Three-dimensional elliptic grid generation technique with application to turbomachinery cascades

NASA Technical Reports Server (NTRS)

Chen, S. C.; Schwab, J. R.

1988-01-01

Described is a numerical method for generating 3-D grids for turbomachinery computational fluid dynamic codes. The basic method is general and involves the solution of a quasi-linear elliptic partial differential equation via pointwise relaxation with a local relaxation factor. It allows specification of the grid point distribution on the boundary surfaces, the grid spacing off the boundary surfaces, and the grid orthogonality at the boundary surfaces. A geometry preprocessor constructs the grid point distributions on the boundary surfaces for general turbomachinery cascades. Representative results are shown for a C-grid and an H-grid for a turbine rotor. Two appendices serve as user's manuals for the basic solver and the geometry preprocessor.

Quaternion regularization in celestial mechanics, astrodynamics, and trajectory motion control. III

NASA Astrophysics Data System (ADS)

Chelnokov, Yu. N.

2015-09-01

The present paper1 analyzes the basic problems arising in the solution of problems of the optimum control of spacecraft (SC) trajectory motion (including the Lyapunov instability of solutions of conjugate equations) using the principle of the maximum. The use of quaternion models of astrodynamics is shown to allow: (1) the elimination of singular points in the differential phase and conjugate equations and in their partial analytical solutions; (2) construction of the first integrals of the new quaternion; (3) a considerable decrease of the dimensions of systems of differential equations of boundary value optimization problems with their simultaneous simplification by using the new quaternion variables related with quaternion constants of motion by rotation transformations; (4) construction of general solutions of differential equations for phase and conjugate variables on the sections of SC passive motion in the simplest and most convenient form, which is important for the solution of optimum pulse SC transfers; (5) the extension of the possibilities of the analytical investigation of differential equations of boundary value problems with the purpose of identifying the basic laws of optimum control and motion of SC; (6) improvement of the computational stability of the solution of boundary value problems; (7) a decrease in the required volume of computation.

Stable isotope ratios of carbon and nitrogen and mercury concentrations in 13 toothed whale species taken from the western Pacific Ocean off Japan.

PubMed

Endo, Tetsuya; Hisamichi, Yohsuke; Kimura, Osamu; Haraguchi, Koichi; Lavery, Shane; Dalebout, Merel L; Funahashi, Naoko; Baker, C Scott

2010-04-01

Stable isotope ratios of carbon (partial differential(13)C) and nitrogen (partial differential(15)N) and total mercury (T-Hg) concentrations were measured in red meat samples from 11 odontocete species (toothed whales, dolphins, and porpoises) sold in Japan (n = 96) and in muscle samples from stranded killer whales (n = 6) and melon-headed whales (n = 15), and the analytical data for these species were classified into three regions (northern, central, and southern Japan) depending on the locations in which they were caught or stranded. The partial differential(15)N in the samples from southern Japan tended to be lower than that in samples from the north, whereas both partial differential(13)C and T-Hg concentrations in samples from the south tended to higher than those in samples from northern Japan. Negative correlations were found between the partial differential(13)C and partial differential(15)N values and between the partial differential(15)N value and T-Hg concentrations in the combined samples all three regions (gamma= -0.238, n = 117, P < 0.01). The partial differential(13)C, partial differential(15)N, and T-Hg concentrations in the samples varied more by habitat than by species. Spatial variations in partial differential(13)C, partial differential(15)N, and T-Hg concentrations in the ocean may be the cause of these phenomena.

On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data.

PubMed

Ross, David S; Thurston, George M; Lutzer, Carl V

2008-08-14

In this paper we present a method for determining the free energies of ternary mixtures from light scattering data. We use an approximation that is appropriate for liquid mixtures, which we formulate as a second-order nonlinear partial differential equation. This partial differential equation (PDE) relates the Hessian of the intensive free energy to the efficiency of light scattering in the forward direction. This basic equation applies in regions of the phase diagram in which the mixtures are thermodynamically stable. In regions in which the mixtures are unstable or metastable, the appropriate PDE is the nonlinear equation for the convex hull. We formulate this equation along with continuity conditions for the transition between the two equations at cloud point loci. We show how to discretize this problem to obtain a finite-difference approximation to it, and we present an iterative method for solving the discretized problem. We present the results of calculations that were done with a computer program that implements our method. These calculations show that our method is capable of reconstructing test free energy functions from simulated light scattering data. If the cloud point loci are known, the method also finds the tie lines and tie triangles that describe thermodynamic equilibrium between two or among three liquid phases. A robust method for solving this PDE problem, such as the one presented here, can be a basis for optical, noninvasive means of characterizing the thermodynamics of multicomponent mixtures.

Grid generation for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.; Erlebacher, Gordon

1989-01-01

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.

Grid generation for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.; Erlebacher, Gordon

1987-01-01

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.

A Generalized Model for Transport of Contaminants in Soil by Electric Fields

PubMed Central

Paz-Garcia, Juan M.; Baek, Kitae; Alshawabkeh, Iyad D.; Alshawabkeh, Akram N.

2012-01-01

A generalized model applicable to soils contaminated with multiple species under enhanced boundary conditions during treatment by electric fields is presented. The partial differential equations describing species transport are developed by applying the law of mass conservation to their fluxes. Transport, due to migration, advection and diffusion, of each aqueous component and complex species are combined to produce one partial differential equation hat describes transport of the total analytical concentrations of component species which are the primary dependent variables. This transport couples with geochemical reactions such as aqueous equilibrium, sorption, precipitation and dissolution. The enhanced model is used to simulate electrokinetic cleanup of lead and copper contaminants at an Army Firing Range. Acid enhancement is achieved by the use of adipic acid to neutralize the basic front produced for the cathode electrochemical reaction. The model is able to simulate enhanced application of the process by modifying the boundary conditions. The model showed that kinetics of geochemical reactions, such as metals dissolution/leaching and redox reactions might be significant for realistic prediction of enhanced electrokinetic extraction of metals in real world applications. PMID:22242884

Teaching Modeling with Partial Differential Equations: Several Successful Approaches

ERIC Educational Resources Information Center

Myers, Joseph; Trubatch, David; Winkel, Brian

2008-01-01

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

Composing Models of Geographic Physical Processes

NASA Astrophysics Data System (ADS)

Hofer, Barbara; Frank, Andrew U.

Processes are central for geographic information science; yet geographic information systems (GIS) lack capabilities to represent process related information. A prerequisite to including processes in GIS software is a general method to describe geographic processes independently of application disciplines. This paper presents such a method, namely a process description language. The vocabulary of the process description language is derived formally from mathematical models. Physical processes in geography can be described in two equivalent languages: partial differential equations or partial difference equations, where the latter can be shown graphically and used as a method for application specialists to enter their process models. The vocabulary of the process description language comprises components for describing the general behavior of prototypical geographic physical processes. These process components can be composed by basic models of geographic physical processes, which is shown by means of an example.

Peridynamic Multiscale Finite Element Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Costa, Timothy; Bond, Stephen D.; Littlewood, David John

The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic andmore » local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the art of local models with the flexibility and accuracy of the nonlocal peridynamic model. In the mixed locality method this coupling occurs across scales, so that the nonlocal model can be used to communicate material heterogeneity at scales inappropriate to local partial differential equation models. Additionally, the computational burden of the weak form of the peridynamic model is reduced dramatically by only requiring that the model be solved on local patches of the simulation domain which may be computed in parallel, taking advantage of the heterogeneous nature of next generation computing platforms. Addition- ally, we present a novel Galerkin framework, the 'Ambulant Galerkin Method', which represents a first step towards a unified mathematical analysis of local and nonlocal multiscale finite element methods, and whose future extension will allow the analysis of multiscale finite element methods that mix models across scales under certain assumptions of the consistency of those models.« less

The convergence of the order sequence and the solution function sequence on fractional partial differential equation

NASA Astrophysics Data System (ADS)

Rusyaman, E.; Parmikanti, K.; Chaerani, D.; Asefan; Irianingsih, I.

2018-03-01

One of the application of fractional ordinary differential equation is related to the viscoelasticity, i.e., a correlation between the viscosity of fluids and the elasticity of solids. If the solution function develops into function with two or more variables, then its differential equation must be changed into fractional partial differential equation. As the preliminary study for two variables viscoelasticity problem, this paper discusses about convergence analysis of function sequence which is the solution of the homogenous fractional partial differential equation. The method used to solve the problem is Homotopy Analysis Method. The results show that if given two real number sequences (αn) and (βn) which converge to α and β respectively, then the solution function sequences of fractional partial differential equation with order (αn, βn) will also converge to the solution function of fractional partial differential equation with order (α, β).

A Bifurcation Problem for a Nonlinear Partial Differential Equation of Parabolic Type,

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), BANACH SPACE , MAPPING (TRANSFORMATIONS), SET THEORY, TOPOLOGY, ITERATIONS, STABILITY, THEOREMS

An Extension of the Partial Credit Model with an Application to the Measurement of Change.

ERIC Educational Resources Information Center

Fischer, Gerhard H.; Ponocny, Ivo

1994-01-01

An extension to the partial credit model, the linear partial credit model, is considered under the assumption of a certain linear decomposition of the item x category parameters into basic parameters. A conditional maximum likelihood algorithm for estimating basic parameters is presented and illustrated with simulation and an empirical study. (SLD)

Study on low intensity aeration oxygenation model and optimization for shallow water

NASA Astrophysics Data System (ADS)

Chen, Xiao; Ding, Zhibin; Ding, Jian; Wang, Yi

2018-02-01

Aeration/oxygenation is an effective measure to improve self-purification capacity in shallow water treatment while high energy consumption, high noise and expensive management refrain the development and the application of this process. Based on two-film theory, the theoretical model of the three-dimensional partial differential equation of aeration in shallow water is established. In order to simplify the equation, the basic assumptions of gas-liquid mass transfer in vertical direction and concentration diffusion in horizontal direction are proposed based on engineering practice and are tested by the simulation results of gas holdup which are obtained by simulating the gas-liquid two-phase flow in aeration tank under low-intensity condition. Based on the basic assumptions and the theory of shallow permeability, the model of three-dimensional partial differential equations is simplified and the calculation model of low-intensity aeration oxygenation is obtained. The model is verified through comparing the aeration experiment. Conclusions as follows: (1)The calculation model of gas-liquid mass transfer in vertical direction and concentration diffusion in horizontal direction can reflect the process of aeration well; (2) Under low-intensity conditions, the long-term aeration and oxygenation is theoretically feasible to enhance the self-purification capacity of water bodies; (3) In the case of the same total aeration intensity, the effect of multipoint distributed aeration on the diffusion of oxygen concentration in the horizontal direction is obvious; (4) In the shallow water treatment, reducing the volume of aeration equipment with the methods of miniaturization, array, low-intensity, mobilization to overcome the high energy consumption, large size, noise and other problems can provide a good reference.

On the hierarchy of partially invariant submodels of differential equations

NASA Astrophysics Data System (ADS)

Golovin, Sergey V.

2008-07-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1989-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of partial differential equation solutions in the least squares norm.

Solution of differential equations by application of transformation groups

NASA Technical Reports Server (NTRS)

Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

1968-01-01

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Reciprocal links among differential parenting, perceived partiality, and self-worth: a three-wave longitudinal study.

PubMed

Shebloski, Barbara; Conger, Katherine J; Widaman, Keith F

2005-12-01

This study examined reciprocal links between parental differential treatment, siblings' perception of partiality, and self-worth with 3 waves of data from 384 adolescent sibling dyads. Results suggest that birth-order status was significantly associated with self-worth and perception of maternal and paternal differential treatment. There was a consistent across-time effect of self-worth on perception of parental partiality for later born siblings, but not earlier born siblings, and a consistent effect of differential treatment on perception of partiality for earlier born but not later born siblings. The results contribute new insight into the associations between perception of differential parenting and adolescents' adjustment and the role of birth order. Copyright 2006 APA, all rights reserved).

Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply

NASA Astrophysics Data System (ADS)

Gavrilov, S. N.; Krivtsov, A. M.; Tsvetkov, D. V.

2018-05-01

We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential equations. We perform a continualization procedure and derive an infinite set of linear partial differential equations for covariance variables. An exact analytic solution describing unsteady ballistic heat transfer in the crystal is obtained. It is shown that the stationary spatial profile of the kinetic temperature caused by a point source of heat supply of constant intensity is described by the Macdonald function of zero order. A comparison with the results obtained in the framework of the classical heat equation is presented. We expect that the results obtained in the paper can be verified by experiments with laser excitation of low-dimensional nanostructures.

Introduction to multigrid methods

NASA Technical Reports Server (NTRS)

Wesseling, P.

1995-01-01

These notes were written for an introductory course on the application of multigrid methods to elliptic and hyperbolic partial differential equations for engineers, physicists and applied mathematicians. The use of more advanced mathematical tools, such as functional analysis, is avoided. The course is intended to be accessible to a wide audience of users of computational methods. We restrict ourselves to finite volume and finite difference discretization. The basic principles are given. Smoothing methods and Fourier smoothing analysis are reviewed. The fundamental multigrid algorithm is studied. The smoothing and coarse grid approximation properties are discussed. Multigrid schedules and structured programming of multigrid algorithms are treated. Robustness and efficiency are considered.

Direct Calculation of the Scattering Amplitude Without Partial Wave Decomposition. III; Inclusion of Correlation Effects

NASA Technical Reports Server (NTRS)

Shertzer, Janine; Temkin, Aaron

2007-01-01

In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.

a Non-Overlapping Discretization Method for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Rosas-Medina, A.; Herrera, I.

2013-05-01

Mathematical models of many systems of interest, including very important continuous systems of Engineering and Science, lead to a great variety of partial differential equations whose solution methods are based on the computational processing of large-scale algebraic systems. Furthermore, the incredible expansion experienced by the existing computational hardware and software has made amenable to effective treatment problems of an ever increasing diversity and complexity, posed by engineering and scientific applications. The emergence of parallel computing prompted on the part of the computational-modeling community a continued and systematic effort with the purpose of harnessing it for the endeavor of solving boundary-value problems (BVPs) of partial differential equations. Very early after such an effort began, it was recognized that domain decomposition methods (DDM) were the most effective technique for applying parallel computing to the solution of partial differential equations, since such an approach drastically simplifies the coordination of the many processors that carry out the different tasks and also reduces very much the requirements of information-transmission between them. Ideally, DDMs intend producing algorithms that fulfill the DDM-paradigm; i.e., such that "the global solution is obtained by solving local problems defined separately in each subdomain of the coarse-mesh -or domain-decomposition-". Stated in a simplistic manner, the basic idea is that, when the DDM-paradigm is satisfied, full parallelization can be achieved by assigning each subdomain to a different processor. When intensive DDM research began much attention was given to overlapping DDMs, but soon after attention shifted to non-overlapping DDMs. This evolution seems natural when the DDM-paradigm is taken into account: it is easier to uncouple the local problems when the subdomains are separated. However, an important limitation of non-overlapping domain decompositions, as that concept is usually understood today, is that interface nodes are shared by two or more subdomains of the coarse-mesh and, therefore, even non-overlapping DDMs are actually overlapping when seen from the perspective of the nodes used in the discretization. In this talk we present and discuss a discretization method in which the nodes used are non-overlapping, in the sense that each one of them belongs to one and only one subdomain of the coarse-mesh.

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

Spatial complexity of solutions of higher order partial differential equations

NASA Astrophysics Data System (ADS)

Kukavica, Igor

2004-03-01

We address spatial oscillation properties of solutions of higher order parabolic partial differential equations. In the case of the Kuramoto-Sivashinsky equation ut + uxxxx + uxx + u ux = 0, we prove that for solutions u on the global attractor, the quantity card {x epsi [0, L]:u(x, t) = lgr}, where L > 0 is the spatial period, can be bounded by a polynomial function of L for all \\lambda\\in{\\Bbb R} . A similar property is proven for a general higher order partial differential equation u_t+(-1)^{s}\\partial_x^{2s}u+ \\sum_{k=0}^{2s-1}v_k(x,t)\\partial_x^k u =0 .

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.

PubMed

Ma, Jinpeng; Sun, Yong; Yuan, Xiaoming; Kurths, Jürgen; Zhan, Meng

2016-01-01

Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

On the Solution of Elliptic Partial Differential Equations on Regions with Corners

DTIC Science & Technology

2015-07-09

In this report we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations . We observe...that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of...efficient numerical algorithms. The results are illustrated by a number of numerical examples. On the solution of elliptic partial differential equations on

5 CFR 841.701 - Purpose and scope.

Code of Federal Regulations, 2011 CFR

2011-01-01

... adjustments (COLA's) for basic benefits under the Federal Employees Retirement System (FERS). (b) This subpart provides the methodology for— (1) Computing COLA's on each type of FERS basic benefit subject to COLA's; and (2) Computing COLA's on annuities partially computed under FERS and partially computed under the...

5 CFR 841.701 - Purpose and scope.

Code of Federal Regulations, 2014 CFR

2014-01-01

... adjustments (COLA's) for basic benefits under the Federal Employees Retirement System (FERS). (b) This subpart provides the methodology for— (1) Computing COLA's on each type of FERS basic benefit subject to COLA's; and (2) Computing COLA's on annuities partially computed under FERS and partially computed under the...

5 CFR 841.701 - Purpose and scope.

Code of Federal Regulations, 2010 CFR

2010-01-01

... adjustments (COLA's) for basic benefits under the Federal Employees Retirement System (FERS). (b) This subpart provides the methodology for— (1) Computing COLA's on each type of FERS basic benefit subject to COLA's; and (2) Computing COLA's on annuities partially computed under FERS and partially computed under the...

5 CFR 841.701 - Purpose and scope.

Code of Federal Regulations, 2013 CFR

2013-01-01

... adjustments (COLA's) for basic benefits under the Federal Employees Retirement System (FERS). (b) This subpart provides the methodology for— (1) Computing COLA's on each type of FERS basic benefit subject to COLA's; and (2) Computing COLA's on annuities partially computed under FERS and partially computed under the...

5 CFR 841.701 - Purpose and scope.

Code of Federal Regulations, 2012 CFR

2012-01-01

... adjustments (COLA's) for basic benefits under the Federal Employees Retirement System (FERS). (b) This subpart provides the methodology for— (1) Computing COLA's on each type of FERS basic benefit subject to COLA's; and (2) Computing COLA's on annuities partially computed under FERS and partially computed under the...

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

Improving the developability profile of pyrrolidine progesterone receptor partial agonists

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kallander, Lara S.; Washburn, David G.; Hoang, Tram H.

2010-09-17

The previously reported pyrrolidine class of progesterone receptor partial agonists demonstrated excellent potency but suffered from serious liabilities including hERG blockade and high volume of distribution in the rat. The basic pyrrolidine amine was intentionally converted to a sulfonamide, carbamate, or amide to address these liabilities. The evaluation of the degree of partial agonism for these non-basic pyrrolidine derivatives and demonstration of their efficacy in an in vivo model of endometriosis is disclosed herein.

Mathematical model for Dengue with three states of infection

NASA Astrophysics Data System (ADS)

Hincapie, Doracelly; Ospina, Juan

2012-06-01

A mathematical model for dengue with three states of infection is proposed and analyzed. The model consists in a system of differential equations. The three states of infection are respectively asymptomatic, partially asymptomatic and fully asymptomatic. The model is analyzed using computer algebra software, specifically Maple, and the corresponding basic reproductive number and the epidemic threshold are computed. The resulting basic reproductive number is an algebraic synthesis of all epidemic parameters and it makes clear the possible control measures. The microscopic structure of the epidemic parameters is established using the quantum theory of the interactions between the atoms and radiation. In such approximation, the human individual is represented by an atom and the mosquitoes are represented by radiation. The force of infection from the mosquitoes to the humans is considered as the transition probability from the fundamental state of atom to excited states. The combination of computer algebra software and quantum theory provides a very complete formula for the basic reproductive number and the possible control measures tending to stop the propagation of the disease. It is claimed that such result may be important in military medicine and the proposed method can be applied to other vector-borne diseases.

Transduction of NeuroD2 protein induced neural cell differentiation.

PubMed

Noda, Tomohide; Kawamura, Ryuzo; Funabashi, Hisakage; Mie, Masayasu; Kobatake, Eiry

2006-11-01

NeuroD2, one of the neurospecific basic helix-loop-helix transcription factors, has the ability to induce neural differentiation in undifferentiated cells. In this paper, we show that transduction of NeuroD2 protein induced mouse neuroblastoma cell line N1E-115 into neural differentiation. NeuroD2 has two basic-rich domains, one is nuclear localization signal (NLS) and the other is basic region of basic helix-loop-helix (basic). We constructed some mutants of NeuroD2, ND2(Delta100-115) (lack of NLS), ND2(Delta123-134) (lack of basic) and ND2(Delta100-134) (lack of both NLS and basic) for transduction experiments. Using these proteins, we have shown that NLS region of NeuroD2 plays a role of protein transduction. Continuous addition of NeuroD2 protein resulted in N1E-115 cells adopting neural morphology after 4 days and Tau mRNA expression was increased. These results suggest that neural differentiation can be induced by direct addition of NeuroD2 protein.

An approach to get thermodynamic properties from speed of sound

NASA Astrophysics Data System (ADS)

Núñez, M. A.; Medina, L. A.

2017-01-01

An approach for estimating thermodynamic properties of gases from the speed of sound u, is proposed. The square u2, the compression factor Z and the molar heat capacity at constant volume C V are connected by two coupled nonlinear partial differential equations. Previous approaches to solving this system differ in the conditions used on the range of temperature values [Tmin,Tmax]. In this work we propose the use of Dirichlet boundary conditions at Tmin, Tmax. The virial series of the compression factor Z = 1+Bρ+Cρ2+… and other properties leads the problem to the solution of a recursive set of linear ordinary differential equations for the B, C. Analytic solutions of the B equation for Argon are used to study the stability of our approach and previous ones under perturbation errors of the input data. The results show that the approach yields B with a relative error bounded basically by that of the boundary values and the error of other approaches can be some orders of magnitude lager.

Construction and accuracy of partial differential equation approximations to the chemical master equation.

PubMed

Grima, Ramon

2011-11-01

The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

Stepwise Analysis of Differential Item Functioning Based on Multiple-Group Partial Credit Model.

ERIC Educational Resources Information Center

Muraki, Eiji

1999-01-01

Extended an Item Response Theory (IRT) method for detection of differential item functioning to the partial credit model and applied the method to simulated data using a stepwise procedure. Then applied the stepwise DIF analysis based on the multiple-group partial credit model to writing trend data from the National Assessment of Educational…

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

Cost Reporting at a Navy Branch Clinic

DTIC Science & Technology

1993-03-01

John Wiley & Sons, 1991. 15 Horngren , Charles, Cost Accounting -=A Managerial Emphasis, 5th Edition, Prentice Hall, Inc., Englewood Cliffs, N.J., 1982...traditionally reported under a partial cost reporting system. By applying basic principles of managerial accounting , a full cost reporting system is...traditionally reported under a partial cost reporting system. By applying basic principles of managerial accounting , a proposed full cost reporting

Evaluation of computed tomography numbers for treatment planning of lung cancer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mira, J.G.; Fullerton, G.D.; Ezekiel, J.

1982-09-01

Computerized tomography numbers (CTN) were evaluated in 32 computerized tomography scans performed on patients with carcinoma of the lung, with the aim of evaluating CTN in normal (lung, blood, muscle, etc) and pathologic tissues (tumor, atelectasis, effusion, post-radiation fibrosis). Our main findings are: 1. Large individual CTN variations are encountered in both normal and pathologic tissues, above and below mean values. Hence, absolute numbers are meaningless. Measurements of any abnormal intrathoracic structure should be compared in relation to normal tissue CTN values in the same scan. 2. Tumor and complete atelectasis have CTN basically similar to soft tissue. Hence, thesemore » numbers are not useful for differential diagnosis. 3. Effusions usually have lower CTN and can be distinguished from previous situations. 4. Dosimetry based on uniform lung density assumptions (i.e., 300 mg/cm/sup 3/) might produce substantial dose errors as lung CTN exhibit variations indicating densities well above and below this value. 5. Preliminary information indicates that partial atelectasis and incipient post-radiation fibrosis can have very low CTN. Hence, they can be differentiated from solid tumors in certain cases, and help in differential diagnosis of post radiation recurrence within the radiotherapy field versus fibrosis.« less

Time Parallel Solution of Linear Partial Differential Equations on the Intel Touchstone Delta Supercomputer

NASA Technical Reports Server (NTRS)

Toomarian, N.; Fijany, A.; Barhen, J.

1993-01-01

Evolutionary partial differential equations are usually solved by decretization in time and space, and by applying a marching in time procedure to data and algorithms potentially parallelized in the spatial domain.

A regularization method for extrapolation of solar potential magnetic fields

NASA Technical Reports Server (NTRS)

Gary, G. A.; Musielak, Z. E.

1992-01-01

The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

Fem Formulation of Heat Transfer in Cylindrical Porous Medium

NASA Astrophysics Data System (ADS)

Azeem; Khaleed, H. M. T.; Soudagar, Manzoor Elahi M.

2017-08-01

Heat transfer in porous medium can be derived from the fundamental laws of flow in porous region ass given by Henry Darcy. The fluid flow and energy transport inside the porous medium can be described with the help of momentum and energy equations. The heat transfer in cylindrical porous medium differs from its counterpart in radial and axial coordinates. The present work is focused to discuss the finite element formulation of heat transfer in cylindrical porous medium. The basic partial differential equations are derived using Darcy law which is the converted into a set of algebraic equations with the help of finite element method. The resulting equations are solved by matrix method for two solution variables involved in the coupled equations.

Thermal diffusion effect on MHD mixed convective flow along a vertically inclined plate: A casson fluid flow

NASA Astrophysics Data System (ADS)

Prasad, D. V. V. Krishna; Chaitanya, G. S. Krishna; Raju, R. Srinivasa

2018-05-01

The nature of Casson fluid on MHD free convective flow of over an impulsively started infinite vertically inclined plate in presence of thermal diffusion (Soret), thermal radiation, heat and mass transfer effects is studied. The basic governing nonlinear coupled partial differential equations are solved numerically using finite element method. The relevant physical parameters appearing in velocity, temperature and concentration profiles are analyzed and discussed through graphs. Finally, the results for velocity profiles and the reduced Nusselt and Sherwood numbers are obtained and compared with previous results in the literature and are found to be in excellent agreement. Applications of the present study would be useful in magnetic material processing and chemical engineering systems.

Suddenly included: cultural differences in experiencing re-inclusion.

PubMed

Pfundmair, Michaela; Graupmann, Verena; Du, Hongfei; Frey, Dieter; Aydin, Nilüfer

2015-03-01

In the current research, we examined whether re-inclusion (i.e. the change from a previous state of exclusion to a new state of inclusion) was perceived differently by people with individualistic and collectivistic cultural backgrounds. Individualists (German and Austrian participants) but not collectivists (Chinese participants) experienced re-inclusion differently than continued inclusion: While collectivistic participants did not differentiate between both kinds of inclusion, individualistic participants showed reduced fulfilment of their psychological needs under re-inclusion compared to continued inclusion. The results moreover revealed that only participants from individualistic cultures expressed more feelings of exclusion when re-included than when continually included. These exclusionary feelings partially mediated the relationship between the different states of inclusion and basic need fulfilment. © 2014 International Union of Psychological Science.

Fast computation of derivative based sensitivities of PSHA models via algorithmic differentiation

NASA Astrophysics Data System (ADS)

Leövey, Hernan; Molkenthin, Christian; Scherbaum, Frank; Griewank, Andreas; Kuehn, Nicolas; Stafford, Peter

2015-04-01

Probabilistic seismic hazard analysis (PSHA) is the preferred tool for estimation of potential ground-shaking hazard due to future earthquakes at a site of interest. A modern PSHA represents a complex framework which combines different models with possible many inputs. Sensitivity analysis is a valuable tool for quantifying changes of a model output as inputs are perturbed, identifying critical input parameters and obtaining insight in the model behavior. Differential sensitivity analysis relies on calculating first-order partial derivatives of the model output with respect to its inputs. Moreover, derivative based global sensitivity measures (Sobol' & Kucherenko '09) can be practically used to detect non-essential inputs of the models, thus restricting the focus of attention to a possible much smaller set of inputs. Nevertheless, obtaining first-order partial derivatives of complex models with traditional approaches can be very challenging, and usually increases the computation complexity linearly with the number of inputs appearing in the models. In this study we show how Algorithmic Differentiation (AD) tools can be used in a complex framework such as PSHA to successfully estimate derivative based sensitivities, as is the case in various other domains such as meteorology or aerodynamics, without no significant increase in the computation complexity required for the original computations. First we demonstrate the feasibility of the AD methodology by comparing AD derived sensitivities to analytically derived sensitivities for a basic case of PSHA using a simple ground-motion prediction equation. In a second step, we derive sensitivities via AD for a more complex PSHA study using a ground motion attenuation relation based on a stochastic method to simulate strong motion. The presented approach is general enough to accommodate more advanced PSHA studies of higher complexity.

Mathematical Modelling of Continuous Biotechnological Processes

ERIC Educational Resources Information Center

Pencheva, T.; Hristozov, I.; Shannon, A. G.

2003-01-01

Biotechnological processes (BTP) are characterized by a complicated structure of organization and interdependent characteristics. Partial differential equations or systems of partial differential equations are used for their behavioural description as objects with distributed parameters. Modelling of substrate without regard to dispersion…

Fault Tolerant Optimal Control.

DTIC Science & Technology

1982-08-01

subsystem is modelled by deterministic or stochastic finite-dimensional vector differential or difference equations. The parameters of these equations...is no partial differential equation that must be solved. Thus we can sidestep the inability to solve the Bellman equation for control problems with x...transition models and cost functionals can be reduced to the search for solutions of nonlinear partial differential equations using ’verification

Differential geometry techniques for sets of nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Estabrook, Frank B.

1990-01-01

An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.

A procedure to construct exact solutions of nonlinear fractional differential equations.

PubMed

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

Algebraic and geometric structures of analytic partial differential equations

NASA Astrophysics Data System (ADS)

Kaptsov, O. V.

2016-11-01

We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Gröbner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds.

Basic fibroblastic growth factor affects the osteogenic differentiation of dental pulp stem cells in a treatment-dependent manner.

PubMed

Qian, J; Jiayuan, W; Wenkai, J; Peina, W; Ansheng, Z; Shukai, S; Shafei, Z; Jun, L; Longxing, N

2015-07-01

To determine how basic fibroblastic growth factor (bFGF) affected the osteogenic differentiation of human dental pulp stem cells (DPSCs) in vitro and in vivo. Basic fibroblastic growth factor stimulation of DPSCs was divided into a pre-treatment period and an osteogenic differentiation period. Alizarin red quantification experiments and alkaline phosphatase activity quantification assay were performed to examine the osteogenic differentiation of DPSCs after different bFGF stimulation. Quantification reverse transcription polymerase chain reaction was used to analyze the osteogenic gene expression of DPSCs after different bFGF stimulation. In addition, DPSCs that received the 1 and 2 weeks bFGF pre-treatments as in the in vitro experiments were mineralized for 1 week and seeded into hydroxyapatite/tricalcium phosphate (HA/TCP) pills and subcutaneously transplanted into naked mice for 2 or 3 months. The transplants were removed, sliced and stained using Modified Ponceau Trichrome Stain to observe the formation of mineralized tissue. Basic fibroblastic growth factor stimulation in the osteogenic differentiation period decreased the in vitro osteogenic differentiation ability of DPSCs. One week pre-treatment with bFGF increased the in vitro osteogenic differentiation ability of DPSCs, whereas 2 weeks pre-treatment with bFGF decreased the in vitro osteogenic differentiation ability of DPSCs. The pre-treatment period was vital for the osteogenic differentiation of DPSCs in vitro. The in vivo results were similar to the in vitro results. Basic fibroblastic growth factor affected the osteogenic differentiation of DPSCs in a treatment-dependent manner both in vitro and in vivo. © 2014 International Endodontic Journal. Published by John Wiley & Sons Ltd.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Constructing general partial differential equations using polynomial and neural networks.

PubMed

Zjavka, Ladislav; Pedrycz, Witold

2016-01-01

Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

[ZHANG Tangfa's characteristics of acupuncture academic ideology and clinical treatment of syndrome differentiation].

PubMed

Zhang, Hongxing

2015-10-01

Through collecting and sorting of works, literature and medical cases regarding professor ZHANG Tangfa, it is found that his acupuncture academic ideology and clinical treatment of syndrome differentiation can be summarized as: tracing the source and paying attention to basic theory, especially the meridian theory and conception vessel and governor vessel; focusing on acupuncture manipulation and emphasizing acupuncture basic skills; highly valuing treating spirit, acquiring and maintaining needling sensation; underlining "three differentiations" that is consisted of syndrome differentiation, disease differentiation and meridian differentiation to guide the clinical prescriptions of acupoints; exploring and ingenious use of scalp acupuncture; being concerned on research of difficult and complicated diseases; advocating comparative studies to optimize the clinical treatment plan; proposing the combination of Chinese and western medicine, including diagnosis, treatment and basic theory, to improve the clinical therapeutic effects of acupuncture.

On new classes of solutions of nonlinear partial differential equations in the form of convergent special series

NASA Astrophysics Data System (ADS)

Filimonov, M. Yu.

2017-12-01

The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

Güner, Özkan; Cevikel, Adem C.

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

On implicit abstract neutral nonlinear differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernández, Eduardo, E-mail: lalohm@ffclrp.usp.br; O’Regan, Donal, E-mail: donal.oregan@nuigalway.ie

2016-04-15

In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.

Oscillation of certain higher-order neutral partial functional differential equations.

PubMed

Li, Wei Nian; Sheng, Weihong

2016-01-01

In this paper, we study the oscillation of certain higher-order neutral partial functional differential equations with the Robin boundary conditions. Some oscillation criteria are established. Two examples are given to illustrate the main results in the end of this paper.

Pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations

NASA Astrophysics Data System (ADS)

Al-Islam, Najja Shakir

In this Dissertation, the existence of pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations is established. For that, (Al-Islam [4]) is first studied and then obtained under some suitable assumptions. That is, the existence of pseudo almost periodic solutions to a hyperbolic second-order partial differential equation with delay. The second-order partial differential equation (1) represents a mathematical model for the dynamics of gas absorption, given by uxt+a x,tux=Cx,t,u x,t , u0,t=4 t, 1 where a : [0, L] x RR , C : [0, L] x R x RR , and ϕ : RR are (jointly) continuous functions ( t being the greatest integer function) and L > 0. The results in this Dissertation generalize those of Poorkarimi and Wiener [22]. Secondly, a generalization of the above-mentioned system consisting of the non-linear hyperbolic second-order partial differential equation uxt+a x,tux+bx,t ut+cx,tu=f x,t,u, x∈ 0,L,t∈ R, 2 equipped with the boundary conditions ux,0 =40x, u0,t=u 0t, uxx,0=y 0x, x∈0,L, t∈R, 3 where a, b, c : [0, L ] x RR and f : [0, L] x R x RR are (jointly) continuous functions is studied. Under some suitable assumptions, the existence and uniqueness of pseudo almost periodic solutions to particular cases, as well as the general case of the second-order hyperbolic partial differential equation (2) are studied. The results of all studies contained within this text extend those obtained by Aziz and Meyers [6] in the periodic setting.

Reversible effects of oxygen partial pressure on genes associated with placental angiogenesis and differentiation in primary-term cytotrophoblast cell culture.

PubMed

Debiève, F; Depoix, C; Gruson, D; Hubinont, C

2013-09-01

Timely regulated changes in oxygen partial pressure are important for placental formation. Disturbances could be responsible for pregnancy-related diseases like preeclampsia and intrauterine growth restriction. We aimed to (i) determine the effect of oxygen partial pressure on cytotrophoblast differentiation; (ii) measure mRNA expression and protein secretion from genes associated with placental angiogenesis; and (iii) determine the reversibility of these effects at different oxygen partial pressures. Term cytotrophoblasts were incubated at 21% and 2.5% O2 for 96 hr, or were switched between the two oxygen concentrations after 48 hr. Real-time PCR and enzyme-linked immunosorbent assays (ELISAs) were used to evaluate cell fusion and differentiation, measuring transcript levels for those genes involved in cell fusion and placental angiogenesis, including VEGF, PlGF, VEGFR1, sVEGFR1, sENG, INHA, and GCM1. Cytotrophoblasts underwent fusion and differentiation in 2.5% O2 . PlGF expression was inhibited while sVEGFR1 expression increased. VEGF and sENG mRNA expressions increased in 2.5% compared to 21% O2 , but no protein was detected in the cell supernatants. Finally, GCM1 mRNA expression increased during trophoblast differentiation at 21% O2 , but was inhibited at 2.5% O2 . These mRNA expression effects were reversed by returning the cells to 21% O2 . Thus, low-oxygen partial pressure does not inhibit term-cytotrophoblast cell fusion and differentiation in vitro. Lowering the oxygen partial pressure from 21% to 2.5% caused normal-term trophoblasts to reversibly modify their expression of genes associated with placental angiogenesis. This suggests that modifications observed in pregnancy diseases such as preeclampsia or growth retardation are probably due to an extrinsic effect on trophoblasts. Copyright © 2013 Wiley Periodicals, Inc.

Lattice Boltzmann model for high-order nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Lattice Boltzmann model for high-order nonlinear partial differential equations.

PubMed

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

BOOK REVIEW: Partial Differential Equations in General Relativity

NASA Astrophysics Data System (ADS)

Halburd, Rodney G.

2008-11-01

Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed proofs of the main results in a self-contained book of reasonable length. Instead, the author concentrates on providing key definitions together with their motivations and explaining the main results, tools and difficulties for each topic. There is a section at the end of each chapter which points the reader to appropriate literature for further details. In this way, Rendall manages to describe the central issues concerning many subjects. Each of the twelve chapters (except for one on functional analysis) contains an important application to general relativity. For example, the chapter on ODEs discusses Bianchi spacetimes and the Einstein constraint equations are discussed in the chapter on elliptic equations. In the chapter on hyperbolic equations, the Einstein dust system is considered in the context of Leray hyperbolicity and Gowdy spacetimes are analysed in the section on Fuchsian methods. The book concludes with four chapters purely on applications to general relativity, namely The Cauchy problem for the Einstein equations, Global results, The Einstein-Vlasov system and The Einstein-scalar field systems. On reading this book, someone with a basic understanding of relativity could rapidly develop a picture, painted in broad brush strokes, of the main problems and tools in the area. It would be particularly useful for someone, such as a graduate student, just entering the field, or for someone who wants a general idea of the main issues. For those who want to go further, a lot more reading will be necessary but the author has sign-posted appropriate entry points to the literature throughout the book. Ultimately, this is a very technical subject and this book can only provide an overview. I believe that Alan Rendall's book is a valuable contribution to the field of mathematical relativity.

Entropy and convexity for nonlinear partial differential equations

PubMed Central

Ball, John M.; Chen, Gui-Qiang G.

2013-01-01

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue. PMID:24249768

Oxidation Behavior of Carbon Fiber-Reinforced Composites

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2008-01-01

OXIMAP is a numerical (FEA-based) solution tool capable of calculating the carbon fiber and fiber coating oxidation patterns within any arbitrarily shaped carbon silicon carbide composite structure as a function of time, temperature, and the environmental oxygen partial pressure. The mathematical formulation is derived from the mechanics of the flow of ideal gases through a chemically reacting, porous solid. The result of the formulation is a set of two coupled, non-linear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined at each time step using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The non-linear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual finite element method, allowing for the solution of the differential equations numerically.

Entropy and convexity for nonlinear partial differential equations.

PubMed

Ball, John M; Chen, Gui-Qiang G

2013-12-28

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.

Differential phase measurements of D-region partial reflections

NASA Technical Reports Server (NTRS)

Wiersma, D. J.; Sechrist, C. F., Jr.

1972-01-01

Differential phase partial reflection measurements were used to deduce D region electron density profiles. The phase difference was measured by taking sums and differences of amplitudes received on an array of crossed dipoles. The reflection model used was derived from Fresnel reflection theory. Seven profiles obtained over the period from 13 October 1971 to 5 November 1971 are presented, along with the results from simultaneous measurements of differential absorption. Some possible sources of error and error propagation are discussed. A collision frequency profile was deduced from the electron concentration calculated from differential phase and differential absorption.

Morphological Analysis of Live Undifferentiated Cells Derived from Induced Pluripotent Stem Cells.

PubMed

Osawa, Yukihiko; Miyamoto, Tomoyuki; Ohno, Setsuyo; Ohno, Eiji

2018-01-01

Induced pluripotent stem (iPS) cells possess pluripotency and self-renewal ability. Therefore, iPS cells are expected to be useful in regenerative medicine. However, iPS cells form malignant immature teratomas after transplantation into animals, even after differentiation induction. It has been suggested that undifferentiated cells expressing Nanog that remain after differentiation induction are responsible for teratoma formation. Various methods of removing these undifferentiated cells have therefore been investigated, but few methods involve morphological approaches, which may induce less cell damage. In addition, for cells derived from iPS cells to be applied in regenerative medicine, they must be alive. However, detailed morphological analysis of live undifferentiated cells has not been performed. For the above reasons, we assessed the morphological features of live undifferentiated cells remaining after differentiation induction as a basic investigation into the clinical application of iPS cells. As a result, live undifferentiated cells remaining after differentiation induction exhibited a round or oval cytoplasm about 12 μm in diameter and a nucleus. They exhibited nucleo-cytoplasmic (N/C) ratio of about 60% and eccentric nuclei, and they possessed partially granule-like structures in the cytoplasm and prominent nucleoli. Although they were similar to iPS cells, they were smaller than live iPS cells. Furthermore, very small cells were present among undifferentiated cells after differentiation induction. These results suggest that the removal of undifferentiated cells may be possible using the morphological features of live iPS cells and undifferentiated cells after differentiation induction. In addition, this study supports safe regenerative medicine using iPS cells.

Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

DTIC Science & Technology

1983-12-01

numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

Petrographic, geochemical and isotopic evidence of crustal assimilation processes in the Ponte Nova alkaline mafic-ultramafic massif, SE Brazil

NASA Astrophysics Data System (ADS)

Azzone, Rogério Guitarrari; Montecinos Munoz, Patricio; Enrich, Gaston Eduardo Rojas; Alves, Adriana; Ruberti, Excelso; Gomes, Celsode Barros

2016-09-01

Crustal assimilation plus crystal fractionation processes of different basanite magma batches control the evolution of the Ponte Nova cretaceous alkaline mafic-ultramafic massif in SE Brazil. This massif is composed of several intrusions, the main ones with a cumulate character. Disequilibrium features in the early-crystallized phases (e.g., corrosion and sieve textures in cores of clinopyroxene crystals, spongy-cellular-textured plagioclase crystals, gulf corrosion texture in olivine crystals) and classical hybridization textures (e.g., blade biotite and acicular apatite crystals) provide strong evidence of open-system behavior. All samples are olivine- and nepheline-normative rocks with basic-ultrabasic and potassic characters and variable incompatible element enrichments. The wide ranges of whole-rock 87Sr/86Sri and 143Nd/144Ndi ratios (0.70432-0.70641 and 0.512216-0.512555, respectively) are indicative of crustal contribution from the Precambrian basement host rocks. Plagioclase and apatite 87Sr/86Sr ratios (0.70422-0.70927) obtained for the most primitive samples of each intrusion indicate disequilibrium conditions from early- to principal-crystallization stages. Isotope mixing-model curves between the least contaminated alkaline basic magma and heterogeneous local crustal components indicate that each intrusion of the massif is differentiated from the others by varied degrees of crustal contribution. The primary mechanisms of crustal contribution to the Ponte Nova massif involve the assimilation of host rock xenoliths during the development of the chamber environment and the assimilation of partial melts from the surrounding host rocks. Thermodynamic models using the melts algorithm indicate that parental alkaline basic magmas can be strongly affected by contamination processes subsequently to their initial stages of crystallization when there is sufficient energy to assimilate partial melts of crustal host rocks. The assimilation processes are considered to be responsible for the increse in the K2O/Na2O, Ba/Sr and Rb/Sr ratios. This enrichment was associated with the relevant role of biotite breakdown in the assimilated host rock partial melts. The petrological model for the Ponte Nova massif is explained as repeated influxes of antecryst-laden basanite magmas that deposited most of their suspended crystals on the floor of the upper-crust magma chamber. Each intrusion is representative of relatively primitive olivine- and clinopyroxene-phyric basanites that had assimilated different degrees of partial melts of heterogeneous host rocks. This study reveals the relevant role of crustal assimilation processes in the magmatic evolution of nepheline-normative rocks, especially in upper-crust chamber environments.

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

PubMed

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

Multi-level adaptive finite element methods. 1: Variation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1979-01-01

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation

NASA Astrophysics Data System (ADS)

Şenol, Mehmet; Alquran, Marwan; Kasmaei, Hamed Daei

2018-06-01

In this paper, we present analytic-approximate solution of time-fractional Zakharov-Kuznetsov equation. This model demonstrates the behavior of weakly nonlinear ion acoustic waves in a plasma bearing cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Basic definitions of fractional derivatives are described in the Caputo sense. Perturbation-iteration algorithm (PIA) and residual power series method (RPSM) are applied to solve this equation with success. The convergence analysis is also presented for both methods. Numerical results are given and then they are compared with the exact solutions. Comparison of the results reveal that both methods are competitive, powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.

Acoustic plane waves incident on an oblique clamped panel in a rectangular duct

NASA Technical Reports Server (NTRS)

Unz, H.; Roskam, J.

1980-01-01

The theory of acoustic plane waves incident on an oblique clamped panel in a rectangular duct was developed from basic theoretical concepts. The coupling theory between the elastic vibrations of the panel (plate) and the oblique incident acoustic plane wave in infinite space was considered in detail, and was used for the oblique clamped panel in the rectangular duct. The partial differential equation which governs the vibrations of the clamped panel (plate) was modified by adding to it stiffness (spring) forces and damping forces. The Transmission Loss coefficient and the Noise Reduction coefficient for oblique incidence were defined and derived in detail. The resonance frequencies excited by the free vibrations of the oblique finite clamped panel (plate) were derived and calculated in detail for the present case.

Unsteady mixed convection flow of Casson fluid past an inclined stretching sheet in the presence of nanoparticles

NASA Astrophysics Data System (ADS)

Rawi, N. A.; Ilias, M. R.; Lim, Y. J.; Isa, Z. M.; Shafie, S.

2017-09-01

The influence of nanoparticles on the unsteady mixed convection flow of Casson fluid past an inclined stretching sheet is investigated in this paper. The effect of gravity modulation on the flow is also considered. Carboxymethyl cellulose solution (CMC) is chosen as the base fluid and copper as nanoparticles. The basic governing nonlinear partial differential equations are transformed using appropriate similarity transformation and solved numerically using an implicit finite difference scheme by means of the Keller-box method. The effect of nanoparticles volume fraction together with the effect of inclination angle and Casson parameter on the enhancement of heat transfer of Casson nanofluid is discussed in details. The velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number are presented and analyzed.

Canonical coordinates for partial differential equations

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1988-01-01

Necessary and sufficient conditions are found under which operators of the form Sigma (m, j=1) x (2) sub j + X sub O can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.

Canonical coordinates for partial differential equations

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

Necessary and sufficient conditions are found under which operators of the form Sigma(m, j=1) X(2)sub j + X sub 0 can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.

Differentiation of Organically and Conventionally Grown Tomatoes by Chemometric Analysis of Combined Data from Proton Nuclear Magnetic Resonance and Mid-infrared Spectroscopy and Stable Isotope Analysis.

PubMed

Hohmann, Monika; Monakhova, Yulia; Erich, Sarah; Christoph, Norbert; Wachter, Helmut; Holzgrabe, Ulrike

2015-11-04

Because the basic suitability of proton nuclear magnetic resonance spectroscopy ((1)H NMR) to differentiate organic versus conventional tomatoes was recently proven, the approach to optimize (1)H NMR classification models (comprising overall 205 authentic tomato samples) by including additional data of isotope ratio mass spectrometry (IRMS, δ(13)C, δ(15)N, and δ(18)O) and mid-infrared (MIR) spectroscopy was assessed. Both individual and combined analytical methods ((1)H NMR + MIR, (1)H NMR + IRMS, MIR + IRMS, and (1)H NMR + MIR + IRMS) were examined using principal component analysis (PCA), partial least squares discriminant analysis (PLS-DA), linear discriminant analysis (LDA), and common components and specific weight analysis (ComDim). With regard to classification abilities, fused data of (1)H NMR + MIR + IRMS yielded better validation results (ranging between 95.0 and 100.0%) than individual methods ((1)H NMR, 91.3-100%; MIR, 75.6-91.7%), suggesting that the combined examination of analytical profiles enhances authentication of organically produced tomatoes.

Tomographic multiaxis-differential optical absorption spectroscopy observations of Sun-illuminated targets: a technique providing well-defined absorption paths in the boundary layer

NASA Astrophysics Data System (ADS)

Frins, Erna; Bobrowski, Nicole; Platt, Ulrich; Wagner, Thomas

2006-08-01

A novel experimental procedure to measure the near-surface distribution of atmospheric trace gases by using passive multiaxis differential absorption optical spectroscopy (MAX-DOAS) is proposed. The procedure consists of pointing the receiving telescope of the spectrometer to nonreflecting surfaces or to bright targets placed at known distances from the measuring device, which are illuminated by sunlight. We show that the partial trace gas absorptions between the top of the atmosphere and the target can be easily removed from the measured total absorption. Thus it is possible to derive the average concentration of trace gases such as NO2, HCHO, SO2, H2O, Glyoxal, BrO, and others along the line of sight between the instrument and the target similar to the well-known long-path DOAS observations (but with much less expense). If tomographic arrangements are used, even two- or three-dimensional trace gas distributions can be retrieved. The basic assumptions of the proposed method are confirmed by test measurements taken across the city of Heidelberg.

Modeling biological gradient formation: combining partial differential equations and Petri nets.

PubMed

Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J

2016-01-01

Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.

What’s in a Surname? Physique, Aptitude, and Sports Type Comparisons between Tailors and Smiths

PubMed Central

Voracek, Martin; Rieder, Stephan; Stieger, Stefan; Swami, Viren

2015-01-01

Combined heredity of surnames and physique, coupled with past marriage patterns and trade-specific physical aptitude and selection factors, may have led to differential assortment of bodily characteristics among present-day men with specific trade-reflecting surnames (Tailor vs. Smith). Two studies reported here were partially consistent with this genetic-social hypothesis, first proposed by Bäumler (1980). Study 1 (N = 224) indicated significantly higher self-rated physical aptitude for prototypically strength-related activities (professions, sports, hobbies) in a random sample of Smiths. The counterpart effect (higher aptitude for dexterity-related activities among Tailors) was directionally correct, but not significant, and Tailor-Smith differences in basic physique variables were nil. Study 2 examined two large total-population-of-interest datasets (Austria/Germany combined, and UK: N = 7001 and 20532) of men’s national high-score lists for track-and-field events requiring different physiques. In both datasets, proportions of Smiths significantly increased from light-stature over medium-stature to heavy-stature sports categories. The predicted counterpart effect (decreasing prevalences of Tailors along these categories) was not supported. Related prior findings, the viability of possible alternative interpretations of the evidence (differential positive selection for trades and occupations, differential endogamy and assortative mating patterns, implicit egotism effects), and directions for further inquiry are discussed in conclusion. PMID:26161803

What's in a Surname? Physique, Aptitude, and Sports Type Comparisons between Tailors and Smiths.

PubMed

Voracek, Martin; Rieder, Stephan; Stieger, Stefan; Swami, Viren

2015-01-01

Combined heredity of surnames and physique, coupled with past marriage patterns and trade-specific physical aptitude and selection factors, may have led to differential assortment of bodily characteristics among present-day men with specific trade-reflecting surnames (Tailor vs. Smith). Two studies reported here were partially consistent with this genetic-social hypothesis, first proposed by Bäumler (1980). Study 1 (N = 224) indicated significantly higher self-rated physical aptitude for prototypically strength-related activities (professions, sports, hobbies) in a random sample of Smiths. The counterpart effect (higher aptitude for dexterity-related activities among Tailors) was directionally correct, but not significant, and Tailor-Smith differences in basic physique variables were nil. Study 2 examined two large total-population-of-interest datasets (Austria/Germany combined, and UK: N = 7001 and 20,532) of men's national high-score lists for track-and-field events requiring different physiques. In both datasets, proportions of Smiths significantly increased from light-stature over medium-stature to heavy-stature sports categories. The predicted counterpart effect (decreasing prevalences of Tailors along these categories) was not supported. Related prior findings, the viability of possible alternative interpretations of the evidence (differential positive selection for trades and occupations, differential endogamy and assortative mating patterns, implicit egotism effects), and directions for further inquiry are discussed in conclusion.

5 CFR 842.614 - Computation of partial annuity reduction.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 5 Administrative Personnel 2 2010-01-01 2010-01-01 false Computation of partial annuity reduction... SERVICE REGULATIONS (CONTINUED) FEDERAL EMPLOYEES RETIREMENT SYSTEM-BASIC ANNUITY Survivor Elections § 842.614 Computation of partial annuity reduction. If a court order or the death of a current or former...

29 CFR 1904.2 - Partial exemption for establishments in certain industries.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 29 Labor 5 2013-07-01 2013-07-01 false Partial exemption for establishments in certain industries... Partial exemption for establishments in certain industries. (a) Basic requirement. (1) If your business establishment is classified in a specific low hazard retail, service, finance, insurance or real estate industry...

Ordinary differential equations.

PubMed

Lebl, Jiří

2013-01-01

In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice. As an example, we work out the equations arising in Michaelis-Menten kinetics and give a short introduction to using Matlab for their numerical solution.

Testing for Differential Item Functioning with Measures of Partial Association

ERIC Educational Resources Information Center

Woods, Carol M.

2009-01-01

Differential item functioning (DIF) occurs when an item on a test or questionnaire has different measurement properties for one group of people versus another, irrespective of mean differences on the construct. There are many methods available for DIF assessment. The present article is focused on indices of partial association. A family of average…

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

EPA Science Inventory

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic_¯¯parabolic (convection_¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

Reverse engineering of aircraft wing data using a partial differential equation surface model

NASA Astrophysics Data System (ADS)

Huband, Jacalyn Mann

Reverse engineering is a multi-step process used in industry to determine a production representation of an existing physical object. This representation is in the form of mathematical equations that are compatible with computer-aided design and computer-aided manufacturing (CAD/CAM) equipment. The four basic steps to the reverse engineering process are data acquisition, data separation, surface or curve fitting, and CAD/CAM production. The surface fitting step determines the design representation of the object, and thus is critical to the success or failure of the reverse engineering process. Although surface fitting methods described in the literature are used to model a variety of surfaces, they are not suitable for reversing aircraft wings. In this dissertation, we develop and demonstrate a new strategy for reversing a mathematical representation of an aircraft wing. The basis of our strategy is to take an aircraft design model and determine if an inverse model can be derived. A candidate design model for this research is the partial differential equation (PDE) surface model, proposed by Bloor and Wilson and used in the Rapid Airplane Parameter Input Design (RAPID) tool at the NASA-LaRC Geolab. There are several basic mathematical problems involved in reversing the PDE surface model: (i) deriving a computational approximation of the surface function; (ii) determining a radial parametrization of the wing; (iii) choosing mathematical models or classes of functions for representation of the boundary functions; (iv) fitting the boundary data points by the chosen boundary functions; and (v) simultaneously solving for the axial parameterization and the derivative boundary functions. The study of the techniques to solve the above mathematical problems has culminated in a reverse PDE surface model and two reverse PDE surface algorithms. One reverse PDE surface algorithm recovers engineering design parameters for the RAPID tool from aircraft wing data and the other generates a PDE surface model with spline boundary functions from an arbitrary set of grid points. Our numerical tests show that the reverse PDE surface model and the reverse PDE surface algorithms can be used for the reverse engineering of aircraft wing data.

Magnetic Evidence for a Partially Differentiated Carbonaceous Chondrite Parent Body and Possible Implications for Asteroid 21 Lutetia

NASA Astrophysics Data System (ADS)

Weiss, Benjamin; Carporzen, L.; Elkins-Tanton, L.; Shuster, D. L.; Ebel, D. S.; Gattacceca, J.; Binzel, R. P.

2010-10-01

The origin of remanent magnetization in the CV carbonaceous chondrite Allende has been a longstanding mystery. The possibility of a core dynamo like that known for achondrite parent bodies has been discounted because chondrite parent bodies are assumed to be undifferentiated. Here we report that Allende's magnetization was acquired over several million years (Ma) during metasomatism on the parent planetesimal in a > 20 microtesla field 8-9 Ma after solar system formation. This field was present too recently and directionally stable for too long to have been the generated by the protoplanetary disk or young Sun. The field intensity is in the range expected for planetesimal core dynamos (Weiss et al. 2010), suggesting that CV chondrites are derived from the outer, unmelted layer of a partially differentiated body with a convecting metallic core (Elkins-Tanton et al. 2010). This suggests that asteroids with differentiated interiors could be present today but masked under chondritic surfaces. In fact, CV chondrites are spectrally similar to many members of the Eos asteroid family whose spectral diversity has been interpreted as evidence for a partially differentiated parent asteroid (Mothe-Diniz et al. 2008). CV chondrite spectral and polarimetric data also resemble those of asteroid 21 Lutetia (e.g., Belskaya et al. 2010), recently encountered by the Rosetta spacecraft. Ground-based measurements of Lutetia indicate a high density of 2.4-5.1 g cm-3 (Drummond et al. 2010), while radar data seem to rule out a metallic surface composition (Shepard et al. 2008). If Rosetta spacecraft measurements confirm a high density and a CV-like surface composition for Lutetia, then we propose Lutetia may be an example of a partially differentiated carbonaceous chondrite parent body. Regardless, the very existence of primitive achondrites, which contain evidence of both relict chondrules and partial melting, are prima facie evidence for the formation of partially differentiated bodies.

Differential Curing In Fiber/Resin Laminates

NASA Technical Reports Server (NTRS)

Webster, Charles N.

1989-01-01

Modified layup schedule counteracts tendency toward delamination. Improved manufacturing process resembles conventional process, except prepregs partially cured laid on mold in sequence in degree of partial cure decreases from mold side to bag side. Degree of partial cure of each layer at time of layup selected by controlling storage and partial-curing temperatures of prepreg according to Arrhenius equation for rate of gel of resin as function of temperature and time from moment of mixing. Differential advancement of cure in layers made large enough to offset effect of advance bag-side heating in oven or autoclave. Technique helps prevent entrapment of volatile materials during manufacturing of fiber/resin laminates.

A homotopy analysis method for the nonlinear partial differential equations arising in engineering

NASA Astrophysics Data System (ADS)

Hariharan, G.

2017-05-01

In this article, we have established the homotopy analysis method (HAM) for solving a few partial differential equations arising in engineering. This technique provides the solutions in rapid convergence series with computable terms for the problems with high degree of nonlinear terms appearing in the governing differential equations. The convergence analysis of the proposed method is also discussed. Finally, we have given some illustrative examples to demonstrate the validity and applicability of the proposed method.

Beyond generalized hair cells: Molecular cues for hair cell types

PubMed Central

Jahan, Israt; Pan, Ning; Kersigo, Jennifer; Fritzsch, Bernd

2012-01-01

Basic helix-loop-helix (bHLH) transcription factors (TFs) are crucial for inner ear neurosensory development. The proneural TF Atoh1 regulates the differentiation of hair cells (HCs) whereas Neurog1 and Neurod1 regulate specification and differentiation of neurons, respectively, but also affect HC development. Expression of Delta and Jagged ligands in nascent HCs and Notch receptors in supporting cells induce supporting cell differentiation through the regulation of neurogenic bHLH TFs (such as Hes1, Hes5) and suppression of limited Atoh1 expression. In sensorineural hearing loss, HCs are lost followed by supporting cells and progressive degeneration of neurons, at least in rodents. Regaining complete hearing may require reconstituting the organ of Corti (OC) from scratch, including the two types of HCs, inner (IHC) and outer (OHC) hair cells with the precise sorting of two types of afferent (type I and II) and efferent (lateral, LOC and medial, MOC olivo-cochlear) innervation. We review effects of bHLH TF dosage and their cross-regulation to differentiate HC types in the OC. We categorize findings of specific gene expressions in HCs: 1. as markers without meaning for the regeneration task, 2. as stabilizers who are needed to maintain or complete differentiation, and 3. as decision making genes, expressed and acting early enough to be useful in this process. Only one TF has been characterized that fits the last aspect: Atoh1. We propose that temporal and intensity variations of Atoh1 are naturally modulated to differentiate specific types of HCs. Importantly, the molecular means to modify the Atoh1 expression are at least partially understood and can be readily implemented in the attempts to regenerate specific types of HCs. PMID:23201032

Parent Ratings of ADHD Symptoms: Generalized Partial Credit Model Analysis of Differential Item Functioning across Gender

ERIC Educational Resources Information Center

Gomez, Rapson

2012-01-01

Objective: Generalized partial credit model, which is based on item response theory (IRT), was used to test differential item functioning (DIF) for the "Diagnostic and Statistical Manual of Mental Disorders" (4th ed.), inattention (IA), and hyperactivity/impulsivity (HI) symptoms across boys and girls. Method: To accomplish this, parents completed…

An electric-analog simulation of elliptic partial differential equations using finite element theory

USGS Publications Warehouse

Franke, O.L.; Pinder, G.F.; Patten, E.P.

1982-01-01

Elliptic partial differential equations can be solved using the Galerkin-finite element method to generate the approximating algebraic equations, and an electrical network to solve the resulting matrices. Some element configurations require the use of networks containing negative resistances which, while physically realizable, are more expensive and time-consuming to construct. ?? 1982.

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

PubMed

Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

2014-01-01

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

Isolation of stress responsive Psb A gene from rice (Oryza sativa l.) using differential display.

PubMed

Tyagi, Aruna; Chandra, Arti

2006-08-01

Differential display (DD) experiments were performed on drought-tolerant rice (Oryza sativa L.) genotype N22 to identify both upregulated and downregulated partial cDNAs with respect to moisture stress. DNA polymorphism was detected between drought-stressed and control leaf tissues on the DD gels. A partial cDNA showing differential expression, with respect to moisture stress was isolated from the gel. Northern blotting analysis was performed using this cDNA as a probe and it was observed that mRNA corresponding to this transcript was accumulated to high level in rice leaves under water deficit stress. At the DNA sequence level, the partial cDNA showed homology with psb A gene encoding for Dl protein.

Thin-film Faraday patterns in three dimensions

NASA Astrophysics Data System (ADS)

Richter, Sebastian; Bestehorn, Michael

2017-04-01

We investigate the long time evolution of a thin fluid layer in three spatial dimensions located on a horizontal planar substrate. The substrate is subjected to time-periodic external vibrations in normal and in tangential direction with respect to the plane surface. The governing partial differential equation system of our model is obtained from the incompressible Navier-Stokes equations considering the limit of a thin fluid geometry and using the long wave lubrication approximation. It includes inertia and viscous friction. Numerical simulations evince the existence of persistent spatially complex surface patterns (periodic and quasiperiodic) for certain superpositions of two vertical excitations and initial conditions. Additional harmonic lateral excitations cause deformations but retain the basic structure of the patterns. Horizontal ratchet-shaped forces lead to a controllable lateral movement of the fluid. A Floquet analysis is used to determine the stability of the linearized system.

Physics, mathematics and numerics of particle adsorption on fluid interfaces

NASA Astrophysics Data System (ADS)

Schmuck, Markus; Pavliotis, Grigorios A.; Kalliadasis, Serafim

2012-11-01

We study two arbitrary immiscible fuids where one phase contains small particles of the size of the interface and smaller. We primarily focus on charge-free particles with wetting characteristics described by the contact angle formed at the interface between the two phases and the particles. Based on the experimental observation that particles are adsorbed on the interface to reduce the interfacial energy and hence the surface tension as well, we formulate a free-energy functional that accounts for these physical effects. Using elements from calculus of variations and formal gradient flow theory, we derive partial differential equations describing the location of the interface and the density of the particles in the fluid phases. Via numerical experiments we analyse the time evolution of the surface tension, the particle concentration, and the free energy over time and reflect basic experimentally observed phenomena.

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

NASA Technical Reports Server (NTRS)

Chen, C.-J.; Naseri-Neshat, H.; Ho, K.-S.

1981-01-01

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

Genetic control of adult neurogenesis: interplay of differentiation, proliferation and survival modulates new neurons function, and memory circuits

PubMed Central

Tirone, Felice; Farioli-Vecchioli, Stefano; Micheli, Laura; Ceccarelli, Manuela; Leonardi, Luca

2013-01-01

Within the hippocampal circuitry, the basic function of the dentate gyrus is to transform the memory input coming from the enthorinal cortex into sparse and categorized outputs to CA3, in this way separating related memory information. New neurons generated in the dentate gyrus during adulthood appear to facilitate this process, allowing a better separation between closely spaced memories (pattern separation). The evidence underlying this model has been gathered essentially by ablating the newly adult-generated neurons. This approach, however, does not allow monitoring of the integration of new neurons into memory circuits and is likely to set in motion compensatory circuits, possibly leading to an underestimation of the role of new neurons. Here we review the background of the basic function of the hippocampus and of the known properties of new adult-generated neurons. In this context, we analyze the cognitive performance in mouse models generated by us and others, with modified expression of the genes Btg2 (PC3/Tis21), Btg1, Pten, BMP4, etc., where new neurons underwent a change in their differentiation rate or a partial decrease of their proliferation or survival rate rather than ablation. The effects of these modifications are equal or greater than full ablation, suggesting that the architecture of circuits, as it unfolds from the interaction between existing and new neurons, can have a greater functional impact than the sheer number of new neurons. We propose a model which attempts to measure and correlate the set of cellular changes in the process of neurogenesis with the memory function. PMID:23734097

Molecular cloning and characterization of a new basic peroxidase cDNA from soybean hypocotyls infected with Phytophthora sojae f.sp. glycines.

PubMed

Yi, S Y; Hwang, B K

1998-10-31

Differential display techniques were used to isolate cDNA clones corresponding to genes which were expressed in soybean hypocotyls by Phytophthora sojae f.sp. glycines infection. With a partial cDNA clone C20CI4 from the differential display PCR as a probe, a new basic peroxidase cDNA clone, designated GMIPER1, was isolated from a cDNA library of soybean hypocotyls infected with P. sojae f.sp. glycines. Sequence analysis revealed that the peroxidase clone encodes a mature protein of 35,813 Da with a putative signal peptide of 27 amino acids in its N-terminus. The amino acid sequence of the soybean peroxidase GMIPER1 is between 54-75% identical to other plant peroxidases including a soybean seed coat peroxidase. Southern blot analysis indicated that multiple copies of sequences related to GMIPER1 exist in the soybean genome. The mRNAs corresponding to the GMIPER1 cDNA accumulated predominantly in the soybean hypocotyls infected with the incompatible race of P. sojae f.sp. glycines, but were expressed at low levels in the compatible interaction. Soybean GMIPER1 mRNAs were not expressed in hypocotyls, leaves, stems, and roots of soybean seedlings. However, treatments with ethephon, salicylic acid or methyl jasmonate induced the accumulation of the GMIPER1 mRNAs in the different organs of soybean. These results suggest that the GMIPER1 gene encoding a putative pathogen-induced peroxidase may play an important role in induced resistance of soybean to P. sojae f.sp. glycines and in response to various external stresses.

Generalized Lie symmetry approach for fractional order systems of differential equations. III

NASA Astrophysics Data System (ADS)

Singla, Komal; Gupta, R. K.

2017-06-01

The generalized Lie symmetry technique is proposed for the derivation of point symmetries for systems of fractional differential equations with an arbitrary number of independent as well as dependent variables. The efficiency of the method is illustrated by its application to three higher dimensional nonlinear systems of fractional order partial differential equations consisting of the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov system, (3 + 1)-dimensional Burgers system, and (3 + 1)-dimensional Navier-Stokes equations. With the help of derived Lie point symmetries, the corresponding invariant solutions transform each of the considered systems into a system of lower-dimensional fractional partial differential equations.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

Basic Sciences Fertilizing Clinical Microbiology and Infection Management

PubMed Central

2017-01-01

Abstract Basic sciences constitute the most abundant sources of creativity and innovation, as they are based on the passion of knowing. Basic knowledge, in close and fertile contact with medical and public health needs, produces distinct advancements in applied sciences. Basic sciences play the role of stem cells, providing material and semantics to construct differentiated tissues and organisms and enabling specialized functions and applications. However, eventually processes of “practice deconstruction” might reveal basic questions, as in de-differentiation of tissue cells. Basic sciences, microbiology, infectious diseases, and public health constitute an epistemological gradient that should also be an investigational continuum. The coexistence of all these interests and their cross-fertilization should be favored by interdisciplinary, integrative research organizations working simultaneously in the analytical and synthetic dimensions of scientific knowledge. PMID:28859345

Concatenons as the solutions for non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Kudryashov, N. A.; Volkov, A. K.

2017-07-01

New class of solutions for nonlinear partial differential equations is introduced. We call them the concaten solutions. As an example we consider equations for the description of wave processes in the Fermi-Pasta-Ulam mass chain and construct the concatenon solutions for these equation. Stability of the concatenon-type solutions is investigated numerically. Interaction between the concatenon and solitons is discussed.

Hidden physics models: Machine learning of nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Raissi, Maziar; Karniadakis, George Em

2018-03-01

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Ding, Xiao-Li; Nieto, Juan J.

2017-11-01

In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

Partial slip effect in the flow of MHD micropolar nanofluid flow due to a rotating disk - A numerical approach

NASA Astrophysics Data System (ADS)

Ramzan, Muhammad; Chung, Jae Dong; Ullah, Naeem

The aim of present exploration is to study the flow of micropolar nanofluid due to a rotating disk in the presence of magnetic field and partial slip condition. The governing coupled partial differential equations are reduced to nonlinear ordinary differential equations using appropriate transformations. The differential equations are solved numerically by using Maple dsolve command with option numeric which utilize Runge-Kutta fourth-fifth order Fehlberg technique. A comparison to previous study is also added to validate the present results. Moreover, behavior of different parameters on velocity, microrotation, temperature and concentration of nanofluid are presented via graphs and tables. It is noted that the slip effect and magnetic field decay the velocity and microrotation or spin component.

The Uniform Convergence of Eigenfunction Expansions of Schrödinger Operator in the Nikolskii Classes {H}_{p}^{\\alpha }(\\bar{\\Omega })

NASA Astrophysics Data System (ADS)

Jamaludin, N. A.; Ahmedov, A.

2017-09-01

Many boundary value problems in the theory of partial differential equations can be solved by separation methods of partial differential equations. When Schrödinger operator is considered then the influence of the singularity of potential on the solution of the partial differential equation is interest of researchers. In this paper the problems of the uniform convergence of the eigenfunction expansions of the functions from corresponding to the Schrödinger operator with the potential from classes of Sobolev are investigated. The spectral function corresponding to the Schrödinger operator is estimated in closed domain. The isomorphism of the Nikolskii classes is applied to prove uniform convergence of eigenfunction expansions of Schrödinger operator in closed domain.

Low-Degree Partial Melting Experiments of CR and H Chondrite Compositions: Implications for Asteroidal Magmatism Recorded in GRA 06128 and GRA 06129 T

NASA Technical Reports Server (NTRS)

Usui, T.; Jones, John H.; Mittlefehldt, D. W.

2010-01-01

Studies of differentiated meteorites have revealed a diversity of differentiation processes on their parental asteroids; these differentiation mechanisms range from whole-scale melting to partial melting without the core formation [e.g., 1]. Recently discovered paired achondrites GRA 06128 and GRA 06129 (hereafter referred to as GRA) represent unique asteroidal magmatic processes. These meteorites are characterized by high abundances of sodic plagioclase and alkali-rich whole-rock compositions, implying that they could originate from a low-degree partial melt from a volatile-rich oxidized asteroid [e.g., 2, 3, 4]. These conditions are consistent with the high abundances of highly siderophile elements, suggesting that their parent asteroid did not segregate a metallic core [2]. In this study, we test the hypothesis that low-degree partial melts of chondritic precursors under oxidizing conditions can explain the whole-rock and mineral chemistry of GRA based on melting experiments of synthesized CR- and H-chondrite compositions.

The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

NASA Technical Reports Server (NTRS)

Ito, K.

1983-01-01

Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.

Trigonometric Integrals via Partial Fractions

ERIC Educational Resources Information Center

Chen, H.; Fulford, M.

2005-01-01

Parametric differentiation is used to derive the partial fractions decompositions of certain rational functions. Those decompositions enable us to integrate some new combinations of trigonometric functions.

Exp-function method for solving fractional partial differential equations.

PubMed

Zheng, Bin

2013-01-01

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

Application of partial differential equation modeling of the control/structural dynamics of flexible spacecraft

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr.; Rajiyah, H.

1991-01-01

Partial differential equations for modeling the structural dynamics and control systems of flexible spacecraft are applied here in order to facilitate systems analysis and optimization of these spacecraft. Example applications are given, including the structural dynamics of SCOLE, the Solar Array Flight Experiment, the Mini-MAST truss, and the LACE satellite. The development of related software is briefly addressed.

Effect of Partially Fluorinated N-Alkyl-Substituted Piperidine-2-carboxamides on Pharmacologically Relevant Properties.

PubMed

Vorberg, Raffael; Trapp, Nils; Zimmerli, Daniel; Wagner, Björn; Fischer, Holger; Kratochwil, Nicole A; Kansy, Manfred; Carreira, Erick M; Müller, Klaus

2016-10-06

The modulation of pharmacologically relevant properties of N-alkyl-piperidine-2-carboxamides was studied by selective introduction of 1-3 fluorine atoms into the n-propyl and n-butyl side chains of the local anesthetics ropivacaine and levobupivacaine. The basicity modulation by nearby fluorine substituents is essentially additive and exhibits an exponential attenuation as a function of topological distance between fluorine and the basic center. The intrinsic lipophilicity of the neutral piperidine derivatives displays the characteristic response noted for partially fluorinated alkyl groups attached to neutral heteroaryl systems. However, basicity decrease by nearby fluorine substituents affects lipophilicities at neutral pH, so that all partially fluorinated derivatives are of similar or higher lipophilicity than their non-fluorinated parents. Aqueous solubilities were found to correlate inversely with lipophilicity with a significant contribution from crystal packing energies, as indicated by variations in melting point temperatures. All fluorinated derivatives were found to be somewhat more readily oxidized in human liver microsomes, the rates of degradation correlating with increasing lipophilicity. Because the piperidine-2-carboxamide core is chiral, pairs with enantiomeric N-alkyl groups are diastereomeric. While little response to such stereoisomerism was observed for basicity or lipophilicity, more pronounced variations were observed for melting point temperatures and oxidative degradation. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Topics in spectral methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1985-01-01

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

Effect of evaporative surface cooling on thermographic assessment of burn depth

NASA Technical Reports Server (NTRS)

Anselmo, V. J.; Zawacki, B. E.

1977-01-01

Differences in surface temperature between evaporating and nonevaporating, partial- and full-thickness burn injuries were studied in 20 male, white guinea pigs. Evaporative cooling can disguise the temperature differential of the partial-thickness injury and lead to a false full-thickness diagnosis. A full-thickness burn with blister intact may retain enough heat to result in a false partial-thickness diagnosis. By the fourth postburn day, formation of a dry eschar may allow a surface temperature measurement without the complication of differential evaporation. For earlier use of thermographic information, evaporation effects must be accounted for or eliminated.

Solving Differential Equations in R: Package deSolve

EPA Science Inventory

In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...

The Generation of Three-Dimensional Body-Fitted Coordinate Systems for Viscous Flow Problems.

DTIC Science & Technology

1982-07-01

Geometries," NASA TM X-3206, 1975. iq p] Papers Written Under The Contract 1. "Basic Differential Models For Coordinate Generation ", Z . U. A. Warsi...8217 Ii (C) (4’) p Figure 1. Coordinate Surfaces fr. I • BASIC DIFFERENTIAL MODELS FOR COORDINATE GENERATION Z . U. A. WARSI* Department of Aerospace

A higher order numerical method for time fractional partial differential equations with nonsmooth data

NASA Astrophysics Data System (ADS)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 by directly approximating the integer-order derivative with some finite difference quotients in the definition of the Caputo fractional derivative, see also Lv and Xu [20] (2016), where k is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. In this paper, we first obtain a similar approximation scheme to the Riemann-Liouville fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 as in Gao et al. [11] (2014) by approximating the Hadamard finite-part integral with the piecewise quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 < α < 1 for any fixed tn > 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

Taguchi method for partial differential equations with application in tumor growth.

PubMed

Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena

2014-01-01

The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Ma, Wen-Xiu; Zhou, Yuan

2018-02-01

Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u = 2(ln ⁡ f) x and u = 2(ln ⁡ f) xx, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations.

Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Warsi, Z. U. A.; Mastin, C. W.

1982-01-01

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

Shift-connected SIMD array architectures for digital optical computing systems, with algorithms for numerical transforms and partial differential equations

NASA Astrophysics Data System (ADS)

Drabik, Timothy J.; Lee, Sing H.

1986-11-01

The intrinsic parallelism characteristics of easily realizable optical SIMD arrays prompt their present consideration in the implementation of highly structured algorithms for the numerical solution of multidimensional partial differential equations and the computation of fast numerical transforms. Attention is given to a system, comprising several spatial light modulators (SLMs), an optical read/write memory, and a functional block, which performs simple, space-invariant shifts on images with sufficient flexibility to implement the fastest known methods for partial differential equations as well as a wide variety of numerical transforms in two or more dimensions. Either fixed or floating-point arithmetic may be used. A performance projection of more than 1 billion floating point operations/sec using SLMs with 1000 x 1000-resolution and operating at 1-MHz frame rates is made.

Using some results about the Lie evolution of differential operators to obtain the Fokker-Planck equation for non-Hamiltonian dynamical systems of interest

NASA Astrophysics Data System (ADS)

Bianucci, Marco

2018-05-01

Finding the generalized Fokker-Planck Equation (FPE) for the reduced probability density function of a subpart of a given complex system is a classical issue of statistical mechanics. Zwanzig projection perturbation approach to this issue leads to the trouble of resumming a series of commutators of differential operators that we show to correspond to solving the Lie evolution of first order differential operators along the unperturbed Liouvillian of the dynamical system of interest. In this paper, we develop in a systematic way the procedure to formally solve this problem. In particular, here we show which the basic assumptions are, concerning the dynamical system of interest, necessary for the Lie evolution to be a group on the space of first order differential operators, and we obtain the coefficients of the so-evolved operators. It is thus demonstrated that if the Liouvillian of the system of interest is not a first order differential operator, in general, the FPE structure breaks down and the master equation contains all the power of the partial derivatives, up to infinity. Therefore, this work shed some light on the trouble of the ubiquitous emergence of both thermodynamics from microscopic systems and regular regression laws at macroscopic scales. However these results are very general and can be applied also in other contexts that are non-Hamiltonian as, for example, geophysical fluid dynamics, where important events, like El Niño, can be considered as large time scale phenomena emerging from the observation of few ocean degrees of freedom of a more complex system, including the interaction with the atmosphere.

Changes in Naval Aviation Basic Instrument Flight Training: An Analysis.

DTIC Science & Technology

1985-12-01

position to the desired attitude in relation to the horizon [Refs. 4,5: pp.2,16-3]. C. BASIC INSTRUMENT FLIGHT TRAINING The objective of basic...were related to the treatment lecture: 1. Basic Air Work (BAW) 2. Partial Panel 3. Unusual Attitudes (full panel) 4. Initial Climb to Altitude (ICA) 5...of student aviators was compared. The modifi- cations consisted of a lecture concentrating on the fundamentals of attitude instrument flight. One group

An approximation theory for nonlinear partial differential equations with applications to identification and control

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1982-01-01

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Research on Nonlinear Dynamical Systems.

DTIC Science & Technology

1983-01-10

Applied Math., to appear. [26] Variational inequalities and flow in porous media, LCDS’Lecture Notes, Brown University #LN 82-1, July 1982. [27] On...approximation schemes for parabolic and hyperbolic systems of partial differential equations, including higher order equations of elasticity based on the...51,58,59,63,64,69]. Finally, stability and bifurcation in parabolic partial differential equations is the focus of [64,65,67,72,73]. In addition to these broad

Geometric properties of commutative subalgebras of partial differential operators

NASA Astrophysics Data System (ADS)

Zheglov, A. B.; Kurke, H.

2015-05-01

We investigate further algebro-geometric properties of commutative rings of partial differential operators, continuing our research started in previous articles. In particular, we start to explore the simplest and also certain known examples of quantum algebraically completely integrable systems from the point of view of a recent generalization of Sato's theory, developed by the first author. We give a complete characterization of the spectral data for a class of 'trivial' commutative algebras and strengthen geometric properties known earlier for a class of known examples. We also define a kind of restriction map from the moduli space of coherent sheaves with fixed Hilbert polynomial on a surface to an analogous moduli space on a divisor (both the surface and the divisor are part of the spectral data). We give several explicit examples of spectral data and corresponding algebras of commuting (completed) operators, producing as a by-product interesting examples of surfaces that are not isomorphic to spectral surfaces of any (maximal) commutative ring of partial differential operators of rank one. Finally, we prove that any commutative ring of partial differential operators whose normalization is isomorphic to the ring of polynomials k \\lbrack u,t \\rbrack is a Darboux transformation of a ring of operators with constant coefficients. Bibliography: 39 titles.

MESOSCOPIC MODELING OF STOCHASTIC REACTION-DIFFUSION KINETICS IN THE SUBDIFFUSIVE REGIME

PubMed Central

BLANC, EMILIE; ENGBLOM, STEFAN; HELLANDER, ANDREAS; LÖTSTEDT, PER

2017-01-01

Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model of subdiffusion into an accurate and consistent reaction-subdiffusion computational framework. Two different possible models of chemical reaction are revealed and some basic dynamic properties are derived. In certain cases those mesoscopic models have a direct interpretation at the macroscopic level as fractional partial differential equations in a bounded time interval. Through analysis and numerical experiments we estimate the macroscopic effects of reactions under subdiffusive mixing. The models display properties observed also in experiments: for a short time interval the behavior of the diffusion and the reaction is ordinary, in an intermediate interval the behavior is anomalous, and at long times the behavior is ordinary again. PMID:29046618

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

PubMed

Das, Shankar P; Yoshimori, Akira

2013-10-01

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

Applications of the ETEM for obtaining optical soliton solutions for the Lakshmanan-Porsezian-Daniel model

NASA Astrophysics Data System (ADS)

Manafian, Jalil; Foroutan, Mohammadreza; Guzali, Aref

2017-11-01

This paper examines the effectiveness of an integration scheme which is called the extended trial equation method (ETEM) for solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the Lakshmanan-Porsezian-Daniel (LPD) equation with Kerr and power laws of nonlinearity which describes higher-order dispersion, full nonlinearity and spatiotemporal dispersion is considered, and as an achievement, a series of exact travelling-wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of LPD equation. The movement of obtained solutions is shown graphically, which helps to understand the physical phenomena of this optical soliton equation. Many other such types of nonlinear equations arising in basic fabric of communications network technology and nonlinear optics can also be solved by this method.

Induction of motor neuron differentiation by transduction of Olig2 protein.

PubMed

Mie, Masayasu; Kaneko, Mami; Henmi, Fumiaki; Kobatake, Eiry

2012-10-26

Olig2 protein, a member of the basic helix-loop-helix transcription factor family, was introduced into the mouse embryonic carcinoma cell line P19 for induction of motor neuron differentiation. We show that Olig2 protein has the ability to permeate the cell membrane without the addition of a protein transduction domain (PTD), similar to other basic helix-loop-helix transcription factors such as MyoD and NeuroD2. Motor neuron differentiation was evaluated for the elongation of neurites and the expression of choline acetyltransferase (ChAT) mRNA, a differentiation marker of motor neurons. By addition of Olig2 protein, motor neuron differentiation was induced in P19 cells. Copyright © 2012 Elsevier Inc. All rights reserved.

Facts about Hib Disease. ARC Facts.

ERIC Educational Resources Information Center

Association for Retarded Citizens, Arlington, TX.

The fact sheet provides basic information about Hib Disease in young children, which may involve a bacterial meningitis causing mental retardation, hearing loss, partial blindness, speech disorders, partial paralysis, behavioral problems, or seizures. Stressed is prevention of Hib Disease through immunization. The question and answer format…

Basic Sciences Fertilizing Clinical Microbiology and Infection Management.

PubMed

Baquero, Fernando

2017-08-15

Basic sciences constitute the most abundant sources of creativity and innovation, as they are based on the passion of knowing. Basic knowledge, in close and fertile contact with medical and public health needs, produces distinct advancements in applied sciences. Basic sciences play the role of stem cells, providing material and semantics to construct differentiated tissues and organisms and enabling specialized functions and applications. However, eventually processes of "practice deconstruction" might reveal basic questions, as in de-differentiation of tissue cells. Basic sciences, microbiology, infectious diseases, and public health constitute an epistemological gradient that should also be an investigational continuum. The coexistence of all these interests and their cross-fertilization should be favored by interdisciplinary, integrative research organizations working simultaneously in the analytical and synthetic dimensions of scientific knowledge. © The Author 2017. Published by Oxford University Press for the Infectious Diseases Society of America.

Basic Communication Course Annual. Volume 8.

ERIC Educational Resources Information Center

Newburger, Craig, Ed.

This volume of an annual collection presents 13 essays relating to instruction in the basic communication course. Six of the essays are on the theme of cultural diversity in the basic course. The essays are: "The Differential Impact of a Basic Public Speaking Course on Perceived Communication Competencies in Class, Work, and Social…

Basic principles of Hasse diagram technique in chemistry.

PubMed

Brüggemann, Rainer; Voigt, Kristina

2008-11-01

Principles of partial order applied to ranking are explained. The Hasse diagram technique (HDT) is the application of partial order theory based on a data matrix. In this paper, HDT is introduced in a stepwise procedure, and some elementary theorems are exemplified. The focus is to show how the multivariate character of a data matrix is realized by HDT and in which cases one should apply other mathematical or statistical methods. Many simple examples illustrate the basic theoretical ideas. Finally, it is shown that HDT is a useful alternative for the evaluation of antifouling agents, which was originally performed by amoeba diagrams.

DVS-SOFTWARE: An Effective Tool for Applying Highly Parallelized Hardware To Computational Geophysics

NASA Astrophysics Data System (ADS)

Herrera, I.; Herrera, G. S.

2015-12-01

Most geophysical systems are macroscopic physical systems. The behavior prediction of such systems is carried out by means of computational models whose basic models are partial differential equations (PDEs) [1]. Due to the enormous size of the discretized version of such PDEs it is necessary to apply highly parallelized super-computers. For them, at present, the most efficient software is based on non-overlapping domain decomposition methods (DDM). However, a limiting feature of the present state-of-the-art techniques is due to the kind of discretizations used in them. Recently, I. Herrera and co-workers using 'non-overlapping discretizations' have produced the DVS-Software which overcomes this limitation [2]. The DVS-software can be applied to a great variety of geophysical problems and achieves very high parallel efficiencies (90%, or so [3]). It is therefore very suitable for effectively applying the most advanced parallel supercomputers available at present. In a parallel talk, in this AGU Fall Meeting, Graciela Herrera Z. will present how this software is being applied to advance MOD-FLOW. Key Words: Parallel Software for Geophysics, High Performance Computing, HPC, Parallel Computing, Domain Decomposition Methods (DDM)REFERENCES [1]. Herrera Ismael and George F. Pinder, Mathematical Modelling in Science and Engineering: An axiomatic approach", John Wiley, 243p., 2012. [2]. Herrera, I., de la Cruz L.M. and Rosas-Medina A. "Non Overlapping Discretization Methods for Partial, Differential Equations". NUMER METH PART D E, 30: 1427-1454, 2014, DOI 10.1002/num 21852. (Open source) [3]. Herrera, I., & Contreras Iván "An Innovative Tool for Effectively Applying Highly Parallelized Software To Problems of Elasticity". Geofísica Internacional, 2015 (In press)

7 CFR 1000.76 - Payments by a handler operating a partially regulated distributing plant.

Code of Federal Regulations, 2010 CFR

2010-01-01

..., compute a Class I differential price by subtracting Class III price from the current month's Class I price... by which the Class I differential price exceeds the producer price differential, both prices to be... Class I differential price nor the adjusted producer price differential shall be less than zero; (3) For...

Teaching Computational Geophysics Classes using Active Learning Techniques

NASA Astrophysics Data System (ADS)

Keers, H.; Rondenay, S.; Harlap, Y.; Nordmo, I.

2016-12-01

We give an overview of our experience in teaching two computational geophysics classes at the undergraduate level. In particular we describe The first class is for most students the first programming class and assumes that the students have had an introductory course in geophysics. In this class the students are introduced to basic Matlab skills: use of variables, basic array and matrix definition and manipulation, basic statistics, 1D integration, plotting of lines and surfaces, making of .m files and basic debugging techniques. All of these concepts are applied to elementary but important concepts in earthquake and exploration geophysics (including epicentre location, computation of travel time curves for simple layered media plotting of 1D and 2D velocity models etc.). It is important to integrate the geophysics with the programming concepts: we found that this enhances students' understanding. Moreover, as this is a 3 year Bachelor program, and this class is taught in the 2nd semester, there is little time for a class that focusses on only programming. In the second class, which is optional and can be taken in the 4th or 6th semester, but often is also taken by Master students we extend the Matlab programming to include signal processing and ordinary and partial differential equations, again with emphasis on geophysics (such as ray tracing and solving the acoustic wave equation). This class also contains a project in which the students have to write a brief paper on a topic in computational geophysics, preferably with programming examples. When teaching these classes it was found that active learning techniques, in which the students actively participate in the class, either individually, in pairs or in groups, are indispensable. We give a brief overview of the various activities that we have developed when teaching theses classes.

Thermal evolution of a partially differentiated H chondrite parent body

NASA Astrophysics Data System (ADS)

Abrahams, J. N. H.; Bryson, J. F. J.; Weiss, B. P.; Nimmo, F.

2016-12-01

It has traditionally been assumed that planetesimals either melted entirely or remained completely undifferentiated as they accreted. The unmelted textures and cooling histories of chondrites have been used to argue that these meteorites originated from bodies that never differentiated. However, paleomagnetic measurements indicate that some chondrites (e.g., the H chondrite Portales Valley and several CV chondrites) were magnetized by a core dynamo magnetic field, implying that their parent bodies were partially differentiated. It has been unclear, however, whether planetesimal histories consistent with dynamo production can also be consistent with the diversity of chondrite cooling rates and ages. To address this, we modeled the thermal evolution of the H chondrite parent body, considering a variety of accretion histories and parent body radii. We considered partial differentiation using two-stage accretion involving the initial formation and differentiation of a small body, followed by the later addition of low thermal conductivity chondritic material that remains mostly unmelted. We were able to reproduce the measured thermal evolution of multiple H chondrites for a range of parent body parameters, including initial radii from 70-150 km, chondritic layer thicknesses from 50 km to over 100 km, and second stage accretion times of 2.5-3 Myr after solar system formation. Our predicted rates of core cooling and crystallization are consistent with dynamo generation by compositional convection beginning 60-200 Myr after solar system formation and lasting for at least tens of millions of years. This is consistent with magnetic studies of Portales Valley [Bryson et al., this meeting]. In summary, we find that thermal models of partial differentiation are consistent the radiometric ages, magnetization, and cooling rates of a diversity H chondrites.

Some remarks on the numerical solution of parabolic partial differential equations

NASA Astrophysics Data System (ADS)

Campagna, R.; Cuomo, S.; Leveque, S.; Toraldo, G.; Giannino, F.; Severino, G.

2017-11-01

Numerous environmental/engineering applications relying upon the theory of diffusion phenomena into chaotic environments have recently stimulated the interest toward the numerical solution of parabolic partial differential equations (PDEs). In the present paper, we outline a formulation of the mathematical problem underlying a quite general diffusion mechanism in the natural environments, and we shortly emphasize some remarks concerning the applicability of the (straightforward) finite difference method. An illustration example is also presented.

The Refinement-Tree Partition for Parallel Solution of Partial Differential Equations

PubMed Central

Mitchell, William F.

1998-01-01

Dynamic load balancing is considered in the context of adaptive multilevel methods for partial differential equations on distributed memory multiprocessors. An approach that periodically repartitions the grid is taken. The important properties of a partitioning algorithm are presented and discussed in this context. A partitioning algorithm based on the refinement tree of the adaptive grid is presented and analyzed in terms of these properties. Theoretical and numerical results are given. PMID:28009355

The Refinement-Tree Partition for Parallel Solution of Partial Differential Equations.

PubMed

Mitchell, William F

1998-01-01

Dynamic load balancing is considered in the context of adaptive multilevel methods for partial differential equations on distributed memory multiprocessors. An approach that periodically repartitions the grid is taken. The important properties of a partitioning algorithm are presented and discussed in this context. A partitioning algorithm based on the refinement tree of the adaptive grid is presented and analyzed in terms of these properties. Theoretical and numerical results are given.

Observability of discretized partial differential equations

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1988-01-01

It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Cellular Automata for Spatiotemporal Pattern Formation from Reaction-Diffusion Partial Differential Equations

NASA Astrophysics Data System (ADS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.

A convex penalty for switching control of partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Clason, Christian; Rund, Armin; Kunisch, Karl

2016-01-19

A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.

Numerical methods for large-scale, time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Turkel, E.

1979-01-01

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.

Spectral methods for time dependent partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1983-01-01

The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

Stability analysis of multigrid acceleration methods for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Fay, John F.

1990-01-01

A calculation is made of the stability of various relaxation schemes for the numerical solution of partial differential equations. A multigrid acceleration method is introduced, and its effects on stability are explored. A detailed stability analysis of a simple case is carried out and verified by numerical experiment. It is shown that the use of multigrids can speed convergence by several orders of magnitude without adversely affecting stability.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

NASA Astrophysics Data System (ADS)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

From crater functions to partial differential equations: a new approach to ion bombardment induced nonequilibrium pattern formation.

PubMed

Norris, Scott A; Brenner, Michael P; Aziz, Michael J

2009-06-03

We develop a methodology for deriving continuum partial differential equations for the evolution of large-scale surface morphology directly from molecular dynamics simulations of the craters formed from individual ion impacts. Our formalism relies on the separation between the length scale of ion impact and the characteristic scale of pattern formation, and expresses the surface evolution in terms of the moments of the crater function. We demonstrate that the formalism reproduces the classical Bradley-Harper results, as well as ballistic atomic drift, under the appropriate simplifying assumptions. Given an actual set of converged molecular dynamics moments and their derivatives with respect to the incidence angle, our approach can be applied directly to predict the presence and absence of surface morphological instabilities. This analysis represents the first work systematically connecting molecular dynamics simulations of ion bombardment to partial differential equations that govern topographic pattern-forming instabilities.

Partial differential equations constrained combinatorial optimization on an adiabatic quantum computer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh

Partial differential equation-constrained combinatorial optimization (PDECCO) problems are a mixture of continuous and discrete optimization problems. PDECCO problems have discrete controls, but since the partial differential equations (PDE) are continuous, the optimization space is continuous as well. Such problems have several applications, such as gas/water network optimization, traffic optimization, micro-chip cooling optimization, etc. Currently, no efficient classical algorithm which guarantees a global minimum for PDECCO problems exists. A new mapping has been developed that transforms PDECCO problem, which only have linear PDEs as constraints, into quadratic unconstrained binary optimization (QUBO) problems that can be solved using an adiabatic quantum optimizer (AQO). The mapping is efficient, it scales polynomially with the size of the PDECCO problem, requires only one PDE solve to form the QUBO problem, and if the QUBO problem is solved correctly and efficiently on an AQO, guarantees a global optimal solution for the original PDECCO problem.

PetIGA: A framework for high-performance isogeometric analysis

DOE PAGES

Dalcin, Lisandro; Collier, Nathaniel; Vignal, Philippe; ...

2016-05-25

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equations, which simplifies the development of large-scale scientific codes, provides a rich environment for prototyping, and separates parallelism from algorithm choice. We describe the implementation of PetIGA, and exemplify its use by solving a model nonlinear problem. To illustrate the robustness and flexibility ofmore » PetIGA, we solve some challenging nonlinear partial differential equations that include problems in both solid and fluid mechanics. Lastly, we show strong scaling results on up to 4096 cores, which confirm the suitability of PetIGA for large scale simulations.« less

On Partial Fraction Decompositions by Repeated Polynomial Divisions

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2017-01-01

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

Ion-Exchange Chromatography: Basic Principles and Application.

PubMed

Cummins, Philip M; Rochfort, Keith D; O'Connor, Brendan F

2017-01-01

Ion-Exchange Chromatography (IEC) allows for the separation of ionizable molecules on the basis of differences in charge properties. Its large sample-handling capacity, broad applicability (particularly to proteins and enzymes), moderate cost, powerful resolving ability, and ease of scale-up and automation have led to it becoming one of the most versatile and widely used of all liquid chromatography (LC) techniques. In this chapter, we review the basic principles of IEC, as well as the broader criteria for selecting IEC conditions. By way of further illustration, we outline basic laboratory protocols to partially purify a soluble serine peptidase from bovine whole brain tissue, covering crude tissue extract preparation through to partial purification of the target enzyme using anion-exchange chromatography. Protocols for assaying total protein and enzyme activity in both pre- and post-IEC fractions are also described.

A Model for the Oxidation of Carbon Silicon Carbide Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2004-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of carbon silicon carbide (C/SiC) composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The numerical method is demonstrated by utilizing the method to model the carbon oxidation and weight loss behavior of C/SiC specimens during thermogravimetric experiments. The numerical method is used to study the physics of carbon oxidation in carbon silicon carbide composites.

The Basic Principle of Calculus?

ERIC Educational Resources Information Center

Hardy, Michael

2011-01-01

A simple partial version of the Fundamental Theorem of Calculus can be presented on the first day of the first-year calculus course, and then relied upon repeatedly in assigned problems throughout the course. With that experience behind them, students can use the partial version to understand the full-fledged Fundamental Theorem, with further…

How Coaches' Motivations Mediate Between Basic Psychological Needs and Well-Being/Ill-Being.

PubMed

Alcaraz, Saul; Torregrosa, Miquel; Viladrich, Carme

2015-01-01

The purpose of the present research was to test how behavioral regulations are mediated between basic psychological needs and psychological well-being and ill-being in a sample of team-sport coaches. Based on self-determination theory, we hypothesized a model where satisfaction and thwarting of the basic psychological needs predicted coaches' behavioral regulations, which in turn led them to experience well-being (i.e., subjective vitality, positive affect) or ill-being (i.e., perceived stress, negative affect). Three-hundred and two coaches participated in the study (Mage = 25.97 years; 82% male). For each instrument employed, the measurement model with the best psychometric properties was selected from a sequence of nested models sustained by previous research, including exploratory structural equation models and confirmatory factor analysis. These measurement models were included in 3 structural equation models to test for mediation: partial mediation, complete mediation, and absence of mediation. The results provided support for the partial mediation model. Coaches' motivation mediated the relationships from both relatedness need satisfaction and basic psychological needs thwarting for coaches' well-being. In contrast, relationships between basic psychological needs satisfaction and thwarting and ill-being were only predicted by direct effects. Our results highlight that 3 conditions seem necessary for coaches to experience psychological well-being in their teams: basic psychological needs satisfaction, especially relatedness; lack of basic psychological needs thwarting; and self-determined motivation.

Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane

NASA Astrophysics Data System (ADS)

Abd-El-Malek, Mina B.; Kassem, Magda M.; Meky, Mohammed L. M.

2002-03-01

The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

PubMed

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

PubMed Central

Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

2015-01-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

Multirate Integration Properties of Waveform Relaxation with Applications to Circuit Simulation and Parallel Computation

DTIC Science & Technology

1985-11-18

Greenberg and K. Sakallah at Digital Equipment Corporation, and C-F. Chen, L Nagel, and P. ,. Subrahmanyam at AT&T Bell Laboratories, both for providing...Circuit Theory McGraw-Hill, 1969. [37] R. Courant and D. Hilbert , Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics...McGraw-Hill, N.Y., 1965. Page 161 [44) R. Courant and D. Hilbert , Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics

A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial-Differential-Equation Outputs. Revised

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume

1998-01-01

We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.

The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

The aim of this paper is to examine the Riemann-Lanczos equations and how they can be made integrable. They consist of a system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order tensor potential field called the Lanczos tensor. Our approach is based on the theory of jet bundles, where all field variables and all their partial derivatives of all relevant orders are treated as independent variables alongside the local manifold coordinates (xa) on the given space-time manifold M. This approach is adopted in (a) Cartan's method of exterior differential systems, (b) Vessiot's dual method using vector field systems, and (c) the Janet-Riquier theory of systems of partial differential equations. All three methods allow for the most general situations under which integrability conditions can be found. They give equivalent results, namely, that involutivity is always achieved at all generic points of the jet manifold M after a finite number of prolongations. Two alternative methods that appear in the general relativity literature to find integrability conditions for the Riemann-Lanczos equations generate new partial differential equations for the Lanczos potential that introduce a source term, which is nonlinear in the components of the Riemann tensor. We show that such sources do not occur when either of method (a), (b), or (c) are used.

Quantitative evaluation method for differentiation of C2C12 myoblasts by ultrasonic microscopy

NASA Astrophysics Data System (ADS)

Takanashi, Kyoichi; Washiya, Mamoru; Ota, Kazuki; Yoshida, Sachiko; Hozumi, Naohiro; Kobayashi, Kazuto

2017-07-01

Cell differentiation was evaluated by ultrasonic microscopy. However, there were some regions that showed a lower acoustic impedance than the culture liquid. It was considered that, in such regions, the cells were not perfectly in contact with the film substrate. Hence, a waveform analysis was performed, and compensated acoustic impedances in such regions were in a reasonable range of values. By the same analysis, the displacements of partially floated cells were also successfully calculated. The elapsed day transitions of the compensated acoustic impedances and displacements were successfully evaluated. In the process of differentiation, actin fibers comprising the cytoskeleton are supposed to loosen in order to induce cellular fusion. In addition, the progress in cell differentiation accompanied by a change into a three-dimensional structure can partially be assessed by the displacement between a cell and a cultured film. Hence, we believe that cell differentiation can be evaluated using an ultrasonic microscope.

An Improved Heaviside Approach to Partial Fraction Expansion and Its Applications

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2009-01-01

In this note, we present an improved Heaviside approach to compute the partial fraction expansions of proper rational functions. This method uses synthetic divisions to determine the unknown partial fraction coefficients successively, without the need to use differentiation or to solve a system of linear equations. Examples of its applications in…

Application of the Sumudu Transform to Discrete Dynamic Systems

ERIC Educational Resources Information Center

Asiru, Muniru Aderemi

2003-01-01

The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, integro-differential equations and…

Effects of partial reinforcement and time between reinforced trials on terminal response rate in pigeon autoshaping.

PubMed

Gottlieb, Daniel A

2006-03-01

Partial reinforcement often leads to asymptotically higher rates of responding and number of trials with a response than does continuous reinforcement in pigeon autoshaping. However, comparisons typically involve a partial reinforcement schedule that differs from the continuous reinforcement schedule in both time between reinforced trials and probability of reinforcement. Two experiments examined the relative contributions of these two manipulations to asymptotic response rate. Results suggest that the greater responding previously seen with partial reinforcement is primarily due to differential probability of reinforcement and not differential time between reinforced trials. Further, once established, differences in responding are resistant to a change in stimulus and contingency. Secondary response theories of autoshaped responding (theories that posit additional response-augmenting or response-attenuating mechanisms specific to partial or continuous reinforcement) cannot fully accommodate the current body of data. It is suggested that researchers who study pigeon autoshaping train animals on a common task prior to training them under different conditions.

Student Physical Therapists' Competence and Self-Confidence in Basic Clinical Assessment and Musculoskeletal Differential Diagnosis.

PubMed

Alexander, Kathleen M; Olsen, Janette; Seiger, Cindy; Peterson, Teri S

2016-01-01

Student physical therapists are expected to learn and confidently perform technical skills while integrating nontechnical behavioral and cognitive skills in their examinations and interventions. The purpose of this study was to compare the self-confidence of entry-level doctoral student physical therapists during foundational assessment and musculoskeletal differential diagnosis courses and the students' competencies based on skills examinations. Methods using qualitative and quantitative procedures. Student physical therapists (n=27) participated in a basic assessment course followed by a musculoskeletal differential diagnosis course. The students completed confidence surveys prior to skills examinations in both courses. A random sample of students participated in focus groups, led by a researcher outside the physical therapy department. Student confidence did not correlate with competency scores. At the end of the basic clinical assessment course and the beginning of the differential diagnosis course, students' confidence was significantly below baseline. However, by the end of the differential diagnosis course, student confidence had returned to original baseline levels. Over three semesters, the students lost confidence and then regained confidence in their abilities. Additional experience and practice influenced perceived confidence. However, increased competence may have been associated with poor self-appraisal skills instead of increased competency.

Business model for sensor-based fall recognition systems.

PubMed

Fachinger, Uwe; Schöpke, Birte

2014-01-01

AAL systems require, in addition to sophisticated and reliable technology, adequate business models for their launch and sustainable establishment. This paper presents the basic features of alternative business models for a sensor-based fall recognition system which was developed within the context of the "Lower Saxony Research Network Design of Environments for Ageing" (GAL). The models were developed parallel to the R&D process with successive adaptation and concretization. An overview of the basic features (i.e. nine partial models) of the business model is given and the mutual exclusive alternatives for each partial model are presented. The partial models are interconnected and the combinations of compatible alternatives lead to consistent alternative business models. However, in the current state, only initial concepts of alternative business models can be deduced. The next step will be to gather additional information to work out more detailed models.

Basic numerical competences in large-scale assessment data: Structure and long-term relevance.

PubMed

Hirsch, Stefa; Lambert, Katharina; Coppens, Karien; Moeller, Korbinian

2018-03-01

Basic numerical competences are seen as building blocks for later numerical and mathematical achievement. The current study aimed at investigating the structure of early numeracy reflected by different basic numerical competences in kindergarten and its predictive value for mathematical achievement 6 years later using data from large-scale assessment. This allowed analyses based on considerably large sample sizes (N > 1700). A confirmatory factor analysis indicated that a model differentiating five basic numerical competences at the end of kindergarten fitted the data better than a one-factor model of early numeracy representing a comprehensive number sense. In addition, these basic numerical competences were observed to reliably predict performance in a curricular mathematics test in Grade 6 even after controlling for influences of general cognitive ability. Thus, our results indicated a differentiated view on early numeracy considering basic numerical competences in kindergarten reflected in large-scale assessment data. Consideration of different basic numerical competences allows for evaluating their specific predictive value for later mathematical achievement but also mathematical learning difficulties. Copyright © 2017 Elsevier Inc. All rights reserved.

Some Theoretical Aspects of Nonzero Sum Differential Games and Applications to Combat Problems

DTIC Science & Technology

1971-06-01

the Equilibrium Solution . 7 Hamilton-Jacobi-Bellman Partial Differential Equations ............. .............. 9 Influence Function Differential...Linearly .......... ............ 18 Problem Statement .......... ............ 18 Formulation of LJB Equations, Influence Function Equations and the TPBVP...19 Control Lawe . . .. ...... ........... 21 Conditions for Influence Function Continuity along Singular Surfaces

A partial differential equation for pseudocontact shift.

PubMed

Charnock, G T P; Kuprov, Ilya

2014-10-07

It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density. The equation enables straightforward PCS prediction and analysis in systems with delocalized unpaired electrons, particularly for the nuclei located in their immediate vicinity. It is also shown that the probability density of the unpaired electron may be extracted, using a regularization procedure, from PCS data.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 2: Two-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

A two-step semidirect procedure is developed to accelerate the one-step procedure described in NASA TP-2529. For a set of constant coefficient model problems, the acceleration factor increases from 1 to 2 as the one-step procedure convergence rate decreases from + infinity to 0. It is also shown numerically that the two-step procedure can substantially accelerate the convergence of the numerical solution of many partial differential equations (PDE's) with variable coefficients.

Nonlinear grid error effects on numerical solution of partial differential equations

NASA Technical Reports Server (NTRS)

Dey, S. K.

1980-01-01

Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.

Exact Solutions for the Integrable Sixth-Order Drinfeld-Sokolov-Satsuma-Hirota System by the Analytical Methods.

PubMed

Manafian Heris, Jalil; Lakestani, Mehrdad

2014-01-01

We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G'/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.

Parameter estimation problems for distributed systems using a multigrid method

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo; Dutt, Pravir

1990-01-01

The problem of estimating spatially varying coefficients of partial differential equations is considered from observation of the solution and of the right hand side of the equation. It is assumed that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation.

Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Dey, C.; Dey, S. K.

1983-01-01

An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

DISCHARGE AND DEPTH BEHIND A PARTIALLY BREACHED DAM.

USGS Publications Warehouse

Chen, Cheng-lung

1987-01-01

The role that the velocity-distribution correction factor plays in the determination of the flood discharge and corresponding flow depth behind a partially breached dam is investigated. Assumption of a uniformly progressive flow for an established dam-break flood in a rectangular channel of infinite extent leads to the formulation of a theoretical relation between the depth and velocity of flow expressed in differential form. Integrating this ordinary differential equation, one can express the velocity in terms of the depth.

Introducing the Improved Heaviside Approach to Partial Fraction Decomposition to Undergraduate Students: Results and Implications from a Pilot Study

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2012-01-01

Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important…

Strongly nonlinear parabolic variational inequalities.

PubMed

Browder, F E; Brézis, H

1980-02-01

An existence and uniqueness result is established for a general class of variational inequalities for parabolic partial differential equations of the form partial differentialu/ partial differentialt + A(u) + g(u) = f with g nondecreasing but satisfying no growth condition. The proof is based upon a type of compactness result for solutions of variational inequalities that should find a variety of other applications.

Anomalous diffusion associated with nonlinear fractional derivative fokker-planck-like equation: exact time-dependent solutions

PubMed

Bologna; Tsallis; Grigolini

2000-08-01

We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives ( partial differential/ partial differentialt)P(x,t)=D( partial differential(gamma)/ partial differentialx(gamma))[P(x,t)](nu). Exact time-dependent solutions are found for nu=(2-gamma)/(1+gamma)(-infinity

Predicting chromatin architecture from models of polymer physics.

PubMed

Bianco, Simona; Chiariello, Andrea M; Annunziatella, Carlo; Esposito, Andrea; Nicodemi, Mario

2017-03-01

We review the picture of chromatin large-scale 3D organization emerging from the analysis of Hi-C data and polymer modeling. In higher mammals, Hi-C contact maps reveal a complex higher-order organization, extending from the sub-Mb to chromosomal scales, hierarchically folded in a structure of domains-within-domains (metaTADs). The domain folding hierarchy is partially conserved throughout differentiation, and deeply correlated to epigenomic features. Rearrangements in the metaTAD topology relate to gene expression modifications: in particular, in neuronal differentiation models, topologically associated domains (TADs) tend to have coherent expression changes within architecturally conserved metaTAD niches. To identify the nature of architectural domains and their molecular determinants within a principled approach, we discuss models based on polymer physics. We show that basic concepts of interacting polymer physics explain chromatin spatial organization across chromosomal scales and cell types. The 3D structure of genomic loci can be derived with high accuracy and its molecular determinants identified by crossing information with epigenomic databases. In particular, we illustrate the case of the Sox9 locus, linked to human congenital disorders. The model in-silico predictions on the effects of genomic rearrangements are confirmed by available 5C data. That can help establishing new diagnostic tools for diseases linked to chromatin mis-folding, such as congenital disorders and cancer.

From the big five to the general factor of personality: a dynamic approach.

PubMed

Micó, Joan C; Amigó, Salvador; Caselles, Antonio

2014-10-28

An integrating and dynamic model of personality that allows predicting the response of the basic factors of personality, such as the Big Five Factors (B5F) or the general factor of personality (GFP) to acute doses of drug is presented in this paper. Personality has a dynamic nature, i.e., as a consequence of a stimulus, the GFP dynamics as well as each one of the B5F of personality dynamics can be explained by the same model (a system of three coupled differential equations). From this invariance hypothesis, a partial differential equation, whose solution relates the GFP with each one of the B5F, is deduced. From this dynamic approach, a co-evolution of the GFP and each one of the B5F occurs, rather than an unconnected evolution, as a consequence of the same stimulus. The hypotheses and deductions are validated through an experimental design centered on the individual, where caffeine is the considered stimulus. Thus, as much from a theoretical point of view as from an applied one, the models here proposed open a new perspective in the understanding and study of personality like a global system that interacts intimately with the environment, being a clear bet for the high level inter-disciplinary research.

A Unified Introduction to Ordinary Differential Equations

ERIC Educational Resources Information Center

Lutzer, Carl V.

2006-01-01

This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)

Leukotactin-1/CCL15 induces cell migration and differentiation of human eosinophilic leukemia EoL-1 cells through PKCdelta activation.

PubMed

Lee, Ji-Sook; Kim, In Sik

2010-06-01

Leukotactin-1 (Lkn-1)/CCL15 is a CC chemokine that binds to the CCR1 and CCR3. Lkn-1 functions as an essential factor in the migration of monocytes, lymphocytes, and neutrophils. Although eosinophils express both receptors, the role of Lkn-1 in immature eosinophils remains to be elucidated. In this present study, we investigated the contribution of the CCR1-binding chemokines to chemotactic activity and in the differentiation in the human eosinophilic leukemia cell line EoL-1. Lkn-1 induced the stronger migration of EoL-1 cells than other CCR1-binding chemokines such as RANTES/CCL5, MIP-1alpha/CCL3 and HCC-4/CCL16. Lkn-1-induced chemotaxis was inhibited by pertussis toxin, an inhibitor of G(i)/G(o) protein; U73122, an inhibitor of phospholipase C and rottlerin, an inhibitor of protein kinase C delta (PKCdelta). Lkn-1 increased PKCdelta activity, which was partially blocked by the pertussis toxin and U73122. Lkn-1 enhanced the butyric acid-induced differentiation via PKCdelta after binding to the increased CCR1 because Lkn-1 caused EoL-1 cells to change morphologically into mature eosinophil-like cells. Likewise, Lkn-1 increased the expression of both eosinophil peroxidase (EPO) and the major basic protein (MBP). PKCdelta activation due to Lkn-1 is involved in migration, as well as the butyric acid-induced differentiation. This finding contributes to an understanding of CC chemokines in eosinophil biology and to the development of novel therapies for the treatment of eosinophilic disorders. This study suggests the pivotal roles of Lkn-1 in the regulation of the movement and development of eosinophils.

Role of Alternative Polyadenylation during Adipogenic Differentiation: An In Silico Approach

PubMed Central

Spangenberg, Lucía; Correa, Alejandro; Dallagiovanna, Bruno; Naya, Hugo

2013-01-01

Post-transcriptional regulation of stem cell differentiation is far from being completely understood. Changes in protein levels are not fully correlated with corresponding changes in mRNAs; the observed differences might be partially explained by post-transcriptional regulation mechanisms, such as alternative polyadenylation. This would involve changes in protein binding, transcript usage, miRNAs and other non-coding RNAs. In the present work we analyzed the distribution of alternative transcripts during adipogenic differentiation and the potential role of miRNAs in post-transcriptional regulation. Our in silico analysis suggests a modest, consistent, bias in 3′UTR lengths during differentiation enabling a fine-tuned transcript regulation via small non-coding RNAs. Including these effects in the analyses partially accounts for the observed discrepancies in relative abundance of protein and mRNA. PMID:24143171

(N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Lu, Dianchen; Wang, Jun

2017-07-01

In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.

Homogeneous partial differential equations for superpositions of indeterminate functions of several variables

NASA Astrophysics Data System (ADS)

Asai, Kazuto

2009-02-01

We determine essentially all partial differential equations satisfied by superpositions of tree type and of a further special type. These equations represent necessary and sufficient conditions for an analytic function to be locally expressible as an analytic superposition of the type indicated. The representability of a real analytic function by a superposition of this type is independent of whether that superposition involves real-analytic functions or C^{\\rho}-functions, where the constant \\rho is determined by the structure of the superposition. We also prove that the function u defined by u^n=xu^a+yu^b+zu^c+1 is generally non-representable in any real (resp. complex) domain as f\\bigl(g(x,y),h(y,z)\\bigr) with twice differentiable f and differentiable g, h (resp. analytic f, g, h).

Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.

2005-09-01

We present a double ultraspherical spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomogeneous mixed boundary conditions. The differential equations with their boundary and initial conditions are reduced to systems of ordinary differential equations for the time-dependent expansion coefficients. These systems are greatly simplified by using tensor matrix algebra, and are solved by using the step-by-step method. Numerical applications of how to use these methods are described. Numerical results obtained compare favorably with those of the analytical solutions. Accurate double ultraspherical spectral approximations for Poisson's and Helmholtz's equations are also noted. Numerical experiments show that spectral approximation based on Chebyshev polynomials of the first kind is not always better than others based on ultraspherical polynomials.

Isotropic differential phase contrast microscopy for quantitative phase bio-imaging.

PubMed

Chen, Hsi-Hsun; Lin, Yu-Zi; Luo, Yuan

2018-05-16

Quantitative phase imaging (QPI) has been investigated to retrieve optical phase information of an object and applied to biological microscopy and related medical studies. In recent examples, differential phase contrast (DPC) microscopy can recover phase image of thin sample under multi-axis intensity measurements in wide-field scheme. Unlike conventional DPC, based on theoretical approach under partially coherent condition, we propose a new method to achieve isotropic differential phase contrast (iDPC) with high accuracy and stability for phase recovery in simple and high-speed fashion. The iDPC is simply implemented with a partially coherent microscopy and a programmable thin-film transistor (TFT) shield to digitally modulate structured illumination patterns for QPI. In this article, simulation results show consistency of our theoretical approach for iDPC under partial coherence. In addition, we further demonstrate experiments of quantitative phase images of a standard micro-lens array, as well as label-free live human cell samples. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Evaluating Feynman integrals by the hypergeometry

NASA Astrophysics Data System (ADS)

Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Gu, Zhi-Hua; Zhang, Hai-Bin

2018-02-01

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop B0 and massless C0 functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.

Auto-Bäcklund transformations for a matrix partial differential equation

NASA Astrophysics Data System (ADS)

Gordoa, P. R.; Pickering, A.

2018-07-01

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then use these auto-Bäcklund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Bäcklund transformations of the matrix second Painlevé equation to derive a discrete matrix first Painlevé equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painlevé equation. The application of this technique to the auto-Bäcklund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painlevé equation, and which does not seem to have been thus derived previously.

Boundary-fitted curvilinear coordinate systems for solution of partial differential equations on fields containing any number of arbitrary two-dimensional bodies

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Thames, F. C.; Mastin, C. W.

1977-01-01

A method is presented for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected two-dimensional region containing any number of arbitrarily shaped bodies. No restrictions are placed on the shape of the boundaries, which may even be time-dependent, and the approach is not restricted in principle to two dimensions. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system in the physical plane. A number of examples of coordinate systems and application thereof to the solution of partial differential equations are given. The FORTRAN computer program and instructions for use are included.

Solving Partial Differential Equations in a data-driven multiprocessor environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaudiot, J.L.; Lin, C.M.; Hosseiniyar, M.

1988-12-31

Partial differential equations can be found in a host of engineering and scientific problems. The emergence of new parallel architectures has spurred research in the definition of parallel PDE solvers. Concurrently, highly programmable systems such as data-how architectures have been proposed for the exploitation of large scale parallelism. The implementation of some Partial Differential Equation solvers (such as the Jacobi method) on a tagged token data-flow graph is demonstrated here. Asynchronous methods (chaotic relaxation) are studied and new scheduling approaches (the Token No-Labeling scheme) are introduced in order to support the implementation of the asychronous methods in a data-driven environment.more » New high-level data-flow language program constructs are introduced in order to handle chaotic operations. Finally, the performance of the program graphs is demonstrated by a deterministic simulation of a message passing data-flow multiprocessor. An analysis of the overhead in the data-flow graphs is undertaken to demonstrate the limits of parallel operations in dataflow PDE program graphs.« less

Using the phase-space imager to analyze partially coherent imaging systems: bright-field, phase contrast, differential interference contrast, differential phase contrast, and spiral phase contrast

NASA Astrophysics Data System (ADS)

Mehta, Shalin B.; Sheppard, Colin J. R.

2010-05-01

Various methods that use large illumination aperture (i.e. partially coherent illumination) have been developed for making transparent (i.e. phase) specimens visible. These methods were developed to provide qualitative contrast rather than quantitative measurement-coherent illumination has been relied upon for quantitative phase analysis. Partially coherent illumination has some important advantages over coherent illumination and can be used for measurement of the specimen's phase distribution. However, quantitative analysis and image computation in partially coherent systems have not been explored fully due to the lack of a general, physically insightful and computationally efficient model of image formation. We have developed a phase-space model that satisfies these requirements. In this paper, we employ this model (called the phase-space imager) to elucidate five different partially coherent systems mentioned in the title. We compute images of an optical fiber under these systems and verify some of them with experimental images. These results and simulated images of a general phase profile are used to compare the contrast and the resolution of the imaging systems. We show that, for quantitative phase imaging of a thin specimen with matched illumination, differential phase contrast offers linear transfer of specimen information to the image. We also show that the edge enhancement properties of spiral phase contrast are compromised significantly as the coherence of illumination is reduced. The results demonstrate that the phase-space imager model provides a useful framework for analysis, calibration, and design of partially coherent imaging methods.

Saturation behavior: a general relationship described by a simple second-order differential equation.

PubMed

Kepner, Gordon R

2010-04-13

The numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches. For the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study. The second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical constants governing the behavior of these phenomena led to an alternative perspective on saturation behavior kinetics. Their essential commonality was revealed by this analysis, based on the second-order differential equation.

A Second-Generation Interactive Classroom Television System for the Partially Sighted.

ERIC Educational Resources Information Center

Genensky, S. M.; And Others

The interactive classroom television system (ICTS) that is described permits partially sighted students and their teachers to be in continuous, two-way visual communication. It was implemented in Rowland Heights, California, as part of the second phase of a project aimed at evaluating how the ICTS helps in teaching basic skills to partially…

A novel principle for partial agonism of liver X receptor ligands. Competitive recruitment of activators and repressors.

PubMed

Albers, Michael; Blume, Beatrix; Schlueter, Thomas; Wright, Matthew B; Kober, Ingo; Kremoser, Claus; Deuschle, Ulrich; Koegl, Manfred

2006-02-24

Partial, selective activation of nuclear receptors is a central issue in molecular endocrinology but only partly understood. Using LXRs as an example, we show here that purely agonistic ligands can be clearly and quantitatively differentiated from partial agonists by the cofactor interactions they induce. Although a pure agonist induces a conformation that is incompatible with the binding of repressors, partial agonists such as GW3965 induce a state where the interaction not only with coactivators, but also corepressors is clearly enhanced over the unliganded state. The activities of the natural ligand 22(R)-hydroxycholesterol and of a novel quinazolinone ligand, LN6500 can be further differentiated from GW3965 and T0901317 by their weaker induction of coactivator binding. Using biochemical and cell-based assays, we show that the natural ligand of LXR is a comparably weak partial agonist. As predicted, we find that a change in the coactivator to corepressor ratio in the cell will affect NCoR recruiting compounds more dramatically than NCoR-dissociating compounds. Our data show how competitive binding of coactivators and corepressors can explain the tissue-specific behavior of partial agonists and open up new routes to a rational design of partial agonists for LXRs.

Differentiated Staffing.

ERIC Educational Resources Information Center

Nassau County Board of Cooperative Educational Services, Westbury, NY.

This is a compilation of articles examining many aspects of differentiated staffing and creating a basic document for all school districts. The articles are grouped into seven sections: 1) "Why Change?"; 2) "A Consideration of Staffing Problems"; 3) "Critics and Crusaders: An Analysis of Differentiated Staffing" (subsections on concept and…

Activation of TRPV2 negatively regulates the differentiation of mouse brown adipocytes.

PubMed

Sun, Wuping; Uchida, Kunitoshi; Takahashi, Nobuyuki; Iwata, Yuko; Wakabayashi, Shigeo; Goto, Tsuyoshi; Kawada, Teruo; Tominaga, Makoto

2016-09-01

Transient receptor potential vanilloid 2 (TRPV2) acts as a Ca(2+)-permeable non-selective cation channel that has been reported to be sensitive to temperature, mechanical force, and some chemicals. We recently showed that TRPV2 is critical for maintenance of the thermogenic function of brown adipose tissue in mice. However, the involvement of TRPV2 in the differentiation of brown adipocytes remains unexplored. We found that the expression of TRPV2 was dramatically increased during the differentiation of brown adipocytes. Non-selective TRPV2 agonists (2-aminoethoxydiphenyl borate and lysophosphatidylcholine) inhibited the differentiation of brown adipocytes in a dose-dependent manner during the early stage of differentiation of brown adipocytes. The inhibition was rescued by a TRPV2-selective antagonist, SKF96365 (SKF). Mechanical force, which activates TRPV2, also inhibited the differentiation of brown adipocytes in a strength-dependent manner, and the effect was reversed by SKF. In addition, the inhibition of adipocyte differentiation by either TRPV2 ligand or mechanical stimulation was significantly smaller in the cells from TRPV2KO mice. Moreover, calcineurin inhibitors, cyclosporine A and FK506, partially reversed TRPV2 activation-induced inhibition of brown adipocyte differentiation. Thus, we conclude that TRPV2 might be involved in the modulation of brown adipocyte differentiation partially via a calcineurin pathway.

Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries

NASA Astrophysics Data System (ADS)

Startsev, Sergey Ya.

2017-05-01

The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the corresponding system. We demonstrate that a system has the above property if and only if this system admits a full set of formal integrals (i.e., differential operators which map symmetries into integrals of the system). As a consequence, such systems possess both direct and inverse Noether operators (in the terminology of a work by B. Fuchssteiner and A.S. Fokas who have used these terms for operators that map cosymmetries into symmetries and perform transformations in the opposite direction). Systems admitting Noether operators are not exhausted by Euler-Lagrange systems and the systems with formal integrals. In particular, a hyperbolic system admits an inverse Noether operator if a differential substitution maps this system into a system possessing an inverse Noether operator.

Professional Competence and Basic Ability-Oriented Game Theory Analysis of China's Higher Vocational College English Teaching

ERIC Educational Resources Information Center

Zhang, Jian

2012-01-01

To strengthen the professional competence and basic ability is the objective requirements of the Chinese higher vocational college English teaching, while the positioning of the teaching objectives is partial to a "prisoner's dilemma" in game situations that any party will result in. To get rid of the "dilemma", we have to…

World Perspective Case Descriptions on Educational Programs for Adults: Hong Kong.

ERIC Educational Resources Information Center

Mak, Grace

Adult basic education (ABE) in Hong Kong includes mostly basic Chinese, but also some arithmetic and English. The emphasis is on teaching learners life skills. Both government-run programs and partially government-subsidized programs run by voluntary agencies such as Caritas and the YMCA are common. A case study was made of the Caritas ABE Centre…

Ultrasound speckle reduction based on fractional order differentiation.

PubMed

Shao, Dangguo; Zhou, Ting; Liu, Fan; Yi, Sanli; Xiang, Yan; Ma, Lei; Xiong, Xin; He, Jianfeng

2017-07-01

Ultrasound images show a granular pattern of noise known as speckle that diminishes their quality and results in difficulties in diagnosis. To preserve edges and features, this paper proposes a fractional differentiation-based image operator to reduce speckle in ultrasound. An image de-noising model based on fractional partial differential equations with balance relation between k (gradient modulus threshold that controls the conduction) and v (the order of fractional differentiation) was constructed by the effective combination of fractional calculus theory and a partial differential equation, and the numerical algorithm of it was achieved using a fractional differential mask operator. The proposed algorithm has better speckle reduction and structure preservation than the three existing methods [P-M model, the speckle reducing anisotropic diffusion (SRAD) technique, and the detail preserving anisotropic diffusion (DPAD) technique]. And it is significantly faster than bilateral filtering (BF) in producing virtually the same experimental results. Ultrasound phantom testing and in vivo imaging show that the proposed method can improve the quality of an ultrasound image in terms of tissue SNR, CNR, and FOM values.

Back to the Basics: Birmingham, Alabama, Measurement and Scale

ERIC Educational Resources Information Center

Handley, Lawrence R.; Lockwood, Catherine M.; Handley, Nathan

2005-01-01

"Back to the Basics: Birmingham, Alabama" is the fourth in a series of workshops that focus on teaching foundational map reading and spatial differentiation skills. It is the second published exercise from the Back to the Basics series developed by the Wetland Education through Maps and Aerial Photography (WETMAAP) Program (see…

Back to the Basics: Lake Tahoe, California/Nevada--Spatial Measurement

ERIC Educational Resources Information Center

Handley, Lawrence R.; Lockwood, Catherine M.; Handley, Nathan

2006-01-01

"Back to the Basics: South Lake Tahoe, California/Nevada" continues the series of exercises on teaching foundational map reading and spatial differentiation skills. It is the third published exercise from the Back to the Basics series developed by the Wetland Education through Maps and Aerial Photography (WETMAAP) Program. The current…

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Numerical method based on the lattice Boltzmann model for the Fisher equation.

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.

Generation of three-dimensional body-fitted grids by solving hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, an extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Generation of three-dimensional body-fitted grids by solving hyperbolic and parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Steger, Joseph L.

1989-01-01

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Computer transformation of partial differential equations into any coordinate system

NASA Technical Reports Server (NTRS)

Sullivan, R. D.

1977-01-01

The use of tensors to provide a compact way of writing partial differential equations in a form valid in all coordinate systems is discussed. In order to find solutions to the equations with their boundary conditions they must be expressed in terms of the coordinate system under consideration. The process of arriving at these expressions from the tensor formulation was automated by a software system, TENSR. An allied system that analyzes the resulting expressions term by term and drops those that are negligible is also described.

Partial differential equation models in macroeconomics.

PubMed

Achdou, Yves; Buera, Francisco J; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin

2014-11-13

The purpose of this article is to get mathematicians interested in studying a number of partial differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come from models designed to study some of the most important questions in economics. At the same time, they are highly interesting for mathematicians because their structure is often quite difficult. We present a number of examples of such PDEs, discuss what is known about their properties, and list some open questions for future research. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Lie algebras and linear differential equations.

NASA Technical Reports Server (NTRS)

Brockett, R. W.; Rahimi, A.

1972-01-01

Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

On the continuous differentiability of inter-spike intervals of synaptically connected cortical spiking neurons in a neuronal network.

PubMed

Kumar, Gautam; Kothare, Mayuresh V

2013-12-01

We derive conditions for continuous differentiability of inter-spike intervals (ISIs) of spiking neurons with respect to parameters (decision variables) of an external stimulating input current that drives a recurrent network of synaptically connected neurons. The dynamical behavior of individual neurons is represented by a class of discontinuous single-neuron models. We report here that ISIs of neurons in the network are continuously differentiable with respect to decision variables if (1) a continuously differentiable trajectory of the membrane potential exists between consecutive action potentials with respect to time and decision variables and (2) the partial derivative of the membrane potential of spiking neurons with respect to time is not equal to the partial derivative of their firing threshold with respect to time at the time of action potentials. Our theoretical results are supported by showing fulfillment of these conditions for a class of known bidimensional spiking neuron models.

Modelica buildings library

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wetter, Michael; Zuo, Wangda; Nouidui, Thierry S.

This paper describes the Buildings library, a free open-source library that is implemented in Modelica, an equation-based object-oriented modeling language. The library supports rapid prototyping, as well as design and operation of building energy and control systems. First, we describe the scope of the library, which covers HVAC systems, multi-zone heat transfer and multi-zone airflow and contaminant transport. Next, we describe differentiability requirements and address how we implemented them. We describe the class hierarchy that allows implementing component models by extending partial implementations of base models of heat and mass exchangers, and by instantiating basic models for conservation equations andmore » flow resistances. We also describe associated tools for pre- and post-processing, regression tests, co-simulation and real-time data exchange with building automation systems. Furthermore, the paper closes with an example of a chilled water plant, with and without water-side economizer, in which we analyzed the system-level efficiency for different control setpoints.« less

Elasticity solutions for a class of composite laminate problems with stress singularities

NASA Technical Reports Server (NTRS)

Wang, S. S.

1983-01-01

A study on the fundamental mechanics of fiber-reinforced composite laminates with stress singularities is presented. Based on the theory of anisotropic elasticity and Lekhnitskii's complex-variable stress potentials, a system of coupled governing partial differential equations are established. An eigenfunction expansion method is introduced to determine the orders of stress singularities in composite laminates with various geometric configurations and material systems. Complete elasticity solutions are obtained for this class of singular composite laminate mechanics problems. Homogeneous solutions in eigenfunction series and particular solutions in polynomials are presented for several cases of interest. Three examples are given to illustrate the method of approach and the basic nature of the singular laminate elasticity solutions. The first problem is the well-known laminate free-edge stress problem, which has a rather weak stress singularity. The second problem is the important composite delamination problem, which has a strong crack-tip stress singularity. The third problem is the commonly encountered bonded composite joints, which has a complex solution structure with moderate orders of stress singularities.

Multigrid methods with space–time concurrency

DOE PAGES

Falgout, R. D.; Friedhoff, S.; Kolev, Tz. V.; ...

2017-10-06

Here, we consider the comparison of multigrid methods for parabolic partial differential equations that allow space–time concurrency. With current trends in computer architectures leading towards systems with more, but not faster, processors, space–time concurrency is crucial for speeding up time-integration simulations. In contrast, traditional time-integration techniques impose serious limitations on parallel performance due to the sequential nature of the time-stepping approach, allowing spatial concurrency only. This paper considers the three basic options of multigrid algorithms on space–time grids that allow parallelism in space and time: coarsening in space and time, semicoarsening in the spatial dimensions, and semicoarsening in the temporalmore » dimension. We develop parallel software and performance models to study the three methods at scales of up to 16K cores and introduce an extension of one of them for handling multistep time integration. We then discuss advantages and disadvantages of the different approaches and their benefit compared to traditional space-parallel algorithms with sequential time stepping on modern architectures.« less

A multivariate variational objective analysis-assimilation method. Part 1: Development of the basic model

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Ochs, Harry T., III

1988-01-01

The variational method of undetermined multipliers is used to derive a multivariate model for objective analysis. The model is intended for the assimilation of 3-D fields of rawinsonde height, temperature and wind, and mean level temperature observed by satellite into a dynamically consistent data set. Relative measurement errors are taken into account. The dynamic equations are the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation. The model Euler-Lagrange equations are eleven linear and/or nonlinear partial differential and/or algebraic equations. A cyclical solution sequence is described. Other model features include a nonlinear terrain-following vertical coordinate that eliminates truncation error in the pressure gradient terms of the horizontal momentum equations and easily accommodates satellite observed mean layer temperatures in the middle and upper troposphere. A projection of the pressure gradient onto equivalent pressure surfaces removes most of the adverse impacts of the lower coordinate surface on the variational adjustment.

The Amniote Oculomotor Complex.

PubMed

Company, Verónica; Moreno-Bravo, Juan Antonio; Perez-Balaguer, Ariadna; Puelles, Eduardo

2018-04-16

The oculomotor (OM) complex is a combination of somatic and parasympatethic neurons. The correct development and wiring of this cranial pair is essential to perform basic functions: eyeball and eyelid movements, pupillary constriction, and lens accommodation. The improper formation or function of this nucleus leads pathologies such as strabismus. We describe the OM organization and function in different vertebrate brains, including chick, mouse, and human. The morphological localization is detailed, as well as the spatial relation with the trochlear nucleus in order to adjust some misleading anatomical topographic descriptions. We detailed the signaling processes needed for the specification of the OM neurons. The transcriptional programs driven the specification and differentiation of these neurons are partially determined. We summarized recent genetic studies that have led to the identification of guidance mechanisms involved in the migration, axon pathfinding, and targeting of the OM neurons. Finally, we overviewed the pathology associated to genetic malformations in the OM development and related clinical alterations. Anat Rec, 2018. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

A Mathematical Formulation of the SCOLE Control Problem. Part 2: Optimal Compensator Design

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1988-01-01

The study initiated in Part 1 of this report is concluded and optimal feedback control (compensator) design for stability augmentation is considered, following the mathematical formulation developed in Part 1. Co-located (rate) sensors and (force and moment) actuators are assumed, and allowing for both sensor and actuator noise, stabilization is formulated as a stochastic regulator problem. Specializing the general theory developed by the author, a complete, closed form solution (believed to be new with this report) is obtained, taking advantage of the fact that the inherent structural damping is light. In particular, it is possible to solve in closed form the associated infinite-dimensional steady-state Riccati equations. The SCOLE model involves associated partial differential equations in a single space variable, but the compensator design theory developed is far more general since it is given in the abstract wave equation formulation. The results thus hold for any multibody system so long as the basic model is linear.

Multigrid methods with space–time concurrency

DOE Office of Scientific and Technical Information (OSTI.GOV)

Falgout, R. D.; Friedhoff, S.; Kolev, Tz. V.

Here, we consider the comparison of multigrid methods for parabolic partial differential equations that allow space–time concurrency. With current trends in computer architectures leading towards systems with more, but not faster, processors, space–time concurrency is crucial for speeding up time-integration simulations. In contrast, traditional time-integration techniques impose serious limitations on parallel performance due to the sequential nature of the time-stepping approach, allowing spatial concurrency only. This paper considers the three basic options of multigrid algorithms on space–time grids that allow parallelism in space and time: coarsening in space and time, semicoarsening in the spatial dimensions, and semicoarsening in the temporalmore » dimension. We develop parallel software and performance models to study the three methods at scales of up to 16K cores and introduce an extension of one of them for handling multistep time integration. We then discuss advantages and disadvantages of the different approaches and their benefit compared to traditional space-parallel algorithms with sequential time stepping on modern architectures.« less

On the global well-posedness theory for a class of PDE models for criminal activity

NASA Astrophysics Data System (ADS)

Rodríguez, N.

2013-10-01

We study a class of ‘reaction-advection-diffusion’ system of partial differential equations, which can be taken as basic models for criminal activity. This class of models are based on routine activity theory and other theories, such as the ‘repeat and near-repeat victimization effect’ and were first introduced in Short et al. (2008) [11]. In these models the criminal density is advected by a velocity field that depends on a scalar field, which measures the appeal to commit a crime. We refer to this scalar field as the attractiveness field. We prove local well-posedness of solutions for the general class of models. Furthermore, we prove global well-posedness of solutions to a fully-parabolic system with a velocity field that depends logarithmically on the attractiveness field. Our final result is the global well-posedness of solutions the fully-parabolic system with velocity field that depends linearly on the attractiveness field for small initial mass.

Modelica buildings library

DOE PAGES

Wetter, Michael; Zuo, Wangda; Nouidui, Thierry S.; ...

2013-03-13

This paper describes the Buildings library, a free open-source library that is implemented in Modelica, an equation-based object-oriented modeling language. The library supports rapid prototyping, as well as design and operation of building energy and control systems. First, we describe the scope of the library, which covers HVAC systems, multi-zone heat transfer and multi-zone airflow and contaminant transport. Next, we describe differentiability requirements and address how we implemented them. We describe the class hierarchy that allows implementing component models by extending partial implementations of base models of heat and mass exchangers, and by instantiating basic models for conservation equations andmore » flow resistances. We also describe associated tools for pre- and post-processing, regression tests, co-simulation and real-time data exchange with building automation systems. Furthermore, the paper closes with an example of a chilled water plant, with and without water-side economizer, in which we analyzed the system-level efficiency for different control setpoints.« less

A unified framework for mesh refinement in random and physical space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Jing; Stinis, Panos

In recent work we have shown how an accurate reduced model can be utilized to perform mesh renement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity from the large to the small scales of the solution. Since this is not always available, we present in the current work a framework which shares the merits and basic idea of the previous approach but does not require an explicit knowledge of a reduced model. Moreover, the current framework can be applied for renement in both randommore » and physical space. In this manuscript we focus on the application to random space mesh renement. We study examples of increasing difficulty (from ordinary to partial differential equations) which demonstrate the effciency and versatility of our approach. We also provide some results from the application of the new framework to physical space mesh refinement.« less

[Post-polio syndrome. A case report].

PubMed

Bartman, Wojciech; Biernawska, Jolanta; ŁAbuz-Roszak, Beata; Kumor, Klaudiusz; Pierzchała, Krystyna

2004-01-01

Certain acute anterior poliomyelitis survivors express complaints of abnormal fatigue, weakness and muscular atrophy many years after acute onset. These are basic clinical symptoms of so-called post-polio syndrome (PPS). PPS is characterized by a relatively slow, but progressive pathological muscular process, in some cases leading to functional impairment of daily living and professional activity. Breathing, speaking and swallowing impairment are common but not severe medical problems of post-polio patients. Diagnosis is usually based on a typical medical history, electromyographic investigation and exclusion of other diseases presenting similar features. We report a case of PPS in a 49-year-old woman diagnosed in the Neurological Department in Zabrze. Thirty six years after acute anterior poliomyelitis with partial recovery, new symptoms of fatigue, muscular atrophy, exertional dyspnea, walking impairment and joint pain developed. Electromyography revealed features of coexisting spinal denervation and reinnervation in tested muscles. The differential diagnosis excluded other neuromuscular diseases. The patient fulfilled clinical and electromyographic criteria of PPS.

Basic and applied problems in developmental biology and immunobiology of cestode infections: Hymenolepis, Taenia and Echinococcus.

PubMed

Ito, A

2015-02-01

Differentiation and development of parasites, including longevity in host animals, are thought to be governed by host-parasite interactions. In this review, several topics on the developmental biology of cestode infections are discussed from immunobiological perspective with a focus on Hymenolepis, Taenia and Echinococcus infections. The basic premise of this review is that 'differentiation and development of cestodes' are somehow affected by host immune responses with an evolutionary history. © 2014 John Wiley & Sons Ltd.

Predicting the payload capability of cable logging systems including the effect of partial suspension

Treesearch

Gary D. Falk

1981-01-01

A systematic procedure for predicting the payload capability of running, live, and standing skylines is presented. Three hand-held calculator programs are used to predict payload capability that includes the effect of partial suspension. The programs allow for predictions for downhill yarding and for yarding away from the yarder. The equations and basic principles...

Leadership for Differentiating Schools & Classrooms.

ERIC Educational Resources Information Center

Tomlinson, Carol Ann; Allan, Susan Demirsky

Differentiation is simply a teacher attending to the learning needs of a particular student or small group of students, rather than teaching a class as though all individuals in it were basically alike. This book explores in 10 chapters how school leaders can develop responsive, personalized, and differentiated classrooms: (1) "Understanding…

Product and Quotient Rules from Logarithmic Differentiation

ERIC Educational Resources Information Center

Chen, Zhibo

2012-01-01

A new application of logarithmic differentiation is presented, which provides an alternative elegant proof of two basic rules of differentiation: the product rule and the quotient rule. The proof can intrigue students, help promote their critical thinking and rigorous reasoning and deepen their understanding of previously encountered concepts. The…

Melt segregation from partially molten source regions - The importance of melt density and source region size

NASA Technical Reports Server (NTRS)

Stolper, E.; Hager, B. H.; Walker, D.; Hays, J. F.

1981-01-01

An investigation is conducted regarding the changes expected in the density contrast between basic melts and peridotites with increasing pressure using the limited data available on the compressibilities of silicate melts and data on the densities of mantle minerals. It is concluded that since compressibilities of silicate melts are about an order of magnitude greater than those of mantle minerals, the density contrast between basic melts and mantle minerals must diminish significantly with increasing pressure. An earlier analysis regarding the migration of liquid in partially molten source regions conducted by Walker et al. (1978) is extended, giving particular attention to the influence of the diminished density contrast between melt and residual crystals with increasing source region depth and to the influence of source region size. This analysis leads to several generalizations concerning the factors influencing the depths at which magmas will segregate from their source regions and the degrees of partial melting that can be achieved in these source regions before melt segregation occurs.

Effect of partial heating at mid of vertical plate adjacent to porous medium

NASA Astrophysics Data System (ADS)

Mulla, Mohammed Fahimuddin; Pallan, Khalid. M.; Al-Rashed, A. A. A. A.

2018-05-01

Heat and mass transfer in porous medium due to heating of vertical plate at mid-section is analyzed for various physical parameters. The heat and mass transfer in porous medium is modeled with the help of momentum, energy and concentration equations in terms of non-dimensional partial differential equations. The partial differential equations are converted into simpler form of algebraic equations with the help of finite element method. A computer code is developed to assemble the matrix form of algebraic equations into global matrices and then to solve them in an iterative manner to obtain the temperature, concentration and streamline distribution inside the porous medium. It is found that the heat transfer behavior of porous medium heated at middle section is considerably different from other cases.

[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (1)].

PubMed

Murase, Kenya

2014-01-01

Utilization of differential equations and methods for solving them in medical physics are presented. First, the basic concept and the kinds of differential equations were overviewed. Second, separable differential equations and well-known first-order and second-order differential equations were introduced, and the methods for solving them were described together with several examples. In the next issue, the symbolic and series expansion methods for solving differential equations will be mainly introduced.

A result on differential inequalities and its application to higher order trajectory derivatives

NASA Technical Reports Server (NTRS)

Gunderson, R. W.

1973-01-01

A result on differential inequalities is obtained by considering the adjoint differential equation of the variational equation of the right side of the inequality. The main theorem is proved using basic results on differentiability of solutions with respect to initial conditions. The result is then applied to the problem of determining solution behavior using comparison techniques.

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras

PubMed Central

Gazizov, R. K.

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures. PMID:28265184

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras.

PubMed

Gainetdinova, A A; Gazizov, R K

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.

Paleomagnetic Evidence for Partial Differentiation of the Silicate-Bearing IIE Iron Meteorite Parent Body

NASA Astrophysics Data System (ADS)

Maurel, C.; Bryson, J. F. J.; Weiss, B. P.; Scholl, A.

2016-12-01

The identification of dozens of petrologically diverse chondritic and achondritic meteoritic groups indicates that a diversity of planetesimals formed in the early solar system. It is commonly thought that planetesimals formed as either unmelted or else fully differentiated bodies, implying that chondrites and achondrites cannot have originated on a single body. However, it has been suggested that partially melted bodies with chondritic crusts and achondritic interiors may also have formed. This alternative proposal is supported by the recent identification of post-accretional remanent magnetization in CV, H chondrites, and also possibly in CM chondrites, which has been interpreted as possible evidence for a core dynamo on their parent bodies. Other piece of evidence suggesting the existence of partially differentiated bodies is the existence of the silicate-bearing IIE iron meteorites. The IIEs are composed of a Fe-Ni alloy matrix containing a mixture of chondritic, primitive achondritic, and chondritic silicate inclusions that likely formed on a single parent body. Therefore, IIEs may sample all three putative layers of a layered, partially differentiated body. On the other hand, the siderophile element compositions of the matrix metal demonstrate that it is not the product of fractional crystallization of a molten core. This suggests that the matrix metal is derived from isolated reservoirs of metal in the mantle and/or crust. It is unknown whether a large-scale metallic core, not represented by known meteorite samples, also formed on the same parent planetesimal. We can search for evidence of a molten, advecting core by assessing whether IIE irons contain remanent magnetization produced by a core dynamo. With this goal, we studied the paleomagnetism of a cloudy zone (CZ) interface in the Fe-Ni matrix of the IIE iron Colomera using X-ray photoelectron emission microscopy (XPEEM). Our initial results suggest that a steady, intense magnetic field was present during the gradual formation of the CZ. This may indicate the existence of an advecting core on the IIE parent body, which would support the hypothesis of a partially differentiated structure. We are continuing to test this conclusion with further XPEEM measurements on Colomera and other IIE irons.

Paleomagnetic Evidence for Partial Differentiation of the Silicate-Bearing IIE Iron Meteorite Parent Body

NASA Astrophysics Data System (ADS)

Maurel, C.; Bryson, J. F. J.; Weiss, B. P.; Scholl, A.

2017-12-01

The identification of dozens of petrologically diverse chondritic and achondritic meteoritic groups indicates that a diversity of planetesimals formed in the early solar system. It is commonly thought that planetesimals formed as either unmelted or else fully differentiated bodies, implying that chondrites and achondrites cannot have originated on a single body. However, it has been suggested that partially melted bodies with chondritic crusts and achondritic interiors may also have formed. This alternative proposal is supported by the recent identification of post-accretional remanent magnetization in CV, H chondrites, and also possibly in CM chondrites, which has been interpreted as possible evidence for a core dynamo on their parent bodies. Other piece of evidence suggesting the existence of partially differentiated bodies is the existence of the silicate-bearing IIE iron meteorites. The IIEs are composed of a Fe-Ni alloy matrix containing a mixture of chondritic, primitive achondritic, and chondritic silicate inclusions that likely formed on a single parent body. Therefore, IIEs may sample all three putative layers of a layered, partially differentiated body. On the other hand, the siderophile element compositions of the matrix metal demonstrate that it is not the product of fractional crystallization of a molten core. This suggests that the matrix metal is derived from isolated reservoirs of metal in the mantle and/or crust. It is unknown whether a large-scale metallic core, not represented by known meteorite samples, also formed on the same parent planetesimal. We can search for evidence of a molten, advecting core by assessing whether IIE irons contain remanent magnetization produced by a core dynamo. With this goal, we studied the paleomagnetism of a cloudy zone (CZ) interface in the Fe-Ni matrix of the IIE iron Colomera using X-ray photoelectron emission microscopy (XPEEM). Our initial results suggest that a steady, intense magnetic field was present during the gradual formation of the CZ. This may indicate the existence of an advecting core on the IIE parent body, which would support the hypothesis of a partially differentiated structure. We are continuing to test this conclusion with further XPEEM measurements on Colomera and other IIE irons.

Cytochemical evaluation of the Guard procedure a regressive staining method for demonstrating chromosomal basic proteins. I. Effects of fixation, blocking reactions, selective extractions, and polyacid "differentiation".

PubMed

Cowden, R R; Rasch, E M; Curtis, S K

1976-08-12

Appropriately fixed preparations stained by a modification of the Guard (1959) reaction for "sex chromatin" display selective staining of interphase chromatin and mitotic or meiotic chromosomes. This is a regressive staining method which seems to depend on the selective displacement of an acidic dye from less basic structures, and retention of the dye at more basic sites. The results obtained with the reaction can be controlled by the length of time that the preparations are "differentiated" in solutions containing phosphomolybdic and phosphotungstic acids (polyacids). After three- or four-hour exposures to polyacid solutions, all chromatin is stained. However, with longer differentiation, "condensed" chromatin can be stained preferentially. Of a number of fixatives investigated, only 10% formalin, ethanol-acetic acid (3:1), and Bouin's solution proved useful. Others resulted in diminished specificity or a total loss of selectivity. The most intense staining was obtained after formalin fixation. Less intense dyebinding was observed after fixation in 3:1 - probably due to extraction of some histone fractions-and the least amount of dye was bound in Bouin's-fixed chromatin - probably due to blockage of arginine residues by picric acid. The reaction was not affected by enzymatic removal of nucleic acids or the extraction of lipids. It was diminished by treatment with trypsin or weak acetylation, and it was completely prevented by strong acetylation, deamination, or extraction of basic proteins with HCl. The results presented suggest that the modified Guard (1959) procedure selectively demonstrates basic nucleoproteins. Further, by the use of regressive differentiation in polyacid solutions, the retention of dye in more condensed chromatin can be favored.

[Inequities in health: socio-demographic and spatial analysis of breast cancer in women from Córdoba, Argentina].

PubMed

Tumas, Natalia; Pou, Sonia Alejandra; Díaz, María Del Pilar

To identify sociodemographic determinants associated with the spatial distribution of the breast cancer incidence in the province of Córdoba, Argentina, in order to reveal underlying social inequities. An ecological study was developed in Córdoba (26 counties as geographical units of analysis). The spatial autocorrelation of the crude and standardised incidence rates of breast cancer, and the sociodemographic indicators of urbanization, fertility and population ageing were estimated using Moran's index. These variables were entered into a Geographic Information System for mapping. Poisson multilevel regression models were adjusted, establishing the breast cancer incidence rates as the response variable, and by selecting sociodemographic indicators as covariables and the percentage of households with unmet basic needs as adjustment variables. In Córdoba, Argentina, a non-random pattern in the spatial distribution of breast cancer incidence rates and in certain sociodemographic indicators was found. The mean increase in annual urban population was inversely associated with breast cancer, whereas the proportion of households with unmet basic needs was directly associated with this cancer. Our results define social inequity scenarios that partially explain the geographical differentials in the breast cancer burden in Córdoba, Argentina. Women residing in socioeconomically disadvantaged households and in less urbanized areas merit special attention in future studies and in breast cancer public health activities. Copyright © 2017 SESPAS. Publicado por Elsevier España, S.L.U. All rights reserved.

Integration of Basic Knowledge Models for the Simulation of Cereal Foods Processing and Properties.

PubMed

Kristiawan, Magdalena; Kansou, Kamal; Valle, Guy Della

Cereal processing (breadmaking, extrusion, pasting, etc.) covers a range of mechanisms that, despite their diversity, can be often reduced to a succession of two core phenomena: (1) the transition from a divided solid medium (the flour) to a continuous one through hydration, mechanical, biochemical, and thermal actions and (2) the expansion of a continuous matrix toward a porous structure as a result of the growth of bubble nuclei either by yeast fermentation or by water vaporization after a sudden pressure drop. Modeling them is critical for the domain, but can be quite challenging to address with mechanistic approaches relying on partial differential equations. In this chapter we present alternative approaches through basic knowledge models (BKM) that integrate scientific and expert knowledge, and possess operational interest for domain specialists. Using these BKMs, simulations of two cereal foods processes, extrusion and breadmaking, are provided by focusing on the two core phenomena. To support the use by non-specialists, these BKMs are implemented as computer tools, a Knowledge-Based System developed for the modeling of the flour mixing operation or Ludovic ® , a simulation software for twin screw extrusion. They can be applied to a wide domain of compositions, provided that the data on product rheological properties are available. Finally, it is stated that the use of such systems can help food engineers to design cereal food products and predict their texture properties.

Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendices; Index.

Student Solution Manual for Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendix.

Computational Algorithms or Identification of Distributed Parameter Systems

DTIC Science & Technology

1993-04-24

delay-differential equations, Volterra integral equations, and partial differential equations with memory terms . In particular we investigated a...tested for estimating parameters in a Volterra integral equation arising from a viscoelastic model of a flexible structure with Boltzmann damping. In...particular, one of the parameters identified was the order of the derivative in Volterra integro-differential equations containing fractional

Planning and problem-solving training for patients with schizophrenia: a randomized controlled trial

PubMed Central

2011-01-01

Background The purpose of this study was to assess whether planning and problem-solving training is more effective in improving functional capacity in patients with schizophrenia than a training program addressing basic cognitive functions. Methods Eighty-nine patients with schizophrenia were randomly assigned either to a computer assisted training of planning and problem-solving or a training of basic cognition. Outcome variables included planning and problem-solving ability as well as functional capacity, which represents a proxy measure for functional outcome. Results Planning and problem-solving training improved one measure of planning and problem-solving more strongly than basic cognition training, while two other measures of planning did not show a differential effect. Participants in both groups improved over time in functional capacity. There was no differential effect of the interventions on functional capacity. Conclusion A differential effect of targeting specific cognitive functions on functional capacity could not be established. Small differences on cognitive outcome variables indicate a potential for differential effects. This will have to be addressed in further research including longer treatment programs and other settings. Trial registration ClinicalTrials.gov NCT00507988 PMID:21527028

A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport.

PubMed

Zhang, Kejiang; Achari, Gopal; Li, Hua

2009-11-03

Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability-possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.

A Model for Siderophile Element Distribution in Planetary Differentiation

NASA Technical Reports Server (NTRS)

Humayun, M.; Rushmer, T.; Rankenburg, K.; Brandon, A. D.

2005-01-01

Planetary differentiation begins with partial melting of small planetesimals. At low degrees of partial melting, a sulfur-rich liquid segregates by physical mechanisms including deformation-assisted porous flow. Experimental studies of the physical mechanisms by which Fe-S melts segregate from the silicate matrix of a molten H chondrite are part of a companion paper. Geochemical studies of these experimental products revealed that metallic liquids were in equilibrium with residual metal in the H chondrite matrix. This contribution explores the geochemical signatures produced by early stages of core formation. Particularly, low-degree partial melt segregation of Fe-S liquids leaves residual metal in the silicate matrix. Some achondrites appear to be residues of partial melting, e.g., ureilites, which are known to contain metal. The metal in these achondrites may show a distinct elemental signature. To quantify the effect of sulfur on siderophile element contents of residual metal we have developed a model based on recent parametrizations of equilibrium solid metal-liquid metal partitioning experiments.

Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving fronts

USGS Publications Warehouse

Huang, W.; Zheng, Lingyun; Zhan, X.

2002-01-01

Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement. Copyright ?? 2002 John Wiley and Sons, Ltd.

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

NASA Technical Reports Server (NTRS)

Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Discussion summary: Fictitious domain methods

NASA Technical Reports Server (NTRS)

Glowinski, Rowland; Rodrigue, Garry

1991-01-01

Fictitious Domain methods are constructed in the following manner: Suppose a partial differential equation is to be solved on an open bounded set, Omega, in 2-D or 3-D. Let R be a rectangle domain containing the closure of Omega. The partial differential equation is first solved on R. Using the solution on R, the solution of the equation on Omega is then recovered by some procedure. The advantage of the fictitious domain method is that in many cases the solution of a partial differential equation on a rectangular region is easier to compute than on a nonrectangular region. Fictitious domain methods for solving elliptic PDEs on general regions are also very efficient when used on a parallel computer. The reason is that one can use the many domain decomposition methods that are available for solving the PDE on the fictitious rectangular region. The discussion on fictitious domain methods began with a talk by R. Glowinski in which he gave some examples of a variational approach to ficititious domain methods for solving the Helmholtz and Navier-Stokes equations.

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods. Appendix 2

NASA Technical Reports Server (NTRS)

Prudhomme, C.; Rovas, D. V.; Veroy, K.; Machiels, L.; Maday, Y.; Patera, A. T.; Turinici, G.; Zang, Thomas A., Jr. (Technical Monitor)

2002-01-01

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

Statistical theory for the Kardar-Parisi-Zhang equation in (1+1) dimensions.

PubMed

Masoudi, A A; Shahbazi, F; Davoudi, J; Tabar, M Reza Rahimi

2002-02-01

The Kardar-Parisi-Zhang (KPZ) equation in (1+1) dimensions dynamically develops sharply connected valley structures within which the height derivative is not continuous. We develop a statistical theory for the KPZ equation in (1+1) dimensions driven with a random forcing that is white in time and Gaussian-correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient P(h-h*, partial differential(x)h,t) when the forcing correlation length is much smaller than the system size and much larger than the typical sharp valley width. In the time scales before the creation of the sharp valleys, we find the exact generating function of h-h* and partial differential(x)h. The time scale of the sharp valley formation is expressed in terms of the force characteristics. In the stationary state, when the sharp valleys are fully developed, finite-size corrections to the scaling laws of the structure functions left angle bracket(h-h*)(n)(partial differential(x)h)(m)right angle bracket are also obtained.

A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

NASA Astrophysics Data System (ADS)

Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

2015-12-01

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

Algorithm refinement for stochastic partial differential equations: II. Correlated systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alexander, Francis J.; Garcia, Alejandro L.; Tartakovsky, Daniel M.

2005-08-10

We analyze a hybrid particle/continuum algorithm for a hydrodynamic system with long ranged correlations. Specifically, we consider the so-called train model for viscous transport in gases, which is based on a generalization of the random walk process for the diffusion of momentum. This discrete model is coupled with its continuous counterpart, given by a pair of stochastic partial differential equations. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass and momentum conservation. This methodology is an extension of our stochastic Algorithm Refinement (AR) hybrid for simple diffusion [F. Alexander, A. Garcia,more » D. Tartakovsky, Algorithm refinement for stochastic partial differential equations: I. Linear diffusion, J. Comput. Phys. 182 (2002) 47-66]. Results from a variety of numerical experiments are presented for steady-state scenarios. In all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the long-range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude.« less

Correlation-coefficient-based fast template matching through partial elimination.

PubMed

Mahmood, Arif; Khan, Sohaib

2012-04-01

Partial computation elimination techniques are often used for fast template matching. At a particular search location, computations are prematurely terminated as soon as it is found that this location cannot compete with an already known best match location. Due to the nonmonotonic growth pattern of the correlation-based similarity measures, partial computation elimination techniques have been traditionally considered inapplicable to speed up these measures. In this paper, we show that partial elimination techniques may be applied to a correlation coefficient by using a monotonic formulation, and we propose basic-mode and extended-mode partial correlation elimination algorithms for fast template matching. The basic-mode algorithm is more efficient on small template sizes, whereas the extended mode is faster on medium and larger templates. We also propose a strategy to decide which algorithm to use for a given data set. To achieve a high speedup, elimination algorithms require an initial guess of the peak correlation value. We propose two initialization schemes including a coarse-to-fine scheme for larger templates and a two-stage technique for small- and medium-sized templates. Our proposed algorithms are exact, i.e., having exhaustive equivalent accuracy, and are compared with the existing fast techniques using real image data sets on a wide variety of template sizes. While the actual speedups are data dependent, in most cases, our proposed algorithms have been found to be significantly faster than the other algorithms.

Mathematics for Physics

NASA Astrophysics Data System (ADS)

Stone, Michael; Goldbart, Paul

2009-07-01

Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index.

Legendre-tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1986-01-01

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

On the integration of a class of nonlinear systems of ordinary differential equations

NASA Astrophysics Data System (ADS)

Talyshev, Aleksandr A.

2017-11-01

For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.

Legendre-Tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1983-01-01

The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

State-resolved differential and integral cross sections for the Ne + H{sub 2}{sup +} (v = 0–2, j = 0) → NeH{sup +} + H reaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Hui; Yao, Cui-Xia; He, Xiao-Hu

State-to-state quantum dynamic calculations for the proton transfer reaction Ne + H{sub 2}{sup +} (v = 0–2, j = 0) are performed on the most accurate LZHH potential energy surface, with the product Jacobi coordinate based time-dependent wave packet method including the Coriolis coupling. The J = 0 reaction probabilities for the title reaction agree well with previous results in a wide range of collision energy of 0.2-1.2 eV. Total integral cross sections are in reasonable agreement with the available experiment data. Vibrational excitation of the reactant is much more efficient in enhancing the reaction cross sections than translational andmore » rotational excitation. Total differential cross sections are found to be forward-backward peaked with strong oscillations, which is the indication of the complex-forming mechanism. As the collision energy increases, state-resolved differential cross section changes from forward-backward symmetric peaked to forward scattering biased. This forward bias can be attributed to the larger J partial waves, which makes the reaction like an abstraction process. Differential cross sections summed over two different sets of J partial waves for the v = 0 reaction at the collision energy of 1.2 eV are plotted to illustrate the importance of large J partial waves in the forward bias of the differential cross sections.« less

Partial Fractions via Calculus

ERIC Educational Resources Information Center

Bauldry, William C.

2018-01-01

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

Differential geometric methods in system theory.

NASA Technical Reports Server (NTRS)

Brockett, R. W.

1971-01-01

Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.

The moral affiliations of disgust: a functional MRI study.

PubMed

Moll, Jorge; de Oliveira-Souza, Ricardo; Moll, Fernanda Tovar; Ignácio, Fátima Azevedo; Bramati, Ivanei E; Caparelli-Dáquer, Egas M; Eslinger, Paul J

2005-03-01

Recent investigations in cognitive neuroscience have shown that ordinary human behavior is guided by emotions that are uniquely human in their experiential and interpersonal aspects. These "moral emotions" contribute importantly to human social behavior and derive from the neurobehavioral reorganization of the basic plan of emotions that pervade mammalian life. Disgust is one prototypic emotion with multiple domains that include viscerosomatic reaction patterns and subjective experiences linked to (a) the sensory properties of a class of natural stimuli, (b) a set of aversive experiences and (c) a unique mode of experiencing morality. In the current investigation, we tested the hypotheses that (a) the experience of disgust devoid of moral connotations ("pure disgust") can be subjectively and behaviorally differentiated from the experience of disgust disguised in the moral emotion of "indignation" and that (b) pure disgust and indignation may have partially overlapping neural substrates. Thirteen normal adult volunteers were investigated with functional magnetic resonance imaging as they read a series of statements depicting scenarios of pure disgust, indignation, and neutral emotion. After the scanning procedure, they assigned one basic and one moral emotion to each stimulus from an array of six basic and seven moral emotions. Results indicated that (a) emotional stimuli may evoke pure disgust with or without indignation, (b) these different aspects of the experience of disgust could be elicited by a set of written statements, and (c) pure disgust and indignation recruited both overlapping and distinct brain regions, mainly in the frontal and temporal lobes. This work underscores the importance of the prefrontal and orbitofrontal cortices in moral judgment and in the automatic attribution of morality to social events. Human disgust encompasses a variety of emotional experiences that are ingrained in frontal, temporal, and limbic networks.

Conformational statistics of stiff macromolecules as solutions to partial differential equations on the rotation and motion groups

PubMed

Chirikjian; Wang

2000-07-01

Partial differential equations (PDE's) for the probability density function (PDF) of the position and orientation of the distal end of a stiff macromolecule relative to its proximal end are derived and solved. The Kratky-Porod wormlike chain, the Yamakawa helical wormlike chain, and the original and revised Marko-Siggia models are examples of stiffness models to which the present formulation is applied. The solution technique uses harmonic analysis on the rotation and motion groups to convert PDE's governing the PDF's of interest into linear algebraic equations which have mathematically elegant solutions.

On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

1994-01-01

It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

Noniterative three-dimensional grid generation using parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1985-01-01

A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.

Double diffusive conjugate heat transfer: Part III

NASA Astrophysics Data System (ADS)

Soudagar, Manzoor Elahi M.; Azeem

2018-05-01

The placement of a small solid wall towards cold surface of square porous cavity affects the heat transfer behavior of porous region due to restriction of fluid motion in the region occupied by solid wall. An investigation of heat transfer is carried out to understand the fluid flow and heat transfer behavior in porous cavity by solving the governing partial differential equations. Galerkin's approach is used to convert the partial differential equations into algebraic form of equations by applying finite element method. The heat transfer increases for solid towards right surface as compared to the case of solid at center of cavity.

Complexity of parallel implementation of domain decomposition techniques for elliptic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gropp, W.D.; Keyes, D.E.

1988-03-01

The authors discuss the parallel implementation of preconditioned conjugate gradient (PCG)-based domain decomposition techniques for self-adjoint elliptic partial differential equations in two dimensions on several architectures. The complexity of these methods is described on a variety of message-passing parallel computers as a function of the size of the problem, number of processors and relative communication speeds of the processors. They show that communication startups are very important, and that even the small amount of global communication in these methods can significantly reduce the performance of many message-passing architectures.

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Chen, Lin-Jie; Ma, Chang-Feng

2010-01-01

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form ut + αuux + βunux + γuxx + δuxxx + ζuxxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions.

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

NASA Astrophysics Data System (ADS)

Chen, Shanzhen; Jiang, Xiaoyun

2012-08-01

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

An efficient numerical scheme for the study of equal width equation

NASA Astrophysics Data System (ADS)

Ghafoor, Abdul; Haq, Sirajul

2018-06-01

In this work a new numerical scheme is proposed in which Haar wavelet method is coupled with finite difference scheme for the solution of a nonlinear partial differential equation. The scheme transforms the partial differential equation to a system of algebraic equations which can be solved easily. The technique is applied to equal width equation in order to study the behaviour of one, two, three solitary waves, undular bore and soliton collision. For efficiency and accuracy of the scheme, L2 and L∞ norms and invariants are computed. The results obtained are compared with already existing results in literature.

Examination of the Film "My Father and My Son" According to the Basic Concepts of Multigenerational Family Therapy

ERIC Educational Resources Information Center

Acar, Tulin; Voltan-Acar, Nilufer

2013-01-01

The aim of this study was to evaluate the basic concepts of multigenerational Family Therapy and to evaluate the scenes of the film ''My Father and My Son'' according to these concepts. For these purposes firstly basic concepts of Multigenerational Family Therapy such as differentiation of self, triangles/triangulation, nuclear family emotional…

Differentiation of magma oceans and the thickness of the depleted layer on Venus

NASA Technical Reports Server (NTRS)

Solomatov, V. S.; Stevenson, D. J.

1993-01-01

Various arguments suggest that Venus probably has no asthenosphere, and it is likely that beneath the crust there is a highly depleted and highly viscous mantle layer which was probably formed in the early history of the planet when it was partially or completely molten. Models of crystallization of magma oceans suggest that just after crystallization of a hypothetical magma ocean, the internal structure of Venus consists of a crust up to about 70 km thickness, a depleted layer up to about 500 km, and an enriched lower layer which probably consists of an undepleted 'lower mantle' and heavy enriched accumulates near the core-mantle boundary. Partial or even complete melting of Venus due to large impacts during the formation period eventually results in differentiation. However, the final result of such a differentiation can vary from a completely differentiated mantle to an almost completely preserved homogeneous mantle depending on competition between convection and differentiation: between low viscosity ('liquid') convection and crystal settling at small crystal fractions, or between high viscosity ('solid') convection and percolation at large crystal fractions.

On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

NASA Astrophysics Data System (ADS)

Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad

2017-01-01

In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.

GENDER BASED DIFFERENCES IN ENDOCRINE AND REPRODUCTIVE TOXICITY

EPA Science Inventory

Basic differences in male versus female reproductive physiology lead to differentials in their respective susceptibilities to chemical insult as evidenced by a variety of observations. As individuals undergo maturation from prenatal sex differentiation through pubertal developme...

Differentiation-dependent rearrangements of actin filaments and microtubules hinder apical endocytosis in urothelial cells.

PubMed

Tratnjek, Larisa; Romih, Rok; Kreft, Mateja Erdani

2017-08-01

During differentiation, superficial urothelial cells (UCs) of the urinary bladder form the apical surface, which is almost entirely covered by urothelial plaques containing densely packed uroplakin particles. These urothelial plaques are the main structural components of the blood-urine permeability barrier in the urinary bladder. We have shown previously that endocytosis from the apical plasma membrane decreases during urothelial cell differentiation. Here, we investigated the role of actin filament and microtubule rearrangements in apical endocytosis of differentiating UCs cells using hyperplastic and normoplastic porcine urothelial models. Partially differentiated normal porcine UCs contained actin filaments in the subapical cytoplasm, while microtubules had a net-like appearance. In highly differentiated UCs, actin filaments mostly disappeared from the subapical cytoplasm and microtubules remained as a thin layer close to the apical plasma membrane. Inhibition of actin filament formation with cytochalasin-D in partially differentiated UCs caused a decrease in apical endocytosis. Depolymerisation of microtubules with nocodazole did not prevent endocytosis of the endocytotic marker WGA into the subapical cytoplasm; however, it abolished WGA transport to endolysosomal compartments in the central cytoplasm. Cytochalasin-D or nocodazole treatment did not significantly change apical endocytosis in highly differentiated UCs. In conclusion, we showed that the physiological differentiation-dependent or chemically induced redistribution and reorganization of actin filaments and microtubules impair apical endocytosis in UCs. Importantly, reduced apical endocytosis due to cytoskeletal rearrangements in highly differentiated UCs, together with the formation of rigid urothelial plaques, reinforces the barrier function of the urothelium.

Application of basic physics principles to clinical neuroradiology: differentiating artifacts from true pathology on MRI.

PubMed

Hakky, Michael; Pandey, Shilpa; Kwak, Ellie; Jara, Hernan; Erbay, Sami H

2013-08-01

This article outlines artifactual findings commonly encountered in neuroradiologic MRI studies and offers clues to differentiate them from true pathology on the basis of their physical properties. Basic MR physics concepts are used to shed light on the causes of these artifacts. MRI is one of the most commonly used techniques in neuroradiology. Unfortunately, MRI is prone to image distortion and artifacts that can be difficult to identify. Using the provided case illustrations, practical clues, and relevant physical applications, radiologists may devise algorithms to troubleshoot these artifacts.

Differential Effects of Full and Partial Notes on Learning Outcomes and Attendance

ERIC Educational Resources Information Center

Cornelius, Tara L.; Owen-DeSchryver, Jamie

2008-01-01

Although college instructors are increasingly providing students with online notes, research is equivocal on how such notes affect student outcomes. This study examined partial versus full notes in introductory psychology classes while controlling for initial levels of student knowledge and academic ability. Results suggested that students…

Socioeconomic Disparities in Alcohol-Related Mortality in Sweden, 1991-2006: A Register-Based Follow-Up Study.

PubMed

Budhiraja, Meenal; Landberg, Jonas

2016-05-01

To examine whether apparent stability of overall alcohol-related mortality in Sweden during a period when traditionally strict alcohol policies went through a series of liberalizations and overall alcohol mortality remained stable, concealed a heterogeneity across socioeconomic groups (defined by educational level); and whether an increase occurred in the contribution of alcohol-related mortality to overall mortality differentials. Drawing on cause of death data linked to census records for the period 1991-2006, we computed annual age-standardized and sex-specific rates of alcohol-related mortality for groups with low, intermediate and high education. Alcohol-related mortality was considerably higher in lower educational groups for both men and women. For men, the trends in alcohol-related mortality were roughly stable for all education groups, and there were no signs of increasing inequalities by education. For women, alcohol-related mortality increased significantly for the low-education group whereas the two higher education groups showed no significant time trends, thus resulting in a widened educational gap in alcohol mortality for women. Alcohol's contribution to the overall mortality differentials declined for men and was basically unchanged for women. The findings provide only partial support to the hypothesis that the liberalizations of Swedish alcohol policy have been followed by a general increase in socioeconomic disparities in alcohol-related mortality. © The Author 2015. Medical Council on Alcohol and Oxford University Press. All rights reserved.

Oligodendrocyte progenitor cells proliferate and survive in an immature state following treatment with an axolemma-enriched fraction

PubMed Central

Becker-Catania, Sara G; Nelson, Julie K; Olivares, Shantel; Chen, Shu-Jen; DeVries, George H

2011-01-01

The ability of an AEF (axolemma-enriched fraction) to influence the proliferation, survival and differentiation of OPC (oligodendrocyte progenitor cells) was evaluated. Following addition of AEF to cultured OPC, the AEF associated with the outer surface of OPC so that subsequent metabolic events were likely mediated by direct AEF-OPC contact. Addition of AEF to the cultured OPC resulted in a dose- and time-dependent increase in proliferation that was partially dependent on Akt (protein kinase B) and MAPK (mitogen-activated protein kinase) activation. The major mitogen in an AEF-SE (soluble 2.0 M NaCl extract of the AEF) was identified as aFGF (acidic fibroblast growth factor) and accounted for 50% of the mitogenicity. The remaining 50% of the mitogenicity had properties consistent with bFGF (basic fibroblast growth factor) but was not unequivocally identified. Under conditions that limit the survival of OPC in culture, AEF treatment prolonged the survival of the OPC. Antigenic and morphological examination of the AEF-treated OPC indicated that the AEF treatment helped the OPC survive in a more immature state. The potential downstream metabolic pathways potentially activated in OPC by AEF and the consequences of these activated pathways are discussed. The results of these studies are consistent with the view that direct contact of axons with OPC stimulates their proliferation and survival while preventing their differentiation. PMID:21345173

A reciprocal effects model of the temporal ordering of basic psychological needs and motivation.

PubMed

Martinent, Guillaume; Guillet-Descas, Emma; Moiret, Sophie

2015-04-01

Using self-determination theory as the framework, we examined the temporal ordering between satisfaction and thwarting of basic psychological needs and motivation. We accomplished this goal by using a two-wave 7-month partial least squares path modeling approach (PLS-PM) among a sample of 94 adolescent athletes (Mage = 15.96) in an intensive training setting. The PLS-PM results showed significant paths leading: (a) from T1 satisfaction of basic psychological need for competence to T2 identified regulation, (b) from T1 external regulation to T2 thwarting and satisfaction of basic psychological need for competence, and (c) from T1 amotivation to T2 satisfaction of basic psychological need for relatedness. Overall, our results suggest that the relationship between basic psychological need and motivation varied depending on the type of basic need and motivation assessed. Basic psychological need for competence predicted identified regulation over time whereas amotivation and external regulation predicted basic psychological need for relatedness or competence over time.

Viability and neural differentiation of mesenchymal stem cells derived from the umbilical cord following perinatal asphyxia.

PubMed

Aly, H; Mohsen, L; Badrawi, N; Gabr, H; Ali, Z; Akmal, D

2012-09-01

Hypoxia-ischemia is the leading cause of neurological handicaps in newborns worldwide. Mesenchymal stem cells (MSCs) collected from fresh cord blood of asphyxiated newborns have the potential to regenerate damaged neural tissues. The aim of this study was to examine the capacity for MSCs to differentiate into neural tissue that could subsequently be used for autologous transplantation. We collected cord blood samples from full-term newborns with perinatal hypoxemia (n=27), healthy newborns (n=14) and non-hypoxic premature neonates (n=14). Mononuclear cells were separated, counted, and then analyzed by flow cytometry to assess various stem cell populations. MSCs were isolated by plastic adherence and characterized by morphology. Cells underwent immunophenotyping and trilineage differentiation potential. They were then cultured in conditions favoring neural differentiation. Neural lineage commitment was detected using immunohistochemical staining for glial fibrillary acidic protein, tubulin III and oligodendrocyte marker O4 antibodies. Mononuclear cell count and viability did not differ among the three groups of infants. Neural differentiation was best demonstrated in the cells derived from hypoxia-ischemia term neonates, of which 69% had complete and 31% had partial neural differentiation. Cells derived from preterm neonates had the least amount of neural differentiation, whereas partial differentiation was observed in only 12%. These findings support the potential utilization of umbilical cord stem cells as a source for autologous transplant in asphyxiated neonates.

Depression partially mediated the relationship between basic psychological needs and quality of life among people living with HIV.

PubMed

Majeed, Zahraa; van Wijngaarden, Edwin; Dolan, James G; Shah, Krupa N

2017-11-01

Few studies have examined the relationship between basic psychological needs (BPN), depression and quality of life (QOL) in people living with HIV (PLWH). This cross-sectional study (N = 65; 37% females, 37% Caucasian, mean age = 55 ± 6 years, mean CD4 count = 668 ± 368 cells/mm 3 , average duration of HIV = 18 ± 4 years) found that BPN frustration was related with lower QOL. The strength of this relationship was reduced after controlling for depression. This suggests that depression partially mediated the relationship between BPN and QOL. BPN and depression may be specific targets for psychosocial interventions aimed at improving QOL in PLWH to promote successful aging.

Local algebraic analysis of differential systems

NASA Astrophysics Data System (ADS)

Kaptsov, O. V.

2015-06-01

We propose a new approach for studying the compatibility of partial differential equations. This approach is a synthesis of the Riquier method, Gröbner basis theory, and elements of algebraic geometry. As applications, we consider systems including the wave equation and the sine-Gordon equation.

A theory of fine structure image models with an application to detection and classification of dementia.

PubMed

O'Neill, William; Penn, Richard; Werner, Michael; Thomas, Justin

2015-06-01

Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible.

Contamination levels of mercury in the muscle of female and male spiny dogfishes (Squalus acanthias) caught off the coast of Japan.

PubMed

Endo, Tetsuya; Hisamichi, Yohsuke; Kimura, Osamu; Kotaki, Yuichi; Kato, Yoshihisa; Ohta, Chiho; Koga, Nobuyuki; Haraguchi, Koichi

2009-11-01

We analyzed the total mercury (T-Hg) and stable isotopes of (13)C and (15)N in the muscle of spiny dogfish (Squalus acanthias) caught off the coast of Japan. The average body length of the female spiny dogfish sampled (94.9+/-20.2 cm, 50.5-131.0 cm, n=40) was significantly larger than that of the males sampled (77.8+/-10.8 cm, 55.5-94.0 cm, n=35), although the ages of the samples were unknown. The T-Hg concentration in the muscle samples rapidly increased after maturity in the females (larger than about 120 cm) and males (larger than about 90 cm), followed by a continued gradual increase. Contamination level of T-Hg in female muscle samples (0.387+/-0.378 microg(wet g)(-1), n=40) was slightly higher than that in male muscle samples (0.316+/-0.202 microg(wet g)(-1), n=35), probably due to the greater longevity of females. In contrast, the contamination level of T-Hg in females smaller than 94.0 cm in length (0.204+/-0.098 microg(wet g)(-1), n=20) was slightly lower than that in the males, probably due to the faster growth rate of females. Although the partial differential(13)C and partial differential(15)N values in the muscle samples increased with an increase in body length, there were no significant differences between the females (-17.2+/-0.4 per thousand and 12.4+/-0.9 per thousand, respectively) and males (-17.3+/-0.4 per thousand and 12.4+/-0.8 per thousand, respectively). A positive correlation was found between partial differential(13)C and partial differential(15)N values, suggesting trophic enrichment due to the growth.

A three operator split-step method covering a larger set of non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Zia, Haider

2017-06-01

This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

ERIC Educational Resources Information Center

Camporesi, Roberto

2011-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…

Basic mechanisms governing solar-cell efficiency

NASA Technical Reports Server (NTRS)

Lindholm, F. A.; Neugroschel, A.; Sah, C. T.

1976-01-01

The efficiency of a solar cell depends on the material parameters appearing in the set of differential equations that describe the transport, recombination, and generation of electrons and holes. This paper describes the many basic mechanisms occurring in semiconductors that can control these material parameters.

A Model for the Oxidation of C/SiC Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2003-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of C/SiC composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. Within the mathematical formulation, two diffusion mechanisms are possible: (1) the relative diffusion of one species with respect to the mixture, which is concentration gradient driven and (2) the diffusion associated with the average velocity of the gas mixture, which is total gas pressure gradient driven. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations must be solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of space and time. The local rate of carbon oxidation is determined as a function of space and time using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The end result is a numerical scheme capable of determining the variation of the local carbon oxidation rates as a function of space and time for any arbitrary C/SiC composite structures.

Dynamic characteristics of a variable-mass flexible missile

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1970-01-01

The general motion of a variable mass flexible missile with internal flow and aerodynamic forces is considered. The resulting formulation comprises six ordinary differential equations for rigid body motion and three partial differential equations for elastic motion. The simultaneous differential equations are nonlinear and possess time-dependent coefficients. The differential equations are solved by a semi-analytical method leading to a set of purely ordinary differential equations which are then solved numerically. A computer program was developed for the numerical solution and results are presented for a given set of initial conditions.

Discovery and Optimization of Low-Storage Runge-Kutta Methods

DTIC Science & Technology

2015-06-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS DISCOVERY AND OPTIMIZATION OF LOW-STORAGE RUNGE-KUTTA METHODS by Matthew T. Fletcher June 2015... methods are an important family of iterative methods for approximating the solutions of ordinary differential equations (ODEs) and differential...algebraic equations (DAEs). It is common to use an RK method to discretize in time when solving time dependent partial differential equations (PDEs) with a

The decay widths, the decay constants, and the branching fractions of a resonant state

NASA Astrophysics Data System (ADS)

de la Madrid, Rafael

2015-08-01

We introduce the differential and the total decay widths of a resonant (Gamow) state decaying into a continuum of stable states. When the resonance has several decay modes, we introduce the corresponding partial decay widths and branching fractions. In the approximation that the resonance is sharp, the expressions for the differential, partial and total decay widths of a resonant state bear a close resemblance with the Golden Rule. In such approximation, the branching fractions of a resonant state are the same as the standard branching fractions obtained by way of the Golden Rule. We also introduce dimensionless decay constants along with their associated differential decay constants, and we express experimentally measurable quantities such as the branching fractions and the energy distributions of decay events in terms of those dimensionless decay constants.

Spherical means of solutions of partial differential equations in a conical region

NASA Technical Reports Server (NTRS)

Ting, L.

1974-01-01

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear ti surfaces. The spherical mean is the average of u over a constant ti surface. The conditions on the linear differential operator, L, and on the orthogonal coordinates (ti, eta, zeta) are established so that the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be determined directly as a problem with only space variable. Conditions are then established so that the spherical mean of the solution in one concial region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

Asymptotic analysis of the local potential approximation to the Wetterich equation

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Sarkar, Sarben

2018-06-01

This paper reports a study of the nonlinear partial differential equation that arises in the local potential approximation to the Wetterich formulation of the functional renormalization group equation. A cut-off-dependent shift of the potential in this partial differential equation is performed. This shift allows a perturbative asymptotic treatment of the differential equation for large values of the infrared cut-off. To leading order in perturbation theory the differential equation becomes a heat equation, where the sign of the diffusion constant changes as the space-time dimension D passes through 2. When D  <  2, one obtains a forward heat equation whose initial-value problem is well-posed. However, for D  >  2 one obtains a backward heat equation whose initial-value problem is ill-posed. For the special case D  =  1 the asymptotic series for cubic and quartic models is extrapolated to the small infrared-cut-off limit by using Padé techniques. The effective potential thus obtained from the partial differential equation is then used in a Schrödinger-equation setting to study the stability of the ground state. For cubic potentials it is found that this Padé procedure distinguishes between a -symmetric theory and a conventional Hermitian theory (g real). For an theory the effective potential is nonsingular and has a stable ground state but for a conventional theory the effective potential is singular. For a conventional Hermitian theory and a -symmetric theory (g  >  0) the results are similar; the effective potentials in both cases are nonsingular and possess stable ground states.

Patterns of differentiation among endangered pondberry populations

Treesearch

Craig S Echt; Dennis Deemer; Danny Gustafson

2011-01-01

Pondberry, Lindera melissifolia, is an endangered and partially clonally reproducing shrub species found in isolated populations that inhabit seasonally wet depressions in forested areas of the lower Mississippi River alluvial valley and southeastern regions of the United States. With eleven microsatellite loci, we quantified population genetic differentiation and...

D{sub {infinity}}-differential A{sub {infinity}}-algebras and spectral sequences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lapin, S V

2002-02-28

In the present paper the construction of a D{sub {infinity}}-differential A{sub {infinity}}-(co)algebra is introduced and basic homotopy properties of this construction are studied. The connection between D{sub {infinity}}-differential A{sub {infinity}}-(co)algebras and spectral sequences is established, which enables us to construct the structure of an A{sub {infinity}} -coalgebra on the Milnor coalgebra directly from the differentials of the Adams spectral sequence.

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.

2006-05-01

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

Partial differential equation models in the socio-economic sciences.

PubMed

Burger, Martin; Caffarelli, Luis; Markowich, Peter A

2014-11-13

Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences. The application of PDEs in the latter is a promising field, but widely quite open and leading to a variety of novel mathematical challenges. In this introductory article of the Theme Issue, we will provide an overview of the field and its recent boosting topics. Moreover, we will put the contributions to the Theme Issue in an appropriate perspective. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Estimating varying coefficients for partial differential equation models.

PubMed

Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J

2017-09-01

Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data. © 2017, The International Biometric Society.

Survey of the status of finite element methods for partial differential equations

NASA Technical Reports Server (NTRS)

Temam, Roger

1986-01-01

The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

An Elementary Introduction to Recently Developed Computational Methods for Solving Singularly Perturbed Partial Differential Equations Arising in Science and Engineering

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Srivastava, Akanksha

2013-01-01

This paper presents a survey of innovative approaches of the most effective computational techniques for solving singular perturbed partial differential equations, which are useful because of their numerical and computer realizations. Many applied problems appearing in semiconductors theory, biochemistry, kinetics, theory of electrical chains, economics, solid mechanics, fluid dynamics, quantum mechanics, and many others can be modelled as singularly perturbed systems. Here, we summarize a wide range of research articles published by numerous researchers during the last ten years to get a better view of the present scenario in this area of research.

A semi-direct procedure using a local relaxation factor and its application to an internal flow problem

NASA Technical Reports Server (NTRS)

Chang, S. C.

1984-01-01

Generally, fast direct solvers are not directly applicable to a nonseparable elliptic partial differential equation. This limitation, however, is circumvented by a semi-direct procedure, i.e., an iterative procedure using fast direct solvers. An efficient semi-direct procedure which is easy to implement and applicable to a variety of boundary conditions is presented. The current procedure also possesses other highly desirable properties, i.e.: (1) the convergence rate does not decrease with an increase of grid cell aspect ratio, and (2) the convergence rate is estimated using the coefficients of the partial differential equation being solved.

Solution of partial differential equations on vector and parallel computers

NASA Technical Reports Server (NTRS)

Ortega, J. M.; Voigt, R. G.

1985-01-01

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.

Unsteady boundary layer flow over a sphere in a porous medium

NASA Astrophysics Data System (ADS)

Mohammad, Nurul Farahain; Waini, Iskandar; Kasim, Abdul Rahman Mohd; Majid, Nurazleen Abdul

2017-08-01

This study focuses on the problem of unsteady boundary layer flow over a sphere in a porous medium. The governing equations which consists of a system of dimensional partial differential equations is applied with dimensionless parameter in order to attain non-dimensional partial differential equations. Later, the similarity transformation is performed in order to attain nonsimilar governing equations. Afterwards, the nonsimilar governing equations are solved numerically by using the Keller-Box method in Octave programme. The effect of porosity parameter is examined on separation time, velocity profile and skin friction of the unsteady flow. The results attained are presented in the form of table and graph.

Analytical solutions for systems of partial differential-algebraic equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2014-01-01

This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.

Time-partitioning simulation models for calculation on parallel computers

NASA Technical Reports Server (NTRS)

Milner, Edward J.; Blech, Richard A.; Chima, Rodrick V.

1987-01-01

A technique allowing time-staggered solution of partial differential equations is presented in this report. Using this technique, called time-partitioning, simulation execution speedup is proportional to the number of processors used because all processors operate simultaneously, with each updating of the solution grid at a different time point. The technique is limited by neither the number of processors available nor by the dimension of the solution grid. Time-partitioning was used to obtain the flow pattern through a cascade of airfoils, modeled by the Euler partial differential equations. An execution speedup factor of 1.77 was achieved using a two processor Cray X-MP/24 computer.

Combination of oriented partial differential equation and shearlet transform for denoising in electronic speckle pattern interferometry fringe patterns.

PubMed

Xu, Wenjun; Tang, Chen; Gu, Fan; Cheng, Jiajia

2017-04-01

It is a key step to remove the massive speckle noise in electronic speckle pattern interferometry (ESPI) fringe patterns. In the spatial-domain filtering methods, oriented partial differential equations have been demonstrated to be a powerful tool. In the transform-domain filtering methods, the shearlet transform is a state-of-the-art method. In this paper, we propose a filtering method for ESPI fringe patterns denoising, which is a combination of second-order oriented partial differential equation (SOOPDE) and the shearlet transform, named SOOPDE-Shearlet. Here, the shearlet transform is introduced into the ESPI fringe patterns denoising for the first time. This combination takes advantage of the fact that the spatial-domain filtering method SOOPDE and the transform-domain filtering method shearlet transform benefit from each other. We test the proposed SOOPDE-Shearlet on five experimentally obtained ESPI fringe patterns with poor quality and compare our method with SOOPDE, shearlet transform, windowed Fourier filtering (WFF), and coherence-enhancing diffusion (CEDPDE). Among them, WFF and CEDPDE are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. The experimental results have demonstrated the good performance of the proposed SOOPDE-Shearlet.

Improved Sensitivity Relations in State Constrained Optimal Control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bettiol, Piernicola, E-mail: piernicola.bettiol@univ-brest.fr; Frankowska, Hélène, E-mail: frankowska@math.jussieu.fr; Vinter, Richard B., E-mail: r.vinter@imperial.ac.uk

2015-04-15

Sensitivity relations in optimal control provide an interpretation of the costate trajectory and the Hamiltonian, evaluated along an optimal trajectory, in terms of gradients of the value function. While sensitivity relations are a straightforward consequence of standard transversality conditions for state constraint free optimal control problems formulated in terms of control-dependent differential equations with smooth data, their verification for problems with either pathwise state constraints, nonsmooth data, or for problems where the dynamic constraint takes the form of a differential inclusion, requires careful analysis. In this paper we establish validity of both ‘full’ and ‘partial’ sensitivity relations for an adjointmore » state of the maximum principle, for optimal control problems with pathwise state constraints, where the underlying control system is described by a differential inclusion. The partial sensitivity relation interprets the costate in terms of partial Clarke subgradients of the value function with respect to the state variable, while the full sensitivity relation interprets the couple, comprising the costate and Hamiltonian, as the Clarke subgradient of the value function with respect to both time and state variables. These relations are distinct because, for nonsmooth data, the partial Clarke subdifferential does not coincide with the projection of the (full) Clarke subdifferential on the relevant coordinate space. We show for the first time (even for problems without state constraints) that a costate trajectory can be chosen to satisfy the partial and full sensitivity relations simultaneously. The partial sensitivity relation in this paper is new for state constraint problems, while the full sensitivity relation improves on earlier results in the literature (for optimal control problems formulated in terms of Lipschitz continuous multifunctions), because a less restrictive inward pointing hypothesis is invoked in the proof, and because it is validated for a stronger set of necessary conditions.« less

A Fresh Look at Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

ERIC Educational Resources Information Center

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…

An Introduction to Computational Physics

NASA Astrophysics Data System (ADS)

Pang, Tao

2010-07-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

Parallel Algorithm Solves Coupled Differential Equations

NASA Technical Reports Server (NTRS)

Hayashi, A.

1987-01-01

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

NASA Astrophysics Data System (ADS)

Katsaounis, T. D.

2005-02-01

The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using Diffpack and MPI are also presented. Chapter 2 presents the overlapping domain decomposition method for solving PDEs. It is well known that these methods are suitable for parallel processing. The first part of the chapter covers the mathematical formulation of the method as well as algorithmic and implementational issues. The second part presents a serial and a parallel implementational framework within the programming environment of Diffpack. The chapter closes by showing how to solve two application examples with the overlapping domain decomposition method using Diffpack. Chapter 3 is a tutorial about how to incorporate the multigrid solver in Diffpack. The method is illustrated by examples such as a Poisson solver, a general elliptic problem with various types of boundary conditions and a nonlinear Poisson type problem. In chapter 4 the mixed finite element is introduced. Technical issues concerning the practical implementation of the method are also presented. The main difficulties of the efficient implementation of the method, especially in two and three space dimensions on unstructured grids, are presented and addressed in the framework of Diffpack. The implementational process is illustrated by two examples, namely the system formulation of the Poisson problem and the Stokes problem. Chapter 5 is closely related to chapter 4 and addresses the problem of how to solve efficiently the linear systems arising by the application of the mixed finite element method. The proposed method is block preconditioning. Efficient techniques for implementing the method within Diffpack are presented. Optimal block preconditioners are used to solve the system formulation of the Poisson problem, the Stokes problem and the bidomain model for the electrical activity in the heart. The subject of chapter 6 is systems of PDEs. Linear and nonlinear systems are discussed. Fully implicit and operator splitting methods are presented. Special attention is paid to how existing solvers for scalar equations in Diffpack can be used to derive fully implicit solvers for systems. The proposed techniques are illustrated in terms of two applications, namely a system of PDEs modelling pipeflow and a two-phase porous media flow. Stochastic PDEs is the topic of chapter 7. The first part of the chapter is a simple introduction to stochastic PDEs; basic analytical properties are presented for simple models like transport phenomena and viscous drag forces. The second part considers the numerical solution of stochastic PDEs. Two basic techniques are presented, namely Monte Carlo and perturbation methods. The last part explains how to implement and incorporate these solvers into Diffpack. Chapter 8 describes how to operate Diffpack from Python scripts. The main goal here is to provide all the programming and technical details in order to glue the programming environment of Diffpack with visualization packages through Python and in general take advantage of the Python interfaces. Chapter 9 attempts to show how to use numerical experiments to measure the performance of various PDE solvers. The authors gathered a rather impressive list, a total of 14 PDE solvers. Solvers for problems like Poisson, Navier--Stokes, elasticity, two-phase flows and methods such as finite difference, finite element, multigrid, and gradient type methods are presented. The authors provide a series of numerical results combining various solvers with various methods in order to gain insight into their computational performance and efficiency. In Chapter 10 the authors consider a computationally challenging problem, namely the computation of the electrical activity of the human heart. After a brief introduction on the biology of the problem the authors present the mathematical models involved and a numerical method for solving them within the framework of Diffpack. Chapter 11 and 12 are closely related; actually they could have been combined in a single chapter. Chapter 11 introduces several mathematical models used in finance, based on the Black--Scholes equation. Chapter 12 considers several numerical methods like Monte Carlo, lattice methods, finite difference and finite element methods. Implementation of these methods within Diffpack is presented in the last part of the chapter. Chapter 13 presents how the finite element method is used for the modelling and analysis of elastic structures. The authors describe the structural elements of Diffpack which include popular elements such as beams and plates and examples are presented on how to use them to simulate elastic structures. Chapter 14 describes an application problem, namely the extrusion of aluminum. This is a rather\\endcolumn complicated process which involves non-Newtonian flow, heat transfer and elasticity. The authors describe the systems of PDEs modelling the underlying process and use a finite element method to obtain a numerical solution. The implementation of the numerical method in Diffpack is presented along with some applications. The last chapter, chapter 15, focuses on mathematical and numerical models of systems of PDEs governing geological processes in sedimentary basins. The underlying mathematical model is solved using the finite element method within a fully implicit scheme. The authors discuss the implementational issues involved within Diffpack and they present results from several examples. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall the book is well written, the subject of each chapter is well presented and can serve as a reference for graduate students, researchers and engineers who are interested in the numerical solution of partial differential equations modelling various applications.

5 CFR 532.501 - Definitions.

Code of Federal Regulations, 2010 CFR

2010-01-01

... of seven consecutive calendar days. Basic workweek for full time employees means the days and hours... scheduled administrative workweek. Night shift differential means the differential paid the employee when... day or in excess of 40 hours in an administrative workweek, and includes irregular or occasional...

Towards a General-Purpose Belief Maintenance System.

DTIC Science & Technology

1987-04-01

reason using normal two or three-valued logic or using probabilistic values to represent partial belief. The design of the Belief Maintenance System is...as simply a generalization of Truth Maintenance Systems. whose possible reasoning tasks are a superset of those for a TMS. 2. DESIGN The design of...become support links in that they provide partial evidence in favor of a node. The basic design consists of three parts: (1) the conceptual control

Evolving gene regulation networks into cellular networks guiding adaptive behavior: an outline how single cells could have evolved into a centralized neurosensory system

PubMed Central

Fritzsch, Bernd; Jahan, Israt; Pan, Ning; Elliott, Karen L.

2014-01-01

Understanding the evolution of the neurosensory system of man, able to reflect on its own origin, is one of the major goals of comparative neurobiology. Details of the origin of neurosensory cells, their aggregation into central nervous systems and associated sensory organs, their localized patterning into remarkably different cell types aggregated into variably sized parts of the central nervous system begin to emerge. Insights at the cellular and molecular level begin to shed some light on the evolution of neurosensory cells, partially covered in this review. Molecular evidence suggests that high mobility group (HMG) proteins of pre-metazoans evolved into the definitive Sox [SRY (sex determining region Y)-box] genes used for neurosensory precursor specification in metazoans. Likewise, pre-metazoan basic helix-loop-helix (bHLH) genes evolved in metazoans into the group A bHLH genes dedicated to neurosensory differentiation in bilaterians. Available evidence suggests that the Sox and bHLH genes evolved a cross-regulatory network able to synchronize expansion of precursor populations and their subsequent differentiation into novel parts of the brain or sensory organs. Molecular evidence suggests metazoans evolved patterning gene networks early and not dedicated to neuronal development. Only later in evolution were these patterning gene networks tied into the increasing complexity of diffusible factors, many of which were already present in pre-metazoans, to drive local patterning events. It appears that the evolving molecular basis of neurosensory cell development may have led, in interaction with differentially expressed patterning genes, to local network modifications guiding unique specializations of neurosensory cells into sensory organs and various areas of the central nervous system. PMID:25416504

Evolving gene regulatory networks into cellular networks guiding adaptive behavior: an outline how single cells could have evolved into a centralized neurosensory system.

PubMed

Fritzsch, Bernd; Jahan, Israt; Pan, Ning; Elliott, Karen L

2015-01-01

Understanding the evolution of the neurosensory system of man, able to reflect on its own origin, is one of the major goals of comparative neurobiology. Details of the origin of neurosensory cells, their aggregation into central nervous systems and associated sensory organs and their localized patterning leading to remarkably different cell types aggregated into variably sized parts of the central nervous system have begun to emerge. Insights at the cellular and molecular level have begun to shed some light on the evolution of neurosensory cells, partially covered in this review. Molecular evidence suggests that high mobility group (HMG) proteins of pre-metazoans evolved into the definitive Sox [SRY (sex determining region Y)-box] genes used for neurosensory precursor specification in metazoans. Likewise, pre-metazoan basic helix-loop-helix (bHLH) genes evolved in metazoans into the group A bHLH genes dedicated to neurosensory differentiation in bilaterians. Available evidence suggests that the Sox and bHLH genes evolved a cross-regulatory network able to synchronize expansion of precursor populations and their subsequent differentiation into novel parts of the brain or sensory organs. Molecular evidence suggests metazoans evolved patterning gene networks early, which were not dedicated to neuronal development. Only later in evolution were these patterning gene networks tied into the increasing complexity of diffusible factors, many of which were already present in pre-metazoans, to drive local patterning events. It appears that the evolving molecular basis of neurosensory cell development may have led, in interaction with differentially expressed patterning genes, to local network modifications guiding unique specializations of neurosensory cells into sensory organs and various areas of the central nervous system.

Anisotropic norm-oriented mesh adaptation for a Poisson problem

NASA Astrophysics Data System (ADS)

Brèthes, Gautier; Dervieux, Alain

2016-10-01

We present a novel formulation for the mesh adaptation of the approximation of a Partial Differential Equation (PDE). The discussion is restricted to a Poisson problem. The proposed norm-oriented formulation extends the goal-oriented formulation since it is equation-based and uses an adjoint. At the same time, the norm-oriented formulation somewhat supersedes the goal-oriented one since it is basically a solution-convergent method. Indeed, goal-oriented methods rely on the reduction of the error in evaluating a chosen scalar output with the consequence that, as mesh size is increased (more degrees of freedom), only this output is proven to tend to its continuous analog while the solution field itself may not converge. A remarkable quality of goal-oriented metric-based adaptation is the mathematical formulation of the mesh adaptation problem under the form of the optimization, in the well-identified set of metrics, of a well-defined functional. In the new proposed formulation, we amplify this advantage. We search, in the same well-identified set of metrics, the minimum of a norm of the approximation error. The norm is prescribed by the user and the method allows addressing the case of multi-objective adaptation like, for example in aerodynamics, adaptating the mesh for drag, lift and moment in one shot. In this work, we consider the basic linear finite-element approximation and restrict our study to L2 norm in order to enjoy second-order convergence. Numerical examples for the Poisson problem are computed.

Influence of Stationary Crossflow Modulation on Secondary Instability

NASA Technical Reports Server (NTRS)

Choudhari, Meelan M.; Li, Fei; Paredes, Pedro

2016-01-01

A likely scenario for swept wing transition on subsonic aircraft with natural laminar flow involves the breakdown of stationary crossflow vortices via high frequency secondary instability. A majority of the prior research on this secondary instability has focused on crossflow vortices with a single dominant spanwise wavelength. This paper investigates the effects of the spanwise modulation of stationary crossflow vortices at a specified wavelength by a subharmonic stationary mode. Secondary instability of the modulated crossflow pattern is studied using planar, partial-differential-equation based eigenvalue analysis. Computations reveal that weak modulation by the first subharmonic of the input stationary mode leads to mode splitting that is particularly obvious for Y-type secondary modes that are driven by the wall-normal shear of the basic state. Thus, for each Y mode corresponding to the fundamental wavelength of results in unmodulated train of crossflow vortices, the modulated flow supports a pair of secondary modes with somewhat different amplification rates. The mode splitting phenomenon suggests that a more complex stationary modulation such as that induced by natural surface roughness would yield a considerably richer spectrum of secondary instability modes. Even modest levels of subharmonic modulation are shown to have a strong effect on the overall amplification of secondary disturbances, particularly the Z-modes driven by the spanwise shear of the basic state. Preliminary computations related to the nonlinear breakdown of these secondary disturbances provide interesting insights into the process of crossflow transition in the presence of the first subharmonic of the dominant stationary vortex.

Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry.

PubMed

Tang, Chen; Lu, Wenjing; Chen, Song; Zhang, Zhen; Li, Botao; Wang, Wenping; Han, Lin

2007-10-20

We extend and refine previous work [Appl. Opt. 46, 2907 (2007)]. Combining the coupled nonlinear partial differential equations (PDEs) denoising model with the ordinary differential equations enhancement method, we propose the new denoising and enhancing model for electronic speckle pattern interferometry (ESPI) fringe patterns. Meanwhile, we propose the backpropagation neural networks (BPNN) method to obtain unwrapped phase values based on a skeleton map instead of traditional interpolations. We test the introduced methods on the computer-simulated speckle ESPI fringe patterns and experimentally obtained fringe pattern, respectively. The experimental results show that the coupled nonlinear PDEs denoising model is capable of effectively removing noise, and the unwrapped phase values obtained by the BPNN method are much more accurate than those obtained by the well-known traditional interpolation. In addition, the accuracy of the BPNN method is adjustable by changing the parameters of networks such as the number of neurons.

Numerical study of unsteady Williamson fluid flow and heat transfer in the presence of MHD through a permeable stretching surface

NASA Astrophysics Data System (ADS)

Bibi, Madiha; Khalil-Ur-Rehman; Malik, M. Y.; Tahir, M.

2018-04-01

In the present article, unsteady flow field characteristics of the Williamson fluid model are explored. The nanosized particles are suspended in the flow regime having the interaction of a magnetic field. The fluid flow is induced due to a stretching permeable surface. The flow model is controlled through coupled partial differential equations to the used shooting method for a numerical solution. The obtained partial differential equations are converted into ordinary differential equations as an initial value problem. The shooting method is used to find a numerical solution. The mathematical modeling yields physical parameters, namely the Weissenberg number, the Prandtl number, the unsteadiness parameter, the magnetic parameter, the mass transfer parameter, the Lewis number, the thermophoresis parameter and Brownian parameters. It is found that the Williamson fluid velocity, temperature and nanoparticles concentration are a decreasing function of the unsteadiness parameter.

CANNABINOID AND OPIOID MODULATION OF SOCIAL PLAY BEHAVIOR IN ADOLESCENT RATS: DIFFERENTIAL BEHAVIORAL MECHANISMS

PubMed Central

Trezza, Viviana; Vanderschuren, Louk J.M.J.

2008-01-01

We have recently shown that the pharmacological mechanisms through which cannabinoid and opioid drugs influence social play behavior in adolescent rats can be partially dissociated. Here, we characterize the effects of the direct cannabinoid agonist WIN55,212-2, the indirect cannabinoid agonist URB597 and the opioid agonist morphine on social play at the behavioral level. By treating either one or both partners of the test dyad, we show that these drugs differentially affect play solicitation and play responsiveness. By testing these drugs in animals which were either familiar or unfamiliar to the test cage, we show that environmental factors differentially modulate the effects of cannabinoid and opioid drugs on social play. These results support and extend our previous findings suggesting that, although cannabinoid and opioid systems interact in the modulation of social play behavior in adolescent rats, they do so through partially dissociable behavioral and pharmacological mechanisms. PMID:18434104

Partial differential equation-based localization of a monopole source from a circular array.

PubMed

Ando, Shigeru; Nara, Takaaki; Levy, Tsukassa

2013-10-01

Wave source localization from a sensor array has long been the most active research topics in both theory and application. In this paper, an explicit and time-domain inversion method for the direction and distance of a monopole source from a circular array is proposed. The approach is based on a mathematical technique, the weighted integral method, for signal/source parameter estimation. It begins with an exact form of the source-constraint partial differential equation that describes the unilateral propagation of wide-band waves from a single source, and leads to exact algebraic equations that include circular Fourier coefficients (phase mode measurements) as their coefficients. From them, nearly closed-form, single-shot and multishot algorithms are obtained that is suitable for use with band-pass/differential filter banks. Numerical evaluation and several experimental results obtained using a 16-element circular microphone array are presented to verify the validity of the proposed method.

Spherical means of solutions of partial differential equations in a conical region

NASA Technical Reports Server (NTRS)

Ting, L.

1975-01-01

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear xi lines and by two truncating xi surfaces. The spherical mean is the average of u over a constant xi surface. Conditions on the linear differential operator, L, and on the orthogonal coordinates xi, eta, and zeta are established so that the problem for the determination of the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be reduced to a problem with only one space variable. Conditions are then established so that the spherical mean of the solution in one conical region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

On asymptotic behavior and energy distribution for some one-dimensional non-parabolic diffusion problems

NASA Astrophysics Data System (ADS)

Kim, Seonghak; Yan, Baisheng

2018-06-01

We study some non-parabolic diffusion problems in one space dimension, where the diffusion flux exhibits forward and backward nature of the Perona–Malik, Höllig or non-Fourier type. Classical weak solutions to such problems are constructed in a way to capture some expected and unexpected properties, including anomalous asymptotic behaviors and energy dissipation or allocation. Specific properties of solutions will depend on the type of the diffusion flux, but the primary method of our study relies on reformulating diffusion equations involved as an inhomogeneous partial differential inclusion and on constructing solutions from the differential inclusion by a combination of the convex integration and Baire’s category methods. In doing so, we introduce the appropriate notion of subsolutions of the partial differential inclusion and their transition gauge, which plays a pivotal role in dealing with some specific features of the constructed weak solutions.

Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations

NASA Astrophysics Data System (ADS)

Berkeley, George; Igonin, Sergei

2016-07-01

Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux-Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita-Itoh-Bogoyavlensky, Toda, and Adler-Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new.

Apolipoprotein E promotes lipid accumulation and differentiation in human adipocytes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lasrich, Dorothee; Bartelt, Alexander; Grewal, Thomas, E-mail: thomas.grewal@sydney.edu.au

Several studies in mice indicate a role for apolipoprotein E (APOE) in lipid accumulation and adipogenic differentiation in adipose tissue. However, little is yet known if APOE functions in a similar manner in human adipocytes. This prompted us to compare lipid loading and expression of adipocyte differentiation markers in APOE-deficient and control adipocytes using the differentiated human mesenchymal stem cell line hMSC-Tert as well as primary human and mouse adipocytes as model systems. Differentiated hMSC-Tert were stably transduced with or without siRNA targeting APOE while murine adipocytes were isolated from wild type and Apoe knockout mice. Human APOE knockdown hMSC-Tertmore » adipocytes accumulated markedly less triglycerides compared to control cells. This correlated with strongly decreased gene expression levels of adipocyte markers such as adiponectin (ADIPOQ) and fatty acid binding protein 4 (FABP4) as well as the key transcription factor driving adipocyte differentiation, peroxisome proliferator activator receptor gamma (PPARG), in particular the PPARG2 isoform. Similarly, differentiation of murine Apoe-deficient adipocytes was characterized by reduced gene expression of Adipoq, Fabp4 and Pparg. Interestingly, incubation of APOE-deficient hMSC-Tert adipocytes with conditioned media from APOE3-overexpressing adipocytes or APOE-containing Very Low Density Lipoprotein (VLDL) partially restored triglyceride accumulation, but were unable to induce adipocyte differentiation, as judged by expression of adipocyte markers. Taken together, depletion of endogenous APOE in human adipocytes severely impairs lipid accumulation, which is associated with an inability to initiate differentiation. - Highlights: • Immortalized human mesenchymal stem cells were used to study adipocyte development. • Knockdown of endogenous APOE lead to impaired lipid accumulation and adipogenesis. • APOE supplementation partially restored lipid accumulation but not differentiation. • Findings suggest dual functions of APOE for lipid accumulation and differentiation.« less

Geometric Error Analysis in Applied Calculus Problem Solving

ERIC Educational Resources Information Center

Usman, Ahmed Ibrahim

2017-01-01

The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…

DIFFERENTIAL ANALYZER

DOEpatents

Sorensen, E.G.; Gordon, C.M.

1959-02-10

Improvements in analog eomputing machines of the class capable of evaluating differential equations, commonly termed differential analyzers, are described. In general form, the analyzer embodies a plurality of basic computer mechanisms for performing integration, multiplication, and addition, and means for directing the result of any one operation to another computer mechanism performing a further operation. In the device, numerical quantities are represented by the rotation of shafts, or the electrical equivalent of shafts.

Experimental study of eclogitization and melting of basic rocks at P = 4 GPa and T = 1200-1400°C

NASA Astrophysics Data System (ADS)

Gorbachev, N. S.; Shapovalov, Yu. B.; Kostyuk, A. V.

2017-06-01

Experimental study of gabbro-norite eclogitization and melting at P = 4 GPa has made it possible to reveal the effective influence of fluid and temperature on the phase relationships. The melt composition varies from andesite-dacite in "dry conditions" to phonolite and carbonate in the presence of a fluid. The Grt-containing melting curve is replaced by the Cpx-containing liquidus as the temperature changes or a fluid is added. Hence, the possible presence of "garnetitite" and "clinopyroxenite" in the upper mantle was proved experimentally. The ultimate pressure of the spinel facies at the depth of the eclogite upper mantle is controlled by the stability of Cht ≤ 4 GPa. The revealed similarity of the spectra of REE-adakite, tonalite-trondhjemite-granodiorite (TTG), and melts formed under the partial melting of eclogitized gabbro-norite does not contradict the existing ideas of the eclogite source of the TTG rocks. Wide variations in the interphase microelement distribution factors D (Grt, Cpx)/L are indicative of effective fractionation of the microelements in the course of eclogite melting and differentiation.

A Discrete Probability Function Method for the Equation of Radiative Transfer

NASA Technical Reports Server (NTRS)

Sivathanu, Y. R.; Gore, J. P.

1993-01-01

A discrete probability function (DPF) method for the equation of radiative transfer is derived. The DPF is defined as the integral of the probability density function (PDF) over a discrete interval. The derivation allows the evaluation of the PDF of intensities leaving desired radiation paths including turbulence-radiation interactions without the use of computer intensive stochastic methods. The DPF method has a distinct advantage over conventional PDF methods since the creation of a partial differential equation from the equation of transfer is avoided. Further, convergence of all moments of intensity is guaranteed at the basic level of simulation unlike the stochastic method where the number of realizations for convergence of higher order moments increases rapidly. The DPF method is described for a representative path with approximately integral-length scale-sized spatial discretization. The results show good agreement with measurements in a propylene/air flame except for the effects of intermittency resulting from highly correlated realizations. The method can be extended to the treatment of spatial correlations as described in the Appendix. However, information regarding spatial correlations in turbulent flames is needed prior to the execution of this extension.

A large-grain mapping approach for multiprocessor systems through data flow model. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kim, Hwa-Soo

1991-01-01

A large-grain level mapping method is presented of numerical oriented applications onto multiprocessor systems. The method is based on the large-grain data flow representation of the input application and it assumes a general interconnection topology of the multiprocessor system. The large-grain data flow model was used because such representation best exhibits inherited parallelism in many important applications, e.g., CFD models based on partial differential equations can be presented in large-grain data flow format, very effectively. A generalized interconnection topology of the multiprocessor architecture is considered, including such architectural issues as interprocessor communication cost, with the aim to identify the 'best matching' between the application and the multiprocessor structure. The objective is to minimize the total execution time of the input algorithm running on the target system. The mapping strategy consists of the following: (1) large-grain data flow graph generation from the input application using compilation techniques; (2) data flow graph partitioning into basic computation blocks; and (3) physical mapping onto the target multiprocessor using a priority allocation scheme for the computation blocks.

Numerical simulation of advective-dispersive multisolute transport with sorption, ion exchange and equilibrium chemistry

USGS Publications Warehouse

Lewis, F.M.; Voss, C.I.; Rubin, Jacob

1986-01-01

A model was developed that can simulate the effect of certain chemical and sorption reactions simultaneously among solutes involved in advective-dispersive transport through porous media. The model is based on a methodology that utilizes physical-chemical relationships in the development of the basic solute mass-balance equations; however, the form of these equations allows their solution to be obtained by methods that do not depend on the chemical processes. The chemical environment is governed by the condition of local chemical equilibrium, and may be defined either by the linear sorption of a single species and two soluble complexation reactions which also involve that species, or binary ion exchange and one complexation reaction involving a common ion. Partial differential equations that describe solute mass balance entirely in the liquid phase are developed for each tenad (a chemical entity whose total mass is independent of the reaction process) in terms of their total dissolved concentration. These equations are solved numerically in two dimensions through the modification of an existing groundwater flow/transport computer code. (Author 's abstract)

Miocene calc-alkaline heritage in the pliocene postcollisional volcanism of monte arci (Sardinia, Italy)

NASA Astrophysics Data System (ADS)

Cioni, Roberto; Clocchiatti, Robert; Di Paola, Giovanni M.; Santacroce, Roberto; Tonarini, Sonia

1982-10-01

At Monte Arci alkaline (hawaiites to trachytes), subalkaline with a marked calc-alkaline character (basalts to dacites) and rhyolitic lavas were erupted almost simultaneously in Late Pliocene time. Major- and trace-element chemistry, microprobe mineralogy and isotopic data suggest a partial melting origin for both rhyolites and subalkaline rocks. Different sources are however inferred for two rock series: homogeneous, calc-alkaline in nature for subalkaline rocks; unhomogeneous, richer in 87Sr, for rhyolitic ones. Crystal fractionation differentiation from subcrustal alkali-basalts should have been the main process in the genesis of alkaline rocks. Large-scale contaminations with rhyolitic and/or alkaline rocks are evident in many of these lavas. Such a complicated magmatic association characterizes an area where volcanism related to post-collisional tensional movements in Pliocene time superimposes to Middle Miocene calc-alkaline basic volcanism related to previous subduction processes. The Pliocene volcanic history of Monte Arci emphasizes the influence of the paleogeodynamic environment on the nature of magmas erupted in post-continental collision areas, that are frequently difficult to arrange in the usual schemas connecting magma composition with tectonic setting.

Real-time optical laboratory solution of parabolic differential equations

NASA Technical Reports Server (NTRS)

Casasent, David; Jackson, James

1988-01-01

An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

Symmetry groups of integro-differential equations for linear thermoviscoelastic materials with memory

NASA Astrophysics Data System (ADS)

Zhou, L.-Q.; Meleshko, S. V.

2017-07-01

The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

NASA Astrophysics Data System (ADS)

Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

2010-11-01

In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

An Introduction to Computational Physics - 2nd Edition

NASA Astrophysics Data System (ADS)

Pang, Tao

2006-01-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

Intuitive Understanding of Solutions of Partially Differential Equations

ERIC Educational Resources Information Center

Kobayashi, Y.

2008-01-01

This article uses diagrams that help the observer see how solutions of the wave equation and heat conduction equation are obtained. The analytical approach cannot necessarily show the mechanisms of the key to the solution without transforming the differential equation into a more convenient form by separation of variables. The visual clues based…

Partial wave analysis for folded differential cross sections

NASA Astrophysics Data System (ADS)

Machacek, J. R.; McEachran, R. P.

2018-03-01

The value of modified effective range theory (MERT) and the connection between differential cross sections and phase shifts in low-energy electron scattering has long been recognized. Recent experimental techniques involving magnetically confined beams have introduced the concept of folded differential cross sections (FDCS) where the forward (θ ≤ π/2) and backward scattered (θ ≥ π/2) projectiles are unresolved, that is the value measured at the angle θ is the sum of the signal for particles scattered into the angles θ and π - θ. We have developed an alternative approach to MERT in order to analyse low-energy folded differential cross sections for positrons and electrons. This results in a simplified expression for the FDCS when it is expressed in terms of partial waves and thereby enables one to extract the first few phase shifts from a fit to an experimental FDCS at low energies. Thus, this method predicts forward and backward angle scattering (0 to π) using only experimental FDCS data and can be used to determine the total elastic cross section solely from experimental results at low-energy, which are limited in angular range.

Tumor necrosis factor-alpha antagonists: differential clinical effects by different biotechnological molecules.

PubMed

Licastro, F; Chiappelli, M; Ianni, M; Porcellini, E

2009-01-01

Inhibitors of tumor necrosis factor-alpha have deeply changed the therapy of several inflammatory human diseases. For instance, clinical management of rheumatoid arthritis, psoriatic arthritis and ankylosing spondylitis have profoundly benefited after the introduction of new therapeutic tools, such as antagonist of TNF-alpha molecule. These drugs include etanercept, a soluble TNF-alpha receptor antagonist, three anti-TNF-alpha antibodies, adalimumab, infliximab, golimumab and certolizumab a humanized Fab fragment combined with polyethylene glycol. These compounds efficiently inhibit several TNF-alpha biological-mediated effects, however, they have also shown differential clinical efficacy in several trials from different autoimmune diseases. It is of clinical relevance that non-responders to one of these drugs often positively responded to another. Different mechanisms of action and diversity in pharmacokinetics of these three compounds may partially explain different clinical effects. However, partially diverse pathogenetic mechanisms in different diseases also contribute to differential therapeutic responses. Therefore, these apparently homogeneous agents can not be considered equivalent in their clinically efficacy. Differential therapeutic actions of these drugs may be advantageously used in clinical practice and further improve the great potential of individual TNF-alpha inhibitors.

Closed-form expressions for state-to-state charge-transfer differential cross sections in a modified Faddeev three-body approach

NASA Astrophysics Data System (ADS)

Adivi, E. Ghanbari; Brunger, M. J.; Bolorizadeh, M. A.; Campbell, L.

2007-02-01

The second-order Faddeev-Watson-Lovelace approximation in a modified form is applied to charge transfer from hydrogenlike target atoms by a fully stripped energetic projectile ion. The state-to-state, nlm→n'l'm' , partial transition amplitudes are calculated analytically. The method is specifically applied to the collision of protons with hydrogen atoms, where differential cross sections of different transitions are calculated for incident energies of 2.8 and 5.0MeV . It is shown that the Thomas peak is present in all transition cross sections. The partial cross sections are then summed and compared with the available forward-angle experimental data, showing good agreement.

Nebo: An efficient, parallel, and portable domain-specific language for numerically solving partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Earl, Christopher; Might, Matthew; Bagusetty, Abhishek

This study presents Nebo, a declarative domain-specific language embedded in C++ for discretizing partial differential equations for transport phenomena on multiple architectures. Application programmers use Nebo to write code that appears sequential but can be run in parallel, without editing the code. Currently Nebo supports single-thread execution, multi-thread execution, and many-core (GPU-based) execution. With single-thread execution, Nebo performs on par with code written by domain experts. With multi-thread execution, Nebo can linearly scale (with roughly 90% efficiency) up to 12 cores, compared to its single-thread execution. Moreover, Nebo’s many-core execution can be over 140x faster than its single-thread execution.

Analytical Derivation of Power Laws in Firm Size Variables from Gibrat's Law and Quasi-inversion Symmetry: A Geomorphological Approach

NASA Astrophysics Data System (ADS)

Ishikawa, Atushi; Fujimoto, Shouji; Mizuno, Takayuki; Watanabe, Tsutomu

2014-03-01

We start from Gibrat's law and quasi-inversion symmetry for three firm size variables (i.e., tangible fixed assets K, number of employees L, and sales Y) and derive a partial differential equation to be satisfied by the joint probability density function of K and L. We then transform K and L, which are correlated, into two independent variables by applying surface openness used in geomorphology and provide an analytical solution to the partial differential equation. Using worldwide data on the firm size variables for companies, we confirm that the estimates on the power-law exponents of K, L, and Y satisfy a relationship implied by the theory.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

PubMed

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Nebo: An efficient, parallel, and portable domain-specific language for numerically solving partial differential equations

DOE PAGES

Earl, Christopher; Might, Matthew; Bagusetty, Abhishek; ...

2016-01-26

This study presents Nebo, a declarative domain-specific language embedded in C++ for discretizing partial differential equations for transport phenomena on multiple architectures. Application programmers use Nebo to write code that appears sequential but can be run in parallel, without editing the code. Currently Nebo supports single-thread execution, multi-thread execution, and many-core (GPU-based) execution. With single-thread execution, Nebo performs on par with code written by domain experts. With multi-thread execution, Nebo can linearly scale (with roughly 90% efficiency) up to 12 cores, compared to its single-thread execution. Moreover, Nebo’s many-core execution can be over 140x faster than its single-thread execution.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models

PubMed Central

Xing, W. W.; Triantafyllidis, V.

2017-01-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach. PMID:28484327

Separation of Variables and Superintegrability; The symmetry of solvable systems

NASA Astrophysics Data System (ADS)

Kalnins, Ernest G.; Kress, Jonathan M.; Miller, Willard, Jr.

2018-06-01

Separation of variables methods for solving partial differential equations are of immense theoretical and practical importance in mathematical physics. They are the most powerful tool known for obtaining explicit solutions of the partial differential equations of mathematical physics. The purpose of this book is to give an up-to-date presentation of the theory of separation of variables and its relation to superintegrability. Collating and presenting it in a unified, updated and a more accessible manner, the results scattered in the literature that the authors have prepared is an invaluable resource for mathematicians and mathematical physicists in particular, as well as science, engineering, geological and biological researchers interested in explicit solutions.

Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion

NASA Astrophysics Data System (ADS)

Zhang, Wei-Guo; Li, Zhe; Liu, Yong-Jun

2018-01-01

In this paper, we study the pricing problem of the continuously monitored fixed and floating strike geometric Asian power options in a mixed fractional Brownian motion environment. First, we derive both closed-form solutions and mixed fractional partial differential equations for fixed and floating strike geometric Asian power options based on delta-hedging strategy and partial differential equation method. Second, we present the lower and upper bounds of the prices of fixed and floating strike geometric Asian power options under the assumption that both risk-free interest rate and volatility are interval numbers. Finally, numerical studies are performed to illustrate the performance of our proposed pricing model.

Second-order oriented partial-differential equations for denoising in electronic-speckle-pattern interferometry fringes.

PubMed

Tang, Chen; Han, Lin; Ren, Hongwei; Zhou, Dongjian; Chang, Yiming; Wang, Xiaohang; Cui, Xiaolong

2008-10-01

We derive the second-order oriented partial-differential equations (PDEs) for denoising in electronic-speckle-pattern interferometry fringe patterns from two points of view. The first is based on variational methods, and the second is based on controlling diffusion direction. Our oriented PDE models make the diffusion along only the fringe orientation. The main advantage of our filtering method, based on oriented PDE models, is that it is very easy to implement compared with the published filtering methods along the fringe orientation. We demonstrate the performance of our oriented PDE models via application to two computer-simulated and experimentally obtained speckle fringes and compare with related PDE models.

A note on the accuracy of spectral method applied to nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

Spectral methods in time for a class of parabolic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ierley, G.; Spencer, B.; Worthing, R.

1992-09-01

In this paper, we introduce a fully spectral solution for the partial differential equation u[sub t] + uu[sub x] + vu[sub xx] + [mu]u[sub xxx] + [lambda]u[sub xxxx] = O. For periodic boundary conditions in space, the use of a Fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a Chebyshev series. Boundary conditions other than periodic may still be treated with reasonable, though lesser, efficiency. for all cases, very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time.more » 14 refs., 9 figs.« less

Differential Facial Responses to Four Basic Tastes in Newborns.

ERIC Educational Resources Information Center

Rosentstein, Diana; Oster, Harriet

1988-01-01

Investigated the distinctiveness and recognizability of taste-elicited facial expressions in 12 newborns two hours of age. Findings demonstrated that newborns differentiate sour and bitter from each other and from salty, and discriminate between sweet and nonsweet. Judges accurately identified newborns' responses to sucrose, but systematically…

Differential formulation of the gyrokinetic Landau operator

DOE PAGES

Hirvijoki, Eero; Brizard, Alain J.; Pfefferlé, David

2017-01-05

Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this work investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Finally, based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.

Complex partial status epilepticus: a recurrent problem.

PubMed Central

Cockerell, O C; Walker, M C; Sander, J W; Shorvon, S D

1994-01-01

Twenty patients with complex partial status epilepticus were identified retrospectively from a specialist neurology hospital. Seventeen patients experienced recurrent episodes of complex partial status epilepticus, often occurring at regular intervals, usually over many years, and while being treated with effective anti-epileptic drugs. No unifying cause for the recurrences, and no common epilepsy aetiologies, were identified. In spite of the frequency of recurrence and length of history, none of the patients showed any marked evidence of cognitive or neurological deterioration. Complex partial status epilepticus is more common than is generally recognised, should be differentiated from other forms of non-convulsive status, and is often difficult to treat. PMID:8021671

Lactobacillus strain diversity based on partial hsp60 gene sequences and design of PCR-restriction fragment length polymorphism assays for species identification and differentiation.

PubMed

Blaiotta, Giuseppe; Fusco, Vincenzina; Ercolini, Danilo; Aponte, Maria; Pepe, Olimpia; Villani, Francesco

2008-01-01

A phylogenetic tree showing diversities among 116 partial (499-bp) Lactobacillus hsp60 (groEL, encoding a 60-kDa heat shock protein) nucleotide sequences was obtained and compared to those previously described for 16S rRNA and tuf gene sequences. The topology of the tree produced in this study showed a Lactobacillus species distribution similar, but not identical, to those previously reported. However, according to the most recent systematic studies, a clear differentiation of 43 single-species clusters was detected/identified among the sequences analyzed. The slightly higher variability of the hsp60 nucleotide sequences than of the 16S rRNA sequences offers better opportunities to design or develop molecular assays allowing identification and differentiation of either distant or very closely related Lactobacillus species. Therefore, our results suggest that hsp60 can be considered an excellent molecular marker for inferring the taxonomy and phylogeny of members of the genus Lactobacillus and that the chosen primers can be used in a simple PCR procedure allowing the direct sequencing of the hsp60 fragments. Moreover, in this study we performed a computer-aided restriction endonuclease analysis of all 499-bp hsp60 partial sequences and we showed that the PCR-restriction fragment length polymorphism (RFLP) patterns obtainable by using both endonucleases AluI and TacI (in separate reactions) can allow identification and differentiation of all 43 Lactobacillus species considered, with the exception of the pair L. plantarum/L. pentosus. However, the latter species can be differentiated by further analysis with Sau3AI or MseI. The hsp60 PCR-RFLP approach was efficiently applied to identify and to differentiate a total of 110 wild Lactobacillus strains (including closely related species, such as L. casei and L. rhamnosus or L. plantarum and L. pentosus) isolated from cheese and dry-fermented sausages.

Fractional vector calculus and fluid mechanics

NASA Astrophysics Data System (ADS)

Lazopoulos, Konstantinos A.; Lazopoulos, Anastasios K.

2017-04-01

Basic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85-104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy's flow in porous media is studied.

Survival of partially differentiated mouse embryonic stem cells in the scala media of the guinea pig cochlea.

PubMed

Hildebrand, Michael S; Dahl, Hans-Henrik M; Hardman, Jennifer; Coleman, Bryony; Shepherd, Robert K; de Silva, Michelle G

2005-12-01

The low regenerative capacity of the hair cells of the mammalian inner ear is a major obstacle for functional recovery following sensorineural hearing loss. A potential treatment is to replace damaged tissue by transplantation of stem cells. To test this approach, undifferentiated and partially differentiated mouse embryonic stem (ES) cells were delivered into the scala media of the deafened guinea pig cochlea. Transplanted cells survived in the scala media for a postoperative period of at least nine weeks, evidenced by histochemical and direct fluorescent detection of enhanced green fluorescent protein (EGFP). Transplanted cells were discovered near the spiral ligament and stria vascularis in the endolymph fluid of the scala media. In some cases, cells were observed close to the damaged organ of Corti structure. There was no evidence of significant immunological rejection of the implanted ES cells despite the absence of immunosuppression. Our surgical approach allowed efficient delivery of ES cells to the scala media while preserving the delicate structures of the cochlea. This is the first report of the survival of partially differentiated ES cells in the scala media of the mammalian cochlea, and it provides support for the potential of cell-based therapies for sensorineural hearing impairment.

Survival of Partially Differentiated Mouse Embryonic Stem Cells in the Scala Media of the Guinea Pig Cochlea

PubMed Central

Hildebrand, Michael S.; Dahl, Hans-Henrik M.; Hardman, Jennifer; Coleman, Bryony; Shepherd, Robert K.

2005-01-01

The low regenerative capacity of the hair cells of the mammalian inner ear is a major obstacle for functional recovery following sensorineural hearing loss. A potential treatment is to replace damaged tissue by transplantation of stem cells. To test this approach, undifferentiated and partially differentiated mouse embryonic stem (ES) cells were delivered into the scala media of the deafened guinea pig cochlea. Transplanted cells survived in the scala media for a postoperative period of at least nine weeks, evidenced by histochemical and direct fluorescent detection of enhanced green fluorescent protein (EGFP). Transplanted cells were discovered near the spiral ligament and stria vascularis in the endolymph fluid of the scala media. In some cases, cells were observed close to the damaged organ of Corti structure. There was no evidence of significant immunological rejection of the implanted ES cells despite the absence of immunosuppression. Our surgical approach allowed efficient delivery of ES cells to the scala media while preserving the delicate structures of the cochlea. This is the first report of the survival of partially differentiated ES cells in the scala media of the mammalian cochlea, and it provides support for the potential of cell-based therapies for sensorineural hearing impairment. PMID:16208453

Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.

PubMed

Cooper, F; Hyman, J M; Khare, A

2001-08-01

Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial differential equation from a four-parameter Lagrangian where the nonlinear dispersion gives rise to solitons with compact support (compactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations. The compactons formed from arbitrary initial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapplicability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying the processes beyond integrability. We have found explicit formulas for multiple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compacton is the minimum of a reduced Hamiltonian and is the only one that is stable.

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vidal-Codina, F., E-mail: fvidal@mit.edu; Nguyen, N.C., E-mail: cuongng@mit.edu; Giles, M.B., E-mail: mike.giles@maths.ox.ac.uk

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basismore » approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.« less

NonMarkov Ito Processes with 1- state memory

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2010-08-01

A Markov process, by definition, cannot depend on any previous state other than the last observed state. An Ito process implies the Fokker-Planck and Kolmogorov backward time partial differential eqns. for transition densities, which in turn imply the Chapman-Kolmogorov eqn., but without requiring the Markov condition. We present a class of Ito process superficially resembling Markov processes, but with 1-state memory. In finance, such processes would obey the efficient market hypothesis up through the level of pair correlations. These stochastic processes have been mislabeled in recent literature as 'nonlinear Markov processes'. Inspired by Doob and Feller, who pointed out that the ChapmanKolmogorov eqn. is not restricted to Markov processes, we exhibit a Gaussian Ito transition density with 1-state memory in the drift coefficient that satisfies both of Kolmogorov's partial differential eqns. and also the Chapman-Kolmogorov eqn. In addition, we show that three of the examples from McKean's seminal 1966 paper are also nonMarkov Ito processes. Last, we show that the transition density of the generalized Black-Scholes type partial differential eqn. describes a martingale, and satisfies the ChapmanKolmogorov eqn. This leads to the shortest-known proof that the Green function of the Black-Scholes eqn. with variable diffusion coefficient provides the so-called martingale measure of option pricing.

Differential pathway coupling efficiency of the activated insulin receptor drives signaling selectivity by XMetA, an allosteric partial agonist antibody

USDA-ARS?s Scientific Manuscript database

XMetA, an anti-insulin receptor (IR) monoclonal antibody, is an allosteric partial agonist of the IR. We have previously reported that XMetA activates the “metabolic-biased” Akt kinase signaling pathway while having little or no effect on the “mitogenic” MAPK signaling pathwayof ERK 1/2. To inves...

Differential pathway coupling efficiency of the activated insulin receptor drives signaling selectivity by xmeta, an allosteric partial agonist antibody

USDA-ARS?s Scientific Manuscript database

XMetA, an anti-insulin receptor (IR) monoclonal antibody, is an allosteric partial agonist of the IR. We have previously reported that XMetA activates the “metabolic-biased” Akt kinase signaling pathway while having little or no effect on the “mitogenic” MAPK signaling pathwayof ERK 1/2. To inves...

Law and Foreign Policy: Problems in Intercultural Communications.

ERIC Educational Resources Information Center

Bozeman, Adda B.

The values and norms of Western law are not universally accepted as basic values and norms in other cultures. Therefore, the contractual processes of Western law should not be considered the basic foundation for all foreign policy negotiations. In Western cultures, principles of law are differentiated from other values based on religion, ethics,…

Measuring Individual Differences in Sensitivities to Basic Emotions in Faces

ERIC Educational Resources Information Center

Suzuki, Atsunobu; Hoshino, Takahiro; Shigemasu, Kazuo

2006-01-01

The assessment of individual differences in facial expression recognition is normally required to address two major issues: (1) high agreement level (ceiling effect) and (2) differential difficulty levels across emotions. We propose a new assessment method designed to quantify individual differences in the recognition of the six basic emotions,…

Language Management Theory as One Approach in Language Policy and Planning

ERIC Educational Resources Information Center

Nekvapil, Jirí

2016-01-01

Language Policy and Planning is currently a significantly diversified research area and thus it is not easy to find common denominators that help to define basic approaches within it. Richard B. Baldauf attempted to do so by differentiating between four basic approaches: (1) the classical approach, (2) the language management approach (Language…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mehmood, Rashid; Yasuhara, Noriko; Oe, Souichi

The transition from undifferentiated pluripotent cells to terminally differentiated neurons is coordinated by a repertoire of transcription factors. NeuroD1 is a type II basic helix loop helix (bHLH) transcription factor that plays critical roles in neuronal differentiation and maintenance in the central nervous system. Its dimerization with E47, a type I bHLH transcription factor, leads to the transcriptional regulation of target genes. Mounting evidence suggests that regulating the localization of transcription factors contributes to the regulation of their activity during development as defects in their localization underlie a variety of developmental disorders. In this study, we attempted to understand themore » nuclear import mannerisms of NeuroD1 and E47. We found that the nuclear import of NeuroD1 and E47 is energy-dependent and involves the Ran-mediated pathway. Herein, we demonstrate that NeuroD1 and E47 can dimerize inside the cytoplasm before their nuclear import. Moreover, this dimerization promotes nuclear import as the nuclear accumulation of NeuroD1 was enhanced in the presence of E47 in an in vitro nuclear import assay, and NLS-deficient NeuroD1 was successfully imported into the nucleus upon E47 overexpression. NeuroD1 also had a similar effect on the nuclear accumulation of NLS-deficient E47. These findings suggest a novel role for dimerization that may promote, at least partially, the nuclear import of transcription factors allowing them to function efficiently in the nucleus.« less

Differentiation for Gifted Learners: Going beyond the Basics

ERIC Educational Resources Information Center

Heacox, Diane; Cash, Richard M.

2014-01-01

Within a group of advanced learners, the variety of abilities, talents, interests, and learning styles can be formidable. For the first time, this book connects the unique learning differences among gifted students to the specific teaching methods used to tailor their educational experiences. Differentiated instruction for gifted and talented…

Determining Dissolved Oxygen Levels

ERIC Educational Resources Information Center

Boucher, Randy

2010-01-01

This project was used in a mathematical modeling and introduction to differential equations course for first-year college students. The students worked in two-person groups and were given three weeks to complete the project. Students were given this project three weeks into the course, after basic first order linear differential equation and…

Pipette-based Method to Study Embryoid Body Formation Derived from Mouse and Human Pluripotent Stem Cells Partially Recapitulating Early Embryonic Development Under Simulated Microgravity Conditions

NASA Astrophysics Data System (ADS)

Shinde, Vaibhav; Brungs, Sonja; Hescheler, Jürgen; Hemmersbach, Ruth; Sachinidis, Agapios

2016-06-01

The in vitro differentiation of pluripotent stem cells partially recapitulates early in vivo embryonic development. More recently, embryonic development under the influence of microgravity has become a primary focus of space life sciences. In order to integrate the technique of pluripotent stem cell differentiation with simulated microgravity approaches, the 2-D clinostat compatible pipette-based method was experimentally investigated and adapted for investigating stem cell differentiation processes under simulated microgravity conditions. In order to keep residual accelerations as low as possible during clinorotation, while also guaranteeing enough material for further analysis, stem cells were exposed in 1-mL pipettes with a diameter of 3.5 mm. The differentiation of mouse and human pluripotent stem cells inside the pipettes resulted in the formation of embryoid bodies at normal gravity (1 g) after 24 h and 3 days. Differentiation of the mouse pluripotent stem cells on a 2-D pipette-clinostat for 3 days also resulted in the formation of embryoid bodies. Interestingly, the expression of myosin heavy chain was downregulated when cultivation was continued for an additional 7 days at normal gravity. This paper describes the techniques for culturing and differentiation of pluripotent stem cells and exposure to simulated microgravity during culturing or differentiation on a 2-D pipette clinostat. The implementation of these methodologies along with -omics technologies will contribute to understand the mechanisms regulating how microgravity influences early embryonic development.

Impact of a Differential Learning Approach on Practical Exam Performance: A Controlled Study in a Preclinical Dental Course.

PubMed

Pabel, Sven-Olav; Pabel, Anne-Kathrin; Schmickler, Jan; Schulz, Xenia; Wiegand, Annette

2017-09-01

The aim of this study was to evaluate if differential learning in a preclinical dental course impacted the performance of dental students in a practical exam (preparation of a gold partial crown) immediately after the training session and 20 weeks later compared to conventional learning. This controlled study was performed in a preclinical course in operative dentistry at a dental school in Germany. Third-year students were trained in preparing gold partial crowns by using either the conventional learning (n=41) or the differential learning approach (n=32). The differential learning approach consisted of 20 movement exercises with a continuous change of movement execution during the learning session, while the conventional learning approach was mainly based on repetition, a methodological series of exercises, and correction of preparations during the training phase. Practical exams were performed immediately after the training session (T1) and 20 weeks later (T2, retention test). Preparations were rated by four independent and blinded examiners. At T1, no significant difference between the performance (exam passed) of the two groups was detected (conventional learning: 54.3%, differential learning: 68.0%). At T2, significantly more students passed the exam when trained by the differential learning approach (68.8%) than by the conventional learning approach (18.9%). Interrater reliability was moderate (Kappa: 0.57, T1) or substantial (Kappa: 0.67, T2), respectively. These results suggest that a differential learning approach can increase the manual skills of dental students.

Differential geometry based solvation model. III. Quantum formulation

PubMed Central

Chen, Zhan; Wei, Guo-Wei

2011-01-01

Solvation is of fundamental importance to biomolecular systems. Implicit solvent models, particularly those based on the Poisson-Boltzmann equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces are commonly used in the implicit solvent theory. Recently, we have introduced differential geometry based solvation models which allow the solvent-solute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the Euler-Lagrange variation, we derive a system of three coupled governing equations, i.e., the generalized Poisson-Boltzmann equation for the electrostatic potential, the generalized Laplace-Beltrami equation for the solvent-solute boundary, and the Kohn-Sham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model. PMID:22112067

A theory of fine structure image models with an application to detection and classification of dementia

PubMed Central

Penn, Richard; Werner, Michael; Thomas, Justin

2015-01-01

Background Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. Methods In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. Results We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Conclusions Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible. PMID:26029638

Differential gene expression in the siphonophore Nanomia bijuga (Cnidaria) assessed with multiple next-generation sequencing workflows.

PubMed

Siebert, Stefan; Robinson, Mark D; Tintori, Sophia C; Goetz, Freya; Helm, Rebecca R; Smith, Stephen A; Shaner, Nathan; Haddock, Steven H D; Dunn, Casey W

2011-01-01

We investigated differential gene expression between functionally specialized feeding polyps and swimming medusae in the siphonophore Nanomia bijuga (Cnidaria) with a hybrid long-read/short-read sequencing strategy. We assembled a set of partial gene reference sequences from long-read data (Roche 454), and generated short-read sequences from replicated tissue samples that were mapped to the references to quantify expression. We collected and compared expression data with three short-read expression workflows that differ in sample preparation, sequencing technology, and mapping tools. These workflows were Illumina mRNA-Seq, which generates sequence reads from random locations along each transcript, and two tag-based approaches, SOLiD SAGE and Helicos DGE, which generate reads from particular tag sites. Differences in expression results across workflows were mostly due to the differential impact of missing data in the partial reference sequences. When all 454-derived gene reference sequences were considered, Illumina mRNA-Seq detected more than twice as many differentially expressed (DE) reference sequences as the tag-based workflows. This discrepancy was largely due to missing tag sites in the partial reference that led to false negatives in the tag-based workflows. When only the subset of reference sequences that unambiguously have tag sites was considered, we found broad congruence across workflows, and they all identified a similar set of DE sequences. Our results are promising in several regards for gene expression studies in non-model organisms. First, we demonstrate that a hybrid long-read/short-read sequencing strategy is an effective way to collect gene expression data when an annotated genome sequence is not available. Second, our replicated sampling indicates that expression profiles are highly consistent across field-collected animals in this case. Third, the impacts of partial reference sequences on the ability to detect DE can be mitigated through workflow choice and deeper reference sequencing.

Differential Gene Expression in the Siphonophore Nanomia bijuga (Cnidaria) Assessed with Multiple Next-Generation Sequencing Workflows

PubMed Central

Siebert, Stefan; Robinson, Mark D.; Tintori, Sophia C.; Goetz, Freya; Helm, Rebecca R.; Smith, Stephen A.; Shaner, Nathan; Haddock, Steven H. D.; Dunn, Casey W.

2011-01-01

We investigated differential gene expression between functionally specialized feeding polyps and swimming medusae in the siphonophore Nanomia bijuga (Cnidaria) with a hybrid long-read/short-read sequencing strategy. We assembled a set of partial gene reference sequences from long-read data (Roche 454), and generated short-read sequences from replicated tissue samples that were mapped to the references to quantify expression. We collected and compared expression data with three short-read expression workflows that differ in sample preparation, sequencing technology, and mapping tools. These workflows were Illumina mRNA-Seq, which generates sequence reads from random locations along each transcript, and two tag-based approaches, SOLiD SAGE and Helicos DGE, which generate reads from particular tag sites. Differences in expression results across workflows were mostly due to the differential impact of missing data in the partial reference sequences. When all 454-derived gene reference sequences were considered, Illumina mRNA-Seq detected more than twice as many differentially expressed (DE) reference sequences as the tag-based workflows. This discrepancy was largely due to missing tag sites in the partial reference that led to false negatives in the tag-based workflows. When only the subset of reference sequences that unambiguously have tag sites was considered, we found broad congruence across workflows, and they all identified a similar set of DE sequences. Our results are promising in several regards for gene expression studies in non-model organisms. First, we demonstrate that a hybrid long-read/short-read sequencing strategy is an effective way to collect gene expression data when an annotated genome sequence is not available. Second, our replicated sampling indicates that expression profiles are highly consistent across field-collected animals in this case. Third, the impacts of partial reference sequences on the ability to detect DE can be mitigated through workflow choice and deeper reference sequencing. PMID:21829563

GRHL3/GET1 and Trithorax Group Members Collaborate to Activate the Epidermal Progenitor Differentiation Program

PubMed Central

Hopkin, Amelia Soto; Gordon, William; Klein, Rachel Herndon; Espitia, Francisco; Daily, Kenneth; Zeller, Michael; Baldi, Pierre; Andersen, Bogi

2012-01-01

The antagonistic actions of Polycomb and Trithorax are responsible for proper cell fate determination in mammalian tissues. In the epidermis, a self-renewing epithelium, previous work has shown that release from Polycomb repression only partially explains differentiation gene activation. We now show that Trithorax is also a key regulator of epidermal differentiation, not only through activation of genes repressed by Polycomb in progenitor cells, but also through activation of genes independent of regulation by Polycomb. The differentiation associated transcription factor GRHL3/GET1 recruits the ubiquitously expressed Trithorax complex to a subset of differentiation genes. PMID:22829784

Basic results on the equations of magnetohydrodynamics of partially ionized inviscid plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nunez, Manuel

2009-10-15

The equations of evolution of partially ionized plasmas have been far more studied in one of their many simplifications than in its original form. They present a relation between the velocity of each species, plus the magnetic and electric fields, which yield as an analog of Ohm's law a certain elliptic equation. Therefore, the equations represent a functional evolution system, not a classical one. Nonetheless, a priori estimates and theorems of existence may be obtained in appropriate Sobolev spaces.

Autonomy support, basic psychological needs and well-being in Mexican athletes.

PubMed

López-Walle, Jeanette; Balaguer, Isabel; Castillo, Isabel; Tristán, José

2012-11-01

Based on Basic Needs Theory, one of the mini-theories of Self-determination Theory (Ryan & Deci, 2002), the present study had two objectives: (a) to test a model in the Mexican sport context based on the following sequence: perceived coach autonomy support, basic psychological needs satisfaction, and psychological well-being, and b) to analyze the mediational effect of the satisfaction of perceived coach autonomy support on indicators of psychological well-being (satisfaction with life and subjective vitality). Six hundred and sixty-nine young Mexican athletes (Boys = 339; Girls = 330; M(age) = 13.95) filled out a questionnaire assessing the study variables. Structural equations analyses revealed that perceived coach autonomy support predicted satisfaction of the basic psychological needs for autonomy, competence, and relatedness. Furthermore, basic need satisfaction predicted subjective vitality and satisfaction with life. Autonomy, competence and relatedness partially mediated the path from perceived coach autonomy support to psychological well-being in young Mexican athletes.

Population response of the northern red-backed vole (Clethrionomys rutilus) to differentially cut white spruce forest.

Treesearch

Stephen D. West; R. Glenn Ford; John C. Zasada

1980-01-01

The population response of the northern red-backed vole (Clethrionomys rutilus) to a differentially cut white spruce (Picea glauca) forest 30 km southwest of Fairbanks, Alaska, was monitored by simultaneous livetrapping in a clearcut, in a partially cut or shelterwood area, and in an area of uncut forest. During the first...

Solution of Poisson's Equation with Global, Local and Nonlocal Boundary Conditions

ERIC Educational Resources Information Center

Aliev, Nihan; Jahanshahi, Mohammad

2002-01-01

Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…

Direct Shear Failure in Reinforced Concrete Beams under Impulsive Loading

DTIC Science & Technology

1983-09-01

115 References ............... ............................. 119 Tables . ............................. 124 Figures ............ 1..............30...8217. : = differentiable functions of time 1 = elastic modulus enhancement function 4) 41’ = constants for a given mode W’, = frequency w tfirst thickness-shear...are defined by linear partial differential equations. The analytic results are compared to data gathered on one-way slabs loaded with impulsive blast

A Probabilistic-Numerical Approximation for an Obstacle Problem Arising in Game Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gruen, Christine, E-mail: christine.gruen@univ-brest.fr

We investigate a two-player zero-sum stochastic differential game in which one of the players has more information on the game than his opponent. We show how to construct numerical schemes for the value function of this game, which is given by the solution of a quasilinear partial differential equation with obstacle.

Steam tables for pure water as an ActiveX component in Visual Basic 6.0

NASA Astrophysics Data System (ADS)

Verma, Mahendra P.

2003-11-01

The IAPWS-95 formulation for the thermodynamic properties of pure water was implemented as an ActiveX component ( SteamTables) in Visual Basic 6.0. For input parameters as temperature ( T=190-2000 K) and pressure ( P=3.23×10 -8-10,000 MPa) the program SteamTables calculates the following properties: volume ( V), density ( D), compressibility factor ( Z0), internal energy ( U), enthalpy ( H), Gibbs free energy ( G), Helmholtz free energy ( A), entropy ( S), heat capacity at constant pressure ( Cp), heat capacity at constant volume ( Cv), coefficient of thermal expansion ( CTE), isothermal compressibility ( Ziso), velocity of sound ( VelS), partial derivative of P with T at constant V (d Pd T), partial derivative of T with V at constant P (d Td V), partial derivative of V with P at constant T (d Vd P), Joule-Thomson coefficient ( JTC), isothermal throttling coefficient ( IJTC), viscosity ( Vis), thermal conductivity ( ThrmCond), surface tension ( SurfTen), Prandtl number ( PrdNum) and dielectric constant ( DielCons) for the liquid and vapor phases of pure water. It also calculates T as a function of P (or P as a function of T) along the sublimation, saturation and critical isochor curves, depending on the values of P (or T). The SteamTables can be incorporated in a program in any computer language, which supports object link embedding (OLE) in the Windows environment. An application of SteamTables is illustrated in a program in Visual Basic 6.0 to tabulate the values of the thermodynamic properties of water and vapor. Similarly, four functions, Temperature(Press), Pressure(Temp), State(Temp, Press) and WtrStmTbls(Temp, Press, Nphs, Nprop), where Temp, Press, Nphs and Nprop are temperature, pressure, phase number and property number, respectively, are written in Visual Basic for Applications (VBA) to use the SteamTables in a workbook in MS-Excel.

Validity of GNRB® arthrometer compared to Telos™ in the assessment of partial anterior cruciate ligament tears.

PubMed

Lefevre, N; Bohu, Y; Naouri, J F; Klouche, S; Herman, S

2014-02-01

The main goal of this study was to compare the results of the GNRB(®) arthrometer to those of Telos™ in the diagnosis of partial thickness tears of the anterior cruciate ligament (ACL). A prospective study performed January-December 2011 included all patients presenting with a partial or full-thickness ACL tears without ACL reconstruction and with a healthy contralateral knee. Anterior laxity was measured in all patients by the Telos™ and GNRB(®) devices. This series included 139 patients, mean age 30.7 ± 9.3 years. Arthroscopic reconstruction was performed in 109 patients, 97 for complete tears and 12 single bundle reconstructions for partial thickness tears. Conservative treatment was proposed in 30 patients with a partial thickness tear. The correlation between the two devices was evaluated by the Spearman coefficient. The optimal laxity thresholds were determined with ROC curves, and the diagnostic value of the tests was assessed by the area under the curve (AUC). The differential laxities of full and partial thickness tears were significantly different with the two tests. The correlation between the results of laxity measurement with the two devices was fair, with the strongest correlation between Telos™ 250 N and GNRB(®) 250 N (r = 0.46, p = 0.00001). Evaluation of the AUC showed that the informative value of all tests was fair with the best results with the GNRB(®) 250 N: AUC = 0.89 [95 % CI 0.83-0.94]. The optimal differential laxity threshold with the GNRB(®) 250 N was 2.5 mm (Se = 84 %, Sp = 81 %). The diagnostic value of GNRB(®) was better than Telos™ for ACL partial thickness tears.

Multigrid Methods

NASA Technical Reports Server (NTRS)

1981-01-01

Developments in numerical solution of certain types of partial differential equations by rapidly converging sequences of operations on supporting grids that range from very fine to very coarse are presented.

Grid generation by elliptic partial differential equations for a tri-element Augmentor-Wing airfoil

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1982-01-01

Two efforts to numerically simulate the flow about the Augmentor-Wing airfoil in the cruise configuration using the GRAPE elliptic partial differential equation grid generator algorithm are discussed. The Augmentor-Wing consists of a main airfoil with a slotted trailing edge for blowing and two smaller airfoils shrouding the blowing jet. The airfoil and the algorithm are described, and the application of GRAPE to an unsteady viscous flow simulation and a transonic full-potential approach is considered. The procedure involves dividing a complicated flow region into an arbitrary number of zones and ensuring continuity of grid lines, their slopes, and their point distributions across the zonal boundaries. The method for distributing the body-surface grid points is discussed.

Towards developing robust algorithms for solving partial differential equations on MIMD machines

NASA Technical Reports Server (NTRS)

Saltz, Joel H.; Naik, Vijay K.

1988-01-01

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Learning partial differential equations via data discovery and sparse optimization

NASA Astrophysics Data System (ADS)

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Towards developing robust algorithms for solving partial differential equations on MIMD machines

NASA Technical Reports Server (NTRS)

Saltz, J. H.; Naik, V. K.

1985-01-01

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part II: Application to Partial Differential Equations

DOE PAGES

Pawlowski, Roger P.; Phipps, Eric T.; Salinger, Andrew G.; ...

2012-01-01

A template-based generic programming approach was presented in Part I of this series of papers [Sci. Program. 20 (2012), 197–219] that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertaintymore » quantification results for a 3D PDE application.« less

An ansatz for solving nonlinear partial differential equations in mathematical physics.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd

2016-01-01

In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

Learning partial differential equations via data discovery and sparse optimization.

PubMed

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Learning partial differential equations via data discovery and sparse optimization

PubMed Central

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection. PMID:28265183

Proceedings of the Dundee Conference (10th) Held in Dundee, Scotland on July 1988. Ordinary and Partial Differential Equations. Volume 2

DTIC Science & Technology

1988-07-01

a priori inequalities with applications to R J Knops boundary value problems 40 Singular systems of differential equations V G Sigiilito S L...Stochastic functional differential equations S E A Mohammed 100 Optimal control of variational inequalities 125 Ennio de Giorgi Colloquium V Barbu P Kr e...location of the period-doubled bifurcation point varies slightly with Zc [ 3 ]. In addition, no significant effect is found if a smoother functional

DOE Office of Scientific and Technical Information (OSTI.GOV)

Isa, Sharena Mohamad; Ali, Anati

In this paper, the hydromagnetic flow of dusty fluid over a vertical stretching sheet with thermal radiation is investigated. The governing partial differential equations are reduced to nonlinear ordinary differential equations using similarity transformation. These nonlinear ordinary differential equations are solved numerically using Runge-Kutta Fehlberg fourth-fifth order method (RKF45 Method). The behavior of velocity and temperature profiles of hydromagnetic fluid flow of dusty fluid is analyzed and discussed for different parameters of interest such as unsteady parameter, fluid-particle interaction parameter, the magnetic parameter, radiation parameter and Prandtl number on the flow.

Heat transfer in a micropolar fluid over a stretching sheet with Newtonian heating.

PubMed

Qasim, Muhammad; Khan, Ilyas; Shafie, Sharidan

2013-01-01

This article looks at the steady flow of Micropolar fluid over a stretching surface with heat transfer in the presence of Newtonian heating. The relevant partial differential equations have been reduced to ordinary differential equations. The reduced ordinary differential equation system has been numerically solved by Runge-Kutta-Fehlberg fourth-fifth order method. Influence of different involved parameters on dimensionless velocity, microrotation and temperature is examined. An excellent agreement is found between the present and previous limiting results.

[Differential diagnosis of chronic myeloic leucemia in infancy (author's transl)].

PubMed

Binder, C; Pichler, E; Radaskiewicz, T; Scheibenreiter, S

1976-01-01

A 3 months old girl presented with significant enlargement of liver, spleen and lymphnodes, with moderate anemia, thrombopenia and leucocytosis. In the differential count there was a shift to the left and an increase of monocyte-like cells (35%). Differential diagnosis included leucemoid reaction, infectious mononucleosis, myelo-proliferative disorder with a missing C chromosome and chronic myeloid leucemia. Clinical symptoms, cytochemistry and caryotype of bone marrow cells suggested infantile chronic myeloic leucemia and normal ALP index and possibly normal HbF. Treatment with 6-mercaptopurine was followed by partial remission. The therapeutic consequences of exact differential diagnosis are discussed.

Social Concepts and Judgments: A Semantic Differential Analysis of the Concepts Feminist, Man, and Woman

ERIC Educational Resources Information Center

Pierce, W. David; Sydie, R. A.; Stratkotter, Rainer

2003-01-01

Male and female participants (N = 274) made judgments about the social concepts of "feminist," "man," and "woman" on 63 semantic differential items. Factor analysis identified three basic dimensions termed evaluative, potency, and activity as well as two secondary factors called expressiveness and sexuality. Results for the evaluative dimension…

The evolution of the moon and the terrestrial planets

NASA Technical Reports Server (NTRS)

Toksoez, M. N.; Johnston, D. H.

1974-01-01

The thermal evolutions of the Moon, Mars, Venus and Mercury are calculated theoretically starting from cosmochemical condensation models. An assortment of geological, geochemical and geophysical data are used to constrain both the present day temperatures and the thermal histories of the planets' interiors. Such data imply that the planets were heated during or shortly after formation and that all the terrestrial planets started their differentiations early in their history. The moon, smallest in size, is characterized as a differentiated body with a crust, a thick solid mantle and an interior region which may be partially molten. Mars, intermediate in size, is assumed to have differentiated an Fe-FeS core. Venus is characterized as a planet not unlike the earth in many respects. Core formation has occurred probably during the first billion years after the formation. Mercury, which probably has a large core, may have a 500 km thick solid lithosphere and a partially molten core if it is assumed that some heat sources exist in the core.

Period of vibration of axially vibrating truly nonlinear rod

NASA Astrophysics Data System (ADS)

Cveticanin, L.

2016-07-01

In this paper the axial vibration of a muscle whose fibers are parallel to the direction of muscle compression is investigated. The model is a clamped-free rod with a strongly nonlinear elastic property. Axial vibration is described by a nonlinear partial differential equation. A solution of the equation is constructed for special initial conditions by using the method of separation of variables. The partial differential equation is separated into two uncoupled strongly nonlinear second order differential equations. Both equations, with displacement function and with time function are exactly determined. Exact solutions are given in the form of inverse incomplete and inverse complete Beta function. Using boundary and initial conditions, the frequency of vibration is obtained. It has to be mentioned that the determined frequency represents the exact analytic description for the axially vibrating truly nonlinear clamped-free rod. The procedure suggested in this paper is applied for calculation of the frequency of the longissimus dorsi muscle of a cow. The influence of elasticity order and elasticity coefficient on the frequency property is tested.

Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2013-12-01

The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.

The Programming Language Python In Earth System Simulations

NASA Astrophysics Data System (ADS)

Gross, L.; Imranullah, A.; Mora, P.; Saez, E.; Smillie, J.; Wang, C.

2004-12-01

Mathematical models in earth sciences base on the solution of systems of coupled, non-linear, time-dependent partial differential equations (PDEs). The spatial and time-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

Compensation of Emergency Medical Technician (EMT)-Basics and Paramedics.

PubMed

Studnek, Jonathan R

2016-12-01

The objective of this paper is to identify factors associated with compensation for Emergency Medical Technician (EMT)-Basics and Paramedics and assess whether these associations have changed over the period 1999-2008. Data obtained from the Longitudinal EMT Attributes and Demographic Study (LEADS) surveys, a mail survey of a random, stratified sample of nationally certified EMT-Basics and Paramedics, were analyzed. For the 1999-2003 period, analyses included all respondents providing Emergency Medical Services (EMS). With the addition of a survey in 2004 about volunteers, it was possible to exclude volunteers from these analyses. Over 60% of EMT-Basics reported being either compensated or noncompensated volunteers in the 2004-2008 period. This was substantially and significantly greater than the proportion of EMT-Paramedic volunteers (<25%). The EMT-Paramedics earned significantly more than EMT-Basics, with differentials of $11,000-$18,000 over the course of the study. The major source of earnings disparity was type of organization: respondents employed by fire-based EMS agencies reported significantly higher earnings than other respondents, at both the EMT-Basic and EMT-Paramedic levels. Males also earned significantly more than females, with annual earnings differentials ranging from $7,000 to $15,000. There are a number of factors associated with compensation disparities within the EMS profession. These include type of service (ie, fire-based vs. other types of agencies) and gender. The reasons for these disparities warrant further investigation. Studnek JR . Compensation of Emergency Medical Technician (EMT)-Basics and Paramedics. Prehosp Disaster Med. 2016;31(Suppl. 1):s87-s95.

42 CFR 418.76 - Condition of participation: Hospice aide and homemaker services.

Code of Federal Regulations, 2010 CFR

2010-10-01

... following basic checklist: (A) Bed bath. (B) Sponge, tub, and shower bath. (C) Hair shampoo (sink, tub, and... professionals and volunteers). (3) Had been subjected to an extended (or partial extended) survey as a result of...

42 CFR 418.76 - Condition of participation: Hospice aide and homemaker services.

Code of Federal Regulations, 2012 CFR

2012-10-01

... following basic checklist: (A) Bed bath. (B) Sponge, tub, and shower bath. (C) Hair shampoo (sink, tub, and... professionals and volunteers). (3) Had been subjected to an extended (or partial extended) survey as a result of...

42 CFR 418.76 - Condition of participation: Hospice aide and homemaker services.

Code of Federal Regulations, 2011 CFR

2011-10-01

... following basic checklist: (A) Bed bath. (B) Sponge, tub, and shower bath. (C) Hair shampoo (sink, tub, and... professionals and volunteers). (3) Had been subjected to an extended (or partial extended) survey as a result of...

42 CFR 418.76 - Condition of participation: Hospice aide and homemaker services.

Code of Federal Regulations, 2014 CFR

2014-10-01

... following basic checklist: (A) Bed bath. (B) Sponge, tub, and shower bath. (C) Hair shampoo (sink, tub, and... professionals and volunteers). (3) Had been subjected to an extended (or partial extended) survey as a result of...

42 CFR 418.76 - Condition of participation: Hospice aide and homemaker services.

Code of Federal Regulations, 2013 CFR

2013-10-01

... following basic checklist: (A) Bed bath. (B) Sponge, tub, and shower bath. (C) Hair shampoo (sink, tub, and... professionals and volunteers). (3) Had been subjected to an extended (or partial extended) survey as a result of...

Metabolism of two Go alpha isoforms in neuronal cells during differentiation.

PubMed

Brabet, P; Pantaloni, C; Bockaert, J; Homburger, V

1991-07-15

We have previously shown that undifferentiated N1E-115 neuroblastoma cells express only one isoform of Go alpha (pI = 5.8), whereas differentiated neuroblastoma cells expressed, in addition to this isoform, another Go alpha with a more acidic pI (5.55). Moreover, primary cultures of cerebellar granule cells, which are extremely well differentiated cells yielding a high density of synapses, expressed only a single Go alpha isoform with a pI of 5.55 (Brabet, P., Pantaloni, C., Rodriguez Martinez, J., Bockaert, J., and Homburger, V. (1990) J. Neurochem. 54, 1310-1320). In this report, using biosynthetic labeling with [35S]methionine and specific quantitative immunoprecipitation with a polyclonal antibody raised against the purified Go alpha protein, we have determined 1) the degradation rate of total Go alpha (sum of the two isoforms) in differentiated as well as in undifferentiated neuroblastoma cells and in cerebellar granule cells, 2) the degradation rates of each isoform in differentiated neuroblastoma cells. The t 1/2 for total Go alpha protein degradation was very different in the three neuronal cell populations and was 28 +/- 5 h (n = 5), 58 +/- 9 h (n = 5), and 154 +/- 22 h (n = 6) in undifferentiated, differentiated neuroblastoma, and granule cells, respectively. Using two-dimensional gel analysis of immunoprecipitates, we have also determined the individual t 1/2 for degradation of each Go alpha isoform in differentiated neuroblastoma cells, in which the two Go alpha isoforms were expressed. Results indicated that the two Go alpha isoforms exhibit similar t1/2 for degradation (49 +/- 5 h, n = 3). Thus, the t1/2 for degradation of the more basic Go alpha isoform is higher in differentiated neuroblastoma cells (49 +/- 5 h, n = 3) than in undifferentiated neuroblastoma cells (28 +/- 5 h, n = 5) which expressed only the more basic Go alpha isoform. It can be concluded that the degradation rate of the more basic Go alpha isoform is not a characteristic of the protein itself but depends on the state of the cell differentiation. The comparison between the t1/2 for degradation of the more acidic Go alpha isoform is differentiated neuroblastoma cells (51 +/- 6 h, n = 3) with that of cerebellar granule cells (154 +/- 22 h, n = 6) suggests that there is also a decrease in the degradation rate of the more acidic Go alpha isoform during differentiation.(ABSTRACT TRUNCATED AT 400 WORDS)

Polytomous Differential Item Functioning and Violations of Ordering of the Expected Latent Trait by the Raw Score

ERIC Educational Resources Information Center

DeMars, Christine E.

2008-01-01

The graded response (GR) and generalized partial credit (GPC) models do not imply that examinees ordered by raw observed score will necessarily be ordered on the expected value of the latent trait (OEL). Factors were manipulated to assess whether increased violations of OEL also produced increased Type I error rates in differential item…

Early differentiation of the Moon: Experimental and modeling studies

NASA Technical Reports Server (NTRS)

Longhi, J.

1986-01-01

Major accomplishments include the mapping out of liquidus boundaries of lunar and meteoritic basalts at low pressure; the refinement of computer models that simulate low pressure fractional crystallization; the development of a computer model to calculate high pressure partial melting of the lunar and Martian interiors; and the proposal of a hypothesis of early lunar differentiation based upon terrestrial analogs.

On the Well-Definedness of the Order of an Ordinary Differential Equation

ERIC Educational Resources Information Center

Dobbs, David E.

2006-01-01

It is proved that if the differential equations "y[(n)] = f(x,y,y[prime],...,y[(n-1)])" and "y[(m)] = g(x,y,y[prime],...,y[(m-1)])" have the same particular solutions in a suitable region where "f" and "g" are continuous real-valued functions with continuous partial derivatives (alternatively, continuous functions satisfying the classical…

Portent of Heine's Reciprocal Square Root Identity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cohl, H W

Precise efforts in theoretical astrophysics are needed to fully understand the mechanisms that govern the structure, stability, dynamics, formation, and evolution of differentially rotating stars. Direct computation of the physical attributes of a star can be facilitated by the use of highly compact azimuthal and separation angle Fourier formulations of the Green's functions for the linear partial differential equations of mathematical physics.

A Multilevel Algorithm for the Solution of Second Order Elliptic Differential Equations on Sparse Grids

NASA Technical Reports Server (NTRS)

Pflaum, Christoph

1996-01-01

A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.

Multilevel Mediation: Cumulative Contextual Risk, Maternal Differential Treatment, and Children's Behavior within Families

ERIC Educational Resources Information Center

Meunier, Jean Christophe; Boyle, Michael; O'Connor, Thomas G.; Jenkins, Jennifer M.

2013-01-01

This study tests the hypothesis that links between contextual risk and children's outcomes are partially explained by differential parenting. Using multi-informant measurement and including up to four children per family (M[subscript age] = 3.51, SD = 2.38) in a sample of 397 families, indirect effects (through maternal differential…

Bmi1 regulates murine intestinal stem cell proliferation and self-renewal downstream of Notch.

PubMed

López-Arribillaga, Erika; Rodilla, Verónica; Pellegrinet, Luca; Guiu, Jordi; Iglesias, Mar; Roman, Angel Carlos; Gutarra, Susana; González, Susana; Muñoz-Cánoves, Pura; Fernández-Salguero, Pedro; Radtke, Freddy; Bigas, Anna; Espinosa, Lluís

2015-01-01

Genetic data indicate that abrogation of Notch-Rbpj or Wnt-β-catenin pathways results in the loss of the intestinal stem cells (ISCs). However, whether the effect of Notch is direct or due to the aberrant differentiation of the transit-amplifying cells into post-mitotic goblet cells is unknown. To address this issue, we have generated composite tamoxifen-inducible intestine-specific genetic mouse models and analyzed the expression of intestinal differentiation markers. Importantly, we found that activation of β-catenin partially rescues the differentiation phenotype of Rbpj deletion mutants, but not the loss of the ISC compartment. Moreover, we identified Bmi1, which is expressed in the ISC and progenitor compartments, as a gene that is co-regulated by Notch and β-catenin. Loss of Bmi1 resulted in reduced proliferation in the ISC compartment accompanied by p16(INK4a) and p19(ARF) (splice variants of Cdkn2a) accumulation, and increased differentiation to the post-mitotic goblet cell lineage that partially mimics Notch loss-of-function defects. Finally, we provide evidence that Bmi1 contributes to ISC self-renewal. © 2015. Published by The Company of Biologists Ltd.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghafarian, M.; Ariaei, A., E-mail: ariaei@eng.ui.ac.ir

The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique tomore » solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube-beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results.« less

Genomic regions with a history of divergent selection affect fitness of hybrids between two butterfly species.

PubMed

Gompert, Zachariah; Lucas, Lauren K; Nice, Chris C; Fordyce, James A; Forister, Matthew L; Buerkle, C Alex

2012-07-01

Speciation is the process by which reproductively isolated lineages arise, and is one of the fundamental means by which the diversity of life increases. Whereas numerous studies have documented an association between ecological divergence and reproductive isolation, relatively little is known about the role of natural selection in genome divergence during the process of speciation. Here, we use genome-wide DNA sequences and Bayesian models to test the hypothesis that loci under divergent selection between two butterfly species (Lycaeides idas and L. melissa) also affect fitness in an admixed population. Locus-specific measures of genetic differentiation between L. idas and L. melissa and genomic introgression in hybrids varied across the genome. The most differentiated genetic regions were characterized by elevated L. idas ancestry in the admixed population, which occurs in L. idas-like habitat, consistent with the hypothesis that local adaptation contributes to speciation. Moreover, locus-specific measures of genetic differentiation (a metric of divergent selection) were positively associated with extreme genomic introgression (a metric of hybrid fitness). Interestingly, concordance of differentiation and introgression was only partial. We discuss multiple, complementary explanations for this partial concordance. © 2012 The Author(s).

Partial melting of lower oceanic crust gabbro: Constraints from poikilitic clinopyroxene primocrysts

NASA Astrophysics Data System (ADS)

Leuthold, Julien; Lissenberg, C. Johan; O'Driscoll, Brian; Karakas, Ozge; Falloon, Trevor; Klimentyeva, Dina N.; Ulmer, Peter

2018-03-01

Successive magma batches underplate, ascend, stall and erupt along spreading ridges, building the oceanic crust. It is therefore important to understand the processes and conditions under which magma differentiates at mid ocean ridges. Although fractional crystallization is considered to be the dominant mechanism for magma differentiation, open-system igneous complexes also experience Melting-Assimilation-Storage-Hybridization (MASH, Hildreth and Moorbath, 1988) processes. Here, we examine crystal-scale records of partial melting in lower crustal gabbroic cumulates from the slow-spreading Atlantic oceanic ridge (Kane Megamullion; collected with Jason ROV) and the fast-spreading East Pacific Rise (Hess Deep; IODP expedition 345). Clinopyroxene oikocrysts in these gabbros preserve marked intra-crystal geochemical variations that point to crystallization-dissolution episodes of the gabbro eutectic assemblage. Kane Megamullion and Hess Deep clinopyroxene core1 primocrysts and their plagioclase inclusions indicate crystallization from high temperature basalt (>1160 and >1200°C, respectively), close to clinopyroxene saturation temperature (<50% and <25% crystallization). Step-like compatible Cr (and co-varying Al) and incompatible Ti, Zr, Y and rare earth elements (REE) decrease from anhedral core1 to overgrown core2, while Mg# and Sr/Sr* ratios increase. We show that partial resorption textures and geochemical zoning result from partial melting of REE-poor lower oceanic crust gabbroic cumulate (protolith) following intrusion by hot primitive mantle-derived melt, and subsequent overgrowth crystallization (refertilization) from a hybrid melt. In addition, towards the outer rims of crystals, Ti, Zr, Y and the REE strongly increase and Al, Cr, Mg#, Eu/Eu* and Sr/Sr* decrease, suggesting crystallization either from late-stage percolating relatively differentiated melt or from in situ trapped melt. Intrusion of primitive hot reactive melt and percolation of interstitial differentiated melt are two distinct MASH processes in the lower oceanic crust. They are potentially fundamental mechanisms for generating the wide compositional variation observed in mid-ocean ridge basalts. We furthermore propose that such processes operate at both slow- and fast-spreading ocean ridges. Thermal numerical modelling shows that the degree of lower crustal partial melting at slow-spreading ridges can locally increase up to 50%, but the overall crustal melt volume is low (less than ca. 5% of total mantle-derived and crustal melts; ca. 20% in fast-spreading ridges).

Portable Lock-in Amplifier-Based Electrochemical Method to Measure an Array of 64 Sensors for Point-of-Care Applications.

PubMed

Hrdý, Radim; Kynclová, Hana; Klepáčová, Ivana; Bartošík, Martin; Neužil, Pavel

2017-09-05

We present a portable lock-in amplifier-based electrochemical sensing system. The basic unit (cluster) consists of four electrochemical cells (EC), each containing one pseudoreference electrode (PRE) and one working electrode (WE). All four ECs are simultaneously interrogated, each at different frequencies, with square wave pulses superposed on a sawtooth signal for cyclic voltammetry (CV). Lock-in amplification provides independent read-out of four signals, with excellent noise suppression. We expanded a single cluster system into an array of 16 clusters by using electronic switches. The chip with an array of ECs was fabricated using planar technology with a gap between a WE and a PRE of ≈2 μm, which results in partial microelectrode-type behavior. The basic electrode characterization was performed with the model case using a ferricyanide-ferrocyanide redox couple (Fe 2+ /Fe 3+ ) reaction, performing CV and differential pulse voltammetry (DPV). We then used this system to perform cyclic lock-in voltammetry (CLV) to measure concurrently responses of the four ECs. We repeated this method with all 64 ECs on the chip. The standard deviation of a peak oxidation and reduction current in a single channel consisting of 13 ECs was ≈7.46% and ≈5.6%, respectively. The four-EC configuration in each measured spot allows determination of nonperforming ECs and, thus, to eliminate potential false results. This system is built in a portable palm-size format suitable for point-of-care applications. It can perform either individual or multiple measurements of active compounds, such as biomarkers.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).

PubMed

Murase, Kenya

2016-01-01

In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.

Quantum κ-deformed differential geometry and field theory

NASA Astrophysics Data System (ADS)

Mercati, Flavio

2016-03-01

I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

On computing Gröbner bases in rings of differential operators

NASA Astrophysics Data System (ADS)

Ma, Xiaodong; Sun, Yao; Wang, Dingkang

2011-05-01

Insa and Pauer presented a basic theory of Groebner basis for differential operators with coefficients in a commutative ring in 1998, and a criterion was proposed to determine if a set of differential operators is a Groebner basis. In this paper, we will give a new criterion such that Insa and Pauer's criterion could be concluded as a special case and one could compute the Groebner basis more efficiently by this new criterion.

Differential diagnosis of hyperkalemia: an update to a complex problem.

PubMed

Eleftheriadis, T; Leivaditis, K; Antoniadi, G; Liakopoulos, V

2012-10-01

Hyperkalemia is a relative common and sometimes life threatening electorlyte disorder. Although its symptomatic treatment is relatively easy, since precise therapeutic algorithms are available, its differential diagnosis is more complicated. The present review aims to unfold the differential diagnosis of hypekalemia using a pathophysiological, albeit clinically useful, approach. The basic elements of potassium homeostasis are provided, the causes of hyperkalemia are categorized and analysed and finally the required for the diferrential diagnosis laboratory tests are mentioned.

Back to the basics: Birmingham, Alabama, measurement and scale

USGS Publications Warehouse

Handley, L.R.; Lockwood, C.M.; Handley, N.

2005-01-01

Back to the Basics: Birmingham, Alabama is the fourth in a series of workshops that focus on teaching foundational map reading and spatial differentiation skills. It is the second published exercise from the Back to the Basics series developed by the Wetland Education through Maps and Aerial Photography (WETMAAP) Program (see Journal of Geography 103, 5: 226-230). Like its predecessor, the current exercise is modified from the Birmingham Back to the Basics workshop offered during the annual National Council for Geographic Education meeting. The focus of this exercise is on scale and measurement, foundational skills for spatial thinking and analysis. ?? 2005 National Council for Geographic Education.

A systematic literature review of Burgers' equation with recent advances

NASA Astrophysics Data System (ADS)

Bonkile, Mayur P.; Awasthi, Ashish; Lakshmi, C.; Mukundan, Vijitha; Aswin, V. S.

2018-06-01

Even if numerical simulation of the Burgers' equation is well documented in the literature, a detailed literature survey indicates that gaps still exist for comparative discussion regarding the physical and mathematical significance of the Burgers' equation. Recently, an increasing interest has been developed within the scientific community, for studying non-linear convective-diffusive partial differential equations partly due to the tremendous improvement in computational capacity. Burgers' equation whose exact solution is well known, is one of the famous non-linear partial differential equations which is suitable for the analysis of various important areas. A brief historical review of not only the mathematical, but also the physical significance of the solution of Burgers' equation is presented, emphasising current research strategies, and the challenges that remain regarding the accuracy, stability and convergence of various schemes are discussed. One of the objectives of this paper is to discuss the recent developments in mathematical modelling of Burgers' equation and thus open doors for improvement. No claim is made that the content of the paper is new. However, it is a sincere effort to outline the physical and mathematical importance of Burgers' equation in the most simplified ways. We throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary / partial differential equations.

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

PubMed

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Incorporating Conservation Zone Effectiveness for Protecting Biodiversity in Marine Planning

PubMed Central

Makino, Azusa; Klein, Carissa J.; Beger, Maria; Jupiter, Stacy D.; Possingham, Hugh P.

2013-01-01

Establishing different types of conservation zones is becoming commonplace. However, spatial prioritization methods that can accommodate multiple zones are poorly understood in theory and application. It is typically assumed that management regulations across zones have differential levels of effectiveness (“zone effectiveness”) for biodiversity protection, but the influence of zone effectiveness on achieving conservation targets has not yet been explored. Here, we consider the zone effectiveness of three zones: permanent closure, partial protection, and open, for planning for the protection of five different marine habitats in the Vatu-i-Ra Seascape, Fiji. We explore the impact of differential zone effectiveness on the location and costs of conservation priorities. We assume that permanent closure zones are fully effective at protecting all habitats, open zones do not contribute towards the conservation targets and partial protection zones lie between these two extremes. We use four different estimates for zone effectiveness and three different estimates for zone cost of the partial protection zone. To enhance the practical utility of the approach, we also explore how much of each traditional fishing ground can remain open for fishing while still achieving conservation targets. Our results show that all of the high priority areas for permanent closure zones would not be a high priority when the zone effectiveness of the partial protection zone is equal to that of permanent closure zones. When differential zone effectiveness and costs are considered, the resulting marine protected area network consequently increases in size, with more area allocated to permanent closure zones to meet conservation targets. By distributing the loss of fishing opportunity equitably among local communities, we find that 84–88% of each traditional fishing ground can be left open while still meeting conservation targets. Finally, we summarize the steps for developing marine zoning that accounts for zone effectiveness. PMID:24223870

Computation of partially invariant solutions for the Einstein Walker manifolds' identifying equations

NASA Astrophysics Data System (ADS)

Nadjafikhah, Mehdi; Jafari, Mehdi

2013-12-01

In this paper, partially invariant solutions (PISs) method is applied in order to obtain new four-dimensional Einstein Walker manifolds. This method is based on subgroup classification for the symmetry group of partial differential equations (PDEs) and can be regarded as the generalization of the similarity reduction method. For this purpose, those cases of PISs which have the defect structure δ=1 and are resulted from two-dimensional subalgebras are considered in the present paper. Also it is shown that the obtained PISs are distinct from the invariant solutions that obtained by similarity reduction method.

Seismological Signature of Chemical Differentiation of Earth's Upper Mantle

NASA Astrophysics Data System (ADS)

Matsukage, K. N.; Nishihara, Y.; Karato, S.

2004-12-01

Chemical differentiation from a primitive rock (such as pyrolite) to harzburgite due to partial melting and melt extraction is one of the most important mechanisms that causes the chemical heterogeneity in Earth's upper mantle. In this study, we investigate the seismic signature of chemical differentiation that helps mapping chemical heterogeneity in the upper mantle. The relation between chemical differentiation and its seismological signature is not straightforward because a large number of unknown parameters are involved although the seismological observations provide only a few parameters (e.g., VP, VS, QP). Therefore it is critical to identify a small number of parameters by which the gross trend of chemical evolution can be described. The variation in major element composition in natural samples reflect complicated processes that include not only partial melting but also other complex processes (e.g., metasomatism, influx melting). We investigate the seismic velocities of hypothetical but well-defined simple chemical differentiation processes (e.g., partial melting of various pressure conditions, addition of Si-rich melt or fluid), which cover the chemical variation of the natural mantle peridotites with various tectonic settings (mid ocean ridge, island arc and continent). The seismic velocities of the peridotites were calculated to 13 GPa and 1730 K. We obtained two major conclusions. First is that the variations of seismic velocities of upper mantle peridotites can be interpreted in terms of a few distinct parameters. For one class of peridotites which is formed by simple partial melting (e.g. mid-ocean ridges peridotites), seismic velocities can be described in terms of one parameter, namely Mg# (=Mg/(Mg+Fe) atomic ratio). In contrast, some of the peridotites in the continental (cratonic) environment with high silica content and high Mg# need at least two parameters (such as Mg# and Opx# (the volume fraction of orthopyroxene)) are needed to characterize their seismic velocities. Second is the jump of seismic velocity at 300 km in harzburgite that is caused by orthorhombic (opx) to high-pressure monoclinic phase transition in MgSiO3 pyroxene. If opx-rich harzburgite (the maximum content of opx in continental harzburgite is ˜45 vol%) exists at around 300km, the maximum contrast of jump would be 2.5 % for VS and 0.9 % for VP. This phase transition will correspond to the seismological discontinuity around 300km (X-discontinuity).

Differential Reinforcement of Alternative Behavior Increases Resistance to Extinction: Clinical Demonstration, Animal Modeling, and Clinical Test of One Solution

ERIC Educational Resources Information Center

Mace, F. Charles; McComas, Jennifer J.; Mauro, Benjamin C.; Progar, Patrick R.; Taylor, Bridget; Ervin, Ruth; Zangrillo, Amanda N.

2010-01-01

Basic research with pigeons on behavioral momentum suggests that differential reinforcement of alternative behavior (DRA) can increase the resistance of target behavior to change. This finding suggests that clinical applications of DRA may inadvertently increase the persistence of target behavior even as it decreases its frequency. We conducted…

Climate Modeling in the Calculus and Differential Equations Classroom

ERIC Educational Resources Information Center

Kose, Emek; Kunze, Jennifer

2013-01-01

Students in college-level mathematics classes can build the differential equations of an energy balance model of the Earth's climate themselves, from a basic understanding of the background science. Here we use variable albedo and qualitative analysis to find stable and unstable equilibria of such a model, providing a problem or perhaps a…

Back to Basics: Incomplete Knowledge of Differential Object Marking in Spanish Heritage Speakers

ERIC Educational Resources Information Center

Montrul, Silvina; Bowles, Melissa

2009-01-01

The obligatory use of the preposition a with animate, specific direct objects in Spanish ("Juan conoce a Maria" "Juan knows Maria") is a well-known instance of Differential Object Marking (DOM; Torrego, 1998; Leonetti, 2004). Recent studies have documented the loss and/or incomplete acquisition of several grammatical features in Spanish heritage…

Gender Differentials in Returns to Education in Spain

ERIC Educational Resources Information Center

Arrazola, Maria; De Hevia, Jose

2006-01-01

In this article, rates of return to education for men and women have been estimated for the Spanish case, controlling for the biases appearing in the least squares estimation of the basic Mincerian equation. The results show that the returns for women are greater than those for men. The gender differential increases when taking into account the…

"Something You Have to Do"--Why Do Parents of Children with Developmental Disabilities Seek a Differential Diagnosis?

ERIC Educational Resources Information Center

Watson, Shelley L.

2008-01-01

This basic interpretive study addressed the reasons why parents seek a differential diagnosis for their child who has a developmental disability. Fourteen parents were interviewed about why they sought a label for the disabilities of their child. Participants included six parents of children with identified genetic conditions, three parents of…

Overview of Power Quality and Integrated Testing at JSC

NASA Technical Reports Server (NTRS)

Davies, Francis

2018-01-01

This presentation describes the basic philosophy behind integrated testing and partially integrated testing. It lists some well known errors in space systems that were or could have been caught during integrated testing. Two examples of integrated testing at the Johnson Space Center (JSC) are mentioned, and then an overview of two test facilities that do power testing (partially integrated testing) at JSC are presented, with information on the capabilities of each. Finally a list of three projects that has problems caught during power quality or Electromagnetic Interference (EMI) testing is presented.

Lactobacillus Strain Diversity Based on Partial hsp60 Gene Sequences and Design of PCR-Restriction Fragment Length Polymorphism Assays for Species Identification and Differentiation▿ †

PubMed Central

Blaiotta, Giuseppe; Fusco, Vincenzina; Ercolini, Danilo; Aponte, Maria; Pepe, Olimpia; Villani, Francesco

2008-01-01

A phylogenetic tree showing diversities among 116 partial (499-bp) Lactobacillus hsp60 (groEL, encoding a 60-kDa heat shock protein) nucleotide sequences was obtained and compared to those previously described for 16S rRNA and tuf gene sequences. The topology of the tree produced in this study showed a Lactobacillus species distribution similar, but not identical, to those previously reported. However, according to the most recent systematic studies, a clear differentiation of 43 single-species clusters was detected/identified among the sequences analyzed. The slightly higher variability of the hsp60 nucleotide sequences than of the 16S rRNA sequences offers better opportunities to design or develop molecular assays allowing identification and differentiation of either distant or very closely related Lactobacillus species. Therefore, our results suggest that hsp60 can be considered an excellent molecular marker for inferring the taxonomy and phylogeny of members of the genus Lactobacillus and that the chosen primers can be used in a simple PCR procedure allowing the direct sequencing of the hsp60 fragments. Moreover, in this study we performed a computer-aided restriction endonuclease analysis of all 499-bp hsp60 partial sequences and we showed that the PCR-restriction fragment length polymorphism (RFLP) patterns obtainable by using both endonucleases AluI and TacI (in separate reactions) can allow identification and differentiation of all 43 Lactobacillus species considered, with the exception of the pair L. plantarum/L. pentosus. However, the latter species can be differentiated by further analysis with Sau3AI or MseI. The hsp60 PCR-RFLP approach was efficiently applied to identify and to differentiate a total of 110 wild Lactobacillus strains (including closely related species, such as L. casei and L. rhamnosus or L. plantarum and L. pentosus) isolated from cheese and dry-fermented sausages. PMID:17993558

Ion-exchange chromatography: basic principles and application to the partial purification of soluble mammalian prolyl oligopeptidase.

PubMed

Cummins, Philip M; Dowling, Oonagh; O'Connor, Brendan F

2011-01-01

Ion-exchange chromatography (IEC) allows for the separation of ionizable molecules on the basis of differences in charge properties. Its large sample-handling capacity, broad applicability (particularly to proteins and enzymes), moderate cost, powerful resolving ability, and ease of scale-up and automation have led to it becoming one of the most versatile and widely used of all liquid chromatography (LC) techniques. In this chapter, we review the basic principles of IEC, as well as the broader criteria for selecting IEC conditions. By way of further illustration, we outline protocols necessary to partially purify a serine peptidase from bovine whole brain cytosolic fraction, covering crude tissue extract preparation through to partial purification of the target enzyme using anion-exchange chromatography. Protocols for assaying total protein and enzyme activity in both pre- and post-IEC fractions are also described. The target serine peptidase, prolyl oligopeptidase (POP, EC3.4.21.26), is an 80-kDa enzyme with endopeptidase activity towards peptide substrates of ≤30 amino acids. POP is a ubiquitous post-proline cleaving enzyme with particularly high expression levels in the mammalian brain, where it participates in the metabolism of neuroactive peptides and peptide-like hormones (e.g. thyroliberin, gonadotropin-releasing hormone).

A fully Sinc-Galerkin method for Euler-Bernoulli beam models

NASA Technical Reports Server (NTRS)

Smith, R. C.; Bowers, K. L.; Lund, J.

1990-01-01

A fully Sinc-Galerkin method in both space and time is presented for fourth-order time-dependent partial differential equations with fixed and cantilever boundary conditions. The Sinc discretizations for the second-order temporal problem and the fourth-order spatial problems are presented. Alternate formulations for variable parameter fourth-order problems are given which prove to be especially useful when applying the forward techniques to parameter recovery problems. The discrete system which corresponds to the time-dependent partial differential equations of interest are then formulated. Computational issues are discussed and a robust and efficient algorithm for solving the resulting matrix system is outlined. Numerical results which highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.

A framework for simultaneous aerodynamic design optimization in the presence of chaos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Günther, Stefanie, E-mail: stefanie.guenther@scicomp.uni-kl.de; Gauger, Nicolas R.; Wang, Qiqi

Integrating existing solvers for unsteady partial differential equations into a simultaneous optimization method is challenging due to the forward-in-time information propagation of classical time-stepping methods. This paper applies the simultaneous single-step one-shot optimization method to a reformulated unsteady constraint that allows for both forward- and backward-in-time information propagation. Especially in the presence of chaotic and turbulent flow, solving the initial value problem simultaneously with the optimization problem often scales poorly with the time domain length. The new formulation relaxes the initial condition and instead solves a least squares problem for the discrete partial differential equations. This enables efficient one-shot optimizationmore » that is independent of the time domain length, even in the presence of chaos.« less

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

Stencil computations for PDE-based applications with examples from DUNE and hypre

DOE Office of Scientific and Technical Information (OSTI.GOV)

Engwer, C.; Falgout, R. D.; Yang, U. M.

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend themore » software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.« less

Inclusion of exact exchange in the noniterative partial-differential-equation method of electron-molecule scattering - Application to e-N2

NASA Technical Reports Server (NTRS)

Weatherford, C. A.; Onda, K.; Temkin, A.

1985-01-01

The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.

A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

NASA Technical Reports Server (NTRS)

Tzes, Anthony P.; Yurkovich, Stephen; Langer, F. Dieter

1989-01-01

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

Mathematical Analysis and Optimization of Infiltration Processes

NASA Technical Reports Server (NTRS)

Chang, H.-C.; Gottlieb, D.; Marion, M.; Sheldon, B. W.

1997-01-01

A variety of infiltration techniques can be used to fabricate solid materials, particularly composites. In general these processes can be described with at least one time dependent partial differential equation describing the evolution of the solid phase, coupled to one or more partial differential equations describing mass transport through a porous structure. This paper presents a detailed mathematical analysis of a relatively simple set of equations which is used to describe chemical vapor infiltration. The results demonstrate that the process is controlled by only two parameters, alpha and beta. The optimization problem associated with minimizing the infiltration time is also considered. Allowing alpha and beta to vary with time leads to significant reductions in the infiltration time, compared with the conventional case where alpha and beta are treated as constants.

Miscibility, Crystallization, and Rheological Behavior of Solution Casting Poly(3-hydroxybutyrate)/poly(ethylene succinate) Blends Probed by Differential Scanning Calorimetry, Rheology, and Optical Microscope Techniques

NASA Astrophysics Data System (ADS)

Sun, Wei-hua; Qiao, Xiao-ping; Cao, Qi-kun; Liu, Jie-ping

2010-02-01

The miscibility and crystallization of solution casting biodegradable poly(3-hydroxybutyrate)/poly(ethylene succinate) (PHB/PES) blends was investigated by differential scanning calorimetry, rheology, and optical microscopy. The blends showed two glass transition temperatures and a depression of melting temperature of PHB with compositions in phase diagram, which indicated that the blend was partially miscible. The morphology observation supported this result. It was found that the PHB and PES can crystallize simultaneously or upon stepwise depending on the crystallization temperatures and compositions. The spherulite growth rate of PHB increased with increasing of PES content. The influence of compositions on the spherulitic growth rate for the partially miscible polymer blends was discussed.

Stencil computations for PDE-based applications with examples from DUNE and hypre

DOE PAGES

Engwer, C.; Falgout, R. D.; Yang, U. M.

2017-02-24

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend themore » software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.« less

Modeling tree crown dynamics with 3D partial differential equations.

PubMed

Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry

2014-01-01

We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.

Jeffrey fluid effect on free convective over a vertically inclined plate with magnetic field: A numerical approach

NASA Astrophysics Data System (ADS)

Rao, J. Anand; Raju, R. Srinivasa; Bucchaiah, C. D.

2018-05-01

In this work, the effect of magnetohydrodynamic natural or free convective of an incompressible, viscous and electrically conducting non-newtonian Jeffrey fluid over a semi-infinite vertically inclined permeable moving plate embedded in a porous medium in the presence of heat absorption, heat and mass transfer. By using non-dimensional quantities, the fundamental governing non-linear partial differential equations are transformed into linear partial differential equations and these equations together with associated boundary conditions are solved numerically by using versatile, extensively validated, variational finite element method. The sway of important key parameters on hydrodynamic, thermal and concentration boundary layers are examined in detail and the results are shown graphically. Finally the results are compared with the works published previously and found to be excellent agreement.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.

Stable multi-domain spectral penalty methods for fractional partial differential equations

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

Mean field games with congestion

NASA Astrophysics Data System (ADS)

Achdou, Yves; Porretta, Alessio

2018-03-01

We consider a class of systems of time dependent partial differential equations which arise in mean field type models with congestion. The systems couple a backward viscous Hamilton-Jacobi equation and a forward Kolmogorov equation both posed in $(0,T)\\times (\\mathbb{R}^N /\\mathbb{Z}^N)$. Because of congestion and by contrast with simpler cases, the latter system can never be seen as the optimality conditions of an optimal control problem driven by a partial differential equation. The Hamiltonian vanishes as the density tends to $+\\infty$ and may not even be defined in the regions where the density is zero. After giving a suitable definition of weak solutions, we prove the existence and uniqueness results of the latter under rather general assumptions. No restriction is made on the horizon $T$.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

Isostable reduction with applications to time-dependent partial differential equations.

PubMed

Wilson, Dan; Moehlis, Jeff

2016-07-01

Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.

Workload Characterization of CFD Applications Using Partial Differential Equation Solvers

NASA Technical Reports Server (NTRS)

Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)

1998-01-01

Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE solver workloads and high performance computing platforms and is useful for tuning these applications.

Online sequential Monte Carlo smoother for partially observed diffusion processes

NASA Astrophysics Data System (ADS)

Gloaguen, Pierre; Étienne, Marie-Pierre; Le Corff, Sylvain

2018-12-01

This paper introduces a new algorithm to approximate smoothed additive functionals of partially observed diffusion processes. This method relies on a new sequential Monte Carlo method which allows to compute such approximations online, i.e., as the observations are received, and with a computational complexity growing linearly with the number of Monte Carlo samples. The original algorithm cannot be used in the case of partially observed stochastic differential equations since the transition density of the latent data is usually unknown. We prove that it may be extended to partially observed continuous processes by replacing this unknown quantity by an unbiased estimator obtained for instance using general Poisson estimators. This estimator is proved to be consistent and its performance are illustrated using data from two models.

CpG methylation patterns and decitabine treatment response in acute myeloid leukemia cells and normal hematopoietic precursors

PubMed Central

Negrotto, Soledad; Ng, Kwok Peng; Jankowska, Ania M.; Bodo, Juraj; Gopalan, Banu; Guinta, Kathryn; Mulloy, James C.; Hsi, Eric; Maciejewski, Jaroslaw; Saunthararajah, Yogen

2011-01-01

The DNA hypomethylating drug decitabine maintains normal hematopoietic stem cell (HSC) self-renewal but induces terminal differentiation in acute myeloid leukemia (AML) cells. The basis for these contrasting cell-fates, and for selective CpG hypomethylation by decitabine, is poorly understood. Promoter CpGs, with methylation measured by microarray, were classified by the direction of methylation change with normal myeloid maturation. In AML cells, the methylation pattern at maturation-responsive CpG suggested at least partial maturation. Consistent with partial maturation, in gene expression analyses, AML cells expressed high levels of the key lineage-specifying factor CEBPA, but relatively low levels of the key late-differentiation driver CEBPE. In methylation analysis by mass-spectrometry, CEBPE promoter CpG that are usually hypomethylated during granulocyte maturation were significantly hypermethylated in AML cells. Decitabine treatment induced cellular differentiation of AML cells, and the largest methylation decreases were at CpG that are hypomethylated with myeloid maturation, including CEBPE promoter CpG. In contrast, decitabine-treated normal HSC retained immature morphology, and methylation significantly decreased at CpG that are less methylated in immature cells. High expression of lineage-specifying factor and aberrant epigenetic repression of some key late-differentiation genes distinguishes AML cells from normal HSC and could explain the contrasting differentiation and methylation responses to decitabine. PMID:21836612

Phenolic Analysis and Theoretic Design for Chinese Commercial Wines' Authentication.

PubMed

Li, Si-Yu; Zhu, Bao-Qing; Reeves, Malcolm J; Duan, Chang-Qing

2018-01-01

To develop a robust tool for Chinese commercial wines' varietal, regional, and vintage authentication, phenolic compounds in 121 Chinese commercial dry red wines were detected and quantified by using high-performance liquid chromatography triple-quadrupole mass spectrometry (HPLC-QqQ-MS/MS), and differentiation abilities of principal component analysis (PCA), partial least squares discriminant analysis (PLS-DA), and orthogonal partial least squares discriminant analysis (OPLS-DA) were compared. Better than PCA and PLS-DA, OPLS-DA models used to differentiate wines according to their varieties (Cabernet Sauvignon or other varieties), regions (east or west Cabernet Sauvignon wines), and vintages (young or old Cabernet Sauvignon wines) were ideally established. The S-plot provided in OPLS-DA models showed the key phenolic compounds which were both statistically and biochemically significant in sample differentiation. Besides, the potential of the OPLS-DA models in deeper sample differentiating of more detailed regional and vintage information of wines was proved optimistic. On the basis of our results, a promising theoretic design for wine authentication was further proposed for the first time, which might be helpful in practical authentication of more commercial wines. The phenolic data of 121 Chinese commercial dry red wines was processed with different statistical tools for varietal, regional, and vintage differentiation. A promising theoretical design was summarized, which might be helpful for wine authentication in practical situation. © 2017 Institute of Food Technologists®.

Correlation effects in elastic e-N2 scattering

NASA Technical Reports Server (NTRS)

Huo, Winifred M.; Lima, Marco A. P.; Gibson, Thomas L.; Mckoy, Vincent

1987-01-01

The Schwinger multichannel formulation has been applied to study the role of electron correlation in low-energy e-N2 scattering. For the five nonresonant partial-wave channels studied here, angular correlation is found to be much more important than radial correlation. The calculated total and differential cross sections agree well with experiment except for the differential cross sections at 1.5 eV.

Differential regulation of oligodendrocyte markers by glucocorticoids: Post-transcriptional regulation of both proteolipid protein and myelin basic protein and transcriptional regulation of glycerol phosphate dehydrogenase

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumar, S.; Cole, R.; Chiappelli, F.

During neonatal development glucocorticoids potentiate oligodendrocyte differentiation and myelinogenesis by regulating the expression of myelin basic protein, proteolipid protein, and glycerol phosphate dehydrogenase. The actual locus at which hydrocortisone exerts its developmental influence on glial physiology is, however, not well understood. Gycerol phosphate dehydrogenase is glucocorticoid-inducible in oligodendrocytes at all stages of development both in vivo and in vitro. In newborn rat cerebral cultures, between 9 and 15 days in vitro, a 2- to 3-fold increase in myelin basic protein and proteolipid protein mRNA levels occurs in oligodendrocytes within 12 hr of hydrocortisone treatment. Immunostaining demonstrates that this increase inmore » mRNAs is followed by a 2- to 3-fold increase in the protein levels within 24 hr. In vitro transcription assays performed with oligodendrocyte nuclei show an 11-fold increase in the transcriptional activity of glycerol phosphate dehydrogenase in response to hydrocortisone but no increase in transcription of myelin basic protein or proteolipid protein. These results indicate that during early myelinogeneis, glucocorticoids influence the expression of key oligodendroglial markers by different processes: The expression of glycerol phosphate dehydrogenase is regulated at the transcriptional level, whereas the expression of myelin basic protein and proteolipid protein is modulated via a different, yet uncharacterized, mechanism involving post-transcriptional regulation.« less

Chromatin in embryonic stem cell neuronal differentiation.

PubMed

Meshorer, E

2007-03-01

Chromatin, the basic regulatory unit of the eukaryotic genetic material, is controlled by epigenetic mechanisms including histone modifications, histone variants, DNA methylation and chromatin remodeling. Cellular differentiation involves large changes in gene expression concomitant with alterations in genome organization and chromatin structure. Such changes are particularly evident in self-renewing pluripotent embryonic stem cells, which begin, in terms of cell fate, as a tabula rasa, and through the process of differentiation, acquire distinct identities. Here I describe the changes in chromatin that accompany neuronal differentiation, particularly of embryonic stem cells, and discuss how chromatin serves as the master regulator of cellular destiny.

Linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

NASA Astrophysics Data System (ADS)

Camporesi, Roberto

2011-06-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and the variation of constants method. The approach presented here can be used in a first course on differential equations for science and engineering majors.

Nonlinear differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis ismore » on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.« less

Rasch-Master's Partial Credit Model in the assessment of children's creativity in drawings.

PubMed

Nakano, Tatiana de Cássia; Primi, Ricardo

2014-01-01

The purpose of the present study was to use the Partial Credit Model to study the factors of the Test of Creativity in Children and identify which characteristics of the creative person would be more effective to differentiate subjects according to their ability level. A sample of 1426 students from first to eighth grades answered the instrument. The Partial Credits model was used to estimate the ability of the subjects and item difficulties on a common scale for each of the four factors, indicating which items required a higher level of creativity to be scored and will differentiate the more creative individuals. The results demonstrated that the greater part of the characteristics showed good fit indices, with values between 0.80 and 1.30 both infit and outfit, indicating a response pattern consistent with the model. The characteristics of Unusual Perspective, Expression of Emotion and Originality have been identified as better predictors of creative performance because requires greater ability level (usually above two standard deviation). These results may be used in the future development of an instrument's reduced form or simplification of the current correction model.

Negative differential resistance in partially fluorinated graphene films

NASA Astrophysics Data System (ADS)

Antonova, I. V.; Shojaei, S.; Sattari-Esfahlan, S. M.; Kurkina, Irina I.

2017-07-01

Partially fluorinated graphene films were created by chemical functionalization of graphene layers in an aqueous solution of hydrofluoric acid. The formation of graphene islands or graphene quantum dots (GQDs) and a fluorinated graphene network is demonstrated in such films. Negative differential resistance (NDR) resulting from the formation of the potential barrier system in the films was observed for different fluorination degrees of suspension. The origin of the NDR varies with an increase in the fluorination degree of the suspension. Numerical calculations were performed to elucidate the tunneling between adjacent energy levels and creation of NDR. It was found that in the case of films with smaller flake and smaller GQD sizes, multi-peak NDR appears in the I-V curve. We predict that the NDR peak position shifts towards lower voltage with a decrease in the GQD size. Surprisingly, we observed a negative step-like valley for positive biases in the I-V curve of samples. Our findings with detailed analysis shed light on understanding the mechanisms of the NDR phenomenon in a partially fluorinated graphene system.

Working memory component processes: isolating BOLD signal changes.

PubMed

Motes, Michael A; Rypma, Bart

2010-01-15

The chronology of the component processes subserving working memory (WM) and hemodynamic response lags has hindered the use of fMRI for exploring neural substrates of WM. In the present study, however, participants completed full trials that involved encoding two or six letters, maintaining the memory set over a delay, and then deciding whether a probe was in the memory set or not. Additionally, they completed encode-only, encode-and-maintain, and encode-and-decide partial trials intermixed with the full trials. The inclusion of partial trials allowed for the isolation of BOLD signal changes to the different trial periods. The results showed that only lateral and medial prefrontal cortex regions differentially responded to the 2- and 6-letter memory sets over the trial periods, showing greater activation to 6-letter sets during the encode and maintain trial periods. Thus, the data showed the differential involvement of PFC in the encoding and maintenance of supra- and sub-capacity memory sets and show the efficacy of using fMRI partial trial methods to study WM component processes.

Working Memory Component Processes: Isolating BOLD Signal-Changes

PubMed Central

Motes, Michael A.; Rypma, Bart

2009-01-01

The chronology of the component processes subserving working memory (WM) and hemodynamic response lags have hindered the use of fMRI for exploring neural substrates of WM. In the present study, however, participants completed full trials that involved encoding two or six letters, maintaining the memory-set over a delay, and then deciding whether a probe was in the memory-set or not. Additionally, they completed encode only, encode and maintain, and encode and decide partial-trials intermixed with the full-trials. The inclusion of partial-trials allowed for the isolation of BOLD signal-changes to the different trial-periods. The results showed that only lateral and medial prefrontal cortex regions differentially responded to the 2- and 6-letter memory-sets over the trial-periods, showing greater activation to 6-letter sets during the encode and maintain trial-periods. Thus, the data showed the differential involvement of PFC in the encoding and maintenance of supra- and sub-capacity memory-sets and show the efficacy of using fMRI partial-trial methods to study WM component processes. PMID:19732840

Differential diagnosis of hyperkalemia: an update to a complex problem

PubMed Central

Eleftheriadis, T; Leivaditis, K; Antoniadi, G; Liakopoulos, V

2012-01-01

Hyperkalemia is a relative common and sometimes life threatening electorlyte disorder. Although its symptomatic treatment is relatively easy, since precise therapeutic algorithms are available, its differential diagnosis is more complicated. The present review aims to unfold the differential diagnosis of hypekalemia using a pathophysiological, albeit clinically useful, approach. The basic elements of potassium homeostasis are provided, the causes of hyperkalemia are categorized and analysed and finally the required for the diferrential diagnosis laboratory tests are mentioned. PMID:23935306

Basic concepts and techniques of dental implants.

PubMed

Tagliareni, Jonathan M; Clarkson, Earl

2015-04-01

Dental implants provide completely edentulous and partial edentulous patients the function and esthetics they had with natural dentition. It is critical to understand and apply predictable surgical principles when treatment planning and surgically restoring edentulous spaces with implants. This article defines basic implant concepts that should be meticulously followed for predictable results when treating patients and restoring dental implants. Topics include biological and functional considerations, biomechanical considerations, preoperative assessments, medical history and risk assessments, oral examinations, radiographic examinations, contraindications, and general treatment planning options. Copyright © 2015 Elsevier Inc. All rights reserved.

Analytical results for post-buckling behaviour of plates in compression and in shear

NASA Technical Reports Server (NTRS)

Stein, M.

1985-01-01

The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

Comparison of transcript profiles in different life stages of the nematode Globodera pallida under different host potato genotypes.

PubMed

Palomares-Rius, Juan E; Hedley, Pete E; Cock, Peter J A; Morris, Jenny A; Jones, John T; Vovlas, Nikos; Blok, Vivian

2012-12-01

The potato cyst nematodes (PCNs) Globodera pallida and Globodera rostochiensis are important parasites of potato. PCNs undergo complex biotrophic interactions with their hosts that involve gene expression changes in both the nematode and the host plant. The aim of this study was to determine key genes that are differentially expressed in Globodera pallida life cycle stages and during the initiation of the feeding site in susceptible and partially resistant potato genotypes. For this purpose, two microarray experiments were designed: (i) a comparison of eggs, infective second-stage juveniles (J2s) and sedentary parasitic-stage J2s (SJ2); (ii) a comparison of SJ2s at 8 days after inoculation (DAI) in the susceptible cultivar (Desirée) and two partially resistant lines. The results showed differential expression of G. pallida genes during the stages studied, including previously characterized effectors. In addition, a large number of genes changed their expression between SJ2s in the susceptible cultivar and those infecting partially resistant lines; the number of genes with modified expression was lower when the two partially resistant lines were compared. Moreover, a histopathological study was performed at several time points (7, 14 and 30 DAI) and showed the similarities between both partially resistant lines with a delay and degeneration in the formation of the syncytia in comparison with the susceptible cultivar. Females at 30 DAI in partially resistant lines showed a delay in their development in comparison with those in the susceptible cultivar. © 2012 THE AUTHORS. MOLECULAR PLANT PATHOLOGY © 2012 BSPP AND BLACKWELL PUBLISHING LTD.