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.
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.
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.
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.
A new algebraic transition model based on stress length function
NASA Astrophysics Data System (ADS)
Xiao, Meng-Juan; She, Zhen-Su
2016-11-01
Transition, as one of the two biggest challenges in turbulence research, is of critical importance for engineering application. For decades, the fundamental research seems to be unable to capture the quantitative details in real transition process. On the other hand, numerous empirical parameters in engineering transition models provide no unified description of the transition under varying physical conditions. Recently, we proposed a symmetry-based approach to canonical wall turbulence based on stress length function, which is here extended to describe the transition via a new algebraic transition model. With a multi-layer analytic form of the stress length function in both the streamwise and wall normal directions, the new model gives rise to accurate description of the mean field and friction coefficient, comparing with both the experimental and DNS results at different inlet conditions. Different types of transition process, such as the transition with varying incoming turbulence intensities or that with blow and suck disturbance, are described by only two or three model parameters, each of which has their own specific physical interpretation. Thus, the model enables one to extract physical information from both experimental and DNS data to reproduce the transition process, which may prelude to a new class of generalized transition model for engineering applications.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Sjögren, Torbjörn; Johansson, Arne V.
2000-06-01
A simple and straightforward method is presented for the derivation and calibration of algebraic nonlinear models for terms in Reynolds stress turbulence closures. The method extensively utilizes data from direct numerical simulations to allow an investigation of the model performance over the entire Reynolds stress anisotropy-invariant map. The model constants are determined from the condition of minimizing the mean square error over the invariant map, in order to give good model behavior for as wide a class as possible of flow situations. A low Reynolds number closure is proposed based on the most general form for closing the Reynolds stress transport equations in terms of Reynolds stresses and total dissipation rate. It is shown that forcing the closure to satisfy realizability in a strict sense leads to a good model behavior even for the complicated flow situation near a wall, without any use of ad-hoc wall damping functions in the closure. The model behavior in homogeneous turbulent flow is analyzed by formulating equations for invariant measures, yielding several quite general results for the behavior of the present and other existing models. A new approach to the modeling effects of rotation in the context of Reynolds stress closures is presented and tested for some different homogeneous flows subjected to rotation.
Algebraic stress model for axial flow in a bare rod-bundle
de Lemos, M.J.S.
1987-01-01
The problem of predicting transport properties for momentum and heat across the boundaries of interconnected channels has been the subject of many investigations. In the particular case of axial flow through rod-bundles, transport coefficients for channel faces aligned with rod centers are known to be considerably higher than those calculated by simple isotropic theories. And yet, it was been found that secondary flows play only a minor role in this overall transport, being turbulence highly enhanced across that hypothetical surface. In order to numerically predict the correct amount of the quantity being transported, the approach taken by many investigators was then to artificially increase the diffusion coefficient obtained via a simple isopropic theory (usually the standard k-epsilon model) and numerically match the correct experimentally observed mixing rates. The present paper reports an attempt to describe the turbulent stresses by means of an Algebraic Stress Model for turbulence. Relative turbulent kinetic energy distribution in all three directions are presented and compared with experiments in a square lattice. The strong directional dependence of transport terms are then obtained via a model for the Reynolds stresses. The results identify a need for a better representation of the mean-flow field part of the pressure-strain correlation term.
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.
A comparison of three algebraic stress closures for combustor flow calculations
NASA Technical Reports Server (NTRS)
Nikjooy, M.; So, R. M. C.; Hwang, B. C.
1985-01-01
A comparison is made of the performance of two locally nonequilibrium and one equilibrium algebraic stress closures in calculating combustor flows. Effects of four different pressure-strain models on these closure models are also analyzed. The results show that the pressure-strain models have a much greater influence on the calculated mean velocity and turbulence field than the algebraic stress closures, and that the best mean strain model for the pressure-strain terms is that proposed by Launder, Reece and Rodi (1975). However, the equilibrium algebraic stress closure with the Rotta return-to-isotropy model (1951) for the pressure-strain terms gives as good a correlation with measurements as when the Launder et al. mean strain model is included in the pressure-strain model. Finally, comparison of the calculations with the standard k-epsilon closure results show that the algebraic stress closures are better suited for simple turbulent flow calculations.
MODEL IDENTIFICATION AND COMPUTER ALGEBRA.
Bollen, Kenneth A; Bauldry, Shawn
2010-10-07
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.
Bohr model as an algebraic collective model
Rowe, D. J.; Welsh, T. A.; Caprio, M. A.
2009-05-15
Developments and applications are presented of an algebraic version of Bohr's collective model. Illustrative examples show that fully converged calculations can be performed quickly and easily for a large range of Hamiltonians. As a result, the Bohr model becomes an effective tool in the analysis of experimental data. The examples are chosen both to confirm the reliability of the algebraic collective model and to show the diversity of results that can be obtained by its use. The focus of the paper is to facilitate identification of the limitations of the Bohr model with a view to developing more realistic, computationally tractable models.
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)
Using Students' Interests as Algebraic Models
ERIC Educational Resources Information Center
Whaley, Kenneth A.
2012-01-01
Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…
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 = - Â†Âϕ with the operators ÂandÂ† 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”.
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.
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.
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.
Current algebra and the nonlinear σ-model
NASA Astrophysics Data System (ADS)
Ghosh, S.
2007-06-01
We present the current algebra of a particular form in the nonlinear σ-model. The algebra has a non-Abelian form with field-dependent structure functions. We comment on the connection of the model with noncommutative space.
Kac-Moody algebra and nonlinear sigma model
NASA Astrophysics Data System (ADS)
Ogura, Waichi; Hosoya, Akio
1985-12-01
We investigate the nonlinear sigma model over an arbitrary homogeneous space. Then it is shown that the sigma model realizes the Kac-Moody algebra as current algebra only if the homogeneous space is restricted to the group manifold.
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.
Lie-algebraic solutions of the type IIB matrix model
NASA Astrophysics Data System (ADS)
Chatzistavrakidis, Athanasios
2011-11-01
A systematic search for Lie-algebra solutions of the type IIB matrix model is performed. Our survey is based on the classification of all Lie algebras for dimensions up to five and of all nilpotent Lie algebras of dimension six. It is shown that Lie-type solutions of the equations of motion of the type IIB matrix model exist and they correspond to certain nilpotent and solvable Lie algebras. Their representation in terms of Hermitian matrices is discussed in detail. These algebras give rise to certain noncommutative spaces for which the corresponding star products are provided. Finally the issue of constructing quantized compact nilmanifolds and solvmanifolds based on the above algebras is addressed.
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.
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.…
Chain models on hecke algebra for corner type representations
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Ogievetsky, O. V.; Os'kin, A. F.
2008-04-01
We consider the integrable open chain models formulated in terms of generators of the Hecke algebra. The spectrum of Hamiltonians for the open Hecke chains of finite size with free boundary conditions is deduced for special (comer type) irreducible representations of the Hecke algebra.
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
Applied Algebra: The Modeling Technique of Least Squares
ERIC Educational Resources Information Center
Zelkowski, Jeremy; Mayes, Robert
2008-01-01
The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)
Category-theoretic models of algebraic computer systems
NASA Astrophysics Data System (ADS)
Kovalyov, S. P.
2016-01-01
A computer system is said to be algebraic if it contains nodes that implement unconventional computation paradigms based on universal algebra. A category-based approach to modeling such systems that provides a theoretical basis for mapping tasks to these systems' architecture is proposed. The construction of algebraic models of general-purpose computations involving conditional statements and overflow control is formally described by a reflector in an appropriate category of algebras. It is proved that this reflector takes the modulo ring whose operations are implemented in the conventional arithmetic processors to the Łukasiewicz logic matrix. Enrichments of the set of ring operations that form bases in the Łukasiewicz logic matrix are found.
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.
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.
NASA Astrophysics Data System (ADS)
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
2011-10-01
Consider a tensor product of finite-dimensional irreducible ??;N+1-modules and its decomposition into irreducible modules. The ??;N+1 Gaudin model assigns to each multiplicity space of that decomposition a commutative (Bethe) algebra of linear operators acting on the multiplicity space. The Bethe ansatz method is a method to find eigenvectors and eigenvalues of the Bethe algebra. One starts with a critical point of a suitable (master) function and constructs an eigenvector of the Bethe algebra. In this paper we consider the algebra of functions on the critical set of the associated master function and show that the action of this algebra on itself is isomorphic to the action of the Bethe algebra on a suitable subspace of the multiplicity space. As a byproduct we prove that the Bethe vectors corresponding to different critical points of the master function are linearly independent and, in particular, nonzero.
Calculus and design of discrete velocity models using computer algebra
NASA Astrophysics Data System (ADS)
Babovsky, Hans; Grabmeier, Johannes
2016-11-01
In [2, 3], a framework for a calculus with Discrete Velocity Models (DVM) has been derived. The rotatonal symmetry of the discrete velocities can be modelled algebraically by the action of the cyclic group C4 - or including reflections of the dihedral group D4. Taking this point of view, the linearized collision operator can be represented in a compact form as a matrix of elements in the group algebra. Or in other words, by choosing a special numbering it exhibits a certain block structure which lets it appear as a matrix with entries in a certain polynomial ring. A convenient way for approaching such a structure is the use of a computer algebra system able to treat these (predefined) algebraic structures. We used the computer algebra system FriCAS/AXIOM [4, 5] for the generation of the velocity and the collision sets and for the analysis of the structure of the collision operator. Concerning the fluid dynamic limit, the system provides the characterization of sets of collisions and their contribution to the flow parameters. It allows the design of rotationally invariant symmetric models for prescribed Prandtl numbers. The implementation in FriCAS/AXIOM is explained and its results for a 25-velocity model are presented.
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.
Optical linear algebra processors: noise and error-source modeling.
Casasent, D; Ghosh, A
1985-06-01
The modeling of system and component noise and error sources in optical linear algebra processors (OLAP's) 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.
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…
An algebraic approach to modeling in software engineering
Loegel, G.J. |; Ravishankar, C.V.
1993-09-01
Our work couples the formalism of universal algebras with the engineering techniques of mathematical modeling to develop a new approach to the software engineering process. Our purpose in using this combination is twofold. First, abstract data types and their specification using universal algebras can be considered a common point between the practical requirements of software engineering and the formal specification of software systems. Second, mathematical modeling principles provide us with a means for effectively analyzing real-world systems. We first use modeling techniques to analyze a system and then represent the analysis using universal algebras. The rest of the software engineering process exploits properties of universal algebras that preserve the structure of our original model. This paper describes our software engineering process and our experience using it on both research and commercial systems. We need a new approach because current software engineering practices often deliver software that is difficult to develop and maintain. Formal software engineering approaches use universal algebras to describe ``computer science`` objects like abstract data types, but in practice software errors are often caused because ``real-world`` objects are improperly modeled. There is a large semantic gap between the customer`s objects and abstract data types. In contrast, mathematical modeling uses engineering techniques to construct valid models for real-world systems, but these models are often implemented in an ad hoc manner. A combination of the best features of both approaches would enable software engineering to formally specify and develop software systems that better model real systems. Software engineering, like mathematical modeling, should concern itself first and foremost with understanding a real system and its behavior under given circumstances, and then with expressing this knowledge in an executable form.
Directed Abelian algebras and their application to stochastic models
NASA Astrophysics Data System (ADS)
Alcaraz, F. C.; Rittenberg, V.
2008-10-01
With each directed acyclic graph (this includes some D -dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D -dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D . One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent στ=3/2 ). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found στ=1.780±0.005 .
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.
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.
Algebraic spin liquid in an exactly solvable spin model
Yao, Hong; Zhang, Shou-Cheng; Kivelson, Steven A.; /Stanford U., Phys. Dept.
2010-03-25
We have proposed an exactly solvable quantum spin-3/2 model on a square lattice. Its ground state is a quantum spin liquid with a half integer spin per unit cell. The fermionic excitations are gapless with a linear dispersion, while the topological 'vison' excitations are gapped. Moreover, the massless Dirac fermions are stable. Thus, this model is, to the best of our knowledge, the first exactly solvable model of half-integer spins whose ground state is an 'algebraic spin liquid.'
Generalization of Richardson-Gaudin models to rank-2 algebras
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.
Models of quadratic quantum algebras and their relation to classical superintegrable systems
Kalnins, E. G.; Miller, W.; Post, S.
2009-05-15
We show how to construct realizations (models) of quadratic algebras for 2D second order superintegrable systems in terms of differential or difference operators in one variable. We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.
The Hamiltonian of the quantum trigonometric Calogero-Sutherland model in the exceptional algebra E8
NASA Astrophysics Data System (ADS)
Fernández Núñez, J.; García Fuertes, W.; Perelomov, A. M.
2009-01-01
We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model for the Lie algebra E8 and coupling constant κ by using the fundamental irreducible characters of the algebra as dynamical independent variables.
Cognitive load and modelling of an algebra problem
NASA Astrophysics Data System (ADS)
Chinnappan, Mohan
2010-09-01
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 integration of core concepts with processes that are at play. Results here also show that modelling a problem that is set within an authentic context helps learners develop a better appreciation of variables and relations that constitute the model. The teacher's scaffolding actions revealed the use of strategies that foster the development of connected, meaningful and more useable algebraic knowledge.
Algebraic model checking for Boolean gene regulatory networks.
Tran, Quoc-Nam
2011-01-01
We present a computational method in which modular and Groebner bases (GB) computation in Boolean rings are used for solving problems in Boolean gene regulatory networks (BN). In contrast to other known algebraic approaches, the degree of intermediate polynomials during the calculation of Groebner bases using our method will never grow resulting in a significant improvement in running time and memory space consumption. We also show how calculation in temporal logic for model checking can be done by means of our direct and efficient Groebner basis computation in Boolean rings. We present our experimental results in finding attractors and control strategies of Boolean networks to illustrate our theoretical arguments. The results are promising. Our algebraic approach is more efficient than the state-of-the-art model checker NuSMV on BNs. More importantly, our approach finds all solutions for the BN problems.
An anisotropic subgrid stress model for high aspect ratio grids
NASA Astrophysics Data System (ADS)
Moser, Robert; Haering, Sigfried
2016-11-01
Standard algebraic eddy viscosity subgrid stress models are formulated based on scalar measures of the local grid, and implicitly assume that the resolution is isotropic. However, complex simulation domains and computational costs associated with problems of engineering interest often necessitate grids with high aspect ratio cells. We present an anisotropic extension of Metias and Lesieur's structure function subgrid stress model. Unlike existing algebraic SGS models, this model is constructed directly through the composition of resolution and resolved turbulence anisotropy. Comparisons with filtered DNS of forced isotropic homogeneous turbulence show the model to significantly outperform general isotropic SGS models with increasing resolution anisotropy.
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.
Nuclear structure and triaxiality with the algebraic collective model
Caprio, M. A.; Rowe, D. J.; Welsh, T. A.
2009-01-28
A tractable scheme for numerical diagonalization of the Bohr Hamiltonian, based on SU(1,1)xSO(5) algebraic methods, has recently been proposed. The direct product basis obtained from an optimally chosen set of SU(1,1){beta} wave functions and the SO(5) spherical harmonics {psi}{sub v{alpha}}{sub LM}({gamma},{omega}) provides an exceedingly efficient basis for numerical solution, as compared to conventional diagonalization in a five-dimensional oscillator basis. In this contribution, the status of the SU(1,1)xSO(5) algebraic collective model is summarized and applications are presented. In particular, the transition from axially symmetric to triaxial structure is explored.
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.
A linear algebra model for quasispecies
NASA Astrophysics Data System (ADS)
García-Pelayo, Ricardo
2002-06-01
In the present work we present a simple model of the population genetics of quasispecies. We show that the error catastrophe arises because in Biology the mutation rates are almost zero and the mutations themselves are almost neutral. We obtain and discuss previously known results from the point of view of this model. New results are: the fitness of a sequence in terms of its abundance in the quasispecies, a formula for the stable distribution of a quasispecies in which the fitness depends only on the Hamming distance to the master sequence, the time it takes the master sequence to generate a stable quasispecies (such as in the infection by a virus) and the fitness of quasispecies.
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.
Is the full susceptibility of the square-lattice Ising model a differentially algebraic function?
NASA Astrophysics Data System (ADS)
Guttmann, A. J.; Jensen, I.; Maillard, J.-M.; Pantone, J.
2016-12-01
We study the class of non-holonomic power series with integer coefficients that reduce, modulo primes, or powers of primes, to algebraic functions. In particular we try to determine whether the susceptibility of the square-lattice Ising model belongs to this class, and more broadly whether the susceptibility is a solution of a differentially algebraic equation. Initial results on Tutte's nonlinear ordinary differential equation (ODE) and other simple quadratic nonlinear ODEs suggest that a large set of differentially algebraic power series solutions with integer coefficients might reduce to algebraic functions modulo primes, or powers of primes. Since diagonals of rational functions are well-known to reduce, modulo primes, or powers of primes, to algebraic functions, a large subset of differentially algebraic power series with integer coefficients may be viewed as a natural ‘nonlinear’ generalisation of diagonals of rational functions. Here we give several examples of series with integer coefficients and non-zero radius of convergence that reduce to algebraic functions modulo (almost) every prime (or power of a prime). These examples satisfy differentially algebraic equations with the encoding polynomial occasionally possessing quite high degree (and thus difficult to identify even with long series). These examples shed important light on the very nature of such differentially algebraic series. Additionally, we have extended both the high- and low-temperature Ising square-lattice susceptibility series to 5043 coefficients. We find that even this long series is insufficient to determine whether it reduces to algebraic functions modulo 3, 5, etc. This negative result is in contrast to the comparatively easy confirmation that the corresponding series reduce to algebraic functions modulo powers of 2. Finally we show that even with 5043 terms we are unable to identify an underlying differentially algebraic equation for the susceptibility, ruling out a number of
Algebraic direct methods for few-atoms structure models.
Hauptman, Herbert A; Guo, D Y; Xu, Hongliang; Blessing, Robert H
2002-07-01
As a basis for direct-methods phasing at very low resolution for macromolecular crystal structures, normalized structure-factor algebra is presented for few-atoms structure models with N = 1, 2, 3, em leader equal atoms or polyatomic globs per unit cell. Main results include: [see text]. Triplet discriminant Delta(hk) and triplet weight W(hk) parameters, a approximately 4.0 and b approximately 3.0, respectively, were determined empirically in numerical error analyses. Tests with phases calculated for few-atoms 'super-glob' models of the protein apo-D-glyceraldehyde-3-phosphate dehydrogenase (approximately 10000 non-H atoms) showed that low-resolution phases from the new few-atoms tangent formula were much better than conventional tangent formula phases for N = 2 and 3; phases from the two formulae were essentially the same for N > or = 4.
Algebraic geometrization of the Kuramoto model: Equilibria and stability analysis
NASA Astrophysics Data System (ADS)
Mehta, Dhagash; Daleo, Noah S.; Dörfler, Florian; Hauenstein, Jonathan D.
2015-05-01
Finding equilibria of the finite size Kuramoto model amounts to solving a nonlinear system of equations, which is an important yet challenging problem. We translate this into an algebraic geometry problem and use numerical methods to find all of the equilibria for various choices of coupling constants K, natural frequencies, and on different graphs. We note that for even modest sizes (N ˜ 10-20), the number of equilibria is already more than 100 000. We analyze the stability of each computed equilibrium as well as the configuration of angles. Our exploration of the equilibrium landscape leads to unexpected and possibly surprising results including non-monotonicity in the number of equilibria, a predictable pattern in the indices of equilibria, counter-examples to conjectures, multi-stable equilibrium landscapes, scenarios with only unstable equilibria, and multiple distinct extrema in the stable equilibrium distribution as a function of the number of cycles in the graph.
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.
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.
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…
A novel feature of the Kac-Moody algebra and nonlinear integrable models
NASA Astrophysics Data System (ADS)
Kawai, E.
1991-11-01
New light is shed on the Kac-Moody algebra to reveal its remarkable unknown feature which can be traced back to its curious connection with the Virasoro algebra. Further implication of this novel feature is examined and explicated in the context of nonlinear integrable models.
Patchev, Vladimir K.; Patchev, Alexandre V.
2006-01-01
Illustrating the complexity of the stress response and its multifaceted manifestations is the leading idea of this overview of experimental paradigms used for stress induction in laboratory animals. The description of key features of models based on naturalistic stressors, pharmacological challenges, and genomic manipulations is complemented by comprehensive analysis of physiological, behavioral, neurochemical, and endocrine changes and their appropriatness as outcome readouts. Particular attention has been paid to the role of sex and age as determinants of the dynamics of the stress response. Possible translational applications of stress-inducing paradigms as models of disease are briefly sketched. PMID:17290800
Algebraic Statistical Model for Biochemical Network Dynamics Inference.
Linder, Daniel F; Rempala, Grzegorz A
2013-12-01
With modern molecular quantification methods, like, for instance, high throughput sequencing, biologists may perform multiple complex experiments and collect longitudinal data on RNA and DNA concentrations. Such data may be then used to infer cellular level interactions between the molecular entities of interest. One method which formalizes such inference is the stoichiometric algebraic statistical model (SASM) of [2] which allows to analyze the so-called conic (or single source) networks. Despite its intuitive appeal, up until now the SASM has been only heuristically studied on few simple examples. The current paper provides a more formal mathematical treatment of the SASM, expanding the original model to a wider class of reaction systems decomposable into multiple conic subnetworks. In particular, it is proved here that on such networks the SASM enjoys the so-called sparsistency property, that is, it asymptotically (with the number of observed network trajectories) discards the false interactions by setting their reaction rates to zero. For illustration, we apply the extended SASM to in silico data from a generic decomposable network as well as to biological data from an experimental search for a possible transcription factor for the heat shock protein 70 (Hsp70) in the zebrafish retina.
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.
NASA Astrophysics Data System (ADS)
Fernández Núñez, J.; García Fuertes, W.; Perelomov, A. M.
2005-07-01
The quantum trigonometric Calogero-Sutherland models related to Lie algebras admit a parametrization in which the dynamical variables are the characters of the fundamental representations of the algebra. We develop here this approach for the case of the exceptional Lie algebra E6.
Cohomology, cocyles and the current algebra for the nonlinear σ-model
NASA Astrophysics Data System (ADS)
Fujiwara, Takanori; Kitakado, Shinsaku; Nonoyama, Tatsuhiko
1985-05-01
Using the idea of cohomology defined for the Lie algebra of gauge transformations, we examine the extension of the current algebra for the system of the gauged nonlinear σ-model. An anomalous term in the current commutation relation is constructed and shown to be equivalent to that arising in the gauged nonlinear σ-model with the Wess-Zumino term. The relation with the anomalous Schwinger term given by Faddeev is also discussed.
Kac-Moody Algebra for Two Dimensional Principal Chiral Models
NASA Astrophysics Data System (ADS)
Chou, Kuang-Chao; Song, Xing-Chang
A Darboux transformation depending on single continuous parameter t is constructed for a principal chiral field. The transformation forms a nonlinear representation of the group for any fixed value of t. Part of the kernel in the Riemann-Hilbert transform is shown to be related to the Darboux transformation with its generators forming a Kac-Moody algebra. Conserved currents associated with the Kac-Moody algebra of the linearized equations and the Nöether current for the group transformations with fixed value of t are obtained.
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.
2016-10-01
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.
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'…
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.
NASA Astrophysics Data System (ADS)
Weatheritt, Jack; Sandberg, Richard
2016-11-01
This paper presents a novel and promising approach to turbulence model formulation, rather than putting forward a particular new model. Evolutionary computation has brought symbolic regression of scalar fields into the domain of algorithms and this paper describes a novel expansion of Gene Expression Programming for the purpose of tensor modeling. By utilizing high-fidelity data and uncertainty measures, mathematical models for tensors are created. The philosophy behind the framework is to give freedom to the algorithm to produce a constraint-free model; its own functional form that was not previously imposed. Turbulence modeling is the target application, specifically the improvement of separated flow prediction. Models are created by considering the anisotropy of the turbulent stress tensor and formulating non-linear constitutive stress-strain relationships. A previously unseen flow field is computed and compared to the baseline linear model and an established non-linear model of comparable complexity. The results are highly encouraging.
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.
NASA Astrophysics Data System (ADS)
Hallagan, Jean E.
2006-05-01
The purpose of this article is to describe a middle school mathematics teacher's model of his students' responses to algebraic tasks involving equivalent expressions and the distributive property. The teacher engaged in two model-eliciting activities designed for teachers by creating a library of his students' work and an accompanying "Ways of Thinking"[WOT] sheet (Doerr & Lesh, 2003). These activities were designed to help reveal the teachers' models of students' algebraic thinking and to promote the development of that model. Results of the analysis showed that the teacher developed a clearer understanding of the role of a variable in algebraic instruction. The teacher employed visual strategies for the first time and began to perceive their usefulness in helping students understand the equivalence of two expressions.
Signs and Tools of Algebraic Reasoning: A Study of Models among Fifth Grade Students
ERIC Educational Resources Information Center
Richardson, Kerri
2012-01-01
This study focuses on the types of models created by students during algebraic pattern finding tasks. Attention is also given to the change in models over time. This is an important area of study because a closer look is needed to better understand the models created during mathematical activity, especially in the elementary classroom. It is…
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.
Mathematical Modelling and the Learning Trajectory: Tools to Support the Teaching of Linear Algebra
ERIC Educational Resources Information Center
Cárcamo Bahamonde, Andrea Dorila; Fortuny Aymemí, Josep Maria; Gómez i Urgellés, Joan Vicenç
2017-01-01
In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…
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…
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.
The algebraic cluster model: Structure of 16O
NASA Astrophysics Data System (ADS)
Bijker, R.; Iachello, F.
2017-01-01
We discuss an algebraic treatment of four-body clusters which includes both continuous and discrete symmetries. In particular, tetrahedral configurations with Td symmetry are analyzed with respect to the energy spectrum, transition form factors and B (EL) values. It is concluded that the low-lying spectrum of 16O can be described by four α particles at the vertices of a regular tetrahedron, not as a rigid structure but rather a more floppy structure with relatively large rotation-vibration interactions and Coriolis forces.
ERIC Educational Resources Information Center
Hallagan, Jean E.
2006-01-01
The purpose of this article is to describe a middle school mathematics teacher's model of his students' responses to algebraic tasks involving equivalent expressions and the distributive property. The teacher engaged in two model-eliciting activities designed for teachers by creating a library of his students' work and an accompanying "Ways…
Mathematical modelling in engineering: an alternative way to teach Linear Algebra
NASA Astrophysics Data System (ADS)
Domínguez-García, S.; García-Planas, M. I.; Taberna, J.
2016-10-01
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 classroom approach in which students modelled real-world problems and turn gain a deeper knowledge of the Linear Algebra subject. Considering that most students are digital natives, we use the e-portfolio as a tool of communication between students and teachers, besides being a good place making the work visible. In this article, we present an overview of the design and implementation of a project-based learning for a Linear Algebra course taught during the 2014-2015 at the 'ETSEIB'of Universitat Politècnica de Catalunya (UPC).
A note on probabilistic models over strings: the linear algebra approach.
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.
Tectonic stress - Models and magnitudes
NASA Technical Reports Server (NTRS)
Solomon, S. C.; Bergman, E. A.; Richardson, R. M.
1980-01-01
It is shown that global data on directions of principal stresses in plate interiors can serve as a test of possible plate tectonic force models. Such tests performed to date favor force models in which ridge pushing forces play a significant role. For such models the general magnitude of regional deviatoric stresses is comparable to the 200-300 bar compressive stress exerted by spreading ridges. An alternative approach to estimating magnitudes of regional deviatoric stresses from stress orientations is to seek regions of local stress either demonstrably smaller than or larger than the regional stresses. The regional stresses in oceanic intraplate regions are larger than the 100-bar compression exerted by the Ninetyeast Ridge and less than the bending stresses (not less than 1 kbar) beneath Hawaii.
ERIC Educational Resources Information Center
Capani, Antonio; De Dominicis, Gabriel
This paper proposes a model for a general interface between people and Computer Algebra Systems (CAS). The main features in the CAS interface are data navigation and the possibility of accessing powerful remote machines. This model is based on the idea of session management, in which the main engine of the tool enables interactions with the…
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.
Using computer algebra and SMT-solvers to analyze a mathematical model of cholera propagation
NASA Astrophysics Data System (ADS)
Trujillo Arredondo, Mariana
2014-06-01
We analyze a mathematical model for the transmission of cholera. The model is already defined and involves variables such as the pathogen agent, which in this case is the bacterium Vibrio cholera, and the human population. The human population is divided into three classes: susceptible, infectious and removed. Using Computer Algebra, specifically Maple we obtain two equilibrium states: the disease free state and the endemic state. Using Maple it is possible to prove that the disease free state is locally asymptotically stable if and only if R0 < 1. Using Maple it is possible to prove that the endemic equilibrium state is locally stable when it exists, it is to say when R0 > 1. Using the package Red-Log of the Computer algebra system Reduce and the SMT-Solver Z3Py it is possible to obtain numerical conditions for the model. The formula for the basic reproductive number makes a synthesis with all epidemic parameters in the model. Also it is possible to make numerical simulations which are very illustrative about the epidemic patters that are expected to be observed in real situations. We claim that these kinds of software are very useful in the analysis of epidemic models given that the symbolic computation provides algebraic formulas for the basic reproductive number and such algebraic formulas are very useful to derive control measures. For other side, computer algebra software is a powerful tool to make the stability analysis for epidemic models given that the all steps in the stability analysis can be made automatically: finding the equilibrium points, computing the jacobian, computing the characteristic polynomial for the jacobian, and applying the Routh-Hurwitz theorem to the characteristic polynomial. Finally, using SMT-Solvers is possible to make automatically checks of satisfiability, validity and quantifiers elimination being these computations very useful to analyse complicated epidemic models.
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.
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.
Existence of standard models of conic fibrations over non-algebraically-closed fields
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.
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…
Implementing a Flipped Instructional Model in College Algebra: Profiles of Student Activity
ERIC Educational Resources Information Center
Lesseig, Kristin; Krouss, Paul
2017-01-01
Flipped instruction is increasing in popularity, however research that moves beyond descriptions of its implementation in mathematics classes is lacking. We sought to better understand how students taking an introductory college algebra course used the resources provided within a flipped instructional model and how students viewed such resources…
NASA Technical Reports Server (NTRS)
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.
Global identifiability of linear compartmental models--a computer algebra algorithm.
Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C
1998-01-01
A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.
Stress inoculation modeled in mice
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
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…
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.
Entanglement in a model for Hawking radiation: An application of quadratic algebras
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.
The periodic table of real geometric algebras, bits of space-time, and the Standard Model.
NASA Astrophysics Data System (ADS)
Marks, Dennis
2007-04-01
Real geometric algebras Rn;s in n dimensions with signature s are isomorphic to algebras of real, complex, or quaternionic matrices R(2^n 2), C(2^n-1 2), or H(2^n-2 2), or of block diagonal matrices ^2R(2^n-1 2) or ^2H(2^n-3 2), for | ( s+3 )8-4 | = 1, 2, 3, 0, or 4, respectively. Only for n = 2 or 4 and s = 0 or 2 is Rn;s isomorphic to real nxn matrices R(n). R2;2 and R2;0 describe the Euclidean plane and the Minkowskian plane. Their direct product, R4;2 = R2;0 R2;2, describes 4-d space-time with signature + + + -- and with dynamical elements (position, spin, momentum, and action) that satisfy the Heisenberg commutation relations. Quantum mechanics emerges naturally. Electromagnetism, described by U(1) C R1;-1, has one time-like coordinate; the weak force, described by SU(2) SO(3) R3;3, has three space-like coordinates. Thus the real algebra of the symmetry group of the electro-weak force is isomorphic to the real algebra of space-time. Finally, R8;2 = R4;0 R4;2 is isomorphic to R(16), into which can be fit three generations of weakly interacting Fermi doublets and three generations of three colors of quarks. Every 8 dimensions thereafter, geometric algebras factor into direct products of R(16), interpreted as a 4-d hexadecimal space-time lattice with four additional internal coordinates for the Standard Model.
Mishra, Bud
2009-07-06
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.
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
The Wheeler-DeWitt Equation in Filćhenkov Model: The Lie Algebraic Approach
NASA Astrophysics Data System (ADS)
Panahi, H.; Zarrinkamar, S.; Baradaran, M.
2016-11-01
The Wheeler-DeWitt equation in Filćhenkov model with terms related to strings, dust, relativistic matter, bosons and fermions, and ultra stiff matter is solved in a quasi-exact analytical manner via the Lie algebraic approach. In the calculations, using the representation theory of sl(2), the general (N+1)-dimensional matrix equation is constructed whose determinant yields the solutions of the problem.
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
2011-01-01
Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. Results We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Conclusions Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on
A Reynolds stress model for near-wall turbulence
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1993-01-01
The paper formulates a tensorially consistent near-wall second-order closure model. Redistributive terms in the Reynolds stress equations are modeled by an elliptic relaxation equation in order to represent strongly nonhomogeneous effects produced by the presence of walls; this replaces the quasi-homogeneous algebraic models that are usually employed, and avoids the need for ad hoc damping functions. The model is solved for channel flow and boundary layers with zero and adverse pressure gradients. Good predictions of Reynolds stress components, mean flow, skin friction, and displacement thickness are obtained in various comparisons to experimental and direct numerical simulation data. The model is also applied to a boundary layer flowing along a wall with a 90-deg, constant-radius, convex bend.
Closure of the algebra of constraints for a nonprojectable Horava model
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.
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)
NASA Astrophysics Data System (ADS)
Fernández Núñez, J.; García Fuertes, W.; Perelomov, A. M.
2005-10-01
We reexpress the quantum Calogero-Sutherland model for the Lie algebra E7 and the particular value of the coupling constant κ =1 by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to develop a systematic procedure to obtain all the Clebsch-Gordan series required to perform the change of variables. We describe how the resulting quantum Hamiltonian operator can be used to compute more characters and Clebsch-Gordan series for this exceptional algebra.
Colloquium: An algebraic model of localized surface plasmons and their interactions
NASA Astrophysics Data System (ADS)
Davis, T. J.; Gómez, D. E.
2017-01-01
Although localized surface plasmons in metal nanoparticles can be modeled by Maxwells equations, the difficulty in solving them forces many researchers to use numerical methods. Such methods give accurate results but rarely provide much insight into the complex behaviors of the surface plasmons, nor do they provide a means to choose a configuration of metal nanoparticles to achieve a desired optical response. This Colloquium presents a simple algebraic approach for modeling localized surface plasmons, their excitation by light, and their interactions with one another. Although the method is not numerically accurate it yields useful insight into plasmon behavior and provides a basis for the design of complex plasmonic devices. The approach relies on a description of the surface plasmons in terms of a set of eigenmodes. However, the functional form of these modes is not usually required and the entire problem is reduced to a simple algebra involving the plasmon amplitudes, resonance terms, and their mutual coupling. The algebraic method is derived from an electrostatic formalism, appropriate for near-field interactions at optical frequencies, which is then used to demonstrate a variety of optical effects associated with localized surface plasmons, such as plasmon hybridization, induced transparency, Fano resonances, optical phase detection, and all-optical modulation, among others.
Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; Salinger, Andrew G.; Price, Stephen
2016-10-06
A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigrid hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.
Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; ...
2016-10-06
A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigridmore » hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.« less
Geometrostatis and the current algebra of nonlinear sigma models on supergroup manifolds
NASA Astrophysics Data System (ADS)
Kobayashi, K.
1987-02-01
The radiative correction of nonlinear sigma models on supermanifolds that have invertible metrics is investigated. It will be shown that the equation of motion for Riemannian supergravity (nonstandard supergravity) is derived from a consistency condition. This condition can be satisfied in the case of supergroup manifolds. We shall explicitly construct the model following the methods of Braaten, Curtright, and Zachos [E. Braaten, T. L. Curtright, and C. K. Zachos, Nucl. Phys. B 260, 630 (1985)] and of Witten [E. Witten, Commun. Math. Phys. 92, 455 (1984)]. Finally, super-Kac-Moody algebras of these models are derived.
New boson realization of the Lipkin model obeying the su(2)-algebra
NASA Astrophysics Data System (ADS)
Tsue, Yasuhiko; Providência, Constança; da Providência, João; Yamamura, Masatoshi
2015-06-01
A new boson representation of the su(2)-algebra proposed by the present authors for describing the damped and amplified oscillator is examined in the Lipkin model as one of the simple many-fermion models. This boson representation is expressed in terms of two kinds of bosons with a certain positive parameter. In order to describe the case of any fermion number, a third boson is introduced. Through this examination, it is concluded that this representation is very workable for the boson realization of the Lipkin model in any fermion number.
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…
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.
NASA Astrophysics Data System (ADS)
Fernández Núñez, J.; García Fuertes, W.; Perelomov, A. M.
2003-11-01
We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra D4 in terms of a set of Weyl-invariant variables, namely, the characters of the fundamental representations of the Lie algebra. This parametrization allows us to solve for the energy eigenfunctions of the theory and to study properties of the system of orthogonal polynomials associated with them such as recurrence relations and generating functions.
Petzold, L.R.; Rosen, J.B.
1997-12-30
Differential-algebraic equations arise in a wide variety of engineering and scientific problems. Relatively little work has been done regarding sensitivity analysis and model reduction for this class of problems. Efficient methods for sensitivity analysis are required in model development and as an intermediate step in design optimization of engineering processes. Reduced order models are needed for modelling complex physical phenomena like turbulent reacting flows, where it is not feasible to use a fully-detailed model. The objective of this work has been to develop numerical methods and software for sensitivity analysis and model reduction of nonlinear differential-algebraic systems, including large-scale systems. In collaboration with Peter Brown and Alan Hindmarsh of LLNL, the authors developed an algorithm for finding consistent initial conditions for several widely occurring classes of differential-algebraic equations (DAEs). The new algorithm is much more robust than the previous algorithm. It is also very easy to use, having been designed to require almost no information about the differential equation, Jacobian matrix, etc. in addition to what is already needed to take the subsequent time steps. The new algorithm has been implemented in a version of the software for solution of large-scale DAEs, DASPK, which has been made available on the internet. The new methods and software have been used to solve a Tokamak edge plasma problem at LLNL which could not be solved with the previous methods and software because of difficulties in finding consistent initial conditions. The capability of finding consistent initial values is also needed for the sensitivity and optimization efforts described in this paper.
2014-01-01
Background A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. Results This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. Conclusions The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate
Application of the algebraic RNG model for transition simulation. [renormalization group theory
NASA Technical Reports Server (NTRS)
Lund, Thomas S.
1990-01-01
The algebraic form of the RNG model of Yakhot and Orszag (1986) is investigated as a transition model for the Reynolds averaged boundary layer equations. It is found that the cubic equation for the eddy viscosity contains both a jump discontinuity and one spurious root. A yet unpublished transformation to a quartic equation is shown to remove the numerical difficulties associated with the discontinuity, but only at the expense of merging both the physical and spurious root of the cubic. Jumps between the branches of the resulting multiple-valued solution are found to lead to oscillations in flat plate transition calculations. Aside from the oscillations, the transition behavior is qualitatively correct.
Using process algebra to develop predator-prey models of within-host parasite dynamics.
McCaig, Chris; Fenton, Andy; Graham, Andrea; Shankland, Carron; Norman, Rachel
2013-07-21
As a first approximation of immune-mediated within-host parasite dynamics we can consider the immune response as a predator, with the parasite as its prey. In the ecological literature of predator-prey interactions there are a number of different functional responses used to describe how a predator reproduces in response to consuming prey. Until recently most of the models of the immune system that have taken a predator-prey approach have used simple mass action dynamics to capture the interaction between the immune response and the parasite. More recently Fenton and Perkins (2010) employed three of the most commonly used prey-dependent functional response terms from the ecological literature. In this paper we make use of a technique from computing science, process algebra, to develop mathematical models. The novelty of the process algebra approach is to allow stochastic models of the population (parasite and immune cells) to be developed from rules of individual cell behaviour. By using this approach in which individual cellular behaviour is captured we have derived a ratio-dependent response similar to that seen in the previous models of immune-mediated parasite dynamics, confirming that, whilst this type of term is controversial in ecological predator-prey models, it is appropriate for models of the immune system.
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.
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.
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.
Modeling boyciana-fish-human interaction with partial differential algebraic equations.
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.
Numerical algebraic geometry for model selection and its application to the life sciences
Gross, Elizabeth; Davis, Brent; Ho, Kenneth L.; Bates, Daniel J.
2016-01-01
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation and model selection. These are all optimization problems, well known to be challenging due to nonlinearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data are available. Here, we consider polynomial models (e.g. mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometrical structures relating models and data, and we demonstrate its utility on examples from cell signalling, synthetic biology and epidemiology. PMID:27733697
Numerical algebraic geometry for model selection and its application to the life sciences.
Gross, Elizabeth; Davis, Brent; Ho, Kenneth L; Bates, Daniel J; Harrington, Heather A
2016-10-01
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation and model selection. These are all optimization problems, well known to be challenging due to nonlinearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data are available. Here, we consider polynomial models (e.g. mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometrical structures relating models and data, and we demonstrate its utility on examples from cell signalling, synthetic biology and epidemiology.
NASA Astrophysics Data System (ADS)
Zhang, Shunli; Zhang, Dinghua; Gong, Hao; Ghasemalizadeh, Omid; Wang, Ge; Cao, Guohua
2014-11-01
Iterative algorithms, such as the algebraic reconstruction technique (ART), are popular for image reconstruction. For iterative reconstruction, the area integral model (AIM) is more accurate for better reconstruction quality than the line integral model (LIM). However, the computation of the system matrix for AIM is more complex and time-consuming than that for LIM. Here, we propose a fast and accurate method to compute the system matrix for AIM. First, we calculate the intersection of each boundary line of a narrow fan-beam with pixels in a recursive and efficient manner. Then, by grouping the beam-pixel intersection area into six types according to the slopes of the two boundary lines, we analytically compute the intersection area of the narrow fan-beam with the pixels in a simple algebraic fashion. Overall, experimental results show that our method is about three times faster than the Siddon algorithm and about two times faster than the distance-driven model (DDM) in computation of the system matrix. The reconstruction speed of our AIM-based ART is also faster than the LIM-based ART that uses the Siddon algorithm and DDM-based ART, for one iteration. The fast reconstruction speed of our method was accomplished without compromising the image quality.
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.
Thermoregulatory modeling for cold stress.
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.
A posteriori testing of algebraic flame surface density models for LES
NASA Astrophysics Data System (ADS)
Ma, T.; Stein, O. T.; Chakraborty, N.; Kempf, A. M.
2013-06-01
In the application of Large Eddy Simulation (LES) to premixed combustion, the unknown filtered chemical source term can be modelled by the generalised flame surface density (FSD) using algebraic models for the wrinkling factor Ξ. The present study compares the behaviour of the various models by first examining the effect of sub-grid turbulent velocity fluctuation on Ξ through a one-dimensional analysis and by the LES of the ORACLES burner (Nguyen, Bruel, and Reichstadt, Flow, Turbulence and Combustion Vol. 82 [2009], pp. 155-183) and the Volvo Rig (Sjunnesson, Nelsson, and Max, Laser Anemometry, Vol. 3 [1991], pp. 83-90; Sjunnesson, Henrikson, and Löfström, AIAA Journal, Vol. 28 [1992], pp. AIAA-92-3650). Several sensitivity studies on parameters such as the turbulent viscosity and the grid resolution are also carried out. A statistically 1-D analysis of turbulent flame propagation reveals that counter gradient transport of the progress variable needs to be accounted for to obtain a realistic flame thickness from the simulations using algebraic FSD based closure. The two burner setups are found to operate mainly within the wrinkling/corrugated flamelet regime based on the premixed combustion diagram for LES (Pitsch and Duchamp de Lageneste, Proceedings of the Combustion Institute, Vol. 29 [2002], pp. 2001-2008) and this suggests that the models are operating within their ideal range. The performance of the algebraic models are then assessed by comparing velocity statistics, followed by a detailed error analysis for the ORACLES burner. Four of the tested models were found to perform reasonably well against experiments, and one of these four further excels in being the most grid-independent. For the Volvo Rig, more focus is placed upon the comparison of temperature data and identifying changes in flame structure amongst the different models. It is found that the few models which largely over-predict velocities in the ORACLES case and volume averaged ? in a
NASA Astrophysics Data System (ADS)
Chekhov, L. O.; Eynard, B.; Marchal, O.
2011-02-01
We construct the solution of the loop equations of the β-ensemble model in a form analogous to the solution in the case of the Hermitian matrices β = 1. The solution for β = 1 is expressed in terms of the algebraic spectral curve given by y2 = U(x). The spectral curve for arbitrary β converts into the Schrödinger equation (ħ∂)2 - U(x) ψ(x) = 0, where ħ ∝ {{( {{{sqrt β - 1} {sqrt β }}} {{{sqrt β - 1} {sqrt β }}} {sqrt β }}} )} N}}. The basic ingredients of the method based on the algebraic solution retain their meaning, but we use an alternative approach to construct a solution of the loop equations in which the resolvents are given separately in each sector. Although this approach turns out to be more involved technically, it allows consistently defining the B-cycle structure for constructing the quantum algebraic curve (a D-module of the form y2 - U(x), where [y, x] = ħ) and explicitly writing the correlation functions and the corresponding symplectic invariants Fh or the terms of the free energy in an 1/N2-expansion at arbitrary ħ. The set of "flat" coordinates includes the potential times tk and the occupation numbers tilde \\varepsilon _α . We define and investigate the properties of the A- and B-cycles, forms of the first, second, and third kinds, and the Riemann bilinear identities. These identities allow finding the singular part of mathcal{F}_0 , which depends only on tilde \\varepsilon _α.
Algebraic solutions for two-level pairing model in IBM-2 and IVBM
NASA Astrophysics Data System (ADS)
Jalili-Majarshin, A.; Jafarizadeh, M. A.; Fouladi, N.
2016-09-01
In this paper the affine SU(1,1) approach is applied to numerically solve two pairing problems. A dynamical symmetry limit of the two-fluid interacting boson model-2 (IBM-2) and of the interacting vector boson model (IVBM) defined through the chains U_{π}(6) ⊗ U_{ν}(6) supset SO_{π}(5)⊗ SO_{ν}(5) supset SO_{π}(3) ⊗ SO_{ν}(3) supset SO(3) and U(6) supset U_{π}(3) ⊗ U_{ν}(3) supset SO_{π}(3) ⊗ SO_{ν}(3) supset SO(3) are introduced, respectively. The quantum phase transition between spherical and γ-soft shapes in medium-mass nuclei is analyzed using U(5) leftrightarrow SO(6) transitional nuclei in IBM-2 and one case U_{π}(3) ⊗ U_{ν}(3) leftrightarrow SO(6) transitional nuclei in IVBM found by using an infinite dimensional algebraic method based on affine SU(1,1) Lie algebra. The calculated energy spectra, energy ratio and energy staggering of Mo isotopes are compared with experimental results. The interplay between phase transitions and configuration mixing of intruder excitations between spherical vibrations and the γ-soft shapes in Mo isotopes is succinctly addressed and displays fingerprints of the transitional dynamical symmetry E(5).
ηc elastic and transition form factors: Contact interaction and algebraic model
NASA Astrophysics Data System (ADS)
Bedolla, Marco A.; Raya, Khépani; Cobos-Martínez, J. J.; Bashir, Adnan
2016-05-01
For the flavor-singlet heavy-quark system of charmonia in the pseudoscalar [ηc(1 S ) ] channel, we calculate the elastic (EFF) and transition form factors (TFFs) [ηc(1 S )→γ γ* ] for a wide range of photon momentum transfer squared (Q2). The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equation and Bethe-Salpeter equation treatment of a vector×vector contact interaction. We also employ an algebraic model, developed earlier to describe the light-quark systems. It correctly correlates infrared and ultraviolet dynamics of quantum chromodynamics (QCD). The contact interaction results agree with the lattice data for low Q2. For Q2≥Q02 , the results start deviating from the lattice results by more than 20%. Q02≈2.5 GeV2 for the EFF, and ≈25 GeV2 for the TFF. We also present the results for the EFF, TFF, and ηc(1 S ) parton distribution amplitude for the algebraic model. Wherever the comparison is possible, these results are in excellent agreement with the lattice, perturbative QCD, results obtained through a Schwinger-Dyson equation-Bethe-Salpeter equation study, employing refined truncations, and the experimental findings of the BABAR experiment.
Multiobjective algebraic synthesis of neural control systems by implicit model following.
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.
McCaig, Chris; Begon, Mike; Norman, Rachel; Shankland, Carron
2011-03-01
Changing scale, for example, the ability to move seamlessly from an individual-based model to a population-based model, is an important problem in many fields. In this paper, we introduce process algebra as a novel solution to this problem in the context of models of infectious disease spread. Process algebra allows us to describe a system in terms of the stochastic behaviour of individuals, and is a technique from computer science. We review the use of process algebra in biological systems, and the variety of quantitative and qualitative analysis techniques available. The analysis illustrated here solves the changing scale problem: from the individual behaviour we can rigorously derive equations to describe the mean behaviour of the system at the level of the population. The biological problem investigated is the transmission of infection, and how this relates to individual interactions.
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.
NASA Astrophysics Data System (ADS)
Tsue, Yasuhiko; Providência, Constança; Providência, João da; Yamamura, Masatoshi
2016-08-01
The minimum weight states of the Lipkin model consisting of n single-particle levels and obeying the SU(n) algebra are investigated systematically. The basic idea is to use the SU(2) algebra, which is independent of the SU(n) algebra. This idea has already been presented by the present authors in the case of the conventional Lipkin model consisting of two single-particle levels and obeying the SU(2) algebra. If this idea is followed, the minimum weight states are determined for any fermion number appropriately occupying n single-particle levels. Naturally, the conventional minimum weight state is included: all fermions occupy energetically the lowest single-particle level in the absence of interaction. The cases n=2, 3, 4, and 5 are discussed in some detail.
NASA Astrophysics Data System (ADS)
Sokolov, Vladimir V.; Turbiner, Alexander V.
2015-04-01
The potential of the A2 quantum elliptic model (three-body Calogero-Moser elliptic model) is defined by the pairwise three-body interaction through the Weierstrass ℘-function and has a single coupling constant. A change of variables has been found, which are A2 elliptic invariants, such that the potential becomes a rational function, while the flat space metric, as well as its associated vector, are polynomials in two variables. It is shown that the model possesses the hidden sl(3) algebra—the Hamiltonian is an element of the universal enveloping algebra {{U}sl(3)} for the arbitrary coupling constant—thus, it is equivalent to the sl(3)-quantum Euler-Arnold top. The integral, in a form of the third order differential operator with polynomial coefficients, is constructed explicitly, being also an element of {{U}sl(3)}. It is shown that there exists a discrete sequence of the coupling constants for which a finite number of polynomial eigenfunctions, up to a (non-singular) gauge factor, occurs. For these values of the coupling constants there exists a particular integral: it commutes with the Hamiltonian in action on the space of polynomial eigenfunctions, and the Hamiltonian is invariant with respect to two-dimensional projective transformations. It is shown that the A2 model has another hidden algebra {{g}(2)} introduced in Rosenbaum et al (1998 Int. J. Mod. Phys. A 13 3885). The potential of the G2 quantum elliptic model (three-body Wolfes elliptic model) is defined by the pairwise and three-body interactions through the Weierstrass ℘-function and has two coupling constants. A change of variables has been found, which are G2 elliptic invariants, such that the potential becomes a rational function, while the flat space metric, as well as its associated vector, are polynomials in two variables. It is shown the model possesses the hidden {{g}(2)} algebra. It is shown that there exists a discrete family of the coupling constants for which a finite number of
ERIC Educational Resources Information Center
Xin, Yan Ping; Si, Luo; Hord, Casey; Zhang, Dake; Cetinas, Suleyman; Park, Joo Young
2012-01-01
The study explored the effects of a computer-assisted COnceptual Model-based Problem-Solving (COMPS) program on multiplicative word-problem-solving performance of students with learning disabilities or difficulties. The COMPS program emphasizes mathematical modeling with algebraic expressions of relations. Participants were eight fourth and fifth…
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.
Conceptual explanation for the algebra in the noncommutative approach to the standard model.
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.
Free differential algebras and pure spinor action in IIB superstring sigma models
NASA Astrophysics Data System (ADS)
Oda, Ichiro; Tonin, Mario
2011-06-01
In this paper we extend to the case of IIB superstring sigma models the method proposed in hep-th/10023500 to derive the pure spinor approach for type IIA sigma models. In particular, starting from the (Free) Differential Algebra and superspace parametrization of type IIB supergravity, extended to include the BRST differential and all the ghosts, we derive the BRST transformations of fields and ghosts as well as the standard pure spinor constraints for the ghosts λ related to supersymmetry. Moreover, using the method first proposed by us, we derive the pure spinor action for type IIB superstrings in curved supergravity backgrounds (on shell), in full agreement with the action first obtained by Berkovits and Howe.
Algebraic Nonlinear Collective Motion
NASA Astrophysics Data System (ADS)
Troupe, J.; Rosensteel, G.
1998-11-01
Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real numberΛ. TheΛ=0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positiveΛ, the droplets have a neck that becomes more pronounced asΛincreases; for negativeΛ, the droplets contain a spherical bubble of radius |Λ|1/3. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes (Λ>0) and bubble and two-fluid nuclei (Λ<0).
Modelling and temporal performances evaluation of networked control systems using (max, +) algebra
NASA Astrophysics Data System (ADS)
Ammour, R.; Amari, S.
2015-01-01
In this paper, we address the problem of temporal performances evaluation of producer/consumer networked control systems. The aim is to develop a formal method for evaluating the response time of this type of control systems. Our approach consists on modelling, using Petri nets classes, the behaviour of the whole architecture including the switches that support multicast communications used by this protocol. (max, +) algebra formalism is then exploited to obtain analytical formulas of the response time and the maximal and minimal bounds. The main novelty is that our approach takes into account all delays experienced at the different stages of networked automation systems. Finally, we show how to apply the obtained results through an example of networked control system.
Extension of the algebraic transition model for the wall roughness effect
NASA Astrophysics Data System (ADS)
Straka, Petr; Příhoda, Jaromír
2016-03-01
The contribution deals with the simulation of the laminar/turbulent transition taking into account the effect of wall roughness. The correlation for the transition onset proposed by Straka and Příhoda [1] was modified for the effect of the wall roughness using the correlation according to Boyle and Stripf [2]. This correlation derived for the wall roughness formed by regularly distributed truncated cones was modified for flows over the distributed wall roughness. The algebraic transition model proposed by Straka and Příhoda [1] with the modified relation for the transition onset was verified by means of the incompressible flat-plate boundary-layer and the compressible flow through the turbine blade cascade with rough blades.
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.
The algebra of the general Markov model on phylogenetic trees and networks.
Sumner, J G; Holland, B R; Jarvis, P D
2012-04-01
It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the associated Hadamard transformation, and providing an analogous augmentation of the general Markov model has thus far been elusive. In this paper, we rectify this shortcoming by showing how to extend the general Markov model on trees to include incompatible edges; and even further to more general network models. This is achieved by exploring the algebra of the generators of the continuous-time Markov chain together with the “splitting” operator that generates the branching process on phylogenetic trees. For simplicity, we proceed by discussing the two state case and then show that our results are easily extended to more states with little complication. Intriguingly, upon restriction of the two state general Markov model to the parameter space of the binary symmetric model, our extension is indistinguishable from the Hadamard approach only on trees; as soon as any incompatible splits are introduced the two approaches give rise to differing probability distributions with disparate structure. Through exploration of a simple example, we give an argument that our extension to more general networks has desirable properties that the previous approaches do not share. In particular, our construction allows for convergent evolution of previously divergent lineages; a property that is of significant interest for biological applications.
NASA Astrophysics Data System (ADS)
Liu, Chao; Zhang, Qingling; Zhang, Xue; Duan, Xiaodong
2009-09-01
A differential-algebraic model system which considers a prey-predator system with stage structure for prey and harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, dynamic behavior of the proposed model system with and without discrete time delay is investigated. Local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting, and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium; Furthermore, local stability of the model system with discrete time delay is studied. It reveals that the discrete time delay has a destabilizing effect in the population dynamics, and a phenomenon of Hopf bifurcation occurs as the discrete time delay increases through a certain threshold. Finally, numerical simulations are carried out to show the consistency with theoretical analysis obtained in this paper.
Stress induced obesity: lessons from rodent models of stress
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
An algebraic model of an associative noise-like coding memory.
Bottini, S
1980-01-01
A mathematical model of an associative memory is presented, sharing with the optical holography memory systems the properties which establish an analogy with biological memory. This memory system--developed from Gabor's model of memory--is based on a noise-like coding of the information by which it realizes a distributed, damage-tolerant, "equipotential" storage through simultaneous state changes of discrete substratum elements. Each two associated items being stored are coded by each other by means of two noise-like patterns obtained from them through a randomizing preprocessing. The algebraic transformations operating the information storage and retrieval are matrix-vector products involving Toeplitz type matrices. Several noise-like coded memory traces are superimposed on a common substratum without crosstalk interference; moreover, extraneous noise added to these memory traces does not injure the stored information. The main performances shown by this memory model are: i) the selective, complete recovering of stored information from incomplete keys, both mixed with extraneous information and translated from the position learnt; ii) a dynamic recollection where the information just recovered acts as a new key for a sequential retrieval process; iii) context-dependent responses. The hypothesis that the information is stored in the nervous system through a noise-like coding is suggested. The model has been simulated on a digital computer using bidimensional images.
Algebraic and group structure for bipartite anisotropic Ising model on a non-local basis
NASA Astrophysics Data System (ADS)
Delgado, Francisco
2015-01-01
Entanglement is considered a basic physical resource for modern quantum applications as Quantum Information and Quantum Computation. Interactions based on specific physical systems able to generate and sustain entanglement are subject to deep research to get understanding and control on it. Atoms, ions or quantum dots are considered key pieces in quantum applications because they are elements in the development toward a scalable spin-based quantum computer through universal and basic quantum operations. Ising model is a type of interaction generating entanglement in quantum systems based on matter. In this work, a general bipartite anisotropic Ising model including an inhomogeneous magnetic field is analyzed in a non-local basis. This model summarizes several particular models presented in literature. When evolution is expressed in the Bell basis, it shows a regular block structure suggesting a SU(2) decomposition. Then, their algebraic properties are analyzed in terms of a set of physical parameters which define their group structure. In particular, finite products of pulses in this interaction are analyzed in terms of SU(4) covering. Thus, evolution denotes remarkable properties, in particular those related potentially with entanglement and control, which give a fruitful arena for further quantum developments and generalization.
Wei, Hui; Ren, Yuan; Wang, Zi Yan
2013-10-01
The implementation of Hubel-Wiesel hypothesis that orientation selectivity of a simple cell is based on ordered arrangement of its afferent cells has some difficulties. It requires the receptive fields (RFs) of those ganglion cells (GCs) and LGN cells to be similar in size and sub-structure and highly arranged in a perfect order. It also requires an adequate number of regularly distributed simple cells to match ubiquitous edges. However, the anatomical and electrophysiological evidence is not strong enough to support this geometry-based model. These strict regularities also make the model very uneconomical in both evolution and neural computation. We propose a new neural model based on an algebraic method to estimate orientations. This approach synthesizes the guesses made by multiple GCs or LGN cells and calculates local orientation information subject to a group of constraints. This algebraic model need not obey the constraints of Hubel-Wiesel hypothesis, and is easily implemented with a neural network. By using the idea of a satisfiability problem with constraints, we also prove that the precision and efficiency of this model are mathematically practicable. The proposed model makes clear several major questions which Hubel-Wiesel model does not account for. Image-rebuilding experiments are conducted to check whether this model misses any important boundary in the visual field because of the estimation strategy. This study is significant in terms of explaining the neural mechanism of orientation detection, and finding the circuit structure and computational route in neural networks. For engineering applications, our model can be used in orientation detection and as a simulation platform for cell-to-cell communications to develop bio-inspired eye chips.
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.…
NASA Astrophysics Data System (ADS)
Saldarriaga Vargas, Clarita
When there are diseases affecting large populations where the social, economic and cultural diversity is significant within the same region, the biological parameters that determine the behavior of the dispersion disease analysis are affected by the selection of different individuals. Therefore and because of the variety and magnitude of the communities at risk of contracting dengue disease around all over the world, suggest defining differentiated populations with individual contributions in the results of the dispersion dengue disease analysis. In this paper those conditions were taken in account when several epidemiologic models were analyzed. Initially a stability analysis was done for a SEIR mathematical model of Dengue disease without differential susceptibility. Both free disease and endemic equilibrium states were found in terms of the basic reproduction number and were defined in the Theorem (3.1). Then a DSEIR model was solved when a new susceptible group was introduced to consider the effects of important biological parameters of non-homogeneous populations in the spreading analysis. The results were compiled in the Theorem (3.2). Finally Theorems (3.3) and (3.4) resumed the basic reproduction numbers for three and n different susceptible groups respectively, giving an idea of how differential susceptibility affects the equilibrium states. The computations were done using an algorithmic method implemented in Maple 11, a general-purpose computer algebra system.
Calculus domains modelled using an original bool algebra based on polygons
NASA Astrophysics Data System (ADS)
Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.
2016-08-01
Analytical and numerical computer based models require analytical definitions of the calculus domains. The paper presents a method to model a calculus domain based on a bool algebra which uses solid and hollow polygons. The general calculus relations of the geometrical characteristics that are widely used in mechanical engineering are tested using several shapes of the calculus domain in order to draw conclusions regarding the most effective methods to discretize the domain. The paper also tests the results of several CAD commercial software applications which are able to compute the geometrical characteristics, being drawn interesting conclusions. The tests were also targeting the accuracy of the results vs. the number of nodes on the curved boundary of the cross section. The study required the development of an original software consisting of more than 1700 computer code lines. In comparison with other calculus methods, the discretization using convex polygons is a simpler approach. Moreover, this method doesn't lead to large numbers as the spline approximation did, in that case being required special software packages in order to offer multiple, arbitrary precision. The knowledge resulted from this study may be used to develop complex computer based models in engineering.
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.
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.
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.
"Generalized" algebraic Bethe ansatz, Gaudin-type models and Zp-graded classical r-matrices
NASA Astrophysics Data System (ADS)
Skrypnyk, T.
2016-12-01
We consider quantum integrable systems associated with reductive Lie algebra gl (n) and Cartan-invariant non-skew-symmetric classical r-matrices. We show that under certain restrictions on the form of classical r-matrices "nested" or "hierarchical" Bethe ansatz usually based on a chain of subalgebras gl (n) ⊃ gl (n - 1) ⊃ . . . ⊃ gl (1) is generalized onto the other chains or "hierarchies" of subalgebras. We show that among the r-matrices satisfying such the restrictions there are "twisted" or Zp-graded non-skew-symmetric classical r-matrices. We consider in detail example of the generalized Gaudin models with and without external magnetic field associated with Zp-graded non-skew-symmetric classical r-matrices and find the spectrum of the corresponding Gaudin-type hamiltonians using nested Bethe ansatz scheme and a chain of subalgebras gl (n) ⊃ gl (n -n1) ⊃ gl (n -n1 -n2) ⊃ gl (n - (n1 + . . . +np-1)), where n1 +n2 + . . . +np = n.
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.
NASA Astrophysics Data System (ADS)
Thiamova, G.; Rowe, D. J.; Caprio, M. A.
2012-12-01
Recent developments and applications of an algebraic version of Bohr's collective model, known as the algebraic collective model (ACM), have shown that fully converged calculations can be performed for a large range of Hamiltonians. Examining the algebraic structure underlying the Bohr model (BM) has also clarified its relationship with the interacting boson model (IBM), with which it has related solvable limits and corresponding dynamical symmetries. In particular, the algebraic structure of the IBM is obtained as a compactification of the BM and conversely the BM is regained in various contraction limits of the IBM. In a previous paper, corresponding contractions were identified and confirmed numerically for axially-symmetric states of relatively small deformation. In this paper, we extend the comparisons to realistic deformations and compare results of the two models in the rotor-vibrator limit. These models describe rotations and vibrations about an axially symmetric prolate or oblate rotor, and rotations and vibrations of a triaxial rotor. It is determined that most of the standard results of the BM can be obtained as contraction limits of the IBM in its U(5)-SO(6) dynamical symmetries.
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.
NASA Astrophysics Data System (ADS)
Fernandez-Nunez, J.; Garcia-Fuertes, W.; Perelomov, A. M.
We re-express the quantum Calogero-Sutherland model for the Lie algebra $E_6$ and the particular value of the coupling constant $\\kappa=1$ by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to develop a systematic procedure to obtain all the Clebsch-Gordan series required to perform the change of variables. We describe how the resulting quantum Hamiltonian operator can be used to compute more characters and Clebsch-Gordan series for this exceptional algebra.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Skrypnyk, T. V.
2016-10-01
We construct quantum integrable systems associated with the Lie algebra gl( n) and non-skew-symmetric "shifted and twisted" rational r-matrices. The obtained models include Gaudin-type models with and without an external magnetic field, n-level ( n-1)-mode Jaynes-Cummings-Dicke-type models in the Λ-configuration, a vector generalization of Bose-Hubbard dimers, etc. We diagonalize quantum Hamiltonians of the constructed integrable models using a nested Bethe ansatz.
Djurfeldt, Mikael
2012-07-01
The connection-set algebra (CSA) is a novel and general formalism for the description of connectivity in neuronal network models, from small-scale to large-scale structure. The algebra provides operators to form more complex sets of connections from simpler ones and also provides parameterization of such sets. CSA is expressive enough to describe a wide range of connection patterns, including multiple types of random and/or geometrically dependent connectivity, and can serve as a concise notation for network structure in scientific writing. CSA implementations allow for scalable and efficient representation of connectivity in parallel neuronal network simulators and could even allow for avoiding explicit representation of connections in computer memory. The expressiveness of CSA makes prototyping of network structure easy. A C+ + version of the algebra has been implemented and used in a large-scale neuronal network simulation (Djurfeldt et al., IBM J Res Dev 52(1/2):31-42, 2008b) and an implementation in Python has been publicly released.
Dynamics of gelling liquids: algebraic relaxation.
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.
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…
Developing Pre-Algebraic Thinking in Generalizing Repeating Pattern Using SOLO Model
ERIC Educational Resources Information Center
Lian, Lim Hooi; Yew, Wun Thiam
2011-01-01
In this paper, researchers discussed the application of the generalization perspective in helping the primary school pupils to develop their pre-algebraic thinking in generalizing repeating pattern. There are two main stages of the generalization perspective had been adapted, namely investigating and generalizing the pattern. Since the Biggs and…
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…
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.
Key Contextual Features of Algebra Word Problems: A Theoretical Model and Review of the Literature.
ERIC Educational Resources Information Center
Nasser, Ramzi; Carifio, James
One of the four algebra word problem structures found in K-12 textbooks is the propositional relation structure (Mayer, 1982). This type of problem asks students to establish equivalences between the variables or noun referents in the problem. The literature available indicates that students have inordinate difficulties, when trying to solve a…
Meanings Generated while Using Algebraic-Like Formalism to Construct and Control Animated Models
ERIC Educational Resources Information Center
Kynigos, Chronis; Psycharis, Giorgos; Moustaki, Foteini
2010-01-01
This paper reports on a design experiment conducted to explore the construction of meanings by 17 year old students, emerging from their interpretations and uses of algebraic like formalism. The students worked collaboratively in groups of two or three, using MoPiX, a constructionist computational environment with which they could create concrete…
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…
NASA Astrophysics Data System (ADS)
Mikhalev, A. V.; Pinchuk, I. A.
2005-06-01
The structure of Steinberg conformal algebras is studied; these are analogues of Steinberg groups (algebras, superalgebras).A Steinberg conformal algebra is defined as an abstract algebra by a system of generators and relations between the generators. It is proved that a Steinberg conformal algebra is the universal central extension of the corresponding conformal Lie algebra; the kernel of this extension is calculated.
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.
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.
Classical Exchange Algebra of the Nonlinear Sigma Model on a Supercoset Target with Bbb Z2n Grading
NASA Astrophysics Data System (ADS)
Ke, San-Min; Li, Xin-Ying; Wang, Chun; Yue, Rui-Hong
2011-10-01
The classical exchange algebra satisfied by the monodromy matrix of the nonlinear sigma model on a supercoset target with Bbb Z2n grading is derived using a first-order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints. This enables us to show that the conserved charges of the theory are in involution. When n = 2, our results coincide with the results given by Magro for the pure spinor description of AdS5 × S5 string theory (when the ghost terms are omitted).
NASA Astrophysics Data System (ADS)
Mukhamedov, Farrukh; Barhoumi, Abdessatar; Souissi, Abdessatar
2016-12-01
It is known that the disordered phase of the classical Ising model on the Caley tree is extreme in some region of the temperature. If one considers the Ising model with competing interactions on the same tree, then about the extremity of the disordered phase there is no any information. In the present paper, we first aiming to analyze the correspondence between Gibbs measures and QMC's on trees. Namely, we establish that states associated with translation invariant Gibbs measures of the model can be seen as diagonal quantum Markov chains on some quasi local algebra. Then as an application of the established correspondence, we study some algebraic property of the disordered phase of the Ising model with competing interactions on the Cayley tree of order two. More exactly, we prove that a state corresponding to the disordered phase is not quasi-equivalent to other states associated with translation invariant Gibbs measures. This result shows how the translation invariant states relate to each other, which is even a new phenomena in the classical setting. To establish the main result we basically employ methods of quantum Markov chains.
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…
José, Marco V; Morgado, Eberto R; Govezensky, Tzipe
2011-07-01
Herein, we rigorously develop novel 3-dimensional algebraic models called Genetic Hotels of the Standard Genetic Code (SGC). We start by considering the primeval RNA genetic code which consists of the 16 codons of type RNY (purine-any base-pyrimidine). Using simple algebraic operations, we show how the RNA code could have evolved toward the current SGC via two different intermediate evolutionary stages called Extended RNA code type I and II. By rotations or translations of the subset RNY, we arrive at the SGC via the former (type I) or via the latter (type II), respectively. Biologically, the Extended RNA code type I, consists of all codons of the type RNY plus codons obtained by considering the RNA code but in the second (NYR type) and third (YRN type) reading frames. The Extended RNA code type II, comprises all codons of the type RNY plus codons that arise from transversions of the RNA code in the first (YNY type) and third (RNR) nucleotide bases. Since the dimensions of remarkable subsets of the Genetic Hotels are not necessarily integer numbers, we also introduce the concept of algebraic fractal dimension. A general decoding function which maps each codon to its corresponding amino acid or the stop signals is also derived. The Phenotypic Hotel of amino acids is also illustrated. The proposed evolutionary paths are discussed in terms of the existing theories of the evolution of the SGC. The adoption of 3-dimensional models of the Genetic and Phenotypic Hotels will facilitate the understanding of the biological properties of the SGC.
Modelling Crustal Stress in Southern Ontario
NASA Astrophysics Data System (ADS)
Baird, A.; McKinnon, S. D.
2004-12-01
Analysis of stress measurement data from the near-surface to crustal depths in southern Ontario show a misalignment between the direction of tectonic loading and the orientation of the major horizontal principal stress. The compressive stress field appears to be oriented subparallel to the major terrane boundaries such as the Grenville Front, the Central Medisedimentary Belt boundary zone and the Composite Arc Belt boundary zone. This suggests that the stress field has been modified by these deep crustal scale fault zones. In order to test this hypothesis, a geomechanical model was constructed using the three-dimensional discontinuum stress analysis code 3DEC. The model consists of a 45 km thick crust of southern Ontario in which the major crustal scale fault zones are represented as discrete faults. Lateral velocity boundary conditions were applied to the sides of the model in the direction of tectonic loading in order to generate the horizontal compressive stress field. Preliminary results show that for low strength (low friction angle and cohesion), fault slip results in the stress field rotating toward the strike of the faults, consistent with the observed direction of misalignment with the tectonic loading direction. Further analysis of the model may be used to provide constraints on the strength of these faults.
Symplectic Clifford Algebraic Field Theory.
NASA Astrophysics Data System (ADS)
Dixon, Geoffrey Moore
We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.
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.
Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids
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
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.
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.
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.
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.
Revised Reynolds Stress and Triple Product Models
NASA Technical Reports Server (NTRS)
Olsen, Michael E.; Lillard, Randolph P.
2017-01-01
Revised versions of Lag methodology Reynolds-stress and triple product models are applied to accepted test cases to assess the improvement, or lack thereof, in the prediction capability of the models. The Bachalo-Johnson bump flow is shown as an example for this abstract submission.
NASA Astrophysics Data System (ADS)
Nikolaev, A. G.; Tanchik, E. A.
2016-05-01
A model of the stress-strain state of a unidirectional fiber composite is proposed. A cylindrical sample of an elastic material whose fibers are cylindrical inclusions is considered. The generatrix of inclusions is parallel to the axis of the sample. The distribution of fibers in the sample is modeled with sixteen inclusions forming a tetragonal structure. It is assumed that the sample is subjected to a piecewise constant normal load and the fibers are in a perfect contact with the matrix. The boundary conditions of the problem are satisfied exactly with the help of the generalized Fourier method. The problem is reduced to an infinite system of linear algebraic equations, which is solved numerically by the method of reduction. An analysis of stress distribution in the areas of their highest concentration is given.
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.
NASA Astrophysics Data System (ADS)
Vaninsky, Alexander
2011-04-01
This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.
A fiber-bridging model with stress gradient effects
NASA Astrophysics Data System (ADS)
Yi, Sun; Tao, Li
2000-05-01
A fiber-bridging model with stress gradient effects is proposed for unidirectional fiber-reinforced composites. The stress gradient terms are introduced by solving a micromechanical model under a non-uniform stress loading. It is shown that the stress gradient effect is significant on both the fiber-bridging stress distribution and the value of the critical load of fiber failure.
Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras
NASA Astrophysics Data System (ADS)
Zhang, Tianjie; Gao, Xing; Guo, Li
2016-10-01
The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.
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.
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).
Derive Workshop Matrix Algebra and Linear Algebra.
ERIC Educational Resources Information Center
Townsley Kulich, Lisa; Victor, Barbara
This document presents the course content for a workshop that integrates the use of the computer algebra system Derive with topics in matrix and linear algebra. The first section is a guide to using Derive that provides information on how to write algebraic expressions, make graphs, save files, edit, define functions, differentiate expressions,…
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.
NASA Astrophysics Data System (ADS)
Letellier, Christophe; Amaral, Gleison F. V.; Aguirre, Luis A.
2007-06-01
The characterization of chaotic attractors has been a widely addressed problem and there are now many different techniques to define their nature in a rather accurate way, at least in the case of a three-dimensional system. Nevertheless, the link between the structure of the ordinary differential equations and the topology of their solutions is still missing and only a few necessary conditions on the algebraic structure are known today. By using a feedback circuit analysis, it is shown that it is possible to identify the relevant terms of the equations, that is, the terms that really contribute to the structure of the phase portrait. Such analysis also provides some guidelines for constructing piecewise affine models. Moreover, equivalence classes can be defined on the basis of the active feedback circuits involved.
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
Po, Hoi Chun; Zhou, Qi
2015-08-13
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.
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…
Danker, Jared F; Anderson, John R
2007-04-15
In naturalistic algebra problem solving, the cognitive processes of representation and retrieval are typically confounded, in that transformations of the equations typically require retrieval of mathematical facts. Previous work using cognitive modeling has associated activity in the prefrontal cortex with the retrieval demands of algebra problems and activity in the posterior parietal cortex with the transformational demands of algebra problems, but these regions tend to behave similarly in response to task manipulations (Anderson, J.R., Qin, Y., Sohn, M.-H., Stenger, V.A., Carter, C.S., 2003. An information-processing model of the BOLD response in symbol manipulation tasks. Psychon. Bull. Rev. 10, 241-261; Qin, Y., Carter, C.S., Silk, E.M., Stenger, A., Fissell, K., Goode, A., Anderson, J.R., 2004. The change of brain activation patterns as children learn algebra equation solving. Proc. Natl. Acad. Sci. 101, 5686-5691). With this study we attempt to isolate activity in these two regions by using a multi-step algebra task in which transformation (parietal) is manipulated in the first step and retrieval (prefrontal) is manipulated in the second step. Counter to our initial predictions, both brain regions were differentially active during both steps. We designed two cognitive models, one encompassing our initial assumptions and one in which both processes were engaged during both steps. The first model provided a poor fit to the behavioral and neural data, while the second model fit both well. This simultaneously emphasizes the strong relationship between retrieval and representation in mathematical reasoning and demonstrates that cognitive modeling can serve as a useful tool for understanding task manipulations in neuroimaging experiments.
The Application of a Computer Algebra System as a Tool in College Algebra.
ERIC Educational Resources Information Center
Mayes, Robert L.
1995-01-01
Students (n=61) in an experimental course stressing active student involvement and the use of a computer algebra system scored higher than students (n=76) in a traditional college algebra course on final measures of inductive reasoning, visualization, and problem solving while maintaining equivalent manipulation and computation skills. (Author/MLB)
Stresses Modelling Across The Andean Subduction Zone
NASA Astrophysics Data System (ADS)
Romanyuk, T.; Rebetsky, Yu.; Goetze, H.-J.
A tectonophysical model, including geological-geophysical-tectonic structure, phys- ical properties of the medium (density and rheology), and its loading mechanism (boundary conditions on forces and movements) is constructed along a 21S profile. The model stresses and strains produced by separate plate motions and density inho- mogeneities and by their net effect. The inferred results are qualitatively compared with the stress state parameters of the medium, reconstructed from data on the earth- quake centroid moment tensor, and with the available tectonic, geological, and geo- physical data. The orientation analysis of the principal deviatoric axes of maximum compression and extension yields evidence for a few deformation mechanisms that function both along the subducting slab and in the junction zone of the oceanic and continental plates. The inferred intense rearrangement areas of the stress field indicate possible fragmentation zones in the oceanic plate. Focal mechanisms of earthquakes at depths below 70 km yield evidence of over-lithostatic tectonic dilatation; along with mathematical modeling results, this supports the idea of a more rapid motion of the lower denser part of the slab beneath South America as compared with its overlying portions. Plate motions directly control solely the stresses within the subducting slab and around its shallower (above 50 km) parts. The recent tectonics and stresses in the Andean mountain belt are dominated by density inhomogeneities. Stress distribution details caused by density inhomogeneities are shown to correlate well with large-scale geological features. Thus, the Pre-Cordilleran fault zone separating coastal zones from the Andean mountain belt distinctly correlates with the reorientation of the deviatoric compression-extension axes. The entire thickened crust of the belt is under conditions of over-lithostatic dilatation, and the inferred zones of the negative total isotropic pres- sure correlate with local dilatation
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…
Mechanically induced residual stresses: Modelling and characterisation
NASA Astrophysics Data System (ADS)
Stranart, Jean-Claude E.
Accurate characterisation of residual stress represents a major challenge to the engineering community. This is because it is difficult to validate the measurement and the accuracy is doubtful. It is with this in mind that the current research program concerning the characterisation of mechanically induced residual stresses was undertaken. Specifically, the cold expansion of fastener holes and the shot peening treatment of aerospace alloys, aluminium 7075 and titanium Ti-6Al-4V, are considered. The objective of this study is to characterise residual stresses resulting from cold working using three powerful techniques. These are: (i) theoretical using three dimensional non-linear finite element modelling, (ii) semi-destructive using a modified incremental hole drilling technique and (iii) nondestructive using a newly developed guided wave method supplemented by traditional C-scan measurements. The three dimensional finite element results of both simultaneous and sequential cold expansion of two fastener holes revealed the importance of the separation distance, the expansion level and the loading history upon the development and growth of the plastic zone and unloading residual stresses. It further showed that the commonly adopted two dimensional finite element models are inaccurate and incapable of predicting these residual stresses. Similarly, the dynamic elasto-plastic finite element studies of shot peening showed that the depth of the compressed layer, surface and sub-surface residual stresses are significantly influenced by the shot characteristics. Furthermore, the results reveal that the separation distance between two simultaneously impacting shots governs the plastic zone development and its growth. In the semi-destructive incremental hole drilling technique, the accuracy of the newly developed calibration coefficients and measurement techniques were verified with a known stress field and the method was used to measure peening residual stresses. Unlike
The Sandpile Model: Optimal Stress and Hormesis
Stark, Martha
2011-01-01
The sandpile model (developed by chaos theorists) is an elegant visual metaphor for the cumulative impact of environmental stressors on complex adaptive systems – an impact that is paradoxical by virtue of the fact that the grains of sand being steadily added to the gradually evolving sandpile are the occasion for both its disruption and its repair. As a result, complex adaptive systems are continuously refashioning themselves at ever-higher levels of complexity and integration – not just in spite of “stressful” input from the outside but by way of it. Stressful input is therefore inherently neither bad (“poison”) nor good (“medication”). Rather, it will be how well the system (be it sandpile or living system) is able to process, integrate, and adapt to the stressful input that will make of it either a growth-disrupting (sandpile-destabilizing) event or a growth-promoting (sandpile-restabilizing) opportunity. Too much stress – “traumatic stress” – will be too overwhelming for the system to manage, triggering instead devastating breakdown. Too little stress will provide too little impetus for transformation and growth, serving instead simply to reinforce the system’s status quo. But just the right amount of stress – “optimal stress” – will provoke recovery by activating the system’s innate capacity to heal itself. PMID:22423229
Animal Models of Stress Urinary Incontinence
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
Intra Plate Stresses Using Finite Element Modelling
NASA Astrophysics Data System (ADS)
Jayalakshmi, S.; Raghukanth, S. T. G.
2016-10-01
One of the most challenging problems in the estimation of seismic hazard is the ability to quantify seismic activity. Empirical models based on the available earthquake catalogue are often used to obtain activity of source regions. The major limitation with this approach is the lack of sufficient data near a specified source. The non-availability of data poses difficulties in obtaining distribution of earthquakes with large return periods. Such events recur over geological time scales during which tectonic processes, including mantle convection, formation of faults and new plate boundaries, are likely to take place. The availability of geometries of plate boundaries, plate driving forces, lithospheric stress field and GPS measurements has provided numerous insights on the mechanics of tectonic plates. In this article, a 2D finite element model of Indo-Australian plate is developed with the focus of representing seismic activity in India. The effect of large scale geological features including sedimentary basins, fold belts and cratons on the stress field in India is explored in this study. In order to address long term behaviour, the orientation of stress field and tectonic faults of the present Indo- Australian plate are compared with a reconstructed stress field from the early Miocene (20 Ma).
Quantum cluster algebras and quantum nilpotent algebras
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
Quasi-explicit algebraic turbulence closures for compressible reacting flows
NASA Astrophysics Data System (ADS)
Adumitroaie, Virgil
A consistent and complete set of quasi-explicit algebraic closures for turbulent reacting flows is proposed as approximate solutions to the full second order moment equations. Quasi-explicit algebraic scalar flux models that are valid for three-dimensional turbulent flows are derived from a hierarchy of second-order moment closures. The mathematical procedure is based on the Cayley-Hamilton theorem and is an extension of the scheme developed by Taulbee (1992). Several closures for the pressure-scalar gradient correlations are considered and explicit algebraic relations are provided for the velocity-scalar correlations in both non-reacting and reacting flows. In the latter, the role of the Damkohler number is exhibited in isothermal turbulent flows with nonpremixed reactants. The relationship between these closures and traditional models based on the linear gradient diffusion approximation is theoretically established. The results of model predictions are assessed via comparison with available laboratory data in turbulent jet flows. The development of the quasi-explicit algebraic models for Reynolds stresses, temperature fluxes and reacting scalar fluxes is extended to high-speed turbulent reacting flows under a density weighted average formalism. New closures are proposed for the pressure-strain and the pressure-scalar gradient correlations. These accommodate compressibility corrections subject to the magnitude of the turbulent Mach number, the density gradient, the pressure gradient and the mean dilatation effects. Non-reacting and reacting flows with heat release are considered. In the latter, a second-order irreversible chemical reactions in turbulent flows with initially segregated reactants is considered. The models are tested in simple compressible free-shear flows. Comparisons are made between the full second order moment computations and the algebraic closure predictions. For a mixing layer, experimental data are used to validate the predicted results.
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.
The Adaptive Calibration Model of stress responsivity
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
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).
Testing a Military Family Stress Model.
Gewirtz, Abigail H; DeGarmo, David S; Zamir, Osnat
2017-03-15
The current study examines a military family stress model, evaluating associations between deployment-related stressors (i.e., deployment length/number, posttraumatic stress disorder [PTSD] symptoms) and parent, child, parenting, and dyadic adjustment among families in which a parent had previously deployed to Iraq or Afghanistan in the recent conflicts. Married families (N = 293) with at least one child between the ages of 4 and 12 were recruited from a Midwestern state. Service members were from the Reserve Component (National Guard or Reserves); fathers (N = 253) and/or mothers had deployed (N = 45) to the recent conflicts in the Middle East. Multiple-method (observations of parenting and couple interactions; questionnaires) and multiple informant measures were gathered online and in the homes of participants, from parents, children, and teachers. Findings demonstrated associations between mothers' and fathers' PTSD symptoms and a latent variable of child adjustment comprising teacher, parent, and child report. Mothers' but not fathers' PTSD symptoms were also associated with dyadic adjustment and parenting practices; parenting practices were in turn associated with child adjustment. The results are discussed in terms of their implications for military family stress research and interventions to support and strengthen parents and families after deployment.
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
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.
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…
ERIC Educational Resources Information Center
Miller, L. Diane; England, David A.
1989-01-01
Describes a study in a large metropolitan high school to ascertain what influence the use of regular writing in algebra classes would have on students' attitudes towards algebra and their skills in algebra. Reports the simpler and more direct the writing topics the better. (MVL)
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.
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…
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…
Ternary Virasoro - Witt algebra.
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.
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.
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
ERIC Educational Resources Information Center
Hitt, Fernando; Saboya, Mireille; Zavala, Carlos Cortés
2017-01-01
Part of the research community that has followed the Early Algebra paradigm is currently delimiting the differences between arithmetic thinking and algebraic thinking. This trend could prevent new research approaches to the problem of learning algebra, hiding the importance of considering an arithmetico-algebraic thinking, a new approach which…
Stress Process Model for Individuals With Dementia
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
Unstressing intemperate models: how cold stress undermines mouse modeling.
Karp, Christopher L
2012-06-04
Mus musculus enjoys pride of place at the center of contemporary biomedical research. Despite being the current model system of choice for in vivo mechanistic analysis, mice have clear limitations. The literature is littered with examples of therapeutic approaches that showed promise in mouse models but failed in clinical trials. More generally, mice often provide poor mimics of the human diseases being modeled. Available data suggest that the cold stress to which laboratory mice are ubiquitously subjected profoundly affects mouse physiology in ways that impair the modeling of human homeostasis and disease. Experimental attention to this key, albeit largely ignored, environmental variable is likely to have a broad transformative effect on biomedical research.
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.
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.
Conformal current algebra in two dimensions
NASA Astrophysics Data System (ADS)
Ashok, Sujay K.; Benichou, Raphael; Troost, Jan
2009-06-01
We construct a non-chiral current algebra in two dimensions consistent with conformal invariance. We show that the conformal current algebra is realized in non-linear sigma-models on supergroup manifolds with vanishing Killing form, with or without a Wess-Zumino term. The current algebra is computed using two distinct methods. First we exploit special algebraic properties of supergroups to compute the exact two- and three-point functions of the currents and from them we infer the current algebra. The algebra is also calculated by using conformal perturbation theory about the Wess-Zumino-Witten point and resumming the perturbation series. We also prove that these models realize a non-chiral Kac-Moody algebra and construct an infinite set of commuting operators that is closed under the action of the Kac-Moody generators. The supergroup models that we consider include models with applications to statistical mechanics, condensed matter and string theory. In particular, our results may help to systematically solve and clarify the quantum integrability of PSU(n|n) models and their cosets, which appear prominently in string worldsheet models on anti-deSitter spaces.
Kouri, Donald J; Markovich, Thomas; Maxwell, Nicholas; Bodmann, Bernhard G
2009-07-02
We discuss a periodic variant of the Heisenberg-Weyl algebra, associated with the group of translations and modulations on the circle. Our study of uncertainty minimizers leads to a periodic version of canonical coherent states. Unlike the canonical, Cartesian case, there are states for which the uncertainty product associated with the generators of the algebra vanishes. Next, we explore the supersymmetric (SUSY) quantum mechanical setting for the uncertainty-minimizing states and interpret them as leading to a family of "hindered rotors". Finally, we present a standard quantum mechanical treatment of one of these hindered rotor systems, including numerically generated eigenstates and energies.
Computational algebraic geometry for statistical modeling FY09Q2 progress.
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.
Discrete Minimal Surface Algebras
NASA Astrophysics Data System (ADS)
Arnlind, Joakim; Hoppe, Jens
2010-05-01
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
An Algebraic Model of Adaptive Optics for Continuous-Wave Thermal Blooming.
1979-01-01
blooming. The aberrations modeled generally include those applied by an adaptive optics system to compensate the naturally occurring ones. For the...results when applied to thermal blooming. However, the analysis suggests novel remedies that will tend to optimize the corrections made, thus better realizing the full potential of adaptive optics . (Author)
Augustin, Christoph M; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J; Niederer, Steven A; Haase, Gundolf; Plank, Gernot
2016-01-15
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
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
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
Linear Algebraic Modeling of Power Flow in the HMP500-3 Transmission
2012-08-01
Tracked Vehicle Cross-Drive Transmission – Split-Torque Path Hydrostatic / Mechanical CVT – Six Planetary Gear Sets • Three in “Range Pack...becomes a fixed ratio • Model has Four Planetaries , One HSU – Each Planetary has sun gear , planet carrier, ring gear elements – HSU has A-end, B...losses estimated after solution 14-16 AUG 2012 UNCLASSIFIED: Distribution Statement A. Approved for public release. 4 Planetary Gear Equations
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.
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.
Towards modeling hydrodynamic stress limitations on transpiration
NASA Astrophysics Data System (ADS)
Matheny, A. M.; Bohrer, G.; Ivanov, V. Y.; Stoy, P. C.
2011-12-01
Evapotranspiration is one of the major forcing functions of Earth's climate, providing the link for the soil-plant-water continuum. Current models for transpiration assume a coupling between stomatal conductance and soil moisture through empirical relationships that do not resolve the hydrodynamic process of water movement from the soil to the leaves. This approach does not take advantage of recent advances in our understanding of water flow and storage in the trees, or of tree and canopy structure. It has been suggested that stomata respond to water potential in the leaf and branch, and that this hydrodynamic response is a mechanism for hydraulic limitation of stomatal conductance. Hydraulic limitations in forest ecosystems are common and are known to control transpiration when the soil is drying or when vapor pressure deficit (VPD) is very large. Hydraulic limitation can also impact stomatal apertures under conditions of adequate soil moisture and lower evaporative demand. Hydrodynamic stresses at the tree level act at several time scales, including the fast, minute-hour scale. These dynamics are faster than the time scales of hours to days at which drying soil will affect stomata conductance. The lack of representation of the tree-hydrodynamic process should therefore lead to atypical intra-daily patterns of error in results of current models. We use a large-scale comparison between observations and land-surface models to characterize the patterns of intra-daily error in simulated water flux. Through the use of the North American Carbon Program (NACP) dataset, more than 10 years of water flux data for 35 Fluxnet sites in the US and Canada have been analyzed. The diurnal error for each of the 24 models represented in this dataset allows the models to be categorized and evaluated on their ability to accurately predict the fast temporal dynamics of transpiration in different ecosystems and atmospheric forcing. Among well calibrated models, two general error
Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution.
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.
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.
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.
Expanding Stress Generation Theory: Test of a Transdiagnostic Model
Conway, Christopher C.; Hammen, Constance; Brennan, Patricia A.
2016-01-01
Originally formulated to understand the recurrence of depressive disorders, the stress generation hypothesis has recently been applied in research on anxiety and externalizing disorders. Results from these investigations, in combination with findings of extensive comorbidity between depression and other mental disorders, suggest the need for an expansion of stress generation models to include the stress generating effects of transdiagnostic pathology as well as those of specific syndromes. Employing latent variable modeling techniques to parse the general and specific elements of commonly co-occurring Axis I syndromes, the current study examined the associations of transdiagnostic internalizing and externalizing dimensions with stressful life events over time. Analyses revealed that, after adjusting for the covariation between the dimensions, internalizing was a significant predictor of interpersonal dependent stress, whereas externalizing was a significant predictor of noninterpersonal dependent stress. Neither latent dimension was associated with the occurrence of independent, or fateful, stressful life events. At the syndrome level, once variance due to the internalizing factor was partialled out, unipolar depression contributed incrementally to the generation of interpersonal dependent stress. In contrast, the presence of panic disorder produced a “stress inhibition” effect, predicting reduced exposure to interpersonal dependent stress. Additionally, dysthymia was associated with an excess of noninterpersonal dependent stress. The latent variable modeling framework used here is discussed in terms of its potential as an integrative model for stress generation research. PMID:22428789
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)
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.
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
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.
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…
Modeling of stresses at grain boundaries with respect to occurrence of stress corrosion cracking
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.
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.
Prediction of Algebraic Instabilities
NASA Astrophysics Data System (ADS)
Zaretzky, Paula; King, Kristina; Hill, Nicole; Keithley, Kimberlee; Barlow, Nathaniel; Weinstein, Steven; Cromer, Michael
2016-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A new methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to the governing differential equation (or dispersion relation) describing wave propagation in dispersive media. Several types of algebraic instabilities are explored in the context of both linear and nonlinear waves.
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)
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.
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.
Gauged Ads-Maxwell Algebra and Gravity
NASA Astrophysics Data System (ADS)
Durka, R.; Kowalski-Glikman, J.; Szczachor, M.
We deform the anti-de Sitter algebra by adding additional generators {Z}ab, forming in this way the negative cosmological constant counterpart of the Maxwell algebra. We gauge this algebra and construct a dynamical model with the help of a constrained BF theory. It turns out that the resulting theory is described by the Einstein-Cartan action with Holst term, and the gauge fields associated with the Maxwell generators {Z}ab appear only in topological terms that do not influence dynamical field equations. We briefly comment on the extension of this construction, which would lead to a nontrivial Maxwell fields dynamics.
[Chronic stress model in New Zealand white rabbit with hyperlipidemia].
Yu, Z M; Wang, M; Chen, K; Xiao, L Y; Deng, X T; Gong, T
2017-02-21
Objective: To establish and evaluate chronic stress model in New Zealand white rabbit with hyperlipidemia. Methods: A total of 45 clearing grade male New Zealand white rabbits were divided into four groups with random number table method: control (CON), normal diet combined with chronic stress for 8 weeks (CON+ CS), high fat diet (HFD) and high fat diet for 4 weeks combined with chronic stress for 8 weeks (HFD+ CS). Both social stress and physical stress methods were adopted.One-way ANOVA was used for comparison among groups. Results: (1) Chronic stress model assessments: ①body weight, the weight gain of stress groups was significantly reduced; ②behavioral assessment, rabbits exposed to stress in CON+ CS and HFD+ CS group [54%±7%, 55%±5%] exhibited more inactivity behavior than CON and HFD group [27%±5.28%, 34%±6%, P<0.01, P<0.05]; ③serum indexes: after stress regime for 4 weeks, cortisol of HFD+ CS was higher than HFD group [(60±5) ng/ml vs (38±4) ng/ml, P=0.001]. After 8 weeks, the serum levels of hs-CRP and IL-6 also elevated. (2) The effect of hyperlipidemia on chronic stress: compared with CON+ CS, HFD+ CS group showed more inactivity behavior and rising levels of cortisol, hs-CRP and IL-6. (3) Blood lipids: chronic stress induced raised serum total cholesterol. Conclusions: (1)Chronic stress model in rabbit with hyperlipidemia could be successfully established with 4-week high lipid feed followed by social stress combined with physical stress for 8 weeks.(2) Hyperlipidemia and chronic stress influences each other.
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.
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.
Causal Model of Stress and Coping: Women in Management.
ERIC Educational Resources Information Center
Long, Bonita C.; And Others
1992-01-01
Tested model of managerial women's (n=249) stress. Model was developed from Lazarus's theoretical framework of stress/coping and incorporated causal antecedent constructs (demographics, sex role attitudes, agentic traits), mediating constructs (environment, appraisals, engagement coping, disengagement coping), and outcomes (work performance,…
Ice, Gillian H; Sadruddin, Aalyia F A; Vagedes, Amy; Yogo, Jaja; Juma, Elizabeth
2012-06-01
Globally, a growing number of grandparents are caring for their grandchildren. The impact and burden associated with increases in custodial grandparenting, however, may differ by culture. In the United States, the caregiving role has been shown to be a significant source of stress for older adults. In cultures in which grandparents are more commonly involved in the care of young children, however, increasing caregiving roles may not be viewed as stressful. This study examines the impact of caregiving on perceived and physiological measures of stress among 640 Luo elders (60+) in western Kenya, where high HIV prevalence among younger-to-middle aged adults has led to a heavy burden of orphan care. Perceived stress levels were measured using the Luo Perceived Stress Scale (LPSS). Salivary cortisol and casual blood pressure were used as biomarkers of stress. Results were analyzed using random mixed effects models. Overall this study showed that caregivers have higher levels of perceived stress than non-caregivers. For women, household composition, including the number of orphans and adults in the homestead impacted perceived stress. Among men, those who perceived caregiving as burdensome had higher perceived stress. Despite the association between caregiving and perceived stress, there was a minimal relationship between caregiving and the two biomarkers of stress. This may be because caregiving is superimposed onto other stressors and therefore has a minimal physiological impact. These results highlight the importance of local context in determining the impact of the caregiving role on older adult well-being.
Superintegrability in Two Dimensions and the Racah-Wilson Algebra
NASA Astrophysics Data System (ADS)
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
2014-08-01
The analysis of the most general second-order superintegrable system in two dimensions: the generic 3-parameter model on the 2-sphere is cast in the framework of the Racah problem for the algebra. The Hamiltonian of the 3-parameter system and the generators of its quadratic symmetry algebra are seen to correspond to the total and intermediate Casimir operators of the combination of three algebras, respectively. The construction makes explicit the isomorphism between the Racah-Wilson algebra, which is the fundamental algebraic structure behind the Racah problem for , and the invariance algebra of the generic 3-parameter system. It also provides an explanation for the occurrence of the Racah polynomials as overlap coefficients in this context. The irreducible representations of the Racah-Wilson algebra are reviewed as well as their connection with the Askey scheme of classical orthogonal polynomials.
Oxidative Stress in Genetic Mouse Models of Parkinson's Disease
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
Setting up virgin stress conditions in discrete element models
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
NASA Technical Reports Server (NTRS)
Sindir, M. M.
1983-01-01
This paper presents a numerical study of the effects of expansion ratio on two-dimensional separating and reattaching flows in plane backward-facing step geometries with parallel walls. Closure of the Reynolds equations was achieved by four different turbulence models: k-epsilon, 'modified' k-epsilon, algebraic stress, and 'modified' algebraic stress models. The k-epsilon model relates the Reynolds stresses to the mean rate of strain through the definition of an isotropic turbulent viscosity. The more advanced algebraic stress model calculates the stresses from implicit algebraic relationships containing the stresses themselves, the mean rate of strain, and the turbulent kinetic energy and its dissipation rate. 'Modified' versions of the models employ a new dissipation rate equation whose production term was made more sensitive to streamwise curvature effects. A new nonequilibrium wall function treatment proposed by Chieng and Launder (1980) was also incorporated into each model.
Bicovariant quantum algebras and quantum Lie algebras
NASA Astrophysics Data System (ADS)
Schupp, Peter; Watts, Paul; Zumino, Bruno
1993-10-01
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(mathfrak{G}_q ) to U q g, given by elements of the pure braid group. These operators—the “reflection matrix” Y≡L + SL - being a special case—generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N).
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…
Parastatistics Algebras and Combinatorics
NASA Astrophysics Data System (ADS)
Popov, T.
2005-03-01
We consider the algebras spanned by the creation parafermionic and parabosonic operators which give rise to generalized parastatistics Fock spaces. The basis of such a generalized Fock space can be labelled by Young tableaux which are combinatorial objects. By means of quantum deformations a nice combinatorial structure of the algebra of the plactic monoid that lies behind the parastatistics is revealed.
Algebraic Reasoning through Patterns
ERIC Educational Resources Information Center
Rivera, F. D.; Becker, Joanne Rossi
2009-01-01
This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…
Learning Activity Package, Algebra.
ERIC Educational Resources Information Center
Evans, Diane
A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…
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.
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 dissertation,…
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…
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.
A model analysis of static stress in the vestibular membranes
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
Anisotropic stress and stability in modified gravity models
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.
Severe Life Stress and Oxidative Stress in the Brain: From Animal Models to Human Pathology
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
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.
NASA Astrophysics Data System (ADS)
Sati, Hisham; Schreiber, Urs
2017-03-01
We uncover higher algebraic structures on Noether currents and BPS charges. It is known that equivalence classes of conserved currents form a Lie algebra. We show that at least for target space symmetries of higher parameterized WZW-type sigma-models this naturally lifts to a Lie ( p + 1)-algebra structure on the Noether currents themselves. Applied to the Green-Schwarz-type action functionals for super p-brane sigma-models this yields super Lie ( p+1)-algebra refinements of the traditional BPS brane charge extensions of supersymmetry algebras. We discuss this in the generality of higher differential geometry, where it applies also to branes with (higher) gauge fields on their worldvolume. Applied to the M5-brane sigma-model we recover and properly globalize the M-theory super Lie algebra extension of 11-dimensional superisometries by 2-brane and 5-brane charges. Passing beyond the infinitesimal Lie theory we find cohomological corrections to these charges in higher analogy to the familiar corrections for D-brane charges as they are lifted from ordinary cohomology to twisted K-theory. This supports the proposal that M-brane charges live in a twisted cohomology theory.
Specifying initial stress for dynamic heterogeneous earthquake source models
Andrews, D.J.; Barall, M.
2011-01-01
Dynamic rupture calculations using heterogeneous stress drop that is random and self-similar with a power-law spatial spectrum have great promise of producing realistic ground-motion predictions. We present procedures to specify initial stress for random events with a target rupture length and target magnitude. The stress function is modified in the depth dimension to account for the brittle-ductile transition at the base of the seismogenic zone. Self-similar fluctuations in stress drop are tied in this work to the long-wavelength stress variation that determines rupture length. Heterogeneous stress is related to friction levels in order to relate the model to physical concepts. In a variant of the model, there are high-stress asperities with low background stress. This procedure has a number of advantages: (1) rupture stops naturally, not at artificial barriers; (2) the amplitude of short-wavelength fluctuations of stress drop is not arbitrary: the spectrum is fixed to the long-wavelength fluctuation that determines rupture length; and (3) large stress drop can be confined to asperities occupying a small fraction of the total rupture area, producing slip distributions with enhanced peaks.
A model of Barchan dunes including lateral shear stress.
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.
A finite element model for residual stress in repair welds
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.
Modeling of thermal stresses in welds
Zacharia, T.; Aramayo, G.A.
1993-12-31
The transient stress distribution in a Sigmajig test specimen resulting from mechanical and thermal loading was calculated for a Type 316 stainless steel specimen using finite element analysis. The study attempted to resolve the relationship between the dynamic stress distribution, particularly near the trailing edge of the pool, and the observed cracking behavior in the test specimen. The initiation and propagation of the crack during welding was visually monitored using a stroboscopic vision system. The numerical results were used to understand the initiation and propagation of hot-cracks during controlled welding of a specimen subjected to external restraint.
Tectonic stressing in California modeled from GPS observations
NASA Astrophysics Data System (ADS)
Parsons, Tom
2006-03-01
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.
Tectonic stressing in California modeled from GPS observations
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.
Transactional Model of Coping, Appraisals, and Emotional Reactions to Stress.
ERIC Educational Resources Information Center
Brack, Greg; McCarthy, Christopher J.
A study investigated the relationship of transactional models of stress management and appraisal-emotion relationships to emotions produced by taking a new job. The participants, 231 graduate students, completed measures of cognitive appraisals, stress coping resources, and emotional reactions at the time of taking a new job and some time later.…
A Model of Teacher Stress and Its Implications for Management.
ERIC Educational Resources Information Center
Leach, David J.
1984-01-01
After summarizing research into the sources and correlates of teacher stress, this article defines and proposes a model of work-related stress in school, incorporating current concepts and research findings. Strategies for coping with the buildup of environmental stressors are developed for application at various administrative levels within the…
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
Algebraic invariants for homotopy types
NASA Astrophysics Data System (ADS)
Blanc, David
1999-11-01
We define a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the [Pi]-algebra [pi][low asterisk]X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract [Pi]-algebra can be realized as the homotopy [Pi]-algebra of a space.
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,…
Modeling perceived stress via HRV and accelerometer sensor streams.
Wu, Min; Cao, Hong; Nguyen, Hai-Long; Surmacz, Karl; Hargrove, Caroline
2015-08-01
Discovering and modeling of stress patterns of human beings is a key step towards achieving automatic stress monitoring, stress management and healthy lifestyle. As various wearable sensors become popular, it becomes possible for individuals to acquire their own relevant sensory data and to automatically assess their stress level on the go. Previous studies for stress analysis were conducted in the controlled laboratory and clinic settings. These studies are not suitable for stress monitoring in one's daily life as various physical activities may affect the physiological signals. In this paper, we address such issue by integrating two modalities of sensors, i.e., HRV sensors and accelerometers, to monitor the perceived stress levels in daily life. We gathered both the heart and the motion data from 8 participants continuously for about 2 weeks. We then extracted features from both sensory data and compared the existing machine learning methods for learning personalized models to interpret the perceived stress levels. Experimental results showed that Bagging classifier with feature selection is able to achieve a prediction accuracy 85.7%, indicating our stress monitoring on daily basis is fairly practical.
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.
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
Pseudo-Riemannian Novikov algebras
NASA Astrophysics Data System (ADS)
Chen, Zhiqi; Zhu, Fuhai
2008-08-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.
Vector Preisach modeling of magnetic materials under stress
NASA Astrophysics Data System (ADS)
Ktena, A.
2015-02-01
The Preisach formalism is used to model magnetic hysteresis loops in soft magnetic materials subject to tensile stress. The model uses the Stoner-Wohlfarth mechanism of coherent rotation and dispersion of easy axes to capture the vector response of the magnetization. The Preisach density is constructed as the weighed sum of normal probability density functions (pdf) for the regions of high and low induction. The model parameters reflect the effect of strain: increased pinning, modelled by the central pdf parameters; enhanced anisotropy dispersion modelled by the angular dispersion of easy axes. Upon removal of the tensile stress, compressive residual stresses give rise to effective demagnetizing fields leading to lower differential permeability with a two-peak profile. As deformation levels increase, the amplitude of and the relative distance between the two permeability peaks changes which is reflected in the side density parameters. Modelling results are in qualitative agreement with the experimental data. The potential and limitations of the model are discussed.
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.
Stress and Sleep Reactivity: A Prospective Investigation of the Stress-Diathesis Model of Insomnia
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
NASA Astrophysics Data System (ADS)
Markarian, Nikita
2017-03-01
We introduce Weyl n-algebras and show how their factorization complex may be used to define invariants of manifolds. In the appendix, we heuristically explain why these invariants must be perturbative Chern-Simons invariants.
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)
Jordan Algebraic Quantum Categories
NASA Astrophysics Data System (ADS)
Graydon, Matthew; Barnum, Howard; Ududec, Cozmin; Wilce, Alexander
2015-03-01
State cones in orthodox quantum theory over finite dimensional complex Hilbert spaces enjoy two particularly essential features: homogeneity and self-duality. Orthodox quantum theory is not, however, unique in that regard. Indeed, all finite dimensional formally real Jordan algebras -- arenas for generalized quantum theories with close algebraic kinship to the orthodox theory -- admit homogeneous self-dual positive cones. We construct categories wherein these theories are unified. The structure of composite systems is cast from universal tensor products of the universal C*-algebras enveloping ambient spaces for the constituent state cones. We develop, in particular, a notion of composition that preserves the local distinction of constituent systems in quaternionic quantum theory. More generally, we explicitly derive the structure of hybrid quantum composites with subsystems of arbitrary Jordan algebraic type.
Accounting Equals Applied Algebra.
ERIC Educational Resources Information Center
Roberts, Sondra
1997-01-01
Argues that students should be given mathematics credits for completing accounting classes. Demonstrates that, although the terminology is different, the mathematical concepts are the same as those used in an introductory algebra class. (JOW)
Quantum walks, deformed relativity and Hopf algebra symmetries.
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.
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.
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.
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.
Modeling of grain boundary stresses in Alloy 600
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.
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
Models and Methods to Investigate Acute Stress Responses in Cattle
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
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.
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.
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.
A stress-coping model of mental illness stigma: I. Predictors of cognitive stress appraisal.
Rüsch, Nicolas; Corrigan, Patrick W; Wassel, Abigail; Michaels, Patrick; Olschewski, Manfred; Wilkniss, Sandra; Batia, Karen
2009-05-01
Stigma can be a major stressor for individuals with schizophrenia and other mental illnesses. It is unclear, however, why some stigmatized individuals appraise stigma as more stressful, while others feel they can cope with the potential harm posed by public prejudice. We tested the hypothesis that the level of perceived public stigma and personal factors such as rejection sensitivity, perceived legitimacy of discrimination and ingroup perceptions (group value; group identification; entitativity, or the perception of the ingroup of people with mental illness as a coherent unit) predict the cognitive appraisal of stigma as a stressor. Stigma stress appraisal refers to perceived stigma-related harm exceeding perceived coping resources. Stress appraisal, stress predictors and social cue recognition were assessed in 85 people with schizophrenia, schizoaffective or affective disorders. Stress appraisal did not differ between diagnostic subgroups, but was positively correlated with rejection sensitivity. Higher levels of perceived societal stigma and holding the group of people with mental illness in low regard (low group value) independently predicted high stigma stress appraisal. These predictors remained significant after controlling for social cognitive deficits, depressive symptoms and diagnosis. Our findings support the model that public and personal factors predict stigma stress appraisal among people with mental illness, independent of diagnosis and clinical symptoms. Interventions that aim to reduce the impact of stigma on people with mental illness could focus on variables such as rejection sensitivity, a personal vulnerability factor, low group value and the cognitive appraisal of stigma as a stressor.
Propagation of dissection in a residually-stressed artery model.
Wang, Lei; Roper, Steven M; Hill, Nicholas A; Luo, Xiaoyu
2017-02-01
This paper studies dissection propagation subject to internal pressure in a residually-stressed two-layer arterial model. The artery is assumed to be infinitely long, and the resultant plane strain problem is solved using the extended finite element method. The arterial layers are modelled using the anisotropic hyperelastic Holzapfel-Gasser-Ogden model, and the tissue damage due to tear propagation is described using a linear cohesive traction-separation law. Residual stress in the arterial wall is determined by an opening angle [Formula: see text] in a stress-free configuration. An initial tear is introduced within the artery which is subject to internal pressure. Quasi-static solutions are computed to determine the critical value of the pressure, at which the dissection starts to propagate. Our model shows that the dissection tends to propagate radially outwards. Interestingly, the critical pressure is higher for both very short and very long tears. The simulations also reveal that the inner wall buckles for longer tears, which is supported by clinical CT scans. In all simulated cases, the critical pressure is found to increase with the opening angle. In other words, residual stress acts to protect the artery against tear propagation. The effect of residual stress is more prominent when a tear is of intermediate length ([Formula: see text]90[Formula: see text] arc length). There is an intricate balance between tear length, wall buckling, fibre orientation, and residual stress that determines the tear propagation.
Vertebral stress of a cervical spine model under dynamic load.
Sadegh, A M; Tchako, A
2000-01-01
The objective of this study is to develop cervical spine models that predict the stresses in each vertebra by taking account of the biodynamic characteristics of the neck. The loads and the moments at the head point (Occipital Condyle) used for the models were determined by the rigid body dynamic response of the head due to G-z acceleration. The experimental data used were collected from the biodynamic responses of human volunteers during an acceleration in the z direction on the drop tower facility at Armstrong Laboratory at Wright Patterson Air Force Base (WPAFB). Three finite element models were developed: an elastic local model, viscoelastic local model and complete viscoelastic model. I-DEAS software was used to create the solid models, the loadings and the boundary conditions. Then, ABAQUS finite element software was employed to solve the models, and thus the stresses on each vertebral level were determined. Beam elements with different properties were employed to simulate the ligaments, articular facets and muscles. The complete viscoelastic model was subjected to 11 cases of loadings ranging from 8 G-z to 20 G-z accelerations. The von Mises and Maximum Principal stress fields, which are good indicators of bone failure, were calculated for all the cases. The results indicated that the maximum stress in all cases increased as the magnitude of the acceleration increased. The stresses in the 10 to 12 G-z cases were comfortably below the injury threshold level. The majority of the maximum stresses occurred in C6 and C4 regions.
Modeling of the stress state of the thumb carpometacarpal joint
NASA Astrophysics Data System (ADS)
Anferov, G. M.; Goryacheva, I. G.; Lyubicheva, A. N.; Soldatenkov, I. A.; Su, Fong-Chin; Chang, Chih-Han
2013-07-01
The stress state of the carpometacarpal joint (CMJ)was studied in sound and pathologic states by methods of continuum mechanics. The CMJ geometric model was constructed according to the results of computer processing of the data of tomographic investigations in the extension position, which were obtained at Cheng Kung Medical University (Taiwan). The study of contact interactions in the CML region for a given geometry were performed numerically in the ABAQUS program code. The obtained numerical solutions of contact problems permit comparatively analyzing the stress distribution in the bone tissue for various thumb positions and study the stress state dependence on the bone tissue porosity (osteoporosis), which varies with human age.
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.
Zhang, Tian; Zhang, Daijun; Li, Zhenliang; Cai, Qing
2010-05-01
The calibration of ASMs is a prerequisite for their application to simulation of a wastewater treatment plant. This work should be made based on the evaluation of structural identifiability of model parameters. An EBPR sub-model including denitrification phosphorus removal has been incorporated in ASM2d. Yet no report is presented on the structural identifiability of the parameters in the EBPR sub-model. In this paper, the differential algebra approach was used to address this issue. The results showed that the structural identifiability of parameters in the EBPR sub-model could be improved by increasing the measured variables. The reduction factor eta(NO)(3) was identifiable when combined data of aerobic process and anoxic process were assumed. For K(PP), X(PAO) and q(PHA) of the anaerobic process to be uniquely identifiable, one of them is needed to be determined by other ways. Likewise, if prior information on one of the parameters, K(PHA), X(PAO) and q(PP) of the aerobic process, is known, all the parameters are identifiable. The above results could be of interest to the parameter estimation of the EBPR sub-model. The algorithm proposed in the paper is also suitable for other sub-models of ASMs.
Algebraic mesh quality metrics
KNUPP,PATRICK
2000-04-24
Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. the singular value decomposition is used to study relationships between metrics. Equivalence of the element condition number and mean ratio metrics is proved. Condition number is shown to measure the distance of an element to the set of degenerate elements. Algebraic measures for skew, length ratio, shape, volume, and orientation are defined abstractly, with specific examples given. Combined metrics for shape and volume, shape-volume-orientation are algebraically defined and examples of such metrics are given. Algebraic mesh quality metrics are extended to non-simplical elements. A series of numerical tests verify the theoretical properties of the metrics defined.
Modeling a Galfenol based stress sensor capable of sensing up to three axial stresses
NASA Astrophysics Data System (ADS)
Weetman, Philip; Akhras, George
2013-11-01
A three dimensional rate equation model can be used to calculate the magnetization response in a Galfenol sample under the application of any or all components of stress (axial and shear) [P. Weetman and G. Akhras, J. Appl. Phys. 109, 043902 (2011)]. For a Galfenol based stress sensor, one is essentially interested in the inverse of that calculation: from magnetization measurements, determine which stresses are acting on the system. A conceptual design of a Galfenol based three dimensional dynamical sensor is presented. One assumes the time-varying magnetization and its time derivative in all three directions can be measured for different external magnetic bias fields at different points in time. It is shown that the rate equation model can be used to calculate all the stresses acting on the system from knowledge of the magnetization and the time derivative of magnetization. The necessary calculations are presented and then applied to a sample set of magnetization values, which were generated from a benchmarked sensing model that used up to three axial stresses.
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
Computational modelling of bone cement polymerization: temperature and residual stresses.
Pérez, M A; Nuño, N; Madrala, A; García-Aznar, J M; Doblaré, M
2009-09-01
The two major concerns associated with the use of bone cement are the generation of residual stresses and possible thermal necrosis of surrounding bone. An accurate modelling of these two factors could be a helpful tool to improve cemented hip designs. Therefore, a computational methodology based on previous published works is presented in this paper combining a kinetic and an energy balance equation. New assumptions are that both the elasticity modulus and the thermal expansion coefficient depend on the bone cement polymerization fraction. This model allows to estimate the thermal distribution in the cement which is later used to predict the stress-locking effect, and to also estimate the cement residual stresses. In order to validate the model, computational results are compared with experiments performed on an idealized cemented femoral implant. It will be shown that the use of the standard finite element approach cannot predict the exact temporal evolution of the temperature nor the residual stresses, underestimating and overestimating their value, respectively. However, this standard approach can estimate the peak and long-term values of temperature and residual stresses within acceptable limits of measured values. Therefore, this approach is adequate to evaluate residual stresses for the mechanical design of cemented implants. In conclusion, new numerical techniques should be proposed in order to achieve accurate simulations of the problem involved in cemented hip replacements.
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...
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.
Turbulence Model Predictions of Strongly Curved Flow in a U-Duct
NASA Technical Reports Server (NTRS)
Rumsey, Christopher L.; Gatski, Thomas B.; Morrison, Joseph H.
2000-01-01
The ability of three types of turbulence models to accurately predict the effects of curvature on the flow in a U-duct is studied. An explicit algebraic stress model performs slightly better than one- or two-equation linear eddy viscosity models, although it is necessary to fully account for the variation of the production-to-dissipation-rate ratio in the algebraic stress model formulation. In their original formulations, none of these turbulence models fully captures the suppressed turbulence near the convex wall, whereas a full Reynolds stress model does. Some of the underlying assumptions used in the development of algebraic stress models are investigated and compared with the computed flowfield from the full Reynolds stress model. Through this analysis, the assumption of Reynolds stress anisotropy equilibrium used in the algebraic stress model formulation is found to be incorrect in regions of strong curvature. By the accounting for the local variation of the principal axes of the strain rate tensor, the explicit algebraic stress model correctly predicts the suppressed turbulence in the outer part of the boundary layer near the convex wall.
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…
Supersymmetry in physics: an algebraic overview
Ramond, P.
1983-01-01
In 1970, while attempting to generalize the Veneziano model (string model) to include fermions, I introduced a new algebraic structure which turned out to be a graded Lie algebra; it was used as a spectrum-generating algebra. This approach was soon after generalized to include interactions, yielding a complete model of fermions and boson (RNS model). In an unrelated work in the Soviet Union, it was shown how to generalize the Poincare group to include fermionic charges. However it was not until 1974 that an interacting field theory invariant under the Graded Poincare group in 3 + 1 dimensions was built (WZ model). Supersymmetric field theories turned out to have less divergent ultraviolet behavior than non-supersymmetric field theories. Gravity was generalized to include supersymmetry, to a theory called supergravity. By now many interacting local field theories exhibiting supersymmetry have been built and studied from 1 + 1 to 10 + 1 dimensions. Supersymmetric local field theories in less than 9 + 1 dimensions, can be understood as limits of multilocal (string) supersymmetric theories, in 9 + 1 dimensions. On the other hand, graded Lie algebras have been used in non-relativistic physics as approximate symmetries of Hamiltonians. The most striking such use so far helps comparing even and odd nuclei energy levels. It is believed that graded Lie algebras can be used whenever paired and unpaired fermions excitations can coexist. In this overview of a tremendously large field, I will only survey finite graded Lie algebras and their representations. For non-relativistic applications, all of GLA are potentially useful, while for relativistic applications, only these which include the Poincare group are to be considered.
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.…
Critical exponents from infinite-dimensional symplectic algebras
NASA Astrophysics Data System (ADS)
Altschüler, D.
1985-11-01
Unitary representations of the Virasoro algebra with centrala c = 1 - 6/(n + 2) are important in the study of two-dimensional models in statistical mechanics. It is shown that they can be constructed using Kac-Moody algebras of symplectic type. At the same time, this provides a simple derivation of the critical exponents.
Adaptive Algebraic Multigrid Methods
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.
NASA Astrophysics Data System (ADS)
Durka, R.
2017-04-01
The S-expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups. Including the possibility of the zero element in the resonant decomposition, and associating the Lorentz generator with the semigroup identity element, leads to a wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results, we find all the Maxwell algebras of type {{B}m} , {{C}m} , and the recently introduced {{D}m} . The additional new examples complete the resulting generalization of the bosonic enlargements for an arbitrary number of the Lorentz-like and translational-like generators. Some further prospects concerning enlarging the algebras are discussed, along with providing all the necessary constituents for constructing the gravity actions based on the obtained results.
NASA Astrophysics Data System (ADS)
Roytenberg, Dmitry
2007-11-01
A Lie 2-algebra is a linear category equipped with a functorial bilinear operation satisfying skew-symmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural transformations between Lie 2-algebras can also be defined, yielding a 2-category. Passing to the normalized chain complex gives an equivalence of 2-categories between Lie 2-algebras and certain "up to homotopy" structures on the complex; for strictly skew-symmetric Lie 2-algebras these are L∞-algebras, by a result of Baez and Crans. Lie 2-algebras appear naturally as infinitesimal symmetries of solutions of the Maurer-Cartan equation in some differential graded Lie algebras and L∞-algebras. In particular, (quasi-) Poisson manifolds, (quasi-) Lie bialgebroids and Courant algebroids provide large classes of examples.
Algebra for Gifted Third Graders.
ERIC Educational Resources Information Center
Borenson, Henry
1987-01-01
Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)
A Holistic Approach to Algebra.
ERIC Educational Resources Information Center
Barbeau, Edward J.
1991-01-01
Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)
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.
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.
Stress concentration around an atelectatic region: a finite element model.
Makiyama, A M; Gibson, L J; Harris, R S; Venegas, J G
2014-09-15
Lung parenchyma surrounding an atelectatic region is thought to be subjected to increased stress compared with the rest of the lung. Using 37 hexagonal cells made of linear springs, Mead et al. (1970) measured a stress concentration greater than 30% in the springs surrounding a stiffer central cell. We re-examine the problem using a 2D finite element model of 500 cells made of thin filaments with a non-linear stress-strain relationship. We study the consequences of increasing the central stiff region from one to nine contiguous cells in regular hexagonal honeycombs and random Voronoi honeycombs. The honeycomb structures were uniformly expanded with strains of 15%, 30%, 45% and 55% above their resting, non-deformed geometry. The curve of biaxial stress vs. fractional area change has a similar shape to that of the pressure-volume curve of the lung, showing an initial regime with relatively flat slope and a final regime with decreasing slope, tending toward an asymptote. Regular honeycombs had little variability in the maximum stress in radially oriented filaments adjacent to the central stiff region. In contrast, some filaments in random Voronoi honeycombs were subjected to stress concentration approximately 16 times the average stress concentration in the radially oriented filaments adjacent to the stiff region. These results may have implications in selecting the appropriate strategy for mechanical ventilation in ARDS and defining a "safe" level of alveolar pressure for ventilating atelectatic lungs.
A maxent-stress model for graph layout.
Gansner, Emden R; Hu, Yifan; North, Stephen
2013-06-01
In some applications of graph visualization, input edges have associated target lengths. Dealing with these lengths is a challenge, especially for large graphs. Stress models are often employed in this situation. However, the traditional full stress model is not scalable due to its reliance on an initial all-pairs shortest path calculation. A number of fast approximation algorithms have been proposed. While they work well for some graphs, the results are less satisfactory on graphs of intrinsically high dimension, because some nodes may be placed too close together, or even share the same position. We propose a solution, called the maxent-stress model, which applies the principle of maximum entropy to cope with the extra degrees of freedom. We describe a force-augmented stress majorization algorithm that solves the maxent-stress model. Numerical results show that the algorithm scales well, and provides acceptable layouts for large, nonrigid graphs. This also has potential applications to scalable algorithms for statistical multidimensional scaling (MDS) with variable distances.
Sex differences in the chronic mild stress model of depression.
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.
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.
Modelling global water stress at the monthly time-scale
NASA Astrophysics Data System (ADS)
Wada, Y.; van Beek, L. P. H.; Weingartner, R.; Viviroli, D.; Bierkens, M. F. P.
2009-04-01
It is estimated that currently over one billion people have problems obtaining access to sufficient freshwater resources, while due to population growth and climate change the number of people affected by water scarcity and water stress will rise to four billion by 2050 (UNEP, 1999). To assess current water stress and it development under different socio-ecomomic and climate scenario's Global Hydrological Models (GHMs) are important tools. Until now, GHM-analyses calculating water demand and water availability have been performed on yearly totals only. However, it can be expected that availability of water is often out of phase with water demand and that actual water stress may be underestimated using yearly totals. Also, yearly budgets cannot shed light on the persistence and recurrence time of water stress. In this paper we present an analysis of global water stress based on monthly data of water availability and water demand. Here, severe water stress is defined to occur in case local water demand exceeds 40 percent of the local water availability A 40-year time series of water availibility is obtained by the GHM PCR-GLOBWB forced with CRU meteorological data downscaled to daily time steps using the ERA40 re-analysis dataset. Thus, apart from representing a within-year regime, the water availability analyses also consider between-year climate variability. Availability calculations contain both local precipitation surplus (precipitation minus evaporation), but also upstream river discharge, water in reservoirs, groundwater abstraction as well as green water (soil water used by irrigated crops). Water demand is calculated on a monthly basis for the year 2000, while these monthly values are taken constant over the years. It consists of water demand for agriculture (both rainfed as well as irrigated and lifestock), industry and domestic water use. Domestic water demand as well as the recycling fraction of industrial and domestic water demand for each country are
Modelling global water stress at the monthly time-scale
NASA Astrophysics Data System (ADS)
Wada, Y.; van Beek, R. L.; Viviroli, D.; Weingartner, R.; Bierkens, M. F.
2008-12-01
It is estimated that currently over one billion people have problems obtaining access to sufficient freshwater resources, while due to population growth and climate change the number of people affected by water scarcity and water stress will rise to four billion by 2050 (UNEP, 1999). To assess current water stress and it development under different socio-ecomomic and climate scenario's Global Hydrological Models (GHMs) are important tools. Until now, GHM-analyses calculating water demand and water availability have been performed on yearly totals only. However, it can be expected that availability of water is often out of phase with water demand and that actual water stress may be underestimated using yearly totals. Also, yearly budgets cannot shed light on the persistence and recurrence time of water stress. In this paper we present an analysis of global water stress based on monthly data of water availability and water demand. Here, severe water stress is defined to occur in case local water demand exceeds 40% of the local water availability A 40-year time series of water availibility is obtained by the GHM PCR-GLOBWB forced with CRU meteorological data downscaled to daily time steps using the ERA40 re-analysis dataset. Thus, apart from representing a within-year regime, the water availability analyses also consider between-year climate variability. Availability calculations contain both local precipitation surplus (precipitation minus evaporation), but also upstream river discharge, water in reservoirs, groundwater abstraction as well as green water (soil water used by irrigated crops). Water demand is calculated on a monthly basis for the year 2000, while these monthly values are taken constant over the years. It consists of water demand for agriculture (both rainfed as well as irrigated and lifestock), industry and domestic water use. Domestic water demand as well as the recycling fraction of industrial and domestic water demand for each country are related to
Job stress models for predicting burnout syndrome: a review.
Chirico, Francesco
2016-01-01
In Europe, the Council Directive 89/391 for improvement of workers' safety and health has emphasized the importance of addressing all occupational risk factors, and hence also psychosocial and organizational risk factors. Nevertheless, the construct of "work-related stress" elaborated from EU-OSHA is not totally corresponding with the "psychosocial" risk, that is a broader category of risk, comprising various and different psychosocial risk factors. The term "burnout", without any binding definition, tries to integrate symptoms as well as cause of the burnout process. In Europe, the most important methods developed for the work related stress risk assessment are based on the Cox's transactional model of job stress. Nevertheless, there are more specific models for predicting burnout syndrome. This literature review provides an overview of job burnout, highlighting the most important models of job burnout, such as the Job Strain, the Effort/Reward Imbalance and the Job Demands-Resources models. The difference between these models and the Cox's model of job stress is explored.
Vector magnetic hysteresis modeling of stress annealed galfenol
NASA Astrophysics Data System (ADS)
Adly, A. A.; Davino, D.; Giustiniani, A.; Visone, C.
2013-05-01
In the past years, utilization of magnetostrictive materials has been increasing in different applications including actuation, sensing, and energy harvesting. Special interest has been recently directed to galfenol (iron-gallium alloy). This paper experimentally investigates the vector hysteresis properties of stress-annealed galfenol as well as to test the capability of recently proposed models to mimic those properties. Details of the measurements, model identification, and experimental testing of the model accuracy are reported in the paper.
An algebra of reversible computation.
Wang, Yong
2016-01-01
We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.
Baxter Operator and Archimedean Hecke Algebra
NASA Astrophysics Data System (ADS)
Gerasimov, A.; Lebedev, D.; Oblezin, S.
2008-12-01
In this paper we introduce Baxter integral {mathcal{Q}} -operators for finite-dimensional Lie algebras {mathfrak{gl}_{ell+1}} and {mathfrak{so}_{2ell+1}} . Whittaker functions corresponding to these algebras are eigenfunctions of the {mathcal{Q}}-operators with the eigenvalues expressed in terms of Gamma-functions. The appearance of the Gamma-functions is one of the manifestations of an interesting connection between Mellin-Barnes and Givental integral representations of Whittaker functions, which are in a sense dual to each other. We define a dual Baxter operator and derive a family of mixed Mellin-Barnes-Givental integral representations. Givental and Mellin-Barnes integral representations are used to provide a short proof of the Friedberg-Bump and Bump conjectures for G = GL( ℓ + 1) proved earlier by Stade. We also identify eigenvalues of the Baxter {mathcal{Q}}-operator acting on Whittaker functions with local Archimedean L-factors. The Baxter {mathcal{Q}}-operator introduced in this paper is then described as a particular realization of the explicitly defined universal Baxter operator in the spherical Hecke algebra {mathcal {H}(G(mathbb{R}), K)} , K being a maximal compact subgroup of G. Finally we stress an analogy between {mathcal{Q}}-operators and certain elements of the non-Archimedean Hecke algebra {mathcal {H}(G(mathbb{Q}_p),G(mathbb{Z}_p))}.
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.
Hexagonal tessellations in image algebra
NASA Astrophysics Data System (ADS)
Eberly, David H.; Wenzel, Dennis J.; Longbotham, Harold G.
1990-11-01
In image algebra '' the concept of a coordinate set X is general in that such a set is simply a subset of ndimensional Euclidean space . The standard applications in 2-dimensional image processing use coordinate sets which are rectangular arrays X 72 x ZZm. However some applications may require other geometries for the coordinate set. We look at three such related applications in the context of image algebra. The first application is the modeling of photoreceptors in primate retinas. These receptors are inhomogeneously distributed on the retina. The largest receptor density occurs in the center of the fovea and decreases radially outwards. One can construct a hexagonal tessellation of the retina such that each hexagon contains approximately the same number of receptors. The resulting tessellation called a sunflower heart2 consists of concentric rings of hexagons whose sizes increase as the radius of the ring increases. The second application is the modeling of the primary visual . The neurons are assumed to be uniformly distributed as a regular hexagonal lattice. Cortical neural image coding is modeled by a recursive convolution of the retinal neural image using a special set of filters. The third application involves analysis of a hexagonally-tessellated image where the pixel resolution is variable .
Modeling the response of peach fruit growth to water stress.
Génard, M; Huguet, J G
1996-04-01
We applied a semi-mechanistic model of fresh matter accumulation to peach fruit during the stage of rapid mesocarp development. The model, which is based on simple hypotheses of fluid flows into and out of the fruit, assumes that solution flow into the fruit increases with fruit weight and transpiration per unit weight, and decreases with the maximum daily shrinkage of the trunk, which was used as an indicator of water stress. Fruit transpiration was assumed to increase with fruit size and with radiation. Fruit respiration was considered to be related to fruit growth and to temperature. The model simulates variability in growth among fruits according to climatic conditions, degree of water stress and weight of the fruit at the beginning of the simulation. We used data obtained from well-watered and water-stressed trees grown in containers to estimate model parameters and to test the model. There was close agreement between the simulated and measured values. A sensitivity analysis showed that initial fruit weight partly determined the variation in growth among fruits. The analysis also indicated that there was an optimal irradiance for fruit growth and that the effect of high global radiation on growth varied according to the stage of fruit development. Water stress, which was the most important factor influencing fruit growth, rapidly depressed growth, particularly when applied late in the season.
Effective stress model for partially and fully saturated rocks
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.
Depression, Stress, and Anhedonia: Toward a Synthesis and Integrated Model
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
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.…
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…
Algebraic Thinking through Origami.
ERIC Educational Resources Information Center
Higginson, William; Colgan, Lynda
2001-01-01
Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)
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…
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.
Unified algebraic method to non-Hermitian systems with Lie algebraic linear structure
NASA Astrophysics Data System (ADS)
Zhang, Hong-Biao; Jiang, Guang-Yuan; Wang, Gang-Cheng
2015-07-01
We suggest a generic algebraic method to solve non-Hermitian Hamiltonian systems with Lie algebraic linear structure. Such method can not only unify the non-Hermitian Hamiltonian and the Hermitian Hamiltonian with the same structure but also keep self-consistent between similarity transformation and unitary transformation. To clearly reveal the correctness and physical meaning of such algebraic method, we illustrate our method with two different types of non-Hermitian Hamiltonians: the non-Hermitian Hamiltonian with Heisenberg algebraic linear structure and the non-Hermitian Hamiltonian with su(1, 1) algebraic linear structure. We obtain energy eigenvalues and the corresponding eigenstates of non-Hermitian forced harmonic oscillator with Heisenberg algebra structure via a proper similarity transformation. We also calculate the eigen-problems of general non-Hermitian Hamiltonian with su(1, 1) structure in terms of the similarity transformation. As an application, we focus on studying the non-Hermitian single-mode squeezed and coherent harmonic oscillator system and find that such similarity transformation associated with this model is in fact gauge-like transformation for simple harmonic oscillator.
The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra
NASA Astrophysics Data System (ADS)
Hallowell, Karl; Waldron, Andrew
2007-09-01
Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical evolution equations, and identifying wavefunctions with sections of the symmetric tensor bundle and Noether charges with geometric operators. In general curved spaces these operators obey a deformation of the Fourier-Jacobi Lie algebra of sp(2,R). These results have already been generalized by the authors to arbitrary tensor and spinor bundles using supersymmetric quantum mechanical models and have also been applied to the theory of higher spin particles. These Proceedings review these results in their simplest, symmetric tensor setting. New results on a novel and extremely useful reformulation of the rank 2 deformation of the Fourier-Jacobi Lie algebra in terms of an associative algebra are also presented. This new algebra! was originally motivated by studies of operator orderings in enveloping algebras. It provides a new method that is superior in many respects to common techniques such as Weyl or normal ordering.
Stress transfer efficiency in model composites under dynamic loading
NASA Astrophysics Data System (ADS)
Koimtzoglou, C.; Kostopoulos, V.; Galiotis, C.
The micromechanics of tension-tension fatigue loading in model single-fibre composite geometries is investigated in this paper. In an attempt to emulate the conditions encountered in full carbon fibre composites, the fibres were prestrained prior to the curing process to ensure that they were free of high residual compressive stresses as a result of resin shrinkage. The resulting specimens were grouped into two categories depending on the level of the initial fibre prestrain (case A low, case B high). The cyclic load is designed to be well below the endurance fatigue limit of the polymer matrix ( 0.6%), and to have a frequency low enough to avoid unwanted thermal post curing. Throughout the preparation procedure, as well as during fatigue loading, the fibre stress (strain) was constantly monitored by means of laser Raman spectroscopy. The fibre axial stress distributions at each fatigue step were converted to interfacial shear stress (ISS) distributions, from which important parameters such as the maximum ISS the system can accommodate, the transfer length for efficient stress built-up and the length required for the attainment of maximum ISS were obtained. The results showed that, up to 2×106 loading cycles, the main parameters which affected the stress transfer efficiency at the interface were the fibre fracture process itself and the viscoelastic behaviour of the matrix material.
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.
Algebraic construction of the Darboux matrix revisited
NASA Astrophysics Data System (ADS)
Cieśliński, Jan L.
2009-10-01
We present algebraic construction of Darboux matrices for 1+1-dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case. We discuss different approaches to the Darboux-Bäcklund transformation, based on different λ-dependences of the Darboux matrix: polynomial, sum of partial fractions or the transfer matrix form. We derive symmetric N-soliton formulae in the general case. The matrix spectral parameter and dressing actions in loop groups are also discussed. We describe reductions to twisted loop groups, unitary reductions, the matrix Lax pair for the KdV equation and reductions of chiral models (harmonic maps) to SU(n) and to Grassmann spaces. We show that in the KdV case the nilpotent Darboux matrix generates the binary Darboux transformation. The paper is intended as a review of known results (usually presented in a novel context) but some new results are included as well, e.g., general compact formulae for N-soliton surfaces and linear and bilinear constraints on the nonisospectral Lax pair matrices which are preserved by Darboux transformations.
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.
Algebraic connectivity and graph robustness.
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.
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.
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-06
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.
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)
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"…
Noise limitations in optical linear algebra processors.
Batsell, S G; Jong, T L; Walkup, J F; Krile, T F
1990-05-10
A general statistical noise model is presented for optical linear algebra processors. A statistical analysis which includes device noise, the multiplication process, and the addition operation is undertaken. We focus on those processes which are architecturally independent. Finally, experimental results which verify the analytical predictions are also presented.
A Microcomputer Lab for Algebra & Calculus.
ERIC Educational Resources Information Center
Avery, Chris; And Others
An overview is provided of De Anza College's use of computerized instruction in its mathematics courses. After reviewing the ways in which computer technology is changing math instruction, the paper looks at the use of computers in several course sequences. The instructional model for the algebra sequence is based on a large group format of…
A Linear Algebra Measure of Cluster Quality.
ERIC Educational Resources Information Center
Mather, Laura A.
2000-01-01
Discussion of models for information retrieval focuses on an application of linear algebra to text clustering, namely, a metric for measuring cluster quality based on the theory that cluster quality is proportional to the number of terms that are disjoint across the clusters. Explains term-document matrices and clustering algorithms. (Author/LRW)
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…
A mathematical model of stress generation in microtubule pair interactions
NASA Astrophysics Data System (ADS)
Fang, Fang; Betterton, Meredith; Shelley, Michael
2014-11-01
Microtubules and motor proteins are basic ingredients in many cellular structures and of new biosynthetic ``active'' suspensions. The interaction of microtubules with their surrounding fluid medium depends fundamentally upon the force generation afforded them through cross-linking motile motor proteins. Here we develop a simple mathematical model, based on the statistical mechanics, motor proteins binding and unbinding, to study the generation of active fluid stresses. We study the role and contributions of ``polarity sorting'' and ``tether'' relaxation on the generation of intrinsic, destabilizing stresses.
Modelling Of Residual Stresses Induced By High Speed Milling Process
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.
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.
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.
Reconceptualizing native women's health: an "indigenist" stress-coping model.
Walters, Karina L; Simoni, Jane M
2002-04-01
This commentary presents an "indigenist" model of Native women's health, a stress-coping paradigm that situates Native women's health within the larger context of their status as a colonized people. The model is grounded in empirical evidence that traumas such as the "soul wound" of historical and contemporary discrimination among Native women influence health and mental health outcomes. The preliminary model also incorporates cultural resilience, including as moderators identity, enculturation, spiritual coping, and traditional healing practices. Current epidemiological data on Native women's general health and mental health are reconsidered within the framework of this model.
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.
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.
Modeling and prediction of irradiation assisted stress corrosion cracking
Andresen, P.L.; Ford, F.P.
1995-12-31
Following an introduction to the phenomenology and consequences of irradiation assisted stress corrosion cracking (IASCC), the many common aspects of SCC response in unirradiated and irradiated environments is reviewed. From a secure basis of understanding and predictive modeling under unirradiated conditions, the effects of individual irradiation phenomena are identified and modeled. The individual effects of radiation on segregation, creep/stress relaxation, hardening, and radiolytic water chemistry are modeled based on the best available data, some from proprietary sources. Critical issues are addressed, such as the possibility that radiation produces very high corrosion potentials in crevices/cracks under irradiated conditions. A wide variety of irradiated laboratory data and field observations provides a basis for comparison with prediction and an optimism that, despite an imperfect understanding of irradiation phenomena, it is possible to develop predictive algorithms that characterize IASCC with reasonable accuracy and, from that, to develop an effective approach for life prediction.
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.
Thermal Indices and Thermophysiological Modeling for Heat Stress.
Havenith, George; Fiala, Dusan
2015-12-15
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.
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.
Lee, Jaehoon; Wilczek, Frank
2013-11-27
Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.
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®,…
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.
A quantum affine algebra for the deformed Hubbard chain
NASA Astrophysics Data System (ADS)
Beisert, Niklas; Galleas, Wellington; Matsumoto, Takuya
2012-09-01
The integrable structure of the one-dimensional Hubbard model is based on Shastry's R-matrix and the Yangian of a centrally extended \\mathfrak {sl}(2|2) superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose R-matrix has recently been found. This R-matrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how the algebra reduces to the above-mentioned Yangian and to the conventional quantum affine \\mathfrak {sl}(2|2) algebra in two special limits.
Stress analysis of fracture of atherosclerotic plaques: crack propagation modeling.
Rezvani-Sharif, Alireza; Tafazzoli-Shadpour, Mohammad; Kazemi-Saleh, Davood; Sotoudeh-Anvari, Maryam
2016-12-09
Traditionally, the degree of luminal obstruction has been used to assess the vulnerability of atherosclerotic plaques. However, recent studies have revealed that other factors such as plaque morphology, material properties of lesion components and blood pressure may contribute to the fracture of atherosclerotic plaques. The aim of this study was to investigate the mechanism of fracture of atherosclerotic plaques based on the mechanical stress distribution and fatigue analysis by means of numerical simulation. Realistic models of type V plaques were reconstructed based on histological images. Finite element method was used to determine mechanical stress distribution within the plaque. Assuming that crack propagation initiated at the sites of stress concentration, crack propagation due to pulsatile blood pressure was modeled. Results showed that crack propagation considerably changed the stress field within the plaque and in some cases led to initiation of secondary cracks. The lipid pool stiffness affected the location of crack formation and the rate and direction of crack propagation. Moreover, increasing the mean or pulse pressure decreased the number of cycles to rupture. It is suggested that crack propagation analysis can lead to a better recognition of factors involved in plaque rupture and more accurate determination of vulnerable plaques.
Animal models of post-traumatic stress disorder: face validity
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
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.
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.
Double conformal space-time algebra
NASA Astrophysics Data System (ADS)
Easter, Robert Benjamin; Hitzer, Eckhard
2017-01-01
The Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra G 4,8that extends the concepts introduced with the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) G 8,2 with entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) in spacetime with a new boost operator. The base algebra in which spacetime geometry is modeled is the Space-Time Algebra (STA) G 1,3. Two Conformal Space-Time subalgebras (CSTA) G 2,4 provide spacetime entities for points, flats (incl. worldlines), and hyperbolics, and a complete set of versors for their spacetime transformations that includes rotation, translation, isotropic dilation, hyperbolic rotation (boost), planar reflection, and (pseudo)spherical inversion in rounds or hyperbolics. The DCSTA G 4,8 is a doubling product of two G 2,4 CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new bivector entities for (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime hyperbolics or other surface entities using the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in rounds or hyperbolics. An operation for the directed non-uniform scaling (anisotropic dilation) of the bivector general quadric entities is defined using the boost operator and a spatial projection. DCSTA allows general quadric surfaces to be transformed in spacetime by the same complete set of doubled CSTA versor (i.e., DCSTA versor) operations that are also valid on the doubled CSTA point entity (i.e., DCSTA point) and the other doubled CSTA entities. The new DCSTA bivector entities are formed by extracting values from the DCSTA point entity using specifically defined inner product extraction operators. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the length
Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras
NASA Astrophysics Data System (ADS)
Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent; Kato La, V.
2016-10-01
We discuss a construction scheme for Clifford numbers of arbitrary dimension. The scheme is based upon performing direct products of the Pauli spin and identity matrices. Conjugate fermionic algebras can then be formed by considering linear combinations of the Clifford numbers and the Hermitian conjugates of such combinations. Fermionic algebras are important in investigating systems that follow Fermi-Dirac statistics. We will further comment on the applications of Clifford algebras to Fueter analyticity, twistors, color algebras, M-theory and Leech lattice as well as unification of ancient and modern geometries through them.
ERIC Educational Resources Information Center
Casstevens, Thomas W.; And Others
This document consists of five units which all view applications of mathematics to American politics. The first three view calculus applications, the last two deal with applications of algebra. The first module is geared to teach a student how to: 1) compute estimates of the value of the parameters in negative exponential models; and draw…
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.
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.
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.
Mathematical Modeling of Intravascular Blood Coagulation under Wall Shear Stress
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
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.
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.
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…
Applications of algebraic grid generation
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Smith, Robert E.
1990-01-01
Techniques and applications of algebraic grid generation are described. The techniques are univariate interpolations and transfinite assemblies of univariate interpolations. Because algebraic grid generation is computationally efficient, the use of interactive graphics in conjunction with the techniques is advocated. A flexible approach, which works extremely well in an interactive environment, called the control point form of algebraic grid generation is described. The applications discussed are three-dimensional grids constructed about airplane and submarine configurations.
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.
Stress management affects outcomes in the pathophysiology of an endometriosis model.
Appleyard, Caroline B; Cruz, Myrella L; Hernández, Siomara; Thompson, Kenira J; Bayona, Manuel; Flores, Idhaliz
2015-04-01
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.
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.
f-Deformed Boson Algebra Related to Gentile Statistics
NASA Astrophysics Data System (ADS)
Chung, Won Sang; Hassanabadi, Hassan
2017-02-01
In this paper the deformed boson algebra giving the Gentile distribution function is constructed by using the model of ideal gas of deformed bosons and some properties of a root of unity. As an example we discuss the quantum optical problem related to the Gentile (or f-deformed) boson algebra with large but finite M. For this algebra we construct the Gentile (or f-deformed) coherent state and discuss its nonclassical properties such as sub-Poissonian statistics and anti-bunching effect.
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…
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…
Kawaharada, Mariko; Saijo, Yasuaki; Yoshioka, Eiji; Sato, Tetsuro; Sato, Hirokazu; Kishi, Reiko
2007-04-01
The aim of the present study was to identify relations between occupational stress and occupational class in Japanese civil servants, using two occupational stress models-the Effort-Reward Imbalance (ERI) Model and the Job Demand-Control (JDC) Model. The subjects were employees of three local public organizations. We distributed self-administered questionnaires and assessed occupational stress by ERI and JDC. We used seven occupational categories based on the Standard Occupational Classification for Japan. The data of 6,423 male and 1,606 female subjects were analyzed by logistic regression analysis to obtain odds ratios (OR) for relations between occupational stress and occupational class. In JDC, male clerical workers, transport/communication workers and protective service workers showed a significantly higher OR of being in the high occupational stress group, compared to managers. In ERI, male professionals/technicians, transport/communication workers, clerical workers and protective service workers showed a significantly higher prevalence OR, compared to managers, the two models giving different results. In ERI, female production workers/laborers and clerical workers had a significantly lower prevalence OR, compared to managers. The results of this study showed that occupational stress differed by occupational class and the two occupational stress models gave different results for occupational classes with high occupational stress.
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.}
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
Thermal mechanical stress modeling of GCtM seals
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.
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.
A New Stress-Based Model of Political Extremism
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
A contact stress model for multifingered grasps of rough objects
NASA Technical Reports Server (NTRS)
Sinha, Pramath Raj; Abel, Jacob M.
1990-01-01
The model developed utilizes a contact-stress analysis of an arbitrarily shaped object in a multifingered grasp. The fingers and the object are all treated as elastic bodies, and the region of contact is modeled as a deformable surface patch. The relationship between the friction and normal forces is nonlocal and nonlinear in nature and departs from the Coulomb approximation. The nature of the constraints arising out of conditions for compatibility and static equilibrium motivated the formulation of the model as a nonlinear constrained minimization problem. The model is able to predict the magnitude of the inwardly directed normal forces and both the magnitude and direction of the tangential (friction) forces at each finger-object interface for grasped objects in static equilibrium.
A Minority Stress Model for Suicidal Ideation in Gay Men.
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.
Field Theoretic Investigations in Current Algebra
NASA Astrophysics Data System (ADS)
Jackiw, Roman
The following sections are included: * Introduction * Canonical and Space-Time Constraints in Current Algebra * Canonical Theory of Currents * Space-Time Constraints on Commutators * Space-Time Constraints on Green's Functions * Space-Time Constraints on Ward Identities * Schwinger Terms * Discussion * The Bjorken-Johnson-Low Limit * The π 0 → 2γ Problem * Preliminaries * Sutherland-Veltman Theorem * Model Calculation * Anomalous Ward Identity * Anomalous Commutators * Anomalous Divergence of Axial Current * Discussion * Electroproduction Sum Rules * Preliminaries * Derivation of Sum Rules, Naive Method * Derivation of Sum Rules, Dispersive Method * Model Calculation * Anomalous Commutators * Discussion * Discussion of Anomalies in Current Algebra * Miscellaneous Anomalies * Non-Perturbative Arguments for Anomalies * Models without Anomalies * Discussion * Approximate Scale Symmetry * Introduction * Canonical Theory of Scale and Conformal Transformations * Ward Identities and Trace Identities * False Theorems * True Theorems * EXERCISES * SOLUTIONS
Work stress models and diurnal cortisol variations: The SALVEO study.
Marchand, Alain; Juster, Robert-Paul; Durand, Pierre; Lupien, Sonia J
2016-04-01
The objective of this study was to assess components, subscales, and interactions proposed by the popular Job Demand-Control (JDC), Job Demand-Control-Support (JDCS), and Effort-Reward Imbalance (ERI) work stress models in relation to diurnal variation of the stress hormone cortisol. Participants included 401 day-shift workers employed from a random sampling of 34 Canadian workplaces. Questionnaires included the Job Content Questionnaire to measure psychological demands, decision latitude, and social support as well as the Effort-Reward Imbalance Questionnaire to measure effort, reward, and overcommitment. Salivary cortisol was collected on 2 working days at awaking, +30 min after awaking, 1400h, 1600h, and bedtime. Multilevel regressions with 3 levels (time of day, workers, workplaces) were performed. Results revealed that JDC, JDCS and ERI interactions were not statistically associated with variations in diurnal cortisol concentrations. By contrast when assessing specific work stress subscales, increased psychological demands were linked to decreased bedtime cortisol, increased job recognition was linked to increased cortisol +30 min after waking and at bedtime, and finally increased overcommitment was linked to increased awakening cortisol and decreased cortisol at 1400h, 1600h, and bedtime. Sex moderation effects principally among men were additionally detected for psychological demands, total social support, and supervisor support. Our findings suggest that components and subsubscales of these popular work stress models rather than theorized interactions are more meaningful in explaining diurnal cortisol variations. In particular, psychological demands, job recognition, overcommitment, and to a lesser extent social support at work are the most significant predictors of diurnal cortisol variation in this large sample of Canadian workers. Importantly, the overall effect sizes of these subscales that explained diurnal cortisol concentrations were weak.
Liu, Mi; Xu, Feifei; Tao, Tianqi; Song, Dandan; Li, Dong; Li, Yuzhen; Guo, Yucheng; Liu, Xiuhua
2016-01-01
ABSTRACT Objective Posttraumatic stress disorder (PTSD) is an independent risk factor for cardiovascular diseases. This study investigated the molecular mechanisms underlying myocardial injury induced by simulated PTSD. Methods Sprague-Dawley rats were randomly divided into two groups: control group (n = 18) and PTSD group (n = 30). The PTSD model was replicated using the single prolonged stress (SPS) method. On the 14th day poststress, the apoptotic cells in myocardium were assessed using both TUNEL method and transmission electron microscopy; the protein levels of the endoplasmic reticulum stress (ERS) molecules were measured by using Western blotting analysis. Results Exposure to SPS resulted in characteristic morphologic changes of apoptosis in cardiomyocytes assessed by transmission electron microscopy. Moreover, TUNEL staining was also indicative of the elevated apoptosis rate of cardiomyocytes from the SPS rats (30.69% versus 7.26%, p < .001). Simulated PTSD also induced ERS in myocardium, demonstrated by up-regulation of protein levels of glucose-regulated protein 78 (0.64 versus 0.26, p = .017), calreticulin (p = .040), and CCAAT/enhancer-binding protein-homologous protein (0.95 versus 0.43, p = .047), phosphorylation of protein kinase RNA–like ER kinase (p = .003), and caspase 12 activation (0.30 versus 0.06, p < .001) in myocardium from the SPS rats. The ratio of Bcl-2 to Bax decreased significantly in myocardium from the SPS rats (p = .005). Conclusions The ERS-related apoptosis mediated by the protein kinase RNA–like ER kinase/CCAAT/enhancer-binding protein-homologous protein and caspase 12 pathways may be associated with myocardial injury in a rat model simulating PTSD. This study may advance our understanding of how PTSD contributes to myocardial injury on a molecular level. PMID:27359173
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.
Critical assessment of Reynolds stress turbulence models using homogeneous flows
NASA Astrophysics Data System (ADS)
Shabbir, Aamir; Shih, Tsan-Hsing
1992-12-01
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.
Patterns to Develop Algebraic Reasoning
ERIC Educational Resources Information Center
Stump, Sheryl L.
2011-01-01
What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…
Viterbi/algebraic hybrid decoder
NASA Technical Reports Server (NTRS)
Boyd, R. W.; Ingels, F. M.; Mo, C.
1980-01-01
Decoder computer program is hybrid between optimal Viterbi and optimal algebraic decoders. Tests have shown that hybrid decoder outperforms any strictly Viterbi or strictly algebraic decoder and effectively handles compound channels. Algorithm developed uses syndrome-detecting logic to direct two decoders to assume decoding load alternately, depending on real-time channel characteristics.
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.)
ERIC Educational Resources Information Center
1997
Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…
Elementary maps on nest algebras
NASA Astrophysics Data System (ADS)
Li, Pengtong
2006-08-01
Let , be algebras and let , be maps. An elementary map of is an ordered pair (M,M*) such that for all , . In this paper, the general form of surjective elementary maps on standard subalgebras of nest algebras is described. In particular, such maps are automatically additive.
Linear algebra and image processing
NASA Astrophysics Data System (ADS)
Allali, Mohamed
2010-09-01
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.
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.)
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 the…
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…
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…
NASA Astrophysics Data System (ADS)
Fernández Núñez, J.; García Fuertes, W.; Perelomov, A. M.
2008-02-01
In a previous paper, we studied the characters and Clebsch-Gordan series for the exceptional Lie algebra E7 by relating them to the quantum trigonometric Calogero-Sutherland Hamiltonian with the coupling constant κ = 1. We now extend that approach to the case of an arbitrary coupling constant.
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.
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…
Predictable stress versus unpredictable stress: a comparison in a rodent model of stroke.
Zucchi, Fabíola C R; Kirkland, Scott W; Jadavji, Nafisa M; van Waes, Linda T; Klein, Alexander; Supina, Rebecca D; Metz, Gerlinde A
2009-12-14
Previous studies have associated stress with poor outcome in individuals affected by stroke. It was suggested that the effects of stress depend on the stressor's type and strength. Here we compare the effects of chronic predictable restraint stress and chronic unpredictable variable stress on motor recovery after focal lesion in the rat motor cortex. Adult male rats were pre-trained and tested in skilled reaching and skilled walking tasks. Animals were assigned to daily treatments of either restraint stress or variable stress starting 1 week prior to lesion up to 2 weeks post-lesion. One group served as lesion only control. The results revealed a distinct pattern of recovery and compensation of skilled movement. Animals exposed to predictable restraint stress had significantly lower reaching success at both pre- and post-lesion time points, and higher error rates in skilled walking when compared to lesion controls. Overall, restraint stress induced more pronounced motor impairments prior to and after injury than variable stress. Variable stress increased the number of attempts required to grasp food pellets and changed movement pattern performance. By contrast, variable stress improved limb placement accuracy when compared to lesion controls. The behavioural changes were not accompanied by differences in infarct size. These findings are in agreement with other studies reporting that both chronic predicable restraint stress and unpredictable variable stress influence the course of recovery following stroke, however, restraint stress might affect stroke recovery through a different route than variable stress.
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.
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
NASA Astrophysics Data System (ADS)
Tsue, Yasuhiko; Providência, Constança; Providência, João da; Yamamura, Masatoshi
2016-08-01
Based on the results for the minimum weight states obtained in the previous paper (I), an idea of how to construct the linearly independent basis is proposed for the SU(n) Lipkin model. This idea starts in setting up m independent SU(2) subalgebras in the cases with n=2m and n=2m+1 (m=2,3,4,…). The original representation is re-formed in terms of the spherical tensors for the SU(n) generators built under the SU(2) subalgebras. Through this re-formation, the SU(m) subalgebra can be found. For constructing the linearly independent basis, not only the SU(2) algebras but also the SU(m) subalgebra play a central role. Some concrete results in the cases with n=2, 3, 4, and 5 are presented.
Modeling of stress distributions on the microstructural level in Alloy 600
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.
... flu shot, are less effective for them. Some people cope with stress more effectively than others. It's important to know your limits when it comes to stress, so you can avoid more serious health effects. NIH: National Institute of Mental Health
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)
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…
Vascular wall shear stress in zebrafish model of early atherosclerosis
NASA Astrophysics Data System (ADS)
Choi, Woorak; Seo, Eunseok; Yeom, Eunseop; Lee, Sang Joon
2016-11-01
Although atherosclerosis is a multifactorial disease, the role of hemodynamic force has strong influence on the outbreak of the disease. Low and oscillating wall shear stress (WSS) is associated with the incidence of atherosclerosis. Many researchers have investigated relationships between WSS and the occurrence of atherosclerosis using in vitro and in vivo models. However, these models possess technological limitations in mimicking real biophysiological conditions and monitoring the temporal progression of atherosclerosis. In this study, a hypercholesterolaemic zebrafish model was established as a novel model to resolve these technical limitations. WSS in blood vessels of 15 days post-fertilisation zebrafish was measured using a micro PIV technique, and the spatial distribution of lipids inside blood vessels was quantitatively visualized using a confocal microscopy. As a result, lipids are mainly deposited in the regions of low WSS. The oscillating WSS is not induced by blood flows in the zebrafish disease model. The present hypercholesterolaemic zebrafish model would be useful for understanding the effect of WSS on the early stage of atherosclerosis. This work was supported by the National Research Foundation of Korea (NRF) under a Grant funded by the Korean government (MSIP) (No. 2008-0061991).
Stress magnetization model for magnetostriction in multiferroic composite
NASA Astrophysics Data System (ADS)
Gualdi, A. J.; Zabotto, F. L.; Garcia, D.; de Oliveira, A. J. A.
2013-08-01
An alternative to obtain multiferroic materials is the production of composite materials that combine ferroelectric and magnetic materials. In particular, the use of magnetostrictive materials as ferromagnetic phase in composites is very important because the mechanical stress applied in ferroelectric phase induces the appearance of magnetoelectric effect. In this work, we have proposed a generalized model for the magnetostriction dependence with the magnetization of the 0-3 type composite magnetoelectric materials. Including both piezomagnetic and stress dependence in the magnetostriction, a relevant improvement was reached as compared to the ordinary square magnetization model. Based on the Gibbs free energy expansion, the magnetostriction behavior of the composite (1-x)Pb(Mg1/3Nb2/3)-xPbTiO3/CoFe2O4 at 300 K and 5 K is described. Furthermore, using the piezomagnetic correction, the magnetostriction data for the pure CoFe2O4 is fitted showing that this ferrite presents a relevant piezomagnetic effect.
Abnormal Fear Memory as a Model for Posttraumatic Stress Disorder.
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.
Computer Models of Stress, Allostasis, and Acute and Chronic Diseases
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
Quantum algebra of N superspace
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.
Chronic stress impacts the cardiovascular system: animal models and clinical outcomes.
Golbidi, Saeid; Frisbee, Jefferson C; Laher, Ismail
2015-06-15
Psychological stresses are associated with cardiovascular diseases to the extent that cardiovascular diseases are among the most important group of psychosomatic diseases. The longstanding association between stress and cardiovascular disease exists despite a large ambiguity about the underlying mechanisms. An array of possibilities have been proposed including overactivity of the autonomic nervous system and humoral changes, which then converge on endothelial dysfunction that initiates unwanted cardiovascular consequences. We review some of the features of the two most important stress-activated systems, i.e., the humoral and nervous systems, and focus on alterations in endothelial function that could ensue as a result of these changes. Cardiac and hematologic consequences of stress are also addressed briefly. It is likely that activation of the inflammatory cascade in association with oxidative imbalance represents key pathophysiological components of stress-induced cardiovascular changes. We also review some of the commonly used animal models of stress and discuss the cardiovascular outcomes reported in these models of stress. The unique ability of animals for adaptation under stressful conditions lessens the extrapolation of laboratory findings to conditions of human stress. An animal model of unpredictable chronic stress, which applies various stress modules in a random fashion, might be a useful solution to this predicament. The use of stress markers as indicators of stress intensity is also discussed in various models of animal stress and in clinical studies.
Charge transfer in algebraic quantum field theory
NASA Astrophysics Data System (ADS)
Wright, Jill Dianne
We discuss aspects of the algebraic structure of quantum field theory. We take the view that the superselection structure of a theory should be determinable from the vacuum representation of the observable algebra, and physical properties of the charge. Hence one determines the nature of the charge transfer operations: the automorphisms of the observable algebra corresponding to the movement of charge along space-time paths. New superselection sectors are obtained from the vacuum sector by an automorphism which is a limit of charge transfer operations along paths with an endpoint tending to spacelike infinity. Roberts has shown that for a gauge theory of the first kind, the charge transfer operations for a given charge form a certain kind of 1-cocycle over Minkowski space. The local 1-cohomology group of their equivalence classes corresponds to the superselection structure. The exact definition of the cohomology group depends on the properties of the charge. Using displaced Fock representations of free fields, we develop model field theories which illustrate this structure. The cohomological classification of displaced Fock representations has been elucidated by Araki. For more general representations, explicit determination of the cohomology group is a hard problem. Using our models, we can illustrate ways in which fields with reasonable physical properties depart fromthe abovementioned structure. In 1+1 dimensions, we use the Streater-Wilde model to illustrate explicitly the representation-dependence of the cohomology structure, and the direction-dependence of the limiting charge transfer operation. The cohomology structure may also be representation-dependent in higher-dimensional theories without strict localization of charge, for example the electromagnetic field. The algebraic structure of the electromagnetic field has many other special features, which we discuss in relation to the concept of charge transfer. We also give some indication of the modifications
Investigating Teacher Noticing of Student Algebraic Thinking
ERIC Educational Resources Information Center
Walkoe, Janet Dawn Kim
2013-01-01
Learning algebra is critical for students in the U.S. today. Algebra concepts provide the foundation for much advanced mathematical content. In addition, algebra serves as a gatekeeper to opportunities such as admission to college. Yet many students in the U.S. struggle in algebra classes. Researchers claim that one reason for these difficulties…
Central extensions of Lax operator algebras
NASA Astrophysics Data System (ADS)
Schlichenmaier, M.; Sheinman, O. K.
2008-08-01
Lax operator algebras were introduced by Krichever and Sheinman as a further development of Krichever's theory of Lax operators on algebraic curves. These are almost-graded Lie algebras of current type. In this paper local cocycles and associated almost-graded central extensions of Lax operator algebras are classified. It is shown that in the case when the corresponding finite-dimensional Lie algebra is simple the two-cohomology space is one-dimensional. An important role is played by the action of the Lie algebra of meromorphic vector fields on the Lax operator algebra via suitable covariant derivatives.
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.
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.
Asymptotic aspect of derivations in Banach algebras.
Roh, Jaiok; Chang, Ick-Soon
2017-01-01
We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.
Computing Matrix Representations of Filiform Lie Algebras
NASA Astrophysics Data System (ADS)
Ceballos, Manuel; Núñez, Juan; Tenorio, Ángel F.
In this paper, we compute minimal faithful unitriangular matrix representations of filiform Lie algebras. To do it, we use the nilpotent Lie algebra, g_n, formed of n ×n strictly upper-triangular matrices. More concretely, we search the lowest natural number n such that the Lie algebra g_n contains a given filiform Lie algebra, also computing a representative of this algebra. All the computations in this paper have been done using MAPLE 9.5.
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
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.
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.
Cartooning in Algebra and Calculus
ERIC Educational Resources Information Center
Moseley, L. Jeneva
2014-01-01
This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.
GCD, LCM, and Boolean Algebra?
ERIC Educational Resources Information Center
Cohen, Martin P.; Juraschek, William A.
1976-01-01
This article investigates the algebraic structure formed when the process of finding the greatest common divisor and the least common multiple are considered as binary operations on selected subsets of positive integers. (DT)
NASA Technical Reports Server (NTRS)
Klumpp, A. R.; Lawson, C. L.
1988-01-01
Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.
Algebraic isomorphism in two-dimensional anomalous gauge theories
Carvalhaes, C.G.; Natividade, C.P.
1997-08-01
The operator solution of the anomalous chiral Schwinger model is discussed on the basis of the general principles of Wightman field theory. Some basic structural properties of the model are analyzed taking a careful control on the Hilbert space associated with the Wightman functions. The isomorphism between gauge noninvariant and gauge invariant descriptions of the anomalous theory is established in terms of the corresponding field algebras. We show that (i) the {Theta}-vacuum representation and (ii) the suggested equivalence of vector Schwinger model and chiral Schwinger model cannot be established in terms of the intrinsic field algebra. {copyright} 1997 Academic Press, Inc.
Coherent States for Hopf Algebras
NASA Astrophysics Data System (ADS)
Škoda, Zoran
2007-07-01
Families of Perelomov coherent states are defined axiomatically in the context of unitary representations of Hopf algebras. A global geometric picture involving locally trivial noncommutative fibre bundles is involved in the construction. If, in addition, the Hopf algebra has a left Haar integral, then a formula for noncommutative resolution of identity in terms of the family of coherent states holds. Examples come from quantum groups.
Multiplier operator algebras and applications
Blecher, David P.; Zarikian, Vrej
2004-01-01
The one-sided multipliers of an operator space X are a key to “latent operator algebraic structure” in X. We begin with a survey of these multipliers, together with several of the applications that they have had to operator algebras. We then describe several new results on one-sided multipliers, and new applications, mostly to one-sided M-ideals. PMID:14711990
Visceral obesity and psychosocial stress: a generalised control theory model
NASA Astrophysics Data System (ADS)
Wallace, Rodrick
2016-07-01
The linking of control theory and information theory via the Data Rate Theorem and its generalisations allows for construction of necessary conditions statistical models of body mass regulation in the context of interaction with a complex dynamic environment. By focusing on the stress-related induction of central obesity via failure of HPA axis regulation, we explore implications for strategies of prevention and treatment. It rapidly becomes evident that individual-centred biomedical reductionism is an inadequate paradigm. Without mitigation of HPA axis or related dysfunctions arising from social pathologies of power imbalance, economic insecurity, and so on, it is unlikely that permanent changes in visceral obesity for individuals can be maintained without constant therapeutic effort, an expensive - and likely unsustainable - public policy.
ERIC Educational Resources Information Center
Hitt, Fernando; Morasse, Christian
2009-01-01
Introduction: In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We…
Constitutive Modeling, Nonlinear Behavior, and the Stress-Optic Law
2011-01-01
uncrosslinked PIB following a step shear strain = 2.5. Solid curve is the linear fitting yielding the indicated stress optical coefficient. (top) Ratio of...and solutions. Figure 39 [30] shows that conformance to the stress optic law is maintained during stress relaxation of an uncrosslinked PIB for both...calculation only becoming evident for strain reversals. Figure 16. Stress measured for a PIB melt subjected to a shear strain of 1.77 at t = 0 that was
Stress Evaluation and Model Validation Using Laser Ultrasonics
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.
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
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…
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
Praharso, Nurul F; Tear, Morgan J; Cruwys, Tegan
2017-01-01
The relationship between stressful life transitions and wellbeing is well established, however, the protective role of social connectedness has received mixed support. We test two theoretical models, the Stress Buffering Hypothesis and the Social Identity Model of Identity Change, to determine which best explains the relationship between social connectedness, stress, and wellbeing. Study 1 (N=165) was an experiment in which participants considered the impact of moving cities versus receiving a serious health diagnosis. Study 2 (N=79) was a longitudinal study that examined the adjustment of international students to university over the course of their first semester. Both studies found limited evidence for the buffering role of social support as predicted by the Stress Buffering Hypothesis; instead people who experienced a loss of social identities as a result of a stressor had a subsequent decline in wellbeing, consistent with the Social Identity Model of Identity Change. We conclude that stressful life events are best conceptualised as identity transitions. Such events are more likely to be perceived as stressful and compromise wellbeing when they entail identity loss.
Model Determined for Predicting Fatigue Lives of Metal Matrix Composites Under Mean Stresses
NASA Technical Reports Server (NTRS)
Lerch, Bradley
1997-01-01
Aircraft engine components invariably are subjected to mean stresses over and above the cyclic loads. In monolithic materials, it has been observed that tensile mean stresses are detrimental and compressive mean stresses are beneficial to fatigue life in comparison to a base of zero mean stress. Several mean stress models exist for monolithic metals, but each differ quantitatively in the extent to which detrimental or beneficial effects are ascribed. There have been limited attempts to apply these models to metal matrix composites. At the NASA Lewis Research Center, several mean stress models--the Smith-Watson- Topper, Walker, Normalized Goodman, and Soderberg models--were examined for applicability to this class of composite materials. The Soderberg approach, which normalizes the mean stress to a 0.02-percent yield strength, was shown to best represent the effect of mean stresses over the range covered. The other models varied significantly in their predictability and often failed to predict the composite behavior at very high tensile mean stresses. This work is the first to systematically demonstrate the influence of mean stresses on metal matrix composites and model their effects. Attention also was given to fatigue-cracking mechanisms in the Ti-15-3 matrix and to micromechanics analyses of mean stress effects.
Multifractal vector fields and stochastic Clifford algebra.
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2015-12-01
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Multifractal vector fields and stochastic Clifford algebra
Schertzer, Daniel Tchiguirinskaia, Ioulia
2015-12-15
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Adamec, Robert; Fougere, Dennis; Risbrough, Victoria
2010-07-01
Post traumatic stress disorder (PTSD) is a chronic anxiety disorder initiated by an intensely threatening, traumatic event. There is a great need for more efficacious pharmacotherapy and preventive treatments for PTSD. In animals, corticotropin-releasing factor (CRF) and the CRF1 receptor play a critical role in behavioural and neuroendocrine responses to stress. We tested the hypothesis that CRF1 activation is required for initiation and consolidation of long-term effects of trauma on anxiety-like behaviour in the predator exposure (predator stress) model of PTSD. Male C57BL6 mice were treated with the selective CRF1 antagonist CRA0450 (2, 20 mg/kg) 30 min before or just after predator stress. Long-term effects of stress on rodent anxiety were measured 7 d later using acoustic startle, elevated plus maze (EPM), light/dark box, and hole-board tests. Predator stress increased startle amplitude and delayed startle habituation, increased time in and decreased exits from the dark chamber in the light/dark box test, and decreased risk assessment in the EPM. CRF1 antagonism had limited effects on these behaviours in non-stressed controls, with the high dose decreasing risk assessment in the EPM. However, in stressed animals CRF1 antagonism blocked initiation and consolidation of stressor effects on startle, and returned risk assessment to baseline levels in predator-stressed mice. These findings implicate CRF1 activation in initiation and post-trauma consolidation of predator stress effects on anxiety-like behaviour, specifically on increased arousal as measured by exaggerated startle behaviours. These data support further research of CRF1 antagonists as potential prophylactic treatments for PTSD.
Implementation and model to model intercomparison of 12 heat stress metrics
NASA Astrophysics Data System (ADS)
Buzan, Jonathan R.
Earth system models simulate the dynamics of the most complex systems on our planet with some success. Despite the overwhelming sophistication of these models, which include dynamical interactions of ocean, atmosphere, vegetation, ice, and land-surface properties, they fail to include the most important element. People. Humans are also a complex physical-biological system and coupling of human physiology within an Earth Systems Modeling framework is challenging. This thesis presents results that tackle one particular component of human physiological climate interaction--a representation of heat stress on human physiology. Twelve different metrics were implemented and analyzed. These metrics represent a variety of philosophical approaches to characterizing heat stress: thermal comfort, physiological responses, and first principle physics. We implemented these 12 metrics into the Community Land Model (CLM4.5). All of the metrics implemented measure the covariance of near surface atmospheric variables: temperature, pressure, and humidity. Results show that heat stress may be broken into two regimes; arid and non-arid regions (i.e. the rest of the land surface). Additionally, results show that the highest heat stress zones are a robust feature with low variability. Temperatures vary by +/-3°C as compared to +/-1°C wet bulb temperatures, and is consistent over a vast area of Earth.
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.
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…
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…
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…
Extending the algebraic formalism for genome rearrangements to include linear chromosomes.
Feijão, Pedro; Meidanis, João
2013-01-01
Algebraic rearrangement theory, as introduced by Meidanis and Dias, focuses on representing the order in which genes appear in chromosomes, and applies to circular chromosomes only. By shifting our attention to genome adjacencies, we introduce the adjacency algebraic theory, extending the original algebraic theory to linear chromosomes in a very natural way, also allowing the original algebraic distance formula to be used to the general multichromosomal case, with both linear and circular chromosomes. The resulting distance, which we call algebraic distance here, is very similar to, but not quite the same as, double-cut-and-join distance. We present linear time algorithms to compute it and to sort genomes. We show how to compute the rearrangement distance from the adjacency graph, for an easier comparison with other rearrangement distances. A thorough discussion on the relationship between the chromosomal and adjacency representation is also given, and we show how all classic rearrangement operations can be modeled using the algebraic theory.
Cano, Miguel A.; Heppner, Whitney L.; Stewart, Diana W.; Correa-Fernández, Virmarie; Vidrine, Jennifer Irvin; Li, Yisheng; Cinciripini, Paul M.; Ahluwalia, Jasjit S.; Wetter, David W.
2014-01-01
Mindfulness-based strategies have received empirical support for improving coping with stress and reducing alcohol use. The present study presents a moderated mediation model to explain how mindfulness might promote healthier drinking patterns. This model posits that mindfulness reduces perceived stress, leading to less alcohol use, and also weakens the linkage between stress and alcohol use. African American smokers (N = 399, 51% female, Mage = 42) completed measures of dispositional mindfulness, perceived stress, quantity of alcohol use, frequency of binge drinking, and alcohol use disorder symptoms. Participants with higher levels of dispositional mindfulness reported less psychosocial stress and lower alcohol use on all measures. Furthermore, mindfulness moderated the relationship between perceived stress and quantity of alcohol consumption. Specifically, higher perceived stress was associated with increased alcohol use among participants low, but not high, in mindfulness. Mindfulness may be one strategy to reduce perceived stress and associated alcohol use among African American smokers. PMID:25848408
Novikov algebras with associative bilinear forms
NASA Astrophysics Data System (ADS)
Zhu, Fuhai; Chen, Zhiqi
2007-11-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.
Stress distribution in a premolar 3D model with anisotropic and isotropic enamel.
Munari, Laís S; Cornacchia, Tulimar P M; Moreira, Allyson N; Gonçalves, Jason B; De Las Casas, Estevam B; Magalhães, Cláudia S
2015-08-01
The aim of this study was to compare the areas of stress concentration in a three-dimensional (3D) premolar tooth model with anisotropic or isotropic enamel using the finite element method. A computed tomography was imported to an image processing program to create the tooth model which was exported to a 3D modeling program. The mechanical properties and loading conditions were prescribed in Abaqus. In order to evaluate stresses, axial and oblique loads were applied simulating realistic conditions. Compression stress was observed on the side of load application, and tensile stress was observed on the opposite side. Tensile stress was concentrated mainly in the cervical region and in the alveolar insertion bone. Although stress concentration analyses of the isotropic 3D models produced similar stress distribution results when compared to the anisotropic models, tensile stress values shown by anisotropic models were smaller than the isotropic models. Oblique loads resulted in higher values of tensile stresses, which concentrate mainly in the cervical area of the tooth and in the alveolar bone insertion. Anisotropic properties must be utilized in enamel stress evaluation in non-carious cervical lesions.
NASA Astrophysics Data System (ADS)
Nicolas, B.; Gilbert, M. E.; Paw U, K. T.
2015-12-01
Soil-Vegetation-Atmosphere Transfer (SVAT) models are based upon well understood steady state photosynthetic physiology - the Farquhar-von Caemmerer-Berry model (FvCB). However, representations of physiological stress and damage have not been successfully integrated into SVAT models. Generally, it has been assumed that plants will strive to conserve water at higher temperatures by reducing stomatal conductance or adjusting osmotic balance, until potentially damaging temperatures and the need for evaporative cooling become more important than water conservation. A key point is that damage is the result of combined stresses: drought leads to stomatal closure, less evaporative cooling, high leaf temperature, less photosynthetic dissipation of absorbed energy, all coupled with high light (photosynthetic photon flux density; PPFD). This leads to excess absorbed energy by Photosystem II (PSII) and results in photoinhibition and damage, neither are included in SVAT models. Current representations of photoinhibition are treated as a function of PPFD, not as a function of constrained photosynthesis under heat or water. Thus, it seems unlikely that current models can predict responses of vegetation to climate variability and change. We propose a dynamic model of damage to Rubisco and RuBP-regeneration that accounts, mechanistically, for the interactions between high temperature, light, and constrained photosynthesis under drought. Further, these predictions are illustrated by key experiments allowing model validation. We also integrated this new framework within the Advanced Canopy-Atmosphere-Soil Algorithm (ACASA). Preliminary results show that our approach can be used to predict reasonable photosynthetic dynamics. For instances, a leaf undergoing one day of drought stress will quickly decrease its maximum quantum yield of PSII (Fv/Fm), but it won't recover to unstressed levels for several days. Consequently, cumulative effect of photoinhibition on photosynthesis can cause
Universal Algebraic Varieties and Ideals in Physics:. Field Theory on Algebraic Varieties
NASA Astrophysics Data System (ADS)
Iguchi, Kazumoto
A class of universal algebraic varieties in physics is discussed herein using the concepts of determinant ideals in algebraic geometry. It is shown that these algebraic varieties arise with very different physical contexts in many branches of physics and mathematics from high energy physics theory to chaos theory. In these physical systems the models are constructed by using the fields on usual manifolds such as vector fields in a Euclidean space and a Minkowskian space. But there is a universal mathematical aspect of linear algebra for linear vector spaces, where the linear independency and dependency are described using the Gramians of the vectors. These Gramians form a class of hypersurfaces in a higher-dimensional mathematical space: If there exist g vectors vi in an n-dimensional Euclidean space, the Gramian Gg is given as a g × g determinant Gg=Det[xij] with the inner products xij=(vi,vj), and exists in a g(g-1)/2-[g(g+1)/2-] dimensional space if the vectors are (not) normalized, xii=1 (xii ≠ 1). It is also shown that the Gramians are invariant under automorphisms of the vectors. The mathematical structure of the Gramians is revealed to be equivalent to the concepts of determinant ideals Ig(v), each element of which is a g × g determinant constructed from components of an arbitrary N×N matrix with N>n and which have inclusion relation: R=I0(v)⊃ I1(v) ⊃···⊃ Ig(v) ⊃···, and Ig(v)=0 if g>n. In the various physical systems the ideals naturally emerge to give us dynamical flows on the hypersurfaces, and therefore, it is called the field theory on algebraic varieties. This viewpoint provides us a grand viewpoint in physics and mathematics.
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 factors associated with methamphetamine use among a cross-sectional sample of rural White and Native American adolescents (n = 573). Results of logistic regression analyses revealed mixed support for the stress process model; while stress exposure and family methamphetamine use predicted past year methamphetamine use, the inclusion of these variables failed to attenuate the association between race and past year use.
Modelling of the Reynolds stress redistribution with a wall effect vector
NASA Astrophysics Data System (ADS)
Shima, Nobuyuki; Kobayashi, Hiroshi
2007-04-01
The idea of the elliptic relaxation method of Durbin [1993. A Reynolds stress model for near-wall turbulence. J. Fluid Mech. 249, 465-498] is employed to construct a simpler and numerically more stable model for the Reynolds stress redistribution. The stress redistribution process in near-wall regions is modelled by using a vector which represents the wall effect. The vector is obtained by solving an elliptic equation with a simple wall boundary condition. The present model and Durbin's model are tested in five different flows of fundamental importance. The performance of the present model is comparable to that of the Durbin model with much less numerical effort.
Quantum Q systems: from cluster algebras to quantum current algebras
NASA Astrophysics Data System (ADS)
Di Francesco, Philippe; Kedem, Rinat
2017-02-01
This paper gives a new algebraic interpretation for the algebra generated by the quantum cluster variables of the A_r quantum Q-system (Di Francesco and Kedem in Int Math Res Not IMRN 10:2593-2642, 2014). We show that the algebra can be described as a quotient of the localization of the quantum algebra U_{√{q}}({n}[u,u^{-1}])subset U_{√{q}}(widehat{{sl}}_2), in the Drinfeld presentation. The generating current is made up of a subset of the cluster variables which satisfy the Q-system, which we call fundamental. The other cluster variables are given by a quantum determinant-type formula, and are polynomials in the fundamental generators. The conserved quantities of the discrete evolution (Di Francesco and Kedem in Adv Math 228(1):97-152, 2011) described by quantum Q-system generate the Cartan currents at level 0, in a non-standard polarization. The rest of the quantum affine algebra is also described in terms of cluster variables.
Perrine, Shane A; Eagle, Andrew L; George, Sophie A; Mulo, Kostika; Kohler, Robert J; Gerard, Justin; Harutyunyan, Arman; Hool, Steven M; Susick, Laura L; Schneider, Brandy L; Ghoddoussi, Farhad; Galloway, Matthew P; Liberzon, Israel; Conti, Alana C
2016-04-15
Appropriate animal models of posttraumatic stress disorder (PTSD) are needed because human studies remain limited in their ability to probe the underlying neurobiology of PTSD. Although the single prolonged stress (SPS) model is an established rat model of PTSD, the development of a similarly-validated mouse model emphasizes the benefits and cross-species utility of rodent PTSD models and offers unique methodological advantages to that of the rat. Therefore, the aims of this study were to develop and describe a SPS model for mice and to provide data that support current mechanisms relevant to PTSD. The mouse single prolonged stress (mSPS) paradigm, involves exposing C57Bl/6 mice to a series of severe, multimodal stressors, including 2h restraint, 10 min group forced swim, exposure to soiled rat bedding scent, and exposure to ether until unconsciousness. Following a 7-day undisturbed period, mice were tested for cue-induced fear behavior, effects of paroxetine on cue-induced fear behavior, extinction retention of a previously extinguished fear memory, dexamethasone suppression of corticosterone (CORT) response, dorsal hippocampal glucocorticoid receptor protein and mRNA expression, and prefrontal cortex glutamate levels. Exposure to mSPS enhanced cue-induced fear, which was attenuated by oral paroxetine treatment. mSPS also disrupted extinction retention, enhanced suppression of stress-induced CORT response, increased mRNA expression of dorsal hippocampal glucocorticoid receptors and decreased prefrontal cortex glutamate levels. These data suggest that the mSPS model is a translationally-relevant model for future PTSD research with strong face, construct, and predictive validity. In summary, mSPS models characteristics relevant to PTSD and this severe, multimodal stress modifies fear learning in mice that coincides with changes in the hypothalamo-pituitary-adrenal (HPA) axis, brain glucocorticoid systems, and glutamatergic signaling in the prefrontal cortex.
Using chronic social stress to model postpartum depression in lactating rodents.
Carini, Lindsay M; Murgatroyd, Christopher A; Nephew, Benjamin C
2013-06-10
Exposure to chronic stress is a reliable predictor of depressive disorders, and social stress is a common ethologically relevant stressor in both animals and humans. However, many animal models of depression were developed in males and are not applicable or effective in studies of postpartum females. Recent studies have reported significant effects of chronic social stress during lactation, an ethologically relevant and effective stressor, on maternal behavior, growth, and behavioral neuroendocrinology. This manuscript will describe this chronic social stress paradigm using repeated exposure of a lactating dam to a novel male intruder, and the assessment of the behavioral, physiological, and neuroendocrine effects of this model. Chronic social stress (CSS) is a valuable model for studying the effects of stress on the behavior and physiology of the dam as well as her offspring and future generations. The exposure of pups to CSS can also be used as an early life stress that has long term effects on behavior, physiology, and neuroendocrinology.
Posttraumatic Stress Disorder: A Theoretical Model of the Hyperarousal Subtype
Weston, Charles Stewart E.
2014-01-01
Posttraumatic stress disorder (PTSD) is a frequent and distressing mental disorder, about which much remains to be learned. It is a heterogeneous disorder; the hyperarousal subtype (about 70% of occurrences and simply termed PTSD in this paper) is the topic of this article, but the dissociative subtype (about 30% of occurrences and likely involving quite different brain mechanisms) is outside its scope. A theoretical model is presented that integrates neuroscience data on diverse brain regions known to be involved in PTSD, and extensive psychiatric findings on the disorder. Specifically, the amygdala is a multifunctional brain region that is crucial to PTSD, and processes peritraumatic hyperarousal on grounded cognition principles to produce hyperarousal symptoms. Amygdala activity also modulates hippocampal function, which is supported by a large body of evidence, and likewise amygdala activity modulates several brainstem regions, visual cortex, rostral anterior cingulate cortex (rACC), and medial orbitofrontal cortex (mOFC), to produce diverse startle, visual, memory, numbing, anger, and recklessness symptoms. Additional brain regions process other aspects of peritraumatic responses to produce further symptoms. These contentions are supported by neuroimaging, neuropsychological, neuroanatomical, physiological, cognitive, and behavioral evidence. Collectively, the model offers an account of how responses at the time of trauma are transformed into an extensive array of the 20 PTSD symptoms that are specified in the Diagnostic and Statistical Manual of Mental Disorders, Fifth edition. It elucidates the neural mechanisms of a specific form of psychopathology, and accords with the Research Domain Criteria framework. PMID:24772094
Neuronal modelling of baroreflex response to orthostatic stress
NASA Astrophysics Data System (ADS)
Samin, Azfar
The accelerations experienced in aerial combat can cause pilot loss of consciousness (GLOC) due to a critical reduction in cerebral blood circulation. The development of smart protective equipment requires understanding of how the brain processes blood pressure (BP) information in response to acceleration. We present a biologically plausible model of the Baroreflex to investigate the neural correlates of short-term BP control under acceleration or orthostatic stress. The neuronal network model, which employs an integrate-and-fire representation of a biological neuron, comprises the sensory, motor, and the central neural processing areas that form the Baroreflex. Our modelling strategy is to test hypotheses relating to the encoding mechanisms of multiple sensory inputs to the nucleus tractus solitarius (NTS), the site of central neural processing. The goal is to run simulations and reproduce model responses that are consistent with the variety of available experimental data. Model construction and connectivity are inspired by the available anatomical and neurophysiological evidence that points to a barotopic organization in the NTS, and the presence of frequency-dependent synaptic depression, which provides a mechanism for generating non-linear local responses in NTS neurons that result in quantifiable dynamic global baroreflex responses. The entire physiological range of BP and rate of change of BP variables is encoded in a palisade of NTS neurons in that the spike responses approximate Gaussian 'tuning' curves. An adapting weighted-average decoding scheme computes the motor responses and a compensatory signal regulates the heart rate (HR). Model simulations suggest that: (1) the NTS neurons can encode the hydrostatic pressure difference between two vertically separated sensory receptor regions at +Gz, and use changes in that difference for the regulation of HR; (2) even though NTS neurons do not fire with a cardiac rhythm seen in the afferents, pulse
A novel modelling and simulation method of hip joint surface contact stress.
Wang, Monan; Wang, Lei; Li, Pengcheng; Fu, Yili
2017-01-02
Understanding the hip joint surface contact stress distribution characteristics is helpful to determine hip joint biomechanical features and abnormal pathological behavior. Firstly, a 3-dimensional static hip joint biomechanical model is built using analytical method of model in order to study biomechanical properties including bearing area, stress distribution and the peak value of the contact stress of the femoral head, which reveals the relationship between the biomechanical properties and its geometric parameters. Secondly, based on the finite element analysis of the hip joint model, the contact stress distribution on the surface of femoral head is acquired under the condition of the different joint force and the acetabulum coverage rate. Finally, according to the evaluation of the femoral head surface stress and contact stress peak under different load distribution, accuracy and universality of the biomechanical model is verified.
Peng, Henry T; Edginton, Andrea N; Cheung, Bob
2013-10-01
Physiologically based pharmacokinetic models were developed using MATLAB Simulink® and PK-Sim®. We compared the capability and usefulness of these two models by simulating pharmacokinetic changes of midazolam under exercise and heat stress to verify the usefulness of MATLAB Simulink® as a generic PBPK modeling software. Although both models show good agreement with experimental data obtained under resting condition, their predictions of pharmacokinetics changes are less accurate in the stressful conditions. However, MATLAB Simulink® may be more flexible to include physiologically based processes such as oral absorption and simulate various stress parameters such as stress intensity, duration and timing of drug administration to improve model performance. Further work will be conducted to modify algorithms in our generic model developed using MATLAB Simulink® and to investigate pharmacokinetics under other physiological stress such as trauma.
NASA Astrophysics Data System (ADS)
Dritselis, Chris D.
2017-04-01
In the first part of this study (Dritselis 2016 Fluid Dyn. Res. 48 015507), the Reynolds stress budgets were evaluated through point-particle direct numerical simulations (pp-DNSs) for the particle-laden turbulent flow in a vertical channel with two- and four-way coupling effects. Here several turbulence models are assessed by direct comparison of the particle contribution terms to the budgets, the dissipation rate, the pressure-strain rate, and the transport rate with the model expressions using the pp-DNS data. It is found that the models of the particle sources to the equations of fluid turbulent kinetic energy and dissipation rate cannot represent correctly the physics of the complex interaction between turbulence and particles. A relatively poor performance of the pressure-strain term models is revealed in the particulate flows, while the algebraic models for the dissipation rate of the fluid turbulence kinetic energy and the transport rate terms can adequately reproduce the main trends due to the presence of particles. Further work is generally needed to improve the models in order to account properly for the momentum exchange between the two phases and the effects of particle inertia, gravity and inter-particle collisions.
Finite Element Modeling of In-Situ Stresses near Salt Bodies
NASA Astrophysics Data System (ADS)
Sanz, P.; Gray, G.; Albertz, M.
2011-12-01
The in-situ stress field is modified around salt bodies because salt rock has no ability to sustain shear stresses. A reliable prediction of stresses near salt is important for planning safe and economic drilling programs. A better understanding of in-situ stresses before drilling can be achieved using finite element models that account for the creeping salt behavior and the elastoplastic response of the surrounding sediments. Two different geomechanical modeling techniques can be distinguished: "dynamic" modeling and "static" modeling. "Dynamic" models, also known as forward models, simulate the development of structural processes in geologic time. This technique provides the evolution of stresses and so it is used to simulate the initiation and development of structural features, such as, faults, folds, fractures, and salt diapers. The original or initial configuration and the unknown final configuration of forward models are usually significantly different therefore geometric non-linearities need to be considered. These models may be difficult to constrain when different tectonic, deposition, and erosion events, and the timing among them, needs to be accounted for. While dynamic models provide insight into the stress evolution, in many cases is very challenging, if not impossible, to forward model a configuration to its known present-day geometry; particularly in the case of salt layers that evolve into highly irregular and complex geometries. Alternatively, "static" models use the present-day geometry and present-day far-field stresses to estimate the present-day in-situ stress field inside a domain. In this case, it is appropriate to use a small deformation approach because initial and final configurations should be very similar, and more important, because the equilibrium of stresses should be stated in the present-day initial configuration. The initial stresses and the applied boundary conditions are constrained by the geologic setting and available data