal expansion (CTE) at 16 ppm/ºC. Clustered Cristobalite is the dominant silica phase in SL16 glass-ceramic. The other, designated as NL16 glass-ceramic, exhibited clusters of mixed Cristobalite and Quartz and showed a near-linear thermal strain curve with a same CTE value.

  20. Model for lightcone fluctuations due to stress tensor fluctuations

    NASA Astrophysics Data System (ADS)

    Bessa, C. H. G.; De Lorenci, V. A.; Ford, L. H.; Ribeiro, C. C. H.

    2016-03-01

    We study a model for quantum lightcone fluctuations in which vacuum fluctuations of the electric field and of the squared electric field in a nonlinear dielectric material produce variations in the flight times of probe pulses. When this material has a nonzero third order polarizability, the flight time variations arise from squared electric field fluctuations, and are analogous to effects expected when the stress tensor of a quantized field drives passive spacetime geometry fluctuations. We also discuss the dependence of the squared electric field fluctuations upon the geometry of the material, which in turn determines a sampling function for averaging the squared electric field along the path of the pulse. This allows us to estimate the probability of especially large fluctuations, which is a measure of the probability distribution for quantum stress tensor fluctuations.

  1. A model for hierarchical patterns under mechanical stresses

    NASA Astrophysics Data System (ADS)

    Corson, F.; Henry, H.; Adda-Bedia, M.

    2010-01-01

    We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field method to describe the transition between two states of the tissue, e.g. the differentiation of leaf veins, and consider a layered system where mechanical stresses are generated by differential growth. We present analytical and numerical results for one-dimensional systems, showing that a combination of growth and irreversibility gives rise to hierarchical patterns. Two-dimensional simulations suggest that such a mechanism could account for the hierarchical, reticulate structure of leaf venation networks, yet point to the need for a more detailed treatment of the coupling between growth and mechanical stresses.

  2. Failure Prediction in Fine Blanking Process with Stress Limit Model

    NASA Astrophysics Data System (ADS)

    Tong, Longchang; Manopulo, Niko; Hora, Pavel

    2010-06-01

    Extremely small blanking clearance and nearly sharp edges of blanking tool are the characteristics of fine blanking that produces near net shape parts. The extreme forming conditions make the failure prediction for fine blanking more difficult than for ordinary forming processes. Stress Limit Criterion (SLC) is adopted in this work to perform the failure prediction of 3D fine blanking process. In comparison with the stress triaxiality diagram, SLC is not sensitively affected by complex nonlinear deformation paths and can perform the task as well. However, the parameters that support the model have to be obtained with combination of dedicatedly designed experiments and numerical simulation. The FEM simulation must also be able to provide stable and reliable results.

  3. [Neuroprotection strategies: effect of vinpocetine in vitro oxidative stress models].

    PubMed

    Pereira, Cláudia; Agostinho, Paula; Moreira, Paula I; Duarte, Ana I; Santos, Maria S; Oliveira, Catarina R

    2003-01-01

    Reactive oxygen species (ROS) play an important role in neuronal damage and death that occurs in several neurodegenerative disorders, namely in Alzheimer's disease (AD). The observation that ROS neutralization may slow or reduce the neurodegenerative process associated with those pathologies stimulates the development of new drugs, more efficient and well tolerated, with antioxidant properties. Vinpocetine [14-etoxicarbonyl-3alpha,16alpha-ethyl)-14,15-eburnamine], a vincamine derivative, efficiently protects cells from ROS attack. Recently, the protective effect of vinpocetine was demonstrated using in vitro models of oxidative stress induced by the oxidant pair ascorbate/Fe2+ and by synthetic peptides of the AD-associated b-amyloid protein (Abeta). Results obtained from these in vitro experiences support that additional clinical trials should be carried out using vinpocetine, or vinpocetine derivatives, in order to test its therapeutical or preventive effects in diseases where oxidative stress plays a crucial role. PMID:15631851

  4. A Minority Stress Model for Suicidal Ideation in Gay Men.

    PubMed

    Michaels, Matthew S; Parent, Mike C; Torrey, Carrie L

    2016-02-01

    There is a dearth of research on mechanisms underlying higher rates of suicidal ideation among gay men compared to heterosexual men. The purpose of this study was to establish the link between social/psychological predictor variables and suicidal ideation by testing a hypothesized minority stress model. Structural equation modeling was used to assess the relationships posited in the model using data from a community sample of 167 gay men. Model fit was adequate and hypothesized relationships were partially supported. Also, depressive symptoms partially mediated the relationship between (less) outness predicting suicidal ideation. These findings imply that therapeutic approaches targeting the coming out process may be more effective than approaches targeting internalized homophobia when suicidal ideation is indicated in the clinical presentation of gay and bisexual men. PMID:25981684

  5. A New Stress-Based Model of Political Extremism

    PubMed Central

    Canetti-Nisim, Daphna; Halperin, Eran; Sharvit, Keren; Hobfoll, Stevan E.

    2011-01-01

    Does exposure to terrorism lead to hostility toward minorities? Drawing on theories from clinical and social psychology, we propose a stress-based model of political extremism in which psychological distress—which is largely overlooked in political scholarship—and threat perceptions mediate the relationship between exposure to terrorism and attitudes toward minorities. To test the model, a representative sample of 469 Israeli Jewish respondents was interviewed on three occasions at six-month intervals. Structural Equation Modeling indicated that exposure to terrorism predicted psychological distress (t1), which predicted perceived threat from Palestinian citizens of Israel (t2), which, in turn, predicted exclusionist attitudes toward Palestinian citizens of Israel (t3). These findings provide solid evidence and a mechanism for the hypothesis that terrorism introduces nondemocratic attitudes threatening minority rights. It suggests that psychological distress plays an important role in political decision making and should be incorporated in models drawing upon political psychology. PMID:22140275

  6. How Structure Sense for Algebraic Expressions or Equations Is Related to Structure Sense for Abstract Algebra

    ERIC Educational Resources Information Center

    Novotna, Jarmila; Hoch, Maureen

    2008-01-01

    Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…

  7. In vivo porcine left atrial wall stress: Computational model.

    PubMed

    Di Martino, Elena S; Bellini, Chiara; Schwartzman, David S

    2011-10-13

    Most computational models of the heart have so far concentrated on the study of the left ventricle, mainly using simplified geometries. The same approach cannot be adopted to model the left atrium, whose irregular shape does not allow morphological simplifications. In addition, the deformation of the left atrium during the cardiac cycle strongly depends on the interaction with its surrounding structures. We present a procedure to generate a comprehensive computational model of the left atrium, including physiological loads (blood pressure), boundary conditions (pericardium, pulmonary veins and mitral valve annulus movement) and mechanical properties based on planar biaxial experiments. The model was able to accurately reproduce the in vivo dynamics of the left atrium during the passive portion of the cardiac cycle. A shift in time between the peak pressure and the maximum displacement of the mitral valve annulus allows the appendage to inflate and bend towards the ventricle before the pulling effect associated with the ventricle contraction takes place. The ventricular systole creates room for further expansion of the appendage, which gets in close contact with the pericardium. The temporal evolution of the volume in the atrial cavity as predicted by the finite element simulation matches the volume changes obtained from CT scans. The stress field computed at each time point shows remarkable spatial heterogeneity. In particular, high stress concentration occurs along the appendage rim and in the region surrounding the pulmonary veins. PMID:21907340

  8. Critical assessment of Reynolds stress turbulence models using homogeneous flows

    NASA Technical Reports Server (NTRS)

    Shabbir, Aamir; Shih, Tsan-Hsing

    1992-01-01

    In modeling the rapid part of the pressure correlation term in the Reynolds stress transport equations, extensive use has been made of its exact properties which were first suggested by Rotta. These, for example, have been employed in obtaining the widely used Launder, Reece and Rodi (LRR) model. Some recent proposals have dropped one of these properties to obtain new models. We demonstrate, by computing some simple homogeneous flows, that doing so does not lead to any significant improvements over the LRR model and it is not the right direction in improving the performance of existing models. The reason for this, in our opinion, is that violation of one of the exact properties can not bring in any new physics into the model. We compute thirteen homogeneous flows using LRR (with a recalibrated rapid term constant), IP and SSG models. The flows computed include the flow through axisymmetric contraction; axisymmetric expansion; distortion by plane strain; and homogeneous shear flows with and without rotation. Results show that for most general representation for a model linear in the anisotropic tensor, performs either better or as good as the other two models of the same level.

  9. Heisenberg Groups and their Automorphisms over Algebras with Central Involution

    NASA Astrophysics Data System (ADS)

    Johnson, Robert W.

    2015-08-01

    Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real and complex quadratic spaces with dimension 4 or less. A model for the representations of these Heisenberg groups and automorphism groups is constructed. A pseudo-differential operator enables a parallel treatment of spaces defined over finite and real fields.

  10. Changing Practice, Changing Minds, from Arithmetical to Algebraic Thinking: An Application of the Concerns-Based Adoption Model (CBAM)

    ERIC Educational Resources Information Center

    Tunks, Jeanne; Weller, Kirk

    2009-01-01

    This study examines the process of change among grade 4 teachers (students aged 9-10 years) who participated in a yearlong Teacher Quality Grant innovation program. The concerns-based adoption model (CBAM), which informed the design and implementation of the program, was used to examine the process of change. Two questions guided the…

  11. Handheld Computer Algebra Systems in the Pre-Algebra Classroom

    ERIC Educational Resources Information Center

    Gantz, Linda Ann Galofaro

    2010-01-01

    This mixed method analysis sought to investigate several aspects of student learning in pre-algebra through the use of computer algebra systems (CAS) as opposed to non-CAS learning. This research was broken into two main parts, one which compared results from both the experimental group (instruction using CAS, N = 18) and the control group…

  12. Abstract Algebra to Secondary School Algebra: Building Bridges

    ERIC Educational Resources Information Center

    Christy, Donna; Sparks, Rebecca

    2015-01-01

    The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

  13. Algebra and Algebraic Thinking in School Math: 70th YB

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, 2008

    2008-01-01

    Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…

  14. Adaptive Algebraic Smoothers

    SciTech Connect

    Philip, Bobby; Chartier, Dr Timothy

    2012-01-01

    methods based on Local Sensitivity Analysis (LSA). The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coecient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem.

  15. Statecharts Via Process Algebra

    NASA Technical Reports Server (NTRS)

    Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance

    1999-01-01

    Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics

  16. Algebraic Multigrid Benchmark

    2013-05-06

    AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less

  17. Models of recurrent strike-slip earthquake cycles and the state of crustal stress

    NASA Technical Reports Server (NTRS)

    Lyzenga, Gregory A.; Raefsky, Arthur; Mulligan, Stephanie G.

    1991-01-01

    Numerical models of the strike-slip earthquake cycle, assuming a viscoelastic asthenosphere coupling model, are examined. The time-dependent simulations incorporate a stress-driven fault, which leads to tectonic stress fields and earthquake recurrence histories that are mutually consistent. Single-fault simulations with constant far-field plate motion lead to a nearly periodic earthquake cycle and a distinctive spatial distribution of crustal shear stress. The predicted stress distribution includes a local minimum in stress at depths less than typical seismogenic depths. The width of this stress 'trough' depends on the magnitude of crustal stress relative to asthenospheric drag stresses. The models further predict a local near-fault stress maximum at greater depths, sustained by the cyclic transfer of strain from the elastic crust to the ductile asthenosphere. Models incorporating both low-stress and high-stress fault strength assumptions are examined, under Newtonian and non-Newtonian rheology assumptions. Model results suggest a preference for low-stress (a shear stress level of about 10 MPa) fault models, in agreement with previous estimates based on heat flow measurements and other stress indicators.

  18. Modeling temperature and stress in rocks exposed to the sun

    NASA Astrophysics Data System (ADS)

    Hallet, B.; Mackenzie, P.; Shi, J.; Eppes, M. C.

    2012-12-01

    The potential contribution of solar-driven thermal cycling to the progressive breakdown of surface rocks on the Earth and other planets is recognized but under studied. To shed light on this contribution we have launched a collaborative study integrating modern instrumental and numerical approaches to define surface temperatures, stresses, strains, and microfracture activity in exposed boulders, and to shed light on the thermo-mechanical response of boulders to diurnal solar exposure. The instrumental portion of our study is conducted by M. Eppes and coworkers who have monitored the surface and environmental conditions of two ~30 cm dia. granite boulders (one in North Carolina, one in New Mexico) in the field for one and tow years, respectively. Each boulder is instrumented with 8 thermocouples, 8 strain gauges, a surface moisture sensor and 6 acoustic emission (AE) sensors to monitor microfracture activity continuously and to locate it within 2.5 cm. Herein, we focus on the numerical modeling. Using a commercially available finite element program, MSC.Marc®2008r1, we have developed an adaptable, realistic thermo-mechanical model to investigate quantitatively the temporal and spatial distributions of both temperature and stress throughout a boulder. The model accounts for the effects of latitude and season (length of day and the sun's path relative to the object), atmospheric damping (reduction of solar radiation when traveling through the Earth's atmosphere), radiative interaction between the boulder and its surrounding soil, secondary heat exchange of the rock with air, and transient heat conduction in both rock and soil. Using representative thermal and elastic rock properties, as well as realistic representations of the size, shape and orientation of a boulder instrumented in the field in North Carolina, the model is validated by comparison with direct measurements of temperature and strain on the surface of one boulder exposed to the sun. Using the validated

  19. Modeling of stress distributions on the microstructural level in Alloy 600

    SciTech Connect

    Kozaczek, K.J.; Petrovic, B.G.; Ruud, C.O.; Mcllree, A.R.

    1995-04-01

    Stress distribution in a random polycrystalline material (Alloy 600) was studied using a topologically correct microstructural model. Distributions of von Mises and hydrostatic stresses at the grain vertices, which could be important in intergranular stress corrosion cracking, were analyzed as functions of microstructure, grain orientations and loading conditions. Grain size, shape, and orientation had a more pronounced effect on stress distribution than loading conditions. At grain vertices the stress concentration factor was higher for hydrostatic stress (1.7) than for von Mises stress (1.5). The stress/strain distribution in the volume (grain interiors) is a normal distribution and does not depend on the location of the studied material volume i.e., surface vs/bulk. The analysis of stress distribution in the volume showed the von Mises stress concentration of 1.75 and stress concentration of 2.2 for the hydrostatic pressure. The observed stress concentration is high enough to cause localized plastic microdeformation, even when the polycrystalline aggregate is in the macroscopic elastic regime. Modeling of stresses and strains in polycrystalline materials can identify the microstructures (grain size distributions, texture) intrinsically susceptible to stress/strain concentrations and justify the correctness of applied stress state during the stress corrosion cracking tests. Also, it supplies the information necessary to formulate the local failure criteria and interpret of nondestructive stress measurements.

  20. The Algebra of Complex Numbers.

    ERIC Educational Resources Information Center

    LePage, Wilbur R.

    This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

  1. The Algebra of the Arches

    ERIC Educational Resources Information Center

    Buerman, Margaret

    2007-01-01

    Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…

  2. Online Algebraic Tools for Teaching

    ERIC Educational Resources Information Center

    Kurz, Terri L.

    2011-01-01

    Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)

  3. Condensing Algebra for Technical Mathematics.

    ERIC Educational Resources Information Center

    Greenfield, Donald R.

    Twenty Algebra-Packets (A-PAKS) were developed by the investigator for technical education students at the community college level. Each packet contained a statement of rationale, learning objectives, performance activities, performance test, and performance test answer key. The A-PAKS condensed the usual sixteen weeks of algebra into a six-week…

  4. Linear Algebra and Image Processing

    ERIC Educational Resources Information Center

    Allali, Mohamed

    2010-01-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)

  5. Algebra: Grades 8-12.

    ERIC Educational Resources Information Center

    Instructional Objectives Exchange, Los Angeles, CA.

    A complete set of behavioral objectives for first-year algebra taught in any of grades 8 through 12 is presented. Three to six sample test items and answers are provided for each objective. Objectives were determined by surveying the most used secondary school algebra textbooks. Fourteen major categories are included: (1) whole numbers--operations…

  6. Exploring Algebraic Patterns through Literature.

    ERIC Educational Resources Information Center

    Austin, Richard A.; Thompson, Denisse R.

    1997-01-01

    Presents methods for using literature to develop algebraic thinking in an environment that connects algebra to various situations. Activities are based on the book "Anno's Magic Seeds" with additional resources listed. Students express a constant function, exponential function, and a recursive function in their own words as well as writing about…

  7. Learning Algebra from Worked Examples

    ERIC Educational Resources Information Center

    Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.

    2014-01-01

    For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is…

  8. Thermodynamics. [algebraic structure

    NASA Technical Reports Server (NTRS)

    Zeleznik, F. J.

    1976-01-01

    The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.

  9. Invariants of triangular Lie algebras

    NASA Astrophysics Data System (ADS)

    Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman

    2007-07-01

    Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated.

  10. Abnormal Fear Memory as a Model for Posttraumatic Stress Disorder.

    PubMed

    Desmedt, Aline; Marighetto, Aline; Piazza, Pier-Vincenzo

    2015-09-01

    For over a century, clinicians have consistently described the paradoxical co-existence in posttraumatic stress disorder (PTSD) of sensory intrusive hypermnesia and declarative amnesia for the same traumatic event. Although this amnesia is considered as a critical etiological factor of the development and/or persistence of PTSD, most current animal models in basic neuroscience have focused exclusively on the hypermnesia, i.e., the persistence of a strong fear memory, neglecting the qualitative alteration of fear memory. The latest is characterized by an underrepresentation of the trauma in the context-based declarative memory system in favor of its overrepresentation in a cue-based sensory/emotional memory system. Combining psychological and neurobiological data as well as theoretical hypotheses, this review supports the idea that contextual amnesia is at the core of PTSD and its persistence and that altered hippocampal-amygdalar interaction may contribute to such pathologic memory. In a first attempt to unveil the neurobiological alterations underlying PTSD-related hypermnesia/amnesia, we describe a recent animal model mimicking in mice some critical aspects of such abnormal fear memory. Finally, this line of argument emphasizes the pressing need for a systematic comparison between normal/adaptive versus abnormal/maladaptive fear memory to identify biomarkers of PTSD while distinguishing them from general stress-related, potentially adaptive, neurobiological alterations. PMID:26238378

  11. Computer Models of Stress, Allostasis, and Acute and Chronic Diseases

    PubMed Central

    Goldstein, David S.

    2009-01-01

    The past century has seen a profound shift in diseases of humankind. Acute, unifactorial diseases are being replaced increasingly by multifactorial disorders that arise from complex interactions among genes, environment, concurrent morbidities and treatments, and time. According to the concept of allostasis, there is no single, ideal set of steady-state conditions in life. Allostasis reflects active, adaptive processes that maintain apparent steady states, via multiple, interacting effectors regulated by homeostatic comparators “homeostats.” Stress can be defined as a condition or state in which a sensed discrepancy between afferent information and a setpoint for response leads to activation of effectors, reducing the discrepancy. “Allostatic load” refers to the consequences of sustained or repeated activation of mediators of allostasis. From the analogy of a home temperature control system, the temperature can be maintained at any of a variety of levels (allostatic states) by multiple means (effectors), regulated by a comparator thermostat (homeostat). Stress might exert adverse health consequences via allostatic load. This presentation describes models of homeostatic systems that incorporate negative feedback regulation, multiple effectors, effector sharing, environmental influences, intrinsic obsolescence, and destabilizing positive feedback loops. These models can be used to predict effects of environmental and genetic alterations on allostatic load and therefore on the development of multi-system disorders and failures. PMID:19120114

  12. An Algebra-Integrated Physics and Chemistry Workshop for Teachers as a Model for Increasing the Number of Minority Students in Science and Engineering

    NASA Astrophysics Data System (ADS)

    Obot, V.; Brown, B.; Wu, T.; Wunsch, G.; Miles, A.; Morris, P.; Lindstrom, M.; Allen, J.

    The need to increase minority representation in science and engineering disciplines is well documented. Many strategies for achieving this goal have evolved over the years; yet, minority representation is still minimal. It appears that while students are naturally curious about the universe, once mention is made of mathematics as a pre-requisite to the study of science and engineering, interest seems to wane. Perhaps a possible way to get around this phobia is to incorporate the mathematics into the science courses and the science into the mathematics courses at the secondary level. This will require mathematics and science teachers to work together, re-enforcing each other so that lessons can be truly interdisciplinary. For the past two summers, we have conducted workshops for secondary school mathematics and science teachers in a large urban school district. The workshops are called "Algebra-Integrated Physics and Chemistry". These workshops are designed to introduce the teachers to mathematical modeling of physical and chemical phenomenon. T chnology (graphic calculators) is used to dis covere functions that model a particular process. We have modeled linear functions by looking at the Celsius and Fahrenheit scales. A simple experiment is heating water, measuring the temperature in both Celsius and Fahrenheit scales, plotting Celsius versus Fahrenheit temperatures, and determining their mathematical relationship. At this point, the science teacher can also go into a discussion of the meaning of temperature. In some cases readily available data can be analyzed. The ellipse and Kepler's third law is ideal when studying conic sections. In this case, available data can be used, and by plotting appropriately, cubic functions can be studied and motions of planets in their orbits near and far from the sun can be discussed. This new approach to mathematics and science will take the student to a certain comfort level so that statements such as either " I like science

  13. Open-closed homotopy algebra in mathematical physics

    SciTech Connect

    Kajiura, Hiroshige; Stasheff, Jim

    2006-02-15

    In this paper we discuss various aspects of open-closed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach's open-closed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part of Zwiebach's quantum open-closed string field theory. We clarify the explicit relation of an OCHA with Kontsevich's deformation quantization and with the B-models of homological mirror symmetry. An explicit form of the minimal model for an OCHA is given as well as its relation to the perturbative expansion of open-closed string field theory. We show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures (A{sub {infinity}} algebras) by closed strings (L{sub {infinity}} algebras)

  14. Modeling conductive cooling for thermally stressed dairy cows.

    PubMed

    Gebremedhin, Kifle G; Wu, Binxin; Perano, K

    2016-02-01

    Conductive cooling, which is based on direct contact between a cow lying down and a cooled surface (water mattress, or any other heat exchanger embedded under the bedding), allows heat transfer from the cow to the cooled surface, and thus alleviate heat stress of the cow. Conductive cooling is a novel technology that has the potential to reduce the consumption of energy and water in cooling dairy cows compared to some current practices. A three-dimensional conduction model that simulates cooling thermally-stressed dairy cows was developed. The model used a computational fluid dynamics (CFD) method to characterize the air-flow field surrounding the animal model. The flow field was obtained by solving the continuity and the momentum equations. The heat exchange between the animal and the cooled water mattress as well as between the animal and ambient air was determined by solving the energy equation. The relative humidity was characterized using the species transport equation. The conduction 3-D model was validated against experimental temperature data and the agreement was very good (average error is 4.4% and the range is 1.9-8.3%) for a mesh size of 1117202. Sensitivity analyses were conducted between heat losses (sensible and latent) with respect to air temperature, relative humidity, air velocity, and level of wetness of skin surface to determine which of the parameters affect heat flux more than others. Heat flux was more sensitive to air temperature and level of wetness of the skin surface and less sensitive to relative humidity. PMID:26857982

  15. Infinite Dimensional Algebras and 2+1 Dimensional Field Theory:. yet another View of gl(∞) Some New Algebras

    NASA Astrophysics Data System (ADS)

    Hoppe, Jens

    Over the past years, associative algebras have come to play a major role in several areas of theoretical physics. Firstly, it has been realized that Yang Baxter algebras [1] constitute the relevant structure underlying 1+1 dimensional integrable models; in addition, their relation to braid groups, the theory of knots and links, and the exchange algebras of 1+1 dimensional conformal field theories [2] has been quite well understood by now. Secondly, deformations of Poisson structures that appeared in 2+1 dimensional field theories as infinite dimensional symmetry algebras possess underlying associative structures, which have also been studied in some detail (concerning higher spin theories see, e.g., [3, 4] and references therein, concerning the enveloping algebra of sl(2, C) see, e.g., [5], concerning deformations of diffAT2 — the Lie algebra of infinitesimal area preserving diffeomorphisms of the Torus — see [6, 7, 8, 9]). Ideas on how both investigations could eventually converge (i.e., a relation between 2+1 and 1+1 dimensions) have, e.g., been expressed in [10]. As indicated by the two subtitles there will be two parts to my paper: the first one presents a view on something I met long ago [11], and recently got interested in again [5, 7, 9, 12], while the second part introduces some algebraic structures that seem to be interesting, and possibly new.

  16. Comparison of the Effectiveness of a Traditional Intermediate Algebra Course With That of a Less Rigorous Intermediate Algebra Course in Preparing Students for Success in a Subsequent Mathematics Course

    ERIC Educational Resources Information Center

    Sworder, Steven C.

    2007-01-01

    An experimental two-track intermediate algebra course was offered at Saddleback College, Mission Viejo, CA, between the Fall, 2002 and Fall, 2005 semesters. One track was modeled after the existing traditional California community college intermediate algebra course and the other track was a less rigorous intermediate algebra course in which the…

  17. Interseismic modulation of stress orientations in southern California predicted by geodetically constrained block models

    NASA Astrophysics Data System (ADS)

    Langstaff, M. A.; Loveless, J. P.; Meade, B. J.

    2013-12-01

    We combine stressing rate estimates from geodetically constrained block models with candidate background stress fields to quantify the temporal evolution of stress over the earthquake cycle in southern California. Observations of p-axis rotations have been previously documented both before and after large earthquake events, and postmainshock seismicity indicates ~1.5 deg/yr of p-axis rotation in the vicinities of the Landers, Northridge, Elmore Ranch and Superstition Hills, and Ridgecrest earthquakes. Here we integrate regional stress rate estimates with the annual stress changes generated by interseismic fault system activity to place bounds on the regional background stress magnitudes that may be consistent with the inferred p-axis rotations. These models of time-dependent stress orientations also provide mechanical constraints on the range of stress variability possible through a simple earthquake cycle, including the orientation of stresses just prior to large ruptures.

  18. Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

    ERIC Educational Resources Information Center

    Gonzalez-Vega, Laureano

    1999-01-01

    Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

  19. Constraint algebra in bigravity

    SciTech Connect

    Soloviev, V. O.

    2015-07-15

    The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.

  20. Quantum algebra of N superspace

    SciTech Connect

    Hatcher, Nicolas; Restuccia, A.; Stephany, J.

    2007-08-15

    We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.

  1. Prenatal exposure to escitalopram and/or stress in rats: a prenatal stress model of maternal depression and its treatment

    PubMed Central

    Bourke, Chase H.; Capello, Catherine F.; Rogers, Swati M.; Yu, Megan L.; Boss-Williams, Katherine A.; Weiss, Jay M.; Stowe, Zachary N.; Owens, Michael J.

    2014-01-01

    Rationale A rigorously investigated model of stress and antidepressant administration during pregnancy is needed to evaluate possible effects on the mother. Objective The objective of this study was to develop a model of clinically relevant prenatal exposure to an antidepressant and stress during pregnancy to evaluate the effects on maternal care behavior. Results Female rats implanted with 28 day osmotic minipumps delivering the SSRI escitalopram throughout pregnancy had serum escitalopram concentrations in a clinically observed range (17-65 ng/mL). A separate cohort of pregnant females exposed to a chronic unpredictable mild stress paradigm on gestational days 10-20 showed elevated baseline (305 ng/mL), and acute stress-induced (463 ng/mL), plasma corticosterone concentrations compared to unstressed controls (109 ng/mL). A final cohort of pregnant dams were exposed to saline (control), escitalopram, stress, or stress and escitalopram to determine the effects on maternal care. Maternal behavior was continuously monitored over the first 10 days post parturition. A reduction of 35% in maternal contact and 11% in nursing behavior was observed due to stress during the light cycle. Licking and grooming behavior was unaffected by stress or drug exposure in either the light or dark cycle. Conclusions These data indicate that: 1) clinically relevant antidepressant treatment during human pregnancy can be modeled in rats using escitalopram; 2) chronic mild stress can be delivered in a manner that does not compromise fetal viability; and 3) neither of these prenatal treatments substantially altered maternal care post parturition. PMID:23436130

  2. Stress-induced enhancement of fear learning: an animal model of posttraumatic stress disorder.

    PubMed

    Rau, Vinuta; DeCola, Joseph P; Fanselow, Michael S

    2005-01-01

    Fear is an adaptive response that initiates defensive behavior to protect animals and humans from danger. However, anxiety disorders, such as Posttraumatic Stress Disorder (PTSD), can occur when fear is inappropriately regulated. Fear conditioning can be used to study aspects of PTSD, and we have developed a model in which pre-exposure to a stressor of repeated footshock enhances conditional fear responding to a single context-shock pairing. The experiments in this chapter address interpretations of this effect including generalization and summation or fear, inflation, and altered pain sensitivity. The results of these experiments lead to the conclusion that pre-exposure to shock sensitizes conditional fear responding to similar less intense stressors. This sensitization effect resists exposure therapy (extinction) and amnestic (NMDA antagonist) treatment. The pattern predicts why in PTSD patients, mild stressors cause reactions more appropriate for the original traumatic stressor and why new fears are so readily formed in these patients. This model can facilitate the study of neurobiological mechanisms underlying sensitization of responses observed in PTSD. PMID:16095698

  3. Application of a Reynolds stress model to separating boundary layers

    NASA Technical Reports Server (NTRS)

    Ko, Sung HO

    1993-01-01

    Separating turbulent boundary layers occur in many practical engineering applications. Nonetheless, the physics of separation/reattachment of flows is poorly understood. During the past decade, various turbulence models were proposed and their ability to successfully predict some types of flows was shown. However. prediction of separating/reattaching flows is still a formidable task for model developers. The present study is concerned with the process of separation from a smooth surface. Features of turbulent separating boundary layers that are relevant to modeling include the following: the occurrence of zero wall shear stress, which causes breakdown of the boundary layer approximation; the law of the wall not being satisfied in the mean back flow region; high turbulence levels in the separated region; a significant low-frequency motion in the separation bubble; and the turbulence structure of the separated shear layer being quite different from that of either the mixing layers or the boundary layers. These special characteristics of separating boundary layers make it difficult for simple turbulence models to correctly predict their behavior.

  4. A physical-based pMOSFETs threshold voltage model including the STI stress effect

    NASA Astrophysics Data System (ADS)

    Wei, Wu; Gang, Du; Xiaoyan, Liu; Lei, Sun; Jinfeng, Kang; Ruqi, Han

    2011-05-01

    The physical threshold voltage model of pMOSFETs under shallow trench isolation (STI) stress has been developed. The model is verified by 130 nm technology layout dependent measurement data. The comparison between pMOSFET and nMOSFET model simulations due to STI stress was conducted to show that STI stress induced less threshold voltage shift and more mobility shift for the pMOSFET. The circuit simulations of a nine stage ring oscillator with and without STI stress proved about 11% improvement of average delay time. This indicates the importance of STI stress consideration in circuit design.

  5. Application of magnetomechanical hysteresis modeling of magnetic techniques for monitoring neutron embrittlement and biaxial stress

    SciTech Connect

    Sablik, M.J.; Kwun, H.; Burkhardt, G.L.

    1993-01-31

    Research was done on the biaxial stress problem accomplished in the first half of the second year. All of the work done was preparatory to magnetic measurements. Issues addressed were: construction of a model for extracting changes in the magnetic properties of a specimen from the readings of an indirect sensor; initial development of a model for how biaxial stress alters the intrinsic magnetic properties of thespecimen; use of finite element stress analysis modeling to determine a detailed shape for the cruciform biaxial stress specimen; and construction of the biaxial stress loading apparatus.

  6. Using Homemade Algebra Tiles To Develop Algebra and Prealgebra Concepts.

    ERIC Educational Resources Information Center

    Leitze, Annette Ricks; Kitt, Nancy A.

    2000-01-01

    Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)

  7. Loop Virasoro Lie conformal algebra

    SciTech Connect

    Wu, Henan Chen, Qiufan; Yue, Xiaoqing

    2014-01-15

    The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.

  8. An Example of Competence-Based Learning: Use of Maxima in Linear Algebra for Engineers

    ERIC Educational Resources Information Center

    Diaz, Ana; Garcia, Alfonsa; de la Villa, Agustin

    2011-01-01

    This paper analyses the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is…

  9. Hopf algebras and Dyson-Schwinger equations

    NASA Astrophysics Data System (ADS)

    Weinzierl, Stefan

    2016-06-01

    In this paper I discuss Hopf algebras and Dyson-Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.

  10. Stress Evaluation and Model Validation Using Laser Ultrasonics

    SciTech Connect

    Dike, Jay J.; Lu, Wei-yang; Peng, Lawrence W.; Wang, James C. F.

    1999-02-01

    Rayleigh surface waves can be used to evaluate surface stresses and through-thickness stress gradients based on acoustoelasticity. Laser based ultrasonic techniques, which generate and detect surface waves, have the advantages of good spatial resolution and remote operation. The techniques have many potential applications. This is the final report of a LDRD project that is the first to exploit the benefits of laser ultrasonics for stress and stress gradient evaluation.

  11. Reynolds stress modeling of separated turbulent flows over helicopters

    NASA Astrophysics Data System (ADS)

    Alpman, Emre

    A numerical investigation of inviscid and viscous flows around three-dimensional complex bodies is made using unstructured meshes. Inviscid flow solutions around an RAH-66 Comanche helicopter fuselage are performed to analyze the aerodynamics of ducted tail rotors in low-power, near-edgewise flow conditions. A numerical solution of the Euler Equations is obtained for the flow over the Comanche fuselage with a uniform actuator disk and blade element models for the FANTAIL(TM); the main rotor is excluded in this study. The solutions are obtained by running the PUMA2 computational fluid dynamics code with an unstructured grid with 2.8 million tetrahedral cells. PUMA2 is an in-house computer code written in ANSI C++. Excellent correlation between the calculations and a variety of static test data are presented and discussed. The dynamic relationship between the antitorque thrust moment and applied collective pitch angle is studied by changing the pitch angle input by five degrees at a rate of 144 degrees per second. Dynamic fan thrust and moment response to applied collective pitch in hover and forward flight are presented and discussed. In order to remove the deficiency of the Euler equations in predicting separated flows, which is mostly the case in helicopter fuselage aerodynamics, a concurrent study is performed to simulate turbulent flows around three-dimensional bodies. Most of the turbulence models in the literature contain simplified assumptions which make them computationally cheap but of limited accuracy. Dramatic improvements in the computer processing speed and parallel processing made it possible to use more complete models, such as Reynolds Stress Models, for turbulent flow simulations around complex geometries, which is the focus of this work. The Reynolds Stress Model consists of coupling Reynolds transport equations with the Favre-Reynolds averaged Navier-Stokes equations, which results in a system of 12 coupled nonlinear partial differential equations

  12. Social Emotional Learning and Educational Stress: A Predictive Model

    ERIC Educational Resources Information Center

    Arslan, Serhat

    2015-01-01

    The purpose of this study is to examine the relationship between social emotional learning and educational stress. Participants were 321 elementary students. Social emotional learning and educational stress scale were used as measures. The relationships between social emotional learning and educational stress were examined using correlation…

  13. Stress, and pathogen response gene expression in modeled microgravity

    NASA Technical Reports Server (NTRS)

    Sundaresan, Alamelu; Pellis, Neal R.

    2006-01-01

    Purpose: Immune suppression in microgravity has been well documented. With the advent of human exploration and long-term space travel, the immune system of the astronaut must be optimally maintained. It is important to investigate the expression patterns of cytokine genes, because they are directly related to immune response. Heat shock proteins (HSPs), also called stress proteins, are a group of proteins that are present in the cells of every life form. These proteins are induced when a cell responds to stressors such as heat, cold and oxygen deprivation. Microgravity is another stressor that may regulate HSPs. Heat shock proteins trigger immune response through activities that occur both inside the cell (intracellular) and outside the cell (extracellular). Knowledge about these two gene groups could lead to establishment of a blueprint of the immune response and adaptation-related genes in the microgravity environment. Methods: Human peripheral blood cells were cultured in 1g (T flask) and modeled microgravity (MMG, rotating-wall vessel) for 24 and 72 hours. Cell samples were collected and subjected to gene array analysis using the Affymetrix HG_U95 array. Data was collected and subjected to a two-way analysis of variance. The genes related to immune and stress responses were analyzed. Results and Conclusions: HSP70 was up-regulated by more than two fold in microgravity culture, while HSP90 was significantly down-regulated. HSP70 is not typically expressed in all kinds of cells, but it is expressed at high levels in stress conditions. HSP70 participates in translation, protein translocation, proteolysis and protein folding, suppressing aggregation and reactivating denatured proteins. Increased serum HSP70 levels correlate with a better outcome for heat-stroke or severe trauma patients. At the same time, elevated serum levels of HSP70 have been detected in patients with peripheral or renal vascular disease. HSP90 has been identified in the cytosol, nucleus and

  14. CULA: hybrid GPU accelerated linear algebra routines

    NASA Astrophysics Data System (ADS)

    Humphrey, John R.; Price, Daniel K.; Spagnoli, Kyle E.; Paolini, Aaron L.; Kelmelis, Eric J.

    2010-04-01

    The modern graphics processing unit (GPU) found in many standard personal computers is a highly parallel math processor capable of nearly 1 TFLOPS peak throughput at a cost similar to a high-end CPU and an excellent FLOPS/watt ratio. High-level linear algebra operations are computationally intense, often requiring O(N3) operations and would seem a natural fit for the processing power of the GPU. Our work is on CULA, a GPU accelerated implementation of linear algebra routines. We present results from factorizations such as LU decomposition, singular value decomposition and QR decomposition along with applications like system solution and least squares. The GPU execution model featured by NVIDIA GPUs based on CUDA demands very strong parallelism, requiring between hundreds and thousands of simultaneous operations to achieve high performance. Some constructs from linear algebra map extremely well to the GPU and others map poorly. CPUs, on the other hand, do well at smaller order parallelism and perform acceptably during low-parallelism code segments. Our work addresses this via hybrid a processing model, in which the CPU and GPU work simultaneously to produce results. In many cases, this is accomplished by allowing each platform to do the work it performs most naturally.

  15. Translating cosmological special relativity into geometric algebra

    NASA Astrophysics Data System (ADS)

    Horn, Martin Erik

    2012-11-01

    Geometric algebra and Clifford algebra are important tools to describe and analyze the physics of the world we live in. Although there is enormous empirical evidence that we are living in four dimensional spacetime, mathematical worlds of higher dimensions can be used to present the physical laws of our world in an aesthetical and didactical more appealing way. In physics and mathematics education we are therefore confronted with the question how these high dimensional spaces should be taught. But as an immediate confrontation of students with high dimensional compactified spacetimes would expect too much from them at the beginning of their university studies, it seems reasonable to approach the mathematics and physics of higher dimensions step by step. The first step naturally is the step from four dimensional spacetime of special relativity to a five dimensional spacetime world. As a toy model for this artificial world cosmological special relativity, invented by Moshe Carmeli, can be used. This five dimensional non-compactified approach describes a spacetime which consists not only of one time dimension and three space dimensions. In addition velocity is regarded as a fifth dimension. This model very probably will not represent physics correctly. But it can be used to discuss and analyze the consequences of an additional dimension in a clear and simple way. Unfortunately Carmeli has formulated cosmological special relativity in standard vector notation. Therefore a translation of cosmological special relativity into the mathematical language of Grassmann and Clifford (Geometric algebra) is given and the physics of cosmological special relativity is discussed.

  16. Stress analysis of 27% scale model of AH-64 main rotor hub

    NASA Technical Reports Server (NTRS)

    Hodges, R. V.

    1985-01-01

    Stress analysis of an AH-64 27% scale model rotor hub was performed. Component loads and stresses were calculated based upon blade root loads and motions. The static and fatigue analysis indicates positive margins of safety in all components checked. Using the format developed here, the hub can be stress checked for future application.

  17. Modelling Occupational Stress and Employee Health and Wellbeing in a Chinese Higher Education Institution

    ERIC Educational Resources Information Center

    Sang, Xiaoli; Teo, Stephen T. T.; Cooper, Cary L.; Bohle, Philip

    2013-01-01

    Extensive change is evident in higher education in the People's Republic of China but there have been few studies of the effect of work stress on wellbeing in the higher education sector. The main aim of this study is to test and refine the ASSET ("An Organizational Stress Screening Tool") model of occupational stress in a sample of 150 academic…

  18. Parent and Adolescent Responses to Poverty Related Stress: Tests of Mediated and Moderated Coping Models

    ERIC Educational Resources Information Center

    Wadsworth, Martha E.; Raviv, Tali; Compas, Bruce E.; Connor-Smith, Jennifer K.

    2005-01-01

    We tested several models of the associations among economic strain, life stress, coping, involuntary stress responses, and psychological symptoms in a sample of 57 parent-adolescent dyads from rural, lower-income families. Economic strain and life stress predicted symptoms for both parents and adolescents. Stressor-symptom specificity was found…

  19. Depression amongst Chinese Adolescents in Hong Kong: An Evaluation of a Stress Moderation Model

    ERIC Educational Resources Information Center

    Ng, Catalina S. M.; Hurry, Jane

    2011-01-01

    Stress has an established association with depression. However, not all adolescents experiencing stressors become depressed and it is helpful to identify potential resilience factors. The current study tests a theoretical extension of a stress-diathesis model of depression in a Chinese context, with stress, coping, family relationships, and…

  20. Methamphetamine Use among Rural White and Native American Adolescents: An Application of the Stress Process Model

    ERIC Educational Resources Information Center

    Eitle, David J.; Eitle, Tamela McNulty

    2013-01-01

    Methamphetamine use has been identified as having significant adverse health consequences, yet we know little about the correlates of its use. Additionally, research has found that Native Americans are at the highest risk for methamphetamine use. Our exploratory study, informed by the stress process model, examines stress and stress buffering…