Berret, Bastien; Darlot, Christian; Jean, Frédéric; Pozzo, Thierry; Papaxanthis, Charalambos; Gauthier, Jean Paul
2008-10-01
An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality
Physical Principles versus Mathematical Rigor.
ERIC Educational Resources Information Center
Patterson, Jim
2000-01-01
While it is most often the case that an understanding of physics can simplify mathematical calculations, occasionally mathematical precision leads directly to a better physical understanding of a situation. Presents an example of a mechanics problem in which careful mathematical derivation can lead directly to a deeper physical understanding of…
Classical and Weak Solutions for Two Models in Mathematical Finance
NASA Astrophysics Data System (ADS)
Gyulov, Tihomir B.; Valkov, Radoslav L.
2011-12-01
We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.
Scaffolding Mathematical Modelling with a Solution Plan
ERIC Educational Resources Information Center
Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner
2015-01-01
In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…
A Mathematical Solution to the Motorway Problem
ERIC Educational Resources Information Center
Michaelson, Matthew T.
2009-01-01
This article presents a mathematical solution to a motorway problem. The motorway problem is an excellent application in optimisation. As it integrates the concepts of trigonometric functions and differentiation, the motorway problem can be used quite effectively as the basis for an assessment tool in senior secondary mathematics subjects.…
Complementary variational principle and duality in mathematical programming.
NASA Technical Reports Server (NTRS)
Chan, W. L.; Leininger, G. G.; Farison, J. B.
1973-01-01
The relationship between the complementary variational principle and duality in mathematical programming is demonstrated through a geometric approach in a Hilbert space setting. A necessary and sufficient condition for the existence of such a principle is given in the case of a convex functional constrained by linear dynamics. Its relationship to the Kuhn-Tucker saddle point theory is indicated. Applications to various programming and control problems are discussed.
Intellectual Engagement and Other Principles of Mathematics Instruction
ERIC Educational Resources Information Center
Peterson, Blake E.; Corey, Douglas L.; Lewis, Benjamin M.; Bukarau, Jared
2013-01-01
In this article, mathematics teachers in the United States were asked what constitutes a high-quality mathematics lesson. The returned responses varied greatly. This same question was asked of Japanese teachers also. For a clearer picture both American and Japanese teachers were directed to comment on videotaped mathematics lessons taught in both…
Acceleration of neutrons in a scheme of a tautochronous mathematical pendulum (physical principles)
Rivlin, Lev A
2010-12-09
We consider the physical principles of neutron acceleration through a multiple synchronous interaction with a gradient rf magnetic field in a scheme of a tautochronous mathematical pendulum. (laser applications and other aspects of quantum electronics)
ERIC Educational Resources Information Center
Nagle, Courtney; Moore-Russo, Deborah
2014-01-01
This article provides an initial comparison of the Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics by examining the fundamental notion of slope. Each set of standards is analyzed using eleven previously identified conceptualizations of slope. Both sets of standards emphasize Functional Property,…
Connection of Scattering Principles: A Visual and Mathematical Tour
ERIC Educational Resources Information Center
Broggini, Filippo; Snieder, Roel
2012-01-01
Inverse scattering, Green's function reconstruction, focusing, imaging and the optical theorem are subjects usually studied as separate problems in different research areas. We show a physical connection between the principles because the equations that rule these "scattering principles" have a similar functional form. We first lead the reader…
ERIC Educational Resources Information Center
Howe, Christine; Luthman, Stefanie; Ruthven, Kenneth; Mercer, Neil; Hofmann, Riikka; Ilie, Sonia; Guardia, Paula
2015-01-01
Reflecting concerns about student attainment and participation in mathematics and science, the Effecting Principled Improvement in STEM Education ("epiSTEMe") project attempted to support pedagogical advancement in these two disciplines. Using principles identified as effective in the research literature (and combining these in a novel…
Student Engagement and Teacher Guidance in Meaningful Mathematics: Enduring Principles
ERIC Educational Resources Information Center
Freeman, Gregory D.; Lucius, Lisa B.
2008-01-01
In mathematics, developing a conceptual understanding and observing properly modeled methods rarely lead to successful student performance. The student must participate. As with bike riding, participation with monitoring and guidance makes initial efforts meaningful and beneficial. In this article, the authors share a bike riding experience and…
Solution of mathematical programming formulations of subgame perfect equilibrium problems
Macal, C.M.; Hurter, A.P.
1992-02-12
Mathematical programming models have been developed to represent imperfectly competitive (oligopolistic) market structures and the interdependencies of decision-making units in establishing prices and production levels. The solution of these models represents an economic equilibrium. A subgame perfect equilibrium formulation explicitly considers that each agent`s strategies depend on the current state of the system; the state depends solely on previous decisions made by the economic agents. The structure of an industry-wide model that is formulated as a subgame perfect equilibrium problem is a matrix of simultaneous mathematical programming problems, where the rows represent time periods and the columns represent agents. This paper formally defines the subgame perfect equilibrium problem that includes mathematical programs for agent decision problems, and it characterizes the feasible space in a way that is conducive to the solution of the problem. The existence of equilibrium solutions on convex subspaces of the feasible region is proved, and this set is shown to contain the subgame perfect equilibrium solutions. A procedure for computing equilibrium solutions and systematically searching the subspaces is illustrated by a numerical example.
Advance directives: principles, problems, and solutions for physicians.
Hoffman, B F; Humniski, A
1997-04-01
Given the passage of recent legislation, the appearance of common-law reports in Canada and the United States, and the practical problems of implementation of advance directives in health care, physicians should understand the principles and issues involved. In this article, the advantages, disadvantages, and practical solutions to the problems are explored. Family physicians, geriatricians, neurologists, and psychiatrists are most likely to be consulted about advance directives in health care. PMID:12382657
ERIC Educational Resources Information Center
Gabrielson, Curtis A.; Hsi, Sherry
2012-01-01
This paper articulates and illustrates design principles that guided the development of a set of hands-on teaching activities for the national science and mathematics curricula at junior-high and high-school level education in Timor-Leste, a small, low-income nation in Southeast Asia. A partnership between a university, an international science…
ERIC Educational Resources Information Center
Doabler, Christian T.; Fien, Hank; Nelson-Walker, Nancy J.; Baker, Scott K.
2012-01-01
The present review builds on earlier research that evaluated the curricular features of core math programs to improve the performances of students with or at risk for mathematics difficulties. In this review, three elementary math programs, at Grades 2 and 4, were evaluated for the presence of eight instructional principles. Math intervention…
ERIC Educational Resources Information Center
Moschkovich, Judit
2013-01-01
In this essay, the author describes principles for equitable mathematics teaching practices for English Language Learners (ELLs) and outlines guidelines for materials to support such practices. Although research cannot provide a recipe for equitable teaching practices for ELLs, teachers, educators, and administrators can use this set of…
Mathematical, physical and numerical principles essential for models of turbulent mixing
Sharp, David Howland; Lim, Hyunkyung; Yu, Yan; Glimm, James G
2009-01-01
We propose mathematical, physical and numerical principles which are important for the modeling of turbulent mixing, especially the classical and well studied Rayleigh-Taylor and Richtmyer-Meshkov instabilities which involve acceleration driven mixing of a fluid discontinuity layer, by a steady accerleration or an impulsive force.
A new mathematical solution for predicting char activation reactions
Rafsanjani, H.H.; Jamshidi, E.; Rostam-Abadi, M.
2002-01-01
The differential conservation equations that describe typical gas-solid reactions, such as activation of coal chars, yield a set of coupled second-order partial differential equations. The solution of these coupled equations by exact analytical methods is impossible. In addition, an approximate or exact solution only provides predictions for either reaction- or diffusion-controlling cases. A new mathematical solution, the quantize method (QM), was applied to predict the gasification rates of coal char when both chemical reaction and diffusion through the porous char are present. Carbon conversion rates predicted by the QM were in closer agreement with the experimental data than those predicted by the random pore model and the simple particle model. ?? 2002 Elsevier Science Ltd. All rights reserved.
ERIC Educational Resources Information Center
Große, Cornelia S.
2014-01-01
It is commonly suggested to mathematics teachers to present learners different methods in order to solve one problem. This so-called "learning with multiple solution methods" is also recommended from a psychological point of view. However, existing research leaves many questions unanswered, particularly concerning the effects of…
Mathematical models of polymer solutions motion and their symmetries
NASA Astrophysics Data System (ADS)
Bozhkov, Yu. D.; Pukhnachev, V. V.; Pukhnacheva, T. P.
2015-10-01
We consider three mathematical models describing motion of aqueous polymer solutions. All of them are derived from equations of Maxwell type viscoelastic medium at small relaxation time. Distinction consists in the choice of time derivative in the rheological constitutive law. Namely, we can choose (a) connective, (b) partial or (c) objective derivative of the strain tensor in time. We found widest symmetry groups admitted by each of these models. Systems (a) and (c) admit the extended Galilei group containing four arbitrary functions of time while the group admitted by system (b) is rather poor. Wide classes of exact solutions are obtained and their behaviors are analyzed if the relaxation viscosity tends to zero. Asymptotic expansion in this solution's parameter describing the flow near a critical point in planar and axially symmetric cases is derived. Analogs of the classical Hagen-Poiseuille and Nusselt solutions are studied too. We found difference in the pressure distribution between solutions calculated on the base of model (c) and two other models.
Using Diagrams as Tools for the Solution of Non-Routine Mathematical Problems
ERIC Educational Resources Information Center
Pantziara, Marilena; Gagatsis, Athanasios; Elia, Iliada
2009-01-01
The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems' structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first…
Effective Computer-Aided Assessment of Mathematics; Principles, Practice and Results
ERIC Educational Resources Information Center
Greenhow, Martin
2015-01-01
This article outlines some key issues for writing effective computer-aided assessment (CAA) questions in subjects with substantial mathematical or statistical content, especially the importance of control of random parameters and the encoding of wrong methods of solution (mal-rules) commonly used by students. The pros and cons of using CAA and…
Ions in solutions: Determining their polarizabilities from first-principles
NASA Astrophysics Data System (ADS)
Molina, John J.; Lectez, Sébastien; Tazi, Sami; Salanne, Mathieu; Dufrêche, Jean-François; Roques, Jérôme; Simoni, Eric; Madden, Paul A.; Turq, Pierre
2011-01-01
Dipole polarizabilities of a series of ions in aqueous solutions are computed from first-principles. The procedure is based on the study of the linear response of the maximally localized Wannier functions to an applied external field, within density functional theory. For most monoatomic cations (Li ^+, Na ^+, K ^+, Rb ^+, Mg ^{2+}, Ca ^{2+} and Sr ^{2+}) the computed polarizabilities are the same as in the gas phase. For Cs ^+ and a series of anions (F ^-, Cl ^-, Br ^- and I ^-), environmental effects are observed, which reduce the polarizabilities in aqueous solutions with respect to their gas phase values. The polarizabilities of H ^+_(aq), OH ^-_(aq) have also been determined along an ab initio molecular dynamics simulation. We observe that the polarizability of a molecule instantaneously switches upon proton transfer events. Finally, we also computed the polarizability tensor in the case of a strongly anisotropic molecular ion, UO _2^{2+}. The results of these calculations will be useful in building interaction potentials that include polarization effects.
First-principles investigation of solute-hydrogen interaction in a α-Ti solid solution
NASA Astrophysics Data System (ADS)
Hu, Q. M.; Xu, D. S.; Yang, R.; Li, D.; Wu, W. T.
2002-08-01
In this paper, a first-principles method is used to calculate the interaction energy between substitutional solute atoms and hydrogen in α-Ti. The results show that simple metal (SM) solute atoms are repulsive to H and therefore are detraps for H, whereas transition metal (TM) solute atoms, with smaller sizes than that of the host atoms, attract H and provide traps for H. The relationship between the interaction energy and lattice distortion as well as the electronic structure is investigated. The SM-H and TM-H interactions are dominated by different factors. The repulsive interaction between SM atoms and H is mainly due to the hybridization between the electrons of SM atoms and H when they are close to each other. The interaction between the TM solutes and H is attributable to the atomic size effect, and can be described satisfactorily by Matsumoto's strain field relaxation model. From the solute-H interaction energy and available measured terminal solubility of hydrogen (TSH), the relationship between the solute trapping of hydrogen and TSH in α-Ti is discussed. No coherent relationship is found between the theoretical hydrogen trapping effect and the experimental TSH in α-Ti alloys.
The Algebra Solution to Mathematics Reform: Completing the Equation
ERIC Educational Resources Information Center
Spielhagen, Frances R.
2011-01-01
How can we increase mathematics achievement among all students? This book provides a straightforward explanation of how changing mathematics tracking policies to provide algebra instruction to all students by at least eighth grade can bring about changes in both student achievement and teacher performance. Spielhagen chronicles the success of a…
Using Predictor-Corrector Methods in Numerical Solutions to Mathematical Problems of Motion
ERIC Educational Resources Information Center
Lewis, Jerome
2005-01-01
In this paper, the author looks at some classic problems in mathematics that involve motion in the plane. Many case problems like these are difficult and beyond the mathematical skills of most undergraduates, but computational approaches often require less insight into the subtleties of the problems and can be used to obtain reliable solutions.…
NASA Astrophysics Data System (ADS)
McInroe, Benjamin; Astley, Henry; Gong, Chaohui; Kawano, Sandy; Schiebel, Perrin; Choset, Howie; Goldman, Daniel I.
The transition from aquatic to terrestrial life presented new challenges to early walkers, necessitating robust locomotion on complex, flowable substrates (e.g. sand, mud). Locomotion on such substrates is sensitive to limb morphology and kinematics. Although early walker morphologies are known, principles of appendage control remain elusive. To reveal limb control strategies that facilitated the invasion of land, we study both robotic and mathematical models. Robot experiments show that an active tail is critical for robust locomotion on granular media, enabling locomotion even with poor foot placement and limited ability to lift the body. Using a granular resistive force theory model, we construct connection vector fields that reveal how appendage coordination and terrain inclination impact locomotor performance. This model replicates experimental results, showing that moving limbs/tail in phase is most effective (suggesting a locomotor template). Varying limb trajectories and contacts, we find gaits for which tail use can be neutral or harmful, suggesting limb-tail coordination to be a nontrivial aspect of locomotion. Our findings show that robot experiments coupled with geometric mechanics provide a general framework to reveal principles of robust terrestrial locomotion. This work was supported by NSF PoLS.
Mathematical modeling of methoxyanabasine C11H16N2O polymer solution ultrafiltration
NASA Astrophysics Data System (ADS)
Satayev, Marat; Shakirov, Birzhan; Mutaliyeva, Botagoz; Satayeva, Lazzat; Altynbekov, Rustem; Baiysbay, Omirbek; Alibekov, Ravshanbek
2012-06-01
This work covers the mathematical modeling of ultrafiltration with immobile membranes for physiologically-active of methoxyanabasine C11H16N2O polymer solution. Methoxyanabasine is used as low toxic antineoplastic drug. On the basis of theoretical and experimental analysis of mass transfer and hydrodynamics, it is offered the mathematical model of permeability of membranes at an ultrafiltration of polymer solutions. Further the formulas for determination of factor of concentration polarization and ultrafiltration selectivity are calculated.
Hamilton's Principle and Approximate Solutions to Problems in Classical Mechanics
ERIC Educational Resources Information Center
Schlitt, D. W.
1977-01-01
Shows how to use the Ritz method for obtaining approximate solutions to problems expressed in variational form directly from the variational equation. Application of this method to classical mechanics is given. (MLH)
Multiple Solutions to Problems in Mathematics Teaching: Do Teachers Really Value Them?
ERIC Educational Resources Information Center
Bingolbali, Erhan
2011-01-01
Solving problems in different ways is strongly advised for mathematics learning and teaching. There is, however, little data available on the examination of teachers' openness to and evaluation of different solutions to the problems. In this paper, the author examines classroom teachers' openness to different solutions (or to what extent they…
Cytokinesis in Prokaryotes and Eukaryotes: Common Principles and Different Solutions
Nanninga, Nanne
2001-01-01
Cytokinesis requires duplication of cellular structures followed by bipolarization of the predivisional cell. As a common principle, this applies to prokaryotes as well as eukaryotes. With respect to eukaryotes, the discussion has focused mainly on Saccharomyces cerevisiae and on Schizosaccharomyces pombe. Escherichia coli and to a lesser extent Bacillus subtilis have been used as prokaryotic examples. To establish a bipolar cell, duplication of a eukaryotic origin of DNA replication as well as its genome is not sufficient. Duplication of the microtubule-organizing center is required as a prelude to mitosis, and it is here that the dynamic cytoskeleton with all its associated proteins comes to the fore. In prokaryotes, a cytoskeleton that pervades the cytoplasm appears to be absent. DNA replication and the concomitant DNA segregation seem to occur without help from extensive cytosolic supramacromolecular assemblies but with help from the elongating cellular envelope. Prokaryotic cytokinesis proceeds through a contracting ring, which has a roughly 100-fold-smaller circumference than its eukaryotic counterpart. Although the ring contains proteins that can be considered as predecessors of actin, tubulin, and microtubule-associated proteins, its macromolecular composition is essentially different. PMID:11381104
Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge
ERIC Educational Resources Information Center
Inoue, Noriyuki
2008-01-01
Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…
Computer Facilitated Mathematical Methods in Chemical Engineering--Similarity Solution
ERIC Educational Resources Information Center
Subramanian, Venkat R.
2006-01-01
High-performance computers coupled with highly efficient numerical schemes and user-friendly software packages have helped instructors to teach numerical solutions and analysis of various nonlinear models more efficiently in the classroom. One of the main objectives of a model is to provide insight about the system of interest. Analytical…
Comparison between analytical and numerical solution of mathematical drying model
NASA Astrophysics Data System (ADS)
Shahari, N.; Rasmani, K.; Jamil, N.
2016-02-01
Drying is often related to the food industry as a process of shifting heat and mass inside food, which helps in preserving food. Previous research using a mass transfer equation showed that the results were mostly concerned with the comparison between the simulation model and the experimental data. In this paper, the finite difference method was used to solve a mass equation during drying using different kinds of boundary condition, which are equilibrium and convective boundary conditions. The results of these two models provide a comparison between the analytical and the numerical solution. The result shows a close match between the two solution curves. It is concluded that the two proposed models produce an accurate solution to describe the moisture distribution content during the drying process. This analysis indicates that we have confidence in the behaviour of moisture in the numerical simulation. This result demonstrated that a combined analytical and numerical approach prove that the system is behaving physically. Based on this assumption, the model of mass transfer was extended to include the temperature transfer, and the result shows a similar trend to those presented in the simpler case.
Osteoprotegerin in Bone Metastases: Mathematical Solution to the Puzzle
Ryser, Marc D.; Qu, Yiding; Komarova, Svetlana V.
2012-01-01
Bone is a common site for cancer metastasis. To create space for their growth, cancer cells stimulate bone resorbing osteoclasts. Cytokine RANKL is a key osteoclast activator, while osteoprotegerin (OPG) is a RANKL decoy receptor and an inhibitor of osteoclastogenesis. Consistently, systemic application of OPG decreases metastatic tumor burden in bone. However, OPG produced locally by cancer cells was shown to enhance osteolysis and tumor growth. We propose that OPG produced by cancer cells causes a local reduction in RANKL levels, inducing a steeper RANKL gradient away from the tumor and towards the bone tissue, resulting in faster resorption and tumor expansion. We tested this hypothesis using a mathematical model of nonlinear partial differential equations describing the spatial dynamics of OPG, RANKL, PTHrP, osteoclasts, tumor and bone mass. We demonstrate that at lower expression rates, tumor-derived OPG enhances the chemotactic RANKL gradient and osteolysis, whereas at higher expression rates OPG broadly inhibits RANKL and decreases osteolysis and tumor burden. Moreover, tumor expression of a soluble mediator inducing RANKL in the host tissue, such as PTHrP, is important for correct orientation of the RANKL gradient. A meta-analysis of OPG, RANKL and PTHrP expression in normal prostate, carcinoma and metastatic tissues demonstrated an increase in expression of OPG, but not RANKL, in metastatic prostate cancer, and positive correlation between OPG and PTHrP in metastatic prostate cancer. The proposed mechanism highlights the importance of the spatial distribution of receptors, decoys and ligands, and can be applied to other systems involving regulation of spatially anisotropic processes. PMID:23093918
Solutions of some problems in applied mathematics using MACSYMA
NASA Technical Reports Server (NTRS)
Punjabi, Alkesh; Lam, Maria
1987-01-01
Various Symbolic Manipulation Programs (SMP) were tested to check the functioning of their commands and suitability under various operating systems. Support systems for SMP were found to be relatively better than the one for MACSYMA. The graphics facilities for MACSYMA do not work as expected under the UNIX operating system. Not all commands for MACSYMA function as described in the manuals. Shape representation is a central issue in computer graphics and computer-aided design. Aside from appearance, there are other application dependent, desirable properties like continuity to certain order, symmetry, axis-independence, and variation-diminishing properties. Several shape representations are studied, which include the Osculatory Method, a Piecewise Cubic Polynomial Method using two different slope estimates, Piecewise Cubic Hermite Form, a method by Harry McLaughlin, and a Piecewise Bezier Method. They are applied to collected physical and chemical data. Relative merits and demerits of these methods are examined. Kinematics of a single link, non-dissipative robot arm is studied using MACSYMA. Lagranian is set-up and Lagrange's equations are derived. From there, Hamiltonian equations of motion are obtained. Equations suggest that bifurcation of solutions can occur, depending upon the value of a single parameter. Using the characteristic function W, the Hamilton-Jacobi equation is derived. It is shown that the H-J equation can be solved in closed form. Analytical solutions to the H-J equation are obtained.
Redox condition in molten salts and solute behavior: A first-principles molecular dynamics study
NASA Astrophysics Data System (ADS)
Nam, Hyo On; Morgan, Dane
2015-10-01
Molten salts technology is of significant interest for nuclear, solar, and other energy systems. In this work, first-principles molecular dynamics (FPMD) was used to model the solute behavior in eutectic LiCl-KCl and FLiBe (Li2BeF4) melts at 773 K and 973 K, respectively. The thermo-kinetic properties for solute systems such as the redox potential, solute diffusion coefficients and structural information surrounding the solute were predicted from FPMD modeling and the calculated properties are generally in agreement with the experiments. In particular, we formulate an approach to model redox energetics vs. chlorine (or fluorine) potential from first-principles approaches. This study develops approaches for, and demonstrates the capabilities of, FPMD to model solute properties in molten salts.
Solution of steady-state one-dimensional conservation laws by mathematical programming
NASA Technical Reports Server (NTRS)
Lavery, J. E.
1989-01-01
Solution techniques for a class of steady-state scalar conservation laws are developed analytically. Discretization by finite-volume formulas is employed to obtain an overdetermined system of algebraic equations, which are then perturbed nonsingularly (with perturbation coefficient = epsilon) and solved using the l(1) mathematical-programming algorithm of Seneta and Steiger (1984); this approach limits the matrix bandwidth to two, so that an explicit solution can be found efficiently. It is shown that, for small values of epsilon, the l(1) solutions exhibit sharp correctly located shocks and are nonoscillatory O(epsilon) approximations of the physically relevant solutions.
ERIC Educational Resources Information Center
Gazit, Avikam; Patkin, Dorit
2012-01-01
The article aims to check the way adults, "some who are" practicing mathematics teachers at elementary school, "some who are" academicians making a career change to mathematics teachers at junior high school and the "rest who are" pre-service mathematics teachers at elementary school, cope with the solution of everyday real-world problems of…
ERIC Educational Resources Information Center
Phelan, Julia; Choi, Kilchan; Vendlinski, Terry; Baker, Eva; Herman, Joan
2011-01-01
The authors describe results from a study of a middle school mathematics formative assessment strategy. They employed a randomized, controlled design to address the following question: Does using our strategy improve student performance on assessments of key mathematical ideas relative to a comparison group? Eighty-five teachers and 4,091 students…
Every Word Problem Has a Solution--The Social Rationality of Mathematical Modelling in Schools.
ERIC Educational Resources Information Center
Reusser, Kurt; Stebler, Rita
1997-01-01
Two experiments involving 67 elementary school and 439 high school students show that students present solutions to many unsolvable problems without showing realistic reactions. Results are discussed with respect to the quality of word problems in teaching mathematics, the culture of teaching and learning, and the issue of social rationality in…
NASA Astrophysics Data System (ADS)
Bogdanov, Alexander; Khramushin, Vasily
2016-02-01
The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.
Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule
NASA Astrophysics Data System (ADS)
Luo, Yousong; Eberhard, Andrew
2005-07-01
A comparison principle for viscosity sub- and super-solutions of second order elliptic partial differential equations is derived using the "fuzzy sum rule" of non-smooth calculus. This method allows us to weaken the assumptions made on the function F when the equation F(x,u,=u,=2u)=0 is under consideration.
First-principles calculations of transition metal solute interactions with hydrogen in tungsten
NASA Astrophysics Data System (ADS)
Kong, Xiang-Shan; Wu, Xuebang; Liu, C. S.; Fang, Q. F.; Hu, Q. M.; Chen, Jun-Ling; Luo, G.-N.
2016-02-01
We have performed systematic first-principles calculations to predict the interaction between transition metal (TM) solutes and hydrogen in the interstitial site as well as the vacancy in tungsten. We showed that the site preference of the hydrogen atom is significantly influenced by the solute atoms, which can be traced to the charge density perturbation in the vicinity of the solute atom. The solute-H interactions are mostly attractive except for Re, which can be well understood in terms of the competition between the chemical and elastic interactions. The chemical interaction dominates the solute-H interaction for the TM solutes with a large atomic volume and small electronegativity compared to tungsten, while the elastic interaction is primarily responsible for the solute-H interaction for the TM solutes with a small atomic volume and large electronegativity relative to tungsten. The presence of a hydrogen atom near the solute atom has a negative effect on the binding of other hydrogen atoms. The large positive binding energies among the solute, vacancy and hydrogen suggest that they would easily form a defect cluster in tungsten, where the solute-vacancy and vacancy-H interaction contribute greatly while the solute-H interaction contributes a little. Our result provides a sound theoretical explanation for recent experimental phenomena of hydrogen retention in the tungsten alloy and further recommends a suitable W-Re-Ta ternary alloy for possible plasma-facing materials (PFMs) including the consideration of the hydrogen retention.
Larsen, Erik Hviid; Sørensen, Jakob Balslev; Sørensen, Jens Nørkær
2000-01-01
A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2–4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241–251), computations predict that 60–80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model
The mathematical structure of the model consists of the coupling of a model for the transport through soils to a model for transport through plants. The coupled model describes uptake of water and solutes by plants from the soil solution. The rate of uptake is a function of the e...
Solute/impurity diffusivities in bcc Fe: A first-principles study
NASA Astrophysics Data System (ADS)
Zhang, Chong; Fu, Jie; Li, Ruihuan; Zhang, Pengbo; Zhao, Jijun; Dong, Chuang
2014-12-01
Chinese low activation martensitic steel (CLAM) has been designed with decreased W content and increased Ta content to improve performance. We performed first-principles calculations to investigate the diffusion properties of solute element (Cr, W, Mn, V, Ta) and C diffusion with a nearby solute element inside bcc Fe. The self-diffusion coefficients and solute diffusion coefficients in Fe host were derived using the nine-frequency model. A relatively lower diffusivity was observed for W in paramagnetic state, implying enriched W concentration inside Fe host. The solute atom interacts strongly with C impurity, depending on the interatomic distance. According to our calculations, formation of Ta carbide precipitates is energetically preferred by trapping C impurity around Ta atom. Our theoretical results are helpful for investigating the evolution of microstructure of steels for engineering applications.
ERIC Educational Resources Information Center
Pierce, Robyn; Stacey, Kaye
2009-01-01
Taking advantage of pedagogical opportunities afforded by new technology requires appropriately designed lessons. This article reports on the use of "lesson study" to research principles for the design of a lesson aiming to take advantage of multiple representations. The lesson, for year 10 students who had personal access to TI-Nspire, focused on…
ERIC Educational Resources Information Center
Yildirim, Sevda; Ersozlu, Zehra Nur
2013-01-01
This study was designed to investigate the relationship between the metacognitive awareness of university students and their solutions to the similar mathematical problem types. Participants were 97 freshmen from department of mathematics at a state university in Turkey. Two different scales were used for data collection: "Metacognitive…
ERIC Educational Resources Information Center
Murata, Aki; Kattubadi, Sailaja
2012-01-01
In considering mathematics problem solving as a model-eliciting activity (Lesh & Doerr, 2003; Lesh & Harel, 2003; Lesh & Zawojewski, 2008), it is important to know "what" students are modeling for the problems: situations or solutions. This study investigated Grade 3 students' mathematization process by examining how they modeled different…
NASA Astrophysics Data System (ADS)
Ginzburg, Vitalii L.
1987-01-01
The first edition of Newton's "Philosophiae Naturalis Principia Mathematica" was published in 1687. The present paper is dedicated to the tricentenary of this event, which is important not just in the history of physics, but of science generally. After the Introduction, the paper continues with the following Sections: Before Newton, Principia, Principia and the method of principles, The nature of gravitation, Critique of Newtonian mechanics and its subsequent development, On Newton, Concluding remarks.
Principles help to analyse but often give no solution--secondary prevention after a cardiac event.
Westin, Lars; Nilstun, Tore
2006-06-01
The aim of this paper is to investigate whether or not ethical conflicts can be identified, analysed and solved using ethical principles. The relation between the physician and the patient with ischemic heart disease (IHD) as life style changes are recommended in a secondary prevention program is used as an example. The principal persons affected (the patient and his or her spouse) and the ethical principles (respect for autonomy, non-maleficence, beneficence and justice) are combined in a two dimensional model. The most important person affected by the recommendations is the patient. His or her autonomy is challenged by the suggested life style changes, the purpose of which is to promote the future wellbeing and health of the patient. The spouse is indirectly involved in and affected by the process. He or she often feels neglected by caregivers. Ethical conflicts can both be identified and analysed using ethical principles, but often no solution is implied. Most (if not all) physicians would strongly encourage life style changes, but surprisingly there is no uncontroversial justification for this conclusion using principles. PMID:17195579
NASA Technical Reports Server (NTRS)
Przekwas, A. J.; Singhal, A. K.; Tam, L. T.
1984-01-01
The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.
Mistry, Piyush R; Pradhan, Vikas H; Desai, Khyati R
2013-01-01
The present paper analytically discusses the phenomenon of fingering in double phase flow through homogenous porous media by using variational iteration method. Fingering phenomenon is a physical phenomenon which occurs when a fluid contained in a porous medium is displaced by another of lesser viscosity which frequently occurred in problems of petroleum technology. In the current investigation a mathematical model is presented for the fingering phenomenon under certain simplified assumptions. An approximate analytical solution of the governing nonlinear partial differential equation is obtained using variational iteration method with the use of Mathematica software. PMID:24348161
Symmetry analysis and exact solutions for nonlinear equations in mathematical physics
NASA Astrophysics Data System (ADS)
Fushchich, Vil'gel'm. I.; Shtelen', Vladimir M.; Serov, Nikolai I.
The book provides an overview of the current status of theoretical-algebraic methods in relation to linear and nonlinear multidimensional equations in mathematical and theoretical physics that are invariant with respect to the Poincare and Galilean groups and the wider Lie groups. Particular attention is given to the construction, in explicit form, of wide classes of accurate solutions to specific nonlinear partial differential equations, such as nonlinear wave equations for scalar, spinor, and vector fields, Young-Mills equations, and nonlinear quantum electrodynamic equations. A group-theory approach is used to analyze the classical three-body problem.
Mochizuki, Koji; Takayama, Kozo
2016-07-01
A prediction method for color changes based on the time-temperature superposition principle (TTSP) was developed for acetaminophen solution. Color changes of acetaminophen solution are caused by the degradation of acetaminophen, such as hydrolysis and oxidation. In principle, the TTSP can be applied to only thermal aging. Therefore, the impact of oxidation on the color changes of acetaminophen solution was verified. The results of our experiment suggested that the oxidation products enhanced the color changes in acetaminophen solution. Next, the color changes of acetaminophen solution samples of the same head space volume after accelerated aging at various temperatures were investigated using the Commission Internationale de l'Eclairage (CIE) LAB color space (a*, b*, L* and ΔE*ab), following which the TTSP was adopted to kinetic analysis of the color changes. The apparent activation energies using the time-temperature shift factor of a*, b*, L* and ΔE*ab were calculated as 72.4, 69.2, 72.3 and 70.9 (kJ/mol), respectively, which are similar to the values for acetaminophen hydrolysis reported in the literature. The predicted values of a*, b*, L* and ΔE*ab at 40 °C were obtained by calculation using Arrhenius plots. A comparison between the experimental and predicted values for each color parameter revealed sufficiently high R(2) values (>0.98), suggesting the high reliability of the prediction. The kinetic analysis using TTSP was successfully applied to predicting the color changes under the controlled oxygen amount at any temperature and for any length of time. PMID:26559666
NASA Astrophysics Data System (ADS)
Hansen, S. K.
2009-12-01
A widely used treatment of coupling between mobile and immobile zones in mathematical transport models assumes continuity of aqueous concentration across the zone interface and estimates cross-interface flux using a standard expression, based on Fick's Law. This particular formulation has been used in numerous existing papers, including key analytical solutions for discretely fractured porous media. In cases where matrix sorption retards diffusion in the immobile zone, this is often handled by employing a retardation coefficient other than unity in the model. In this circumstance, it can be shown that the standard formulation ceases to enforce mass balance across the interface between the mobile and immobile zones. The standard treatment generates incorrect results--even if the environment has been characterized perfectly. A novel analysis proves the existence of this mathematical error and shows how to correct it, without introducing any additional physical information. A summary of the analysis, as well as its implications (including the invalidation of parts of a number of published analytic solutions) will be discussed.
Transition metal solute interactions with point defects in fcc iron from first principles
NASA Astrophysics Data System (ADS)
Hepburn, D. J.; MacLeod, E.; Ackland, G. J.
2015-07-01
We present a comprehensive set of first-principles electronic structure calculations of the properties of substitutional transition metal solutes and point defects in austenite (face-centered cubic, paramagnetic Fe). Clear trends were observed in these quantities across the transition metal series, with solute-defect interactions strongly related to atomic size, and only weakly related to more subtle details of magnetic or electronic structure. Oversized solutes act as strong traps for both vacancy and self-interstitial defects and as nucleation sites for the development of protovoids and small self-interstitial loops. The consequent reduction in defect mobility and net defect concentrations in the matrix explains the observation of reduced swelling and radiation-induced segregation. Our analysis of vacancy-mediated solute diffusion demonstrates that below about 400 K Ni and Co will be dragged by vacancies and their concentrations should be enhanced at defect sinks. Cr and Cu show opposite behavior and are depleted at defect sinks. The stable configuration of some oversized solutes is neither interstitial nor substitutional; rather they occupy two adjacent lattice sites. The diffusion of these solutes proceeds by a novel mechanism, which has important implications for the nucleation and growth of complex oxide nanoparticles contained in oxide dispersion strengthened steels. Interstitial-mediated solute diffusion is negligible for all except the magnetic solutes (Cr, Mn, Co, and Ni). Our results are consistent across several antiferromagnetic states and surprising qualitative similarities with ferromagnetic (body-centered cubic) Fe were observed; this implies that our conclusions will be valid for paramagnetic iron.
Phase Diagram of Pb(Zr,Ti)O{sub 3} Solid Solutions from First Principles
Kornev, Igor A.; Bellaiche, L.; Janolin, P.-E.; Dkhil, B.; Suard, E.
2006-10-13
A first-principles-derived scheme that incorporates ferroelectric and antiferrodistortive degrees of freedom is developed to study finite-temperature properties of Pb(Zr{sub 1-x}Ti{sub x})O{sub 3} solid solution near its morphotropic phase boundary. The use of this numerical technique (i) resolves controversies about the monoclinic ground state for some Ti compositions (ii) leads to the discovery of an overlooked phase, and (iii) yields three multiphase points that are each associated with four phases. Additional neutron diffraction measurements strongly support some of these predictions.
Phase Diagram of Pb(Zr,Ti)O3 Solid Solutions from First Principles
NASA Astrophysics Data System (ADS)
Kornev, Igor A.; Bellaiche, L.; Janolin, P.-E.; Dkhil, B.; Suard, E.
2006-10-01
A first-principles-derived scheme that incorporates ferroelectric and antiferrodistortive degrees of freedom is developed to study finite-temperature properties of Pb(Zr1-xTix)O3 solid solution near its morphotropic phase boundary. The use of this numerical technique (i) resolves controversies about the monoclinic ground state for some Ti compositions, (ii) leads to the discovery of an overlooked phase, and (iii) yields three multiphase points that are each associated with four phases. Additional neutron diffraction measurements strongly support some of these predictions.
ERIC Educational Resources Information Center
Sarfo, Frederick Kwaku; Eshun, Grace; Elen, Jan; Adentwi, Kobina Impraim
2014-01-01
Introduction: In this study, the effectiveness of two different interventions was investigated. The effects of a concrete abstract intervention and a regular method of teaching intervention were compared. Both interventions were designed in line with the specifications of classical principles of instructional design for learning mathematics in the…
Dynamical Principles of Emotion-Cognition Interaction: Mathematical Images of Mental Disorders
Rabinovich, Mikhail I.; Muezzinoglu, Mehmet K.; Strigo, Irina; Bystritsky, Alexander
2010-01-01
The key contribution of this work is to introduce a mathematical framework to understand self-organized dynamics in the brain that can explain certain aspects of itinerant behavior. Specifically, we introduce a model based upon the coupling of generalized Lotka-Volterra systems. This coupling is based upon competition for common resources. The system can be regarded as a normal or canonical form for any distributed system that shows self-organized dynamics that entail winnerless competition. Crucially, we will show that some of the fundamental instabilities that arise in these coupled systems are remarkably similar to endogenous activity seen in the brain (using EEG and fMRI). Furthermore, by changing a small subset of the system's parameters we can produce bifurcations and metastable sequential dynamics changing, which bear a remarkable similarity to pathological brain states seen in psychiatry. In what follows, we will consider the coupling of two macroscopic modes of brain activity, which, in a purely descriptive fashion, we will label as cognitive and emotional modes. Our aim is to examine the dynamical structures that emerge when coupling these two modes and relate them tentatively to brain activity in normal and non-normal states. PMID:20877723
A unified electrostatic and cavitation model for first-principles molecular dynamics in solution
NASA Astrophysics Data System (ADS)
Scherlis, Damián A.; Fattebert, Jean-Luc; Gygi, François; Cococcioni, Matteo; Marzari, Nicola
2006-02-01
The electrostatic continuum solvent model developed by [Fattebert and Gygi J. Comput. Chem. 23, 662 (2002); Int. J. Quantum Chem. 93, 139 (2003)] is combined with a first-principles formulation of the cavitation energy based on a natural quantum-mechanical definition for the surface of a solute. Despite its simplicity, the cavitation contribution calculated by this approach is found to be in remarkable agreement with that obtained by more complex algorithms relying on a large set of parameters. Our model allows for very efficient Car-Parrinello simulations of finite or extended systems in solution and demonstrates a level of accuracy as good as that of established quantum-chemistry continuum solvent methods. We apply this approach to the study of tetracyanoethylene dimers in dichloromethane, providing valuable structural and dynamical insights on the dimerization phenomenon.
A unified electrostatic and cavitation model for first-principles molecular dynamics in solution
Scherlis, D A; Fattebert, J; Gygi, F; Cococcioni, M; Marzari, N
2005-11-14
The electrostatic continuum solvent model developed by Fattebert and Gygi is combined with a first-principles formulation of the cavitation energy based on a natural quantum-mechanical definition for the surface of a solute. Despite its simplicity, the cavitation contribution calculated by this approach is found to be in remarkable agreement with that obtained by more complex algorithms relying on a large set of parameters. The model allows for very efficient Car-Parrinello simulations of finite or extended systems in solution, and demonstrates a level of accuracy as good as that of established quantum-chemistry continuum solvent methods. They apply this approach to the study of tetracyanoethylene dimers in dichloromethane, providing valuable structural and dynamical insights on the dimerization phenomenon.
Atta-Fynn, Raymond; Biswas, Parthapratim
2009-07-01
Localized basis ab initio molecular dynamics simulation within the density functional framework has been used to generate realistic configurations of amorphous silicon carbide (a-SiC). Our approach consists of constructing a set of smart initial configurations that conform to essential geometrical and structural aspects of the materials obtained from experimental data, which is subsequently driven via a first-principles force field to obtain the best solution in a reduced solution space. A combination of a priori information (primarily structural and topological) along with the ab initio optimization of the total energy makes it possible to model a large system size (1000 atoms) without compromising the quantum mechanical accuracy of the force field to describe the complex bonding chemistry of Si and C. The structural, electronic and vibrational properties of the models have been studied and compared to existing theoretical models and available data from experiments. We demonstrate that the approach is capable of producing large, realistic configurations of a-SiC from first-principles simulation that display its excellent structural and electronic properties. Our study reveals the presence of predominant short range order in the material originating from heteronuclear Si-C bonds with a coordination defect concentration as small as 5% and a chemical disorder parameter of about 8%. PMID:21828477
ERIC Educational Resources Information Center
Waters, William Meade, Jr.
The objective of the study was to determine the effect which a unit dealing with recursive definitions would have on students' achievement in applying the principle of mathematical induction (PMI). Twenty-four secondary school students were randomly assigned to control and experimental groups. Students in the control group studied programmed units…
The Display and Input of Mathematical Symbols on the Web: Questions and Technical Solutions
ERIC Educational Resources Information Center
Zhi-Feng, Eric; Liu, Ming-Chun Cheng; Liu, Syhan-Ming Yuan; Lo, Win-Tsung
2004-01-01
This study proposed practical ways to display mathematical formula on the Web and input mathematical formulae onto the Web according to the authors' successful experience of implementing mathematical forum which allowed displaying and inputting mathematical notations and equations. Authors believe that this study will pose more questions and…
ERIC Educational Resources Information Center
Guberman, Raisa; Leikin, Roza
2013-01-01
The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers' knowledge. It is aimed at exploring the development of teachers' mathematical and pedagogical conceptions…
NASA Astrophysics Data System (ADS)
Li, Y.; Ma, X.; Su, N.
2013-12-01
The movement of water and solute into and through the vadose zone is, in essence, an issue of immiscible displacement in pore-space network of a soil. Therefore, multiphase flow and transport in porous media, referring to three medium: air, water, and the solute, pose one of the largest unresolved challenges for porous medium fluid seepage. However, this phenomenon has always been largely neglected. It is expected that a reliable analysis model of the multi-phase flow in soil can truly reflect the process of natural movement about the infiltration, which is impossible to be observed directly. In such cases, geophysical applications of the nuclear magnetic resonance (NMR) provides the opportunity to measure the water movements into soils directly over a large scale from tiny pore to regional scale, accordingly enable it available both on the laboratory and on the field. In addition, the NMR provides useful information about the pore space properties. In this study, we proposed both laboratory and field experiments to measure the multi-phase flow parameters, together with optimize the model in computer programming based on the fractional partial differential equations (fPDE). In addition, we establish, for the first time, an infiltration model including solute flowing with water, which has huge influence on agriculture and soil environment pollution. Afterwards, with data collected from experiments, we simulate the model and analyze the spatial variability of parameters. Simulations are also conducted according to the model to evaluate the effects of airflow on water infiltration and other effects such as solute and absorption. It has significant meaning to oxygen irrigation aiming to higher crop yield, and shed more light into the dam slope stability. In summary, our framework is a first-time model added in solute to have a mathematic analysis with the fPDE and more instructive to agriculture activities.
First principles study of the aggregation of oligo and polythiophene cations in solution
Scherlis, D A; Fattebert, J; Marzari, N
2005-11-14
The stacking of positively charged (or doped) terthiophene oligomers and quaterthiophene polymers in solution is investigated applying a recently developed unified electrostatic and cavitation model for first-principles calculations in a continuum solvent. The thermodynamic and structural patterns of the dimerization are explored in different solvents, and the distinctive roles of polarity and surface tension are characterized and analyzed. Interestingly, we discover a saturation in the stabilization effect of the dielectric screening that takes place at rather small values of {epsilon}{sub 0}. Moreover, we address the interactions in trimers of terthiophene cations, with the aim of generalizing the results obtained for the dimers to the case of higher order stacks and nanoaggregates.
Phase diagram of PZT solid solutions near the morphotropic phase boundary from first principles
NASA Astrophysics Data System (ADS)
Kornev, I.; Bellaiche, L.; Janolin, P.-E.; Dkhil, B.; Suard, E.
2007-03-01
A first-principles-derived scheme, that incorporates ferroelectric and antiferrodistortive degrees of freedom, is developed to study finite-temperature properties of Pb(Zr1-xTix)O3 solid solutions near its morphotropic phase boundary [1]. The use of this numerical technique (i) resolves controversies about the monoclinic ground-state for some Ti compositions, (ii) leads to the discovery of an overlooked phase, and (iii) yields three multiphase points, that are each associated with four phases. Additional neutron diffraction measurements strongly support some of these predictions. [1] Igor A. Kornev, L. Bellaiche, P.-E. Janolin, B. Dkhil, and E. Suard, Phys. Rev. Lett. 97, 157601 (2006) This work is supported by ONR grants N00014-04-1-0413, N00014-01-1-0600 and N00014-01-1-0365, by NSF grant DMR- 0404335, and by DOE grant DE-FG02-05ER46188.
Defect and solute properties in dilute Fe-Cr-Ni austenitic alloys from first principles
NASA Astrophysics Data System (ADS)
Klaver, T. P. C.; Hepburn, D. J.; Ackland, G. J.
2012-05-01
We present results of an extensive set of first-principles density functional theory calculations of point defect formation, binding, and clustering energies in austenitic Fe with dilute concentrations of Cr and Ni solutes. A large number of possible collinear magnetic structures were investigated as appropriate reference states for austenite. We found that the antiferromagnetic single- and double-layer structures with tetragonal relaxation of the unit cell were the most suitable reference states and highlighted the inherent instabilities in the ferromagnetic states. Test calculations for the presence and influence of noncollinear magnetism were performed but proved mostly negative. We calculate the vacancy formation energy to be between 1.8 and 1.95 eV. Vacancy cluster binding was initially weak at 0.1 eV for divacancies but rapidly increased with additional vacancies. Clusters of up to six vacancies were studied and a highly stable octahedral cluster and stacking fault tetrahedron were found with total binding energies of 2.5 and 2.3 eV, respectively. The <100> dumbbell was found to be the most stable self-interstitial with a formation energy of between 3.2 and 3.6 eV and was found to form strongly bound clusters, consistent with other fcc metals. Pair interaction models were found to be capable of capturing the trends in the defect cluster binding energy data. Solute-solute interactions were found to be weak in general, with a maximal positive binding of 0.1 eV found for Ni-Ni pairs and maximum repulsion found for Cr-Cr pairs of -0.1 eV. Solute cluster binding was found to be consistent with a pair interaction model, with Ni-rich clusters being the most stable. Solute-defect interactions were consistent with Ni and Cr being modestly oversized and undersized solutes, respectively, which is exactly opposite to the experimentally derived size factors for Ni and Cr solutes in type 316 stainless steel and in the pure materials. Ni was found to bind to the vacancy and
Hölzl, Christoph; Kibies, Patrick; Imoto, Sho; Frach, Roland; Suladze, Saba; Winter, Roland; Marx, Dominik; Horinek, Dominik; Kast, Stefan M
2016-04-14
Accurate force fields are one of the major pillars on which successful molecular dynamics simulations of complex biomolecular processes rest. They have been optimized for ambient conditions, whereas high-pressure simulations become increasingly important in pressure perturbation studies, using pressure as an independent thermodynamic variable. Here, we explore the design of non-polarizable force fields tailored to work well in the realm of kilobar pressures - while avoiding complete reparameterization. Our key is to first compute the pressure-induced electronic and structural response of a solute by combining an integral equation approach to include pressure effects on solvent structure with a quantum-chemical treatment of the solute within the embedded cluster reference interaction site model (EC-RISM) framework. Next, the solute's response to compression is taken into account by introducing pressure-dependence into selected parameters of a well-established force field. In our proof-of-principle study, the full machinery is applied to N,N,N-trimethylamine-N-oxide (TMAO) in water being a potent osmolyte that counteracts pressure denaturation. EC-RISM theory is shown to describe well the charge redistribution upon compression of TMAO(aq) to 10 kbar, which is then embodied in force field molecular dynamics by pressure-dependent partial charges. The performance of the high pressure force field is assessed by comparing to experimental and ab initio molecular dynamics data. Beyond its broad usefulness for designing non-polarizable force fields for extreme thermodynamic conditions, a good description of the pressure-response of solutions is highly recommended when constructing and validating polarizable force fields. PMID:27083705
Michałowski, Tadeusz; Pilarski, Bogusław; Asuero, Agustin G; Dobkowska, Agnieszka
2010-10-15
The paper provides a new formulation and analytical proposals based on the isohydric solutions concept. It is particularly stated that a mixture formed, according to titrimetric mode, from a weak acid (HX, C(0)mol/L) and a strong acid (HB, Cmol/L) solutions, assumes constant pH, independently on the volumes of the solutions mixed, provided that the relation C(0)=C+C(2)·10(pK(1)) is valid, where pK(1)=-log K(1), K(1) the dissociation constant for HX. The generalized formulation, referred to the isohydric solutions thus obtained, was extended also to more complex acid-base systems. Particularly in the (HX, HB) system, the titration occurs at constant ionic strength (I) value, not resulting from presence of a basal electrolyte. This very advantageous conjunction of the properties provides, among others, a new, very sensitive method for verification of pK(1) value. The new method is particularly useful for weak acids HX characterized by low pK(1) values. The method was tested experimentally on four acid-base systems (HX, HB), in aqueous and mixed-solvent media and compared with the literature data. Some useful (linear and hyperbolic) correlations were stated and applied for validation of pK(1) values. Finally, some practical applications of analytical interest of the isohydricity (pH constancy) principle as one formulated in this paper were enumerated, proving the usefulness of such a property which has its remote roots in the Arrhenius concept. PMID:20875603
NASA Astrophysics Data System (ADS)
Hölzl, Christoph; Kibies, Patrick; Imoto, Sho; Frach, Roland; Suladze, Saba; Winter, Roland; Marx, Dominik; Horinek, Dominik; Kast, Stefan M.
2016-04-01
Accurate force fields are one of the major pillars on which successful molecular dynamics simulations of complex biomolecular processes rest. They have been optimized for ambient conditions, whereas high-pressure simulations become increasingly important in pressure perturbation studies, using pressure as an independent thermodynamic variable. Here, we explore the design of non-polarizable force fields tailored to work well in the realm of kilobar pressures - while avoiding complete reparameterization. Our key is to first compute the pressure-induced electronic and structural response of a solute by combining an integral equation approach to include pressure effects on solvent structure with a quantum-chemical treatment of the solute within the embedded cluster reference interaction site model (EC-RISM) framework. Next, the solute's response to compression is taken into account by introducing pressure-dependence into selected parameters of a well-established force field. In our proof-of-principle study, the full machinery is applied to N,N,N-trimethylamine-N-oxide (TMAO) in water being a potent osmolyte that counteracts pressure denaturation. EC-RISM theory is shown to describe well the charge redistribution upon compression of TMAO(aq) to 10 kbar, which is then embodied in force field molecular dynamics by pressure-dependent partial charges. The performance of the high pressure force field is assessed by comparing to experimental and ab initio molecular dynamics data. Beyond its broad usefulness for designing non-polarizable force fields for extreme thermodynamic conditions, a good description of the pressure-response of solutions is highly recommended when constructing and validating polarizable force fields.
NASA Astrophysics Data System (ADS)
Ferrando, A.; García-March, M. A.
2016-06-01
We present a novel procedure for solving the Schrödinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use scattering modes, which are solutions to the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore allow the problem to be solved. To construct the scattering modes one needs to obtain a particular set of polynomials, which play an analogous role to Laguerre polynomials for Laguerre–Gaussian modes. We demonstrate here the recurrence relations needed to determine these polynomials. To stress the utility and strength of the method we solve first the problem of an initial Gaussian beam with two positive singularities and a negative one embedded in it. We show that the solution permits one to obtain analytical expressions. These can used to obtain mathematical expressions for meaningful quantities, such as the distance at which the positive and negative singularities merge, closing the loop of a vortex line. Furthermore, we present an example of the calculation of an specific discrete-Gauss state, which is the solution of the diffraction of a Laguerre–Gauss state showing definite angular momentum (that is, a highly charged vortex) by a thin diffractive element showing certain discrete symmetry. We show that this problem is therefore solved in a much simpler way than by using the previous procedure based on the integral Fresnel diffraction method.
Borghero, Francesco; Demontis, Francesco
2016-09-01
In the framework of geometrical optics, we consider the following inverse problem: given a two-parameter family of curves (congruence) (i.e., f(x,y,z)=c_{1},g(x,y,z)=c_{2}), construct the refractive-index distribution function n=n(x,y,z) of a 3D continuous transparent inhomogeneous isotropic medium, allowing for the creation of the given congruence as a family of monochromatic light rays. We solve this problem by following two different procedures: 1. By applying Fermat's principle, we establish a system of two first-order linear nonhomogeneous PDEs in the unique unknown function n=n(x,y,z) relating the assigned congruence of rays with all possible refractive-index profiles compatible with this family. Moreover, we furnish analytical proof that the family of rays must be a normal congruence. 2. By applying the eikonal equation, we establish a second system of two first-order linear homogeneous PDEs whose solutions give the equation S(x,y,z)=const. of the geometric wavefronts and, consequently, all pertinent refractive-index distribution functions n=n(x,y,z). Finally, we make a comparison between the two procedures described above, discussing appropriate examples having exact solutions. PMID:27607492
Predicting Raman Spectra of Aqueous Silica and Alumina Species in Solution From First Principles
NASA Astrophysics Data System (ADS)
Hunt, J. D.; Schauble, E. A.; Manning, C. E.
2006-12-01
Dissolved silica and alumina play an important role in lithospheric fluid chemistry. Silica concentrations in aqueous fluids vary over the range of crustal temperatures and pressures enough to allow for significant mass transport of silica via fluid-rock interaction. The polymerization of silica, and the possible incorporation of alumina into the polymer structure, could afford crystal-like or melt-like sites to otherwise insoluble elements such as titanium, leading to enhanced mobility. Raman spectroscopy in a hydrothermal diamond anvil cell (HDAC) has been used to study silica polymerization at elevated pressure and temperature [Ref. 1, 2], but Raman spectra of expected solutes are not fully understood. We calculated Raman spectra of H4SiO4 monomers, H6Si2O7 dimers, and H6SiAlO_7^- dimers, from first principles using hybrid density functional theory (B3LYP). These spectra take into account the variation in bridging angle (Si-O-Si and Si-O-Al angles) that the dimers will have at a given temperature by calculating a potential energy surface of the dimer as the bridging angle varies, and using a Boltzmann distribution at that temperature to determine relative populations at each geometry. Solution effects can be incorporated by using a polarizable continuum model (PCM), and a potential energy surface has been constructed for the silica dimer using a PCM. The bridging angle variation explains the broadness of the 630 cm^-^1 silica dimer peak observed in HDAC experiments [Ref. 1, 2] at high temperatures. The silica-alumina dimer bridging angle is shown to be stiffer than the silica dimer bridging angle, which results in a much narrower main peak. The synthetic spectrum obtained for the silica-alumina dimer suggests that there may be a higher ratio of complexed alumina to free alumina in solution at highly basic pH than previously estimated [Ref. 3]. References: 1. Zotov, N. and H. Keppler, Chemical Geology, 2002. 184: p. 71-82. 2. Zotov, N. and H. Keppler, American
Cocchietto, Moreno; Blasi, Paolo; Lapasin, Romano; Moro, Chiara; Gallo, Davide; Sava, Gianni
2013-01-01
Purpose: to design, assemble and test a prototype of a novel production plant, suitable for producing microparticles (MPs) by processing highly viscous feed solutions (FSs). Methods: the prototype has been built using a commercial air compressor, a piston pump, an airless spray-gun, a customized air-treatment section, a timer, a rotating base, and a filtration section. Preliminary prototype parameter setting was carried out to individuate the best performing nozzle’s dimension, the nebulization timing, and the CaCl2 concentration in the gelation fluid. In addition, prototype throughput (1 L to 5 L) and the range of practicable feed solution (FS) viscosities were assayed. A set of four batches was prepared in order to characterize the MPs, in terms of mean particle size and distribution, flow properties, swelling, encapsulation efficiency and release. Results: according to a qualitative scoring, the large nozzle was suitable to nebulize FSs at a higher alginate concentration. Conversely, the small nozzle performed better in the processing of FSs with an alginate concentration up to 2% w/v. Only at the highest degree of viscosity, corresponding to 5% w/v of alginate, the FS processing was not technically possible. Among the CaCl2 concentrations considered, 15% w/v was recognized as the most versatile. The prototype appears to be convenient and suitable to grant a high yield starting from 2 L of FS. The flow behavior of the FSs assayed can be satisfactorily described with the Carreau-Yasuda equation and the throughput begins to slightly decrease for FSs at alginate concentrations exceeding 3% w/v. MP morphology was irregular with crumpled shape. The angle of repose indicates a good flowability and the release studies showed gastro-resistance and potential prolonged release applications. Conclusions: the novel prototype of production plant is suitable to process large amounts (2 L or more) of FSs, characterized by a high viscosity, to produce MPs suitable for
NASA Astrophysics Data System (ADS)
Xu, Hongsheng; Wei, Chang; Li, Cunxiong; Deng, Zhigan; Li, Minting; Li, Xingbin
2014-10-01
The dissolution kinetics of hemimorphite with low sulfuric acid solution was investigated at high temperature. The dissolution rate of zinc was obtained as a function of dissolution time under the experimental conditions where the effects of sulfuric acid concentration, temperature, and particle size were studied. The results showed that zinc extraction increased with an increase in temperature and sulfuric acid concentration and with a decrease in particle size. A mathematical model able to describe the process kinetics was developed from the shrinking core model, considering the change of the sulfuric acid concentration during dissolution. It was found that the dissolution process followed a shrinking core model with "ash" layer diffusion as the main rate-controlling step. This finding was supported with a linear relationship between the apparent rate constant and the reciprocal of squared particle radius. The reaction order with respect to sulfuric acid concentration was determined to be 0.7993. The apparent activation energy for the dissolution process was determined to be 44.9 kJ/mol in the temperature range of 373 K to 413 K (100 °C to 140 °C). Based on the shrinking core model, the following equation was established:
NASA Astrophysics Data System (ADS)
Shi, Chengming; Wang, Yang; Hu, Huili; Yang, Ying
2010-06-01
For utilization of the residual heat of flue gas to drive the absorption chillers, a lithium-bromide falling film in vertical tube type generator is presented. A mathematical model was developed to simulate the heat and mass coupled problem of laminar falling film evaporation in vertical tube. In the model, the factor of mass transfer was taken into account in heat transfer performance calculation. The temperature and concentration fields were calculated. Some tests were conducted for the factors such as Re number, heating flux, the inlet concentration and operating pressure which can affect the heat and mass transfer performance in laminar falling film evaporation. The heat transfer performance is enhanced with the increasing of heat flux. An increasing inlet concentration can weaken the heat transfer performance. The operating pressure hardly affects on heat and mass transfer. The bigger inlet Re number means weaker heat transfer effects and stronger mass transfer. The mass transfer obviously restrains the heat transfer in the falling film solution. The relation between dimensionless heat transfer coefficient and the inlet Re number is obtained.
NASA Astrophysics Data System (ADS)
Xu, C.; Mudunuru, M. K.; Nakshatrala, K. B.
2016-06-01
The mechanical response, serviceability, and load-bearing capacity of materials and structural components can be adversely affected due to external stimuli, which include exposure to a corrosive chemical species, high temperatures, temperature fluctuations (i.e., freezing-thawing), cyclic mechanical loading, just to name a few. It is, therefore, of paramount importance in several branches of engineering—ranging from aerospace engineering, civil engineering to biomedical engineering—to have a fundamental understanding of degradation of materials, as the materials in these applications are often subjected to adverse environments. As a result of recent advancements in material science, new materials such as fiber-reinforced polymers and multi-functional materials that exhibit high ductility have been developed and widely used, for example, as infrastructural materials or in medical devices (e.g., stents). The traditional small-strain approaches of modeling these materials will not be adequate. In this paper, we study degradation of materials due to an exposure to chemical species and temperature under large strain and large deformations. In the first part of our research work, we present a consistent mathematical model with firm thermodynamic underpinning. We then obtain semi-analytical solutions of several canonical problems to illustrate the nature of the quasi-static and unsteady behaviors of degrading hyperelastic solids.
X-ray cone-beam computed tomography: principles, applications, challenges and solutions
NASA Astrophysics Data System (ADS)
Noo, Frederic
2010-03-01
In the nineties, x-ray computed tomography, commonly referred to as CT, seemed to be on the track to become old technology, bound to be replaced by more sophisticated techniques such as magnetic resonance imaging, due in particular to the harmful effects of x-ray radiation exposure. Yet, the new century brought with it new technology that allowed a complete change in trends and re-affirmed CT as an essential tool in radiology. For instance, the popularity of CT in 2007 was such that approximately 68.7 million CT examinations were performed in the United States, which was nearly 2.5 times the number of magnetic resonance (MRI) examinations. More than that, CT has expanded beyond its conventional diagnostic role; CT is now used routinely in interventional radiology and also in radiation therapy treatment. The technology advances that allowed the revival of CT are those that made fast, accurate cone-beam data acquisition possible. Nowadays, cone-beam data acquisition allows scanning large volumes with isotropic sub-millimeter spatial resolution in a very fast time, which can be as short as 500ms for cardiac imaging. The principles of cone-beam imaging will be first reviewed. Then a discussion of its applications will be given. Old and new challenges will be presented along the way with current solutions.
Seo, Dong-Hwa; Shin, Hyeyoung; Kang, Kisuk; Kim, Hyungjun; Han, Sang Soo
2014-06-01
We report an innovative route for designing novel functional alloys based on first-principles calculations, which is an isoelectronic solid solution (ISS) of two metal elements to create new characteristics that are not native to the constituent elements. Neither Rh nor Ag exhibits hydrogen storage properties, whereas the Rh50Ag50 ISS exhibits properties similar to Pd; furthermore, Au cannot dissociate H2, and Ir has a higher energy barrier for the H2 dissociation reaction than Pt, whereas the Ir50Au50 ISS can dissociate H2 in a similar way to Pt. In the periodic table, Pd is located between Rh and Ag, and Pt is located between Ir and Au, leading to similar atomic and electronic structures between the pure metals (Pd and Pt) and the ISS alloys (Rh50Ag50 and Ir50Au50). From a practical perspective, the Ir-Au ISS would be more cost-effective to use than pure Pt, and could exhibit catalytic activity equivalent to Pt. Therefore, the Ir50Au50 ISS alloy can be a potential catalyst candidate for the replacement of Pt. PMID:26273859
First-principles study of the solid solution of hydrogen in lanthanum
Schoellhammer, Gunther; Herzig, Peter; Wolf, Walter; Vajda, Peter; Yvon, Klaus
2011-09-01
Results from first-principles investigations of the energetical, structural, electronic, and vibrational properties of model structures probing the metal-rich region of the lanthanum-hydrogen system, i.e., the region of the solid solution of hydrogen in lanthanum, are presented. We have studied the site preference and the ordering tendency of hydrogen atoms interstitially bonded in close-packed lanthanum. Spatially separated hydrogen atoms have turned out to exhibit an energetical preference for the occupation of octahedral interstitial sites at low temperature. Indications for a reversal of the site preference in favor of the occupation of tetrahedral interstitial sites at elevated temperature have been found. Linear arrangements consisting of pairs of octahedrally and/or tetrahedrally coordinated hydrogen atoms collinearly bonded to a central lanthanum atom have turned out to be energetically favorable structure elements. Further stabilization is achieved if such hydrogen pairs are in turn linked together so that extended chains of La-H bonds are formed. Pair formation and chain linking counteract the energetical preference for octahedral coordination observed for separated hydrogen atoms.
NASA Astrophysics Data System (ADS)
Romano, Vittorio; Majorana, Armando; Coco, Marco
2015-12-01
A new algorithm for Monte Carlo simulations of charge transport in semiconductors is devised in order to properly deal with Pauli's exclusion principle in the degenerate case. Applications are presented in the case of monolayer graphene and comparisons with solutions of the Boltzmann equation obtained by using a discontinuous Galerkin method furnish a cross-validation of the proposed approach.
The Problem Is the Solution: Creating Original Problems in Gifted Mathematics Classes
ERIC Educational Resources Information Center
Matsko, Vince; Thomas, Jerald
2014-01-01
The purpose of this exploratory study was to assess the effect of a novel approach to mathematics instruction on gifted high school students' engagement, motivation, and metacognition. Participants in this study included gifted students who were enrolled in a 3-year, residential, specialized mathematics and science high school. Rather than…
Mathematics Teaching and Learning Environments Come of Age: Some New Solutions to Some Old Problems.
ERIC Educational Resources Information Center
White, James E.
1989-01-01
Discussion of teaching college level mathematics using computer algebra systems (CAS) focuses on a new microcomputer-based teaching/learning environment called Computer Algebra and Logo (CAL). Highlights include the teachers' role in the development of mathematics teaching and learning environments; methods and goals of implementation; and…
ERIC Educational Resources Information Center
Livy, Sharyn; Vale, Colleen
2011-01-01
In this article, pre-service teachers' mathematics content knowledge is explored through the analysis of two items about ratio from a Mathematical Competency, Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors and misconceptions in their responses are presented and discussed. Of particular interest was the range…
First-Principles Studies of Conformation and Solution Effects on DNA Transport
NASA Astrophysics Data System (ADS)
Tan, Bikan
DNA charge transport (CT) has attracted considerable attention by the scientific community over the past 20 years. This interest reflects the potential of DNA CT to provide a sensitive route for signaling, whether in the construction of a nano-scale biosensor or as an enzymatic tool to detect damage in the genome. Research in DNA CT began as a quest to determine whether the DNA double helix with pi-stacked base pairs might share the conductive characteristics of pi-stacked solids. Physicists carried out sophisticated experiments to measure the conductivity of DNA. But the means to connect DNA to the electrodes, as well as the conditions under which the conductivity was measured are different among many experiments, as the results of the current measurements. DNA CT was seen to depend upon the connection between electrodes and DNA, and coupling between the DNA base pair stacks. Importantly, for those studies that utilized well-characterized connections to the DNA and preserved the duplex native conformation in buffered solution, significant electron conductivities were achieved. Certainly, the debate among researches has shifted from "Is DNA CT possible?" to "How does it work?". To investigate the remarkable characteristics of the double-helix molecule, we use a first-principle technique combined with molecular dynamics simulations to calculate the transport properties of B-DNA sandwiched between carbon nanotubes via alkane linkers. The quantum results using the NEGF method are calculated from snapshots recorded in MD trajectories. In chapter 1, we will go through the basic quantum and classic theories on which our calculations are based. The subject of DNA structure, electronic properties and its potential application in many fields will be introduced in chapter 2. In chapter 3, we discuss our results towards the understanding of the mechanism of DNA charge transport.
Liu, Wei; Xu, Yichun; Li, Xiangyan; Wu, Xuebang Liu, C. S.; Liang, Yunfeng; Wang, Zhiguang
2015-05-07
Although there have been some investigations on behaviors of solutes in metals under strain, the underlying mechanism of how strain changes the stability of a solute is still unknown. To gain such knowledge, first-principles calculations are performed on substitution energy of transition metal solutes in fcc Al host under rhombohedral strain (RS). Our results show that under RS, substitution energy decreases linearly with the increase of outermost d radius r{sub d} of the solute due to Pauli repulsion. The screened Coulomb interaction increases or decreases the substitution energy of a solute on condition that its Pauling electronegativity scale ϕ{sub P} is less or greater than that of Al under RS. This paper verifies a linear relation of substitution energy change versus r{sub d} and ϕ{sub P} under RS, which might be instructive for composition design of long life alloys serving in high stress condition.
Thermodynamic properties of CexTh1-xO2 solid solution from first-principles calculations
Xiao, Haiyan Y.; Zhang, Yanwen; Weber, William J.
2012-11-02
A systematic study based on first-principles calculations along with a quasi-harmonic approximation has been conducted to calculate the thermodynamic properties of the CexTh1xO2 solid solution. The predicted density, thermal expansion coefficients, heat capacity and thermal conductivity for the CexTh1xO2 solid solution all agree well with the available experimental data. The thermal expansion coefficient for ThO2 increases with CeO2 substitution, and complete substitution shows the highest expansion coefficient. On the other hand, the mixed CexTh1xO2 (0 < x < 1) solid solution generally exhibits lower heat capacity and thermal conductivity than the ThO2 and CeO2 end members. Our calculations indicate a strong effect of Ce concentration on the thermodynamic properties of the CexTh1xO2 solid solution.
ERIC Educational Resources Information Center
Kelly, Angela M.; Gningue, Serigne M.; Qian, Gaoyin
2015-01-01
This study explored the challenges facing 1st-year alternatively certified teachers of mathematics and science in urban middle schools. Four teachers, participants in a National Science Foundation (NSF)-funded Robert Noyce Scholarship Program, were followed from preservice training through their 1st year of teaching, having taken part in…
ERIC Educational Resources Information Center
Wright, Bob
1992-01-01
It is argued that Australian elementary mathematics curricula have been influenced by earlier British and United States educational movements and theories and are out of touch with current research emphasizing a constructivist approach. A new model of young children's numerical development is offered, and recommendations for improving mathematical…
Undergraduate Students' Preference for Procedural to Conceptual Solutions to Mathematical Problems
ERIC Educational Resources Information Center
Engelbrecht, Johann; Bergsten, Christer; Kagesten, Owe
2009-01-01
This article reports on a collaboration project between South Africa and Sweden, in which we want to investigate whether the emphasis in undergraduate mathematics courses for engineering students should be more conceptual than the current traditional way of teaching. On the basis of a review of the distinction between conceptual and procedural…
A first principle particle mesh method for solution SAXS of large bio-molecular systems
NASA Astrophysics Data System (ADS)
Marchi, Massimo
2016-07-01
This paper will show that the solution small angle X-ray scattering (SAXS) intensity of globular and membrane proteins can be efficiently and accurately computed from molecular dynamics trajectories using 3D fast Fourier transforms (FFTs). A suitable particle meshing interpolation, similar to the one used in smooth particle mesh Ewald for electrostatic energies and forces, was combined with a uniform solvent density FFT padding scheme to obtain a convenient SAXS spectral resolution. The CPU time scaling of the method, as a function of system size, is highly favorable and its application to large systems such as solutions of solvated membrane proteins is computationally undemanding. Differently from other approaches, all contributions from the simulation cell are included. This means that the subtraction of the buffer from the solution scattering intensity is straightforward and devoid of artifact due to ad hoc definitions of proximal and distal solvent intensity contributions.
A first principle particle mesh method for solution SAXS of large bio-molecular systems.
Marchi, Massimo
2016-07-28
This paper will show that the solution small angle X-ray scattering (SAXS) intensity of globular and membrane proteins can be efficiently and accurately computed from molecular dynamics trajectories using 3D fast Fourier transforms (FFTs). A suitable particle meshing interpolation, similar to the one used in smooth particle mesh Ewald for electrostatic energies and forces, was combined with a uniform solvent density FFT padding scheme to obtain a convenient SAXS spectral resolution. The CPU time scaling of the method, as a function of system size, is highly favorable and its application to large systems such as solutions of solvated membrane proteins is computationally undemanding. Differently from other approaches, all contributions from the simulation cell are included. This means that the subtraction of the buffer from the solution scattering intensity is straightforward and devoid of artifact due to ad hoc definitions of proximal and distal solvent intensity contributions. PMID:27475396
First-principles study of interactions between substitutional solutes in bcc iron
NASA Astrophysics Data System (ADS)
Gorbatov, O. I.; Delandar, A. Hosseinzadeh; Gornostyrev, Yu N.; Ruban, A. V.; Korzhavyi, P. A.
2016-07-01
Using density functional theory based calculations, employing the locally self-consistent Green's function method and the projected augmented wave method, we develop a database of solute-solute interactions in dilute alloys of bcc Fe. Interactions within the first three coordination shells are computed for the ferromagnetic state as well as for the paramagnetic (disordered local moment) state of the iron matrix. The contribution of lattice relaxations to the defect interaction energy is investigated in the ferromagnetic state. Implications of the obtained results for modeling the phenomena of point defect clustering and phase precipitation in bcc Fe-based alloys and steel are discussed.
NASA Astrophysics Data System (ADS)
Yao, Ruo-Xia; Wang, Wei; Chen, Ting-Hua
2014-11-01
Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.
Some notes on the numerical solution of shear-lag and mathematically related problems
NASA Technical Reports Server (NTRS)
Kuhn, Paul
1939-01-01
The analysis of box beams with shear deformation of the flanges can be reduced to the solution of a differential equation. The same equation is met in other problems of stress analysis. No analytical solutions of this equation can be given for practical cases, and numerical methods of evaluation must be used. Available methods are briefly discussed. Two numerical examples show the application of the step-by-step method of integration to shear-lag problems.
Phase Stability for the Pd-Si System: First-Principles, Experiments, and Solution-Based Modeling
NASA Astrophysics Data System (ADS)
Zhou, S. H.; Huo, Y.; Napolitano, Ralph E.
2016-01-01
The relative stabilities of the compounds in the binary Pd-Si system were assessed using first-principles calculations and experimental methods. Calculations of lattice parameters and enthalpy of formation indicate that Pd5Si-{μ }, Pd9Si_2-{α }, Pd_3Si-{β }, Pd_2Si-{γ }, and PdSi-{δ } are the stable phases at 0 K (-273 °C). X-ray diffraction analyses (XRD) and electron probe microanalysis (EPMA) of the as-solidified and heat-treated samples support the computational findings, except that the PdSi-{δ } phase was not observed at low temperature. Considering both experimental data and first-principles results, the compounds Pd5Si-{μ }, Pd9Si2-{α }, Pd3Si-{β }, and Pd_2Si-{γ } are treated as stable phases down to 0 K (-273 °C), while the PdSi-{δ } is treated as being stable over a limited range, exhibiting a lower bound. Using these findings, a comprehensive solution-based thermodynamic model is formulated for the Pd-Si system, permitting phase diagram calculation. The liquid phase is described using a three-species association model and other phases are treated as solid solutions, where a random substitutional model is adopted for Pd-fcc and Si-dia, and a two-sublattice model is employed for Pd5Si-{μ }, Pd9Si_2-{α }, Pd_3Si-{β }, Pd_2Si-{γ }, and PdSi-{δ }. Model parameters are fitted using available experimental data and first-principles data, and the resulting phase diagram is reported over the full range of compositions.
Phase Stability for the Pd-Si System. First-Principles, Experiments, and Solution-Based Modeling
Zhou, S. H.; Huo, Y.; Napolitano, Ralph E.
2015-11-05
Relative stabilities of the compounds in the binary Pd-Si system were assessed using first-principles calculations and experimental methods. Calculations of lattice parameters and enthalpy of formation indicate that Pd5Si-μ, Pd9Si2-α, Pd3 Si-β, Pd2 Si-γ, and PdSi-δ are the stable phases at 0 K (-273 °C). X-ray diffraction analyses (XRD) and electron probe microanalysis (EPMA) of the as-solidified and heat-treated samples support the computational findings, except that the PdSi-δ phase was not observed at low temperature. Considering both experimental data and first-principles results, the compounds Pd 5 Si-μ, Pd9 Si2-α, Pd3Si-β, and Pd2Si-γ are treated as stable phases down to 0more » K (-273 °C), while the PdSi-δ is treated as being stable over a limited range, exhibiting a lower bound. Using these findings, a comprehensive solution-based thermodynamic model is formulated for the Pd-Si system, permitting phase diagram calculation. Moreover, the liquid phase is described using a three-species association model and other phases are treated as solid solutions, where a random substitutional model is adopted for Pd-fcc and Si-dia, and a two-sublattice model is employed for Pd5Si-μ, Pd9Si2-α, Pd3Si-β, Pd2Si-γ, and PdSi-δ. Model parameters are fitted using available experimental data and first-principles data, and the resulting phase diagram is reported over the full range of compositions.« less
NASA Astrophysics Data System (ADS)
Kerdsongpanya, Sit; Alling, Björn; Eklund, Per
2013-08-01
We have used first-principles calculations to investigate the trends in mixing thermodynamics of ScN-based solid solutions in the cubic B1 structure. 13 different Sc1-xMxN (M = Y, La, Ti, Zr, Hf, V, Nb, Ta, Gd, Lu, Al, Ga, In) and three different ScN1-xAx (A = P, As, Sb) solid solutions are investigated and their trends for forming disordered or ordered solid solutions or to phase separate are revealed. The results are used to discuss suitable candidate materials for different strategies to reduce the high thermal conductivity in ScN-based systems, a material having otherwise promising thermoelectric properties for medium and high temperature applications. Our results indicate that at a temperature of T = 800 °C, Sc1-xYxN; Sc1-xLaxN; Sc1-xGdxN, Sc1-xGaxN, and Sc1-xInxN; and ScN1-xPx, ScN1-xAsx, and ScN1-xSbx solid solutions have phase separation tendency, and thus, can be used for forming nano-inclusion or superlattices, as they are not intermixing at high temperature. On the other hand, Sc1-xTixN, Sc1-xZrxN, Sc1-xHfxN, and Sc1-xLuxN favor disordered solid solutions at T = 800 °C. Thus, the Sc1-xLuxN system is suggested for a solid solution strategy for phonon scattering as Lu has the same valence as Sc and much larger atomic mass.
Experimental validation of new mathematical solutions for orthotropic plates with clamped edges
NASA Astrophysics Data System (ADS)
Sprinťu, Iuliana; Roateşi, Simona
2013-10-01
This paper deals with analytical solutions for the bending deformation of rectangular orthotropic elastic composite plates with various boundary conditions. The models are based on the classical laminated plate theory (CLPT). The Ritz method, in conjunction with the weighted residue method for the coefficients calculation is used to analytically determine the bending solutions of orthotropic laminated plates subjected to uniform pressure on the bottom laminate, having clamped edges or possessing two opposite edges simply supported and the remaining two edges clamped, respectively. Numerical examples of laminated plates considering similar boundary value problems as treated analytically are presented. It is presented the experimental device and the experimental test results, as well. Thorough comparison between analytical solutions, numerical results and experimental data is performed and a good agreement is obtained.
A mathematical model for the transport of a solute through a porous-walled tube
NASA Astrophysics Data System (ADS)
Griffiths, Ian; Shipley, Rebecca
2012-02-01
Predicting the distribution of solutes or particles in flows within porous-walled tubes is essential to inform the design of cross-flow filtration devices. Here we use Taylor-dispersion theory to derive a radially averaged model for solute transport in a tube with porous walls, where the wall Darcy permeability may vary both spatially and in time. Crucially, this model includes solute advection via both radial and axial flow components, as well as diffusion, and the advection, diffusion and uptake coefficients in the averaged equation are explicitly derived. The model is used to explore the specific example of a hollow-fibre membrane bioreactor for tissue engineering applications - here membrane fouling and cell population expansion mean that the effective membrane permeability is intrinsically coupled to both fluid flow and nutrient transport. We conclude by presenting design considerations that promote spatially uniform cell population growth.
NASA Astrophysics Data System (ADS)
Walsh, Stephen L.
2004-01-01
In several recent papers, M.-P. Aubry et al. have argued that "Hedbergian" principles of chronostratigraphy are being violated by the International Commission on Stratigraphy (ICS) when selecting Global Stratotype Sections and Points (GSSPs) for the formal divisions of the geological time scale. The current debate over the definition of the Paleocene/Eocene (P/E) boundary has been a major focus of their arguments. Unfortunately, Aubry et al. have obscured matters by misusing the term "unit stratotype," and by equivocally using the term "stage" for the very different concepts of "synthem" and "global chronostratigraphic stage." The P/E boundary option most repugnant to Aubry et al. (Carbon Isotope Excursion (CIE)=P/E=Thanetian/Ypresian boundary) is perfectly compatible with H.D. Hedberg's views. In contrast, another option preferred by Aubry et al. (recognition of new ˜1 m.y. duration age/stage between Thanetian and Ypresian) is inconsistent with Hedberg's views. Additional problems with the P/E boundary arguments of Aubry et al. include the fact that a "Ypresian unit stratotype" does not exist, the fact that the base of the Ypresian synthem is not immutable, and the fact that the nannofossil Tribrachiatus digitalis is of dubious relevance to the boundary debate. As for chronostratigraphy in general, Aubry et al. have misrepresented Hedberg's views by: (1) falsely claiming that the content of a stage is what determines its boundaries; (2) misunderstanding the general concept of the boundary stratotype; (3) distorting the "base defines boundary" principle; (4) falsely claiming that traditional (pre-GSSP) chronostratigraphic boundaries cannot be changed; (5) falsely implying that traditional stage unit stratotype boundaries can be adjusted by no more than 300,000 years when defining formal age/stage boundaries with GSSPs; (6) falsely claiming that the definition of a geochronologic/chronostratigraphic boundary should precede its correlation; (7) claiming that
NASA Astrophysics Data System (ADS)
Holota, Petr; Nesvadba, Otakar
2014-05-01
In geodesy mathematical techniques for gravity field studies that rest on the concept of the so-called classical solution of boundary value problems, have a rather traditional position. Nevertheless, the range of the tools for treating problems in this field is much wider. For instance the concept of the weak solution met with a considerable attention. From this point of view the approach is associated with constructing the respective integral kernels or Green's function in case we consider the classical solution concept or with the choice and constructing basis functions in case we are lucking for the weak solution of the problem. Within the tools considered we discuss also the use of reproducing kernels. In both the cases (classical or weak) the construction of the apparatus above represents and important technical step. It is not elementary, but for a number of fundamental boundary value problems the solution is known, in particular in the case of a spherical solution domain. The sphere, however, is rather far from the real shape of the Earth, which is interpreted here in terms of a functional analytic norm. The distance has a negative effect on any attempt to reach the solution of the boundary value problems considered (and to bridge the departure of the Earth's surface from the sphere) by an iteration procedure based on a successive application of a solution technique developed for the spherical boundary. From this point of view the construction of the integral kernels and basis functions for an oblate ellipsoid of revolution means a step closer towards reality. In this contribution we on the one hand give an overview of the results already achieved and subsequently develop the topic. The summation of series of ellipsoidal harmonics is one of the key problems in this connection. Hypergeometric functions and series are applied too. We also show where the use of Legendre elliptic integrals adds to the solution of the problem. It is interesting that they do not
ERIC Educational Resources Information Center
McCulloch, Allison W.; Kenney, Rachael H.; Keene, Karen Allen
2013-01-01
This paper reports on a mixed-methods study of 111 Advanced Placement calculus students' self-reports of their graphing calculator use, comfort, and rationale for trusting a solution produced with or without a graphing calculator when checking written work. It was found that there was no association between gender, teacher-reported…
Predicting hardness of covalent/ionic solid solution from first-principles theory
NASA Astrophysics Data System (ADS)
Hu, Q. M.; Kádas, K.; Hogmark, S.; Yang, R.; Johansson, B.; Vitos, L.
2007-09-01
We introduce a hardness formula for the multicomponent covalent and ionic solid solutions. This expression is tested on nitride spinel materials A3N4 (A=C,Si,Ge) and applied to titanium nitrogen carbide (TiN1-xCx with 0⩽x ⩽1), off-stoichiometric transition-metal nitride (TiN1-x and VN1-x with x ⩽0.25), and B-doped semiconductors (C1-xBx, Si1-xBx, and Ge1-xBx with x ⩽0.1). In all cases, the theoretical hardness is in good agreement with experiments.
NASA Technical Reports Server (NTRS)
Beckwith, I. E.
1974-01-01
The purpose of the present note is to show that on a flat plate where both the wall temperature and mean wall pressure are constant, neither of the limitations of parallel flow or of unity for the turbulent Prandtl number are required in order for the Crocco solution to apply to the turbulent boundary-layer flow. It is shown herein that this result is subject to restrictions on the magnitude of pressure fluctuations. The same analysis is generalized to show that the compressible turbulent boundary layer on an isothermal swept flat plate is independent of the spanwise flow if the molecular Prandtl number is unity.
First-principles studies of conformation and solution effects on DNA transport
NASA Astrophysics Data System (ADS)
Tan, Bikan; Hodak, Miroslav; Lu, Wenchang; Bernholc, Jerry
2014-03-01
The electrical conductivity of DNA molecules is of fundamental interest in the life sciences. We use first-principles techniques combined with molecular dynamical (MD) simulations to calculate transport properties of B-DNA connected to carbon nanotubes via alkane linkers. The quantum transport properties are calculated for over a hundred of snapshots recorded in MD trajectories. We discover that the DNA conformation and especially the overlaps between sequential guanine bases play a critical role in electron transport. DNA charge transport is indeed governed by charge delocalization with wavefunctions extent controlled by geometrical overlaps. Solvent atoms also affect the conductivity, with counterions decreasing the conductance by a factor of 2-3. In addition, we find that water molecules around the double helix screen the negatively-charged phosphate groups suppressing the conductance of DNA. Comparing transport properties of 4-base-pair (BP) with 10-BP DNA, we find weak distance dependence of the conductivity. Finally, we discuss the effect of sequence on DNA conductivity.
Hedayat, Assem; Elmoselhi, Hamdi; Shoker, Ahmed
2012-01-01
Objective. Nanotechnology has the potential to improve hemodialysis membrane technology. Thus, a major objective is to understand how to enhance toxic solute fluxes across these membranes. The aim of this concept building study is to review the application of irreversible thermodynamic (IT) to solute fluxes. Methods. We expanded the application of the Nernst-Planck equation to include the Kedem-Katchalsky equation, pH, membrane thickness, pore size, and electric potential as variables. Results. (1) Reducing the membrane's thickness from 25 μm to 25 nm increased the flux of creatinine, β2-microglobulin, and tumor necrosis factor-α (TNF-α) by a thousand times but prevented completely albumin flux, (2) applying an electric potential of 50–400 mV across the membrane enhanced the flux of the respective molecules by 71.167 × 10−3, 38.7905 × 10−8, and 0.595 × 10−13 mol/s, and (3) changing the pH from 7.35 to 7.42 altered the fluxes minimally. Conclusions. The results supported an argument to investigate the application of IT to study forces of fluxes across membranes. Reducing the membrane's thickness—together with the application of an electrical potential—qualities achievable by nanotechnology, can enhance the removal of uremic toxins by many folds. However, changing the pH at a specific membrane thickness does not affect the flux significantly. PMID:23209903
First-principles investigation of vanadium isotope fractionation in solution and during adsorption
NASA Astrophysics Data System (ADS)
Wu, Fei; Qin, Tian; Li, Xuefang; Liu, Yun; Huang, Jen-How; Wu, Zhongqing; Huang, Fang
2015-09-01
Equilibrium fractionation factors of vanadium (V) isotopes among tri- (V(III)), tetra- (V(IV)) and penta-valent (V(V)) inorganic V species in aqueous system and during adsorption of V(V) to goethite are estimated using first-principles calculation. Our results highlight the dependence of V isotope fractionation on valence states and the chemical binding environment. The heavy V isotope (51V) is enriched in the main V species following a sequence of V(III) < V(IV) < V(V). According to our calculations, at 25 °C, the equilibrium isotope fractionation factor between [V5+O2(OH)2]- and [V4+O(H2O)5]2+ (ln α V (V)- V (IV)) is 3.9‰, and the equilibrium isotope fractionation factor between [V5+O2(OH)2]- and [V3+(OH)3(H2O)3] (ln α V (V)- V (III)) is 6.4‰. In addition, isotope fractionation between +5 valence species [V5+O2(OH)2]- and [V5+O2(H2O)4]+ is 1.5‰ at 25 °C, which is caused by their different bond lengths and coordination numbers (CN). Theoretical calculations also show that light V isotope (50V) is preferentially adsorbed on the surface of goethite. Our work reveals that V isotopes can be significantly fractionated in the Earth's surface environments due to redox reaction and mineral adsorption, indicating that V isotope data can be used to monitor toxic V(V) attenuation processes through reduction or adsorption in natural water systems. In addition, a simple mass balance model suggests that V isotope composition of seawater might vary with change of ambient oxygen levels. Thus our theoretical investigations imply a promising future for V isotopes as a potential new paleo-redox tracer.
A mathematical model for the transfer of soil solutes to runoff under water scouring.
Yang, Ting; Wang, Quanjiu; Wu, Laosheng; Zhang, Pengyu; Zhao, Guangxu; Liu, Yanli
2016-11-01
The transfer of nutrients from soil to runoff often causes unexpected pollution in water bodies. In this study, a mathematical model that relates to the detachment of soil particles by water flow and the degree of mixing between overland flow and soil nutrients was proposed. The model assumes that the mixing depth is an integral of average water flow depth, and it was evaluated by experiments with three water inflow rates to bare soil surfaces and to surfaces with eight treatments of different stone coverages. The model predicted outflow rates were compared with the experimentally observed data to test the accuracy of the infiltration parameters obtained by curve fitting the models to the data. Further analysis showed that the comprehensive mixing coefficient (ke) was linearly correlated with Reynolds' number Re (R(2)>0.9), and this relationship was verified by comparing the simulated potassium concentration and cumulative mass with observed data, respectively. The best performance with the bias error analysis (Nash Sutcliffe coefficient of efficiency (NS), relative error (RE) and the coefficient of determination (R(2))) showed that the predicted data by the proposed model was in good agreement with the measured data. Thus the model can be used to guide soil-water and fertilization management to minimize nutrient runoff from cropland. PMID:27344122
NASA Astrophysics Data System (ADS)
Lachhwani, Kailash; Poonia, Mahaveer Prasad
2012-08-01
In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision makers are respectively defined by determining individual optimal solutions of each of the level decision makers. A possible relaxation of the higher level decision is considered for avoiding decision deadlock due to the conflicting nature of objective functions. Then, fuzzy goal programming approach is used for achieving the highest degree of each of the membership goal by minimizing negative deviational variables. We also provide sensitivity analysis with variation of tolerance values on decision vectors to show how the solution is sensitive to the change of tolerance values with the help of a numerical example.
Qi, Tingting; Curnan, Matthew T.; Kim, Seungchul; Bennett, Joseph W.; Grinberg, Ilya; Rappe, Andrew M.
2011-12-15
Oxygen vacancies in perovskite oxide solid solutions are fundamentally interesting and technologically important. However, experimental characterization of the vacancy locations and their impact on electronic structure is challenging. We have carried out first-principles calculations on two Zr-modified solid solutions, Pb(Zn_{1/3}Nb_{2/3})O₃ and Pb(Mg_{1/3}Nb_{2/3})O₃, in which vacancies are present. We find that the vacancies are more likely to reside between low-valent cation-cation pairs than high-valent cation-cation pairs. Based on the analysis of our results, we formulate guidelines that can be used to predict the location of oxygen vacancies in perovskite solid solutions. Our results show that vacancies can have a significant impact on both the conduction and valence band energies, in some cases lowering the band gap by ≈0.5 eV. The effects of vacancies on the electronic band structure can be understood within the framework of crystal field theory.
Qi, Tingting; Curnan, Matthew T.; Kim, Seungchul; Bennett, Joseph W.; Grinberg, Ilya; Rappe, Andrew M.
2011-12-15
Oxygen vacancies in perovskite oxide solid solutions are fundamentally interesting and technologically important. However, experimental characterization of the vacancy locations and their impact on electronic structure is challenging. We have carried out first-principles calculations on two Zr-modified solid solutions, Pb(Zn1/3Nb2/3)O₃ and Pb(Mg1/3Nb2/3)O₃, in which vacancies are present. We find that the vacancies are more likely to reside between low-valent cation-cation pairs than high-valent cation-cation pairs. Based on the analysis of our results, we formulate guidelines that can be used to predict the location of oxygen vacancies in perovskite solid solutions. Our results show that vacancies can have a significant impactmore » on both the conduction and valence band energies, in some cases lowering the band gap by ≈0.5 eV. The effects of vacancies on the electronic band structure can be understood within the framework of crystal field theory.« less
Ferrannini, Ele; Manca, Maria Laura
2015-04-01
Plasma glucose thresholds for diagnosis of type 2 diabetes are currently based on outcome data (risk of retinopathy), an inherently ill-conditioned approach. A radically different approach is to consider the mechanisms that control plasma glucose, rather than its relation to an outcome. We developed a constraint optimization algorithm to find the minimal glucose levels associated with the maximized combination of insulin sensitivity and β-cell function, the two main mechanisms of glucose homeostasis. We used a training cohort of 1,474 subjects (22% prediabetic, 7.7% diabetic) in whom insulin sensitivity was measured by the clamp technique and β-cell function was determined by mathematical modeling of an oral glucose tolerance test. Optimized fasting glucose levels were ≤ 87 and ≤ 89 mg/dl in ≤ 45-yr-old women and men, respectively, and ≤ 92 and ≤ 95 mg/dl in >45-yr-old women and men, respectively; the corresponding optimized 2-h glucose levels were ≤ 96, ≤ 98, ≤ 103, and ≤ 105 mg/dl. These thresholds were validated in three prospective cohorts of nondiabetic subjects (Relationship Between Insulin Sensitivity and Cardiovascular Disease Study, Botnia Study, and Mexico City Diabetes Study) with baseline and follow-up oral glucose tolerance tests. Of 5,593 participants, 452 progressed to diabetes. Similarly, in the three cohorts, subjects with glucose levels above the estimated thresholds had an odds ratio of 3.74 (95% confidence interval = 2.64-5.48) of progressing, substantially higher than the risk carried by baseline conventionally defined prediabetes [odds ratio = 2.32 (95% confidence interval = 1.91-2.81)]. The concept that optimization of glucose concentrations by direct measures of insulin sensitivity and β-cell function identifies gender- and age-specific thresholds that bear on disease progression is proven in a physiologically sound, quantifiable manner. PMID:25552659
NASA Astrophysics Data System (ADS)
Kuhlmann, Arne; Herd, Daniel; Röβler, Benjamin; Gallmann, Eva; Jungbluth, Thomas
In pig production software and electronic systems are widely used for process control and management. Unfortunately most devices on farms are proprietary solutions and autonomically working. To unify data communication of devices in agricultural husbandry, the international standard ISOagriNET (ISO 17532:2007) was developed. It defines data formats and exchange protocols, to link up devices like climate controls, feeding systems and sensors, but also management software. The aim of the research project, "Information and Data Collection in Livestock Systems" is to develop an ISOagriNET compliant IT system, a so called Farming Cell. It integrates all electronic components to acquire the available data and information for pig fattening. That way, an additional benefit to humans, animals and the environment regarding process control and documentation, can be generated. Developing the Farming Cell is very complex; in detail it is very difficult and long-winded to integrate hardware and software by various vendors into an ISOagriNET compliant IT system. This ISOagriNET prototype shows as a test environment the potential of this new standard.
Borba, Carlos Eduardo; da Silva, Edson Antônio; Fagundes-Klen, Márcia R; Kroumov, Alexander D; Guirardello, Reginaldo
2008-03-21
A copper (II) ions biosorption by Sargassum sp. biomass was studied in a fixed bed column at 30 degrees C and pH 3.5. The experimental curves were obtained for the following feed concentrations -2.08, 4.16, 6.42 and 12.72mmol/L of the copper ions. The mathematical models developed by Thomas and Bohart-Adams were used for description of ions sorption process in the column. The models principle hypothesis is that the mass transfer controlling stage of the process is the adsorption kinetics between sorbate and adsorbent. The phenomena such as intraparticle diffusion, a mass transfer external resistance and axial dispersion effects were out of considerations. Some of the models parameters were experimentally determined (rho(B), epsilon, u(0), C(0)) and the others were evaluated on the bases of the experimental data (k(a1), k(a2)). The unique fitting parameter in all models was the adsorption kinetic constant. The identification procedure was based on the least square statistical method. Simulation results show that the models describe well a copper ions sorption process in a fixed bed column. The used models can be considered as useful tools for adsorption process design and optimization in fixed bed column by using algae biomass of Sargassum sp. as an adsorbent. PMID:17706867
Phase Stability for the Pd-Si System. First-Principles, Experiments, and Solution-Based Modeling
Zhou, S. H.; Huo, Y.; Napolitano, Ralph E.
2015-11-05
Relative stabilities of the compounds in the binary Pd-Si system were assessed using first-principles calculations and experimental methods. Calculations of lattice parameters and enthalpy of formation indicate that Pd_{5}Si-μ, Pd_{9}Si_{2}-α, Pd_{3} Si-β, Pd_{2} Si-γ, and PdSi-δ are the stable phases at 0 K (-273 °C). X-ray diffraction analyses (XRD) and electron probe microanalysis (EPMA) of the as-solidified and heat-treated samples support the computational findings, except that the PdSi-δ phase was not observed at low temperature. Considering both experimental data and first-principles results, the compounds Pd _{5} Si-μ, Pd_{9} Si_{2}-α, Pd_{3}Si-β, and Pd_{2}Si-γ are treated as stable phases down to 0 K (-273 °C), while the PdSi-δ is treated as being stable over a limited range, exhibiting a lower bound. Using these findings, a comprehensive solution-based thermodynamic model is formulated for the Pd-Si system, permitting phase diagram calculation. Moreover, the liquid phase is described using a three-species association model and other phases are treated as solid solutions, where a random substitutional model is adopted for Pd-fcc and Si-dia, and a two-sublattice model is employed for Pd_{5}Si-μ, Pd_{9}Si_{2}-α, Pd_{3}Si-β, Pd_{2}Si-γ, and PdSi-δ. Model parameters are fitted using available experimental data and first-principles data, and the resulting phase diagram is reported over the full range of compositions.
Solution of steady-state, two-dimensional conservation laws by mathematical programming
NASA Technical Reports Server (NTRS)
Lavery, John E.
1991-01-01
A truly two-dimensional algorithm is created for solving the steady-state two-dimensional conservation-law problem. An overdetermined system of algebraic equations is obtained through discretization by finite-volume formulas. These equations are perturbed nonsingularly and are solved by an efficient geometrically oriented l(1) procedure. The basic algorithm and the theory for the linear case f(u) = u are presented, and computational results for the nonlinear case f(u) = sq u are also analyzed. It is noted that the l(1) procedure captures boundary shocks as well as oblige and zigzag interior shocks in bands that are one cell wide, and the solution values are accurate up to the edge of the shock.
ERIC Educational Resources Information Center
Hadlock, Charles R
2013-01-01
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
Van Canneyt, Koen; Van Biesen, Wim; Vanholder, Raymond; Segers, Patrick; Verdonck, Pascal; Eloot, Sunny
2013-01-01
Double lumen (DL) central venous catheters (CVC) often suffer from thrombosis, fibrin sheet formation, and/or suction towards the vessel wall, resulting in insufficient blood flow during hemodialysis. Reversing the catheter connection often restores blood flows, but will lead to higher recirculation. Single lumen (SL) CVCs have often fewer flow problems, but they inherently have some degree of recirculation. To assist bedside clinical decision making on optimal catheter application, we investigated mathematically the differences in dialysis adequacy using different modes of access with CVCs. A mathematical model was developed to calculate reduction ratio (RR) and total solute removal (TSR) of urea, methylguanidine (MG), beta-2-microglobulin (β2M), and phosphate (P) during different dialysis scenarios: 4-h dialysis with a well-functioning DL CVC (DL-normal, blood flow QB 350 ml/min), dysfunctional DL CVC (DL-low flow, QB 250), reversed DL CVC (DL-reversed, QB 350, recirculation R = 10%) and 12 Fr SL CVC (effective QB 273). With DL-normal as reference, urea RR was decreased by 3.5% (DL-reversed), 13.0% (SL), and 15.6% (DL-low flow), while urea TSR was decreased by 3.3% (DL-reversed), 13.2% (SL), and 13.5% (DL-low flow). The same trend was found for MG and P. However, β2M RR decreased only 1.5% with SL CVC although TSR decrease was 17.2%, while RR decreased 21.1% with DL-low flow although TSR decrease was only 4.9%. In the case of dysfunctional DL CVCs, reversing the catheter connection and restoring the blood flow did not impair TSR, with 10% recirculation. The SL CVC showed suboptimal TSR results that were similar to those of the dysfunctional DL CVC. PMID:23280082
Use of Mathematical Models to Generate Alternative Solutions to Water Resources Planning Problems
NASA Astrophysics Data System (ADS)
Chang, Shoou-Yuh; Brill, E. Downey, Jr.; Hopkins, Lewis D.
1982-02-01
An optimization model is generally not a perfect representation of a complex real world planning problem. Optimization models, however, can be used to generate alternatives that are good and different so that analysts and decision makers can examine a wide range of alternatives to gain insight and understanding. Modeling to generate alternatives (MGA) techniques have been designed to serve this purpose. This paper provides a preliminary assessment of the capabilities of the Hop, Skip, Jump (HSJ) method, a random method, and a branch and bound/screening (BBS) method for generating good and different alternative solutions. These three methods are illustrated using an example water resources planning problem represented by a mixed integer programing model. Each method yields sets of alternatives that are different from each other, but for each method the alternatives are different in different ways. Given that all three methods are efficient, it may be most fruitful to use more than one method and thereby to consider alternatives that are not only different, but different in different ways.
NASA Astrophysics Data System (ADS)
Piet, David L.
Ferromagnetic microparticles suspended at the interface between immiscible liquids and energized by an external alternating magnetic field show a rich variety of self-assembled structures, from linear snakes to radial asters, elongated wires to spinning chains to less dense clouds of particles called snails. In order to obtain insight into the fundamental physical mechanisms and the overall balance of forces governing self-assembly, we develop a modeling approach based on analytical solutions of the time-averaged Navier-Stokes equations. These analytical expressions for the self-consistent hydrodynamic flows are then employed to modify effective interactions between the particles, which in turn are formulated in terms of the time-averaged quantities. Our method allows effective computational verification of the mechanisms of self-assembly and leads to a testable predictions on the transitions between various self-assembled patterns. In one set of experiments, it was observed that viscosity is the primary driving force that determines whether asters or snakes appear at steady state. In the second set of experiments where hydrodynamics are less critical, the amplitude and frequency of the applied magnetic field determine whether wires, spinners or snails will appear. The ability to better understand what drives self-assembly and how to control which dynamic structures appear is necessary for further development of such structures and their applications.
NASA Astrophysics Data System (ADS)
Stecca, Guglielmo; Siviglia, Annunziato; Blom, Astrid
2014-05-01
synchronous approach, by which all the variables are updated simultaneously. The non-conservative problem which stems from the developed matrix-vector formulation is solved using path-conservative methods. We perform numerical applications by comparison with the above linearised solutions and with the data from laboratory experiments. Results show that our solution approach is robust, general and accurate. References - Hirano, M. (1971), River bed degradation with armoring, Trans. Jpn. Soc. Civ. Eng., (3), 194-195. - Hirano, M. (1972), Studies on variation and equilibrium state of a river bed composed of nonuniform material, Trans. Jpn. Soc. Civ. Eng., (4), 128-129. - Stecca, G., A. Siviglia, and A. Blom, Mathematical analysis of the Saint-Venant-Hirano model for mixed-sediment morphodynamics, Submitted to Water Resources Research
ERIC Educational Resources Information Center
Reusser, Kurt; And Others
The main concern of this paper is on the psychological processes of how students understand and solve mathematical word problems, and on how this knowledge can be applied to computer-based tutoring. It is argued that only a better understanding of the psychological requirements for understanding and solving those problems will lead to…
Schneider, Hans-Jörg
2015-01-01
The lock-and-key concept is discussed with respect to necessary extensions. Formation of supramolecular complexes depends not only, and often not even primarily on an optimal geometric fit between host and guest. Induced fit and allosteric interactions have long been known as important modifications. Different binding mechanisms, the medium used and pH effects can exert a major influence on the affinity. Stereoelectronic effects due to lone pair orientation can lead to variation of binding constants by orders of magnitude. Hydrophobic interactions due to high-energy water inside cavities modify the mechanical lock-and-key picture. That optimal affinities are observed if the cavity is only partially filled by the ligand can be in conflict with the lock-and-key principle. In crystals other forces than those between host and guest often dominate, leading to differences between solid state and solution structures. This is exemplified in particular with calixarene complexes, which by X-ray analysis more often than other hosts show guest molecules outside their cavity. In view of this the particular problems with the identification of weak interactions in crystals is discussed. PMID:25815592
The principle of superposition and its application in ground-water hydraulics
Reilly, Thomas E.; Franke, O. Lehn; Bennett, Gordon D.
1987-01-01
The principle of superposition, a powerful mathematical technique for analyzing certain types of complex problems in many areas of science and technology, has important applications in ground-water hydraulics and modeling of ground-water systems. The principle of superposition states that problem solutions can be added together to obtain composite solutions. This principle applies to linear systems governed by linear differential equations. This report introduces the principle of superposition as it applies to ground-water hydrology and provides background information, discussion, illustrative problems with solutions, and problems to be solved by the reader.
A New Principle in Physiscs: the Principle "Finiteness", and Some Consequences
Abraham Sternlieb
2010-06-25
In this paper I propose a new principle in physics: the principle of "finiteness". It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement results, including their errors, are always finite, the principle of finiteness postulates that the mathematical formulation of "legitimate" laws of physics should prevent exactly zero or infinite solutions. Some consequences of the principle of finiteness are discussed, in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The consequences are derived independently of any other theory or principle in physics. I propose "finiteness" as a postulate (like the constancy of the speed of light in vacuum, "c"), as opposed to a notion whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories, or principles.
Glimm, J.
2009-10-14
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
NASA Astrophysics Data System (ADS)
Benea, M. L.; Benea, O. D.
2016-02-01
The method used for purchasing the corrosion behaviour the WC coatings deposited by plasma spraying, on a martensitic stainless steel substrate consists in measuring the electrochemical potential of the coating, respectively that of the substrate, immersed in a NaCl solution as corrosive agent. The mathematical processing of the obtained experimental results in Matlab allowed us to make some correlations between the electrochemical potential of the coating and the solution temperature is very well described by some curves having equations obtained by interpolation order 4.
NASA Astrophysics Data System (ADS)
Prosandeev, Serguei A.; Cockayne, Eric; Burton, Benjamin; Trepakov, Vladimir; Kapphan, Siegmar; Savinov, Maxim; Jastrabik, Lubomir
2002-11-01
Experiments on K0.957Li0.043TaO3 samples indicate two different relaxation processes (π and π/2). First-principles computations clarify the natures of these relaxations, and yield good agreement with experiment.
Mathematical modeling of molecular diffusion through mucus
Cu, Yen; Saltzman, W. Mark
2008-01-01
The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia. PMID:19135488
NASA Astrophysics Data System (ADS)
Fang, C. M.; Sluiter, M. H. F.; van Huis, M. A.; Zandbergen, H. W.
2012-10-01
First-principles calculations have been performed for a variety of Ni3X (X = C, N) phases, as well as for NiXy (y = 0 to (1)/(3)) solid solutions to clarify the persistent controversy regarding its magnetic state. The calculations show that the solid solution phases based on hexagonal-close-packed (hcp or ɛ-) Ni have relatively high stability for X concentrations greater than about 0.1 whereas the face-centered-cubic (fcc or γ-) Ni phases are favored for smaller X concentration. Hence, during carburization or nitridization of Ni, a phase transformation is to be expected. In spite of the close-packed nature of both hcp- and fcc-based solid solutions, X quenches the magnetization more effectively in fcc than in hcp-based solid solutions. These findings resolve many apparently contradictory experimental observations concerning C- and N-containing Ni alloys in the literature.
NASA Astrophysics Data System (ADS)
Hughes, Barry D.; Ninham, Barry W.
2016-02-01
A single mathematical theme underpins disparate physical phenomena in classical, quantum and statistical mechanical contexts. This mathematical "correspondence principle", a kind of wave-particle duality with glorious realizations in classical and modern mathematical analysis, embodies fundamental geometrical and physical order, and yet in some sense sits on the edge of chaos. Illustrative cases discussed are drawn from classical and anomalous diffusion, quantum mechanics of single particles and ideal gases, quasicrystals and Casimir forces.
ERIC Educational Resources Information Center
Klanderman, David B.; Moore, Mary Webster; Maxwell, Mandi S.; Robbert, Sharon K.
2013-01-01
We describe several service-learning initiatives implemented by the mathematics and education departments. College students with majors and minors in math and math education have helped to design and implement math events for elementary and middle school students. Formal and informal reflections on these service-related experiences have…
Mathematics Projects Handbook.
ERIC Educational Resources Information Center
Hess, Adrien L.
This handbook is designed as a guide for teachers and students in choosing and developing mathematics projects, from simple demonstrations of mathematical problems or principles that the teacher has assigned as classroom learning experiences to complex, sophisticated exhibits, intended for entrance in fairs and competitions. The use of projects to…
ERIC Educational Resources Information Center
ROSEN, ELLEN F.; STOLUROW, LAWRENCE M.
MANIPULATION OF FRAMES WITHIN PROGRAMED MATHEMATICS TEXTS IN ORDER TO STUDY FOUR VARIABLES YIELDED, IN A PREVIOUSLY REPORTED PAPER, CORRELATIONAL DATA (FOR RELATIVELY SMALL TREATMENT GROUPS) THAT ARE PRESENTED HERE. FIRST, THE ORDER OF PRESENTATION OF PROGRAMED MATERIAL (BEFORE, AFTER, AND WITHOUT CONVENTIONAL INSTRUCTION) HAD NO EFFECT ON…
On the Dirichlet's Box Principle
ERIC Educational Resources Information Center
Poon, Kin-Keung; Shiu, Wai-Chee
2008-01-01
In this note, we will focus on several applications on the Dirichlet's box principle in Discrete Mathematics lesson and number theory lesson. In addition, the main result is an innovative game on a triangular board developed by the authors. The game has been used in teaching and learning mathematics in Discrete Mathematics and some high schools in…
ERIC Educational Resources Information Center
Knoche, Wilhelm; Rees, Norman H.
1984-01-01
Background information, procedures, and typical results are provided for an experiment on the decomposition of murexide in acid solution. The experiment, suitable for advanced courses, can be easily performed in a 6-hour laboratory period. (JN)
NASA Technical Reports Server (NTRS)
Eades, J. B., Jr.
1974-01-01
The mathematical developments carried out for this investigation are reported. In addition to describing and discussing the solutions which were acquired, there are compendia of data presented herein which summarize the equations and describe them as representative trace geometries. In this analysis the relative motion problems have been referred to two particular frames of reference; one which is inertially aligned, and one which is (local) horizon oriented. In addition to obtaining the classical initial values solutions, there are results which describe cases having applied specific forces serving as forcing functions. Also, in order to provide a complete state representation the speed components, as well as the displacements, have been described. These coordinates are traced on representative planes analogous to the displacement geometries. By this procedure a complete description of a relative motion is developed; and, as a consequence range rate as well as range information is obtained.
NASA Astrophysics Data System (ADS)
Webb, Garry; Sørensen, Mads Peter; Brio, Moysey; Zakharian, Aramis R.; Moloney, Jerome V.
2004-04-01
The vector Maxwell equations of non-linear optics coupled to a single Lorentz oscillator and with instantaneous Kerr non-linearity are investigated by using Lie symmetry group methods. Lagrangian and Hamiltonian formulations of the equations are obtained. The aim of the analysis is to explore the properties of Maxwell’s equations in non-linear optics, without resorting to the commonly used non-linear Schrödinger (NLS) equation approximation in which a high frequency carrier wave is modulated on long length and time scales due to non-linear sideband wave interactions. This is important in femto-second pulse propagation in which the NLS approximation is expected to break down. The canonical Hamiltonian description of the equations involves the solution of a polynomial equation for the electric field E, in terms of the canonical variables, with possible multiple real roots for E. In order to circumvent this problem, non-canonical Poisson bracket formulations of the equations are obtained in which the electric field is one of the non-canonical variables. Noether’s theorem, and the Lie point symmetries admitted by the equations are used to obtain four conservation laws, including the electromagnetic momentum and energy conservation laws, corresponding to the space and time translation invariance symmetries. The symmetries are used to obtain classical similarity solutions of the equations. The traveling wave similarity solutions for the case of a cubic Kerr non-linearity, are shown to reduce to a single ordinary differential equation for the variable y= E2, where E is the electric field intensity. The differential equation has solutions y= y( ξ), where ξ= z- st is the traveling wave variable and s is the velocity of the wave. These solutions exhibit new phenomena not obtainable by the NLS approximation. The characteristics of the solutions depends on the values of the wave velocity s and the energy integration constant ɛ. Both smooth periodic traveling waves and
Toddlers' Opportunities to Learn Mathematics
ERIC Educational Resources Information Center
Bjorklund, Camilla
2008-01-01
Mathematical knowledge has developed from human activities through thousands of years and is bound to the world and cultures that men and women experience. One can say that mathematics is rooted in humans' everyday life, an environment where people reach agreement regarding principles in mathematics. Through interaction with worldly phenomena and…
STEM Gives Meaning to Mathematics
ERIC Educational Resources Information Center
Hefty, Lukas J.
2015-01-01
The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…
NASA Astrophysics Data System (ADS)
Xiao, Jiusan; Jiang, Bo; Huang, Kai; Jiao, Shuqiang; Zhu, Hongmin
2016-09-01
A series of TiC x N y O z solid solutions were synthesized via solid-state reaction and XRD patterns exhibited a single phase of FCC structure over the whole concentration range. The structural and thermodynamic properties of TiC x N y O z solid solutions were studied using experimental method and first-principles calculations. The difference between the calculated and experimental lattice parameters could be attributed to the vacancies segregated in TiO part. The fitting formulae for lattice parameters and mixing enthalpies were firstly given for TiC x N y O z solid solution over the whole concentration range. The obtained thermodynamic data for TiC x N y O z solid solution properly explained the reaction sequence of the carbothermal reduction of TiO2, providing theoretical foundation for TiC x N y O z solid solution as a kind of prospective material for consuming anode utilized in USTB titanium electrolysis process.
NASA Astrophysics Data System (ADS)
Xiao, Jiusan; Jiang, Bo; Huang, Kai; Jiao, Shuqiang; Zhu, Hongmin
2016-06-01
A series of TiC x N y O z solid solutions were synthesized via solid-state reaction and XRD patterns exhibited a single phase of FCC structure over the whole concentration range. The structural and thermodynamic properties of TiC x N y O z solid solutions were studied using experimental method and first-principles calculations. The difference between the calculated and experimental lattice parameters could be attributed to the vacancies segregated in TiO part. The fitting formulae for lattice parameters and mixing enthalpies were firstly given for TiC x N y O z solid solution over the whole concentration range. The obtained thermodynamic data for TiC x N y O z solid solution properly explained the reaction sequence of the carbothermal reduction of TiO2, providing theoretical foundation for TiC x N y O z solid solution as a kind of prospective material for consuming anode utilized in USTB titanium electrolysis process.
Manko, V. S.; Sanchez-Mondragon, J.; Ruiz, E.
2009-04-15
In this paper we consider a magnetic analog of the double-Reissner-Nordstroem solution and construct the corresponding magnetic potential A{sub {phi}} in the explicit form. The behavior of the resulting solution under the Harrison transformation then naturally singles out the asymmetric black diholes--configurations composed of two nonextreme black holes possessing unequal masses, and charges equal in magnitude but opposite in sign - as its most general subclass for which equilibrium of the black-hole constituents can be achieved with the aid of the external magnetic (or electric) field. We also generalize the double-Reissner-Nordstroem solution to dilaton gravity with arbitrary dilaton coupling, yielding the four-dimensional double-Gibbons-Maeda spacetime. The study of some physical properties of the solutions obtained leads, in particular, to very simple formulas for the areas of the horizons and surface gravities.
McIntosh, Grant J
2013-10-28
A kinetic model of silicate oligomerization in water, up to and including tetramer formation, has been compiled exclusively from rate constants derived from transition state theory based on either quantum chemical data (derived under a hybrid solvation framework) for all bond breaking-forming reactions, or using empirically-based approximated pKa's and diffusion coefficients for rate constants of pH-based and bimolecular steps. The rate constants, based on an exhaustive search of all relevant elementary steps, form the basis of our kinetic model; numerical solution of the resulting rate equations allows the simulation of the reaction system, given a set of initial conditions and with almost no restriction on concentrations, pH, or reaction time, in a matter of only minutes. The model, which we believe contains all possible isomers of both neutral and singly anionic clusters, has been extensively benchmarked and reproduces a number of important experimental observations in the range pH ≈ 4-10. In particular, it provides a good description of the dominant products; product yields and reaction times (also as a function of pH) are in agreement with experiment; the linear relationship between the log of the rate of silica dissolution and pH is well reproduced; the origin of silica scaling naturally arises; and we can also simulate the observed fourth order dependence of the rate of monomer consumption on H4SiO4 concentration. This should be a general approach to exploring solution phase chemistry, and could be a useful complement to more conventional molecular dynamics and Monte Carlo modelling approaches in understanding complex reaction networks in solution. PMID:24026420
NASA Astrophysics Data System (ADS)
Mirme, S.; Mirme, A.
2011-12-01
The paper describes the Nanometer aerosol and Air Ion Spectrometer (NAIS) - a multi-channel aerosol instrument capable of measuring the distribution of ions (charged particles and cluster ions) of both polarities in the electric mobility range from 3.2 to 0.0013 cm2 V-1 s-1 and the distribution of aerosol particles in the size range from 2.0 to 40 nm. We introduce the principles of design, data processing and spectrum deconvolution of the instrument.
NASA Astrophysics Data System (ADS)
Mirme, S.; Mirme, A.
2013-04-01
The paper describes the Neutral cluster and Air Ion Spectrometer (NAIS) - a multichannel aerosol instrument capable of measuring the distribution of ions (charged particles and cluster ions) of both polarities in the electric mobility range from 3.2 to 0.0013 cm2 V-1 s-1 and the distribution of aerosol particles in the size range from 2.0 to 40 nm. We introduce the principles of design, data processing and spectrum deconvolution of the instrument.
NASA Astrophysics Data System (ADS)
Dreybrodt, Wolfgang
1996-04-01
Numerical models of the enlargement of primary fissures in limestone by calcite aggressive water show a complex behavior. If the lengths of the fractures are large and hydraulic heads are low, as is the case in nature, dissolution rates at the exit of the channel determine its development by causing a slow increase of water flow, which after a long gestation time by positive feedback accelerates dramatically within a short time span. Mathematical analysis of simplified approximations yields an analytical expression for the breakthrough time, when this happens, in excellent agreement with the results of a numerical model. This expression quantifies the geometrical, hydraulic, and chemical parameters determining such karst processes. If the lengths of the enlarging channels are small, but hydraulic heads are high, as is the case for artificial hydraulic structures such as dams, it is the widening at the entrance of the flow path which determines the enlargement of the conduit. Within the lifetime of the dam this can cause serious water losses. This can also be explained by mathematical analysis of simplified approximations which yield an analytical threshold condition from which the safety of a dam can be judged. Thus in both cases the dynamic processes of karstification are revealed to gain a deeper understanding of the early development of karst systems. As a further important result, one finds that minimum conditions, below which karstification cannot develop, do not exist.
Ma, Changru; Pietrucci, Fabio; Andreoni, Wanda
2015-07-14
Aqueous monoethanolamine (MEA) solution is commonly used for post-combustion carbon capture via chemical absorption. Extensive research has been carried out to characterize both uptake and release of carbon dioxide (CO2), with the aim of improving process performance. However, an intensive research is still needed on fundamental aspects of the key chemical reactions, to achieve a comprehensive understanding of the cyclic process at the microscopic level and a quantitative assessment. We present several ab initio simulations of MEA solutions at a concentration of 30 wt %-the current standard in the industry-and study the dynamics of key multistep chemical reactions, using the metadynamics technique. Pathways for the entire cycle are investigated and characterized in terms of related free-energy and enthalpy barriers, and of the accompanying variations in both structural and electronic properties. The results of this study lead us to propose, among competing processes, an unforeseen scenario in which the zwitterion acts as sn intermediate not only of CO2 uptake, in the form of carbamate, but also of its release. Rate-limiting steps are the formation of the zwitterion for the former and MEAH(+) deprotonation for the latter. Water is shown to play a multifaceted role, which is crucial in determining the development and the energetics of each step of the reactions. The level of comprehension here achieved for MEA should help defining a strategy for solvent optimization. PMID:26575756
Trinh, Thuat T; Rozanska, Xavier; Delbecq, Françoise; Tuel, Alain; Sautet, Philippe
2016-06-01
The condensation reactions between Ge(OH)4 and Si(OH)4 units in solution are studied to understand the mechanism and stable species during the initial steps of the formation process of Ge containing zeolites under basic conditions. The free energy of formation of (OH)3Ge-O-Ge-(OH)2O(-), (OH)3Si-O-Si-(OH)2O(-), (OH)3Ge-O-Si-(OH)2O(-) and (OH)3Si-O-Ge-(OH)2O(-) dimers is calculated with ab initio molecular dynamics and thermodynamic integration, including an explicit description of the water solvent molecules. Calculations show that the attack of the conjugated base (Ge(OH)3O(-) and Si(OH)3O(-)) proceeds with a smaller barrier at the Ge center. In addition, the formation of the pure germanate dimer is more favorable than that of the germano-silicate structure. These results explain the experimental observation of Ge-Ge and Si-Ge dimer species in solutions, with a few Si-Si ones. PMID:27172391
Jiang, Bo Hou, Na; Huang, Shanyan; Zhou, Gege; Hou, Jungang; Cao, Zhanmin; Zhu, Hongmin
2013-08-15
The lattice parameters, structural stability and electronic structure of titanium oxycarbides (TiC{sub 1−x}O{sub x}, 0≤x≤1) solid solution were investigated by Rietveld refinement and first-principles calculations. Series of TiC{sub 1−x}O{sub x} were precisely synthesized by sintering process under the vacuum. Rietveld refinement results of XRD patterns show the properties of continuous solid solution in TiC{sub 1−x}O{sub x} over the whole composition range. The lattice parameters vary from 0.4324 nm to 0.4194 nm decreasing with increasing oxygen concentration. Results of first-principles calculations reveal that the disorder C/O structure is stable than the order C/O structure. Further investigations of the vacancy in Ti{sub 1−Va}(C{sub 1−x}O{sub x}){sub 1−Va} solid solution present that the structure of vacancy segregated in TiO-part is more stable than the disorder C/O structure, which can be ascribed to the Ti–Ti bond across O-vacancy and the charge redistributed around Ti-vacancy via the analysis of the electron density difference plots and PDOS. - Graphical abstract: XRD of series of titanium oxycarbides (TiC{sub 1−x}O{sub x}, 0≤x≤1) solid solution prepared by adjusting the proportion of TiO in the starting material. Highlights: • Titanium oxycarbides were obtained by sintering TiO and TiC under carefully controlled conditions. • Rietveld refinement results show continuous solid solution with FCC structure in TiC{sub 1−x}O{sub x}. • The disorder C/O structure is stable than the order C/O structure. • Introduction of vacancy segregated in TiO-part is more stable than disorder C/O structure. • Ti–Ti bond across O-vacancy and the charge redistributed around Ti-vacancy enhance structural stability.
NASA Astrophysics Data System (ADS)
Bonetti, Elena; Colli, Pierluigi; Fabrizio, Mauro; Gilardi, Gianni
2016-01-01
We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter χ (related to different symmetries of the crystal lattice in the phase configurations), of the stress (and the displacement u), and of the absolute temperature ϑ. The resulting equations present several technical difficulties to be tackled; in particular, we emphasize the presence of nonlinear coupling terms, higher order dissipative contributions, possibly multivalued operators. As for the evolution of temperature, a highly nonlinear parabolic equation has to be solved for a right hand side that is controlled only in L 1. We prove the existence of a solution for a regularized version by use of a time discretization technique. Then, we perform suitable a priori estimates which allow us pass to the limit and find a weak global-in-time solution to the system.
Making Mathematical Connections by Constructing Tetrahedra
ERIC Educational Resources Information Center
Bergner, Jennifer A.; Groth, Randall E.
2005-01-01
This article describes a polyhedra construction project that illustrates how one activity can address several of the mathematics content standards in the NCTM Principles and Standards for School Mathematics.
Solving Common Mathematical Problems
NASA Technical Reports Server (NTRS)
Luz, Paul L.
2005-01-01
Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.
NASA Astrophysics Data System (ADS)
Khots, Boris; Khots, Dmitriy
2014-12-01
Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.
Khots, Boris; Khots, Dmitriy
2014-12-10
Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.
Munro, Robin E J; Guo, Yike
2009-01-01
Analytical workflow technology, sometimes also called data pipelining, is the fundamental component that provides the scalable analytical middleware that can be used to enable the rapid building and deployment of an analytical application. Analytical workflows enable researchers, analysts and informaticians to integrate and access data and tools from structured and non-structured data sources so that analytics can bridge different silos of information; compose multiple analytical methods and data transformations without coding; rapidly develop applications and solutions by visually constructing analytical workflows that are easy to revise should the requirements change; access domain-specific extensions for specific projects or areas, for example, text extraction, visualisation, reporting, genetics, cheminformatics, bioinformatics and patient-based analytics; automatically deploy workflows directly into web portals and as web services to be part of a service-oriented architecture (SOA). By performing workflow building, using a middleware layer for data integration, it is a relatively simple exercise to visually design an analytical process for data analysis and then publish this as a service to a web browser. All this is encapsulated into what can be referred to as an 'Embedded Analytics' methodology which will be described here with examples covering different scientifically focused data analysis problems. PMID:19597790
Electronic structures of anatase (TiO2)1-x(TaON)x solid solutions: a first-principles study.
Dang, Wenqiang; Chen, Hungru; Umezawa, Naoto; Zhang, Junying
2015-07-21
Sensitizing wide band gap photo-functional materials under visible-light irradiation is an important task for efficient solar energy conversion. Although nitrogen doping into anatase TiO2 has been extensively studied for this purpose, it is hard to increase the nitrogen content in anatase TiO2 because of the aliovalent nitrogen substituted for oxygen, leading to the formation of secondary phases or defects that hamper the migration of photoexcited charge carriers. In this paper, electronic structures of (TiO2)1-x(TaON)x (0 ≤ x ≤ 1) solid solutions, in which the stoichiometry is satisfied with the co-substitution of Ti for Ta along with O for N, are investigated within the anatase crystal structure using first-principles calculations. Our computational results show that the solid solutions have substantially narrower band gaps than TiO2, without introducing any localized energy states in the forbidden gap. In addition, in comparison with the pristine TiO2, the solid solution has a direct band gap when the content of TaON exceeds 0.25, which is advantageous to light absorption. The valence band maximum (VBM) of the solid solutions, which is mainly composed of N 2p states hybridized with O 2p, Ti 3d or Ta 5d orbitals, is higher in energy than that of pristine anatase TiO2 consisting of non-bonding O 2p states. On the other hand, incorporating TaON into TiO2 causes the formation of d-d bonding states through π interactions and substantially lowers the conduction band minimum (CBM) because of the shortened distance between some metal atoms. As a result, the anatase (TiO2)1-x(TaON)x is expected to become a promising visible-light absorber. In addition, some atomic configurations are found to possess exceptionally narrow band gaps. PMID:26096698
2013-01-01
Molybdenum (VI) biosorption process was investigated by marine algae Cystoseria indica pretreated with 0.1 M CaCl2 solution in a packed bed column. The biosorbent was characterized by FTIR, BET and SEM analyses. The results showed that Mo (VI) ions should be chelated with the hydroxyl, carboxyl and amine groups of the biomass. The effects of inlet metal concentration and flow rate on biosorption process were investigated and the experimental breakthrough curves were obtained. Results showed that the maximum biosorption capacity of Ca-pretreated C. indica for Mo (VI) was found to be 18.32 mg/g at optimum flow rate of (1.4 mL/min). The controlled-rate step shifted from external to internal mass transfer limitations, as the flow rate increased. Also, it was observed that the breakthrough and exhaustion time decreased from 17.14 hr to 9.05 hr and from 0.006 h to 0.002 hr respectively, with the increase of flow rate from 0.7 to 2.1 ML/min. The increase in the initial concentration of Mo (VI) solution from 30 to 95 ml min-1 increases the adsorption capacity from 18.32 to 30.19 mg/g and decreases the percentage of Mo (VI) removal from 61 to 38%. Also, the treated volume was the greatest (1.42 L) at the lowest inlet concentration. Column data obtained under different conditions were described using the Thomas, Yoon and Nelson, Yan and Belter models. The breakthrough curve predictions by Belter model were found to be very satisfactory. PMID:23369379
ERIC Educational Resources Information Center
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Wan, Liwen F; Prendergast, David
2014-10-15
The knowledge of Mg solvation structure in the electrolyte is requisite to understand the transport behavior of Mg ions and their dissolution/deposition mechanism at electrolyte/electrode interfaces. In the first established rechargeable Mg-ion battery system [D. Aurbach et al. Nature 2000, 407, 724], the electrolyte is of the dichloro complex (DCC) solution family, Mg(AlCl2BuEt)2/THF, resulting from the reaction of Bu2Mg and EtAlCl2 with a molar ratio of 1:2. There is disagreement in the literature regarding the exact solvation structure of Mg ions in such solutions, i.e., whether Mg(2+) is tetra- or hexacoordinated by a combination of Cl(-) and THF. In this work, theoretical insight into the solvation complexes present is provided based on first-principles molecular dynamics simulations (FPMD). Both Mg monomer and dimer structures are considered in both neutral and positively charged states. We found that, at room temperature, the Mg(2+) ion tends to be tetracoordinated in the THF solution phase instead of hexacoordinated, which is the predominant solid-phase coordination. Simulating the X-ray absorption spectra (XAS) at the Mg K-edge by sampling our FPMD trajectories, our predicted solvation structure can be readily compared with experimental measurements. It is found that when changing from tetra- to hexacoordination, the onset of X-ray absorption should exhibit at least a 1 eV blue shift. We propose that this energy shift can be used to monitor changes in the Mg solvation sphere as it migrates through the electrolyte to electrolyte/electrode interfaces and to elucidate the mechanism of Mg dissolution/deposition. PMID:25243732
Committee on the Undergraduate Program in Mathematics Newsletter Number 6.
ERIC Educational Resources Information Center
Mielke, Paul T., Ed.; And Others
This article presents suggestions to the beginning teacher of college mathematics. It is felt that he should have a knowledge of: (1) the general character of mathematics and its place in our culture, (2) mathematics as a language, (3) mathematics as an art, and (4) mathematics as a science. Suggested principles include: (1) never introduce a new…
English for Students of Mathematics.
ERIC Educational Resources Information Center
Bensoussan, Marsha; Golan, Jonathan
A curriculum unit on English for mathematics students at the University of Haifa is presented. The text content concerns mathematics while integrating language principles. Exercises are included that involve comprehension of geometric diagrams, reading comprehension, word meanings, and restructuring sentences. The 12 sections cover: projective…
Mathematics Projects Handbook. Third Edition.
ERIC Educational Resources Information Center
Hess, Adrien L.; And Others
This handbook is designed as a guide for teachers and students in choosing and developing mathematics projects. Included are materials ranging from simple demonstrations of mathematical problems or principles that the teachers had assigned as classroom learning experiences to complex, sophisticated exhibits intended for fairs and competitions. The…
Mathematics Projects Handbook. Second Edition.
ERIC Educational Resources Information Center
Hess, Adrien L.
This updated handbook is designed as a guide for teachers and students in choosing and developing mathematics projects, from simple demonstrations of mathematical problems or principles that the teacher has assigned as classroom learning experiences to complex, sophisticated exhibits, intended for entries in fairs and competitions. The use of…
ERIC Educational Resources Information Center
Dunlap, Celeste Elizabeth
Much research identifies a gender gap in mathematics and some research points to single-gender mathematics classrooms as a solution to the mathematics gender divide. A 7-week study was conducted in which 5th grade students (N=50) were organized into two mathematics classes. The goal was to examine whether single-gender mathematics classes had an…
The Collective Black and "Principles to Actions"
ERIC Educational Resources Information Center
Martin, Danny Bernard
2015-01-01
In this commentary, Danny Martin describes five key take-aways and two sets of questions that arose from his reading of "Principles to Actions: Ensuring Mathematics Success for All (National Council of Teachers of Mathematics [NCTM], 2014). Martin begins by noting that "Principles to Actions" is clearly a political document that…
Solving Geometry Problems via Mechanical Principles
ERIC Educational Resources Information Center
Man, Yiu Kwong
2004-01-01
The application of physical principles in solving mathematics problems have often been neglected in the teaching of physics or mathematics, especially at the secondary school level. This paper discusses how to apply the mechanical principles to geometry problems via concrete examples, which aims at providing insight and inspirations to physics or…
ERIC Educational Resources Information Center
Reys, Robert; Reys, Rustin
2011-01-01
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…
Physical Principle for Generation of Randomness
NASA Technical Reports Server (NTRS)
Zak, Michail
2009-01-01
A physical principle (more precisely, a principle that incorporates mathematical models used in physics) has been conceived as the basis of a method of generating randomness in Monte Carlo simulations. The principle eliminates the need for conventional random-number generators. The Monte Carlo simulation method is among the most powerful computational methods for solving high-dimensional problems in physics, chemistry, economics, and information processing. The Monte Carlo simulation method is especially effective for solving problems in which computational complexity increases exponentially with dimensionality. The main advantage of the Monte Carlo simulation method over other methods is that the demand on computational resources becomes independent of dimensionality. As augmented by the present principle, the Monte Carlo simulation method becomes an even more powerful computational method that is especially useful for solving problems associated with dynamics of fluids, planning, scheduling, and combinatorial optimization. The present principle is based on coupling of dynamical equations with the corresponding Liouville equation. The randomness is generated by non-Lipschitz instability of dynamics triggered and controlled by feedback from the Liouville equation. (In non-Lipschitz dynamics, the derivatives of solutions of the dynamical equations are not required to be bounded.)
The Principle of General Tovariance
NASA Astrophysics Data System (ADS)
Heunen, C.; Landsman, N. P.; Spitters, B.
2008-06-01
We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical language for combining these ideas is topos theory, a framework earlier proposed for physics by Isham and collaborators. Our principle of general tovariance states that any mathematical structure appearing in the laws of physics must be definable in an arbitrary topos (with natural numbers object) and must be preserved under so-called geometric morphisms. This principle identifies geometric logic as the mathematical language of physics and restricts the constructions and theorems to those valid in intuitionism: neither Aristotle's principle of the excluded third nor Zermelo's Axiom of Choice may be invoked. Subsequently, our equivalence principle states that any algebra of observables (initially defined in the topos Sets) is empirically equivalent to a commutative one in some other topos.
Technical Mathematics: Restructure of Technical Mathematics.
ERIC Educational Resources Information Center
Flannery, Carol A.
Designed to accompany a series of videotapes, this textbook provides information, examples, problems, and solutions relating to mathematics and its applications in technical fields. Chapter I deals with basic arithmetic, providing information on fractions, decimals, ratios, proportions, percentages, and order of operations. Chapter II focuses on…
ERIC Educational Resources Information Center
Silver, Edward A.; Ghousseini, Hala; Gosen, Dana; Charalambous, Charalambos; Strawhun, Beatriz T. Font
2005-01-01
Despite general agreement that students should consider more than one way to solve a complex mathematics problem, this practice is rarely observed in U.S. classrooms. In this paper, we examine data that trace the year-long professional development experience of 12 veteran teachers of middle grades mathematics--experienced users of a…
ERIC Educational Resources Information Center
Scheiter, Katharina; Gerjets, Peter; Schuh, Julia
2010-01-01
In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…
Leadership in Mathematics Education: Roles and Responsibilities
ERIC Educational Resources Information Center
Posamentier, Alfred S.
2013-01-01
This article partitions leadership in mathematics education into two categories: leadership in defining and maintaining important principles in teaching mathematics, and leadership in informing the public about the importance of mathematics today and in the future. Examples of both types of leadership are given in the article. Teacher leaders in…
On Fences, Forms and Mathematical Modeling
ERIC Educational Resources Information Center
Lege, Jerry
2009-01-01
The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…
Improving Mathematics Education: Resources for Decision Making.
ERIC Educational Resources Information Center
Leinwand, Steve, Ed.; Burrill, Gail, Ed.
This report describes the message of current publications in mathematics education. Eight documents were selected to be reviewed which provides a starting point for readers. Papers include: (1) "Principles and Standards for School Mathematics"; (2) "Adding It Up: Helping Children Learn Mathematics"; (3) "How People Learn: Brain, Mind, Experience,…
Using Calculators in Mathematics 12. Student Text.
ERIC Educational Resources Information Center
Rising, Gerald R.; And Others
This student textbook is designed to incorporate programable calculators in grade 12 mathematics. The seven chapters contained in this document are: (1) Using Calculators in Mathematics; (2) Sequences, Series, and Limits; (3) Iteration, Mathematical Induction, and the Binomial Theorem; (4) Applications of the Fundamental Counting Principle; (5)…
ERIC Educational Resources Information Center
Hewitt, Paul G.
2004-01-01
Some teachers have difficulty understanding Bernoulli's principle particularly when the principle is applied to the aerodynamic lift. Some teachers favor using Newton's laws instead of Bernoulli's principle to explain the physics behind lift. Some also consider Bernoulli's principle too difficult to explain to students and avoid teaching it…
Compressed modes for variational problems in mathematics and physics
Ozoliņš, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley
2013-01-01
This article describes a general formalism for obtaining spatially localized (“sparse”) solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger’s equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support (“compressed modes”). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size. PMID:24170861
Identification of the noise using mathematical modelling
NASA Astrophysics Data System (ADS)
Dobeš, Josef; Kozubková, Milada; Mahdal, Miroslav
2016-03-01
In engineering applications the noisiness of a component or the whole device is a common problem. Currently, a lot of effort is put to eliminate noise of the already produced devices, to prevent generation of acoustic waves during the design of new components, or to specify the operating problems based on noisiness change. The experimental method and the mathematical modelling method belong to these identification methods. With the power of today's computers the ability to identify the sources of the noise on the mathematical modelling level is a very appreciated tool for engineers. For example, the noise itself may be generated by the vibration of the solid object, combustion, shock, fluid flow around an object or cavitation at the fluid flow in an object. For the given task generating the noise using fluid flow on the selected geometry and propagation of the acoustic waves and their subsequent identification are solved and evaluated. In this paper the principle of measurement of variables describing the fluid flow field and acoustic field are described. For the solution of fluid flow a mathematical model implemented into the CFD code is used. The mathematical modelling evaluation of the flow field is compared to the experimental data.
Boisvert, Ronald F.; Donahue, Michael J.; Lozier, Daniel W.; McMichael, Robert; Rust, Bert W.
2001-01-01
In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST’s current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years. PMID:27500024
Mathematical marriages: intercourse between mathematics and Semiotic choice.
Wagner, Roy
2009-04-01
This paper examines the interaction between Semiotic choices and the presentation and solution of a family of contemporary mathematical problems centred around the so-called 'stable marriage problem'. I investigate how a socially restrictive choice of signs impacts mathematical production both in terms of problem formation and of solutions. I further note how the choice of gendered language ends up constructing a reality, which duplicates the very structural framework that it imported into mathematical analysis in the first place. I go on to point out some semiotic lines of flight from this interlocking grip of mathematics and gendered language. PMID:19831223
Mathematical foundations of biomechanics.
Niederer, Peter F
2010-01-01
The aim of biomechanics is the analysis of the structure and function of humans, animals, and plants by means of the methods of mechanics. Its foundations are in particular embedded in mathematics, physics, and informatics. Due to the inherent multidisciplinary character deriving from its aim, biomechanics has numerous connections and overlapping areas with biology, biochemistry, physiology, and pathophysiology, along with clinical medicine, so its range is enormously wide. This treatise is mainly meant to serve as an introduction and overview for readers and students who intend to acquire a basic understanding of the mathematical principles and mechanics that constitute the foundation of biomechanics; accordingly, its contents are limited to basic theoretical principles of general validity and long-range significance. Selected examples are included that are representative for the problems treated in biomechanics. Although ultimate mathematical generality is not in the foreground, an attempt is made to derive the theory from basic principles. A concise and systematic formulation is thereby intended with the aim that the reader is provided with a working knowledge. It is assumed that he or she is familiar with the principles of calculus, vector analysis, and linear algebra. PMID:21303323
ERIC Educational Resources Information Center
Jones, Thomas A.
1983-01-01
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)
ERIC Educational Resources Information Center
Hanh, Vu Duc, Ed.
This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
Mathematical principle of planar Z-plasty.
Chu, D Y
2000-01-01
To extend the work of precursors attempting to use Z-plasties with angles that have arbitrary degrees and may or may not be equal in size, a comprehensive study was done to clarify and simplify the correlation among the angles, limbs, and diagonals of the geometrical construction of Z-plasties. In geometry, the truth of a proposition must be proved; it is a question to which the answer must be found. By law and formula, a ternary trigonometric equation was derived from a simplified geometric diagram by a trigonometric approach. A procedure declaration accompanies this formula; neither was previously mentioned in the literature. PMID:10626978
ERIC Educational Resources Information Center
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
Mathematical Modeling and Pure Mathematics
ERIC Educational Resources Information Center
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Bogatko, Stuart A.; Bylaska, Eric J.; Weare, John H.
2010-02-11
Results of parameter-free first principles simulations of a spin up 3d5 Fe3+ ion hydrated in an aqueous solution (64 waters, 30 ps, 300 K) are reported. The first hydration shell associated with the first maximum of the radial distribution function, gFeO(r), at d(Fe-OI) = 2.11-2.15 Å, contains 6 waters with average d(OH) = 0.99 Å, in good agreement with observations. A second shell with average coordination number 13.3 can be identified with average shell radius of d(Fe-OII) = 4.21-4.32 Å. The waters in this hydration shell are coordinated to the first shell via a trigonal H-bond network with d(OI-OII) = 2.7-2.9 Å, also in agreement with experimental measurements. The first shell tilt angle average is 33.4° as compared to the reported value of 41°. Wannier-Boys orbitals (WBO) show an interaction between the unoccupied 3d orbitals of the Fe3+ valence (spin up, 3d5) and the occupied spin down lone pair orbitals of first shell waters. The effect of the spin ordering of the Fe3+ ion on the WBO is not observed beyond the first shell. From this local bond analysis and consistent with other observations, the electronic structure of waters in the second shell is similar to that of a bulk water even in this strongly interacting system. H-bond decomposition shows significant bulk-like structure within the second shell for Fe3+. The vibrational density of states shows a first shell red shift of 230 cm^{-1} for the v1,2v2,v3 overtone, in reasonable agreement with experimental estimates for trivalent cations (300 cm^{-1}). No exchanges between first and second shell were observed. Waters in the second shell exchanged with bulk waters via dissociative and associative mechanisms. Results are compared with an AIMD study of Al3+ and 64 waters. For Fe3+ the average first shell tilt angle is larger and the tilt angle distribution wider. H-bond decomposition shows that second shell to second shell H-bonding is enhanced in Fe3+ suggesting an earlier onset of bulk
Mathematics and the Learning Cycle: How the Brain Works as It Learns Mathematics
ERIC Educational Resources Information Center
Zambo, Ronald; Zambo, Debby
2007-01-01
The National Council of Teachers of Mathematics (NCTM) poses constructivist ideas in its "Principles and Standards for School Mathematics" (2000). NCTM supports mathematics instruction that takes a developmental perspective; starts and builds on what children know; and leads children to construct relational understanding, problem-solving…
NASA Astrophysics Data System (ADS)
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Geometrical Analogies in Mathematics Lessons
ERIC Educational Resources Information Center
Eid, Wolfram
2007-01-01
A typical form of thinking to approach problem solutions humanly is thinking in analogous structures. Therefore school, especially mathematical lessons should help to form and to develop corresponding heuristic abilities of the pupils. In the contribution, a summary of possibilities of mathematics lessons regarding this shall particularly be…
The principle of finiteness - a guideline for physical laws
NASA Astrophysics Data System (ADS)
Sternlieb, Abraham
2013-04-01
I propose a new principle in physics-the principle of finiteness (FP). It stems from the definition of physics as a science that deals with measurable dimensional physical quantities. Since measurement results including their errors, are always finite, FP postulates that the mathematical formulation of legitimate laws in physics should prevent exactly zero or infinite solutions. I propose finiteness as a postulate, as opposed to a statement whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories or principles. Some consequences of FP are discussed, first in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The corrected Lorentz transformations include an additional translation term depending on the minimum length epsilon. The relativistic gamma is replaced by a corrected gamma, that is finite for v=c. To comply with FP, physical laws should include the relevant extremum finite values in their mathematical formulation. An important prediction of FP is that there is a maximum attainable relativistic mass/energy which is the same for all subatomic particles, meaning that there is a maximum theoretical value for cosmic rays energy. The Generalized Uncertainty Principle required by Quantum Gravity is actually a necessary consequence of FP at Planck's scale. Therefore, FP may possibly contribute to the axiomatic foundation of Quantum Gravity.
Experimental Mathematics and Mathematical Physics
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
2009-06-26
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
Principles of optical-data processing techniques
NASA Technical Reports Server (NTRS)
Shulman, A. R.
1968-01-01
Document presents optical-data processing information on a level which will convey the basic principles involved to those having a general technical background. Mathematical discussions are included but are not required for a basic understanding.
ERIC Educational Resources Information Center
Prochazka, Helen
2004-01-01
One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
ERIC Educational Resources Information Center
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
2000-01-01
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
ERIC Educational Resources Information Center
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
ERIC Educational Resources Information Center
Siskiyou County Superintendent of Schools, Yreka, CA.
The purpose of this project was to raise the mathematics skills of 100 mathematically retarded students in grades one through eight by one year through the development of an inservice strategy prepared by four teacher specialists. Also used in the study was a control group of 100 students chosen from the median range of stanines on pretest scores…
ERIC Educational Resources Information Center
MacBeath, John; Swaffield, Sue; Frost, David
2009-01-01
This article provides an overview of the "Carpe Vitam: Leadership for Learning" project, accounting for its provenance and purposes, before focusing on the principles for practice that constitute an important part of the project's legacy. These principles framed the dialogic process that was a dominant feature of the project and are presented,…
NASA Astrophysics Data System (ADS)
Lamport, Leslie
2012-08-01
Buridan's principle asserts that a discrete decision based upon input having a continuous range of values cannot be made within a bounded length of time. It appears to be a fundamental law of nature. Engineers aware of it can design devices so they have an infinitessimal probability of not making a decision quickly enough. Ignorance of the principle could have serious consequences.
ERIC Educational Resources Information Center
McCammon, Richard B.
1979-01-01
The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)
The child may have problems in school, including behavior problems and loss of self-esteem. Some children with mathematics disorder become anxious or afraid when given math problems, making the problem even worse.
ERIC Educational Resources Information Center
Johnson, Jerry
1997-01-01
Presents 12 questions related to a given real-life situation about a man shaving and the number of hairs in his beard in order to help students see the connection between mathematics and the world around them. (ASK)
ERIC Educational Resources Information Center
Gardner, Martin
1978-01-01
Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)
NASA Astrophysics Data System (ADS)
Sarwar, S.; Rashidi, M. M.
2016-07-01
This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.
Mathematics of Experimentally Generated Chemoattractant Gradients.
Postma, Marten; van Haastert, Peter J M
2016-01-01
Many eukaryotic cells move in the direction of a chemical gradient. Several assays have been developed to measure this chemotactic response, but no complete mathematical models of the spatial and temporal gradients are available to describe the fundamental principles of chemotaxis. Here we provide analytical solutions for the gradients formed by release of chemoattractant from a point source by passive diffusion or forced flow (micropipettes) and gradients formed by laminar diffusion in a Zigmond chamber. The results show that gradients delivered with a micropipette are formed nearly instantaneously, are very steep close to the pipette, and have a steepness that is strongly dependent on the distance from the pipette. In contrast, gradients in a Zigmond chamber are formed more slowly, are nearly independent of the distance from the source, and resemble the temporal and spatial properties of the natural cAMP wave that Dictyostelium cells experience during cell aggregation. PMID:27271915
From Square Dance to Mathematics
ERIC Educational Resources Information Center
Bremer, Zoe
2010-01-01
In this article, the author suggests a cross-curricular idea that can link with PE, dance, music and history. Teacher David Schmitz, a maths teacher in Illinois who was also a square dance caller, had developed a maths course that used the standard square dance syllabus to teach mathematical principles. He presents an intensive, two-week course…
Problems of Mathematical Finance by Stochastic Control Methods
NASA Astrophysics Data System (ADS)
Stettner, Łukasz
The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.
ERIC Educational Resources Information Center
Uebelacker, James W.
This module considers ordinary linear differential equations with constant coefficients. The "complex method" used to find solutions is discussed, with numerous examples. The unit includes both problem sets and an exam, with answers provided for both. (MP)
Malkevitch, J. ); McCarthy, D. )
1990-01-01
The papers in this volume represent talks given at the monthly meetings of the Mathematics Section of the New York Academy of Sciences. They reflect the operating philosophy of the Section in its efforts to make a meaningful contribution to the mathematical life of a community that is exceedingly rich in cultural resources and intellectual opportunities. Each week during the academic year a dazzling abundance of mathematical seminars and colloquia is available in the New York metropolitan area. Most of these offer highly technical treatments intended for specialists. At the New York Academy we try to provide a forum of a different sort, where interesting ideas are presented in a congenial atmosphere to a broad mathematical audience. Many of the Section talks contain substantial specialized material, but we ask our speakers to include a strong expository component aimed at working mathematicians presumed to have no expert knowledge of the topic at hand. We urge speakers to try to provide the motivating interest they themselves would like to find in an introduction to a field other than their own. The same advice has been given to the authors of the present papers, with the goal of producing a collection that will be both accessible and stimulating to mathematical minds at large. We have tried to provide variety in the mathematical vistas offered; both pure and applied mathematics are well represented. Since the papers are presented alphabetically by author, some guidance seems appropriate as to what sorts of topics are treated, and where. There are three papers in analysis: those by Engber, Narici and Beckenstein, and Todd. Engber's deals with complex analysis on compact Riemann surfaces; Narici and Beckenstein provide an introduction to analysis on non-Archimendean fields; Todd surveys an area of contemporary functional analysis.
Quantum Mechanics and the Principle of Least Radix Economy
NASA Astrophysics Data System (ADS)
Garcia-Morales, Vladimir
2015-03-01
A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum mechanics is then accomplished and it is used to derive the Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new (pre-geometrical) foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann's principle of classical statistical thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics.
Some unsolved problems in discrete mathematics and mathematical cybernetics
NASA Astrophysics Data System (ADS)
Korshunov, Aleksei D.
2009-10-01
There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.
NASA Astrophysics Data System (ADS)
Gao, Zhe; Kang, Shinhoo
2013-03-01
(Ti00.75W0.25)C and (Ti0.75W0.25)(C0.75N0.25) are the major components of hard materials used, for example, in cutting tools. The material properties of these components were investigated using first principle methods. The elastic constants and moduli indicated that (Ti0.75W0.25)C was expected to yield good mechanical properties, with the exception of a poor shear modulus, at working temperatures, around 800 °C (1073 K), relevant to cutting tool operation. The shear modulus worsened upon substitution of nitrogen for carbon due to unfavorable shifts in the material electronic and vibrational structures. From a thermodynamic perspective, (Ti0.75W0.25)(CN0.25) was more stable due to a lower free energy of formation at T<2000 K.
How Bob Barker Would (Probably) Teach Discrete Mathematics
ERIC Educational Resources Information Center
Urness, Timothy
2010-01-01
This article proposes a discrete mathematics course in which games from "The Price Is Right" are used to engage students in a deeper, practical study of discrete mathematics. The games themselves are not the focus of the course; rather, the mathematical principles of the games give motivation for the concepts being taught. The game examples are…
Motivational Qualities of Mathematical Experiences for Turkish Preservice Kindergarten Teachers
ERIC Educational Resources Information Center
Bintas, Jale
2008-01-01
This study is based on the principle that the mathematical anxiety in preservice kindergarten teachers-to-be should be removed and they should be encouraged towards mathematics. It is expected from teachers-to-be who are able to construct this confidence to prepare exercises improving mathematical ideas for their students. This study was carried…
Towards a simple mathematical theory of citation distributions.
Katchanov, Yurij L
2015-01-01
The paper is written with the assumption that the purpose of a mathematical theory of citation is to explain bibliometric regularities at the level of mathematical formalism. A mathematical formalism is proposed for the appearance of power law distributions in social citation systems. The principal contributions of this paper are an axiomatic characterization of citation distributions in terms of the Ekeland variational principle and a mathematical exploration of the power law nature of citation distributions. Apart from its inherent value in providing a better understanding of the mathematical underpinnings of bibliometric models, such an approach can be used to derive a citation distribution from first principles. PMID:26558180
ERIC Educational Resources Information Center
Lee, Chun-Yi; Chen, Ming-Jang; Chang, Wen-Long
2014-01-01
The aim of this study is to investigate the effects of solution methods and question prompts on generalization and justification of non-routine problem solving for Grade 9 students. The learning activities are based on the context of the frog jumping game. In addition, related computer tools were used to support generalization and justification of…
ERIC Educational Resources Information Center
Catterton, Gene; And Others
This material was developed to be used with the non college-bound student in the senior high school. It provides the student with everyday problems and experiences in which practical mathematical applications are made. The package includes worksheets pertaining to letterhead invoices, sales slips, payroll sheets, inventory sheets, carpentry and…
ERIC Educational Resources Information Center
Lapointe, Archie E.; And Others
In 1990-91, 20 countries (Brazil, Canada, China, England, France, Hungary, Ireland, Israel, Italy, Jordan, Korea, Mozambique, Portugal, Scotland, Slovenia, Soviet Union, Spain, Switzerland, Taiwan, and the United States) surveyed the mathematics and science performance of 13-year-old students (and 14 countries also assessed 9-year-olds in the same…
ERIC Educational Resources Information Center
Rogness, Jonathan
2011-01-01
Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…
Thermodynamics of Dilute Solutions.
ERIC Educational Resources Information Center
Jancso, Gabor; Fenby, David V.
1983-01-01
Discusses principles and definitions related to the thermodynamics of dilute solutions. Topics considered include dilute solution, Gibbs-Duhem equation, reference systems (pure gases and gaseous mixtures, liquid mixtures, dilute solutions), real dilute solutions (focusing on solute and solvent), terminology, standard states, and reference systems.…
Optical absorption and band gap reduction in (Fe1-xCrx)2O3 solid solutions: A first-principles study
Wang, Yong; Lopata, Kenneth A.; Chambers, Scott A.; Govind, Niranjan; Sushko, Petr V.
2013-12-02
We provide a detailed theoretical analysis of the character of optical transitions and band gap reduction in (Fe1-xCrx)2O3 solid solutions using extensive periodic model and embedded cluster calculations. Optical absorption bands for x = 0.0, 0.5, and 1.0 are assigned on the basis of timedependent density functional theory (TDDFT) calculations. A band-gap reduction of as much as 0.7 eV with respect to that of pure α-Fe2O3 is found. This result can be attributed to predominantly two effects: (i) the higher valence band edge for x ≈ 0.5, as compared to those in pure α-Fe2O3 and α-Cr2O3, and, (ii) the appearance of Cr Fe d–d transitions in the solid solutions. Broadening of the valence band due to hybridization of the O 2p states with Fe and Cr 3d states also contributes to band gap reduction.
Perez-Rosas, Norma C.; Gomez-Viquez, Norma L.; Dagnino-Acosta, Adan; Santillan, Moises; Guerrero-Hernandez, Agustín
2015-01-01
The process of Ca2+ release from sarcoplasmic reticulum (SR) comprises 4 phases in smooth muscle cells. Phase 1 is characterized by a large increase of the intracellular Ca2+ concentration ([Ca2+]i) with a minimal reduction of the free luminal SR [Ca2+] ([Ca2+]FSR). Importantly, active SR Ca2+ ATPases (SERCA pumps) are necessary for phase 1 to occur. This situation cannot be explained by the standard kinetics that involves a fixed amount of luminal Ca2+ binding sites. A new mathematical model was developed that assumes an increasing SR Ca2+ buffering capacity in response to an increase of the luminal SR [Ca2+] that is called Kinetics-on-Demand (KonD) model. This approach can explain both phase 1 and the refractory period associated with a recovered [Ca2+]FSR. Additionally, our data suggest that active SERCA pumps are a requisite for KonD to be functional; otherwise luminal SR Ca2+ binding proteins switch to standard kinetics. The importance of KonD Ca2+ binding properties is twofold: a more efficient Ca2+ release process and that [Ca2+]FSR and Ca2+-bound to SR proteins ([Ca2+]BSR) can be regulated separately allowing for Ca2+ release to occur (provided by Ca2+-bound to luminal Ca2+ binding proteins) without an initial reduction of the [Ca2+]FSR. PMID:26390403
Sassaroli, E; O'Neill, B E
2014-11-21
High intensity focused ultrasound (HIFU) operated in thermal mode has been reported to reduce interstitial fluid pressure and improve the penetration of large macromolecules and nanoparticles in tumor and normal tissue. Little is understood about how the interstitial fluid pressure and velocity as well as the interstitial macromolecule transport are affected by HIFU exposure. A mathematical model is presented here which sheds light on the initial biophysical changes brought about HIFU. Our continuum model treats tissue as an effective poro-elastic material that reacts to elevated temperatures with a rapid drop in interstitial elastic modulus. Using parameters from the literature, the model is extrapolated to derive information on the effect in tumors, and to predict its impact on the convective and diffusive transport of macromolecular drugs. The model is first solved using an analytical approximation with step-wise changes at each boundary, and then solved numerically starting from a Gaussian beam approximation of the ultrasound treatment. Our results indicate that HIFU causes a rapid drop in interstitial fluid pressure that may be exploited to facilitate convection of macromolecules from vasculature to the exposed region. However, following a short recovery period in which the interstitial fluid pressure is normalized, transport returns to normal and the advantages disappear over time. The results indicate that this effect is strongest for the delivery of large molecules and nanoparticles that are in the circulation at the time of treatment. The model may be easily applied to more complex situations involving effects on vascular permeability and diffusion. PMID:25327766
NASA Astrophysics Data System (ADS)
Sassaroli, E.; O'Neill, B. E.
2014-11-01
High intensity focused ultrasound (HIFU) operated in thermal mode has been reported to reduce interstitial fluid pressure and improve the penetration of large macromolecules and nanoparticles in tumor and normal tissue. Little is understood about how the interstitial fluid pressure and velocity as well as the interstitial macromolecule transport are affected by HIFU exposure. A mathematical model is presented here which sheds light on the initial biophysical changes brought about HIFU. Our continuum model treats tissue as an effective poro-elastic material that reacts to elevated temperatures with a rapid drop in interstitial elastic modulus. Using parameters from the literature, the model is extrapolated to derive information on the effect in tumors, and to predict its impact on the convective and diffusive transport of macromolecular drugs. The model is first solved using an analytical approximation with step-wise changes at each boundary, and then solved numerically starting from a Gaussian beam approximation of the ultrasound treatment. Our results indicate that HIFU causes a rapid drop in interstitial fluid pressure that may be exploited to facilitate convection of macromolecules from vasculature to the exposed region. However, following a short recovery period in which the interstitial fluid pressure is normalized, transport returns to normal and the advantages disappear over time. The results indicate that this effect is strongest for the delivery of large molecules and nanoparticles that are in the circulation at the time of treatment. The model may be easily applied to more complex situations involving effects on vascular permeability and diffusion.
Sassaroli, E; O’Neill, B E
2014-01-01
High intensity focused ultrasound (HIFU) operated in thermal mode has been reported to reduce interstitial fluid pressure and improve the penetration of large macromolecules and nanoparticles in tumor and normal tissue. Little is understood about how the interstitial fluid pressure and velocity as well as the interstitial macromolecule transport are affected by HIFU exposure. A mathematical model is presented here which sheds light on the initial biophysical changes brought about HIFU. Our continuum model treats tissue as an effective poro-elastic material that reacts to elevated temperatures with a rapid drop in interstitial elastic modulus. Using parameters from the literature, the model is extrapolated to derive information on the effect in tumors, and to predict its impact on the convective and diffusive transport of macromolecular drugs. The model is first solved using an analytical approximation with step-wise changes at each boundary, and then solved numerically starting from a Gaussian beam approximation of the ultrasound treatment. Our results indicate that HIFU causes rapid drop in interstitial fluid pressure that may be exploited to facilitate convection of macromolecules from vasculature to the exposed region. However, following a short recovery period in which the interstitial fluid pressure is normalized, transport returns to normal and the advantages disappear over time. The results indicate that this effect is strongest for the delivery of large molecules and nanoparticles that are in the circulation at the time of treatment. The model may be easily applied to more complex situations involving effects on vascular permeability and diffusion. PMID:25327766
Macklin, R
2003-10-01
Gillon is correct that the four principles provide a sound and useful way of analysing moral dilemmas. As he observes, the approach using these principles does not provide a unique solution to dilemmas. This can be illustrated by alternatives to Gillon's own analysis of the four case scenarios. In the first scenario, a different set of factual assumptions could yield a different conclusion about what is required by the principle of beneficence. In the second scenario, although Gillon's conclusion is correct, what is open to question is his claim that what society regards as the child's best interest determines what really is in the child's best interest. The third scenario shows how it may be reasonable for the principle of beneficence to take precedence over autonomy in certain circumstances, yet like the first scenario, the ethical conclusion relies on a set of empirical assumptions and predictions of what is likely to occur. The fourth scenario illustrates how one can draw different conclusions based on the importance given to the precautionary principle. PMID:14519836
Meeting the Curricular Needs of Academically Low-Achieving Students in Middle Grade Mathematics
ERIC Educational Resources Information Center
Woodward, John; Brown, Cyrus
2006-01-01
An important component of the National Council of Teachers of Mathematics Standards is the equity principle: All students should have access to a coherent, challenging mathematics curriculum. Many in the mathematics reform community have maintained that this principle can be achieved through one well-designed curriculum. However, the extant…
Mathematics Curriculum Guide. Mathematics IV.
ERIC Educational Resources Information Center
Gary City Public School System, IN.
GRADES OR AGES: Grade 12. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The subject matter is presented in four columns: major areas, significant outcomes, observations and suggestions, and films and references. The topics include: sets-relations-functions, circular functions, graphs of circular functions, inverses of circular…
Rhodes, Tim; Guise, Andy; Ndimbii, James; Strathdee, Steffanie; Ngugi, Elizabeth; Platt, Lucy; Kurth, Ann; Cleland, Charles; Vickerman, Peter
2015-01-01
Background and objectives Promoted globally as an evidence-based intervention in the prevention of HIV and treatment of heroin addiction among people who inject drugs (PWID), opioid substitution treatment (OST) can help control emerging HIV epidemics among PWID. With implementation in December 2014, Kenya is the third Sub-Saharan African country to have introduced OST. We combine dynamic mathematical modelling with qualitative sociological research to examine the ‘promise of methadone’ to Kenya. Methods, setting and participants We model the HIV prevention impact of OST in Nairobi, Kenya, at different levels of intervention coverage. We draw on thematic analyses of 109 qualitative interviews with PWID, and 43 with stakeholders, to chart their narratives of expectation in relation to the promise of methadone. Results The modelled impact of OST shows relatively slight reductions in HIV incidence (5–10%) and prevalence (2–4%) over 5 years at coverage levels (around 10%) anticipated in the planned roll-out of OST. However, there is a higher impact with increased coverage, with 40% coverage producing a 20% reduction in HIV incidence, even when accounting for relatively high sexual transmissions. Qualitative findings emphasise a culture of ‘rationed expectation’ in relation to access to care and a ‘poverty of drug treatment opportunity’. In this context, the promise of methadone may be narrated as a symbol of hope—both for individuals and community—in relation to addiction recovery. Conclusions Methadone offers HIV prevention potential, but there is a need to better model the effects of sexual HIV transmission in mediating the impact of OST among PWID in settings characterised by a combination of generalised and concentrated epidemics. We find that individual and community narratives of methadone as hope for recovery coexist with policy narratives positioning methadone primarily in relation to HIV prevention. Our analyses show the value of mixed
A mathematical model of post-instability in fluid mechanics
NASA Technical Reports Server (NTRS)
Zak, M. A.
1982-01-01
Postinstability of fluids is eliminated in numerical models by introducing multivalued velocity fields after discarding the principle of impenetrability. Smooth functions are shown to be incapable of keeping the derivatives from going towards infinity when iterating solutions for the governing equations such as those defined by Navier-Stokes. Enlarging the class of functions is shown to be necessary to eliminate the appearance of imaginary characteristic roots in the systems of arbitrary partial differential equations, a condition which leads to physically impossible motions. The enlarging is demonstrated to be achievable by allowing several individual particles with different velocities to appear at the same point of space, and the subsequent multivaluedness of the solutions is purely a mathematical concern, rather than one of actual physical existence. Applications are provided for an inviscid fluid and for turbulence.
NASA Astrophysics Data System (ADS)
Koonprasert, Sanoe; Sangsawang, Rilrada
2008-09-01
This paper presents the analytical solutions and symbolic computations for the temperature distribution of the annular fin under fully-wet surface condition. During the process of dehumidification, the annular fin is separated into two regions. The mathematical models for each region are based on the conservation of energy principle. An assumption used in this paper is the humidity ratio of the saturated air on the wet surface varies linearly with the local fin temperature. The mathematical models are solved by the Cauchy-Euler Equation and modified Bessel Equation to form analytical solutions. Besides, the symbolic computations are shown by the Maple software to visualize the temperature distribution along the fin.
Woidy, Patrick; Bühl, Michael; Kraus, Florian
2015-04-28
Pentaammine dioxido uranium(VI) dibromide ammonia (1/1), [UO2(NH3)5]Br2·NH3, was synthesized in the form of yellow crystals by the reaction of uranyl bromide, UO2Br2, with dry liquid ammonia. The compound crystallizes orthorhombic in space group Cmcm and is isotypic to [UO2(NH3)5]Cl2·NH3 with a = 13.2499(2), b = 10.5536(1), c = 8.9126(1) Å, V = 1246.29(3) Å(3) and Z = 4 at 123 K. The UO2(2+) cation is coordinated by five ammine ligands and the coordination polyhedron can be best described as pentagonal bipyramid. Car-Parrinello molecular dynamics simulations are reported for [UO2(NH3)5](2+) in the gas phase and in liquid NH3 solution (using the BLYP density functional). According to free-energy simulations, solvation by ammonia has only a small effect on the uranyl-NH3 bond strength. PMID:25797497
NASA Astrophysics Data System (ADS)
Koller, C. M.; Koutná, N.; Ramm, J.; Kolozsvári, S.; Paulitsch, J.; Holec, D.; Mayrhofer, P. H.
2016-02-01
Density Functional Theory applying the generalised gradient approximation is used to study the phase stability of (AlxCr1-x)2O3 solid solutions in the context of physical vapour deposition (PVD). Our results show that the energy of formation for the hexagonal α phase is lower than for the metastable cubic γ and B1-like phases-independent of the Al content x. Even though this suggests higher stability of the α phase, its synthesis by physical vapour deposition is difficult for temperatures below 800 °C. Aluminium oxide and Al-rich oxides typically exhibit a multi-phased, cubic-dominated structure. Using a model system of (Al0.69Cr0.31)2O3 which experimentally yields larger fractions of the desired hexagonal α phase, we show that point defects strongly influence the energetic relationships. Since defects and in particular point defects, are unavoidably present in PVD coatings, they are important factors and can strongly influence the stability regions. We explicitly show that defects with low formation energies (e.g. metal Frenkel pairs) are strongly preferred in the cubic phases, hence a reasonable factor contributing to the observed thermodynamically anomalous phase composition.
ERIC Educational Resources Information Center
Ringer, Catharina W.
2013-01-01
In today's mathematics education, there is an increasing emphasis on students' understanding of the mathematics set forth in standards documents such as the "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics, 2000) and, most recently, the "Common Core State Standards for Mathematics"…
Teaching Mathematical Modeling in Mathematics Education
ERIC Educational Resources Information Center
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
Principles of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Landé, Alfred
2013-10-01
Preface; Introduction: 1. Observation and interpretation; 2. Difficulties of the classical theories; 3. The purpose of quantum theory; Part I. Elementary Theory of Observation (Principle of Complementarity): 4. Refraction in inhomogeneous media (force fields); 5. Scattering of charged rays; 6. Refraction and reflection at a plane; 7. Absolute values of momentum and wave length; 8. Double ray of matter diffracting light waves; 9. Double ray of matter diffracting photons; 10. Microscopic observation of ρ (x) and σ (p); 11. Complementarity; 12. Mathematical relation between ρ (x) and σ (p) for free particles; 13. General relation between ρ (q) and σ (p); 14. Crystals; 15. Transition density and transition probability; 16. Resultant values of physical functions; matrix elements; 17. Pulsating density; 18. General relation between ρ (t) and σ (є); 19. Transition density; matrix elements; Part II. The Principle of Uncertainty: 20. Optical observation of density in matter packets; 21. Distribution of momenta in matter packets; 22. Mathematical relation between ρ and σ; 23. Causality; 24. Uncertainty; 25. Uncertainty due to optical observation; 26. Dissipation of matter packets; rays in Wilson Chamber; 27. Density maximum in time; 28. Uncertainty of energy and time; 29. Compton effect; 30. Bothe-Geiger and Compton-Simon experiments; 31. Doppler effect; Raman effect; 32. Elementary bundles of rays; 33. Jeans' number of degrees of freedom; 34. Uncertainty of electromagnetic field components; Part III. The Principle of Interference and Schrödinger's equation: 35. Physical functions; 36. Interference of probabilities for p and q; 37. General interference of probabilities; 38. Differential equations for Ψp (q) and Xq (p); 39. Differential equation for фβ (q); 40. The general probability amplitude Φβ' (Q); 41. Point transformations; 42. General theorem of interference; 43. Conjugate variables; 44. Schrödinger's equation for conservative systems; 45. Schr
Edwards, A W F
2011-03-01
Ernst Mayr called the first part of the evolutionary synthesis the 'Fisherian synthesis' on account of the dominant role played by R.A. Fisher in forging a mathematical theory of natural selection together with J.B.S. Haldane and Sewall Wright in the decade 1922-1932. It is here argued that Fisher's contribution relied on a close reading of Darwin's work to a much greater extent than did the contributions of Haldane and Wright, that it was synthetic in contrast to their analytic approach and that it was greatly influenced by his friendship with the Darwin family, particularly with Charles's son Leonard. PMID:21423339
NASA Astrophysics Data System (ADS)
Zolgharnein, Javad; Asanjrani, Neda; Bagtash, Maryam; Azimi, Gholamhasan
The nanostructure of γ-alumina was used as an effective adsorbent for simultaneous removing of a mixture of alizarin red and alizarin yellow from aqueous solutions. The Taguchi design and principle component analysis were applied to explore effective parameters for achieving a higher adsorption capacity and removal percentage of the binary mixture containing alizarin red and alizarin yellow. Seven factors including temperature, contact time, initial pH value, the shaker rate, the sorbent dose, and initial concentrations of alizarin red and alizarin yellow in three levels were considered through the Taguchi technique. A L27 orthogonal array was used to determine the signal-to-noise ratio. Then, the removal percentage (R%) and adsorption capacity (q) of the above-mentioned dyes were transformed into an accurate S/N ratio. The Taguchi method indicates that the solution pH has the most contribution in controlling the removal percentage of alizarin red and alizarin yellow. Under optimal condition, the maximum removal percentages of 99% and 78.5%, and the capacity uptake of 54.4 and 39.0 mg g-1 were obtained for both alizarin red and alizarin yellow, respectively. Isotherm modeling and kinetic investigations showed that Langmuir, modified Langmuir, and pseudo-second-order models describe both the adsorption equilibrium and kinetic behavior well. The Fourier transform infrared analysis also firmly confirmed the involving active sites of nano γ-alumina in the adsorption process.
A Study of Visualization for Mathematics Education
NASA Technical Reports Server (NTRS)
Daugherty, Sarah C.
2008-01-01
Graphical representations such as figures, illustrations, and diagrams play a critical role in mathematics and they are equally important in mathematics education. However, graphical representations in mathematics textbooks are static, Le. they are used to illustrate only a specific example or a limited set. of examples. By using computer software to visualize mathematical principles, virtually there is no limit to the number of specific cases and examples that can be demonstrated. However, we have not seen widespread adoption of visualization software in mathematics education. There are currently a number of software packages that provide visualization of mathematics for research and also software packages specifically developed for mathematics education. We conducted a survey of mathematics visualization software packages, summarized their features and user bases, and analyzed their limitations. In this survey, we focused on evaluating the software packages for their use with mathematical subjects adopted by institutions of secondary education in the United States (middle schools and high schools), including algebra, geometry, trigonometry, and calculus. We found that cost, complexity, and lack of flexibility are the major factors that hinder the widespread use of mathematics visualization software in education.
Minimum Principles in Motor Control.
Engelbrecht, Sascha E.
2001-06-01
Minimum (or minimal) principles are mathematical laws that were first used in physics: Hamilton's principle and Fermat's principle of least time are two famous example. In the past decade, a number of motor control theories have been proposed that are formally of the same kind as the minimum principles of physics, and some of these have been quite successful at predicting motor performance in a variety of tasks. The present paper provides a comprehensive review of this work. Particular attention is given to the relation between minimum theories in motor control and those used in other disciplines. Other issues around which the review is organized include: (1) the relation between minimum principles and structural models of motor planning and motor control, (2) the empirically-driven development of minimum principles and the danger of circular theorizing, and (3) the design of critical tests for minimum theories. Some perspectives for future research are discussed in the concluding section of the paper. Copyright 2001 Academic Press. PMID:11401453